MathFunctions.h

// 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/
 */

// IWYU pragma: private
#include "../../InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

EIGEN_INSTANTIATE_GENERIC_MATH_FUNCS_FLOAT(Packet8f)

EIGEN_DOUBLE_PACKET_FUNCTION(atanh, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(log, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(log2, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(exp, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(tanh, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(cbrt, Packet4d)
#ifdef EIGEN_VECTORIZE_AVX2
EIGEN_DOUBLE_PACKET_FUNCTION(sin, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(cos, Packet4d)
#endif
EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet4d)
EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet4d)

// 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 Packet8f psqrt<Packet8f>(const Packet8f& _x) {
  return _mm256_sqrt_ps(_x);
}
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d psqrt<Packet4d>(const Packet4d& _x) {
  return _mm256_sqrt_pd(_x);
}

// Even on Skylake, using Newton iteration is a win for reciprocal square root.
#if EIGEN_FAST_MATH
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8f prsqrt<Packet8f>(const Packet8f& a) {
  // _mm256_rsqrt_ps returns -inf for negative denormals.
  // _mm512_rsqrt**_ps returns -NaN for negative denormals.  We may want
  // consistency here.
  // const Packet8f rsqrt = pselect(pcmp_lt(a, pzero(a)),
  //                                pset1<Packet8f>(-NumTraits<float>::quiet_NaN()),
  //                                _mm256_rsqrt_ps(a));
  return generic_rsqrt_newton_step<Packet8f, /*Steps=*/1>::run(a, _mm256_rsqrt_ps(a));
}

template <>
EIGEN_STRONG_INLINE Packet8f preciprocal<Packet8f>(const Packet8f& a) {
  return generic_reciprocal_newton_step<Packet8f, /*Steps=*/1>::run(a, _mm256_rcp_ps(a));
}

#endif

template <>
EIGEN_STRONG_INLINE Packet8h pfrexp(const Packet8h& a, Packet8h& exponent) {
  Packet8f fexponent;
  const Packet8h out = float2half(pfrexp<Packet8f>(half2float(a), fexponent));
  exponent = float2half(fexponent);
  return out;
}

template <>
EIGEN_STRONG_INLINE Packet8h pldexp(const Packet8h& a, const Packet8h& exponent) {
  return float2half(pldexp<Packet8f>(half2float(a), half2float(exponent)));
}

template <>
EIGEN_STRONG_INLINE Packet8bf pfrexp(const Packet8bf& a, Packet8bf& exponent) {
  Packet8f fexponent;
  const Packet8bf out = F32ToBf16(pfrexp<Packet8f>(Bf16ToF32(a), fexponent));
  exponent = F32ToBf16(fexponent);
  return out;
}

template <>
EIGEN_STRONG_INLINE Packet8bf pldexp(const Packet8bf& a, const Packet8bf& exponent) {
  return F32ToBf16(pldexp<Packet8f>(Bf16ToF32(a), Bf16ToF32(exponent)));
}

BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pcos)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexp)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexp2)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexpm1)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog1p)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog2)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, preciprocal)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, prsqrt)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, psin)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, psqrt)
BF16_PACKET_FUNCTION(Packet8f, Packet8bf, ptanh)

#ifndef EIGEN_VECTORIZE_AVX512FP16
F16_PACKET_FUNCTION(Packet8f, Packet8h, pcos)
F16_PACKET_FUNCTION(Packet8f, Packet8h, pexp)
F16_PACKET_FUNCTION(Packet8f, Packet8h, pexp2)
F16_PACKET_FUNCTION(Packet8f, Packet8h, pexpm1)
F16_PACKET_FUNCTION(Packet8f, Packet8h, plog)
F16_PACKET_FUNCTION(Packet8f, Packet8h, plog1p)
F16_PACKET_FUNCTION(Packet8f, Packet8h, plog2)
F16_PACKET_FUNCTION(Packet8f, Packet8h, preciprocal)
F16_PACKET_FUNCTION(Packet8f, Packet8h, prsqrt)
F16_PACKET_FUNCTION(Packet8f, Packet8h, psin)
F16_PACKET_FUNCTION(Packet8f, Packet8h, psqrt)
F16_PACKET_FUNCTION(Packet8f, Packet8h, ptanh)
#endif

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_MATH_FUNCTIONS_AVX_H