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videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/_autocast_to_full_precision_compositeimplicitautograd_dispatch.h

@@ -0,0 +1,23 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace compositeimplicitautograd {
+
+TORCH_API at::Tensor _autocast_to_full_precision(const at::Tensor & self, bool cuda_enabled, bool cpu_enabled);
+
+} // namespace compositeimplicitautograd
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/_embedding_bag_sparse_backward.h

@@ -0,0 +1,47 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Function.h
+
+#include <ATen/Context.h>
+#include <ATen/DeviceGuard.h>
+#include <ATen/TensorUtils.h>
+#include <ATen/TracerMode.h>
+#include <ATen/core/Generator.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+
+
+
+#include <ATen/ops/_embedding_bag_sparse_backward_ops.h>
+
+namespace at {
+
+
+// aten::_embedding_bag_sparse_backward(Tensor grad, Tensor indices, Tensor offsets, Tensor offset2bag, Tensor bag_size, SymInt num_weights, bool scale_grad_by_freq, int mode, Tensor? per_sample_weights, int padding_idx=-1) -> Tensor
+inline at::Tensor _embedding_bag_sparse_backward(const at::Tensor & grad, const at::Tensor & indices, const at::Tensor & offsets, const at::Tensor & offset2bag, const at::Tensor & bag_size, int64_t num_weights, bool scale_grad_by_freq, int64_t mode, const c10::optional<at::Tensor> & per_sample_weights, int64_t padding_idx=-1) {
+    return at::_ops::_embedding_bag_sparse_backward::call(grad, indices, offsets, offset2bag, bag_size, num_weights, scale_grad_by_freq, mode, per_sample_weights, padding_idx);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, int64_t>::value>>
+  at::Tensor _embedding_bag_sparse_backward(const at::Tensor & grad, const at::Tensor & indices, const at::Tensor & offsets, const at::Tensor & offset2bag, const at::Tensor & bag_size, int64_t num_weights, bool scale_grad_by_freq, int64_t mode, const c10::optional<at::Tensor> & per_sample_weights, int64_t padding_idx=-1) {
+    return at::_ops::_embedding_bag_sparse_backward::call(grad, indices, offsets, offset2bag, bag_size, num_weights, scale_grad_by_freq, mode, per_sample_weights, padding_idx);
+  }
+}
+
+// aten::_embedding_bag_sparse_backward(Tensor grad, Tensor indices, Tensor offsets, Tensor offset2bag, Tensor bag_size, SymInt num_weights, bool scale_grad_by_freq, int mode, Tensor? per_sample_weights, int padding_idx=-1) -> Tensor
+inline at::Tensor _embedding_bag_sparse_backward_symint(const at::Tensor & grad, const at::Tensor & indices, const at::Tensor & offsets, const at::Tensor & offset2bag, const at::Tensor & bag_size, c10::SymInt num_weights, bool scale_grad_by_freq, int64_t mode, const c10::optional<at::Tensor> & per_sample_weights, int64_t padding_idx=-1) {
+    return at::_ops::_embedding_bag_sparse_backward::call(grad, indices, offsets, offset2bag, bag_size, num_weights, scale_grad_by_freq, mode, per_sample_weights, padding_idx);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, c10::SymInt>::value>>
+  at::Tensor _embedding_bag_sparse_backward(const at::Tensor & grad, const at::Tensor & indices, const at::Tensor & offsets, const at::Tensor & offset2bag, const at::Tensor & bag_size, c10::SymInt num_weights, bool scale_grad_by_freq, int64_t mode, const c10::optional<at::Tensor> & per_sample_weights, int64_t padding_idx=-1) {
+    return at::_ops::_embedding_bag_sparse_backward::call(grad, indices, offsets, offset2bag, bag_size, num_weights, scale_grad_by_freq, mode, per_sample_weights, padding_idx);
+  }
+}
+
+}

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/_foreach_log2_cuda_dispatch.h

@@ -0,0 +1,24 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace cuda {
+
+TORCH_API ::std::vector<at::Tensor> _foreach_log2(at::TensorList self);
+TORCH_API void _foreach_log2_(at::TensorList self);
+
+} // namespace cuda
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/_foreach_sign_cuda_dispatch.h

@@ -0,0 +1,24 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace cuda {
+
+TORCH_API ::std::vector<at::Tensor> _foreach_sign(at::TensorList self);
+TORCH_API void _foreach_sign_(at::TensorList self);
+
+} // namespace cuda
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/_indices_copy_native.h

@@ -0,0 +1,22 @@
+#pragma once
+
+// @generated by torchgen/gen.py from NativeFunction.h
+
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+#include <c10/core/QScheme.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <tuple>
+#include <vector>
+
+
+namespace at {
+namespace native {
+TORCH_API at::Tensor & _indices_copy_out(const at::Tensor & self, at::Tensor & out);
+TORCH_API at::Tensor _indices_copy(const at::Tensor & self);
+} // namespace native
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/_log_softmax_backward_data_cuda_dispatch.h

@@ -0,0 +1,25 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace cuda {
+
+TORCH_API at::Tensor _log_softmax_backward_data(const at::Tensor & grad_output, const at::Tensor & output, int64_t dim, at::ScalarType input_dtype);
+TORCH_API at::Tensor & _log_softmax_backward_data_out(at::Tensor & out, const at::Tensor & grad_output, const at::Tensor & output, int64_t dim, at::ScalarType input_dtype);
+TORCH_API at::Tensor & _log_softmax_backward_data_outf(const at::Tensor & grad_output, const at::Tensor & output, int64_t dim, at::ScalarType input_dtype, at::Tensor & out);
+
+} // namespace cuda
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/_rowwise_prune_compositeimplicitautograd_dispatch.h

@@ -0,0 +1,23 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace compositeimplicitautograd {
+
+TORCH_API ::std::tuple<at::Tensor,at::Tensor> _rowwise_prune(const at::Tensor & weight, const at::Tensor & mask, at::ScalarType compressed_indices_dtype);
+
+} // namespace compositeimplicitautograd
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/baddbmm.h

@@ -0,0 +1,39 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Function.h
+
+#include <ATen/Context.h>
+#include <ATen/DeviceGuard.h>
+#include <ATen/TensorUtils.h>
+#include <ATen/TracerMode.h>
+#include <ATen/core/Generator.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+
+
+
+#include <ATen/ops/baddbmm_ops.h>
+
+namespace at {
+
+
+// aten::baddbmm(Tensor self, Tensor batch1, Tensor batch2, *, Scalar beta=1, Scalar alpha=1) -> Tensor
+inline at::Tensor baddbmm(const at::Tensor & self, const at::Tensor & batch1, const at::Tensor & batch2, const at::Scalar & beta=1, const at::Scalar & alpha=1) {
+    return at::_ops::baddbmm::call(self, batch1, batch2, beta, alpha);
+}
+
+// aten::baddbmm.out(Tensor self, Tensor batch1, Tensor batch2, *, Scalar beta=1, Scalar alpha=1, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & baddbmm_out(at::Tensor & out, const at::Tensor & self, const at::Tensor & batch1, const at::Tensor & batch2, const at::Scalar & beta=1, const at::Scalar & alpha=1) {
+    return at::_ops::baddbmm_out::call(self, batch1, batch2, beta, alpha, out);
+}
+// aten::baddbmm.out(Tensor self, Tensor batch1, Tensor batch2, *, Scalar beta=1, Scalar alpha=1, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & baddbmm_outf(const at::Tensor & self, const at::Tensor & batch1, const at::Tensor & batch2, const at::Scalar & beta, const at::Scalar & alpha, at::Tensor & out) {
+    return at::_ops::baddbmm_out::call(self, batch1, batch2, beta, alpha, out);
+}
+
+}

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/block_diag_compositeexplicitautograd_dispatch.h

@@ -0,0 +1,25 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace compositeexplicitautograd {
+
+TORCH_API at::Tensor block_diag(at::TensorList tensors);
+TORCH_API at::Tensor & block_diag_out(at::Tensor & out, at::TensorList tensors);
+TORCH_API at::Tensor & block_diag_outf(at::TensorList tensors, at::Tensor & out);
+
+} // namespace compositeexplicitautograd
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/col2im.h

@@ -0,0 +1,91 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Function.h
+
+#include <ATen/Context.h>
+#include <ATen/DeviceGuard.h>
+#include <ATen/TensorUtils.h>
+#include <ATen/TracerMode.h>
+#include <ATen/core/Generator.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+
+
+
+#include <ATen/ops/col2im_ops.h>
+
+namespace at {
+
+
+// aten::col2im.out(Tensor self, SymInt[2] output_size, int[2] kernel_size, int[2] dilation, int[2] padding, int[2] stride, *, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & col2im_out(at::Tensor & out, const at::Tensor & self, at::IntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride) {
+    return at::_ops::col2im_out::call(self, c10::fromIntArrayRefSlow(output_size), kernel_size, dilation, padding, stride, out);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, int64_t>::value>>
+  at::Tensor & col2im_out(at::Tensor & out, const at::Tensor & self, at::IntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride) {
+    return at::_ops::col2im_out::call(self, c10::fromIntArrayRefSlow(output_size), kernel_size, dilation, padding, stride, out);
+  }
+}
+
+// aten::col2im.out(Tensor self, SymInt[2] output_size, int[2] kernel_size, int[2] dilation, int[2] padding, int[2] stride, *, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & col2im_outf(const at::Tensor & self, at::IntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride, at::Tensor & out) {
+    return at::_ops::col2im_out::call(self, c10::fromIntArrayRefSlow(output_size), kernel_size, dilation, padding, stride, out);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, int64_t>::value>>
+  at::Tensor & col2im_outf(const at::Tensor & self, at::IntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride, at::Tensor & out) {
+    return at::_ops::col2im_out::call(self, c10::fromIntArrayRefSlow(output_size), kernel_size, dilation, padding, stride, out);
+  }
+}
+
+// aten::col2im.out(Tensor self, SymInt[2] output_size, int[2] kernel_size, int[2] dilation, int[2] padding, int[2] stride, *, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & col2im_symint_out(at::Tensor & out, const at::Tensor & self, c10::SymIntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride) {
+    return at::_ops::col2im_out::call(self, output_size, kernel_size, dilation, padding, stride, out);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, c10::SymInt>::value>>
+  at::Tensor & col2im_out(at::Tensor & out, const at::Tensor & self, c10::SymIntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride) {
+    return at::_ops::col2im_out::call(self, output_size, kernel_size, dilation, padding, stride, out);
+  }
+}
+
+// aten::col2im.out(Tensor self, SymInt[2] output_size, int[2] kernel_size, int[2] dilation, int[2] padding, int[2] stride, *, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & col2im_symint_outf(const at::Tensor & self, c10::SymIntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride, at::Tensor & out) {
+    return at::_ops::col2im_out::call(self, output_size, kernel_size, dilation, padding, stride, out);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, c10::SymInt>::value>>
+  at::Tensor & col2im_outf(const at::Tensor & self, c10::SymIntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride, at::Tensor & out) {
+    return at::_ops::col2im_out::call(self, output_size, kernel_size, dilation, padding, stride, out);
+  }
+}
+
+// aten::col2im(Tensor self, SymInt[2] output_size, int[2] kernel_size, int[2] dilation, int[2] padding, int[2] stride) -> Tensor
+inline at::Tensor col2im(const at::Tensor & self, at::IntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride) {
+    return at::_ops::col2im::call(self, c10::fromIntArrayRefSlow(output_size), kernel_size, dilation, padding, stride);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, int64_t>::value>>
+  at::Tensor col2im(const at::Tensor & self, at::IntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride) {
+    return at::_ops::col2im::call(self, c10::fromIntArrayRefSlow(output_size), kernel_size, dilation, padding, stride);
+  }
+}
+
+// aten::col2im(Tensor self, SymInt[2] output_size, int[2] kernel_size, int[2] dilation, int[2] padding, int[2] stride) -> Tensor
+inline at::Tensor col2im_symint(const at::Tensor & self, c10::SymIntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride) {
+    return at::_ops::col2im::call(self, output_size, kernel_size, dilation, padding, stride);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, c10::SymInt>::value>>
+  at::Tensor col2im(const at::Tensor & self, c10::SymIntArrayRef output_size, at::IntArrayRef kernel_size, at::IntArrayRef dilation, at::IntArrayRef padding, at::IntArrayRef stride) {
+    return at::_ops::col2im::call(self, output_size, kernel_size, dilation, padding, stride);
+  }
+}
+
+}

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/expm1_cuda_dispatch.h

@@ -0,0 +1,26 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace cuda {
+
+TORCH_API at::Tensor expm1(const at::Tensor & self);
+TORCH_API at::Tensor & expm1_out(at::Tensor & out, const at::Tensor & self);
+TORCH_API at::Tensor & expm1_outf(const at::Tensor & self, at::Tensor & out);
+TORCH_API at::Tensor & expm1_(at::Tensor & self);
+
+} // namespace cuda
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/fake_quantize_per_channel_affine_ops.h

@@ -0,0 +1,28 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Operator.h
+
+#include <tuple>
+#include <vector>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+namespace _ops {
+
+
+struct TORCH_API fake_quantize_per_channel_affine {
+  using schema = at::Tensor (const at::Tensor &, const at::Tensor &, const at::Tensor &, int64_t, int64_t, int64_t);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::fake_quantize_per_channel_affine")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "fake_quantize_per_channel_affine(Tensor self, Tensor scale, Tensor zero_point, int axis, int quant_min, int quant_max) -> Tensor")
+  static at::Tensor call(const at::Tensor & self, const at::Tensor & scale, const at::Tensor & zero_point, int64_t axis, int64_t quant_min, int64_t quant_max);
+  static at::Tensor redispatch(c10::DispatchKeySet dispatchKeySet, const at::Tensor & self, const at::Tensor & scale, const at::Tensor & zero_point, int64_t axis, int64_t quant_min, int64_t quant_max);
+};
+
+}} // namespace at::_ops

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/fft_rfft_compositeimplicitautograd_dispatch.h

@@ -0,0 +1,28 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace compositeimplicitautograd {
+
+TORCH_API at::Tensor fft_rfft(const at::Tensor & self, c10::optional<int64_t> n=c10::nullopt, int64_t dim=-1, c10::optional<c10::string_view> norm=c10::nullopt);
+TORCH_API at::Tensor fft_rfft_symint(const at::Tensor & self, c10::optional<c10::SymInt> n=c10::nullopt, int64_t dim=-1, c10::optional<c10::string_view> norm=c10::nullopt);
+TORCH_API at::Tensor & fft_rfft_out(at::Tensor & out, const at::Tensor & self, c10::optional<int64_t> n=c10::nullopt, int64_t dim=-1, c10::optional<c10::string_view> norm=c10::nullopt);
+TORCH_API at::Tensor & fft_rfft_outf(const at::Tensor & self, c10::optional<int64_t> n, int64_t dim, c10::optional<c10::string_view> norm, at::Tensor & out);
+TORCH_API at::Tensor & fft_rfft_symint_out(at::Tensor & out, const at::Tensor & self, c10::optional<c10::SymInt> n=c10::nullopt, int64_t dim=-1, c10::optional<c10::string_view> norm=c10::nullopt);
+TORCH_API at::Tensor & fft_rfft_symint_outf(const at::Tensor & self, c10::optional<c10::SymInt> n, int64_t dim, c10::optional<c10::string_view> norm, at::Tensor & out);
+
+} // namespace compositeimplicitautograd
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/frexp_native.h

@@ -0,0 +1,22 @@
+#pragma once
+
+// @generated by torchgen/gen.py from NativeFunction.h
+
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+#include <c10/core/QScheme.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <tuple>
+#include <vector>
+
+
+namespace at {
+namespace native {
+TORCH_API ::std::tuple<at::Tensor,at::Tensor> frexp(const at::Tensor & self);
+TORCH_API ::std::tuple<at::Tensor &,at::Tensor &> frexp_out(const at::Tensor & self, at::Tensor & mantissa, at::Tensor & exponent);
+} // namespace native
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/from_file.h

@@ -0,0 +1,43 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Function.h
+
+#include <ATen/Context.h>
+#include <ATen/DeviceGuard.h>
+#include <ATen/TensorUtils.h>
+#include <ATen/TracerMode.h>
+#include <ATen/core/Generator.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+
+
+
+#include <ATen/ops/from_file_ops.h>
+
+namespace at {
+
+
+// aten::from_file(str filename, bool? shared=None, int? size=0, *, ScalarType? dtype=None, Layout? layout=None, Device? device=None, bool? pin_memory=None) -> Tensor
+inline at::Tensor from_file(c10::string_view filename, c10::optional<bool> shared=c10::nullopt, c10::optional<int64_t> size=0, at::TensorOptions options={}) {
+    return at::_ops::from_file::call(filename, shared, size, optTypeMetaToScalarType(options.dtype_opt()), options.layout_opt(), options.device_opt(), options.pinned_memory_opt());
+}
+// aten::from_file(str filename, bool? shared=None, int? size=0, *, ScalarType? dtype=None, Layout? layout=None, Device? device=None, bool? pin_memory=None) -> Tensor
+inline at::Tensor from_file(c10::string_view filename, c10::optional<bool> shared, c10::optional<int64_t> size, c10::optional<at::ScalarType> dtype, c10::optional<at::Layout> layout, c10::optional<at::Device> device, c10::optional<bool> pin_memory) {
+    return at::_ops::from_file::call(filename, shared, size, dtype, layout, device, pin_memory);
+}
+
+// aten::from_file.out(str filename, bool? shared=None, int? size=0, *, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & from_file_out(at::Tensor & out, c10::string_view filename, c10::optional<bool> shared=c10::nullopt, c10::optional<int64_t> size=0) {
+    return at::_ops::from_file_out::call(filename, shared, size, out);
+}
+// aten::from_file.out(str filename, bool? shared=None, int? size=0, *, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & from_file_outf(c10::string_view filename, c10::optional<bool> shared, c10::optional<int64_t> size, at::Tensor & out) {
+    return at::_ops::from_file_out::call(filename, shared, size, out);
+}
+
+}

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/full_like.h

@@ -0,0 +1,43 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Function.h
+
+#include <ATen/Context.h>
+#include <ATen/DeviceGuard.h>
+#include <ATen/TensorUtils.h>
+#include <ATen/TracerMode.h>
+#include <ATen/core/Generator.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+
+
+
+#include <ATen/ops/full_like_ops.h>
+
+namespace at {
+
+
+// aten::full_like(Tensor self, Scalar fill_value, *, ScalarType? dtype=None, Layout? layout=None, Device? device=None, bool? pin_memory=None, MemoryFormat? memory_format=None) -> Tensor
+inline at::Tensor full_like(const at::Tensor & self, const at::Scalar & fill_value, at::TensorOptions options={}, c10::optional<at::MemoryFormat> memory_format=c10::nullopt) {
+    return at::_ops::full_like::call(self, fill_value, optTypeMetaToScalarType(options.dtype_opt()), options.layout_opt(), options.device_opt(), options.pinned_memory_opt(), c10::impl::check_tensor_options_and_extract_memory_format(options, memory_format));
+}
+// aten::full_like(Tensor self, Scalar fill_value, *, ScalarType? dtype=None, Layout? layout=None, Device? device=None, bool? pin_memory=None, MemoryFormat? memory_format=None) -> Tensor
+inline at::Tensor full_like(const at::Tensor & self, const at::Scalar & fill_value, c10::optional<at::ScalarType> dtype, c10::optional<at::Layout> layout, c10::optional<at::Device> device, c10::optional<bool> pin_memory, c10::optional<at::MemoryFormat> memory_format) {
+    return at::_ops::full_like::call(self, fill_value, dtype, layout, device, pin_memory, memory_format);
+}
+
+// aten::full_like.out(Tensor self, Scalar fill_value, *, MemoryFormat? memory_format=None, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & full_like_out(at::Tensor & out, const at::Tensor & self, const at::Scalar & fill_value, c10::optional<at::MemoryFormat> memory_format=c10::nullopt) {
+    return at::_ops::full_like_out::call(self, fill_value, memory_format, out);
+}
+// aten::full_like.out(Tensor self, Scalar fill_value, *, MemoryFormat? memory_format=None, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & full_like_outf(const at::Tensor & self, const at::Scalar & fill_value, c10::optional<at::MemoryFormat> memory_format, at::Tensor & out) {
+    return at::_ops::full_like_out::call(self, fill_value, memory_format, out);
+}
+
+}

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/glu_jvp.h

@@ -0,0 +1,39 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Function.h
+
+#include <ATen/Context.h>
+#include <ATen/DeviceGuard.h>
+#include <ATen/TensorUtils.h>
+#include <ATen/TracerMode.h>
+#include <ATen/core/Generator.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+
+
+
+#include <ATen/ops/glu_jvp_ops.h>
+
+namespace at {
+
+
+// aten::glu_jvp(Tensor glu, Tensor x, Tensor dx, int dim) -> Tensor
+inline at::Tensor glu_jvp(const at::Tensor & glu, const at::Tensor & x, const at::Tensor & dx, int64_t dim) {
+    return at::_ops::glu_jvp::call(glu, x, dx, dim);
+}
+
+// aten::glu_jvp.out(Tensor glu, Tensor x, Tensor dx, int dim, *, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & glu_jvp_out(at::Tensor & out, const at::Tensor & glu, const at::Tensor & x, const at::Tensor & dx, int64_t dim) {
+    return at::_ops::glu_jvp_out::call(glu, x, dx, dim, out);
+}
+// aten::glu_jvp.out(Tensor glu, Tensor x, Tensor dx, int dim, *, Tensor(a!) out) -> Tensor(a!)
+inline at::Tensor & glu_jvp_outf(const at::Tensor & glu, const at::Tensor & x, const at::Tensor & dx, int64_t dim, at::Tensor & out) {
+    return at::_ops::glu_jvp_out::call(glu, x, dx, dim, out);
+}
+
+}

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/layer_norm.h

@@ -0,0 +1,47 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Function.h
+
+#include <ATen/Context.h>
+#include <ATen/DeviceGuard.h>
+#include <ATen/TensorUtils.h>
+#include <ATen/TracerMode.h>
+#include <ATen/core/Generator.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+
+
+
+#include <ATen/ops/layer_norm_ops.h>
+
+namespace at {
+
+
+// aten::layer_norm(Tensor input, SymInt[] normalized_shape, Tensor? weight=None, Tensor? bias=None, float eps=1e-05, bool cudnn_enable=True) -> Tensor
+inline at::Tensor layer_norm(const at::Tensor & input, at::IntArrayRef normalized_shape, const c10::optional<at::Tensor> & weight={}, const c10::optional<at::Tensor> & bias={}, double eps=1e-05, bool cudnn_enable=true) {
+    return at::_ops::layer_norm::call(input, c10::fromIntArrayRefSlow(normalized_shape), weight, bias, eps, cudnn_enable);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, int64_t>::value>>
+  at::Tensor layer_norm(const at::Tensor & input, at::IntArrayRef normalized_shape, const c10::optional<at::Tensor> & weight={}, const c10::optional<at::Tensor> & bias={}, double eps=1e-05, bool cudnn_enable=true) {
+    return at::_ops::layer_norm::call(input, c10::fromIntArrayRefSlow(normalized_shape), weight, bias, eps, cudnn_enable);
+  }
+}
+
+// aten::layer_norm(Tensor input, SymInt[] normalized_shape, Tensor? weight=None, Tensor? bias=None, float eps=1e-05, bool cudnn_enable=True) -> Tensor
+inline at::Tensor layer_norm_symint(const at::Tensor & input, c10::SymIntArrayRef normalized_shape, const c10::optional<at::Tensor> & weight={}, const c10::optional<at::Tensor> & bias={}, double eps=1e-05, bool cudnn_enable=true) {
+    return at::_ops::layer_norm::call(input, normalized_shape, weight, bias, eps, cudnn_enable);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, c10::SymInt>::value>>
+  at::Tensor layer_norm(const at::Tensor & input, c10::SymIntArrayRef normalized_shape, const c10::optional<at::Tensor> & weight={}, const c10::optional<at::Tensor> & bias={}, double eps=1e-05, bool cudnn_enable=true) {
+    return at::_ops::layer_norm::call(input, normalized_shape, weight, bias, eps, cudnn_enable);
+  }
+}
+
+}

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/leaky_relu_backward_meta_dispatch.h

@@ -0,0 +1,25 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace meta {
+
+TORCH_API at::Tensor leaky_relu_backward(const at::Tensor & grad_output, const at::Tensor & self, const at::Scalar & negative_slope, bool self_is_result);
+TORCH_API at::Tensor & leaky_relu_backward_out(at::Tensor & grad_input, const at::Tensor & grad_output, const at::Tensor & self, const at::Scalar & negative_slope, bool self_is_result);
+TORCH_API at::Tensor & leaky_relu_backward_outf(const at::Tensor & grad_output, const at::Tensor & self, const at::Scalar & negative_slope, bool self_is_result, at::Tensor & grad_input);
+
+} // namespace meta
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/less_ops.h

@@ -0,0 +1,83 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Operator.h
+
+#include <tuple>
+#include <vector>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+namespace _ops {
+
+
+struct TORCH_API less_Scalar_out {
+  using schema = at::Tensor & (const at::Tensor &, const at::Scalar &, at::Tensor &);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::less")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "Scalar_out")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "less.Scalar_out(Tensor self, Scalar other, *, Tensor(a!) out) -> Tensor(a!)")
+  static at::Tensor & call(const at::Tensor & self, const at::Scalar & other, at::Tensor & out);
+  static at::Tensor & redispatch(c10::DispatchKeySet dispatchKeySet, const at::Tensor & self, const at::Scalar & other, at::Tensor & out);
+};
+
+struct TORCH_API less_Scalar {
+  using schema = at::Tensor (const at::Tensor &, const at::Scalar &);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::less")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "Scalar")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "less.Scalar(Tensor self, Scalar other) -> Tensor")
+  static at::Tensor call(const at::Tensor & self, const at::Scalar & other);
+  static at::Tensor redispatch(c10::DispatchKeySet dispatchKeySet, const at::Tensor & self, const at::Scalar & other);
+};
+
+struct TORCH_API less_Tensor_out {
+  using schema = at::Tensor & (const at::Tensor &, const at::Tensor &, at::Tensor &);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::less")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "Tensor_out")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "less.Tensor_out(Tensor self, Tensor other, *, Tensor(a!) out) -> Tensor(a!)")
+  static at::Tensor & call(const at::Tensor & self, const at::Tensor & other, at::Tensor & out);
+  static at::Tensor & redispatch(c10::DispatchKeySet dispatchKeySet, const at::Tensor & self, const at::Tensor & other, at::Tensor & out);
+};
+
+struct TORCH_API less_Tensor {
+  using schema = at::Tensor (const at::Tensor &, const at::Tensor &);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::less")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "Tensor")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "less.Tensor(Tensor self, Tensor other) -> Tensor")
+  static at::Tensor call(const at::Tensor & self, const at::Tensor & other);
+  static at::Tensor redispatch(c10::DispatchKeySet dispatchKeySet, const at::Tensor & self, const at::Tensor & other);
+};
+
+struct TORCH_API less__Scalar {
+  using schema = at::Tensor & (at::Tensor &, const at::Scalar &);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::less_")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "Scalar")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "less_.Scalar(Tensor(a!) self, Scalar other) -> Tensor(a!)")
+  static at::Tensor & call(at::Tensor & self, const at::Scalar & other);
+  static at::Tensor & redispatch(c10::DispatchKeySet dispatchKeySet, at::Tensor & self, const at::Scalar & other);
+};
+
+struct TORCH_API less__Tensor {
+  using schema = at::Tensor & (at::Tensor &, const at::Tensor &);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::less_")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "Tensor")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "less_.Tensor(Tensor(a!) self, Tensor other) -> Tensor(a!)")
+  static at::Tensor & call(at::Tensor & self, const at::Tensor & other);
+  static at::Tensor & redispatch(c10::DispatchKeySet dispatchKeySet, at::Tensor & self, const at::Tensor & other);
+};
+
+}} // namespace at::_ops

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/linalg_ldl_factor_ex_meta.h

@@ -0,0 +1,27 @@
+#pragma once
+
+// @generated by torchgen/gen.py from NativeMetaFunction.h
+
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+#include <c10/core/QScheme.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/TensorIterator.h>
+#include <ATen/TensorMeta.h>
+#include <tuple>
+#include <vector>
+
+namespace at {
+namespace meta {
+
+struct TORCH_API structured_linalg_ldl_factor_ex : public at::impl::MetaBase {
+    
+    
+    void meta(const at::Tensor & self, bool hermitian, bool check_errors);
+};
+
+} // namespace native
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/linalg_lstsq_ops.h

@@ -0,0 +1,39 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Operator.h
+
+#include <tuple>
+#include <vector>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+namespace _ops {
+
+
+struct TORCH_API linalg_lstsq {
+  using schema = ::std::tuple<at::Tensor,at::Tensor,at::Tensor,at::Tensor> (const at::Tensor &, const at::Tensor &, c10::optional<double>, c10::optional<c10::string_view>);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::linalg_lstsq")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "linalg_lstsq(Tensor self, Tensor b, float? rcond=None, *, str? driver=None) -> (Tensor solution, Tensor residuals, Tensor rank, Tensor singular_values)")
+  static ::std::tuple<at::Tensor,at::Tensor,at::Tensor,at::Tensor> call(const at::Tensor & self, const at::Tensor & b, c10::optional<double> rcond, c10::optional<c10::string_view> driver);
+  static ::std::tuple<at::Tensor,at::Tensor,at::Tensor,at::Tensor> redispatch(c10::DispatchKeySet dispatchKeySet, const at::Tensor & self, const at::Tensor & b, c10::optional<double> rcond, c10::optional<c10::string_view> driver);
+};
+
+struct TORCH_API linalg_lstsq_out {
+  using schema = ::std::tuple<at::Tensor &,at::Tensor &,at::Tensor &,at::Tensor &> (const at::Tensor &, const at::Tensor &, c10::optional<double>, c10::optional<c10::string_view>, at::Tensor &, at::Tensor &, at::Tensor &, at::Tensor &);
+  using ptr_schema = schema*;
+  // See Note [static constexpr char* members for windows NVCC]
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(name, "aten::linalg_lstsq")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(overload_name, "out")
+  STATIC_CONSTEXPR_STR_INL_EXCEPT_WIN_CUDA(schema_str, "linalg_lstsq.out(Tensor self, Tensor b, float? rcond=None, *, str? driver=None, Tensor(a!) solution, Tensor(b!) residuals, Tensor(c!) rank, Tensor(d!) singular_values) -> (Tensor(a!) solution, Tensor(b!) residuals, Tensor(c!) rank, Tensor(d!) singular_values)")
+  static ::std::tuple<at::Tensor &,at::Tensor &,at::Tensor &,at::Tensor &> call(const at::Tensor & self, const at::Tensor & b, c10::optional<double> rcond, c10::optional<c10::string_view> driver, at::Tensor & solution, at::Tensor & residuals, at::Tensor & rank, at::Tensor & singular_values);
+  static ::std::tuple<at::Tensor &,at::Tensor &,at::Tensor &,at::Tensor &> redispatch(c10::DispatchKeySet dispatchKeySet, const at::Tensor & self, const at::Tensor & b, c10::optional<double> rcond, c10::optional<c10::string_view> driver, at::Tensor & solution, at::Tensor & residuals, at::Tensor & rank, at::Tensor & singular_values);
+};
+
+}} // namespace at::_ops

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/logcumsumexp_compositeexplicitautograd_dispatch.h

@@ -0,0 +1,25 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace compositeexplicitautograd {
+
+TORCH_API at::Tensor logcumsumexp(const at::Tensor & self, int64_t dim);
+TORCH_API at::Tensor & logcumsumexp_out(at::Tensor & out, const at::Tensor & self, int64_t dim);
+TORCH_API at::Tensor & logcumsumexp_outf(const at::Tensor & self, int64_t dim, at::Tensor & out);
+
+} // namespace compositeexplicitautograd
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/logsumexp_native.h

@@ -0,0 +1,24 @@
+#pragma once
+
+// @generated by torchgen/gen.py from NativeFunction.h
+
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+#include <c10/core/QScheme.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <tuple>
+#include <vector>
+
+
+namespace at {
+namespace native {
+TORCH_API at::Tensor logsumexp(const at::Tensor & self, at::IntArrayRef dim, bool keepdim=false);
+TORCH_API at::Tensor & logsumexp_out(const at::Tensor & self, at::IntArrayRef dim, bool keepdim, at::Tensor & out);
+TORCH_API at::Tensor logsumexp(const at::Tensor & self, at::DimnameList dim, bool keepdim=false);
+TORCH_API at::Tensor & logsumexp_out(const at::Tensor & self, at::DimnameList dim, bool keepdim, at::Tensor & out);
+} // namespace native
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/nested_to_padded_tensor_compositeimplicitautograd_dispatch.h

@@ -0,0 +1,23 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace compositeimplicitautograd {
+
+TORCH_API at::Tensor nested_to_padded_tensor(const at::Tensor & self, double padding, at::OptionalIntArrayRef output_size=c10::nullopt);
+
+} // namespace compositeimplicitautograd
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/reflection_pad3d_backward_cpu_dispatch.h

@@ -0,0 +1,28 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace cpu {
+
+TORCH_API at::Tensor reflection_pad3d_backward(const at::Tensor & grad_output, const at::Tensor & self, at::IntArrayRef padding);
+TORCH_API at::Tensor reflection_pad3d_backward_symint(const at::Tensor & grad_output, const at::Tensor & self, c10::SymIntArrayRef padding);
+TORCH_API at::Tensor & reflection_pad3d_backward_out(at::Tensor & grad_input, const at::Tensor & grad_output, const at::Tensor & self, at::IntArrayRef padding);
+TORCH_API at::Tensor & reflection_pad3d_backward_outf(const at::Tensor & grad_output, const at::Tensor & self, at::IntArrayRef padding, at::Tensor & grad_input);
+TORCH_API at::Tensor & reflection_pad3d_backward_symint_out(at::Tensor & grad_input, const at::Tensor & grad_output, const at::Tensor & self, c10::SymIntArrayRef padding);
+TORCH_API at::Tensor & reflection_pad3d_backward_symint_outf(const at::Tensor & grad_output, const at::Tensor & self, c10::SymIntArrayRef padding, at::Tensor & grad_input);
+
+} // namespace cpu
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/reflection_pad3d_backward_meta_dispatch.h

@@ -0,0 +1,28 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace meta {
+
+TORCH_API at::Tensor reflection_pad3d_backward(const at::Tensor & grad_output, const at::Tensor & self, at::IntArrayRef padding);
+TORCH_API at::Tensor reflection_pad3d_backward_symint(const at::Tensor & grad_output, const at::Tensor & self, c10::SymIntArrayRef padding);
+TORCH_API at::Tensor & reflection_pad3d_backward_out(at::Tensor & grad_input, const at::Tensor & grad_output, const at::Tensor & self, at::IntArrayRef padding);
+TORCH_API at::Tensor & reflection_pad3d_backward_outf(const at::Tensor & grad_output, const at::Tensor & self, at::IntArrayRef padding, at::Tensor & grad_input);
+TORCH_API at::Tensor & reflection_pad3d_backward_symint_out(at::Tensor & grad_input, const at::Tensor & grad_output, const at::Tensor & self, c10::SymIntArrayRef padding);
+TORCH_API at::Tensor & reflection_pad3d_backward_symint_outf(const at::Tensor & grad_output, const at::Tensor & self, c10::SymIntArrayRef padding, at::Tensor & grad_input);
+
+} // namespace meta
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/special_entr_compositeexplicitautogradnonfunctional_dispatch.h

@@ -0,0 +1,23 @@
+#pragma once
+// @generated by torchgen/gen.py from DispatchKeyFunction.h
+
+// NB: The implementing C++ file is RegisterDispatchKey.cpp
+
+// The only #includes we need are for custom classes that have defaults in the C++ API
+#include <c10/core/MemoryFormat.h>
+#include <c10/core/Scalar.h>
+#include <ATen/core/Reduction.h>
+
+// Forward declarations of any types needed in the operator signatures.
+// We can't directly include these classes because it will cause circular include dependencies.
+// This file is included by TensorBody.h, which defines the Tensor class.
+#include <ATen/core/ATen_fwd.h>
+
+namespace at {
+
+namespace compositeexplicitautogradnonfunctional {
+
+TORCH_API at::Tensor special_entr(const at::Tensor & self);
+
+} // namespace compositeexplicitautogradnonfunctional
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/special_legendre_polynomial_p_native.h

@@ -0,0 +1,27 @@
+#pragma once
+
+// @generated by torchgen/gen.py from NativeFunction.h
+
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+#include <c10/core/QScheme.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <tuple>
+#include <vector>
+#include <ATen/ops/special_legendre_polynomial_p_meta.h>
+
+namespace at {
+namespace native {
+struct TORCH_API structured_special_legendre_polynomial_p_out : public at::meta::structured_special_legendre_polynomial_p {
+void impl(const at::Tensor & x, const at::Tensor & n, const at::Tensor & out);
+};
+TORCH_API at::Tensor special_legendre_polynomial_p(const at::Scalar & x, const at::Tensor & n);
+TORCH_API at::Tensor & special_legendre_polynomial_p_out(const at::Scalar & x, const at::Tensor & n, at::Tensor & out);
+TORCH_API at::Tensor special_legendre_polynomial_p(const at::Tensor & x, const at::Scalar & n);
+TORCH_API at::Tensor & special_legendre_polynomial_p_out(const at::Tensor & x, const at::Scalar & n, at::Tensor & out);
+} // namespace native
+} // namespace at

videollama2/lib/python3.10/site-packages/torch/include/ATen/ops/upsample_linear1d_backward.h

@@ -0,0 +1,91 @@
+#pragma once
+
+// @generated by torchgen/gen.py from Function.h
+
+#include <ATen/Context.h>
+#include <ATen/DeviceGuard.h>
+#include <ATen/TensorUtils.h>
+#include <ATen/TracerMode.h>
+#include <ATen/core/Generator.h>
+#include <ATen/core/Reduction.h>
+#include <ATen/core/Tensor.h>
+#include <c10/core/Scalar.h>
+#include <c10/core/Storage.h>
+#include <c10/core/TensorOptions.h>
+#include <c10/util/Deprecated.h>
+#include <c10/util/Optional.h>
+
+
+
+#include <ATen/ops/upsample_linear1d_backward_ops.h>
+
+namespace at {
+
+
+// aten::upsample_linear1d_backward.grad_input(Tensor grad_output, SymInt[1] output_size, SymInt[3] input_size, bool align_corners, float? scales=None, *, Tensor(a!) grad_input) -> Tensor(a!)
+inline at::Tensor & upsample_linear1d_backward_out(at::Tensor & grad_input, const at::Tensor & grad_output, at::IntArrayRef output_size, at::IntArrayRef input_size, bool align_corners, c10::optional<double> scales=c10::nullopt) {
+    return at::_ops::upsample_linear1d_backward_grad_input::call(grad_output, c10::fromIntArrayRefSlow(output_size), c10::fromIntArrayRefSlow(input_size), align_corners, scales, grad_input);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, int64_t>::value>>
+  at::Tensor & upsample_linear1d_backward_out(at::Tensor & grad_input, const at::Tensor & grad_output, at::IntArrayRef output_size, at::IntArrayRef input_size, bool align_corners, c10::optional<double> scales=c10::nullopt) {
+    return at::_ops::upsample_linear1d_backward_grad_input::call(grad_output, c10::fromIntArrayRefSlow(output_size), c10::fromIntArrayRefSlow(input_size), align_corners, scales, grad_input);
+  }
+}
+
+// aten::upsample_linear1d_backward.grad_input(Tensor grad_output, SymInt[1] output_size, SymInt[3] input_size, bool align_corners, float? scales=None, *, Tensor(a!) grad_input) -> Tensor(a!)
+inline at::Tensor & upsample_linear1d_backward_outf(const at::Tensor & grad_output, at::IntArrayRef output_size, at::IntArrayRef input_size, bool align_corners, c10::optional<double> scales, at::Tensor & grad_input) {
+    return at::_ops::upsample_linear1d_backward_grad_input::call(grad_output, c10::fromIntArrayRefSlow(output_size), c10::fromIntArrayRefSlow(input_size), align_corners, scales, grad_input);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, int64_t>::value>>
+  at::Tensor & upsample_linear1d_backward_outf(const at::Tensor & grad_output, at::IntArrayRef output_size, at::IntArrayRef input_size, bool align_corners, c10::optional<double> scales, at::Tensor & grad_input) {
+    return at::_ops::upsample_linear1d_backward_grad_input::call(grad_output, c10::fromIntArrayRefSlow(output_size), c10::fromIntArrayRefSlow(input_size), align_corners, scales, grad_input);
+  }
+}
+
+// aten::upsample_linear1d_backward.grad_input(Tensor grad_output, SymInt[1] output_size, SymInt[3] input_size, bool align_corners, float? scales=None, *, Tensor(a!) grad_input) -> Tensor(a!)
+inline at::Tensor & upsample_linear1d_backward_symint_out(at::Tensor & grad_input, const at::Tensor & grad_output, c10::SymIntArrayRef output_size, c10::SymIntArrayRef input_size, bool align_corners, c10::optional<double> scales=c10::nullopt) {
+    return at::_ops::upsample_linear1d_backward_grad_input::call(grad_output, output_size, input_size, align_corners, scales, grad_input);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, c10::SymInt>::value>>
+  at::Tensor & upsample_linear1d_backward_out(at::Tensor & grad_input, const at::Tensor & grad_output, c10::SymIntArrayRef output_size, c10::SymIntArrayRef input_size, bool align_corners, c10::optional<double> scales=c10::nullopt) {
+    return at::_ops::upsample_linear1d_backward_grad_input::call(grad_output, output_size, input_size, align_corners, scales, grad_input);
+  }
+}
+
+// aten::upsample_linear1d_backward.grad_input(Tensor grad_output, SymInt[1] output_size, SymInt[3] input_size, bool align_corners, float? scales=None, *, Tensor(a!) grad_input) -> Tensor(a!)
+inline at::Tensor & upsample_linear1d_backward_symint_outf(const at::Tensor & grad_output, c10::SymIntArrayRef output_size, c10::SymIntArrayRef input_size, bool align_corners, c10::optional<double> scales, at::Tensor & grad_input) {
+    return at::_ops::upsample_linear1d_backward_grad_input::call(grad_output, output_size, input_size, align_corners, scales, grad_input);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, c10::SymInt>::value>>
+  at::Tensor & upsample_linear1d_backward_outf(const at::Tensor & grad_output, c10::SymIntArrayRef output_size, c10::SymIntArrayRef input_size, bool align_corners, c10::optional<double> scales, at::Tensor & grad_input) {
+    return at::_ops::upsample_linear1d_backward_grad_input::call(grad_output, output_size, input_size, align_corners, scales, grad_input);
+  }
+}
+
+// aten::upsample_linear1d_backward(Tensor grad_output, SymInt[1] output_size, SymInt[3] input_size, bool align_corners, float? scales=None) -> Tensor
+inline at::Tensor upsample_linear1d_backward(const at::Tensor & grad_output, at::IntArrayRef output_size, at::IntArrayRef input_size, bool align_corners, c10::optional<double> scales=c10::nullopt) {
+    return at::_ops::upsample_linear1d_backward::call(grad_output, c10::fromIntArrayRefSlow(output_size), c10::fromIntArrayRefSlow(input_size), align_corners, scales);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, int64_t>::value>>
+  at::Tensor upsample_linear1d_backward(const at::Tensor & grad_output, at::IntArrayRef output_size, at::IntArrayRef input_size, bool align_corners, c10::optional<double> scales=c10::nullopt) {
+    return at::_ops::upsample_linear1d_backward::call(grad_output, c10::fromIntArrayRefSlow(output_size), c10::fromIntArrayRefSlow(input_size), align_corners, scales);
+  }
+}
+
+// aten::upsample_linear1d_backward(Tensor grad_output, SymInt[1] output_size, SymInt[3] input_size, bool align_corners, float? scales=None) -> Tensor
+inline at::Tensor upsample_linear1d_backward_symint(const at::Tensor & grad_output, c10::SymIntArrayRef output_size, c10::SymIntArrayRef input_size, bool align_corners, c10::optional<double> scales=c10::nullopt) {
+    return at::_ops::upsample_linear1d_backward::call(grad_output, output_size, input_size, align_corners, scales);
+}
+namespace symint {
+  template <typename T, typename = std::enable_if_t<std::is_same<T, c10::SymInt>::value>>
+  at::Tensor upsample_linear1d_backward(const at::Tensor & grad_output, c10::SymIntArrayRef output_size, c10::SymIntArrayRef input_size, bool align_corners, c10::optional<double> scales=c10::nullopt) {
+    return at::_ops::upsample_linear1d_backward::call(grad_output, output_size, input_size, align_corners, scales);
+  }
+}
+
+}

vllm/lib/python3.10/site-packages/jsonschema/benchmarks/nested_schemas.py

@@ -0,0 +1,56 @@
+"""
+Validating highly nested schemas shouldn't cause exponential time blowups.
+
+See https://github.com/python-jsonschema/jsonschema/issues/1097.
+"""
+from itertools import cycle
+
+from jsonschema.validators import validator_for
+
+metaschemaish = {
+    "$id": "https://example.com/draft/2020-12/schema/strict",
+    "$schema": "https://json-schema.org/draft/2020-12/schema",
+
+    "$vocabulary": {
+        "https://json-schema.org/draft/2020-12/vocab/core": True,
+        "https://json-schema.org/draft/2020-12/vocab/applicator": True,
+        "https://json-schema.org/draft/2020-12/vocab/unevaluated": True,
+        "https://json-schema.org/draft/2020-12/vocab/validation": True,
+        "https://json-schema.org/draft/2020-12/vocab/meta-data": True,
+        "https://json-schema.org/draft/2020-12/vocab/format-annotation": True,
+        "https://json-schema.org/draft/2020-12/vocab/content": True,
+    },
+    "$dynamicAnchor": "meta",
+
+    "$ref": "https://json-schema.org/draft/2020-12/schema",
+    "unevaluatedProperties": False,
+}
+
+
+def nested_schema(levels):
+    """
+    Produce a schema which validates deeply nested objects and arrays.
+    """
+
+    names = cycle(["foo", "bar", "baz", "quux", "spam", "eggs"])
+    schema = {"type": "object", "properties": {"ham": {"type": "string"}}}
+    for _, name in zip(range(levels - 1), names):
+        schema = {"type": "object", "properties": {name: schema}}
+    return schema
+
+
+validator = validator_for(metaschemaish)(metaschemaish)
+
+if __name__ == "__main__":
+    from pyperf import Runner
+    runner = Runner()
+
+    not_nested = nested_schema(levels=1)
+    runner.bench_func("not nested", lambda: validator.is_valid(not_nested))
+
+    for levels in range(1, 11, 3):
+        schema = nested_schema(levels=levels)
+        runner.bench_func(
+            f"nested * {levels}",
+            lambda schema=schema: validator.is_valid(schema),
+        )

vllm/lib/python3.10/site-packages/jsonschema/benchmarks/unused_registry.py

@@ -0,0 +1,35 @@
+"""
+An unused schema registry should not cause slower validation.
+
+"Unused" here means one where no reference resolution is occurring anyhow.
+
+See https://github.com/python-jsonschema/jsonschema/issues/1088.
+"""
+from pyperf import Runner
+from referencing import Registry
+from referencing.jsonschema import DRAFT201909
+
+from jsonschema import Draft201909Validator
+
+registry = Registry().with_resource(
+    "urn:example:foo",
+    DRAFT201909.create_resource({}),
+)
+
+schema = {"$ref": "https://json-schema.org/draft/2019-09/schema"}
+instance = {"maxLength": 4}
+
+no_registry = Draft201909Validator(schema)
+with_useless_registry = Draft201909Validator(schema, registry=registry)
+
+if __name__ == "__main__":
+    runner = Runner()
+
+    runner.bench_func(
+        "no registry",
+        lambda: no_registry.is_valid(instance),
+    )
+    runner.bench_func(
+        "useless registry",
+        lambda: with_useless_registry.is_valid(instance),
+    )

vllm/lib/python3.10/site-packages/mpmath/ctx_base.py

@@ -0,0 +1,494 @@
+from operator import gt, lt
+
+from .libmp.backend import xrange
+
+from .functions.functions import SpecialFunctions
+from .functions.rszeta import RSCache
+from .calculus.quadrature import QuadratureMethods
+from .calculus.inverselaplace import LaplaceTransformInversionMethods
+from .calculus.calculus import CalculusMethods
+from .calculus.optimization import OptimizationMethods
+from .calculus.odes import ODEMethods
+from .matrices.matrices import MatrixMethods
+from .matrices.calculus import MatrixCalculusMethods
+from .matrices.linalg import LinearAlgebraMethods
+from .matrices.eigen import Eigen
+from .identification import IdentificationMethods
+from .visualization import VisualizationMethods
+
+from . import libmp
+
+class Context(object):
+    pass
+
+class StandardBaseContext(Context,
+    SpecialFunctions,
+    RSCache,
+    QuadratureMethods,
+    LaplaceTransformInversionMethods,
+    CalculusMethods,
+    MatrixMethods,
+    MatrixCalculusMethods,
+    LinearAlgebraMethods,
+    Eigen,
+    IdentificationMethods,
+    OptimizationMethods,
+    ODEMethods,
+    VisualizationMethods):
+
+    NoConvergence = libmp.NoConvergence
+    ComplexResult = libmp.ComplexResult
+
+    def __init__(ctx):
+        ctx._aliases = {}
+        # Call those that need preinitialization (e.g. for wrappers)
+        SpecialFunctions.__init__(ctx)
+        RSCache.__init__(ctx)
+        QuadratureMethods.__init__(ctx)
+        LaplaceTransformInversionMethods.__init__(ctx)
+        CalculusMethods.__init__(ctx)
+        MatrixMethods.__init__(ctx)
+
+    def _init_aliases(ctx):
+        for alias, value in ctx._aliases.items():
+            try:
+                setattr(ctx, alias, getattr(ctx, value))
+            except AttributeError:
+                pass
+
+    _fixed_precision = False
+
+    # XXX
+    verbose = False
+
+    def warn(ctx, msg):
+        print("Warning:", msg)
+
+    def bad_domain(ctx, msg):
+        raise ValueError(msg)
+
+    def _re(ctx, x):
+        if hasattr(x, "real"):
+            return x.real
+        return x
+
+    def _im(ctx, x):
+        if hasattr(x, "imag"):
+            return x.imag
+        return ctx.zero
+
+    def _as_points(ctx, x):
+        return x
+
+    def fneg(ctx, x, **kwargs):
+        return -ctx.convert(x)
+
+    def fadd(ctx, x, y, **kwargs):
+        return ctx.convert(x)+ctx.convert(y)
+
+    def fsub(ctx, x, y, **kwargs):
+        return ctx.convert(x)-ctx.convert(y)
+
+    def fmul(ctx, x, y, **kwargs):
+        return ctx.convert(x)*ctx.convert(y)
+
+    def fdiv(ctx, x, y, **kwargs):
+        return ctx.convert(x)/ctx.convert(y)
+
+    def fsum(ctx, args, absolute=False, squared=False):
+        if absolute:
+            if squared:
+                return sum((abs(x)**2 for x in args), ctx.zero)
+            return sum((abs(x) for x in args), ctx.zero)
+        if squared:
+            return sum((x**2 for x in args), ctx.zero)
+        return sum(args, ctx.zero)
+
+    def fdot(ctx, xs, ys=None, conjugate=False):
+        if ys is not None:
+            xs = zip(xs, ys)
+        if conjugate:
+            cf = ctx.conj
+            return sum((x*cf(y) for (x,y) in xs), ctx.zero)
+        else:
+            return sum((x*y for (x,y) in xs), ctx.zero)
+
+    def fprod(ctx, args):
+        prod = ctx.one
+        for arg in args:
+            prod *= arg
+        return prod
+
+    def nprint(ctx, x, n=6, **kwargs):
+        """
+        Equivalent to ``print(nstr(x, n))``.
+        """
+        print(ctx.nstr(x, n, **kwargs))
+
+    def chop(ctx, x, tol=None):
+        """
+        Chops off small real or imaginary parts, or converts
+        numbers close to zero to exact zeros. The input can be a
+        single number or an iterable::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> chop(5+1e-10j, tol=1e-9)
+            mpf('5.0')
+            >>> nprint(chop([1.0, 1e-20, 3+1e-18j, -4, 2]))
+            [1.0, 0.0, 3.0, -4.0, 2.0]
+
+        The tolerance defaults to ``100*eps``.
+        """
+        if tol is None:
+            tol = 100*ctx.eps
+        try:
+            x = ctx.convert(x)
+            absx = abs(x)
+            if abs(x) < tol:
+                return ctx.zero
+            if ctx._is_complex_type(x):
+                #part_tol = min(tol, absx*tol)
+                part_tol = max(tol, absx*tol)
+                if abs(x.imag) < part_tol:
+                    return x.real
+                if abs(x.real) < part_tol:
+                    return ctx.mpc(0, x.imag)
+        except TypeError:
+            if isinstance(x, ctx.matrix):
+                return x.apply(lambda a: ctx.chop(a, tol))
+            if hasattr(x, "__iter__"):
+                return [ctx.chop(a, tol) for a in x]
+        return x
+
+    def almosteq(ctx, s, t, rel_eps=None, abs_eps=None):
+        r"""
+        Determine whether the difference between `s` and `t` is smaller
+        than a given epsilon, either relatively or absolutely.
+
+        Both a maximum relative difference and a maximum difference
+        ('epsilons') may be specified. The absolute difference is
+        defined as `|s-t|` and the relative difference is defined
+        as `|s-t|/\max(|s|, |t|)`.
+
+        If only one epsilon is given, both are set to the same value.
+        If none is given, both epsilons are set to `2^{-p+m}` where
+        `p` is the current working precision and `m` is a small
+        integer. The default setting typically allows :func:`~mpmath.almosteq`
+        to be used to check for mathematical equality
+        in the presence of small rounding errors.
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> almosteq(3.141592653589793, 3.141592653589790)
+            True
+            >>> almosteq(3.141592653589793, 3.141592653589700)
+            False
+            >>> almosteq(3.141592653589793, 3.141592653589700, 1e-10)
+            True
+            >>> almosteq(1e-20, 2e-20)
+            True
+            >>> almosteq(1e-20, 2e-20, rel_eps=0, abs_eps=0)
+            False
+
+        """
+        t = ctx.convert(t)
+        if abs_eps is None and rel_eps is None:
+            rel_eps = abs_eps = ctx.ldexp(1, -ctx.prec+4)
+        if abs_eps is None:
+            abs_eps = rel_eps
+        elif rel_eps is None:
+            rel_eps = abs_eps
+        diff = abs(s-t)
+        if diff <= abs_eps:
+            return True
+        abss = abs(s)
+        abst = abs(t)
+        if abss < abst:
+            err = diff/abst
+        else:
+            err = diff/abss
+        return err <= rel_eps
+
+    def arange(ctx, *args):
+        r"""
+        This is a generalized version of Python's :func:`~mpmath.range` function
+        that accepts fractional endpoints and step sizes and
+        returns a list of ``mpf`` instances. Like :func:`~mpmath.range`,
+        :func:`~mpmath.arange` can be called with 1, 2 or 3 arguments:
+
+        ``arange(b)``
+            `[0, 1, 2, \ldots, x]`
+        ``arange(a, b)``
+            `[a, a+1, a+2, \ldots, x]`
+        ``arange(a, b, h)``
+            `[a, a+h, a+h, \ldots, x]`
+
+        where `b-1 \le x < b` (in the third case, `b-h \le x < b`).
+
+        Like Python's :func:`~mpmath.range`, the endpoint is not included. To
+        produce ranges where the endpoint is included, :func:`~mpmath.linspace`
+        is more convenient.
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> arange(4)
+            [mpf('0.0'), mpf('1.0'), mpf('2.0'), mpf('3.0')]
+            >>> arange(1, 2, 0.25)
+            [mpf('1.0'), mpf('1.25'), mpf('1.5'), mpf('1.75')]
+            >>> arange(1, -1, -0.75)
+            [mpf('1.0'), mpf('0.25'), mpf('-0.5')]
+
+        """
+        if not len(args) <= 3:
+            raise TypeError('arange expected at most 3 arguments, got %i'
+                            % len(args))
+        if not len(args) >= 1:
+            raise TypeError('arange expected at least 1 argument, got %i'
+                            % len(args))
+        # set default
+        a = 0
+        dt = 1
+        # interpret arguments
+        if len(args) == 1:
+            b = args[0]
+        elif len(args) >= 2:
+            a = args[0]
+            b = args[1]
+        if len(args) == 3:
+            dt = args[2]
+        a, b, dt = ctx.mpf(a), ctx.mpf(b), ctx.mpf(dt)
+        assert a + dt != a, 'dt is too small and would cause an infinite loop'
+        # adapt code for sign of dt
+        if a > b:
+            if dt > 0:
+                return []
+            op = gt
+        else:
+            if dt < 0:
+                return []
+            op = lt
+        # create list
+        result = []
+        i = 0
+        t = a
+        while 1:
+            t = a + dt*i
+            i += 1
+            if op(t, b):
+                result.append(t)
+            else:
+                break
+        return result
+
+    def linspace(ctx, *args, **kwargs):
+        """
+        ``linspace(a, b, n)`` returns a list of `n` evenly spaced
+        samples from `a` to `b`. The syntax ``linspace(mpi(a,b), n)``
+        is also valid.
+
+        This function is often more convenient than :func:`~mpmath.arange`
+        for partitioning an interval into subintervals, since
+        the endpoint is included::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> linspace(1, 4, 4)
+            [mpf('1.0'), mpf('2.0'), mpf('3.0'), mpf('4.0')]
+
+        You may also provide the keyword argument ``endpoint=False``::
+
+            >>> linspace(1, 4, 4, endpoint=False)
+            [mpf('1.0'), mpf('1.75'), mpf('2.5'), mpf('3.25')]
+
+        """
+        if len(args) == 3:
+            a = ctx.mpf(args[0])
+            b = ctx.mpf(args[1])
+            n = int(args[2])
+        elif len(args) == 2:
+            assert hasattr(args[0], '_mpi_')
+            a = args[0].a
+            b = args[0].b
+            n = int(args[1])
+        else:
+            raise TypeError('linspace expected 2 or 3 arguments, got %i' \
+                            % len(args))
+        if n < 1:
+            raise ValueError('n must be greater than 0')
+        if not 'endpoint' in kwargs or kwargs['endpoint']:
+            if n == 1:
+                return [ctx.mpf(a)]
+            step = (b - a) / ctx.mpf(n - 1)
+            y = [i*step + a for i in xrange(n)]
+            y[-1] = b
+        else:
+            step = (b - a) / ctx.mpf(n)
+            y = [i*step + a for i in xrange(n)]
+        return y
+
+    def cos_sin(ctx, z, **kwargs):
+        return ctx.cos(z, **kwargs), ctx.sin(z, **kwargs)
+
+    def cospi_sinpi(ctx, z, **kwargs):
+        return ctx.cospi(z, **kwargs), ctx.sinpi(z, **kwargs)
+
+    def _default_hyper_maxprec(ctx, p):
+        return int(1000 * p**0.25 + 4*p)
+
+    _gcd = staticmethod(libmp.gcd)
+    list_primes = staticmethod(libmp.list_primes)
+    isprime = staticmethod(libmp.isprime)
+    bernfrac = staticmethod(libmp.bernfrac)
+    moebius = staticmethod(libmp.moebius)
+    _ifac = staticmethod(libmp.ifac)
+    _eulernum = staticmethod(libmp.eulernum)
+    _stirling1 = staticmethod(libmp.stirling1)
+    _stirling2 = staticmethod(libmp.stirling2)
+
+    def sum_accurately(ctx, terms, check_step=1):
+        prec = ctx.prec
+        try:
+            extraprec = 10
+            while 1:
+                ctx.prec = prec + extraprec + 5
+                max_mag = ctx.ninf
+                s = ctx.zero
+                k = 0
+                for term in terms():
+                    s += term
+                    if (not k % check_step) and term:
+                        term_mag = ctx.mag(term)
+                        max_mag = max(max_mag, term_mag)
+                        sum_mag = ctx.mag(s)
+                        if sum_mag - term_mag > ctx.prec:
+                            break
+                    k += 1
+                cancellation = max_mag - sum_mag
+                if cancellation != cancellation:
+                    break
+                if cancellation < extraprec or ctx._fixed_precision:
+                    break
+                extraprec += min(ctx.prec, cancellation)
+            return s
+        finally:
+            ctx.prec = prec
+
+    def mul_accurately(ctx, factors, check_step=1):
+        prec = ctx.prec
+        try:
+            extraprec = 10
+            while 1:
+                ctx.prec = prec + extraprec + 5
+                max_mag = ctx.ninf
+                one = ctx.one
+                s = one
+                k = 0
+                for factor in factors():
+                    s *= factor
+                    term = factor - one
+                    if (not k % check_step):
+                        term_mag = ctx.mag(term)
+                        max_mag = max(max_mag, term_mag)
+                        sum_mag = ctx.mag(s-one)
+                        #if sum_mag - term_mag > ctx.prec:
+                        #    break
+                        if -term_mag > ctx.prec:
+                            break
+                    k += 1
+                cancellation = max_mag - sum_mag
+                if cancellation != cancellation:
+                    break
+                if cancellation < extraprec or ctx._fixed_precision:
+                    break
+                extraprec += min(ctx.prec, cancellation)
+            return s
+        finally:
+            ctx.prec = prec
+
+    def power(ctx, x, y):
+        r"""Converts `x` and `y` to mpmath numbers and evaluates
+        `x^y = \exp(y \log(x))`::
+
+            >>> from mpmath import *
+            >>> mp.dps = 30; mp.pretty = True
+            >>> power(2, 0.5)
+            1.41421356237309504880168872421
+
+        This shows the leading few digits of a large Mersenne prime
+        (performing the exact calculation ``2**43112609-1`` and
+        displaying the result in Python would be very slow)::
+
+            >>> power(2, 43112609)-1
+            3.16470269330255923143453723949e+12978188
+        """
+        return ctx.convert(x) ** ctx.convert(y)
+
+    def _zeta_int(ctx, n):
+        return ctx.zeta(n)
+
+    def maxcalls(ctx, f, N):
+        """
+        Return a wrapped copy of *f* that raises ``NoConvergence`` when *f*
+        has been called more than *N* times::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> f = maxcalls(sin, 10)
+            >>> print(sum(f(n) for n in range(10)))
+            1.95520948210738
+            >>> f(10) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: maxcalls: function evaluated 10 times
+
+        """
+        counter = [0]
+        def f_maxcalls_wrapped(*args, **kwargs):
+            counter[0] += 1
+            if counter[0] > N:
+                raise ctx.NoConvergence("maxcalls: function evaluated %i times" % N)
+            return f(*args, **kwargs)
+        return f_maxcalls_wrapped
+
+    def memoize(ctx, f):
+        """
+        Return a wrapped copy of *f* that caches computed values, i.e.
+        a memoized copy of *f*. Values are only reused if the cached precision
+        is equal to or higher than the working precision::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = True
+            >>> f = memoize(maxcalls(sin, 1))
+            >>> f(2)
+            0.909297426825682
+            >>> f(2)
+            0.909297426825682
+            >>> mp.dps = 25
+            >>> f(2) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: maxcalls: function evaluated 1 times
+
+        """
+        f_cache = {}
+        def f_cached(*args, **kwargs):
+            if kwargs:
+                key = args, tuple(kwargs.items())
+            else:
+                key = args
+            prec = ctx.prec
+            if key in f_cache:
+                cprec, cvalue = f_cache[key]
+                if cprec >= prec:
+                    return +cvalue
+            value = f(*args, **kwargs)
+            f_cache[key] = (prec, value)
+            return value
+        f_cached.__name__ = f.__name__
+        f_cached.__doc__ = f.__doc__
+        return f_cached

vllm/lib/python3.10/site-packages/mpmath/ctx_fp.py

@@ -0,0 +1,253 @@
+from .ctx_base import StandardBaseContext
+
+import math
+import cmath
+from . import math2
+
+from . import function_docs
+
+from .libmp import mpf_bernoulli, to_float, int_types
+from . import libmp
+
+class FPContext(StandardBaseContext):
+    """
+    Context for fast low-precision arithmetic (53-bit precision, giving at most
+    about 15-digit accuracy), using Python's builtin float and complex.
+    """
+
+    def __init__(ctx):
+        StandardBaseContext.__init__(ctx)
+
+        # Override SpecialFunctions implementation
+        ctx.loggamma = math2.loggamma
+        ctx._bernoulli_cache = {}
+        ctx.pretty = False
+
+        ctx._init_aliases()
+
+    _mpq = lambda cls, x: float(x[0])/x[1]
+
+    NoConvergence = libmp.NoConvergence
+
+    def _get_prec(ctx): return 53
+    def _set_prec(ctx, p): return
+    def _get_dps(ctx): return 15
+    def _set_dps(ctx, p): return
+
+    _fixed_precision = True
+
+    prec = property(_get_prec, _set_prec)
+    dps = property(_get_dps, _set_dps)
+
+    zero = 0.0
+    one = 1.0
+    eps = math2.EPS
+    inf = math2.INF
+    ninf = math2.NINF
+    nan = math2.NAN
+    j = 1j
+
+    # Called by SpecialFunctions.__init__()
+    @classmethod
+    def _wrap_specfun(cls, name, f, wrap):
+        if wrap:
+            def f_wrapped(ctx, *args, **kwargs):
+                convert = ctx.convert
+                args = [convert(a) for a in args]
+                return f(ctx, *args, **kwargs)
+        else:
+            f_wrapped = f
+        f_wrapped.__doc__ = function_docs.__dict__.get(name, f.__doc__)
+        setattr(cls, name, f_wrapped)
+
+    def bernoulli(ctx, n):
+        cache = ctx._bernoulli_cache
+        if n in cache:
+            return cache[n]
+        cache[n] = to_float(mpf_bernoulli(n, 53, 'n'), strict=True)
+        return cache[n]
+
+    pi = math2.pi
+    e = math2.e
+    euler = math2.euler
+    sqrt2 = 1.4142135623730950488
+    sqrt5 = 2.2360679774997896964
+    phi = 1.6180339887498948482
+    ln2 = 0.69314718055994530942
+    ln10 = 2.302585092994045684
+    euler = 0.57721566490153286061
+    catalan = 0.91596559417721901505
+    khinchin = 2.6854520010653064453
+    apery = 1.2020569031595942854
+    glaisher = 1.2824271291006226369
+
+    absmin = absmax = abs
+
+    def is_special(ctx, x):
+        return x - x != 0.0
+
+    def isnan(ctx, x):
+        return x != x
+
+    def isinf(ctx, x):
+        return abs(x) == math2.INF
+
+    def isnormal(ctx, x):
+        if x:
+            return x - x == 0.0
+        return False
+
+    def isnpint(ctx, x):
+        if type(x) is complex:
+            if x.imag:
+                return False
+            x = x.real
+        return x <= 0.0 and round(x) == x
+
+    mpf = float
+    mpc = complex
+
+    def convert(ctx, x):
+        try:
+            return float(x)
+        except:
+            return complex(x)
+
+    power = staticmethod(math2.pow)
+    sqrt = staticmethod(math2.sqrt)
+    exp = staticmethod(math2.exp)
+    ln = log = staticmethod(math2.log)
+    cos = staticmethod(math2.cos)
+    sin = staticmethod(math2.sin)
+    tan = staticmethod(math2.tan)
+    cos_sin = staticmethod(math2.cos_sin)
+    acos = staticmethod(math2.acos)
+    asin = staticmethod(math2.asin)
+    atan = staticmethod(math2.atan)
+    cosh = staticmethod(math2.cosh)
+    sinh = staticmethod(math2.sinh)
+    tanh = staticmethod(math2.tanh)
+    gamma = staticmethod(math2.gamma)
+    rgamma = staticmethod(math2.rgamma)
+    fac = factorial = staticmethod(math2.factorial)
+    floor = staticmethod(math2.floor)
+    ceil = staticmethod(math2.ceil)
+    cospi = staticmethod(math2.cospi)
+    sinpi = staticmethod(math2.sinpi)
+    cbrt = staticmethod(math2.cbrt)
+    _nthroot = staticmethod(math2.nthroot)
+    _ei = staticmethod(math2.ei)
+    _e1 = staticmethod(math2.e1)
+    _zeta = _zeta_int = staticmethod(math2.zeta)
+
+    # XXX: math2
+    def arg(ctx, z):
+        z = complex(z)
+        return math.atan2(z.imag, z.real)
+
+    def expj(ctx, x):
+        return ctx.exp(ctx.j*x)
+
+    def expjpi(ctx, x):
+        return ctx.exp(ctx.j*ctx.pi*x)
+
+    ldexp = math.ldexp
+    frexp = math.frexp
+
+    def mag(ctx, z):
+        if z:
+            return ctx.frexp(abs(z))[1]
+        return ctx.ninf
+
+    def isint(ctx, z):
+        if hasattr(z, "imag"):   # float/int don't have .real/.imag in py2.5
+            if z.imag:
+                return False
+            z = z.real
+        try:
+            return z == int(z)
+        except:
+            return False
+
+    def nint_distance(ctx, z):
+        if hasattr(z, "imag"):   # float/int don't have .real/.imag in py2.5
+            n = round(z.real)
+        else:
+            n = round(z)
+        if n == z:
+            return n, ctx.ninf
+        return n, ctx.mag(abs(z-n))
+
+    def _convert_param(ctx, z):
+        if type(z) is tuple:
+            p, q = z
+            return ctx.mpf(p) / q, 'R'
+        if hasattr(z, "imag"):    # float/int don't have .real/.imag in py2.5
+            intz = int(z.real)
+        else:
+            intz = int(z)
+        if z == intz:
+            return intz, 'Z'
+        return z, 'R'
+
+    def _is_real_type(ctx, z):
+        return isinstance(z, float) or isinstance(z, int_types)
+
+    def _is_complex_type(ctx, z):
+        return isinstance(z, complex)
+
+    def hypsum(ctx, p, q, types, coeffs, z, maxterms=6000, **kwargs):
+        coeffs = list(coeffs)
+        num = range(p)
+        den = range(p,p+q)
+        tol = ctx.eps
+        s = t = 1.0
+        k = 0
+        while 1:
+            for i in num: t *= (coeffs[i]+k)
+            for i in den: t /= (coeffs[i]+k)
+            k += 1; t /= k; t *= z; s += t
+            if abs(t) < tol:
+                return s
+            if k > maxterms:
+                raise ctx.NoConvergence
+
+    def atan2(ctx, x, y):
+        return math.atan2(x, y)
+
+    def psi(ctx, m, z):
+        m = int(m)
+        if m == 0:
+            return ctx.digamma(z)
+        return (-1)**(m+1) * ctx.fac(m) * ctx.zeta(m+1, z)
+
+    digamma = staticmethod(math2.digamma)
+
+    def harmonic(ctx, x):
+        x = ctx.convert(x)
+        if x == 0 or x == 1:
+            return x
+        return ctx.digamma(x+1) + ctx.euler
+
+    nstr = str
+
+    def to_fixed(ctx, x, prec):
+        return int(math.ldexp(x, prec))
+
+    def rand(ctx):
+        import random
+        return random.random()
+
+    _erf = staticmethod(math2.erf)
+    _erfc = staticmethod(math2.erfc)
+
+    def sum_accurately(ctx, terms, check_step=1):
+        s = ctx.zero
+        k = 0
+        for term in terms():
+            s += term
+            if (not k % check_step) and term:
+                if abs(term) <= 1e-18*abs(s):
+                    break
+            k += 1
+        return s

vllm/lib/python3.10/site-packages/mpmath/ctx_mp.py

@@ -0,0 +1,1339 @@
+"""
+This module defines the mpf, mpc classes, and standard functions for
+operating with them.
+"""
+__docformat__ = 'plaintext'
+
+import functools
+
+import re
+
+from .ctx_base import StandardBaseContext
+
+from .libmp.backend import basestring, BACKEND
+
+from . import libmp
+
+from .libmp import (MPZ, MPZ_ZERO, MPZ_ONE, int_types, repr_dps,
+    round_floor, round_ceiling, dps_to_prec, round_nearest, prec_to_dps,
+    ComplexResult, to_pickable, from_pickable, normalize,
+    from_int, from_float, from_str, to_int, to_float, to_str,
+    from_rational, from_man_exp,
+    fone, fzero, finf, fninf, fnan,
+    mpf_abs, mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul, mpf_mul_int,
+    mpf_div, mpf_rdiv_int, mpf_pow_int, mpf_mod,
+    mpf_eq, mpf_cmp, mpf_lt, mpf_gt, mpf_le, mpf_ge,
+    mpf_hash, mpf_rand,
+    mpf_sum,
+    bitcount, to_fixed,
+    mpc_to_str,
+    mpc_to_complex, mpc_hash, mpc_pos, mpc_is_nonzero, mpc_neg, mpc_conjugate,
+    mpc_abs, mpc_add, mpc_add_mpf, mpc_sub, mpc_sub_mpf, mpc_mul, mpc_mul_mpf,
+    mpc_mul_int, mpc_div, mpc_div_mpf, mpc_pow, mpc_pow_mpf, mpc_pow_int,
+    mpc_mpf_div,
+    mpf_pow,
+    mpf_pi, mpf_degree, mpf_e, mpf_phi, mpf_ln2, mpf_ln10,
+    mpf_euler, mpf_catalan, mpf_apery, mpf_khinchin,
+    mpf_glaisher, mpf_twinprime, mpf_mertens,
+    int_types)
+
+from . import function_docs
+from . import rational
+
+new = object.__new__
+
+get_complex = re.compile(r'^\(?(?P<re>[\+\-]?\d*(\.\d*)?(e[\+\-]?\d+)?)??'
+                         r'(?P<im>[\+\-]?\d*(\.\d*)?(e[\+\-]?\d+)?j)?\)?$')
+
+if BACKEND == 'sage':
+    from sage.libs.mpmath.ext_main import Context as BaseMPContext
+    # pickle hack
+    import sage.libs.mpmath.ext_main as _mpf_module
+else:
+    from .ctx_mp_python import PythonMPContext as BaseMPContext
+    from . import ctx_mp_python as _mpf_module
+
+from .ctx_mp_python import _mpf, _mpc, mpnumeric
+
+class MPContext(BaseMPContext, StandardBaseContext):
+    """
+    Context for multiprecision arithmetic with a global precision.
+    """
+
+    def __init__(ctx):
+        BaseMPContext.__init__(ctx)
+        ctx.trap_complex = False
+        ctx.pretty = False
+        ctx.types = [ctx.mpf, ctx.mpc, ctx.constant]
+        ctx._mpq = rational.mpq
+        ctx.default()
+        StandardBaseContext.__init__(ctx)
+
+        ctx.mpq = rational.mpq
+        ctx.init_builtins()
+
+        ctx.hyp_summators = {}
+
+        ctx._init_aliases()
+
+        # XXX: automate
+        try:
+            ctx.bernoulli.im_func.func_doc = function_docs.bernoulli
+            ctx.primepi.im_func.func_doc = function_docs.primepi
+            ctx.psi.im_func.func_doc = function_docs.psi
+            ctx.atan2.im_func.func_doc = function_docs.atan2
+        except AttributeError:
+            # python 3
+            ctx.bernoulli.__func__.func_doc = function_docs.bernoulli
+            ctx.primepi.__func__.func_doc = function_docs.primepi
+            ctx.psi.__func__.func_doc = function_docs.psi
+            ctx.atan2.__func__.func_doc = function_docs.atan2
+
+        ctx.digamma.func_doc = function_docs.digamma
+        ctx.cospi.func_doc = function_docs.cospi
+        ctx.sinpi.func_doc = function_docs.sinpi
+
+    def init_builtins(ctx):
+
+        mpf = ctx.mpf
+        mpc = ctx.mpc
+
+        # Exact constants
+        ctx.one = ctx.make_mpf(fone)
+        ctx.zero = ctx.make_mpf(fzero)
+        ctx.j = ctx.make_mpc((fzero,fone))
+        ctx.inf = ctx.make_mpf(finf)
+        ctx.ninf = ctx.make_mpf(fninf)
+        ctx.nan = ctx.make_mpf(fnan)
+
+        eps = ctx.constant(lambda prec, rnd: (0, MPZ_ONE, 1-prec, 1),
+            "epsilon of working precision", "eps")
+        ctx.eps = eps
+
+        # Approximate constants
+        ctx.pi = ctx.constant(mpf_pi, "pi", "pi")
+        ctx.ln2 = ctx.constant(mpf_ln2, "ln(2)", "ln2")
+        ctx.ln10 = ctx.constant(mpf_ln10, "ln(10)", "ln10")
+        ctx.phi = ctx.constant(mpf_phi, "Golden ratio phi", "phi")
+        ctx.e = ctx.constant(mpf_e, "e = exp(1)", "e")
+        ctx.euler = ctx.constant(mpf_euler, "Euler's constant", "euler")
+        ctx.catalan = ctx.constant(mpf_catalan, "Catalan's constant", "catalan")
+        ctx.khinchin = ctx.constant(mpf_khinchin, "Khinchin's constant", "khinchin")
+        ctx.glaisher = ctx.constant(mpf_glaisher, "Glaisher's constant", "glaisher")
+        ctx.apery = ctx.constant(mpf_apery, "Apery's constant", "apery")
+        ctx.degree = ctx.constant(mpf_degree, "1 deg = pi / 180", "degree")
+        ctx.twinprime = ctx.constant(mpf_twinprime, "Twin prime constant", "twinprime")
+        ctx.mertens = ctx.constant(mpf_mertens, "Mertens' constant", "mertens")
+
+        # Standard functions
+        ctx.sqrt = ctx._wrap_libmp_function(libmp.mpf_sqrt, libmp.mpc_sqrt)
+        ctx.cbrt = ctx._wrap_libmp_function(libmp.mpf_cbrt, libmp.mpc_cbrt)
+        ctx.ln = ctx._wrap_libmp_function(libmp.mpf_log, libmp.mpc_log)
+        ctx.atan = ctx._wrap_libmp_function(libmp.mpf_atan, libmp.mpc_atan)
+        ctx.exp = ctx._wrap_libmp_function(libmp.mpf_exp, libmp.mpc_exp)
+        ctx.expj = ctx._wrap_libmp_function(libmp.mpf_expj, libmp.mpc_expj)
+        ctx.expjpi = ctx._wrap_libmp_function(libmp.mpf_expjpi, libmp.mpc_expjpi)
+        ctx.sin = ctx._wrap_libmp_function(libmp.mpf_sin, libmp.mpc_sin)
+        ctx.cos = ctx._wrap_libmp_function(libmp.mpf_cos, libmp.mpc_cos)
+        ctx.tan = ctx._wrap_libmp_function(libmp.mpf_tan, libmp.mpc_tan)
+        ctx.sinh = ctx._wrap_libmp_function(libmp.mpf_sinh, libmp.mpc_sinh)
+        ctx.cosh = ctx._wrap_libmp_function(libmp.mpf_cosh, libmp.mpc_cosh)
+        ctx.tanh = ctx._wrap_libmp_function(libmp.mpf_tanh, libmp.mpc_tanh)
+        ctx.asin = ctx._wrap_libmp_function(libmp.mpf_asin, libmp.mpc_asin)
+        ctx.acos = ctx._wrap_libmp_function(libmp.mpf_acos, libmp.mpc_acos)
+        ctx.atan = ctx._wrap_libmp_function(libmp.mpf_atan, libmp.mpc_atan)
+        ctx.asinh = ctx._wrap_libmp_function(libmp.mpf_asinh, libmp.mpc_asinh)
+        ctx.acosh = ctx._wrap_libmp_function(libmp.mpf_acosh, libmp.mpc_acosh)
+        ctx.atanh = ctx._wrap_libmp_function(libmp.mpf_atanh, libmp.mpc_atanh)
+        ctx.sinpi = ctx._wrap_libmp_function(libmp.mpf_sin_pi, libmp.mpc_sin_pi)
+        ctx.cospi = ctx._wrap_libmp_function(libmp.mpf_cos_pi, libmp.mpc_cos_pi)
+        ctx.floor = ctx._wrap_libmp_function(libmp.mpf_floor, libmp.mpc_floor)
+        ctx.ceil = ctx._wrap_libmp_function(libmp.mpf_ceil, libmp.mpc_ceil)
+        ctx.nint = ctx._wrap_libmp_function(libmp.mpf_nint, libmp.mpc_nint)
+        ctx.frac = ctx._wrap_libmp_function(libmp.mpf_frac, libmp.mpc_frac)
+        ctx.fib = ctx.fibonacci = ctx._wrap_libmp_function(libmp.mpf_fibonacci, libmp.mpc_fibonacci)
+
+        ctx.gamma = ctx._wrap_libmp_function(libmp.mpf_gamma, libmp.mpc_gamma)
+        ctx.rgamma = ctx._wrap_libmp_function(libmp.mpf_rgamma, libmp.mpc_rgamma)
+        ctx.loggamma = ctx._wrap_libmp_function(libmp.mpf_loggamma, libmp.mpc_loggamma)
+        ctx.fac = ctx.factorial = ctx._wrap_libmp_function(libmp.mpf_factorial, libmp.mpc_factorial)
+
+        ctx.digamma = ctx._wrap_libmp_function(libmp.mpf_psi0, libmp.mpc_psi0)
+        ctx.harmonic = ctx._wrap_libmp_function(libmp.mpf_harmonic, libmp.mpc_harmonic)
+        ctx.ei = ctx._wrap_libmp_function(libmp.mpf_ei, libmp.mpc_ei)
+        ctx.e1 = ctx._wrap_libmp_function(libmp.mpf_e1, libmp.mpc_e1)
+        ctx._ci = ctx._wrap_libmp_function(libmp.mpf_ci, libmp.mpc_ci)
+        ctx._si = ctx._wrap_libmp_function(libmp.mpf_si, libmp.mpc_si)
+        ctx.ellipk = ctx._wrap_libmp_function(libmp.mpf_ellipk, libmp.mpc_ellipk)
+        ctx._ellipe = ctx._wrap_libmp_function(libmp.mpf_ellipe, libmp.mpc_ellipe)
+        ctx.agm1 = ctx._wrap_libmp_function(libmp.mpf_agm1, libmp.mpc_agm1)
+        ctx._erf = ctx._wrap_libmp_function(libmp.mpf_erf, None)
+        ctx._erfc = ctx._wrap_libmp_function(libmp.mpf_erfc, None)
+        ctx._zeta = ctx._wrap_libmp_function(libmp.mpf_zeta, libmp.mpc_zeta)
+        ctx._altzeta = ctx._wrap_libmp_function(libmp.mpf_altzeta, libmp.mpc_altzeta)
+
+        # Faster versions
+        ctx.sqrt = getattr(ctx, "_sage_sqrt", ctx.sqrt)
+        ctx.exp = getattr(ctx, "_sage_exp", ctx.exp)
+        ctx.ln = getattr(ctx, "_sage_ln", ctx.ln)
+        ctx.cos = getattr(ctx, "_sage_cos", ctx.cos)
+        ctx.sin = getattr(ctx, "_sage_sin", ctx.sin)
+
+    def to_fixed(ctx, x, prec):
+        return x.to_fixed(prec)
+
+    def hypot(ctx, x, y):
+        r"""
+        Computes the Euclidean norm of the vector `(x, y)`, equal
+        to `\sqrt{x^2 + y^2}`. Both `x` and `y` must be real."""
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        return ctx.make_mpf(libmp.mpf_hypot(x._mpf_, y._mpf_, *ctx._prec_rounding))
+
+    def _gamma_upper_int(ctx, n, z):
+        n = int(ctx._re(n))
+        if n == 0:
+            return ctx.e1(z)
+        if not hasattr(z, '_mpf_'):
+            raise NotImplementedError
+        prec, rounding = ctx._prec_rounding
+        real, imag = libmp.mpf_expint(n, z._mpf_, prec, rounding, gamma=True)
+        if imag is None:
+            return ctx.make_mpf(real)
+        else:
+            return ctx.make_mpc((real, imag))
+
+    def _expint_int(ctx, n, z):
+        n = int(n)
+        if n == 1:
+            return ctx.e1(z)
+        if not hasattr(z, '_mpf_'):
+            raise NotImplementedError
+        prec, rounding = ctx._prec_rounding
+        real, imag = libmp.mpf_expint(n, z._mpf_, prec, rounding)
+        if imag is None:
+            return ctx.make_mpf(real)
+        else:
+            return ctx.make_mpc((real, imag))
+
+    def _nthroot(ctx, x, n):
+        if hasattr(x, '_mpf_'):
+            try:
+                return ctx.make_mpf(libmp.mpf_nthroot(x._mpf_, n, *ctx._prec_rounding))
+            except ComplexResult:
+                if ctx.trap_complex:
+                    raise
+                x = (x._mpf_, libmp.fzero)
+        else:
+            x = x._mpc_
+        return ctx.make_mpc(libmp.mpc_nthroot(x, n, *ctx._prec_rounding))
+
+    def _besselj(ctx, n, z):
+        prec, rounding = ctx._prec_rounding
+        if hasattr(z, '_mpf_'):
+            return ctx.make_mpf(libmp.mpf_besseljn(n, z._mpf_, prec, rounding))
+        elif hasattr(z, '_mpc_'):
+            return ctx.make_mpc(libmp.mpc_besseljn(n, z._mpc_, prec, rounding))
+
+    def _agm(ctx, a, b=1):
+        prec, rounding = ctx._prec_rounding
+        if hasattr(a, '_mpf_') and hasattr(b, '_mpf_'):
+            try:
+                v = libmp.mpf_agm(a._mpf_, b._mpf_, prec, rounding)
+                return ctx.make_mpf(v)
+            except ComplexResult:
+                pass
+        if hasattr(a, '_mpf_'): a = (a._mpf_, libmp.fzero)
+        else: a = a._mpc_
+        if hasattr(b, '_mpf_'): b = (b._mpf_, libmp.fzero)
+        else: b = b._mpc_
+        return ctx.make_mpc(libmp.mpc_agm(a, b, prec, rounding))
+
+    def bernoulli(ctx, n):
+        return ctx.make_mpf(libmp.mpf_bernoulli(int(n), *ctx._prec_rounding))
+
+    def _zeta_int(ctx, n):
+        return ctx.make_mpf(libmp.mpf_zeta_int(int(n), *ctx._prec_rounding))
+
+    def atan2(ctx, y, x):
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        return ctx.make_mpf(libmp.mpf_atan2(y._mpf_, x._mpf_, *ctx._prec_rounding))
+
+    def psi(ctx, m, z):
+        z = ctx.convert(z)
+        m = int(m)
+        if ctx._is_real_type(z):
+            return ctx.make_mpf(libmp.mpf_psi(m, z._mpf_, *ctx._prec_rounding))
+        else:
+            return ctx.make_mpc(libmp.mpc_psi(m, z._mpc_, *ctx._prec_rounding))
+
+    def cos_sin(ctx, x, **kwargs):
+        if type(x) not in ctx.types:
+            x = ctx.convert(x)
+        prec, rounding = ctx._parse_prec(kwargs)
+        if hasattr(x, '_mpf_'):
+            c, s = libmp.mpf_cos_sin(x._mpf_, prec, rounding)
+            return ctx.make_mpf(c), ctx.make_mpf(s)
+        elif hasattr(x, '_mpc_'):
+            c, s = libmp.mpc_cos_sin(x._mpc_, prec, rounding)
+            return ctx.make_mpc(c), ctx.make_mpc(s)
+        else:
+            return ctx.cos(x, **kwargs), ctx.sin(x, **kwargs)
+
+    def cospi_sinpi(ctx, x, **kwargs):
+        if type(x) not in ctx.types:
+            x = ctx.convert(x)
+        prec, rounding = ctx._parse_prec(kwargs)
+        if hasattr(x, '_mpf_'):
+            c, s = libmp.mpf_cos_sin_pi(x._mpf_, prec, rounding)
+            return ctx.make_mpf(c), ctx.make_mpf(s)
+        elif hasattr(x, '_mpc_'):
+            c, s = libmp.mpc_cos_sin_pi(x._mpc_, prec, rounding)
+            return ctx.make_mpc(c), ctx.make_mpc(s)
+        else:
+            return ctx.cos(x, **kwargs), ctx.sin(x, **kwargs)
+
+    def clone(ctx):
+        """
+        Create a copy of the context, with the same working precision.
+        """
+        a = ctx.__class__()
+        a.prec = ctx.prec
+        return a
+
+    # Several helper methods
+    # TODO: add more of these, make consistent, write docstrings, ...
+
+    def _is_real_type(ctx, x):
+        if hasattr(x, '_mpc_') or type(x) is complex:
+            return False
+        return True
+
+    def _is_complex_type(ctx, x):
+        if hasattr(x, '_mpc_') or type(x) is complex:
+            return True
+        return False
+
+    def isnan(ctx, x):
+        """
+        Return *True* if *x* is a NaN (not-a-number), or for a complex
+        number, whether either the real or complex part is NaN;
+        otherwise return *False*::
+
+            >>> from mpmath import *
+            >>> isnan(3.14)
+            False
+            >>> isnan(nan)
+            True
+            >>> isnan(mpc(3.14,2.72))
+            False
+            >>> isnan(mpc(3.14,nan))
+            True
+
+        """
+        if hasattr(x, "_mpf_"):
+            return x._mpf_ == fnan
+        if hasattr(x, "_mpc_"):
+            return fnan in x._mpc_
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return False
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isnan(x)
+        raise TypeError("isnan() needs a number as input")
+
+    def isfinite(ctx, x):
+        """
+        Return *True* if *x* is a finite number, i.e. neither
+        an infinity or a NaN.
+
+            >>> from mpmath import *
+            >>> isfinite(inf)
+            False
+            >>> isfinite(-inf)
+            False
+            >>> isfinite(3)
+            True
+            >>> isfinite(nan)
+            False
+            >>> isfinite(3+4j)
+            True
+            >>> isfinite(mpc(3,inf))
+            False
+            >>> isfinite(mpc(nan,3))
+            False
+
+        """
+        if ctx.isinf(x) or ctx.isnan(x):
+            return False
+        return True
+
+    def isnpint(ctx, x):
+        """
+        Determine if *x* is a nonpositive integer.
+        """
+        if not x:
+            return True
+        if hasattr(x, '_mpf_'):
+            sign, man, exp, bc = x._mpf_
+            return sign and exp >= 0
+        if hasattr(x, '_mpc_'):
+            return not x.imag and ctx.isnpint(x.real)
+        if type(x) in int_types:
+            return x <= 0
+        if isinstance(x, ctx.mpq):
+            p, q = x._mpq_
+            if not p:
+                return True
+            return q == 1 and p <= 0
+        return ctx.isnpint(ctx.convert(x))
+
+    def __str__(ctx):
+        lines = ["Mpmath settings:",
+            ("  mp.prec = %s" % ctx.prec).ljust(30) + "[default: 53]",
+            ("  mp.dps = %s" % ctx.dps).ljust(30) + "[default: 15]",
+            ("  mp.trap_complex = %s" % ctx.trap_complex).ljust(30) + "[default: False]",
+        ]
+        return "\n".join(lines)
+
+    @property
+    def _repr_digits(ctx):
+        return repr_dps(ctx._prec)
+
+    @property
+    def _str_digits(ctx):
+        return ctx._dps
+
+    def extraprec(ctx, n, normalize_output=False):
+        """
+        The block
+
+            with extraprec(n):
+                <code>
+
+        increases the precision n bits, executes <code>, and then
+        restores the precision.
+
+        extraprec(n)(f) returns a decorated version of the function f
+        that increases the working precision by n bits before execution,
+        and restores the parent precision afterwards. With
+        normalize_output=True, it rounds the return value to the parent
+        precision.
+        """
+        return PrecisionManager(ctx, lambda p: p + n, None, normalize_output)
+
+    def extradps(ctx, n, normalize_output=False):
+        """
+        This function is analogous to extraprec (see documentation)
+        but changes the decimal precision instead of the number of bits.
+        """
+        return PrecisionManager(ctx, None, lambda d: d + n, normalize_output)
+
+    def workprec(ctx, n, normalize_output=False):
+        """
+        The block
+
+            with workprec(n):
+                <code>
+
+        sets the precision to n bits, executes <code>, and then restores
+        the precision.
+
+        workprec(n)(f) returns a decorated version of the function f
+        that sets the precision to n bits before execution,
+        and restores the precision afterwards. With normalize_output=True,
+        it rounds the return value to the parent precision.
+        """
+        return PrecisionManager(ctx, lambda p: n, None, normalize_output)
+
+    def workdps(ctx, n, normalize_output=False):
+        """
+        This function is analogous to workprec (see documentation)
+        but changes the decimal precision instead of the number of bits.
+        """
+        return PrecisionManager(ctx, None, lambda d: n, normalize_output)
+
+    def autoprec(ctx, f, maxprec=None, catch=(), verbose=False):
+        r"""
+        Return a wrapped copy of *f* that repeatedly evaluates *f*
+        with increasing precision until the result converges to the
+        full precision used at the point of the call.
+
+        This heuristically protects against rounding errors, at the cost of
+        roughly a 2x slowdown compared to manually setting the optimal
+        precision. This method can, however, easily be fooled if the results
+        from *f* depend "discontinuously" on the precision, for instance
+        if catastrophic cancellation can occur. Therefore, :func:`~mpmath.autoprec`
+        should be used judiciously.
+
+        **Examples**
+
+        Many functions are sensitive to perturbations of the input arguments.
+        If the arguments are decimal numbers, they may have to be converted
+        to binary at a much higher precision. If the amount of required
+        extra precision is unknown, :func:`~mpmath.autoprec` is convenient::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> mp.pretty = True
+            >>> besselj(5, 125 * 10**28)    # Exact input
+            -8.03284785591801e-17
+            >>> besselj(5, '1.25e30')   # Bad
+            7.12954868316652e-16
+            >>> autoprec(besselj)(5, '1.25e30')   # Good
+            -8.03284785591801e-17
+
+        The following fails to converge because `\sin(\pi) = 0` whereas all
+        finite-precision approximations of `\pi` give nonzero values::
+
+            >>> autoprec(sin)(pi) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: autoprec: prec increased to 2910 without convergence
+
+        As the following example shows, :func:`~mpmath.autoprec` can protect against
+        cancellation, but is fooled by too severe cancellation::
+
+            >>> x = 1e-10
+            >>> exp(x)-1; expm1(x); autoprec(lambda t: exp(t)-1)(x)
+            1.00000008274037e-10
+            1.00000000005e-10
+            1.00000000005e-10
+            >>> x = 1e-50
+            >>> exp(x)-1; expm1(x); autoprec(lambda t: exp(t)-1)(x)
+            0.0
+            1.0e-50
+            0.0
+
+        With *catch*, an exception or list of exceptions to intercept
+        may be specified. The raised exception is interpreted
+        as signaling insufficient precision. This permits, for example,
+        evaluating a function where a too low precision results in a
+        division by zero::
+
+            >>> f = lambda x: 1/(exp(x)-1)
+            >>> f(1e-30)
+            Traceback (most recent call last):
+              ...
+            ZeroDivisionError
+            >>> autoprec(f, catch=ZeroDivisionError)(1e-30)
+            1.0e+30
+
+
+        """
+        def f_autoprec_wrapped(*args, **kwargs):
+            prec = ctx.prec
+            if maxprec is None:
+                maxprec2 = ctx._default_hyper_maxprec(prec)
+            else:
+                maxprec2 = maxprec
+            try:
+                ctx.prec = prec + 10
+                try:
+                    v1 = f(*args, **kwargs)
+                except catch:
+                    v1 = ctx.nan
+                prec2 = prec + 20
+                while 1:
+                    ctx.prec = prec2
+                    try:
+                        v2 = f(*args, **kwargs)
+                    except catch:
+                        v2 = ctx.nan
+                    if v1 == v2:
+                        break
+                    err = ctx.mag(v2-v1) - ctx.mag(v2)
+                    if err < (-prec):
+                        break
+                    if verbose:
+                        print("autoprec: target=%s, prec=%s, accuracy=%s" \
+                            % (prec, prec2, -err))
+                    v1 = v2
+                    if prec2 >= maxprec2:
+                        raise ctx.NoConvergence(\
+                        "autoprec: prec increased to %i without convergence"\
+                        % prec2)
+                    prec2 += int(prec2*2)
+                    prec2 = min(prec2, maxprec2)
+            finally:
+                ctx.prec = prec
+            return +v2
+        return f_autoprec_wrapped
+
+    def nstr(ctx, x, n=6, **kwargs):
+        """
+        Convert an ``mpf`` or ``mpc`` to a decimal string literal with *n*
+        significant digits. The small default value for *n* is chosen to
+        make this function useful for printing collections of numbers
+        (lists, matrices, etc).
+
+        If *x* is a list or tuple, :func:`~mpmath.nstr` is applied recursively
+        to each element. For unrecognized classes, :func:`~mpmath.nstr`
+        simply returns ``str(x)``.
+
+        The companion function :func:`~mpmath.nprint` prints the result
+        instead of returning it.
+
+        The keyword arguments *strip_zeros*, *min_fixed*, *max_fixed*
+        and *show_zero_exponent* are forwarded to :func:`~mpmath.libmp.to_str`.
+
+        The number will be printed in fixed-point format if the position
+        of the leading digit is strictly between min_fixed
+        (default = min(-dps/3,-5)) and max_fixed (default = dps).
+
+        To force fixed-point format always, set min_fixed = -inf,
+        max_fixed = +inf. To force floating-point format, set
+        min_fixed >= max_fixed.
+
+            >>> from mpmath import *
+            >>> nstr([+pi, ldexp(1,-500)])
+            '[3.14159, 3.05494e-151]'
+            >>> nprint([+pi, ldexp(1,-500)])
+            [3.14159, 3.05494e-151]
+            >>> nstr(mpf("5e-10"), 5)
+            '5.0e-10'
+            >>> nstr(mpf("5e-10"), 5, strip_zeros=False)
+            '5.0000e-10'
+            >>> nstr(mpf("5e-10"), 5, strip_zeros=False, min_fixed=-11)
+            '0.00000000050000'
+            >>> nstr(mpf(0), 5, show_zero_exponent=True)
+            '0.0e+0'
+
+        """
+        if isinstance(x, list):
+            return "[%s]" % (", ".join(ctx.nstr(c, n, **kwargs) for c in x))
+        if isinstance(x, tuple):
+            return "(%s)" % (", ".join(ctx.nstr(c, n, **kwargs) for c in x))
+        if hasattr(x, '_mpf_'):
+            return to_str(x._mpf_, n, **kwargs)
+        if hasattr(x, '_mpc_'):
+            return "(" + mpc_to_str(x._mpc_, n, **kwargs)  + ")"
+        if isinstance(x, basestring):
+            return repr(x)
+        if isinstance(x, ctx.matrix):
+            return x.__nstr__(n, **kwargs)
+        return str(x)
+
+    def _convert_fallback(ctx, x, strings):
+        if strings and isinstance(x, basestring):
+            if 'j' in x.lower():
+                x = x.lower().replace(' ', '')
+                match = get_complex.match(x)
+                re = match.group('re')
+                if not re:
+                    re = 0
+                im = match.group('im').rstrip('j')
+                return ctx.mpc(ctx.convert(re), ctx.convert(im))
+        if hasattr(x, "_mpi_"):
+            a, b = x._mpi_
+            if a == b:
+                return ctx.make_mpf(a)
+            else:
+                raise ValueError("can only create mpf from zero-width interval")
+        raise TypeError("cannot create mpf from " + repr(x))
+
+    def mpmathify(ctx, *args, **kwargs):
+        return ctx.convert(*args, **kwargs)
+
+    def _parse_prec(ctx, kwargs):
+        if kwargs:
+            if kwargs.get('exact'):
+                return 0, 'f'
+            prec, rounding = ctx._prec_rounding
+            if 'rounding' in kwargs:
+                rounding = kwargs['rounding']
+            if 'prec' in kwargs:
+                prec = kwargs['prec']
+                if prec == ctx.inf:
+                    return 0, 'f'
+                else:
+                    prec = int(prec)
+            elif 'dps' in kwargs:
+                dps = kwargs['dps']
+                if dps == ctx.inf:
+                    return 0, 'f'
+                prec = dps_to_prec(dps)
+            return prec, rounding
+        return ctx._prec_rounding
+
+    _exact_overflow_msg = "the exact result does not fit in memory"
+
+    _hypsum_msg = """hypsum() failed to converge to the requested %i bits of accuracy
+using a working precision of %i bits. Try with a higher maxprec,
+maxterms, or set zeroprec."""
+
+    def hypsum(ctx, p, q, flags, coeffs, z, accurate_small=True, **kwargs):
+        if hasattr(z, "_mpf_"):
+            key = p, q, flags, 'R'
+            v = z._mpf_
+        elif hasattr(z, "_mpc_"):
+            key = p, q, flags, 'C'
+            v = z._mpc_
+        if key not in ctx.hyp_summators:
+            ctx.hyp_summators[key] = libmp.make_hyp_summator(key)[1]
+        summator = ctx.hyp_summators[key]
+        prec = ctx.prec
+        maxprec = kwargs.get('maxprec', ctx._default_hyper_maxprec(prec))
+        extraprec = 50
+        epsshift = 25
+        # Jumps in magnitude occur when parameters are close to negative
+        # integers. We must ensure that these terms are included in
+        # the sum and added accurately
+        magnitude_check = {}
+        max_total_jump = 0
+        for i, c in enumerate(coeffs):
+            if flags[i] == 'Z':
+                if i >= p and c <= 0:
+                    ok = False
+                    for ii, cc in enumerate(coeffs[:p]):
+                        # Note: c <= cc or c < cc, depending on convention
+                        if flags[ii] == 'Z' and cc <= 0 and c <= cc:
+                            ok = True
+                    if not ok:
+                        raise ZeroDivisionError("pole in hypergeometric series")
+                continue
+            n, d = ctx.nint_distance(c)
+            n = -int(n)
+            d = -d
+            if i >= p and n >= 0 and d > 4:
+                if n in magnitude_check:
+                    magnitude_check[n] += d
+                else:
+                    magnitude_check[n] = d
+                extraprec = max(extraprec, d - prec + 60)
+            max_total_jump += abs(d)
+        while 1:
+            if extraprec > maxprec:
+                raise ValueError(ctx._hypsum_msg % (prec, prec+extraprec))
+            wp = prec + extraprec
+            if magnitude_check:
+                mag_dict = dict((n,None) for n in magnitude_check)
+            else:
+                mag_dict = {}
+            zv, have_complex, magnitude = summator(coeffs, v, prec, wp, \
+                epsshift, mag_dict, **kwargs)
+            cancel = -magnitude
+            jumps_resolved = True
+            if extraprec < max_total_jump:
+                for n in mag_dict.values():
+                    if (n is None) or (n < prec):
+                        jumps_resolved = False
+                        break
+            accurate = (cancel < extraprec-25-5 or not accurate_small)
+            if jumps_resolved:
+                if accurate:
+                    break
+                # zero?
+                zeroprec = kwargs.get('zeroprec')
+                if zeroprec is not None:
+                    if cancel > zeroprec:
+                        if have_complex:
+                            return ctx.mpc(0)
+                        else:
+                            return ctx.zero
+
+            # Some near-singularities were not included, so increase
+            # precision and repeat until they are
+            extraprec *= 2
+            # Possible workaround for bad roundoff in fixed-point arithmetic
+            epsshift += 5
+            extraprec += 5
+
+        if type(zv) is tuple:
+            if have_complex:
+                return ctx.make_mpc(zv)
+            else:
+                return ctx.make_mpf(zv)
+        else:
+            return zv
+
+    def ldexp(ctx, x, n):
+        r"""
+        Computes `x 2^n` efficiently. No rounding is performed.
+        The argument `x` must be a real floating-point number (or
+        possible to convert into one) and `n` must be a Python ``int``.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> ldexp(1, 10)
+            mpf('1024.0')
+            >>> ldexp(1, -3)
+            mpf('0.125')
+
+        """
+        x = ctx.convert(x)
+        return ctx.make_mpf(libmp.mpf_shift(x._mpf_, n))
+
+    def frexp(ctx, x):
+        r"""
+        Given a real number `x`, returns `(y, n)` with `y \in [0.5, 1)`,
+        `n` a Python integer, and such that `x = y 2^n`. No rounding is
+        performed.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> frexp(7.5)
+            (mpf('0.9375'), 3)
+
+        """
+        x = ctx.convert(x)
+        y, n = libmp.mpf_frexp(x._mpf_)
+        return ctx.make_mpf(y), n
+
+    def fneg(ctx, x, **kwargs):
+        """
+        Negates the number *x*, giving a floating-point result, optionally
+        using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        An mpmath number is returned::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fneg(2.5)
+            mpf('-2.5')
+            >>> fneg(-5+2j)
+            mpc(real='5.0', imag='-2.0')
+
+        Precise control over rounding is possible::
+
+            >>> x = fadd(2, 1e-100, exact=True)
+            >>> fneg(x)
+            mpf('-2.0')
+            >>> fneg(x, rounding='f')
+            mpf('-2.0000000000000004')
+
+        Negating with and without roundoff::
+
+            >>> n = 200000000000000000000001
+            >>> print(int(-mpf(n)))
+            -200000000000000016777216
+            >>> print(int(fneg(n)))
+            -200000000000000016777216
+            >>> print(int(fneg(n, prec=log(n,2)+1)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, dps=log(n,10)+1)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, prec=inf)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, dps=inf)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, exact=True)))
+            -200000000000000000000001
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_'):
+            return ctx.make_mpf(mpf_neg(x._mpf_, prec, rounding))
+        if hasattr(x, '_mpc_'):
+            return ctx.make_mpc(mpc_neg(x._mpc_, prec, rounding))
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fadd(ctx, x, y, **kwargs):
+        """
+        Adds the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        The default precision is the working precision of the context.
+        You can specify a custom precision in bits by passing the *prec* keyword
+        argument, or by providing an equivalent decimal precision with the *dps*
+        keyword argument. If the precision is set to ``+inf``, or if the flag
+        *exact=True* is passed, an exact addition with no rounding is performed.
+
+        When the precision is finite, the optional *rounding* keyword argument
+        specifies the direction of rounding. Valid options are ``'n'`` for
+        nearest (default), ``'f'`` for floor, ``'c'`` for ceiling, ``'d'``
+        for down, ``'u'`` for up.
+
+        **Examples**
+
+        Using :func:`~mpmath.fadd` with precision and rounding control::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fadd(2, 1e-20)
+            mpf('2.0')
+            >>> fadd(2, 1e-20, rounding='u')
+            mpf('2.0000000000000004')
+            >>> nprint(fadd(2, 1e-20, prec=100), 25)
+            2.00000000000000000001
+            >>> nprint(fadd(2, 1e-20, dps=15), 25)
+            2.0
+            >>> nprint(fadd(2, 1e-20, dps=25), 25)
+            2.00000000000000000001
+            >>> nprint(fadd(2, 1e-20, exact=True), 25)
+            2.00000000000000000001
+
+        Exact addition avoids cancellation errors, enforcing familiar laws
+        of numbers such as `x+y-x = y`, which don't hold in floating-point
+        arithmetic with finite precision::
+
+            >>> x, y = mpf(2), mpf('1e-1000')
+            >>> print(x + y - x)
+            0.0
+            >>> print(fadd(x, y, prec=inf) - x)
+            1.0e-1000
+            >>> print(fadd(x, y, exact=True) - x)
+            1.0e-1000
+
+        Exact addition can be inefficient and may be impossible to perform
+        with large magnitude differences::
+
+            >>> fadd(1, '1e-100000000000000000000', prec=inf)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_add(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_add_mpf(y._mpc_, x._mpf_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_add_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_add(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fsub(ctx, x, y, **kwargs):
+        """
+        Subtracts the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        Using :func:`~mpmath.fsub` with precision and rounding control::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fsub(2, 1e-20)
+            mpf('2.0')
+            >>> fsub(2, 1e-20, rounding='d')
+            mpf('1.9999999999999998')
+            >>> nprint(fsub(2, 1e-20, prec=100), 25)
+            1.99999999999999999999
+            >>> nprint(fsub(2, 1e-20, dps=15), 25)
+            2.0
+            >>> nprint(fsub(2, 1e-20, dps=25), 25)
+            1.99999999999999999999
+            >>> nprint(fsub(2, 1e-20, exact=True), 25)
+            1.99999999999999999999
+
+        Exact subtraction avoids cancellation errors, enforcing familiar laws
+        of numbers such as `x-y+y = x`, which don't hold in floating-point
+        arithmetic with finite precision::
+
+            >>> x, y = mpf(2), mpf('1e1000')
+            >>> print(x - y + y)
+            0.0
+            >>> print(fsub(x, y, prec=inf) + y)
+            2.0
+            >>> print(fsub(x, y, exact=True) + y)
+            2.0
+
+        Exact addition can be inefficient and may be impossible to perform
+        with large magnitude differences::
+
+            >>> fsub(1, '1e-100000000000000000000', prec=inf)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_sub(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_sub((x._mpf_, fzero), y._mpc_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_sub_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_sub(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fmul(ctx, x, y, **kwargs):
+        """
+        Multiplies the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        The result is an mpmath number::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fmul(2, 5.0)
+            mpf('10.0')
+            >>> fmul(0.5j, 0.5)
+            mpc(real='0.0', imag='0.25')
+
+        Avoiding roundoff::
+
+            >>> x, y = 10**10+1, 10**15+1
+            >>> print(x*y)
+            10000000001000010000000001
+            >>> print(mpf(x) * mpf(y))
+            1.0000000001e+25
+            >>> print(int(mpf(x) * mpf(y)))
+            10000000001000011026399232
+            >>> print(int(fmul(x, y)))
+            10000000001000011026399232
+            >>> print(int(fmul(x, y, dps=25)))
+            10000000001000010000000001
+            >>> print(int(fmul(x, y, exact=True)))
+            10000000001000010000000001
+
+        Exact multiplication with complex numbers can be inefficient and may
+        be impossible to perform with large magnitude differences between
+        real and imaginary parts::
+
+            >>> x = 1+2j
+            >>> y = mpc(2, '1e-100000000000000000000')
+            >>> fmul(x, y)
+            mpc(real='2.0', imag='4.0')
+            >>> fmul(x, y, rounding='u')
+            mpc(real='2.0', imag='4.0000000000000009')
+            >>> fmul(x, y, exact=True)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_mul(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_mul_mpf(y._mpc_, x._mpf_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_mul_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_mul(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fdiv(ctx, x, y, **kwargs):
+        """
+        Divides the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        The result is an mpmath number::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fdiv(3, 2)
+            mpf('1.5')
+            >>> fdiv(2, 3)
+            mpf('0.66666666666666663')
+            >>> fdiv(2+4j, 0.5)
+            mpc(real='4.0', imag='8.0')
+
+        The rounding direction and precision can be controlled::
+
+            >>> fdiv(2, 3, dps=3)    # Should be accurate to at least 3 digits
+            mpf('0.6666259765625')
+            >>> fdiv(2, 3, rounding='d')
+            mpf('0.66666666666666663')
+            >>> fdiv(2, 3, prec=60)
+            mpf('0.66666666666666667')
+            >>> fdiv(2, 3, rounding='u')
+            mpf('0.66666666666666674')
+
+        Checking the error of a division by performing it at higher precision::
+
+            >>> fdiv(2, 3) - fdiv(2, 3, prec=100)
+            mpf('-3.7007434154172148e-17')
+
+        Unlike :func:`~mpmath.fadd`, :func:`~mpmath.fmul`, etc., exact division is not
+        allowed since the quotient of two floating-point numbers generally
+        does not have an exact floating-point representation. (In the
+        future this might be changed to allow the case where the division
+        is actually exact.)
+
+            >>> fdiv(2, 3, exact=True)
+            Traceback (most recent call last):
+              ...
+            ValueError: division is not an exact operation
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        if not prec:
+            raise ValueError("division is not an exact operation")
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        if hasattr(x, '_mpf_'):
+            if hasattr(y, '_mpf_'):
+                return ctx.make_mpf(mpf_div(x._mpf_, y._mpf_, prec, rounding))
+            if hasattr(y, '_mpc_'):
+                return ctx.make_mpc(mpc_div((x._mpf_, fzero), y._mpc_, prec, rounding))
+        if hasattr(x, '_mpc_'):
+            if hasattr(y, '_mpf_'):
+                return ctx.make_mpc(mpc_div_mpf(x._mpc_, y._mpf_, prec, rounding))
+            if hasattr(y, '_mpc_'):
+                return ctx.make_mpc(mpc_div(x._mpc_, y._mpc_, prec, rounding))
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def nint_distance(ctx, x):
+        r"""
+        Return `(n,d)` where `n` is the nearest integer to `x` and `d` is
+        an estimate of `\log_2(|x-n|)`. If `d < 0`, `-d` gives the precision
+        (measured in bits) lost to cancellation when computing `x-n`.
+
+            >>> from mpmath import *
+            >>> n, d = nint_distance(5)
+            >>> print(n); print(d)
+            5
+            -inf
+            >>> n, d = nint_distance(mpf(5))
+            >>> print(n); print(d)
+            5
+            -inf
+            >>> n, d = nint_distance(mpf(5.00000001))
+            >>> print(n); print(d)
+            5
+            -26
+            >>> n, d = nint_distance(mpf(4.99999999))
+            >>> print(n); print(d)
+            5
+            -26
+            >>> n, d = nint_distance(mpc(5,10))
+            >>> print(n); print(d)
+            5
+            4
+            >>> n, d = nint_distance(mpc(5,0.000001))
+            >>> print(n); print(d)
+            5
+            -19
+
+        """
+        typx = type(x)
+        if typx in int_types:
+            return int(x), ctx.ninf
+        elif typx is rational.mpq:
+            p, q = x._mpq_
+            n, r = divmod(p, q)
+            if 2*r >= q:
+                n += 1
+            elif not r:
+                return n, ctx.ninf
+            # log(p/q-n) = log((p-nq)/q) = log(p-nq) - log(q)
+            d = bitcount(abs(p-n*q)) - bitcount(q)
+            return n, d
+        if hasattr(x, "_mpf_"):
+            re = x._mpf_
+            im_dist = ctx.ninf
+        elif hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            isign, iman, iexp, ibc = im
+            if iman:
+                im_dist = iexp + ibc
+            elif im == fzero:
+                im_dist = ctx.ninf
+            else:
+                raise ValueError("requires a finite number")
+        else:
+            x = ctx.convert(x)
+            if hasattr(x, "_mpf_") or hasattr(x, "_mpc_"):
+                return ctx.nint_distance(x)
+            else:
+                raise TypeError("requires an mpf/mpc")
+        sign, man, exp, bc = re
+        mag = exp+bc
+        # |x| < 0.5
+        if mag < 0:
+            n = 0
+            re_dist = mag
+        elif man:
+            # exact integer
+            if exp >= 0:
+                n = man << exp
+                re_dist = ctx.ninf
+            # exact half-integer
+            elif exp == -1:
+                n = (man>>1)+1
+                re_dist = 0
+            else:
+                d = (-exp-1)
+                t = man >> d
+                if t & 1:
+                    t += 1
+                    man = (t<<d) - man
+                else:
+                    man -= (t<<d)
+                n = t>>1   # int(t)>>1
+                re_dist = exp+bitcount(man)
+            if sign:
+                n = -n
+        elif re == fzero:
+            re_dist = ctx.ninf
+            n = 0
+        else:
+            raise ValueError("requires a finite number")
+        return n, max(re_dist, im_dist)
+
+    def fprod(ctx, factors):
+        r"""
+        Calculates a product containing a finite number of factors (for
+        infinite products, see :func:`~mpmath.nprod`). The factors will be
+        converted to mpmath numbers.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fprod([1, 2, 0.5, 7])
+            mpf('7.0')
+
+        """
+        orig = ctx.prec
+        try:
+            v = ctx.one
+            for p in factors:
+                v *= p
+        finally:
+            ctx.prec = orig
+        return +v
+
+    def rand(ctx):
+        """
+        Returns an ``mpf`` with value chosen randomly from `[0, 1)`.
+        The number of randomly generated bits in the mantissa is equal
+        to the working precision.
+        """
+        return ctx.make_mpf(mpf_rand(ctx._prec))
+
+    def fraction(ctx, p, q):
+        """
+        Given Python integers `(p, q)`, returns a lazy ``mpf`` representing
+        the fraction `p/q`. The value is updated with the precision.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> a = fraction(1,100)
+            >>> b = mpf(1)/100
+            >>> print(a); print(b)
+            0.01
+            0.01
+            >>> mp.dps = 30
+            >>> print(a); print(b)      # a will be accurate
+            0.01
+            0.0100000000000000002081668171172
+            >>> mp.dps = 15
+        """
+        return ctx.constant(lambda prec, rnd: from_rational(p, q, prec, rnd),
+            '%s/%s' % (p, q))
+
+    def absmin(ctx, x):
+        return abs(ctx.convert(x))
+
+    def absmax(ctx, x):
+        return abs(ctx.convert(x))
+
+    def _as_points(ctx, x):
+        # XXX: remove this?
+        if hasattr(x, '_mpi_'):
+            a, b = x._mpi_
+            return [ctx.make_mpf(a), ctx.make_mpf(b)]
+        return x
+
+    '''
+    def _zetasum(ctx, s, a, b):
+        """
+        Computes sum of k^(-s) for k = a, a+1, ..., b with a, b both small
+        integers.
+        """
+        a = int(a)
+        b = int(b)
+        s = ctx.convert(s)
+        prec, rounding = ctx._prec_rounding
+        if hasattr(s, '_mpf_'):
+            v = ctx.make_mpf(libmp.mpf_zetasum(s._mpf_, a, b, prec))
+        elif hasattr(s, '_mpc_'):
+            v = ctx.make_mpc(libmp.mpc_zetasum(s._mpc_, a, b, prec))
+        return v
+    '''
+
+    def _zetasum_fast(ctx, s, a, n, derivatives=[0], reflect=False):
+        if not (ctx.isint(a) and hasattr(s, "_mpc_")):
+            raise NotImplementedError
+        a = int(a)
+        prec = ctx._prec
+        xs, ys = libmp.mpc_zetasum(s._mpc_, a, n, derivatives, reflect, prec)
+        xs = [ctx.make_mpc(x) for x in xs]
+        ys = [ctx.make_mpc(y) for y in ys]
+        return xs, ys
+
+class PrecisionManager:
+    def __init__(self, ctx, precfun, dpsfun, normalize_output=False):
+        self.ctx = ctx
+        self.precfun = precfun
+        self.dpsfun = dpsfun
+        self.normalize_output = normalize_output
+    def __call__(self, f):
+        @functools.wraps(f)
+        def g(*args, **kwargs):
+            orig = self.ctx.prec
+            try:
+                if self.precfun:
+                    self.ctx.prec = self.precfun(self.ctx.prec)
+                else:
+                    self.ctx.dps = self.dpsfun(self.ctx.dps)
+                if self.normalize_output:
+                    v = f(*args, **kwargs)
+                    if type(v) is tuple:
+                        return tuple([+a for a in v])
+                    return +v
+                else:
+                    return f(*args, **kwargs)
+            finally:
+                self.ctx.prec = orig
+        return g
+    def __enter__(self):
+        self.origp = self.ctx.prec
+        if self.precfun:
+            self.ctx.prec = self.precfun(self.ctx.prec)
+        else:
+            self.ctx.dps = self.dpsfun(self.ctx.dps)
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        self.ctx.prec = self.origp
+        return False
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()

vllm/lib/python3.10/site-packages/mpmath/functions/__init__.py

@@ -0,0 +1,14 @@
+from . import functions
+# Hack to update methods
+from . import factorials
+from . import hypergeometric
+from . import expintegrals
+from . import bessel
+from . import orthogonal
+from . import theta
+from . import elliptic
+from . import signals
+from . import zeta
+from . import rszeta
+from . import zetazeros
+from . import qfunctions

vllm/lib/python3.10/site-packages/mpmath/functions/bessel.py

@@ -0,0 +1,1108 @@
+from .functions import defun, defun_wrapped
+
+@defun
+def j0(ctx, x):
+    """Computes the Bessel function `J_0(x)`. See :func:`~mpmath.besselj`."""
+    return ctx.besselj(0, x)
+
+@defun
+def j1(ctx, x):
+    """Computes the Bessel function `J_1(x)`.  See :func:`~mpmath.besselj`."""
+    return ctx.besselj(1, x)
+
+@defun
+def besselj(ctx, n, z, derivative=0, **kwargs):
+    if type(n) is int:
+        n_isint = True
+    else:
+        n = ctx.convert(n)
+        n_isint = ctx.isint(n)
+        if n_isint:
+            n = int(ctx._re(n))
+    if n_isint and n < 0:
+        return (-1)**n * ctx.besselj(-n, z, derivative, **kwargs)
+    z = ctx.convert(z)
+    M = ctx.mag(z)
+    if derivative:
+        d = ctx.convert(derivative)
+        # TODO: the integer special-casing shouldn't be necessary.
+        # However, the hypergeometric series gets inaccurate for large d
+        # because of inaccurate pole cancellation at a pole far from
+        # zero (needs to be fixed in hypercomb or hypsum)
+        if ctx.isint(d) and d >= 0:
+            d = int(d)
+            orig = ctx.prec
+            try:
+                ctx.prec += 15
+                v = ctx.fsum((-1)**k * ctx.binomial(d,k) * ctx.besselj(2*k+n-d,z)
+                    for k in range(d+1))
+            finally:
+                ctx.prec = orig
+            v *= ctx.mpf(2)**(-d)
+        else:
+            def h(n,d):
+                r = ctx.fmul(ctx.fmul(z, z, prec=ctx.prec+M), -0.25, exact=True)
+                B = [0.5*(n-d+1), 0.5*(n-d+2)]
+                T = [([2,ctx.pi,z],[d-2*n,0.5,n-d],[],B,[(n+1)*0.5,(n+2)*0.5],B+[n+1],r)]
+                return T
+            v = ctx.hypercomb(h, [n,d], **kwargs)
+    else:
+        # Fast case: J_n(x), n int, appropriate magnitude for fixed-point calculation
+        if (not derivative) and n_isint and abs(M) < 10 and abs(n) < 20:
+            try:
+                return ctx._besselj(n, z)
+            except NotImplementedError:
+                pass
+        if not z:
+            if not n:
+                v = ctx.one + n+z
+            elif ctx.re(n) > 0:
+                v = n*z
+            else:
+                v = ctx.inf + z + n
+        else:
+            #v = 0
+            orig = ctx.prec
+            try:
+                # XXX: workaround for accuracy in low level hypergeometric series
+                # when alternating, large arguments
+                ctx.prec += min(3*abs(M), ctx.prec)
+                w = ctx.fmul(z, 0.5, exact=True)
+                def h(n):
+                    r = ctx.fneg(ctx.fmul(w, w, prec=max(0,ctx.prec+M)), exact=True)
+                    return [([w], [n], [], [n+1], [], [n+1], r)]
+                v = ctx.hypercomb(h, [n], **kwargs)
+            finally:
+                ctx.prec = orig
+        v = +v
+    return v
+
+@defun
+def besseli(ctx, n, z, derivative=0, **kwargs):
+    n = ctx.convert(n)
+    z = ctx.convert(z)
+    if not z:
+        if derivative:
+            raise ValueError
+        if not n:
+            # I(0,0) = 1
+            return 1+n+z
+        if ctx.isint(n):
+            return 0*(n+z)
+        r = ctx.re(n)
+        if r == 0:
+            return ctx.nan*(n+z)
+        elif r > 0:
+            return 0*(n+z)
+        else:
+            return ctx.inf+(n+z)
+    M = ctx.mag(z)
+    if derivative:
+        d = ctx.convert(derivative)
+        def h(n,d):
+            r = ctx.fmul(ctx.fmul(z, z, prec=ctx.prec+M), 0.25, exact=True)
+            B = [0.5*(n-d+1), 0.5*(n-d+2), n+1]
+            T = [([2,ctx.pi,z],[d-2*n,0.5,n-d],[n+1],B,[(n+1)*0.5,(n+2)*0.5],B,r)]
+            return T
+        v = ctx.hypercomb(h, [n,d], **kwargs)
+    else:
+        def h(n):
+            w = ctx.fmul(z, 0.5, exact=True)
+            r = ctx.fmul(w, w, prec=max(0,ctx.prec+M))
+            return [([w], [n], [], [n+1], [], [n+1], r)]
+        v = ctx.hypercomb(h, [n], **kwargs)
+    return v
+
+@defun_wrapped
+def bessely(ctx, n, z, derivative=0, **kwargs):
+    if not z:
+        if derivative:
+            # Not implemented
+            raise ValueError
+        if not n:
+            # ~ log(z/2)
+            return -ctx.inf + (n+z)
+        if ctx.im(n):
+            return ctx.nan * (n+z)
+        r = ctx.re(n)
+        q = n+0.5
+        if ctx.isint(q):
+            if n > 0:
+                return -ctx.inf + (n+z)
+            else:
+                return 0 * (n+z)
+        if r < 0 and int(ctx.floor(q)) % 2:
+            return ctx.inf + (n+z)
+        else:
+            return ctx.ninf + (n+z)
+    # XXX: use hypercomb
+    ctx.prec += 10
+    m, d = ctx.nint_distance(n)
+    if d < -ctx.prec:
+        h = +ctx.eps
+        ctx.prec *= 2
+        n += h
+    elif d < 0:
+        ctx.prec -= d
+    # TODO: avoid cancellation for imaginary arguments
+    cos, sin = ctx.cospi_sinpi(n)
+    return (ctx.besselj(n,z,derivative,**kwargs)*cos - \
+        ctx.besselj(-n,z,derivative,**kwargs))/sin
+
+@defun_wrapped
+def besselk(ctx, n, z, **kwargs):
+    if not z:
+        return ctx.inf
+    M = ctx.mag(z)
+    if M < 1:
+        # Represent as limit definition
+        def h(n):
+            r = (z/2)**2
+            T1 = [z, 2], [-n, n-1], [n], [], [], [1-n], r
+            T2 = [z, 2], [n, -n-1], [-n], [], [], [1+n], r
+            return T1, T2
+    # We could use the limit definition always, but it leads
+    # to very bad cancellation (of exponentially large terms)
+    # for large real z
+    # Instead represent in terms of 2F0
+    else:
+        ctx.prec += M
+        def h(n):
+            return [([ctx.pi/2, z, ctx.exp(-z)], [0.5,-0.5,1], [], [], \
+                [n+0.5, 0.5-n], [], -1/(2*z))]
+    return ctx.hypercomb(h, [n], **kwargs)
+
+@defun_wrapped
+def hankel1(ctx,n,x,**kwargs):
+    return ctx.besselj(n,x,**kwargs) + ctx.j*ctx.bessely(n,x,**kwargs)
+
+@defun_wrapped
+def hankel2(ctx,n,x,**kwargs):
+    return ctx.besselj(n,x,**kwargs) - ctx.j*ctx.bessely(n,x,**kwargs)
+
+@defun_wrapped
+def whitm(ctx,k,m,z,**kwargs):
+    if z == 0:
+        # M(k,m,z) = 0^(1/2+m)
+        if ctx.re(m) > -0.5:
+            return z
+        elif ctx.re(m) < -0.5:
+            return ctx.inf + z
+        else:
+            return ctx.nan * z
+    x = ctx.fmul(-0.5, z, exact=True)
+    y = 0.5+m
+    return ctx.exp(x) * z**y * ctx.hyp1f1(y-k, 1+2*m, z, **kwargs)
+
+@defun_wrapped
+def whitw(ctx,k,m,z,**kwargs):
+    if z == 0:
+        g = abs(ctx.re(m))
+        if g < 0.5:
+            return z
+        elif g > 0.5:
+            return ctx.inf + z
+        else:
+            return ctx.nan * z
+    x = ctx.fmul(-0.5, z, exact=True)
+    y = 0.5+m
+    return ctx.exp(x) * z**y * ctx.hyperu(y-k, 1+2*m, z, **kwargs)
+
+@defun
+def hyperu(ctx, a, b, z, **kwargs):
+    a, atype = ctx._convert_param(a)
+    b, btype = ctx._convert_param(b)
+    z = ctx.convert(z)
+    if not z:
+        if ctx.re(b) <= 1:
+            return ctx.gammaprod([1-b],[a-b+1])
+        else:
+            return ctx.inf + z
+    bb = 1+a-b
+    bb, bbtype = ctx._convert_param(bb)
+    try:
+        orig = ctx.prec
+        try:
+            ctx.prec += 10
+            v = ctx.hypsum(2, 0, (atype, bbtype), [a, bb], -1/z, maxterms=ctx.prec)
+            return v / z**a
+        finally:
+            ctx.prec = orig
+    except ctx.NoConvergence:
+        pass
+    def h(a,b):
+        w = ctx.sinpi(b)
+        T1 = ([ctx.pi,w],[1,-1],[],[a-b+1,b],[a],[b],z)
+        T2 = ([-ctx.pi,w,z],[1,-1,1-b],[],[a,2-b],[a-b+1],[2-b],z)
+        return T1, T2
+    return ctx.hypercomb(h, [a,b], **kwargs)
+
+@defun
+def struveh(ctx,n,z, **kwargs):
+    n = ctx.convert(n)
+    z = ctx.convert(z)
+    # http://functions.wolfram.com/Bessel-TypeFunctions/StruveH/26/01/02/
+    def h(n):
+        return [([z/2, 0.5*ctx.sqrt(ctx.pi)], [n+1, -1], [], [n+1.5], [1], [1.5, n+1.5], -(z/2)**2)]
+    return ctx.hypercomb(h, [n], **kwargs)
+
+@defun
+def struvel(ctx,n,z, **kwargs):
+    n = ctx.convert(n)
+    z = ctx.convert(z)
+    # http://functions.wolfram.com/Bessel-TypeFunctions/StruveL/26/01/02/
+    def h(n):
+        return [([z/2, 0.5*ctx.sqrt(ctx.pi)], [n+1, -1], [], [n+1.5], [1], [1.5, n+1.5], (z/2)**2)]
+    return ctx.hypercomb(h, [n], **kwargs)
+
+def _anger(ctx,which,v,z,**kwargs):
+    v = ctx._convert_param(v)[0]
+    z = ctx.convert(z)
+    def h(v):
+        b = ctx.mpq_1_2
+        u = v*b
+        m = b*3
+        a1,a2,b1,b2 = m-u, m+u, 1-u, 1+u
+        c, s = ctx.cospi_sinpi(u)
+        if which == 0:
+            A, B = [b*z, s], [c]
+        if which == 1:
+            A, B = [b*z, -c], [s]
+        w = ctx.square_exp_arg(z, mult=-0.25)
+        T1 = A, [1, 1], [], [a1,a2], [1], [a1,a2], w
+        T2 = B, [1], [], [b1,b2], [1], [b1,b2], w
+        return T1, T2
+    return ctx.hypercomb(h, [v], **kwargs)
+
+@defun
+def angerj(ctx, v, z, **kwargs):
+    return _anger(ctx, 0, v, z, **kwargs)
+
+@defun
+def webere(ctx, v, z, **kwargs):
+    return _anger(ctx, 1, v, z, **kwargs)
+
+@defun
+def lommels1(ctx, u, v, z, **kwargs):
+    u = ctx._convert_param(u)[0]
+    v = ctx._convert_param(v)[0]
+    z = ctx.convert(z)
+    def h(u,v):
+        b = ctx.mpq_1_2
+        w = ctx.square_exp_arg(z, mult=-0.25)
+        return ([u-v+1, u+v+1, z], [-1, -1, u+1], [], [], [1], \
+            [b*(u-v+3),b*(u+v+3)], w),
+    return ctx.hypercomb(h, [u,v], **kwargs)
+
+@defun
+def lommels2(ctx, u, v, z, **kwargs):
+    u = ctx._convert_param(u)[0]
+    v = ctx._convert_param(v)[0]
+    z = ctx.convert(z)
+    # Asymptotic expansion (GR p. 947) -- need to be careful
+    # not to use for small arguments
+    # def h(u,v):
+    #    b = ctx.mpq_1_2
+    #    w = -(z/2)**(-2)
+    #    return ([z], [u-1], [], [], [b*(1-u+v)], [b*(1-u-v)], w),
+    def h(u,v):
+        b = ctx.mpq_1_2
+        w = ctx.square_exp_arg(z, mult=-0.25)
+        T1 = [u-v+1, u+v+1, z], [-1, -1, u+1], [], [], [1], [b*(u-v+3),b*(u+v+3)], w
+        T2 = [2, z], [u+v-1, -v], [v, b*(u+v+1)], [b*(v-u+1)], [], [1-v], w
+        T3 = [2, z], [u-v-1, v], [-v, b*(u-v+1)], [b*(1-u-v)], [], [1+v], w
+        #c1 = ctx.cospi((u-v)*b)
+        #c2 = ctx.cospi((u+v)*b)
+        #s = ctx.sinpi(v)
+        #r1 = (u-v+1)*b
+        #r2 = (u+v+1)*b
+        #T2 = [c1, s, z, 2], [1, -1, -v, v], [], [-v+1], [], [-v+1], w
+        #T3 = [-c2, s, z, 2], [1, -1, v, -v], [], [v+1], [], [v+1], w
+        #T2 = [c1, s, z, 2], [1, -1, -v, v+u-1], [r1, r2], [-v+1], [], [-v+1], w
+        #T3 = [-c2, s, z, 2], [1, -1, v, -v+u-1], [r1, r2], [v+1], [], [v+1], w
+        return T1, T2, T3
+    return ctx.hypercomb(h, [u,v], **kwargs)
+
+@defun
+def ber(ctx, n, z, **kwargs):
+    n = ctx.convert(n)
+    z = ctx.convert(z)
+    # http://functions.wolfram.com/Bessel-TypeFunctions/KelvinBer2/26/01/02/0001/
+    def h(n):
+        r = -(z/4)**4
+        cos, sin = ctx.cospi_sinpi(-0.75*n)
+        T1 = [cos, z/2], [1, n], [], [n+1], [], [0.5, 0.5*(n+1), 0.5*n+1], r
+        T2 = [sin, z/2], [1, n+2], [], [n+2], [], [1.5, 0.5*(n+3), 0.5*n+1], r
+        return T1, T2
+    return ctx.hypercomb(h, [n], **kwargs)
+
+@defun
+def bei(ctx, n, z, **kwargs):
+    n = ctx.convert(n)
+    z = ctx.convert(z)
+    # http://functions.wolfram.com/Bessel-TypeFunctions/KelvinBei2/26/01/02/0001/
+    def h(n):
+        r = -(z/4)**4
+        cos, sin = ctx.cospi_sinpi(0.75*n)
+        T1 = [cos, z/2], [1, n+2], [], [n+2], [], [1.5, 0.5*(n+3), 0.5*n+1], r
+        T2 = [sin, z/2], [1, n], [], [n+1], [], [0.5, 0.5*(n+1), 0.5*n+1], r
+        return T1, T2
+    return ctx.hypercomb(h, [n], **kwargs)
+
+@defun
+def ker(ctx, n, z, **kwargs):
+    n = ctx.convert(n)
+    z = ctx.convert(z)
+    # http://functions.wolfram.com/Bessel-TypeFunctions/KelvinKer2/26/01/02/0001/
+    def h(n):
+        r = -(z/4)**4
+        cos1, sin1 = ctx.cospi_sinpi(0.25*n)
+        cos2, sin2 = ctx.cospi_sinpi(0.75*n)
+        T1 = [2, z, 4*cos1], [-n-3, n, 1], [-n], [], [], [0.5, 0.5*(1+n), 0.5*(n+2)], r
+        T2 = [2, z, -sin1], [-n-3, 2+n, 1], [-n-1], [], [], [1.5, 0.5*(3+n), 0.5*(n+2)], r
+        T3 = [2, z, 4*cos2], [n-3, -n, 1], [n], [], [], [0.5, 0.5*(1-n), 1-0.5*n], r
+        T4 = [2, z, -sin2], [n-3, 2-n, 1], [n-1], [], [], [1.5, 0.5*(3-n), 1-0.5*n], r
+        return T1, T2, T3, T4
+    return ctx.hypercomb(h, [n], **kwargs)
+
+@defun
+def kei(ctx, n, z, **kwargs):
+    n = ctx.convert(n)
+    z = ctx.convert(z)
+    # http://functions.wolfram.com/Bessel-TypeFunctions/KelvinKei2/26/01/02/0001/
+    def h(n):
+        r = -(z/4)**4
+        cos1, sin1 = ctx.cospi_sinpi(0.75*n)
+        cos2, sin2 = ctx.cospi_sinpi(0.25*n)
+        T1 = [-cos1, 2, z], [1, n-3, 2-n], [n-1], [], [], [1.5, 0.5*(3-n), 1-0.5*n], r
+        T2 = [-sin1, 2, z], [1, n-1, -n], [n], [], [], [0.5, 0.5*(1-n), 1-0.5*n], r
+        T3 = [-sin2, 2, z], [1, -n-1, n], [-n], [], [], [0.5, 0.5*(n+1), 0.5*(n+2)], r
+        T4 = [-cos2, 2, z], [1, -n-3, n+2], [-n-1], [], [], [1.5, 0.5*(n+3), 0.5*(n+2)], r
+        return T1, T2, T3, T4
+    return ctx.hypercomb(h, [n], **kwargs)
+
+# TODO: do this more generically?
+def c_memo(f):
+    name = f.__name__
+    def f_wrapped(ctx):
+        cache = ctx._misc_const_cache
+        prec = ctx.prec
+        p,v = cache.get(name, (-1,0))
+        if p >= prec:
+            return +v
+        else:
+            cache[name] = (prec, f(ctx))
+            return cache[name][1]
+    return f_wrapped
+
+@c_memo
+def _airyai_C1(ctx):
+    return 1 / (ctx.cbrt(9) * ctx.gamma(ctx.mpf(2)/3))
+
+@c_memo
+def _airyai_C2(ctx):
+    return -1 / (ctx.cbrt(3) * ctx.gamma(ctx.mpf(1)/3))
+
+@c_memo
+def _airybi_C1(ctx):
+    return 1 / (ctx.nthroot(3,6) * ctx.gamma(ctx.mpf(2)/3))
+
+@c_memo
+def _airybi_C2(ctx):
+    return ctx.nthroot(3,6) / ctx.gamma(ctx.mpf(1)/3)
+
+def _airybi_n2_inf(ctx):
+    prec = ctx.prec
+    try:
+        v = ctx.power(3,'2/3')*ctx.gamma('2/3')/(2*ctx.pi)
+    finally:
+        ctx.prec = prec
+    return +v
+
+# Derivatives at z = 0
+# TODO: could be expressed more elegantly using triple factorials
+def _airyderiv_0(ctx, z, n, ntype, which):
+    if ntype == 'Z':
+        if n < 0:
+            return z
+        r = ctx.mpq_1_3
+        prec = ctx.prec
+        try:
+            ctx.prec += 10
+            v = ctx.gamma((n+1)*r) * ctx.power(3,n*r) / ctx.pi
+            if which == 0:
+                v *= ctx.sinpi(2*(n+1)*r)
+                v /= ctx.power(3,'2/3')
+            else:
+                v *= abs(ctx.sinpi(2*(n+1)*r))
+                v /= ctx.power(3,'1/6')
+        finally:
+            ctx.prec = prec
+        return +v + z
+    else:
+        # singular (does the limit exist?)
+        raise NotImplementedError
+
+@defun
+def airyai(ctx, z, derivative=0, **kwargs):
+    z = ctx.convert(z)
+    if derivative:
+        n, ntype = ctx._convert_param(derivative)
+    else:
+        n = 0
+    # Values at infinities
+    if not ctx.isnormal(z) and z:
+        if n and ntype == 'Z':
+            if n == -1:
+                if z == ctx.inf:
+                    return ctx.mpf(1)/3 + 1/z
+                if z == ctx.ninf:
+                    return ctx.mpf(-2)/3 + 1/z
+            if n < -1:
+                if z == ctx.inf:
+                    return z
+                if z == ctx.ninf:
+                    return (-1)**n * (-z)
+        if (not n) and z == ctx.inf or z == ctx.ninf:
+            return 1/z
+        # TODO: limits
+        raise ValueError("essential singularity of Ai(z)")
+    # Account for exponential scaling
+    if z:
+        extraprec = max(0, int(1.5*ctx.mag(z)))
+    else:
+        extraprec = 0
+    if n:
+        if n == 1:
+            def h():
+                # http://functions.wolfram.com/03.07.06.0005.01
+                if ctx._re(z) > 4:
+                    ctx.prec += extraprec
+                    w = z**1.5; r = -0.75/w; u = -2*w/3
+                    ctx.prec -= extraprec
+                    C = -ctx.exp(u)/(2*ctx.sqrt(ctx.pi))*ctx.nthroot(z,4)
+                    return ([C],[1],[],[],[(-1,6),(7,6)],[],r),
+                # http://functions.wolfram.com/03.07.26.0001.01
+                else:
+                    ctx.prec += extraprec
+                    w = z**3 / 9
+                    ctx.prec -= extraprec
+                    C1 = _airyai_C1(ctx) * 0.5
+                    C2 = _airyai_C2(ctx)
+                    T1 = [C1,z],[1,2],[],[],[],[ctx.mpq_5_3],w
+                    T2 = [C2],[1],[],[],[],[ctx.mpq_1_3],w
+                    return T1, T2
+            return ctx.hypercomb(h, [], **kwargs)
+        else:
+            if z == 0:
+                return _airyderiv_0(ctx, z, n, ntype, 0)
+            # http://functions.wolfram.com/03.05.20.0004.01
+            def h(n):
+                ctx.prec += extraprec
+                w = z**3/9
+                ctx.prec -= extraprec
+                q13,q23,q43 = ctx.mpq_1_3, ctx.mpq_2_3, ctx.mpq_4_3
+                a1=q13; a2=1; b1=(1-n)*q13; b2=(2-n)*q13; b3=1-n*q13
+                T1 = [3, z], [n-q23, -n], [a1], [b1,b2,b3], \
+                    [a1,a2], [b1,b2,b3], w
+                a1=q23; b1=(2-n)*q13; b2=1-n*q13; b3=(4-n)*q13
+                T2 = [3, z, -z], [n-q43, -n, 1], [a1], [b1,b2,b3], \
+                    [a1,a2], [b1,b2,b3], w
+                return T1, T2
+            v = ctx.hypercomb(h, [n], **kwargs)
+            if ctx._is_real_type(z) and ctx.isint(n):
+                v = ctx._re(v)
+            return v
+    else:
+        def h():
+            if ctx._re(z) > 4:
+                # We could use 1F1, but it results in huge cancellation;
+                # the following expansion is better.
+                # TODO: asymptotic series for derivatives
+                ctx.prec += extraprec
+                w = z**1.5; r = -0.75/w; u = -2*w/3
+                ctx.prec -= extraprec
+                C = ctx.exp(u)/(2*ctx.sqrt(ctx.pi)*ctx.nthroot(z,4))
+                return ([C],[1],[],[],[(1,6),(5,6)],[],r),
+            else:
+                ctx.prec += extraprec
+                w = z**3 / 9
+                ctx.prec -= extraprec
+                C1 = _airyai_C1(ctx)
+                C2 = _airyai_C2(ctx)
+                T1 = [C1],[1],[],[],[],[ctx.mpq_2_3],w
+                T2 = [z*C2],[1],[],[],[],[ctx.mpq_4_3],w
+                return T1, T2
+        return ctx.hypercomb(h, [], **kwargs)
+
+@defun
+def airybi(ctx, z, derivative=0, **kwargs):
+    z = ctx.convert(z)
+    if derivative:
+        n, ntype = ctx._convert_param(derivative)
+    else:
+        n = 0
+    # Values at infinities
+    if not ctx.isnormal(z) and z:
+        if n and ntype == 'Z':
+            if z == ctx.inf:
+                return z
+            if z == ctx.ninf:
+                if n == -1:
+                    return 1/z
+                if n == -2:
+                    return _airybi_n2_inf(ctx)
+                if n < -2:
+                    return (-1)**n * (-z)
+        if not n:
+            if z == ctx.inf:
+                return z
+            if z == ctx.ninf:
+                return 1/z
+        # TODO: limits
+        raise ValueError("essential singularity of Bi(z)")
+    if z:
+        extraprec = max(0, int(1.5*ctx.mag(z)))
+    else:
+        extraprec = 0
+    if n:
+        if n == 1:
+            # http://functions.wolfram.com/03.08.26.0001.01
+            def h():
+                ctx.prec += extraprec
+                w = z**3 / 9
+                ctx.prec -= extraprec
+                C1 = _airybi_C1(ctx)*0.5
+                C2 = _airybi_C2(ctx)
+                T1 = [C1,z],[1,2],[],[],[],[ctx.mpq_5_3],w
+                T2 = [C2],[1],[],[],[],[ctx.mpq_1_3],w
+                return T1, T2
+            return ctx.hypercomb(h, [], **kwargs)
+        else:
+            if z == 0:
+                return _airyderiv_0(ctx, z, n, ntype, 1)
+            def h(n):
+                ctx.prec += extraprec
+                w = z**3/9
+                ctx.prec -= extraprec
+                q13,q23,q43 = ctx.mpq_1_3, ctx.mpq_2_3, ctx.mpq_4_3
+                q16 = ctx.mpq_1_6
+                q56 = ctx.mpq_5_6
+                a1=q13; a2=1; b1=(1-n)*q13; b2=(2-n)*q13; b3=1-n*q13
+                T1 = [3, z], [n-q16, -n], [a1], [b1,b2,b3], \
+                    [a1,a2], [b1,b2,b3], w
+                a1=q23; b1=(2-n)*q13; b2=1-n*q13; b3=(4-n)*q13
+                T2 = [3, z], [n-q56, 1-n], [a1], [b1,b2,b3], \
+                    [a1,a2], [b1,b2,b3], w
+                return T1, T2
+            v = ctx.hypercomb(h, [n], **kwargs)
+            if ctx._is_real_type(z) and ctx.isint(n):
+                v = ctx._re(v)
+            return v
+    else:
+        def h():
+            ctx.prec += extraprec
+            w = z**3 / 9
+            ctx.prec -= extraprec
+            C1 = _airybi_C1(ctx)
+            C2 = _airybi_C2(ctx)
+            T1 = [C1],[1],[],[],[],[ctx.mpq_2_3],w
+            T2 = [z*C2],[1],[],[],[],[ctx.mpq_4_3],w
+            return T1, T2
+        return ctx.hypercomb(h, [], **kwargs)
+
+def _airy_zero(ctx, which, k, derivative, complex=False):
+    # Asymptotic formulas are given in DLMF section 9.9
+    def U(t): return t**(2/3.)*(1-7/(t**2*48))
+    def T(t): return t**(2/3.)*(1+5/(t**2*48))
+    k = int(k)
+    if k < 1:
+        raise ValueError("k cannot be less than 1")
+    if not derivative in (0,1):
+        raise ValueError("Derivative should lie between 0 and 1")
+    if which == 0:
+        if derivative:
+            return ctx.findroot(lambda z: ctx.airyai(z,1),
+                -U(3*ctx.pi*(4*k-3)/8))
+        return ctx.findroot(ctx.airyai, -T(3*ctx.pi*(4*k-1)/8))
+    if which == 1 and complex == False:
+        if derivative:
+            return ctx.findroot(lambda z: ctx.airybi(z,1),
+                -U(3*ctx.pi*(4*k-1)/8))
+        return ctx.findroot(ctx.airybi, -T(3*ctx.pi*(4*k-3)/8))
+    if which == 1 and complex == True:
+        if derivative:
+            t = 3*ctx.pi*(4*k-3)/8 + 0.75j*ctx.ln2
+            s = ctx.expjpi(ctx.mpf(1)/3) * T(t)
+            return ctx.findroot(lambda z: ctx.airybi(z,1), s)
+        t = 3*ctx.pi*(4*k-1)/8 + 0.75j*ctx.ln2
+        s = ctx.expjpi(ctx.mpf(1)/3) * U(t)
+        return ctx.findroot(ctx.airybi, s)
+
+@defun
+def airyaizero(ctx, k, derivative=0):
+    return _airy_zero(ctx, 0, k, derivative, False)
+
+@defun
+def airybizero(ctx, k, derivative=0, complex=False):
+    return _airy_zero(ctx, 1, k, derivative, complex)
+
+def _scorer(ctx, z, which, kwargs):
+    z = ctx.convert(z)
+    if ctx.isinf(z):
+        if z == ctx.inf:
+            if which == 0: return 1/z
+            if which == 1: return z
+        if z == ctx.ninf:
+            return 1/z
+        raise ValueError("essential singularity")
+    if z:
+        extraprec = max(0, int(1.5*ctx.mag(z)))
+    else:
+        extraprec = 0
+    if kwargs.get('derivative'):
+        raise NotImplementedError
+    # Direct asymptotic expansions, to avoid
+    # exponentially large cancellation
+    try:
+        if ctx.mag(z) > 3:
+            if which == 0 and abs(ctx.arg(z)) < ctx.pi/3 * 0.999:
+                def h():
+                    return (([ctx.pi,z],[-1,-1],[],[],[(1,3),(2,3),1],[],9/z**3),)
+                return ctx.hypercomb(h, [], maxterms=ctx.prec, force_series=True)
+            if which == 1 and abs(ctx.arg(-z)) < 2*ctx.pi/3 * 0.999:
+                def h():
+                    return (([-ctx.pi,z],[-1,-1],[],[],[(1,3),(2,3),1],[],9/z**3),)
+                return ctx.hypercomb(h, [], maxterms=ctx.prec, force_series=True)
+    except ctx.NoConvergence:
+        pass
+    def h():
+        A = ctx.airybi(z, **kwargs)/3
+        B = -2*ctx.pi
+        if which == 1:
+            A *= 2
+            B *= -1
+        ctx.prec += extraprec
+        w = z**3/9
+        ctx.prec -= extraprec
+        T1 = [A], [1], [], [], [], [], 0
+        T2 = [B,z], [-1,2], [], [], [1], [ctx.mpq_4_3,ctx.mpq_5_3], w
+        return T1, T2
+    return ctx.hypercomb(h, [], **kwargs)
+
+@defun
+def scorergi(ctx, z, **kwargs):
+    return _scorer(ctx, z, 0, kwargs)
+
+@defun
+def scorerhi(ctx, z, **kwargs):
+    return _scorer(ctx, z, 1, kwargs)
+
+@defun_wrapped
+def coulombc(ctx, l, eta, _cache={}):
+    if (l, eta) in _cache and _cache[l,eta][0] >= ctx.prec:
+        return +_cache[l,eta][1]
+    G3 = ctx.loggamma(2*l+2)
+    G1 = ctx.loggamma(1+l+ctx.j*eta)
+    G2 = ctx.loggamma(1+l-ctx.j*eta)
+    v = 2**l * ctx.exp((-ctx.pi*eta+G1+G2)/2 - G3)
+    if not (ctx.im(l) or ctx.im(eta)):
+        v = ctx.re(v)
+    _cache[l,eta] = (ctx.prec, v)
+    return v
+
+@defun_wrapped
+def coulombf(ctx, l, eta, z, w=1, chop=True, **kwargs):
+    # Regular Coulomb wave function
+    # Note: w can be either 1 or -1; the other may be better in some cases
+    # TODO: check that chop=True chops when and only when it should
+    #ctx.prec += 10
+    def h(l, eta):
+        try:
+            jw = ctx.j*w
+            jwz = ctx.fmul(jw, z, exact=True)
+            jwz2 = ctx.fmul(jwz, -2, exact=True)
+            C = ctx.coulombc(l, eta)
+            T1 = [C, z, ctx.exp(jwz)], [1, l+1, 1], [], [], [1+l+jw*eta], \
+                [2*l+2], jwz2
+        except ValueError:
+            T1 = [0], [-1], [], [], [], [], 0
+        return (T1,)
+    v = ctx.hypercomb(h, [l,eta], **kwargs)
+    if chop and (not ctx.im(l)) and (not ctx.im(eta)) and (not ctx.im(z)) and \
+        (ctx.re(z) >= 0):
+        v = ctx.re(v)
+    return v
+
+@defun_wrapped
+def _coulomb_chi(ctx, l, eta, _cache={}):
+    if (l, eta) in _cache and _cache[l,eta][0] >= ctx.prec:
+        return _cache[l,eta][1]
+    def terms():
+        l2 = -l-1
+        jeta = ctx.j*eta
+        return [ctx.loggamma(1+l+jeta) * (-0.5j),
+            ctx.loggamma(1+l-jeta) * (0.5j),
+            ctx.loggamma(1+l2+jeta) * (0.5j),
+            ctx.loggamma(1+l2-jeta) * (-0.5j),
+            -(l+0.5)*ctx.pi]
+    v = ctx.sum_accurately(terms, 1)
+    _cache[l,eta] = (ctx.prec, v)
+    return v
+
+@defun_wrapped
+def coulombg(ctx, l, eta, z, w=1, chop=True, **kwargs):
+    # Irregular Coulomb wave function
+    # Note: w can be either 1 or -1; the other may be better in some cases
+    # TODO: check that chop=True chops when and only when it should
+    if not ctx._im(l):
+        l = ctx._re(l)  # XXX: for isint
+    def h(l, eta):
+        # Force perturbation for integers and half-integers
+        if ctx.isint(l*2):
+            T1 = [0], [-1], [], [], [], [], 0
+            return (T1,)
+        l2 = -l-1
+        try:
+            chi = ctx._coulomb_chi(l, eta)
+            jw = ctx.j*w
+            s = ctx.sin(chi); c = ctx.cos(chi)
+            C1 = ctx.coulombc(l,eta)
+            C2 = ctx.coulombc(l2,eta)
+            u = ctx.exp(jw*z)
+            x = -2*jw*z
+            T1 = [s, C1, z, u, c], [-1, 1, l+1, 1, 1], [], [], \
+                [1+l+jw*eta], [2*l+2], x
+            T2 = [-s, C2, z, u],   [-1, 1, l2+1, 1],    [], [], \
+                [1+l2+jw*eta], [2*l2+2], x
+            return T1, T2
+        except ValueError:
+            T1 = [0], [-1], [], [], [], [], 0
+            return (T1,)
+    v = ctx.hypercomb(h, [l,eta], **kwargs)
+    if chop and (not ctx._im(l)) and (not ctx._im(eta)) and (not ctx._im(z)) and \
+        (ctx._re(z) >= 0):
+        v = ctx._re(v)
+    return v
+
+def mcmahon(ctx,kind,prime,v,m):
+    """
+    Computes an estimate for the location of the Bessel function zero
+    j_{v,m}, y_{v,m}, j'_{v,m} or y'_{v,m} using McMahon's asymptotic
+    expansion (Abramowitz & Stegun 9.5.12-13, DLMF 20.21(vi)).
+
+    Returns (r,err) where r is the estimated location of the root
+    and err is a positive number estimating the error of the
+    asymptotic expansion.
+    """
+    u = 4*v**2
+    if kind == 1 and not prime: b = (4*m+2*v-1)*ctx.pi/4
+    if kind == 2 and not prime: b = (4*m+2*v-3)*ctx.pi/4
+    if kind == 1 and prime: b = (4*m+2*v-3)*ctx.pi/4
+    if kind == 2 and prime: b = (4*m+2*v-1)*ctx.pi/4
+    if not prime:
+        s1 = b
+        s2 = -(u-1)/(8*b)
+        s3 = -4*(u-1)*(7*u-31)/(3*(8*b)**3)
+        s4 = -32*(u-1)*(83*u**2-982*u+3779)/(15*(8*b)**5)
+        s5 = -64*(u-1)*(6949*u**3-153855*u**2+1585743*u-6277237)/(105*(8*b)**7)
+    if prime:
+        s1 = b
+        s2 = -(u+3)/(8*b)
+        s3 = -4*(7*u**2+82*u-9)/(3*(8*b)**3)
+        s4 = -32*(83*u**3+2075*u**2-3039*u+3537)/(15*(8*b)**5)
+        s5 = -64*(6949*u**4+296492*u**3-1248002*u**2+7414380*u-5853627)/(105*(8*b)**7)
+    terms = [s1,s2,s3,s4,s5]
+    s = s1
+    err = 0.0
+    for i in range(1,len(terms)):
+        if abs(terms[i]) < abs(terms[i-1]):
+            s += terms[i]
+        else:
+            err = abs(terms[i])
+    if i == len(terms)-1:
+        err = abs(terms[-1])
+    return s, err
+
+def generalized_bisection(ctx,f,a,b,n):
+    """
+    Given f known to have exactly n simple roots within [a,b],
+    return a list of n intervals isolating the roots
+    and having opposite signs at the endpoints.
+
+    TODO: this can be optimized, e.g. by reusing evaluation points.
+    """
+    if n < 1:
+        raise ValueError("n cannot be less than 1")
+    N = n+1
+    points = []
+    signs = []
+    while 1:
+        points = ctx.linspace(a,b,N)
+        signs = [ctx.sign(f(x)) for x in points]
+        ok_intervals = [(points[i],points[i+1]) for i in range(N-1) \
+            if signs[i]*signs[i+1] == -1]
+        if len(ok_intervals) == n:
+            return ok_intervals
+        N = N*2
+
+def find_in_interval(ctx, f, ab):
+    return ctx.findroot(f, ab, solver='illinois', verify=False)
+
+def bessel_zero(ctx, kind, prime, v, m, isoltol=0.01, _interval_cache={}):
+    prec = ctx.prec
+    workprec = max(prec, ctx.mag(v), ctx.mag(m))+10
+    try:
+        ctx.prec = workprec
+        v = ctx.mpf(v)
+        m = int(m)
+        prime = int(prime)
+        if v < 0:
+            raise ValueError("v cannot be negative")
+        if m < 1:
+            raise ValueError("m cannot be less than 1")
+        if not prime in (0,1):
+            raise ValueError("prime should lie between 0 and 1")
+        if kind == 1:
+            if prime: f = lambda x: ctx.besselj(v,x,derivative=1)
+            else:     f = lambda x: ctx.besselj(v,x)
+        if kind == 2:
+            if prime: f = lambda x: ctx.bessely(v,x,derivative=1)
+            else:     f = lambda x: ctx.bessely(v,x)
+        # The first root of J' is very close to 0 for small
+        # orders, and this needs to be special-cased
+        if kind == 1 and prime and m == 1:
+            if v == 0:
+                return ctx.zero
+            if v <= 1:
+                # TODO: use v <= j'_{v,1} < y_{v,1}?
+                r = 2*ctx.sqrt(v*(1+v)/(v+2))
+                return find_in_interval(ctx, f, (r/10, 2*r))
+        if (kind,prime,v,m) in _interval_cache:
+            return find_in_interval(ctx, f, _interval_cache[kind,prime,v,m])
+        r, err = mcmahon(ctx, kind, prime, v, m)
+        if err < isoltol:
+            return find_in_interval(ctx, f, (r-isoltol, r+isoltol))
+        # An x such that 0 < x < r_{v,1}
+        if kind == 1 and not prime: low = 2.4
+        if kind == 1 and prime: low = 1.8
+        if kind == 2 and not prime: low = 0.8
+        if kind == 2 and prime: low = 2.0
+        n = m+1
+        while 1:
+            r1, err = mcmahon(ctx, kind, prime, v, n)
+            if err < isoltol:
+                r2, err2 = mcmahon(ctx, kind, prime, v, n+1)
+                intervals = generalized_bisection(ctx, f, low, 0.5*(r1+r2), n)
+                for k, ab in enumerate(intervals):
+                    _interval_cache[kind,prime,v,k+1] = ab
+                return find_in_interval(ctx, f, intervals[m-1])
+            else:
+                n = n*2
+    finally:
+        ctx.prec = prec
+
+@defun
+def besseljzero(ctx, v, m, derivative=0):
+    r"""
+    For a real order `\nu \ge 0` and a positive integer `m`, returns
+    `j_{\nu,m}`, the `m`-th positive zero of the Bessel function of the
+    first kind `J_{\nu}(z)` (see :func:`~mpmath.besselj`). Alternatively,
+    with *derivative=1*, gives the first nonnegative simple zero
+    `j'_{\nu,m}` of `J'_{\nu}(z)`.
+
+    The indexing convention is that used by Abramowitz & Stegun
+    and the DLMF. Note the special case `j'_{0,1} = 0`, while all other
+    zeros are positive. In effect, only simple zeros are counted
+    (all zeros of Bessel functions are simple except possibly `z = 0`)
+    and `j_{\nu,m}` becomes a monotonic function of both `\nu`
+    and `m`.
+
+    The zeros are interlaced according to the inequalities
+
+    .. math ::
+
+        j'_{\nu,k} < j_{\nu,k} < j'_{\nu,k+1}
+
+        j_{\nu,1} < j_{\nu+1,2} < j_{\nu,2} < j_{\nu+1,2} < j_{\nu,3} < \cdots
+
+    **Examples**
+
+    Initial zeros of the Bessel functions `J_0(z), J_1(z), J_2(z)`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> besseljzero(0,1); besseljzero(0,2); besseljzero(0,3)
+        2.404825557695772768621632
+        5.520078110286310649596604
+        8.653727912911012216954199
+        >>> besseljzero(1,1); besseljzero(1,2); besseljzero(1,3)
+        3.831705970207512315614436
+        7.01558666981561875353705
+        10.17346813506272207718571
+        >>> besseljzero(2,1); besseljzero(2,2); besseljzero(2,3)
+        5.135622301840682556301402
+        8.417244140399864857783614
+        11.61984117214905942709415
+
+    Initial zeros of `J'_0(z), J'_1(z), J'_2(z)`::
+
+        0.0
+        3.831705970207512315614436
+        7.01558666981561875353705
+        >>> besseljzero(1,1,1); besseljzero(1,2,1); besseljzero(1,3,1)
+        1.84118378134065930264363
+        5.331442773525032636884016
+        8.536316366346285834358961
+        >>> besseljzero(2,1,1); besseljzero(2,2,1); besseljzero(2,3,1)
+        3.054236928227140322755932
+        6.706133194158459146634394
+        9.969467823087595793179143
+
+    Zeros with large index::
+
+        >>> besseljzero(0,100); besseljzero(0,1000); besseljzero(0,10000)
+        313.3742660775278447196902
+        3140.807295225078628895545
+        31415.14114171350798533666
+        >>> besseljzero(5,100); besseljzero(5,1000); besseljzero(5,10000)
+        321.1893195676003157339222
+        3148.657306813047523500494
+        31422.9947255486291798943
+        >>> besseljzero(0,100,1); besseljzero(0,1000,1); besseljzero(0,10000,1)
+        311.8018681873704508125112
+        3139.236339643802482833973
+        31413.57032947022399485808
+
+    Zeros of functions with large order::
+
+        >>> besseljzero(50,1)
+        57.11689916011917411936228
+        >>> besseljzero(50,2)
+        62.80769876483536093435393
+        >>> besseljzero(50,100)
+        388.6936600656058834640981
+        >>> besseljzero(50,1,1)
+        52.99764038731665010944037
+        >>> besseljzero(50,2,1)
+        60.02631933279942589882363
+        >>> besseljzero(50,100,1)
+        387.1083151608726181086283
+
+    Zeros of functions with fractional order::
+
+        >>> besseljzero(0.5,1); besseljzero(1.5,1); besseljzero(2.25,4)
+        3.141592653589793238462643
+        4.493409457909064175307881
+        15.15657692957458622921634
+
+    Both `J_{\nu}(z)` and `J'_{\nu}(z)` can be expressed as infinite
+    products over their zeros::
+
+        >>> v,z = 2, mpf(1)
+        >>> (z/2)**v/gamma(v+1) * \
+        ...     nprod(lambda k: 1-(z/besseljzero(v,k))**2, [1,inf])
+        ...
+        0.1149034849319004804696469
+        >>> besselj(v,z)
+        0.1149034849319004804696469
+        >>> (z/2)**(v-1)/2/gamma(v) * \
+        ...     nprod(lambda k: 1-(z/besseljzero(v,k,1))**2, [1,inf])
+        ...
+        0.2102436158811325550203884
+        >>> besselj(v,z,1)
+        0.2102436158811325550203884
+
+    """
+    return +bessel_zero(ctx, 1, derivative, v, m)
+
+@defun
+def besselyzero(ctx, v, m, derivative=0):
+    r"""
+    For a real order `\nu \ge 0` and a positive integer `m`, returns
+    `y_{\nu,m}`, the `m`-th positive zero of the Bessel function of the
+    second kind `Y_{\nu}(z)` (see :func:`~mpmath.bessely`). Alternatively,
+    with *derivative=1*, gives the first positive zero `y'_{\nu,m}` of
+    `Y'_{\nu}(z)`.
+
+    The zeros are interlaced according to the inequalities
+
+    .. math ::
+
+        y_{\nu,k} < y'_{\nu,k} < y_{\nu,k+1}
+
+        y_{\nu,1} < y_{\nu+1,2} < y_{\nu,2} < y_{\nu+1,2} < y_{\nu,3} < \cdots
+
+    **Examples**
+
+    Initial zeros of the Bessel functions `Y_0(z), Y_1(z), Y_2(z)`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> besselyzero(0,1); besselyzero(0,2); besselyzero(0,3)
+        0.8935769662791675215848871
+        3.957678419314857868375677
+        7.086051060301772697623625
+        >>> besselyzero(1,1); besselyzero(1,2); besselyzero(1,3)
+        2.197141326031017035149034
+        5.429681040794135132772005
+        8.596005868331168926429606
+        >>> besselyzero(2,1); besselyzero(2,2); besselyzero(2,3)
+        3.384241767149593472701426
+        6.793807513268267538291167
+        10.02347797936003797850539
+
+    Initial zeros of `Y'_0(z), Y'_1(z), Y'_2(z)`::
+
+        >>> besselyzero(0,1,1); besselyzero(0,2,1); besselyzero(0,3,1)
+        2.197141326031017035149034
+        5.429681040794135132772005
+        8.596005868331168926429606
+        >>> besselyzero(1,1,1); besselyzero(1,2,1); besselyzero(1,3,1)
+        3.683022856585177699898967
+        6.941499953654175655751944
+        10.12340465543661307978775
+        >>> besselyzero(2,1,1); besselyzero(2,2,1); besselyzero(2,3,1)
+        5.002582931446063945200176
+        8.350724701413079526349714
+        11.57419546521764654624265
+
+    Zeros with large index::
+
+        >>> besselyzero(0,100); besselyzero(0,1000); besselyzero(0,10000)
+        311.8034717601871549333419
+        3139.236498918198006794026
+        31413.57034538691205229188
+        >>> besselyzero(5,100); besselyzero(5,1000); besselyzero(5,10000)
+        319.6183338562782156235062
+        3147.086508524556404473186
+        31421.42392920214673402828
+        >>> besselyzero(0,100,1); besselyzero(0,1000,1); besselyzero(0,10000,1)
+        313.3726705426359345050449
+        3140.807136030340213610065
+        31415.14112579761578220175
+
+    Zeros of functions with large order::
+
+        >>> besselyzero(50,1)
+        53.50285882040036394680237
+        >>> besselyzero(50,2)
+        60.11244442774058114686022
+        >>> besselyzero(50,100)
+        387.1096509824943957706835
+        >>> besselyzero(50,1,1)
+        56.96290427516751320063605
+        >>> besselyzero(50,2,1)
+        62.74888166945933944036623
+        >>> besselyzero(50,100,1)
+        388.6923300548309258355475
+
+    Zeros of functions with fractional order::
+
+        >>> besselyzero(0.5,1); besselyzero(1.5,1); besselyzero(2.25,4)
+        1.570796326794896619231322
+        2.798386045783887136720249
+        13.56721208770735123376018
+
+    """
+    return +bessel_zero(ctx, 2, derivative, v, m)

vllm/lib/python3.10/site-packages/mpmath/functions/elliptic.py

@@ -0,0 +1,1431 @@
+r"""
+Elliptic functions historically comprise the elliptic integrals
+and their inverses, and originate from the problem of computing the
+arc length of an ellipse. From a more modern point of view,
+an elliptic function is defined as a doubly periodic function, i.e.
+a function which satisfies
+
+.. math ::
+
+    f(z + 2 \omega_1) = f(z + 2 \omega_2) = f(z)
+
+for some half-periods `\omega_1, \omega_2` with
+`\mathrm{Im}[\omega_1 / \omega_2] > 0`. The canonical elliptic
+functions are the Jacobi elliptic functions. More broadly, this section
+includes  quasi-doubly periodic functions (such as the Jacobi theta
+functions) and other functions useful in the study of elliptic functions.
+
+Many different conventions for the arguments of
+elliptic functions are in use. It is even standard to use
+different parameterizations for different functions in the same
+text or software (and mpmath is no exception).
+The usual parameters are the elliptic nome `q`, which usually
+must satisfy `|q| < 1`; the elliptic parameter `m` (an arbitrary
+complex number); the elliptic modulus `k` (an arbitrary complex
+number); and the half-period ratio `\tau`, which usually must
+satisfy `\mathrm{Im}[\tau] > 0`.
+These quantities can be expressed in terms of each other
+using the following relations:
+
+.. math ::
+
+    m = k^2
+
+.. math ::
+
+    \tau = i \frac{K(1-m)}{K(m)}
+
+.. math ::
+
+    q = e^{i \pi \tau}
+
+.. math ::
+
+    k = \frac{\vartheta_2^2(q)}{\vartheta_3^2(q)}
+
+In addition, an alternative definition is used for the nome in
+number theory, which we here denote by q-bar:
+
+.. math ::
+
+    \bar{q} = q^2 = e^{2 i \pi \tau}
+
+For convenience, mpmath provides functions to convert
+between the various parameters (:func:`~mpmath.qfrom`, :func:`~mpmath.mfrom`,
+:func:`~mpmath.kfrom`, :func:`~mpmath.taufrom`, :func:`~mpmath.qbarfrom`).
+
+**References**
+
+1. [AbramowitzStegun]_
+
+2. [WhittakerWatson]_
+
+"""
+
+from .functions import defun, defun_wrapped
+
+@defun_wrapped
+def eta(ctx, tau):
+    r"""
+    Returns the Dedekind eta function of tau in the upper half-plane.
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> eta(1j); gamma(0.25) / (2*pi**0.75)
+        (0.7682254223260566590025942 + 0.0j)
+        0.7682254223260566590025942
+        >>> tau = sqrt(2) + sqrt(5)*1j
+        >>> eta(-1/tau); sqrt(-1j*tau) * eta(tau)
+        (0.9022859908439376463573294 + 0.07985093673948098408048575j)
+        (0.9022859908439376463573295 + 0.07985093673948098408048575j)
+        >>> eta(tau+1); exp(pi*1j/12) * eta(tau)
+        (0.4493066139717553786223114 + 0.3290014793877986663915939j)
+        (0.4493066139717553786223114 + 0.3290014793877986663915939j)
+        >>> f = lambda z: diff(eta, z) / eta(z)
+        >>> chop(36*diff(f,tau)**2 - 24*diff(f,tau,2)*f(tau) + diff(f,tau,3))
+        0.0
+
+    """
+    if ctx.im(tau) <= 0.0:
+        raise ValueError("eta is only defined in the upper half-plane")
+    q = ctx.expjpi(tau/12)
+    return q * ctx.qp(q**24)
+
+def nome(ctx, m):
+    m = ctx.convert(m)
+    if not m:
+        return m
+    if m == ctx.one:
+        return m
+    if ctx.isnan(m):
+        return m
+    if ctx.isinf(m):
+        if m == ctx.ninf:
+            return type(m)(-1)
+        else:
+            return ctx.mpc(-1)
+    a = ctx.ellipk(ctx.one-m)
+    b = ctx.ellipk(m)
+    v = ctx.exp(-ctx.pi*a/b)
+    if not ctx._im(m) and ctx._re(m) < 1:
+        if ctx._is_real_type(m):
+            return v.real
+        else:
+            return v.real + 0j
+    elif m == 2:
+        v = ctx.mpc(0, v.imag)
+    return v
+
+@defun_wrapped
+def qfrom(ctx, q=None, m=None, k=None, tau=None, qbar=None):
+    r"""
+    Returns the elliptic nome `q`, given any of `q, m, k, \tau, \bar{q}`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> qfrom(q=0.25)
+        0.25
+        >>> qfrom(m=mfrom(q=0.25))
+        0.25
+        >>> qfrom(k=kfrom(q=0.25))
+        0.25
+        >>> qfrom(tau=taufrom(q=0.25))
+        (0.25 + 0.0j)
+        >>> qfrom(qbar=qbarfrom(q=0.25))
+        0.25
+
+    """
+    if q is not None:
+        return ctx.convert(q)
+    if m is not None:
+        return nome(ctx, m)
+    if k is not None:
+        return nome(ctx, ctx.convert(k)**2)
+    if tau is not None:
+        return ctx.expjpi(tau)
+    if qbar is not None:
+        return ctx.sqrt(qbar)
+
+@defun_wrapped
+def qbarfrom(ctx, q=None, m=None, k=None, tau=None, qbar=None):
+    r"""
+    Returns the number-theoretic nome `\bar q`, given any of
+    `q, m, k, \tau, \bar{q}`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> qbarfrom(qbar=0.25)
+        0.25
+        >>> qbarfrom(q=qfrom(qbar=0.25))
+        0.25
+        >>> qbarfrom(m=extraprec(20)(mfrom)(qbar=0.25))  # ill-conditioned
+        0.25
+        >>> qbarfrom(k=extraprec(20)(kfrom)(qbar=0.25))  # ill-conditioned
+        0.25
+        >>> qbarfrom(tau=taufrom(qbar=0.25))
+        (0.25 + 0.0j)
+
+    """
+    if qbar is not None:
+        return ctx.convert(qbar)
+    if q is not None:
+        return ctx.convert(q) ** 2
+    if m is not None:
+        return nome(ctx, m) ** 2
+    if k is not None:
+        return nome(ctx, ctx.convert(k)**2) ** 2
+    if tau is not None:
+        return ctx.expjpi(2*tau)
+
+@defun_wrapped
+def taufrom(ctx, q=None, m=None, k=None, tau=None, qbar=None):
+    r"""
+    Returns the elliptic half-period ratio `\tau`, given any of
+    `q, m, k, \tau, \bar{q}`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> taufrom(tau=0.5j)
+        (0.0 + 0.5j)
+        >>> taufrom(q=qfrom(tau=0.5j))
+        (0.0 + 0.5j)
+        >>> taufrom(m=mfrom(tau=0.5j))
+        (0.0 + 0.5j)
+        >>> taufrom(k=kfrom(tau=0.5j))
+        (0.0 + 0.5j)
+        >>> taufrom(qbar=qbarfrom(tau=0.5j))
+        (0.0 + 0.5j)
+
+    """
+    if tau is not None:
+        return ctx.convert(tau)
+    if m is not None:
+        m = ctx.convert(m)
+        return ctx.j*ctx.ellipk(1-m)/ctx.ellipk(m)
+    if k is not None:
+        k = ctx.convert(k)
+        return ctx.j*ctx.ellipk(1-k**2)/ctx.ellipk(k**2)
+    if q is not None:
+        return ctx.log(q) / (ctx.pi*ctx.j)
+    if qbar is not None:
+        qbar = ctx.convert(qbar)
+        return ctx.log(qbar) / (2*ctx.pi*ctx.j)
+
+@defun_wrapped
+def kfrom(ctx, q=None, m=None, k=None, tau=None, qbar=None):
+    r"""
+    Returns the elliptic modulus `k`, given any of
+    `q, m, k, \tau, \bar{q}`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> kfrom(k=0.25)
+        0.25
+        >>> kfrom(m=mfrom(k=0.25))
+        0.25
+        >>> kfrom(q=qfrom(k=0.25))
+        0.25
+        >>> kfrom(tau=taufrom(k=0.25))
+        (0.25 + 0.0j)
+        >>> kfrom(qbar=qbarfrom(k=0.25))
+        0.25
+
+    As `q \to 1` and `q \to -1`, `k` rapidly approaches
+    `1` and `i \infty` respectively::
+
+        >>> kfrom(q=0.75)
+        0.9999999999999899166471767
+        >>> kfrom(q=-0.75)
+        (0.0 + 7041781.096692038332790615j)
+        >>> kfrom(q=1)
+        1
+        >>> kfrom(q=-1)
+        (0.0 + +infj)
+    """
+    if k is not None:
+        return ctx.convert(k)
+    if m is not None:
+        return ctx.sqrt(m)
+    if tau is not None:
+        q = ctx.expjpi(tau)
+    if qbar is not None:
+        q = ctx.sqrt(qbar)
+    if q == 1:
+        return q
+    if q == -1:
+        return ctx.mpc(0,'inf')
+    return (ctx.jtheta(2,0,q)/ctx.jtheta(3,0,q))**2
+
+@defun_wrapped
+def mfrom(ctx, q=None, m=None, k=None, tau=None, qbar=None):
+    r"""
+    Returns the elliptic parameter `m`, given any of
+    `q, m, k, \tau, \bar{q}`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> mfrom(m=0.25)
+        0.25
+        >>> mfrom(q=qfrom(m=0.25))
+        0.25
+        >>> mfrom(k=kfrom(m=0.25))
+        0.25
+        >>> mfrom(tau=taufrom(m=0.25))
+        (0.25 + 0.0j)
+        >>> mfrom(qbar=qbarfrom(m=0.25))
+        0.25
+
+    As `q \to 1` and `q \to -1`, `m` rapidly approaches
+    `1` and `-\infty` respectively::
+
+        >>> mfrom(q=0.75)
+        0.9999999999999798332943533
+        >>> mfrom(q=-0.75)
+        -49586681013729.32611558353
+        >>> mfrom(q=1)
+        1.0
+        >>> mfrom(q=-1)
+        -inf
+
+    The inverse nome as a function of `q` has an integer
+    Taylor series expansion::
+
+        >>> taylor(lambda q: mfrom(q), 0, 7)
+        [0.0, 16.0, -128.0, 704.0, -3072.0, 11488.0, -38400.0, 117632.0]
+
+    """
+    if m is not None:
+        return m
+    if k is not None:
+        return k**2
+    if tau is not None:
+        q = ctx.expjpi(tau)
+    if qbar is not None:
+        q = ctx.sqrt(qbar)
+    if q == 1:
+        return ctx.convert(q)
+    if q == -1:
+        return q*ctx.inf
+    v = (ctx.jtheta(2,0,q)/ctx.jtheta(3,0,q))**4
+    if ctx._is_real_type(q) and q < 0:
+        v = v.real
+    return v
+
+jacobi_spec = {
+  'sn' : ([3],[2],[1],[4], 'sin', 'tanh'),
+  'cn' : ([4],[2],[2],[4], 'cos', 'sech'),
+  'dn' : ([4],[3],[3],[4], '1', 'sech'),
+  'ns' : ([2],[3],[4],[1], 'csc', 'coth'),
+  'nc' : ([2],[4],[4],[2], 'sec', 'cosh'),
+  'nd' : ([3],[4],[4],[3], '1', 'cosh'),
+  'sc' : ([3],[4],[1],[2], 'tan', 'sinh'),
+  'sd' : ([3,3],[2,4],[1],[3], 'sin', 'sinh'),
+  'cd' : ([3],[2],[2],[3], 'cos', '1'),
+  'cs' : ([4],[3],[2],[1], 'cot', 'csch'),
+  'dc' : ([2],[3],[3],[2], 'sec', '1'),
+  'ds' : ([2,4],[3,3],[3],[1], 'csc', 'csch'),
+  'cc' : None,
+  'ss' : None,
+  'nn' : None,
+  'dd' : None
+}
+
+@defun
+def ellipfun(ctx, kind, u=None, m=None, q=None, k=None, tau=None):
+    try:
+        S = jacobi_spec[kind]
+    except KeyError:
+        raise ValueError("First argument must be a two-character string "
+            "containing 's', 'c', 'd' or 'n', e.g.: 'sn'")
+    if u is None:
+        def f(*args, **kwargs):
+            return ctx.ellipfun(kind, *args, **kwargs)
+        f.__name__ = kind
+        return f
+    prec = ctx.prec
+    try:
+        ctx.prec += 10
+        u = ctx.convert(u)
+        q = ctx.qfrom(m=m, q=q, k=k, tau=tau)
+        if S is None:
+            v = ctx.one + 0*q*u
+        elif q == ctx.zero:
+            if S[4] == '1': v = ctx.one
+            else:           v = getattr(ctx, S[4])(u)
+            v += 0*q*u
+        elif q == ctx.one:
+            if S[5] == '1': v = ctx.one
+            else:           v = getattr(ctx, S[5])(u)
+            v += 0*q*u
+        else:
+            t = u / ctx.jtheta(3, 0, q)**2
+            v = ctx.one
+            for a in S[0]: v *= ctx.jtheta(a, 0, q)
+            for b in S[1]: v /= ctx.jtheta(b, 0, q)
+            for c in S[2]: v *= ctx.jtheta(c, t, q)
+            for d in S[3]: v /= ctx.jtheta(d, t, q)
+    finally:
+        ctx.prec = prec
+    return +v
+
+@defun_wrapped
+def kleinj(ctx, tau=None, **kwargs):
+    r"""
+    Evaluates the Klein j-invariant, which is a modular function defined for
+    `\tau` in the upper half-plane as
+
+    .. math ::
+
+        J(\tau) = \frac{g_2^3(\tau)}{g_2^3(\tau) - 27 g_3^2(\tau)}
+
+    where `g_2` and `g_3` are the modular invariants of the Weierstrass
+    elliptic function,
+
+    .. math ::
+
+        g_2(\tau) = 60 \sum_{(m,n) \in \mathbb{Z}^2 \setminus (0,0)} (m \tau+n)^{-4}
+
+        g_3(\tau) = 140 \sum_{(m,n) \in \mathbb{Z}^2 \setminus (0,0)} (m \tau+n)^{-6}.
+
+    An alternative, common notation is that of the j-function
+    `j(\tau) = 1728 J(\tau)`.
+
+    **Plots**
+
+    .. literalinclude :: /plots/kleinj.py
+    .. image :: /plots/kleinj.png
+    .. literalinclude :: /plots/kleinj2.py
+    .. image :: /plots/kleinj2.png
+
+    **Examples**
+
+    Verifying the functional equation `J(\tau) = J(\tau+1) = J(-\tau^{-1})`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> tau = 0.625+0.75*j
+        >>> tau = 0.625+0.75*j
+        >>> kleinj(tau)
+        (-0.1507492166511182267125242 + 0.07595948379084571927228948j)
+        >>> kleinj(tau+1)
+        (-0.1507492166511182267125242 + 0.07595948379084571927228948j)
+        >>> kleinj(-1/tau)
+        (-0.1507492166511182267125242 + 0.07595948379084571927228946j)
+
+    The j-function has a famous Laurent series expansion in terms of the nome
+    `\bar{q}`, `j(\tau) = \bar{q}^{-1} + 744 + 196884\bar{q} + \ldots`::
+
+        >>> mp.dps = 15
+        >>> taylor(lambda q: 1728*q*kleinj(qbar=q), 0, 5, singular=True)
+        [1.0, 744.0, 196884.0, 21493760.0, 864299970.0, 20245856256.0]
+
+    The j-function admits exact evaluation at special algebraic points
+    related to the Heegner numbers 1, 2, 3, 7, 11, 19, 43, 67, 163::
+
+        >>> @extraprec(10)
+        ... def h(n):
+        ...     v = (1+sqrt(n)*j)
+        ...     if n > 2:
+        ...         v *= 0.5
+        ...     return v
+        ...
+        >>> mp.dps = 25
+        >>> for n in [1,2,3,7,11,19,43,67,163]:
+        ...     n, chop(1728*kleinj(h(n)))
+        ...
+        (1, 1728.0)
+        (2, 8000.0)
+        (3, 0.0)
+        (7, -3375.0)
+        (11, -32768.0)
+        (19, -884736.0)
+        (43, -884736000.0)
+        (67, -147197952000.0)
+        (163, -262537412640768000.0)
+
+    Also at other special points, the j-function assumes explicit
+    algebraic values, e.g.::
+
+        >>> chop(1728*kleinj(j*sqrt(5)))
+        1264538.909475140509320227
+        >>> identify(cbrt(_))      # note: not simplified
+        '((100+sqrt(13520))/2)'
+        >>> (50+26*sqrt(5))**3
+        1264538.909475140509320227
+
+    """
+    q = ctx.qfrom(tau=tau, **kwargs)
+    t2 = ctx.jtheta(2,0,q)
+    t3 = ctx.jtheta(3,0,q)
+    t4 = ctx.jtheta(4,0,q)
+    P = (t2**8 + t3**8 + t4**8)**3
+    Q = 54*(t2*t3*t4)**8
+    return P/Q
+
+
+def RF_calc(ctx, x, y, z, r):
+    if y == z: return RC_calc(ctx, x, y, r)
+    if x == z: return RC_calc(ctx, y, x, r)
+    if x == y: return RC_calc(ctx, z, x, r)
+    if not (ctx.isnormal(x) and ctx.isnormal(y) and ctx.isnormal(z)):
+        if ctx.isnan(x) or ctx.isnan(y) or ctx.isnan(z):
+            return x*y*z
+        if ctx.isinf(x) or ctx.isinf(y) or ctx.isinf(z):
+            return ctx.zero
+    xm,ym,zm = x,y,z
+    A0 = Am = (x+y+z)/3
+    Q = ctx.root(3*r, -6) * max(abs(A0-x),abs(A0-y),abs(A0-z))
+    g = ctx.mpf(0.25)
+    pow4 = ctx.one
+    while 1:
+        xs = ctx.sqrt(xm)
+        ys = ctx.sqrt(ym)
+        zs = ctx.sqrt(zm)
+        lm = xs*ys + xs*zs + ys*zs
+        Am1 = (Am+lm)*g
+        xm, ym, zm = (xm+lm)*g, (ym+lm)*g, (zm+lm)*g
+        if pow4 * Q < abs(Am):
+            break
+        Am = Am1
+        pow4 *= g
+    t = pow4/Am
+    X = (A0-x)*t
+    Y = (A0-y)*t
+    Z = -X-Y
+    E2 = X*Y-Z**2
+    E3 = X*Y*Z
+    return ctx.power(Am,-0.5) * (9240-924*E2+385*E2**2+660*E3-630*E2*E3)/9240
+
+def RC_calc(ctx, x, y, r, pv=True):
+    if not (ctx.isnormal(x) and ctx.isnormal(y)):
+        if ctx.isinf(x) or ctx.isinf(y):
+            return 1/(x*y)
+        if y == 0:
+            return ctx.inf
+        if x == 0:
+            return ctx.pi / ctx.sqrt(y) / 2
+        raise ValueError
+    # Cauchy principal value
+    if pv and ctx._im(y) == 0 and ctx._re(y) < 0:
+        return ctx.sqrt(x/(x-y)) * RC_calc(ctx, x-y, -y, r)
+    if x == y:
+        return 1/ctx.sqrt(x)
+    extraprec = 2*max(0,-ctx.mag(x-y)+ctx.mag(x))
+    ctx.prec += extraprec
+    if ctx._is_real_type(x) and ctx._is_real_type(y):
+        x = ctx._re(x)
+        y = ctx._re(y)
+        a = ctx.sqrt(x/y)
+        if x < y:
+            b = ctx.sqrt(y-x)
+            v = ctx.acos(a)/b
+        else:
+            b = ctx.sqrt(x-y)
+            v = ctx.acosh(a)/b
+    else:
+        sx = ctx.sqrt(x)
+        sy = ctx.sqrt(y)
+        v = ctx.acos(sx/sy)/(ctx.sqrt((1-x/y))*sy)
+    ctx.prec -= extraprec
+    return v
+
+def RJ_calc(ctx, x, y, z, p, r, integration):
+    """
+    With integration == 0, computes RJ only using Carlson's algorithm
+    (may be wrong for some values).
+    With integration == 1, uses an initial integration to make sure
+    Carlson's algorithm is correct.
+    With integration == 2, uses only integration.
+    """
+    if not (ctx.isnormal(x) and ctx.isnormal(y) and \
+        ctx.isnormal(z) and ctx.isnormal(p)):
+        if ctx.isnan(x) or ctx.isnan(y) or ctx.isnan(z) or ctx.isnan(p):
+            return x*y*z
+        if ctx.isinf(x) or ctx.isinf(y) or ctx.isinf(z) or ctx.isinf(p):
+            return ctx.zero
+    if not p:
+        return ctx.inf
+    if (not x) + (not y) + (not z) > 1:
+        return ctx.inf
+    # Check conditions and fall back on integration for argument
+    # reduction if needed. The following conditions might be needlessly
+    # restrictive.
+    initial_integral = ctx.zero
+    if integration >= 1:
+        ok = (x.real >= 0 and y.real >= 0 and z.real >= 0 and p.real > 0)
+        if not ok:
+            if x == p or y == p or z == p:
+                ok = True
+        if not ok:
+            if p.imag != 0 or p.real >= 0:
+                if (x.imag == 0 and x.real >= 0 and ctx.conj(y) == z):
+                    ok = True
+                if (y.imag == 0 and y.real >= 0 and ctx.conj(x) == z):
+                    ok = True
+                if (z.imag == 0 and z.real >= 0 and ctx.conj(x) == y):
+                    ok = True
+        if not ok or (integration == 2):
+            N = ctx.ceil(-min(x.real, y.real, z.real, p.real)) + 1
+            # Integrate around any singularities
+            if all((t.imag >= 0 or t.real > 0) for t in [x, y, z, p]):
+                margin = ctx.j
+            elif all((t.imag < 0 or t.real > 0) for t in [x, y, z, p]):
+                margin = -ctx.j
+            else:
+                margin = 1
+                # Go through the upper half-plane, but low enough that any
+                # parameter starting in the lower plane doesn't cross the
+                # branch cut
+                for t in [x, y, z, p]:
+                    if t.imag >= 0 or t.real > 0:
+                        continue
+                    margin = min(margin, abs(t.imag) * 0.5)
+                margin *= ctx.j
+            N += margin
+            F = lambda t: 1/(ctx.sqrt(t+x)*ctx.sqrt(t+y)*ctx.sqrt(t+z)*(t+p))
+            if integration == 2:
+                return 1.5 * ctx.quadsubdiv(F, [0, N, ctx.inf])
+            initial_integral = 1.5 * ctx.quadsubdiv(F, [0, N])
+            x += N; y += N; z += N; p += N
+    xm,ym,zm,pm = x,y,z,p
+    A0 = Am = (x + y + z + 2*p)/5
+    delta = (p-x)*(p-y)*(p-z)
+    Q = ctx.root(0.25*r, -6) * max(abs(A0-x),abs(A0-y),abs(A0-z),abs(A0-p))
+    g = ctx.mpf(0.25)
+    pow4 = ctx.one
+    S = 0
+    while 1:
+        sx = ctx.sqrt(xm)
+        sy = ctx.sqrt(ym)
+        sz = ctx.sqrt(zm)
+        sp = ctx.sqrt(pm)
+        lm = sx*sy + sx*sz + sy*sz
+        Am1 = (Am+lm)*g
+        xm = (xm+lm)*g; ym = (ym+lm)*g; zm = (zm+lm)*g; pm = (pm+lm)*g
+        dm = (sp+sx) * (sp+sy) * (sp+sz)
+        em = delta * pow4**3 / dm**2
+        if pow4 * Q < abs(Am):
+            break
+        T = RC_calc(ctx, ctx.one, ctx.one+em, r) * pow4 / dm
+        S += T
+        pow4 *= g
+        Am = Am1
+    t = pow4 / Am
+    X = (A0-x)*t
+    Y = (A0-y)*t
+    Z = (A0-z)*t
+    P = (-X-Y-Z)/2
+    E2 = X*Y + X*Z + Y*Z - 3*P**2
+    E3 = X*Y*Z + 2*E2*P + 4*P**3
+    E4 = (2*X*Y*Z + E2*P + 3*P**3)*P
+    E5 = X*Y*Z*P**2
+    P = 24024 - 5148*E2 + 2457*E2**2 + 4004*E3 - 4158*E2*E3 - 3276*E4 + 2772*E5
+    Q = 24024
+    v1 = pow4 * ctx.power(Am, -1.5) * P/Q
+    v2 = 6*S
+    return initial_integral + v1 + v2
+
+@defun
+def elliprf(ctx, x, y, z):
+    r"""
+    Evaluates the Carlson symmetric elliptic integral of the first kind
+
+    .. math ::
+
+        R_F(x,y,z) = \frac{1}{2}
+            \int_0^{\infty} \frac{dt}{\sqrt{(t+x)(t+y)(t+z)}}
+
+    which is defined for `x,y,z \notin (-\infty,0)`, and with
+    at most one of `x,y,z` being zero.
+
+    For real `x,y,z \ge 0`, the principal square root is taken in the integrand.
+    For complex `x,y,z`, the principal square root is taken as `t \to \infty`
+    and as `t \to 0` non-principal branches are chosen as necessary so as to
+    make the integrand continuous.
+
+    **Examples**
+
+    Some basic values and limits::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> elliprf(0,1,1); pi/2
+        1.570796326794896619231322
+        1.570796326794896619231322
+        >>> elliprf(0,1,inf)
+        0.0
+        >>> elliprf(1,1,1)
+        1.0
+        >>> elliprf(2,2,2)**2
+        0.5
+        >>> elliprf(1,0,0); elliprf(0,0,1); elliprf(0,1,0); elliprf(0,0,0)
+        +inf
+        +inf
+        +inf
+        +inf
+
+    Representing complete elliptic integrals in terms of `R_F`::
+
+        >>> m = mpf(0.75)
+        >>> ellipk(m); elliprf(0,1-m,1)
+        2.156515647499643235438675
+        2.156515647499643235438675
+        >>> ellipe(m); elliprf(0,1-m,1)-m*elliprd(0,1-m,1)/3
+        1.211056027568459524803563
+        1.211056027568459524803563
+
+    Some symmetries and argument transformations::
+
+        >>> x,y,z = 2,3,4
+        >>> elliprf(x,y,z); elliprf(y,x,z); elliprf(z,y,x)
+        0.5840828416771517066928492
+        0.5840828416771517066928492
+        0.5840828416771517066928492
+        >>> k = mpf(100000)
+        >>> elliprf(k*x,k*y,k*z); k**(-0.5) * elliprf(x,y,z)
+        0.001847032121923321253219284
+        0.001847032121923321253219284
+        >>> l = sqrt(x*y) + sqrt(y*z) + sqrt(z*x)
+        >>> elliprf(x,y,z); 2*elliprf(x+l,y+l,z+l)
+        0.5840828416771517066928492
+        0.5840828416771517066928492
+        >>> elliprf((x+l)/4,(y+l)/4,(z+l)/4)
+        0.5840828416771517066928492
+
+    Comparing with numerical integration::
+
+        >>> x,y,z = 2,3,4
+        >>> elliprf(x,y,z)
+        0.5840828416771517066928492
+        >>> f = lambda t: 0.5*((t+x)*(t+y)*(t+z))**(-0.5)
+        >>> q = extradps(25)(quad)
+        >>> q(f, [0,inf])
+        0.5840828416771517066928492
+
+    With the following arguments, the square root in the integrand becomes
+    discontinuous at `t = 1/2` if the principal branch is used. To obtain
+    the right value, `-\sqrt{r}` must be taken instead of `\sqrt{r}`
+    on `t \in (0, 1/2)`::
+
+        >>> x,y,z = j-1,j,0
+        >>> elliprf(x,y,z)
+        (0.7961258658423391329305694 - 1.213856669836495986430094j)
+        >>> -q(f, [0,0.5]) + q(f, [0.5,inf])
+        (0.7961258658423391329305694 - 1.213856669836495986430094j)
+
+    The so-called *first lemniscate constant*, a transcendental number::
+
+        >>> elliprf(0,1,2)
+        1.31102877714605990523242
+        >>> extradps(25)(quad)(lambda t: 1/sqrt(1-t**4), [0,1])
+        1.31102877714605990523242
+        >>> gamma('1/4')**2/(4*sqrt(2*pi))
+        1.31102877714605990523242
+
+    **References**
+
+    1. [Carlson]_
+    2. [DLMF]_ Chapter 19. Elliptic Integrals
+
+    """
+    x = ctx.convert(x)
+    y = ctx.convert(y)
+    z = ctx.convert(z)
+    prec = ctx.prec
+    try:
+        ctx.prec += 20
+        tol = ctx.eps * 2**10
+        v = RF_calc(ctx, x, y, z, tol)
+    finally:
+        ctx.prec = prec
+    return +v
+
+@defun
+def elliprc(ctx, x, y, pv=True):
+    r"""
+    Evaluates the degenerate Carlson symmetric elliptic integral
+    of the first kind
+
+    .. math ::
+
+        R_C(x,y) = R_F(x,y,y) =
+            \frac{1}{2} \int_0^{\infty} \frac{dt}{(t+y) \sqrt{(t+x)}}.
+
+    If `y \in (-\infty,0)`, either a value defined by continuity,
+    or with *pv=True* the Cauchy principal value, can be computed.
+
+    If `x \ge 0, y > 0`, the value can be expressed in terms of
+    elementary functions as
+
+    .. math ::
+
+        R_C(x,y) =
+        \begin{cases}
+          \dfrac{1}{\sqrt{y-x}}
+            \cos^{-1}\left(\sqrt{\dfrac{x}{y}}\right),   & x < y \\
+          \dfrac{1}{\sqrt{y}},                          & x = y \\
+          \dfrac{1}{\sqrt{x-y}}
+            \cosh^{-1}\left(\sqrt{\dfrac{x}{y}}\right),  & x > y \\
+        \end{cases}.
+
+    **Examples**
+
+    Some special values and limits::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> elliprc(1,2)*4; elliprc(0,1)*2; +pi
+        3.141592653589793238462643
+        3.141592653589793238462643
+        3.141592653589793238462643
+        >>> elliprc(1,0)
+        +inf
+        >>> elliprc(5,5)**2
+        0.2
+        >>> elliprc(1,inf); elliprc(inf,1); elliprc(inf,inf)
+        0.0
+        0.0
+        0.0
+
+    Comparing with the elementary closed-form solution::
+
+        >>> elliprc('1/3', '1/5'); sqrt(7.5)*acosh(sqrt('5/3'))
+        2.041630778983498390751238
+        2.041630778983498390751238
+        >>> elliprc('1/5', '1/3'); sqrt(7.5)*acos(sqrt('3/5'))
+        1.875180765206547065111085
+        1.875180765206547065111085
+
+    Comparing with numerical integration::
+
+        >>> q = extradps(25)(quad)
+        >>> elliprc(2, -3, pv=True)
+        0.3333969101113672670749334
+        >>> elliprc(2, -3, pv=False)
+        (0.3333969101113672670749334 + 0.7024814731040726393156375j)
+        >>> 0.5*q(lambda t: 1/(sqrt(t+2)*(t-3)), [0,3-j,6,inf])
+        (0.3333969101113672670749334 + 0.7024814731040726393156375j)
+
+    """
+    x = ctx.convert(x)
+    y = ctx.convert(y)
+    prec = ctx.prec
+    try:
+        ctx.prec += 20
+        tol = ctx.eps * 2**10
+        v = RC_calc(ctx, x, y, tol, pv)
+    finally:
+        ctx.prec = prec
+    return +v
+
+@defun
+def elliprj(ctx, x, y, z, p, integration=1):
+    r"""
+    Evaluates the Carlson symmetric elliptic integral of the third kind
+
+    .. math ::
+
+        R_J(x,y,z,p) = \frac{3}{2}
+            \int_0^{\infty} \frac{dt}{(t+p)\sqrt{(t+x)(t+y)(t+z)}}.
+
+    Like :func:`~mpmath.elliprf`, the branch of the square root in the integrand
+    is defined so as to be continuous along the path of integration for
+    complex values of the arguments.
+
+    **Examples**
+
+    Some values and limits::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> elliprj(1,1,1,1)
+        1.0
+        >>> elliprj(2,2,2,2); 1/(2*sqrt(2))
+        0.3535533905932737622004222
+        0.3535533905932737622004222
+        >>> elliprj(0,1,2,2)
+        1.067937989667395702268688
+        >>> 3*(2*gamma('5/4')**2-pi**2/gamma('1/4')**2)/(sqrt(2*pi))
+        1.067937989667395702268688
+        >>> elliprj(0,1,1,2); 3*pi*(2-sqrt(2))/4
+        1.380226776765915172432054
+        1.380226776765915172432054
+        >>> elliprj(1,3,2,0); elliprj(0,1,1,0); elliprj(0,0,0,0)
+        +inf
+        +inf
+        +inf
+        >>> elliprj(1,inf,1,0); elliprj(1,1,1,inf)
+        0.0
+        0.0
+        >>> chop(elliprj(1+j, 1-j, 1, 1))
+        0.8505007163686739432927844
+
+    Scale transformation::
+
+        >>> x,y,z,p = 2,3,4,5
+        >>> k = mpf(100000)
+        >>> elliprj(k*x,k*y,k*z,k*p); k**(-1.5)*elliprj(x,y,z,p)
+        4.521291677592745527851168e-9
+        4.521291677592745527851168e-9
+
+    Comparing with numerical integration::
+
+        >>> elliprj(1,2,3,4)
+        0.2398480997495677621758617
+        >>> f = lambda t: 1/((t+4)*sqrt((t+1)*(t+2)*(t+3)))
+        >>> 1.5*quad(f, [0,inf])
+        0.2398480997495677621758617
+        >>> elliprj(1,2+1j,3,4-2j)
+        (0.216888906014633498739952 + 0.04081912627366673332369512j)
+        >>> f = lambda t: 1/((t+4-2j)*sqrt((t+1)*(t+2+1j)*(t+3)))
+        >>> 1.5*quad(f, [0,inf])
+        (0.216888906014633498739952 + 0.04081912627366673332369511j)
+
+    """
+    x = ctx.convert(x)
+    y = ctx.convert(y)
+    z = ctx.convert(z)
+    p = ctx.convert(p)
+    prec = ctx.prec
+    try:
+        ctx.prec += 20
+        tol = ctx.eps * 2**10
+        v = RJ_calc(ctx, x, y, z, p, tol, integration)
+    finally:
+        ctx.prec = prec
+    return +v
+
+@defun
+def elliprd(ctx, x, y, z):
+    r"""
+    Evaluates the degenerate Carlson symmetric elliptic integral
+    of the third kind or Carlson elliptic integral of the
+    second kind `R_D(x,y,z) = R_J(x,y,z,z)`.
+
+    See :func:`~mpmath.elliprj` for additional information.
+
+    **Examples**
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> elliprd(1,2,3)
+        0.2904602810289906442326534
+        >>> elliprj(1,2,3,3)
+        0.2904602810289906442326534
+
+    The so-called *second lemniscate constant*, a transcendental number::
+
+        >>> elliprd(0,2,1)/3
+        0.5990701173677961037199612
+        >>> extradps(25)(quad)(lambda t: t**2/sqrt(1-t**4), [0,1])
+        0.5990701173677961037199612
+        >>> gamma('3/4')**2/sqrt(2*pi)
+        0.5990701173677961037199612
+
+    """
+    return ctx.elliprj(x,y,z,z)
+
+@defun
+def elliprg(ctx, x, y, z):
+    r"""
+    Evaluates the Carlson completely symmetric elliptic integral
+    of the second kind
+
+    .. math ::
+
+        R_G(x,y,z) = \frac{1}{4} \int_0^{\infty}
+            \frac{t}{\sqrt{(t+x)(t+y)(t+z)}}
+            \left( \frac{x}{t+x} + \frac{y}{t+y} + \frac{z}{t+z}\right) dt.
+
+    **Examples**
+
+    Evaluation for real and complex arguments::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> elliprg(0,1,1)*4; +pi
+        3.141592653589793238462643
+        3.141592653589793238462643
+        >>> elliprg(0,0.5,1)
+        0.6753219405238377512600874
+        >>> chop(elliprg(1+j, 1-j, 2))
+        1.172431327676416604532822
+
+    A double integral that can be evaluated in terms of `R_G`::
+
+        >>> x,y,z = 2,3,4
+        >>> def f(t,u):
+        ...     st = fp.sin(t); ct = fp.cos(t)
+        ...     su = fp.sin(u); cu = fp.cos(u)
+        ...     return (x*(st*cu)**2 + y*(st*su)**2 + z*ct**2)**0.5 * st
+        ...
+        >>> nprint(mpf(fp.quad(f, [0,fp.pi], [0,2*fp.pi])/(4*fp.pi)), 13)
+        1.725503028069
+        >>> nprint(elliprg(x,y,z), 13)
+        1.725503028069
+
+    """
+    x = ctx.convert(x)
+    y = ctx.convert(y)
+    z = ctx.convert(z)
+    zeros = (not x) + (not y) + (not z)
+    if zeros == 3:
+        return (x+y+z)*0
+    if zeros == 2:
+        if x: return 0.5*ctx.sqrt(x)
+        if y: return 0.5*ctx.sqrt(y)
+        return 0.5*ctx.sqrt(z)
+    if zeros == 1:
+        if not z:
+            x, z = z, x
+    def terms():
+        T1 = 0.5*z*ctx.elliprf(x,y,z)
+        T2 = -0.5*(x-z)*(y-z)*ctx.elliprd(x,y,z)/3
+        T3 = 0.5*ctx.sqrt(x)*ctx.sqrt(y)/ctx.sqrt(z)
+        return T1,T2,T3
+    return ctx.sum_accurately(terms)
+
+
+@defun_wrapped
+def ellipf(ctx, phi, m):
+    r"""
+    Evaluates the Legendre incomplete elliptic integral of the first kind
+
+     .. math ::
+
+        F(\phi,m) = \int_0^{\phi} \frac{dt}{\sqrt{1-m \sin^2 t}}
+
+    or equivalently
+
+    .. math ::
+
+        F(\phi,m) = \int_0^{\sin \phi}
+        \frac{dt}{\left(\sqrt{1-t^2}\right)\left(\sqrt{1-mt^2}\right)}.
+
+    The function reduces to a complete elliptic integral of the first kind
+    (see :func:`~mpmath.ellipk`) when `\phi = \frac{\pi}{2}`; that is,
+
+    .. math ::
+
+        F\left(\frac{\pi}{2}, m\right) = K(m).
+
+    In the defining integral, it is assumed that the principal branch
+    of the square root is taken and that the path of integration avoids
+    crossing any branch cuts. Outside `-\pi/2 \le \Re(\phi) \le \pi/2`,
+    the function extends quasi-periodically as
+
+    .. math ::
+
+        F(\phi + n \pi, m) = 2 n K(m) + F(\phi,m), n \in \mathbb{Z}.
+
+    **Plots**
+
+    .. literalinclude :: /plots/ellipf.py
+    .. image :: /plots/ellipf.png
+
+    **Examples**
+
+    Basic values and limits::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> ellipf(0,1)
+        0.0
+        >>> ellipf(0,0)
+        0.0
+        >>> ellipf(1,0); ellipf(2+3j,0)
+        1.0
+        (2.0 + 3.0j)
+        >>> ellipf(1,1); log(sec(1)+tan(1))
+        1.226191170883517070813061
+        1.226191170883517070813061
+        >>> ellipf(pi/2, -0.5); ellipk(-0.5)
+        1.415737208425956198892166
+        1.415737208425956198892166
+        >>> ellipf(pi/2+eps, 1); ellipf(-pi/2-eps, 1)
+        +inf
+        +inf
+        >>> ellipf(1.5, 1)
+        3.340677542798311003320813
+
+    Comparing with numerical integration::
+
+        >>> z,m = 0.5, 1.25
+        >>> ellipf(z,m)
+        0.5287219202206327872978255
+        >>> quad(lambda t: (1-m*sin(t)**2)**(-0.5), [0,z])
+        0.5287219202206327872978255
+
+    The arguments may be complex numbers::
+
+        >>> ellipf(3j, 0.5)
+        (0.0 + 1.713602407841590234804143j)
+        >>> ellipf(3+4j, 5-6j)
+        (1.269131241950351323305741 - 0.3561052815014558335412538j)
+        >>> z,m = 2+3j, 1.25
+        >>> k = 1011
+        >>> ellipf(z+pi*k,m); ellipf(z,m) + 2*k*ellipk(m)
+        (4086.184383622179764082821 - 3003.003538923749396546871j)
+        (4086.184383622179764082821 - 3003.003538923749396546871j)
+
+    For `|\Re(z)| < \pi/2`, the function can be expressed as a
+    hypergeometric series of two variables
+    (see :func:`~mpmath.appellf1`)::
+
+        >>> z,m = 0.5, 0.25
+        >>> ellipf(z,m)
+        0.5050887275786480788831083
+        >>> sin(z)*appellf1(0.5,0.5,0.5,1.5,sin(z)**2,m*sin(z)**2)
+        0.5050887275786480788831083
+
+    """
+    z = phi
+    if not (ctx.isnormal(z) and ctx.isnormal(m)):
+        if m == 0:
+            return z + m
+        if z == 0:
+            return z * m
+        if m == ctx.inf or m == ctx.ninf: return z/m
+        raise ValueError
+    x = z.real
+    ctx.prec += max(0, ctx.mag(x))
+    pi = +ctx.pi
+    away = abs(x) > pi/2
+    if m == 1:
+        if away:
+            return ctx.inf
+    if away:
+        d = ctx.nint(x/pi)
+        z = z-pi*d
+        P = 2*d*ctx.ellipk(m)
+    else:
+        P = 0
+    c, s = ctx.cos_sin(z)
+    return s * ctx.elliprf(c**2, 1-m*s**2, 1) + P
+
+@defun_wrapped
+def ellipe(ctx, *args):
+    r"""
+    Called with a single argument `m`, evaluates the Legendre complete
+    elliptic integral of the second kind, `E(m)`, defined by
+
+        .. math :: E(m) = \int_0^{\pi/2} \sqrt{1-m \sin^2 t} \, dt \,=\,
+            \frac{\pi}{2}
+            \,_2F_1\left(\frac{1}{2}, -\frac{1}{2}, 1, m\right).
+
+    Called with two arguments `\phi, m`, evaluates the incomplete elliptic
+    integral of the second kind
+
+     .. math ::
+
+        E(\phi,m) = \int_0^{\phi} \sqrt{1-m \sin^2 t} \, dt =
+                    \int_0^{\sin z}
+                    \frac{\sqrt{1-mt^2}}{\sqrt{1-t^2}} \, dt.
+
+    The incomplete integral reduces to a complete integral when
+    `\phi = \frac{\pi}{2}`; that is,
+
+    .. math ::
+
+        E\left(\frac{\pi}{2}, m\right) = E(m).
+
+    In the defining integral, it is assumed that the principal branch
+    of the square root is taken and that the path of integration avoids
+    crossing any branch cuts. Outside `-\pi/2 \le \Re(z) \le \pi/2`,
+    the function extends quasi-periodically as
+
+    .. math ::
+
+        E(\phi + n \pi, m) = 2 n E(m) + E(\phi,m), n \in \mathbb{Z}.
+
+    **Plots**
+
+    .. literalinclude :: /plots/ellipe.py
+    .. image :: /plots/ellipe.png
+
+    **Examples for the complete integral**
+
+    Basic values and limits::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> ellipe(0)
+        1.570796326794896619231322
+        >>> ellipe(1)
+        1.0
+        >>> ellipe(-1)
+        1.910098894513856008952381
+        >>> ellipe(2)
+        (0.5990701173677961037199612 + 0.5990701173677961037199612j)
+        >>> ellipe(inf)
+        (0.0 + +infj)
+        >>> ellipe(-inf)
+        +inf
+
+    Verifying the defining integral and hypergeometric
+    representation::
+
+        >>> ellipe(0.5)
+        1.350643881047675502520175
+        >>> quad(lambda t: sqrt(1-0.5*sin(t)**2), [0, pi/2])
+        1.350643881047675502520175
+        >>> pi/2*hyp2f1(0.5,-0.5,1,0.5)
+        1.350643881047675502520175
+
+    Evaluation is supported for arbitrary complex `m`::
+
+        >>> ellipe(0.5+0.25j)
+        (1.360868682163129682716687 - 0.1238733442561786843557315j)
+        >>> ellipe(3+4j)
+        (1.499553520933346954333612 - 1.577879007912758274533309j)
+
+    A definite integral::
+
+        >>> quad(ellipe, [0,1])
+        1.333333333333333333333333
+
+    **Examples for the incomplete integral**
+
+    Basic values and limits::
+
+        >>> ellipe(0,1)
+        0.0
+        >>> ellipe(0,0)
+        0.0
+        >>> ellipe(1,0)
+        1.0
+        >>> ellipe(2+3j,0)
+        (2.0 + 3.0j)
+        >>> ellipe(1,1); sin(1)
+        0.8414709848078965066525023
+        0.8414709848078965066525023
+        >>> ellipe(pi/2, -0.5); ellipe(-0.5)
+        1.751771275694817862026502
+        1.751771275694817862026502
+        >>> ellipe(pi/2, 1); ellipe(-pi/2, 1)
+        1.0
+        -1.0
+        >>> ellipe(1.5, 1)
+        0.9974949866040544309417234
+
+    Comparing with numerical integration::
+
+        >>> z,m = 0.5, 1.25
+        >>> ellipe(z,m)
+        0.4740152182652628394264449
+        >>> quad(lambda t: sqrt(1-m*sin(t)**2), [0,z])
+        0.4740152182652628394264449
+
+    The arguments may be complex numbers::
+
+        >>> ellipe(3j, 0.5)
+        (0.0 + 7.551991234890371873502105j)
+        >>> ellipe(3+4j, 5-6j)
+        (24.15299022574220502424466 + 75.2503670480325997418156j)
+        >>> k = 35
+        >>> z,m = 2+3j, 1.25
+        >>> ellipe(z+pi*k,m); ellipe(z,m) + 2*k*ellipe(m)
+        (48.30138799412005235090766 + 17.47255216721987688224357j)
+        (48.30138799412005235090766 + 17.47255216721987688224357j)
+
+    For `|\Re(z)| < \pi/2`, the function can be expressed as a
+    hypergeometric series of two variables
+    (see :func:`~mpmath.appellf1`)::
+
+        >>> z,m = 0.5, 0.25
+        >>> ellipe(z,m)
+        0.4950017030164151928870375
+        >>> sin(z)*appellf1(0.5,0.5,-0.5,1.5,sin(z)**2,m*sin(z)**2)
+        0.4950017030164151928870376
+
+    """
+    if len(args) == 1:
+        return ctx._ellipe(args[0])
+    else:
+        phi, m = args
+    z = phi
+    if not (ctx.isnormal(z) and ctx.isnormal(m)):
+        if m == 0:
+            return z + m
+        if z == 0:
+            return z * m
+        if m == ctx.inf or m == ctx.ninf:
+            return ctx.inf
+        raise ValueError
+    x = z.real
+    ctx.prec += max(0, ctx.mag(x))
+    pi = +ctx.pi
+    away = abs(x) > pi/2
+    if away:
+        d = ctx.nint(x/pi)
+        z = z-pi*d
+        P = 2*d*ctx.ellipe(m)
+    else:
+        P = 0
+    def terms():
+        c, s = ctx.cos_sin(z)
+        x = c**2
+        y = 1-m*s**2
+        RF = ctx.elliprf(x, y, 1)
+        RD = ctx.elliprd(x, y, 1)
+        return s*RF, -m*s**3*RD/3
+    return ctx.sum_accurately(terms) + P
+
+@defun_wrapped
+def ellippi(ctx, *args):
+    r"""
+    Called with three arguments `n, \phi, m`, evaluates the Legendre
+    incomplete elliptic integral of the third kind
+
+    .. math ::
+
+        \Pi(n; \phi, m) = \int_0^{\phi}
+            \frac{dt}{(1-n \sin^2 t) \sqrt{1-m \sin^2 t}} =
+            \int_0^{\sin \phi}
+            \frac{dt}{(1-nt^2) \sqrt{1-t^2} \sqrt{1-mt^2}}.
+
+    Called with two arguments `n, m`, evaluates the complete
+    elliptic integral of the third kind
+    `\Pi(n,m) = \Pi(n; \frac{\pi}{2},m)`.
+
+    In the defining integral, it is assumed that the principal branch
+    of the square root is taken and that the path of integration avoids
+    crossing any branch cuts. Outside `-\pi/2 \le \Re(\phi) \le \pi/2`,
+    the function extends quasi-periodically as
+
+    .. math ::
+
+        \Pi(n,\phi+k\pi,m) = 2k\Pi(n,m) + \Pi(n,\phi,m), k \in \mathbb{Z}.
+
+    **Plots**
+
+    .. literalinclude :: /plots/ellippi.py
+    .. image :: /plots/ellippi.png
+
+    **Examples for the complete integral**
+
+    Some basic values and limits::
+
+        >>> from mpmath import *
+        >>> mp.dps = 25; mp.pretty = True
+        >>> ellippi(0,-5); ellipk(-5)
+        0.9555039270640439337379334
+        0.9555039270640439337379334
+        >>> ellippi(inf,2)
+        0.0
+        >>> ellippi(2,inf)
+        0.0
+        >>> abs(ellippi(1,5))
+        +inf
+        >>> abs(ellippi(0.25,1))
+        +inf
+
+    Evaluation in terms of simpler functions::
+
+        >>> ellippi(0.25,0.25); ellipe(0.25)/(1-0.25)
+        1.956616279119236207279727
+        1.956616279119236207279727
+        >>> ellippi(3,0); pi/(2*sqrt(-2))
+        (0.0 - 1.11072073453959156175397j)
+        (0.0 - 1.11072073453959156175397j)
+        >>> ellippi(-3,0); pi/(2*sqrt(4))
+        0.7853981633974483096156609
+        0.7853981633974483096156609
+
+    **Examples for the incomplete integral**
+
+    Basic values and limits::
+
+        >>> ellippi(0.25,-0.5); ellippi(0.25,pi/2,-0.5)
+        1.622944760954741603710555
+        1.622944760954741603710555
+        >>> ellippi(1,0,1)
+        0.0
+        >>> ellippi(inf,0,1)
+        0.0
+        >>> ellippi(0,0.25,0.5); ellipf(0.25,0.5)
+        0.2513040086544925794134591
+        0.2513040086544925794134591
+        >>> ellippi(1,1,1); (log(sec(1)+tan(1))+sec(1)*tan(1))/2
+        2.054332933256248668692452
+        2.054332933256248668692452
+        >>> ellippi(0.25, 53*pi/2, 0.75); 53*ellippi(0.25,0.75)
+        135.240868757890840755058
+        135.240868757890840755058
+        >>> ellippi(0.5,pi/4,0.5); 2*ellipe(pi/4,0.5)-1/sqrt(3)
+        0.9190227391656969903987269
+        0.9190227391656969903987269
+
+    Complex arguments are supported::
+
+        >>> ellippi(0.5, 5+6j-2*pi, -7-8j)
+        (-0.3612856620076747660410167 + 0.5217735339984807829755815j)
+
+    Some degenerate cases::
+
+        >>> ellippi(1,1)
+        +inf
+        >>> ellippi(1,0)
+        +inf
+        >>> ellippi(1,2,0)
+        +inf
+        >>> ellippi(1,2,1)
+        +inf
+        >>> ellippi(1,0,1)
+        0.0
+
+    """
+    if len(args) == 2:
+        n, m = args
+        complete = True
+        z = phi = ctx.pi/2
+    else:
+        n, phi, m = args
+        complete = False
+        z = phi
+    if not (ctx.isnormal(n) and ctx.isnormal(z) and ctx.isnormal(m)):
+        if ctx.isnan(n) or ctx.isnan(z) or ctx.isnan(m):
+            raise ValueError
+        if complete:
+            if m == 0:
+                if n == 1:
+                    return ctx.inf
+                return ctx.pi/(2*ctx.sqrt(1-n))
+            if n == 0: return ctx.ellipk(m)
+            if ctx.isinf(n) or ctx.isinf(m): return ctx.zero
+        else:
+            if z == 0: return z
+            if ctx.isinf(n): return ctx.zero
+            if ctx.isinf(m): return ctx.zero
+        if ctx.isinf(n) or ctx.isinf(z) or ctx.isinf(m):
+            raise ValueError
+    if complete:
+        if m == 1:
+            if n == 1:
+                return ctx.inf
+            return -ctx.inf/ctx.sign(n-1)
+        away = False
+    else:
+        x = z.real
+        ctx.prec += max(0, ctx.mag(x))
+        pi = +ctx.pi
+        away = abs(x) > pi/2
+    if away:
+        d = ctx.nint(x/pi)
+        z = z-pi*d
+        P = 2*d*ctx.ellippi(n,m)
+        if ctx.isinf(P):
+            return ctx.inf
+    else:
+        P = 0
+    def terms():
+        if complete:
+            c, s = ctx.zero, ctx.one
+        else:
+            c, s = ctx.cos_sin(z)
+        x = c**2
+        y = 1-m*s**2
+        RF = ctx.elliprf(x, y, 1)
+        RJ = ctx.elliprj(x, y, 1, 1-n*s**2)
+        return s*RF, n*s**3*RJ/3
+    return ctx.sum_accurately(terms) + P