| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| |
|
| | #ifndef EIGEN_MATHFUNCTIONSIMPL_H |
| | #define EIGEN_MATHFUNCTIONSIMPL_H |
| |
|
| | namespace Eigen { |
| |
|
| | namespace internal { |
| |
|
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | template<typename T> |
| | T generic_fast_tanh_float(const T& a_x) |
| | { |
| | |
| | #ifdef EIGEN_VECTORIZE_FMA |
| | const T plus_clamp = pset1<T>(7.99881172180175781f); |
| | const T minus_clamp = pset1<T>(-7.99881172180175781f); |
| | #else |
| | const T plus_clamp = pset1<T>(7.90531110763549805f); |
| | const T minus_clamp = pset1<T>(-7.90531110763549805f); |
| | #endif |
| | const T tiny = pset1<T>(0.0004f); |
| | const T x = pmax(pmin(a_x, plus_clamp), minus_clamp); |
| | const T tiny_mask = pcmp_lt(pabs(a_x), tiny); |
| | |
| | const T alpha_1 = pset1<T>(4.89352455891786e-03f); |
| | const T alpha_3 = pset1<T>(6.37261928875436e-04f); |
| | const T alpha_5 = pset1<T>(1.48572235717979e-05f); |
| | const T alpha_7 = pset1<T>(5.12229709037114e-08f); |
| | const T alpha_9 = pset1<T>(-8.60467152213735e-11f); |
| | const T alpha_11 = pset1<T>(2.00018790482477e-13f); |
| | const T alpha_13 = pset1<T>(-2.76076847742355e-16f); |
| |
|
| | |
| | const T beta_0 = pset1<T>(4.89352518554385e-03f); |
| | const T beta_2 = pset1<T>(2.26843463243900e-03f); |
| | const T beta_4 = pset1<T>(1.18534705686654e-04f); |
| | const T beta_6 = pset1<T>(1.19825839466702e-06f); |
| |
|
| | |
| | const T x2 = pmul(x, x); |
| |
|
| | |
| | T p = pmadd(x2, alpha_13, alpha_11); |
| | p = pmadd(x2, p, alpha_9); |
| | p = pmadd(x2, p, alpha_7); |
| | p = pmadd(x2, p, alpha_5); |
| | p = pmadd(x2, p, alpha_3); |
| | p = pmadd(x2, p, alpha_1); |
| | p = pmul(x, p); |
| |
|
| | |
| | T q = pmadd(x2, beta_6, beta_4); |
| | q = pmadd(x2, q, beta_2); |
| | q = pmadd(x2, q, beta_0); |
| |
|
| | |
| | return pselect(tiny_mask, x, pdiv(p, q)); |
| | } |
| |
|
| | template<typename RealScalar> |
| | EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE |
| | RealScalar positive_real_hypot(const RealScalar& x, const RealScalar& y) |
| | { |
| | |
| | if ((numext::isinf)(x) || (numext::isinf)(y)) |
| | return NumTraits<RealScalar>::infinity(); |
| | if ((numext::isnan)(x) || (numext::isnan)(y)) |
| | return NumTraits<RealScalar>::quiet_NaN(); |
| | |
| | EIGEN_USING_STD(sqrt); |
| | RealScalar p, qp; |
| | p = numext::maxi(x,y); |
| | if(p==RealScalar(0)) return RealScalar(0); |
| | qp = numext::mini(y,x) / p; |
| | return p * sqrt(RealScalar(1) + qp*qp); |
| | } |
| |
|
| | template<typename Scalar> |
| | struct hypot_impl |
| | { |
| | typedef typename NumTraits<Scalar>::Real RealScalar; |
| | static EIGEN_DEVICE_FUNC |
| | inline RealScalar run(const Scalar& x, const Scalar& y) |
| | { |
| | EIGEN_USING_STD(abs); |
| | return positive_real_hypot<RealScalar>(abs(x), abs(y)); |
| | } |
| | }; |
| |
|
| | |
| | |
| | template<typename T> |
| | EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& z) { |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| |
|
| | const T x = numext::real(z); |
| | const T y = numext::imag(z); |
| | const T zero = T(0); |
| | const T w = numext::sqrt(T(0.5) * (numext::abs(x) + numext::hypot(x, y))); |
| |
|
| | return |
| | (numext::isinf)(y) ? std::complex<T>(NumTraits<T>::infinity(), y) |
| | : x == zero ? std::complex<T>(w, y < zero ? -w : w) |
| | : x > zero ? std::complex<T>(w, y / (2 * w)) |
| | : std::complex<T>(numext::abs(y) / (2 * w), y < zero ? -w : w ); |
| | } |
| |
|
| | |
| | template<typename T> |
| | EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& z) { |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| |
|
| | const T x = numext::real(z); |
| | const T y = numext::imag(z); |
| | const T zero = T(0); |
| |
|
| | const T abs_z = numext::hypot(x, y); |
| | const T w = numext::sqrt(T(0.5) * (numext::abs(x) + abs_z)); |
| | const T woz = w / abs_z; |
| | |
| | return |
| | abs_z == zero ? std::complex<T>(NumTraits<T>::infinity(), NumTraits<T>::quiet_NaN()) |
| | : ((numext::isinf)(x) || (numext::isinf)(y)) ? std::complex<T>(zero, zero) |
| | : x == zero ? std::complex<T>(woz, y < zero ? woz : -woz) |
| | : x > zero ? std::complex<T>(woz, -y / (2 * w * abs_z)) |
| | : std::complex<T>(numext::abs(y) / (2 * w * abs_z), y < zero ? woz : -woz ); |
| | } |
| |
|
| | template<typename T> |
| | EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z) { |
| | |
| | T a = numext::abs(z); |
| | EIGEN_USING_STD(atan2); |
| | T b = atan2(z.imag(), z.real()); |
| | return std::complex<T>(numext::log(a), b); |
| | } |
| |
|
| | } |
| |
|
| | } |
| |
|
| | #endif |
| |
|