| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com) |
| // |
| // This Source Code Form is subject to the terms of the Mozilla |
| // Public License v. 2.0. If a copy of the MPL was not distributed |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| |
| #ifndef EIGEN_MATH_FUNCTIONS_AVX_H |
| #define EIGEN_MATH_FUNCTIONS_AVX_H |
| |
| /* The sin and cos functions of this file are loosely derived from |
| * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/ |
| */ |
| |
| namespace Eigen { |
| |
| namespace internal { |
| |
| template <> |
| EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f |
| psin<Packet8f>(const Packet8f& _x) { |
| return psin_float(_x); |
| } |
| |
| template <> |
| EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f |
| pcos<Packet8f>(const Packet8f& _x) { |
| return pcos_float(_x); |
| } |
| |
| template <> |
| EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f |
| plog<Packet8f>(const Packet8f& _x) { |
| return plog_float(_x); |
| } |
| |
| // Exponential function. Works by writing "x = m*log(2) + r" where |
| // "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then |
| // "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1). |
| template <> |
| EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f |
| pexp<Packet8f>(const Packet8f& _x) { |
| return pexp_float(_x); |
| } |
| |
| // Hyperbolic Tangent function. |
| template <> |
| EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f |
| ptanh<Packet8f>(const Packet8f& x) { |
| return internal::generic_fast_tanh_float(x); |
| } |
| |
| template <> |
| EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4d |
| pexp<Packet4d>(const Packet4d& x) { |
| return pexp_double(x); |
| } |
| |
| // Functions for sqrt. |
| // The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step |
| // of Newton's method, at a cost of 1-2 bits of precision as opposed to the |
| // exact solution. It does not handle +inf, or denormalized numbers correctly. |
| // The main advantage of this approach is not just speed, but also the fact that |
| // it can be inlined and pipelined with other computations, further reducing its |
| // effective latency. This is similar to Quake3's fast inverse square root. |
| // For detail see here: http://www.beyond3d.com/content/articles/8/ |
| #if EIGEN_FAST_MATH |
| template <> |
| EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f |
| psqrt<Packet8f>(const Packet8f& _x) { |
| Packet8f half = pmul(_x, pset1<Packet8f>(.5f)); |
| Packet8f denormal_mask = _mm256_and_ps( |
| _mm256_cmp_ps(_x, pset1<Packet8f>((std::numeric_limits<float>::min)()), |
| _CMP_LT_OQ), |
| _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_GE_OQ)); |
| |
| // Compute approximate reciprocal sqrt. |
| Packet8f x = _mm256_rsqrt_ps(_x); |
| // Do a single step of Newton's iteration. |
| x = pmul(x, psub(pset1<Packet8f>(1.5f), pmul(half, pmul(x,x)))); |
| // Flush results for denormals to zero. |
| return _mm256_andnot_ps(denormal_mask, pmul(_x,x)); |
| } |
| #else |
| template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED |
| Packet8f psqrt<Packet8f>(const Packet8f& x) { |
| return _mm256_sqrt_ps(x); |
| } |
| #endif |
| template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED |
| Packet4d psqrt<Packet4d>(const Packet4d& x) { |
| return _mm256_sqrt_pd(x); |
| } |
| #if EIGEN_FAST_MATH |
| |
| template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED |
| Packet8f prsqrt<Packet8f>(const Packet8f& _x) { |
| _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inf, 0x7f800000); |
| _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(nan, 0x7fc00000); |
| _EIGEN_DECLARE_CONST_Packet8f(one_point_five, 1.5f); |
| _EIGEN_DECLARE_CONST_Packet8f(minus_half, -0.5f); |
| _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(flt_min, 0x00800000); |
| |
| Packet8f neg_half = pmul(_x, p8f_minus_half); |
| |
| // select only the inverse sqrt of positive normal inputs (denormals are |
| // flushed to zero and cause infs as well). |
| Packet8f le_zero_mask = _mm256_cmp_ps(_x, p8f_flt_min, _CMP_LT_OQ); |
| Packet8f x = _mm256_andnot_ps(le_zero_mask, _mm256_rsqrt_ps(_x)); |
| |
| // Fill in NaNs and Infs for the negative/zero entries. |
| Packet8f neg_mask = _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_LT_OQ); |
| Packet8f zero_mask = _mm256_andnot_ps(neg_mask, le_zero_mask); |
| Packet8f infs_and_nans = _mm256_or_ps(_mm256_and_ps(neg_mask, p8f_nan), |
| _mm256_and_ps(zero_mask, p8f_inf)); |
| |
| // Do a single step of Newton's iteration. |
| x = pmul(x, pmadd(neg_half, pmul(x, x), p8f_one_point_five)); |
| |
| // Insert NaNs and Infs in all the right places. |
| return _mm256_or_ps(x, infs_and_nans); |
| } |
| |
| #else |
| template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED |
| Packet8f prsqrt<Packet8f>(const Packet8f& x) { |
| _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f); |
| return _mm256_div_ps(p8f_one, _mm256_sqrt_ps(x)); |
| } |
| #endif |
| |
| template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED |
| Packet4d prsqrt<Packet4d>(const Packet4d& x) { |
| _EIGEN_DECLARE_CONST_Packet4d(one, 1.0); |
| return _mm256_div_pd(p4d_one, _mm256_sqrt_pd(x)); |
| } |
| |
| |
| } // end namespace internal |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_MATH_FUNCTIONS_AVX_H |