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/.
// SPDX-License-Identifier: 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(sinh, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(cosh, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(asinh, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(acosh, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(log, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(log10, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(exp, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(log2, 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)
EIGEN_DOUBLE_PACKET_FUNCTION(tan, Packet4d)
#else
// Without AVX2, psincos_double<Packet4d> requires 256-bit integer operations (Packet4l)
// that are not available. Process as two Packet2d halves using the SSE implementation.
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d psin<Packet4d>(const Packet4d& x) {
  return _mm256_insertf128_pd(_mm256_castpd128_pd256(psin(_mm256_castpd256_pd128(x))),
                              psin(_mm256_extractf128_pd(x, 1)), 1);
}
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d pcos<Packet4d>(const Packet4d& x) {
  return _mm256_insertf128_pd(_mm256_castpd128_pd256(pcos(_mm256_castpd256_pd128(x))),
                              pcos(_mm256_extractf128_pd(x, 1)), 1);
}
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d ptan<Packet4d>(const Packet4d& x) {
  return _mm256_insertf128_pd(_mm256_castpd128_pd256(ptan(_mm256_castpd256_pd128(x))),
                              ptan(_mm256_extractf128_pd(x, 1)), 1);
}
 
// AVX-only Packet4d has no integer packet. Classify the bits using the SSE halves
// so subnormals survive DAZ and NaNs survive fast-math.
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4d psign<Packet4d>(const Packet4d& x) {
  return _mm256_insertf128_pd(_mm256_castpd128_pd256(psign(_mm256_castpd256_pd128(x))),
                              psign(_mm256_extractf128_pd(x, 1)), 1);
}
#endif
EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet4d)
EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet4d)
EIGEN_GENERIC_PACKET_FUNCTION(expm1, Packet4d)
EIGEN_DOUBLE_PACKET_FUNCTION(log1p, 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) {
  // generic_reciprocal_newton_step, with its NaN-or-zero test as a single compare: r == 0 or unordered.
  const Packet8f one = pset1<Packet8f>(1.0f);
  const Packet8f x = _mm256_rcp_ps(a);
  const Packet8f refined = pmadd(x, pnmadd(a, x, one), x);
  const Packet8f redo = _mm256_cmp_ps(refined, _mm256_setzero_ps(), _CMP_EQ_UQ);
  return predux_any(redo) ? pselect(redo, pdiv(one, a), refined) : refined;
}
 
#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) {
  // Both results are exact: the mantissa keeps the input's significand, and the exponent is a
  // small integer.
  Packet8f fexponent;
  const Packet8bf out = F32ToBf16Truncate(pfrexp<Packet8f>(Bf16ToF32(a), fexponent));
  exponent = F32ToBf16Truncate(fexponent);
  return out;
}
 
template <>
EIGEN_STRONG_INLINE Packet8bf pldexp(const Packet8bf& a, const Packet8bf& exponent) {
  return F32ToBf16(pldexp<Packet8f>(Bf16ToF32(a), Bf16ToF32(exponent)));
}
 
EIGEN_INSTANTIATE_GENERIC_MATH_FUNCS_BF16(Packet8f, Packet8bf)
 
#ifndef EIGEN_VECTORIZE_AVX512FP16
EIGEN_INSTANTIATE_GENERIC_MATH_FUNCS_F16(Packet8f, Packet8h)
#endif
 
}  // end namespace internal
 
}  // end namespace Eigen
 
#endif  // EIGEN_MATH_FUNCTIONS_AVX_H