Eigen/src/Core/arch/AVX512/MathFunctions.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 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 THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_
#define THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_

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

namespace Eigen {

namespace internal {

#define EIGEN_DECLARE_CONST_Packet16f(NAME, X) \
  const Packet16f p16f_##NAME = pset1<Packet16f>(X)

#define EIGEN_DECLARE_CONST_Packet16f_FROM_INT(NAME, X) \
  const Packet16f p16f_##NAME =  preinterpret<Packet16f,Packet16i>(pset1<Packet16i>(X))

#define EIGEN_DECLARE_CONST_Packet8d(NAME, X) \
  const Packet8d p8d_##NAME = pset1<Packet8d>(X)

#define EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(NAME, X) \
  const Packet8d p8d_##NAME = _mm512_castsi512_pd(_mm512_set1_epi64(X))

#define EIGEN_DECLARE_CONST_Packet16bf(NAME, X) \
  const Packet16bf p16bf_##NAME = pset1<Packet16bf>(X)

#define EIGEN_DECLARE_CONST_Packet16bf_FROM_INT(NAME, X) \
  const Packet16bf p16bf_##NAME =  preinterpret<Packet16bf,Packet16i>(pset1<Packet16i>(X))

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
plog<Packet16f>(const Packet16f& _x) {
  return plog_float(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
plog<Packet8d>(const Packet8d& _x) {
  return plog_double(_x);
}

F16_PACKET_FUNCTION(Packet16f, Packet16h, plog)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog)

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
plog2<Packet16f>(const Packet16f& _x) {
  return plog2_float(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
plog2<Packet8d>(const Packet8d& _x) {
  return plog2_double(_x);
}

F16_PACKET_FUNCTION(Packet16f, Packet16h, plog2)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog2)

// 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 Packet16f
pexp<Packet16f>(const Packet16f& _x) {
  EIGEN_DECLARE_CONST_Packet16f(1, 1.0f);
  EIGEN_DECLARE_CONST_Packet16f(half, 0.5f);
  EIGEN_DECLARE_CONST_Packet16f(127, 127.0f);

  EIGEN_DECLARE_CONST_Packet16f(exp_hi, 88.3762626647950f);
  EIGEN_DECLARE_CONST_Packet16f(exp_lo, -88.3762626647949f);

  EIGEN_DECLARE_CONST_Packet16f(cephes_LOG2EF, 1.44269504088896341f);

  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p0, 1.9875691500E-4f);
  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p1, 1.3981999507E-3f);
  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p2, 8.3334519073E-3f);
  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p3, 4.1665795894E-2f);
  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p4, 1.6666665459E-1f);
  EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p5, 5.0000001201E-1f);

  // Clamp x.
  Packet16f x = pmax(pmin(_x, p16f_exp_hi), p16f_exp_lo);

  // Express exp(x) as exp(m*ln(2) + r), start by extracting
  // m = floor(x/ln(2) + 0.5).
  Packet16f m = _mm512_floor_ps(pmadd(x, p16f_cephes_LOG2EF, p16f_half));

  // Get r = x - m*ln(2). Note that we can do this without losing more than one
  // ulp precision due to the FMA instruction.
  EIGEN_DECLARE_CONST_Packet16f(nln2, -0.6931471805599453f);
  Packet16f r = _mm512_fmadd_ps(m, p16f_nln2, x);
  Packet16f r2 = pmul(r, r);
  Packet16f r3 = pmul(r2, r);

  // Evaluate the polynomial approximant,improved by instruction-level parallelism.
  Packet16f y, y1, y2;
  y  = pmadd(p16f_cephes_exp_p0, r, p16f_cephes_exp_p1);
  y1 = pmadd(p16f_cephes_exp_p3, r, p16f_cephes_exp_p4);
  y2 = padd(r, p16f_1);
  y  = pmadd(y, r, p16f_cephes_exp_p2);
  y1 = pmadd(y1, r, p16f_cephes_exp_p5);
  y  = pmadd(y, r3, y1);
  y  = pmadd(y, r2, y2);

  // Build emm0 = 2^m.
  Packet16i emm0 = _mm512_cvttps_epi32(padd(m, p16f_127));
  emm0 = _mm512_slli_epi32(emm0, 23);

  // Return 2^m * exp(r).
  return pmax(pmul(y, _mm512_castsi512_ps(emm0)), _x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
pexp<Packet8d>(const Packet8d& _x) {
  return pexp_double(_x);
}

F16_PACKET_FUNCTION(Packet16f, Packet16h, pexp)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexp)

template <>
EIGEN_STRONG_INLINE Packet16h pfrexp(const Packet16h& a, Packet16h& exponent) {
  Packet16f fexponent;
  const Packet16h out = float2half(pfrexp<Packet16f>(half2float(a), fexponent));
  exponent = float2half(fexponent);
  return out;
}

template <>
EIGEN_STRONG_INLINE Packet16h pldexp(const Packet16h& a, const Packet16h& exponent) {
  return float2half(pldexp<Packet16f>(half2float(a), half2float(exponent)));
}

template <>
EIGEN_STRONG_INLINE Packet16bf pfrexp(const Packet16bf& a, Packet16bf& exponent) {
  Packet16f fexponent;
  const Packet16bf out = F32ToBf16(pfrexp<Packet16f>(Bf16ToF32(a), fexponent));
  exponent = F32ToBf16(fexponent);
  return out;
}

template <>
EIGEN_STRONG_INLINE Packet16bf pldexp(const Packet16bf& a, const Packet16bf& exponent) {
  return F32ToBf16(pldexp<Packet16f>(Bf16ToF32(a), Bf16ToF32(exponent)));
}

#if EIGEN_FAST_MATH
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
psqrt<Packet16f>(const Packet16f& _x) {
  return generic_sqrt_newton_step<Packet16f>::run(_x, _mm512_rsqrt14_ps(_x));
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
psqrt<Packet8d>(const Packet8d& _x) {
#ifdef EIGEN_VECTORIZE_AVX512ER
  return generic_sqrt_newton_step<Packet8d, /*Steps=*/1>::run(
      _x, _mm512_rsqrt28_pd(_x));
#else
  return generic_sqrt_newton_step<Packet8d, /*Steps=*/2>::run(_x, _mm512_rsqrt14_pd(_x));
#endif
}
#else
template <>
EIGEN_STRONG_INLINE Packet16f psqrt<Packet16f>(const Packet16f& x) {
  return _mm512_sqrt_ps(x);
}

template <>
EIGEN_STRONG_INLINE Packet8d psqrt<Packet8d>(const Packet8d& x) {
  return _mm512_sqrt_pd(x);
}
#endif

F16_PACKET_FUNCTION(Packet16f, Packet16h, psqrt)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psqrt)

// prsqrt for float.
#if defined(EIGEN_VECTORIZE_AVX512ER)
template <>
EIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) {
  return _mm512_rsqrt28_ps(x);
}
#elif EIGEN_FAST_MATH

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
prsqrt<Packet16f>(const Packet16f& _x) {
  return generic_rsqrt_newton_step<Packet16f, /*Steps=*/1>::run(_x, _mm512_rsqrt14_ps(_x));
}
#endif

F16_PACKET_FUNCTION(Packet16f, Packet16h, prsqrt)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, prsqrt)

// prsqrt for double.
#if EIGEN_FAST_MATH
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
prsqrt<Packet8d>(const Packet8d& _x) {
  #ifdef EIGEN_VECTORIZE_AVX512ER
    return generic_rsqrt_newton_step<Packet8d, /*Steps=*/1>::run(_x, _mm512_rsqrt28_pd(_x));
  #else
    return generic_rsqrt_newton_step<Packet8d, /*Steps=*/2>::run(_x, _mm512_rsqrt14_pd(_x));
  #endif
}

template<> EIGEN_STRONG_INLINE Packet16f preciprocal<Packet16f>(const Packet16f& a) {
#ifdef EIGEN_VECTORIZE_AVX512ER
  return _mm512_rcp28_ps(a);
#else
  return generic_reciprocal_newton_step<Packet16f, /*Steps=*/1>::run(a, _mm512_rcp14_ps(a));
#endif
}
#endif

F16_PACKET_FUNCTION(Packet16f, Packet16h, preciprocal)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, preciprocal)

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet16f plog1p<Packet16f>(const Packet16f& _x) {
  return generic_plog1p(_x);
}

F16_PACKET_FUNCTION(Packet16f, Packet16h, plog1p)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog1p)

template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet16f pexpm1<Packet16f>(const Packet16f& _x) {
  return generic_expm1(_x);
}

F16_PACKET_FUNCTION(Packet16f, Packet16h, pexpm1)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexpm1)

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
psin<Packet16f>(const Packet16f& _x) {
  return psin_float(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
pcos<Packet16f>(const Packet16f& _x) {
  return pcos_float(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
pacos<Packet16f>(const Packet16f& _x) {
  return pacos_float(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
pasin<Packet16f>(const Packet16f& _x) {
  return pasin_float(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
patan<Packet16f>(const Packet16f& _x) {
  return patan_float(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
patanh<Packet16f>(const Packet16f& _x) {
  return patanh_float(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d
patan<Packet8d>(const Packet8d& _x) {
  return patan_double(_x);
}

template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f
ptanh<Packet16f>(const Packet16f& _x) {
  return internal::generic_fast_tanh_float(_x);
}

F16_PACKET_FUNCTION(Packet16f, Packet16h, psin)
F16_PACKET_FUNCTION(Packet16f, Packet16h, pcos)
F16_PACKET_FUNCTION(Packet16f, Packet16h, ptanh)

BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psin)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pcos)
BF16_PACKET_FUNCTION(Packet16f, Packet16bf, ptanh)

}  // end namespace internal

}  // end namespace Eigen

#endif  // THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_