Eigen/src/Core/arch/SSE/MathFunctions.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007 Julien Pommier
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.

/* The sin and cos and functions of this file come from
 * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
 */

#ifndef EIGEN_MATH_FUNCTIONS_SSE_H
#define EIGEN_MATH_FUNCTIONS_SSE_H

#include "../../InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f plog<Packet4f>(const Packet4f& _x) {
  return plog_float(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet2d plog<Packet2d>(const Packet2d& _x) {
  return plog_double(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f plog2<Packet4f>(const Packet4f& _x) {
  return plog2_float(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet2d plog2<Packet2d>(const Packet2d& _x) {
  return plog2_double(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f plog1p<Packet4f>(const Packet4f& _x) {
  return generic_plog1p(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f pexpm1<Packet4f>(const Packet4f& _x) {
  return generic_expm1(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f pexp<Packet4f>(const Packet4f& _x)
{
  return pexp_float(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet2d pexp<Packet2d>(const Packet2d& x)
{
  return pexp_double(x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f psin<Packet4f>(const Packet4f& _x)
{
  return psin_float(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f pcos<Packet4f>(const Packet4f& _x)
{
  return pcos_float(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f pacos<Packet4f>(const Packet4f& _x)
{
  return pacos_float(_x);
}

template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet2d patan<Packet2d>(const Packet2d& _x) {
  return patan_double(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f pasin<Packet4f>(const Packet4f& _x)
{
  return pasin_float(_x);
}

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f patan<Packet4f>(const Packet4f& _x)
{
  return patan_float(_x);
}

// Notice that for newer processors, it is counterproductive to use Newton
// iteration for square root. In particular, Skylake and Zen2 processors
// have approximately doubled throughput of the _mm_sqrt_ps instruction
// compared to their predecessors.
template<>EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); }
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet16b psqrt<Packet16b>(const Packet16b& x) { return x; }

#if EIGEN_FAST_MATH
// Even on Skylake, using Newton iteration is a win for reciprocal square root.
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet4f prsqrt<Packet4f>(const Packet4f& x) {
  return generic_rsqrt_newton_step<Packet4f, /*Steps=*/1>::run(x, _mm_rsqrt_ps(x));
}

#ifdef EIGEN_VECTORIZE_FMA
// Trying to speed up reciprocal using Newton-Raphson is counterproductive
// unless FMA is available. Without FMA pdiv(pset1<Packet>(Scalar(1),a)) is
// 30% faster.
template<> EIGEN_STRONG_INLINE Packet4f preciprocal<Packet4f>(const Packet4f& x) {
  return generic_reciprocal_newton_step<Packet4f, /*Steps=*/1>::run(x, _mm_rcp_ps(x));
}
#endif

#endif



// Hyperbolic Tangent function.
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f
ptanh<Packet4f>(const Packet4f& x) {
  return internal::generic_fast_tanh_float(x);
}

} // end namespace internal

namespace numext {

template<>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
float sqrt(const float &x)
{
  return internal::pfirst(internal::Packet4f(_mm_sqrt_ss(_mm_set_ss(x))));
}

template<>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
double sqrt(const double &x)
{
#if EIGEN_COMP_GNUC_STRICT
  // This works around a GCC bug generating poor code for _mm_sqrt_pd
  // See https://gitlab.com/libeigen/eigen/commit/8dca9f97e38970
  return internal::pfirst(internal::Packet2d(__builtin_ia32_sqrtsd(_mm_set_sd(x))));
#else
  return internal::pfirst(internal::Packet2d(_mm_sqrt_pd(_mm_set_sd(x))));
#endif
}

} // end namespace numex

} // end namespace Eigen

#endif // EIGEN_MATH_FUNCTIONS_SSE_H