diff options
Diffstat (limited to 'Eigen/src/Core/arch/AVX512')
| -rw-r--r-- | Eigen/src/Core/arch/AVX512/Complex.h | 422 | ||||
| -rw-r--r-- | Eigen/src/Core/arch/AVX512/MathFunctions.h | 362 | ||||
| -rw-r--r-- | Eigen/src/Core/arch/AVX512/PacketMath.h | 2303 | ||||
| -rw-r--r-- | Eigen/src/Core/arch/AVX512/TypeCasting.h | 89 |
4 files changed, 3176 insertions, 0 deletions
diff --git a/Eigen/src/Core/arch/AVX512/Complex.h b/Eigen/src/Core/arch/AVX512/Complex.h new file mode 100644 index 0000000..49c72b3 --- /dev/null +++ b/Eigen/src/Core/arch/AVX512/Complex.h @@ -0,0 +1,422 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2018 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/. + +#ifndef EIGEN_COMPLEX_AVX512_H +#define EIGEN_COMPLEX_AVX512_H + +namespace Eigen { + +namespace internal { + +//---------- float ---------- +struct Packet8cf +{ + EIGEN_STRONG_INLINE Packet8cf() {} + EIGEN_STRONG_INLINE explicit Packet8cf(const __m512& a) : v(a) {} + __m512 v; +}; + +template<> struct packet_traits<std::complex<float> > : default_packet_traits +{ + typedef Packet8cf type; + typedef Packet4cf half; + enum { + Vectorizable = 1, + AlignedOnScalar = 1, + size = 8, + HasHalfPacket = 1, + + HasAdd = 1, + HasSub = 1, + HasMul = 1, + HasDiv = 1, + HasNegate = 1, + HasSqrt = 1, + HasAbs = 0, + HasAbs2 = 0, + HasMin = 0, + HasMax = 0, + HasSetLinear = 0 + }; +}; + +template<> struct unpacket_traits<Packet8cf> { + typedef std::complex<float> type; + typedef Packet4cf half; + typedef Packet16f as_real; + enum { + size = 8, + alignment=unpacket_traits<Packet16f>::alignment, + vectorizable=true, + masked_load_available=false, + masked_store_available=false + }; +}; + +template<> EIGEN_STRONG_INLINE Packet8cf ptrue<Packet8cf>(const Packet8cf& a) { return Packet8cf(ptrue(Packet16f(a.v))); } +template<> EIGEN_STRONG_INLINE Packet8cf padd<Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(_mm512_add_ps(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet8cf psub<Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(_mm512_sub_ps(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet8cf pnegate(const Packet8cf& a) +{ + return Packet8cf(pnegate(a.v)); +} +template<> EIGEN_STRONG_INLINE Packet8cf pconj(const Packet8cf& a) +{ + const __m512 mask = _mm512_castsi512_ps(_mm512_setr_epi32( + 0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000, + 0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000)); + return Packet8cf(pxor(a.v,mask)); +} + +template<> EIGEN_STRONG_INLINE Packet8cf pmul<Packet8cf>(const Packet8cf& a, const Packet8cf& b) +{ + __m512 tmp2 = _mm512_mul_ps(_mm512_movehdup_ps(a.v), _mm512_permute_ps(b.v, _MM_SHUFFLE(2,3,0,1))); + return Packet8cf(_mm512_fmaddsub_ps(_mm512_moveldup_ps(a.v), b.v, tmp2)); +} + +template<> EIGEN_STRONG_INLINE Packet8cf pand <Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(pand(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet8cf por <Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(por(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet8cf pxor <Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(pxor(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet8cf pandnot<Packet8cf>(const Packet8cf& a, const Packet8cf& b) { return Packet8cf(pandnot(a.v,b.v)); } + +template <> +EIGEN_STRONG_INLINE Packet8cf pcmp_eq(const Packet8cf& a, const Packet8cf& b) { + __m512 eq = pcmp_eq<Packet16f>(a.v, b.v); + return Packet8cf(pand(eq, _mm512_permute_ps(eq, 0xB1))); +} + +template<> EIGEN_STRONG_INLINE Packet8cf pload <Packet8cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet8cf(pload<Packet16f>(&numext::real_ref(*from))); } +template<> EIGEN_STRONG_INLINE Packet8cf ploadu<Packet8cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet8cf(ploadu<Packet16f>(&numext::real_ref(*from))); } + + +template<> EIGEN_STRONG_INLINE Packet8cf pset1<Packet8cf>(const std::complex<float>& from) +{ + return Packet8cf(_mm512_castpd_ps(pload1<Packet8d>((const double*)(const void*)&from))); +} + +template<> EIGEN_STRONG_INLINE Packet8cf ploaddup<Packet8cf>(const std::complex<float>* from) +{ + return Packet8cf( _mm512_castpd_ps( ploaddup<Packet8d>((const double*)(const void*)from )) ); +} +template<> EIGEN_STRONG_INLINE Packet8cf ploadquad<Packet8cf>(const std::complex<float>* from) +{ + return Packet8cf( _mm512_castpd_ps( ploadquad<Packet8d>((const double*)(const void*)from )) ); +} + +template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float>* to, const Packet8cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), from.v); } +template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float>* to, const Packet8cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), from.v); } + +template<> EIGEN_DEVICE_FUNC inline Packet8cf pgather<std::complex<float>, Packet8cf>(const std::complex<float>* from, Index stride) +{ + return Packet8cf(_mm512_castpd_ps(pgather<double,Packet8d>((const double*)(const void*)from, stride))); +} + +template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet8cf>(std::complex<float>* to, const Packet8cf& from, Index stride) +{ + pscatter((double*)(void*)to, _mm512_castps_pd(from.v), stride); +} + +template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet8cf>(const Packet8cf& a) +{ + return pfirst(Packet2cf(_mm512_castps512_ps128(a.v))); +} + +template<> EIGEN_STRONG_INLINE Packet8cf preverse(const Packet8cf& a) { + return Packet8cf(_mm512_castsi512_ps( + _mm512_permutexvar_epi64( _mm512_set_epi32(0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7), + _mm512_castps_si512(a.v)))); +} + +template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet8cf>(const Packet8cf& a) +{ + return predux(padd(Packet4cf(extract256<0>(a.v)), + Packet4cf(extract256<1>(a.v)))); +} + +template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet8cf>(const Packet8cf& a) +{ + return predux_mul(pmul(Packet4cf(extract256<0>(a.v)), + Packet4cf(extract256<1>(a.v)))); +} + +template <> +EIGEN_STRONG_INLINE Packet4cf predux_half_dowto4<Packet8cf>(const Packet8cf& a) { + __m256 lane0 = extract256<0>(a.v); + __m256 lane1 = extract256<1>(a.v); + __m256 res = _mm256_add_ps(lane0, lane1); + return Packet4cf(res); +} + +EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet8cf,Packet16f) + +template<> EIGEN_STRONG_INLINE Packet8cf pdiv<Packet8cf>(const Packet8cf& a, const Packet8cf& b) +{ + Packet8cf num = pmul(a, pconj(b)); + __m512 tmp = _mm512_mul_ps(b.v, b.v); + __m512 tmp2 = _mm512_shuffle_ps(tmp,tmp,0xB1); + __m512 denom = _mm512_add_ps(tmp, tmp2); + return Packet8cf(_mm512_div_ps(num.v, denom)); +} + +template<> EIGEN_STRONG_INLINE Packet8cf pcplxflip<Packet8cf>(const Packet8cf& x) +{ + return Packet8cf(_mm512_shuffle_ps(x.v, x.v, _MM_SHUFFLE(2, 3, 0 ,1))); +} + +//---------- double ---------- +struct Packet4cd +{ + EIGEN_STRONG_INLINE Packet4cd() {} + EIGEN_STRONG_INLINE explicit Packet4cd(const __m512d& a) : v(a) {} + __m512d v; +}; + +template<> struct packet_traits<std::complex<double> > : default_packet_traits +{ + typedef Packet4cd type; + typedef Packet2cd half; + enum { + Vectorizable = 1, + AlignedOnScalar = 0, + size = 4, + HasHalfPacket = 1, + + HasAdd = 1, + HasSub = 1, + HasMul = 1, + HasDiv = 1, + HasNegate = 1, + HasSqrt = 1, + HasAbs = 0, + HasAbs2 = 0, + HasMin = 0, + HasMax = 0, + HasSetLinear = 0 + }; +}; + +template<> struct unpacket_traits<Packet4cd> { + typedef std::complex<double> type; + typedef Packet2cd half; + typedef Packet8d as_real; + enum { + size = 4, + alignment = unpacket_traits<Packet8d>::alignment, + vectorizable=true, + masked_load_available=false, + masked_store_available=false + }; +}; + +template<> EIGEN_STRONG_INLINE Packet4cd padd<Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(_mm512_add_pd(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet4cd psub<Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(_mm512_sub_pd(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet4cd pnegate(const Packet4cd& a) { return Packet4cd(pnegate(a.v)); } +template<> EIGEN_STRONG_INLINE Packet4cd pconj(const Packet4cd& a) +{ + const __m512d mask = _mm512_castsi512_pd( + _mm512_set_epi32(0x80000000,0x0,0x0,0x0,0x80000000,0x0,0x0,0x0, + 0x80000000,0x0,0x0,0x0,0x80000000,0x0,0x0,0x0)); + return Packet4cd(pxor(a.v,mask)); +} + +template<> EIGEN_STRONG_INLINE Packet4cd pmul<Packet4cd>(const Packet4cd& a, const Packet4cd& b) +{ + __m512d tmp1 = _mm512_shuffle_pd(a.v,a.v,0x0); + __m512d tmp2 = _mm512_shuffle_pd(a.v,a.v,0xFF); + __m512d tmp3 = _mm512_shuffle_pd(b.v,b.v,0x55); + __m512d odd = _mm512_mul_pd(tmp2, tmp3); + return Packet4cd(_mm512_fmaddsub_pd(tmp1, b.v, odd)); +} + +template<> EIGEN_STRONG_INLINE Packet4cd ptrue<Packet4cd>(const Packet4cd& a) { return Packet4cd(ptrue(Packet8d(a.v))); } +template<> EIGEN_STRONG_INLINE Packet4cd pand <Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(pand(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet4cd por <Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(por(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet4cd pxor <Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(pxor(a.v,b.v)); } +template<> EIGEN_STRONG_INLINE Packet4cd pandnot<Packet4cd>(const Packet4cd& a, const Packet4cd& b) { return Packet4cd(pandnot(a.v,b.v)); } + +template <> +EIGEN_STRONG_INLINE Packet4cd pcmp_eq(const Packet4cd& a, const Packet4cd& b) { + __m512d eq = pcmp_eq<Packet8d>(a.v, b.v); + return Packet4cd(pand(eq, _mm512_permute_pd(eq, 0x55))); +} + +template<> EIGEN_STRONG_INLINE Packet4cd pload <Packet4cd>(const std::complex<double>* from) +{ EIGEN_DEBUG_ALIGNED_LOAD return Packet4cd(pload<Packet8d>((const double*)from)); } +template<> EIGEN_STRONG_INLINE Packet4cd ploadu<Packet4cd>(const std::complex<double>* from) +{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet4cd(ploadu<Packet8d>((const double*)from)); } + +template<> EIGEN_STRONG_INLINE Packet4cd pset1<Packet4cd>(const std::complex<double>& from) +{ + #ifdef EIGEN_VECTORIZE_AVX512DQ + return Packet4cd(_mm512_broadcast_f64x2(pset1<Packet1cd>(from).v)); + #else + return Packet4cd(_mm512_castps_pd(_mm512_broadcast_f32x4( _mm_castpd_ps(pset1<Packet1cd>(from).v)))); + #endif +} + +template<> EIGEN_STRONG_INLINE Packet4cd ploaddup<Packet4cd>(const std::complex<double>* from) { + return Packet4cd(_mm512_insertf64x4( + _mm512_castpd256_pd512(ploaddup<Packet2cd>(from).v), ploaddup<Packet2cd>(from+1).v, 1)); +} + +template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet4cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); } +template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet4cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); } + +template<> EIGEN_DEVICE_FUNC inline Packet4cd pgather<std::complex<double>, Packet4cd>(const std::complex<double>* from, Index stride) +{ + return Packet4cd(_mm512_insertf64x4(_mm512_castpd256_pd512( + _mm256_insertf128_pd(_mm256_castpd128_pd256(ploadu<Packet1cd>(from+0*stride).v), ploadu<Packet1cd>(from+1*stride).v,1)), + _mm256_insertf128_pd(_mm256_castpd128_pd256(ploadu<Packet1cd>(from+2*stride).v), ploadu<Packet1cd>(from+3*stride).v,1), 1)); +} + +template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet4cd>(std::complex<double>* to, const Packet4cd& from, Index stride) +{ + __m512i fromi = _mm512_castpd_si512(from.v); + double* tod = (double*)(void*)to; + _mm_storeu_pd(tod+0*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,0)) ); + _mm_storeu_pd(tod+2*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,1)) ); + _mm_storeu_pd(tod+4*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,2)) ); + _mm_storeu_pd(tod+6*stride, _mm_castsi128_pd(_mm512_extracti32x4_epi32(fromi,3)) ); +} + +template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet4cd>(const Packet4cd& a) +{ + __m128d low = extract128<0>(a.v); + EIGEN_ALIGN16 double res[2]; + _mm_store_pd(res, low); + return std::complex<double>(res[0],res[1]); +} + +template<> EIGEN_STRONG_INLINE Packet4cd preverse(const Packet4cd& a) { + return Packet4cd(_mm512_shuffle_f64x2(a.v, a.v, (shuffle_mask<3,2,1,0>::mask))); +} + +template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet4cd>(const Packet4cd& a) +{ + return predux(padd(Packet2cd(_mm512_extractf64x4_pd(a.v,0)), + Packet2cd(_mm512_extractf64x4_pd(a.v,1)))); +} + +template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet4cd>(const Packet4cd& a) +{ + return predux_mul(pmul(Packet2cd(_mm512_extractf64x4_pd(a.v,0)), + Packet2cd(_mm512_extractf64x4_pd(a.v,1)))); +} + +template<> struct conj_helper<Packet4cd, Packet4cd, false,true> +{ + EIGEN_STRONG_INLINE Packet4cd pmadd(const Packet4cd& x, const Packet4cd& y, const Packet4cd& c) const + { return padd(pmul(x,y),c); } + + EIGEN_STRONG_INLINE Packet4cd pmul(const Packet4cd& a, const Packet4cd& b) const + { + return internal::pmul(a, pconj(b)); + } +}; + +template<> struct conj_helper<Packet4cd, Packet4cd, true,false> +{ + EIGEN_STRONG_INLINE Packet4cd pmadd(const Packet4cd& x, const Packet4cd& y, const Packet4cd& c) const + { return padd(pmul(x,y),c); } + + EIGEN_STRONG_INLINE Packet4cd pmul(const Packet4cd& a, const Packet4cd& b) const + { + return internal::pmul(pconj(a), b); + } +}; + +template<> struct conj_helper<Packet4cd, Packet4cd, true,true> +{ + EIGEN_STRONG_INLINE Packet4cd pmadd(const Packet4cd& x, const Packet4cd& y, const Packet4cd& c) const + { return padd(pmul(x,y),c); } + + EIGEN_STRONG_INLINE Packet4cd pmul(const Packet4cd& a, const Packet4cd& b) const + { + return pconj(internal::pmul(a, b)); + } +}; + +EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet4cd,Packet8d) + +template<> EIGEN_STRONG_INLINE Packet4cd pdiv<Packet4cd>(const Packet4cd& a, const Packet4cd& b) +{ + Packet4cd num = pmul(a, pconj(b)); + __m512d tmp = _mm512_mul_pd(b.v, b.v); + __m512d denom = padd(_mm512_permute_pd(tmp,0x55), tmp); + return Packet4cd(_mm512_div_pd(num.v, denom)); +} + +template<> EIGEN_STRONG_INLINE Packet4cd pcplxflip<Packet4cd>(const Packet4cd& x) +{ + return Packet4cd(_mm512_permute_pd(x.v,0x55)); +} + +EIGEN_DEVICE_FUNC inline void +ptranspose(PacketBlock<Packet8cf,4>& kernel) { + PacketBlock<Packet8d,4> pb; + + pb.packet[0] = _mm512_castps_pd(kernel.packet[0].v); + pb.packet[1] = _mm512_castps_pd(kernel.packet[1].v); + pb.packet[2] = _mm512_castps_pd(kernel.packet[2].v); + pb.packet[3] = _mm512_castps_pd(kernel.packet[3].v); + ptranspose(pb); + kernel.packet[0].v = _mm512_castpd_ps(pb.packet[0]); + kernel.packet[1].v = _mm512_castpd_ps(pb.packet[1]); + kernel.packet[2].v = _mm512_castpd_ps(pb.packet[2]); + kernel.packet[3].v = _mm512_castpd_ps(pb.packet[3]); +} + +EIGEN_DEVICE_FUNC inline void +ptranspose(PacketBlock<Packet8cf,8>& kernel) { + PacketBlock<Packet8d,8> pb; + + pb.packet[0] = _mm512_castps_pd(kernel.packet[0].v); + pb.packet[1] = _mm512_castps_pd(kernel.packet[1].v); + pb.packet[2] = _mm512_castps_pd(kernel.packet[2].v); + pb.packet[3] = _mm512_castps_pd(kernel.packet[3].v); + pb.packet[4] = _mm512_castps_pd(kernel.packet[4].v); + pb.packet[5] = _mm512_castps_pd(kernel.packet[5].v); + pb.packet[6] = _mm512_castps_pd(kernel.packet[6].v); + pb.packet[7] = _mm512_castps_pd(kernel.packet[7].v); + ptranspose(pb); + kernel.packet[0].v = _mm512_castpd_ps(pb.packet[0]); + kernel.packet[1].v = _mm512_castpd_ps(pb.packet[1]); + kernel.packet[2].v = _mm512_castpd_ps(pb.packet[2]); + kernel.packet[3].v = _mm512_castpd_ps(pb.packet[3]); + kernel.packet[4].v = _mm512_castpd_ps(pb.packet[4]); + kernel.packet[5].v = _mm512_castpd_ps(pb.packet[5]); + kernel.packet[6].v = _mm512_castpd_ps(pb.packet[6]); + kernel.packet[7].v = _mm512_castpd_ps(pb.packet[7]); +} + +EIGEN_DEVICE_FUNC inline void +ptranspose(PacketBlock<Packet4cd,4>& kernel) { + __m512d T0 = _mm512_shuffle_f64x2(kernel.packet[0].v, kernel.packet[1].v, (shuffle_mask<0,1,0,1>::mask)); // [a0 a1 b0 b1] + __m512d T1 = _mm512_shuffle_f64x2(kernel.packet[0].v, kernel.packet[1].v, (shuffle_mask<2,3,2,3>::mask)); // [a2 a3 b2 b3] + __m512d T2 = _mm512_shuffle_f64x2(kernel.packet[2].v, kernel.packet[3].v, (shuffle_mask<0,1,0,1>::mask)); // [c0 c1 d0 d1] + __m512d T3 = _mm512_shuffle_f64x2(kernel.packet[2].v, kernel.packet[3].v, (shuffle_mask<2,3,2,3>::mask)); // [c2 c3 d2 d3] + + kernel.packet[3] = Packet4cd(_mm512_shuffle_f64x2(T1, T3, (shuffle_mask<1,3,1,3>::mask))); // [a3 b3 c3 d3] + kernel.packet[2] = Packet4cd(_mm512_shuffle_f64x2(T1, T3, (shuffle_mask<0,2,0,2>::mask))); // [a2 b2 c2 d2] + kernel.packet[1] = Packet4cd(_mm512_shuffle_f64x2(T0, T2, (shuffle_mask<1,3,1,3>::mask))); // [a1 b1 c1 d1] + kernel.packet[0] = Packet4cd(_mm512_shuffle_f64x2(T0, T2, (shuffle_mask<0,2,0,2>::mask))); // [a0 b0 c0 d0] +} + +template<> EIGEN_STRONG_INLINE Packet4cd psqrt<Packet4cd>(const Packet4cd& a) { + return psqrt_complex<Packet4cd>(a); +} + +template<> EIGEN_STRONG_INLINE Packet8cf psqrt<Packet8cf>(const Packet8cf& a) { + return psqrt_complex<Packet8cf>(a); +} + +} // end namespace internal +} // end namespace Eigen + +#endif // EIGEN_COMPLEX_AVX512_H diff --git a/Eigen/src/Core/arch/AVX512/MathFunctions.h b/Eigen/src/Core/arch/AVX512/MathFunctions.h new file mode 100644 index 0000000..6fd726d --- /dev/null +++ b/Eigen/src/Core/arch/AVX512/MathFunctions.h @@ -0,0 +1,362 @@ +// 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_ + +namespace Eigen { + +namespace internal { + +// Disable the code for older versions of gcc that don't support many of the required avx512 instrinsics. +#if EIGEN_GNUC_AT_LEAST(5, 3) || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC >= 1923 + +#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 EIGEN_UNUSED Packet16f +plog<Packet16f>(const Packet16f& _x) { + return plog_float(_x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 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 EIGEN_UNUSED Packet16f +plog2<Packet16f>(const Packet16f& _x) { + return plog2_float(_x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 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 EIGEN_UNUSED 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 EIGEN_UNUSED 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))); +} + +// 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. 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. +#if EIGEN_FAST_MATH +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f +psqrt<Packet16f>(const Packet16f& _x) { + Packet16f neg_half = pmul(_x, pset1<Packet16f>(-.5f)); + __mmask16 denormal_mask = _mm512_kand( + _mm512_cmp_ps_mask(_x, pset1<Packet16f>((std::numeric_limits<float>::min)()), + _CMP_LT_OQ), + _mm512_cmp_ps_mask(_x, _mm512_setzero_ps(), _CMP_GE_OQ)); + + Packet16f x = _mm512_rsqrt14_ps(_x); + + // Do a single step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), pset1<Packet16f>(1.5f))); + + // Flush results for denormals to zero. + return _mm512_mask_blend_ps(denormal_mask, pmul(_x,x), _mm512_setzero_ps()); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d +psqrt<Packet8d>(const Packet8d& _x) { + Packet8d neg_half = pmul(_x, pset1<Packet8d>(-.5)); + __mmask16 denormal_mask = _mm512_kand( + _mm512_cmp_pd_mask(_x, pset1<Packet8d>((std::numeric_limits<double>::min)()), + _CMP_LT_OQ), + _mm512_cmp_pd_mask(_x, _mm512_setzero_pd(), _CMP_GE_OQ)); + + Packet8d x = _mm512_rsqrt14_pd(_x); + + // Do a single step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), pset1<Packet8d>(1.5))); + + // Do a second step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), pset1<Packet8d>(1.5))); + + return _mm512_mask_blend_pd(denormal_mask, pmul(_x,x), _mm512_setzero_pd()); +} +#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 EIGEN_UNUSED Packet16f +prsqrt<Packet16f>(const Packet16f& _x) { + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(inf, 0x7f800000); + _EIGEN_DECLARE_CONST_Packet16f(one_point_five, 1.5f); + _EIGEN_DECLARE_CONST_Packet16f(minus_half, -0.5f); + + Packet16f neg_half = pmul(_x, p16f_minus_half); + + // Identity infinite, negative and denormal arguments. + __mmask16 inf_mask = _mm512_cmp_ps_mask(_x, p16f_inf, _CMP_EQ_OQ); + __mmask16 not_pos_mask = _mm512_cmp_ps_mask(_x, _mm512_setzero_ps(), _CMP_LE_OQ); + __mmask16 not_finite_pos_mask = not_pos_mask | inf_mask; + + // Compute an approximate result using the rsqrt intrinsic, forcing +inf + // for denormals for consistency with AVX and SSE implementations. + Packet16f y_approx = _mm512_rsqrt14_ps(_x); + + // Do a single step of Newton-Raphson iteration to improve the approximation. + // This uses the formula y_{n+1} = y_n * (1.5 - y_n * (0.5 * x) * y_n). + // It is essential to evaluate the inner term like this because forming + // y_n^2 may over- or underflow. + Packet16f y_newton = pmul(y_approx, pmadd(y_approx, pmul(neg_half, y_approx), p16f_one_point_five)); + + // Select the result of the Newton-Raphson step for positive finite arguments. + // For other arguments, choose the output of the intrinsic. This will + // return rsqrt(+inf) = 0, rsqrt(x) = NaN if x < 0, and rsqrt(0) = +inf. + return _mm512_mask_blend_ps(not_finite_pos_mask, y_newton, y_approx); +} +#else + +template <> +EIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) { + _EIGEN_DECLARE_CONST_Packet16f(one, 1.0f); + return _mm512_div_ps(p16f_one, _mm512_sqrt_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 EIGEN_UNUSED Packet8d +prsqrt<Packet8d>(const Packet8d& _x) { + _EIGEN_DECLARE_CONST_Packet8d(one_point_five, 1.5); + _EIGEN_DECLARE_CONST_Packet8d(minus_half, -0.5); + _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(inf, 0x7ff0000000000000LL); + + Packet8d neg_half = pmul(_x, p8d_minus_half); + + // Identity infinite, negative and denormal arguments. + __mmask8 inf_mask = _mm512_cmp_pd_mask(_x, p8d_inf, _CMP_EQ_OQ); + __mmask8 not_pos_mask = _mm512_cmp_pd_mask(_x, _mm512_setzero_pd(), _CMP_LE_OQ); + __mmask8 not_finite_pos_mask = not_pos_mask | inf_mask; + + // Compute an approximate result using the rsqrt intrinsic, forcing +inf + // for denormals for consistency with AVX and SSE implementations. +#if defined(EIGEN_VECTORIZE_AVX512ER) + Packet8d y_approx = _mm512_rsqrt28_pd(_x); +#else + Packet8d y_approx = _mm512_rsqrt14_pd(_x); +#endif + // Do one or two steps of Newton-Raphson's to improve the approximation, depending on the + // starting accuracy (either 2^-14 or 2^-28, depending on whether AVX512ER is available). + // The Newton-Raphson algorithm has quadratic convergence and roughly doubles the number + // of correct digits for each step. + // This uses the formula y_{n+1} = y_n * (1.5 - y_n * (0.5 * x) * y_n). + // It is essential to evaluate the inner term like this because forming + // y_n^2 may over- or underflow. + Packet8d y_newton = pmul(y_approx, pmadd(neg_half, pmul(y_approx, y_approx), p8d_one_point_five)); +#if !defined(EIGEN_VECTORIZE_AVX512ER) + y_newton = pmul(y_newton, pmadd(y_newton, pmul(neg_half, y_newton), p8d_one_point_five)); +#endif + // Select the result of the Newton-Raphson step for positive finite arguments. + // For other arguments, choose the output of the intrinsic. This will + // return rsqrt(+inf) = 0, rsqrt(x) = NaN if x < 0, and rsqrt(0) = +inf. + return _mm512_mask_blend_pd(not_finite_pos_mask, y_newton, y_approx); +} +#else +template <> +EIGEN_STRONG_INLINE Packet8d prsqrt<Packet8d>(const Packet8d& x) { + _EIGEN_DECLARE_CONST_Packet8d(one, 1.0f); + return _mm512_div_pd(p8d_one, _mm512_sqrt_pd(x)); +} +#endif + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +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 EIGEN_UNUSED +Packet16f pexpm1<Packet16f>(const Packet16f& _x) { + return generic_expm1(_x); +} + +F16_PACKET_FUNCTION(Packet16f, Packet16h, pexpm1) +BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexpm1) + +#endif + + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f +psin<Packet16f>(const Packet16f& _x) { + return psin_float(_x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f +pcos<Packet16f>(const Packet16f& _x) { + return pcos_float(_x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 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_ diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h new file mode 100644 index 0000000..34d49ab --- /dev/null +++ b/Eigen/src/Core/arch/AVX512/PacketMath.h @@ -0,0 +1,2303 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 Benoit Steiner (benoit.steiner.goog@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_PACKET_MATH_AVX512_H +#define EIGEN_PACKET_MATH_AVX512_H + +namespace Eigen { + +namespace internal { + +#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD +#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8 +#endif + +#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS +#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32 +#endif + +#ifdef EIGEN_VECTORIZE_FMA +#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD +#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD +#endif +#endif + +typedef __m512 Packet16f; +typedef __m512i Packet16i; +typedef __m512d Packet8d; +typedef eigen_packet_wrapper<__m256i, 1> Packet16h; +typedef eigen_packet_wrapper<__m256i, 2> Packet16bf; + +template <> +struct is_arithmetic<__m512> { + enum { value = true }; +}; +template <> +struct is_arithmetic<__m512i> { + enum { value = true }; +}; +template <> +struct is_arithmetic<__m512d> { + enum { value = true }; +}; + +template<> struct is_arithmetic<Packet16h> { enum { value = true }; }; + +template <> +struct packet_traits<half> : default_packet_traits { + typedef Packet16h type; + // There is no half-size packet for Packet16h. + typedef Packet16h half; + enum { + Vectorizable = 1, + AlignedOnScalar = 1, + size = 16, + HasHalfPacket = 1, + + HasCmp = 1, + HasAdd = 1, + HasSub = 1, + HasMul = 1, + HasDiv = 1, + HasNegate = 1, + HasAbs = 1, + HasAbs2 = 0, + HasMin = 1, + HasMax = 1, + HasConj = 1, + HasSetLinear = 0, + HasLog = 1, + HasLog1p = 1, + HasExpm1 = 1, + HasExp = 1, + HasSqrt = 1, + HasRsqrt = 1, + HasSin = EIGEN_FAST_MATH, + HasCos = EIGEN_FAST_MATH, + HasTanh = EIGEN_FAST_MATH, + HasErf = EIGEN_FAST_MATH, + HasBlend = 0, + HasRound = 1, + HasFloor = 1, + HasCeil = 1, + HasRint = 1, + HasBessel = 1, + HasNdtri = 1 + }; +}; + +template<> struct packet_traits<float> : default_packet_traits +{ + typedef Packet16f type; + typedef Packet8f half; + enum { + Vectorizable = 1, + AlignedOnScalar = 1, + size = 16, + HasHalfPacket = 1, + + HasAbs = 1, + HasMin = 1, + HasMax = 1, + HasConj = 1, + HasBlend = 0, + HasSin = EIGEN_FAST_MATH, + HasCos = EIGEN_FAST_MATH, +#if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT) + HasLog = 1, + HasLog1p = 1, + HasExpm1 = 1, + HasNdtri = 1, + HasBessel = 1, + HasExp = 1, + HasSqrt = EIGEN_FAST_MATH, + HasRsqrt = EIGEN_FAST_MATH, + HasTanh = EIGEN_FAST_MATH, + HasErf = EIGEN_FAST_MATH, +#endif + HasCmp = 1, + HasDiv = 1, + HasRound = 1, + HasFloor = 1, + HasCeil = 1, + HasRint = 1 + }; + }; +template<> struct packet_traits<double> : default_packet_traits +{ + typedef Packet8d type; + typedef Packet4d half; + enum { + Vectorizable = 1, + AlignedOnScalar = 1, + size = 8, + HasHalfPacket = 1, +#if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT) + HasLog = 1, + HasExp = 1, + HasSqrt = EIGEN_FAST_MATH, + HasRsqrt = EIGEN_FAST_MATH, +#endif + HasCmp = 1, + HasDiv = 1, + HasRound = 1, + HasFloor = 1, + HasCeil = 1, + HasRint = 1 + }; +}; + +/* TODO Implement AVX512 for integers +template<> struct packet_traits<int> : default_packet_traits +{ + typedef Packet16i type; + enum { + Vectorizable = 1, + AlignedOnScalar = 1, + size=8 + }; +}; +*/ + +template <> +struct unpacket_traits<Packet16f> { + typedef float type; + typedef Packet8f half; + typedef Packet16i integer_packet; + typedef uint16_t mask_t; + enum { size = 16, alignment=Aligned64, vectorizable=true, masked_load_available=true, masked_store_available=true }; +}; +template <> +struct unpacket_traits<Packet8d> { + typedef double type; + typedef Packet4d half; + enum { size = 8, alignment=Aligned64, vectorizable=true, masked_load_available=false, masked_store_available=false }; +}; +template <> +struct unpacket_traits<Packet16i> { + typedef int type; + typedef Packet8i half; + enum { size = 16, alignment=Aligned64, vectorizable=false, masked_load_available=false, masked_store_available=false }; +}; + +template<> +struct unpacket_traits<Packet16h> { + typedef Eigen::half type; + typedef Packet8h half; + enum {size=16, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false}; +}; + +template <> +EIGEN_STRONG_INLINE Packet16f pset1<Packet16f>(const float& from) { + return _mm512_set1_ps(from); +} +template <> +EIGEN_STRONG_INLINE Packet8d pset1<Packet8d>(const double& from) { + return _mm512_set1_pd(from); +} +template <> +EIGEN_STRONG_INLINE Packet16i pset1<Packet16i>(const int& from) { + return _mm512_set1_epi32(from); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pset1frombits<Packet16f>(unsigned int from) { + return _mm512_castsi512_ps(_mm512_set1_epi32(from)); +} + +template <> +EIGEN_STRONG_INLINE Packet8d pset1frombits<Packet8d>(const numext::uint64_t from) { + return _mm512_castsi512_pd(_mm512_set1_epi64(from)); +} + +template<> EIGEN_STRONG_INLINE Packet16f pzero(const Packet16f& /*a*/) { return _mm512_setzero_ps(); } +template<> EIGEN_STRONG_INLINE Packet8d pzero(const Packet8d& /*a*/) { return _mm512_setzero_pd(); } +template<> EIGEN_STRONG_INLINE Packet16i pzero(const Packet16i& /*a*/) { return _mm512_setzero_si512(); } + +template<> EIGEN_STRONG_INLINE Packet16f peven_mask(const Packet16f& /*a*/) { + return _mm512_castsi512_ps(_mm512_set_epi32(0, -1, 0, -1, 0, -1, 0, -1, + 0, -1, 0, -1, 0, -1, 0, -1)); +} +template<> EIGEN_STRONG_INLINE Packet16i peven_mask(const Packet16i& /*a*/) { + return _mm512_set_epi32(0, -1, 0, -1, 0, -1, 0, -1, + 0, -1, 0, -1, 0, -1, 0, -1); +} +template<> EIGEN_STRONG_INLINE Packet8d peven_mask(const Packet8d& /*a*/) { + return _mm512_castsi512_pd(_mm512_set_epi32(0, 0, -1, -1, 0, 0, -1, -1, + 0, 0, -1, -1, 0, 0, -1, -1)); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pload1<Packet16f>(const float* from) { + return _mm512_broadcastss_ps(_mm_load_ps1(from)); +} +template <> +EIGEN_STRONG_INLINE Packet8d pload1<Packet8d>(const double* from) { + return _mm512_set1_pd(*from); +} + +template <> +EIGEN_STRONG_INLINE Packet16f plset<Packet16f>(const float& a) { + return _mm512_add_ps( + _mm512_set1_ps(a), + _mm512_set_ps(15.0f, 14.0f, 13.0f, 12.0f, 11.0f, 10.0f, 9.0f, 8.0f, 7.0f, 6.0f, 5.0f, + 4.0f, 3.0f, 2.0f, 1.0f, 0.0f)); +} +template <> +EIGEN_STRONG_INLINE Packet8d plset<Packet8d>(const double& a) { + return _mm512_add_pd(_mm512_set1_pd(a), + _mm512_set_pd(7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0)); +} + +template <> +EIGEN_STRONG_INLINE Packet16f padd<Packet16f>(const Packet16f& a, + const Packet16f& b) { + return _mm512_add_ps(a, b); +} +template <> +EIGEN_STRONG_INLINE Packet8d padd<Packet8d>(const Packet8d& a, + const Packet8d& b) { + return _mm512_add_pd(a, b); +} +template <> +EIGEN_STRONG_INLINE Packet16i padd<Packet16i>(const Packet16i& a, + const Packet16i& b) { + return _mm512_add_epi32(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16f psub<Packet16f>(const Packet16f& a, + const Packet16f& b) { + return _mm512_sub_ps(a, b); +} +template <> +EIGEN_STRONG_INLINE Packet8d psub<Packet8d>(const Packet8d& a, + const Packet8d& b) { + return _mm512_sub_pd(a, b); +} +template <> +EIGEN_STRONG_INLINE Packet16i psub<Packet16i>(const Packet16i& a, + const Packet16i& b) { + return _mm512_sub_epi32(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pnegate(const Packet16f& a) { + return _mm512_sub_ps(_mm512_set1_ps(0.0), a); +} +template <> +EIGEN_STRONG_INLINE Packet8d pnegate(const Packet8d& a) { + return _mm512_sub_pd(_mm512_set1_pd(0.0), a); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pconj(const Packet16f& a) { + return a; +} +template <> +EIGEN_STRONG_INLINE Packet8d pconj(const Packet8d& a) { + return a; +} +template <> +EIGEN_STRONG_INLINE Packet16i pconj(const Packet16i& a) { + return a; +} + +template <> +EIGEN_STRONG_INLINE Packet16f pmul<Packet16f>(const Packet16f& a, + const Packet16f& b) { + return _mm512_mul_ps(a, b); +} +template <> +EIGEN_STRONG_INLINE Packet8d pmul<Packet8d>(const Packet8d& a, + const Packet8d& b) { + return _mm512_mul_pd(a, b); +} +template <> +EIGEN_STRONG_INLINE Packet16i pmul<Packet16i>(const Packet16i& a, + const Packet16i& b) { + return _mm512_mullo_epi32(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pdiv<Packet16f>(const Packet16f& a, + const Packet16f& b) { + return _mm512_div_ps(a, b); +} +template <> +EIGEN_STRONG_INLINE Packet8d pdiv<Packet8d>(const Packet8d& a, + const Packet8d& b) { + return _mm512_div_pd(a, b); +} + +#ifdef EIGEN_VECTORIZE_FMA +template <> +EIGEN_STRONG_INLINE Packet16f pmadd(const Packet16f& a, const Packet16f& b, + const Packet16f& c) { + return _mm512_fmadd_ps(a, b, c); +} +template <> +EIGEN_STRONG_INLINE Packet8d pmadd(const Packet8d& a, const Packet8d& b, + const Packet8d& c) { + return _mm512_fmadd_pd(a, b, c); +} +#endif + +template <> +EIGEN_DEVICE_FUNC inline Packet16f pselect(const Packet16f& mask, + const Packet16f& a, + const Packet16f& b) { + __mmask16 mask16 = _mm512_cmp_epi32_mask( + _mm512_castps_si512(mask), _mm512_setzero_epi32(), _MM_CMPINT_EQ); + return _mm512_mask_blend_ps(mask16, a, b); +} + +template <> +EIGEN_DEVICE_FUNC inline Packet8d pselect(const Packet8d& mask, + const Packet8d& a, + const Packet8d& b) { + __mmask8 mask8 = _mm512_cmp_epi64_mask(_mm512_castpd_si512(mask), + _mm512_setzero_epi32(), _MM_CMPINT_EQ); + return _mm512_mask_blend_pd(mask8, a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pmin<Packet16f>(const Packet16f& a, + const Packet16f& b) { + // Arguments are reversed to match NaN propagation behavior of std::min. + return _mm512_min_ps(b, a); +} +template <> +EIGEN_STRONG_INLINE Packet8d pmin<Packet8d>(const Packet8d& a, + const Packet8d& b) { + // Arguments are reversed to match NaN propagation behavior of std::min. + return _mm512_min_pd(b, a); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pmax<Packet16f>(const Packet16f& a, + const Packet16f& b) { + // Arguments are reversed to match NaN propagation behavior of std::max. + return _mm512_max_ps(b, a); +} +template <> +EIGEN_STRONG_INLINE Packet8d pmax<Packet8d>(const Packet8d& a, + const Packet8d& b) { + // Arguments are reversed to match NaN propagation behavior of std::max. + return _mm512_max_pd(b, a); +} + +// Add specializations for min/max with prescribed NaN progation. +template<> +EIGEN_STRONG_INLINE Packet16f pmin<PropagateNumbers, Packet16f>(const Packet16f& a, const Packet16f& b) { + return pminmax_propagate_numbers(a, b, pmin<Packet16f>); +} +template<> +EIGEN_STRONG_INLINE Packet8d pmin<PropagateNumbers, Packet8d>(const Packet8d& a, const Packet8d& b) { + return pminmax_propagate_numbers(a, b, pmin<Packet8d>); +} +template<> +EIGEN_STRONG_INLINE Packet16f pmax<PropagateNumbers, Packet16f>(const Packet16f& a, const Packet16f& b) { + return pminmax_propagate_numbers(a, b, pmax<Packet16f>); +} +template<> +EIGEN_STRONG_INLINE Packet8d pmax<PropagateNumbers, Packet8d>(const Packet8d& a, const Packet8d& b) { + return pminmax_propagate_numbers(a, b, pmax<Packet8d>); +} +template<> +EIGEN_STRONG_INLINE Packet16f pmin<PropagateNaN, Packet16f>(const Packet16f& a, const Packet16f& b) { + return pminmax_propagate_nan(a, b, pmin<Packet16f>); +} +template<> +EIGEN_STRONG_INLINE Packet8d pmin<PropagateNaN, Packet8d>(const Packet8d& a, const Packet8d& b) { + return pminmax_propagate_nan(a, b, pmin<Packet8d>); +} +template<> +EIGEN_STRONG_INLINE Packet16f pmax<PropagateNaN, Packet16f>(const Packet16f& a, const Packet16f& b) { + return pminmax_propagate_nan(a, b, pmax<Packet16f>); +} +template<> +EIGEN_STRONG_INLINE Packet8d pmax<PropagateNaN, Packet8d>(const Packet8d& a, const Packet8d& b) { + return pminmax_propagate_nan(a, b, pmax<Packet8d>); +} + + +#ifdef EIGEN_VECTORIZE_AVX512DQ +template<int I_> EIGEN_STRONG_INLINE Packet8f extract256(Packet16f x) { return _mm512_extractf32x8_ps(x,I_); } +template<int I_> EIGEN_STRONG_INLINE Packet2d extract128(Packet8d x) { return _mm512_extractf64x2_pd(x,I_); } +EIGEN_STRONG_INLINE Packet16f cat256(Packet8f a, Packet8f b) { return _mm512_insertf32x8(_mm512_castps256_ps512(a),b,1); } +#else +// AVX512F does not define _mm512_extractf32x8_ps to extract _m256 from _m512 +template<int I_> EIGEN_STRONG_INLINE Packet8f extract256(Packet16f x) { + return _mm256_castsi256_ps(_mm512_extracti64x4_epi64( _mm512_castps_si512(x),I_)); +} + +// AVX512F does not define _mm512_extractf64x2_pd to extract _m128 from _m512 +template<int I_> EIGEN_STRONG_INLINE Packet2d extract128(Packet8d x) { + return _mm_castsi128_pd(_mm512_extracti32x4_epi32( _mm512_castpd_si512(x),I_)); +} + +EIGEN_STRONG_INLINE Packet16f cat256(Packet8f a, Packet8f b) { + return _mm512_castsi512_ps(_mm512_inserti64x4(_mm512_castsi256_si512(_mm256_castps_si256(a)), + _mm256_castps_si256(b),1)); +} +#endif + +// Helper function for bit packing snippet of low precision comparison. +// It packs the flags from 32x16 to 16x16. +EIGEN_STRONG_INLINE __m256i Pack32To16(Packet16f rf) { + // Split data into small pieces and handle with AVX instructions + // to guarantee internal order of vector. + // Operation: + // dst[15:0] := Saturate16(rf[31:0]) + // dst[31:16] := Saturate16(rf[63:32]) + // ... + // dst[255:240] := Saturate16(rf[255:224]) + __m256i lo = _mm256_castps_si256(extract256<0>(rf)); + __m256i hi = _mm256_castps_si256(extract256<1>(rf)); + __m128i result_lo = _mm_packs_epi32(_mm256_extractf128_si256(lo, 0), + _mm256_extractf128_si256(lo, 1)); + __m128i result_hi = _mm_packs_epi32(_mm256_extractf128_si256(hi, 0), + _mm256_extractf128_si256(hi, 1)); + return _mm256_insertf128_si256(_mm256_castsi128_si256(result_lo), result_hi, 1); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pcmp_eq(const Packet16f& a, const Packet16f& b) { + __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_EQ_OQ); + return _mm512_castsi512_ps( + _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu)); +} +template<> EIGEN_STRONG_INLINE Packet16f pcmp_le(const Packet16f& a, const Packet16f& b) { + __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_LE_OQ); + return _mm512_castsi512_ps( + _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu)); +} + +template<> EIGEN_STRONG_INLINE Packet16f pcmp_lt(const Packet16f& a, const Packet16f& b) { + __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_LT_OQ); + return _mm512_castsi512_ps( + _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu)); +} + +template<> EIGEN_STRONG_INLINE Packet16f pcmp_lt_or_nan(const Packet16f& a, const Packet16f& b) { + __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_NGE_UQ); + return _mm512_castsi512_ps( + _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu)); +} + +template<> EIGEN_STRONG_INLINE Packet16i pcmp_eq(const Packet16i& a, const Packet16i& b) { + __mmask16 mask = _mm512_cmp_epi32_mask(a, b, _CMP_EQ_OQ); + return _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu); +} + + +template <> +EIGEN_STRONG_INLINE Packet8d pcmp_eq(const Packet8d& a, const Packet8d& b) { + __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_EQ_OQ); + return _mm512_castsi512_pd( + _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu)); +} +template <> +EIGEN_STRONG_INLINE Packet8d pcmp_le(const Packet8d& a, const Packet8d& b) { + __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_LE_OQ); + return _mm512_castsi512_pd( + _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu)); +} +template <> +EIGEN_STRONG_INLINE Packet8d pcmp_lt(const Packet8d& a, const Packet8d& b) { + __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_LT_OQ); + return _mm512_castsi512_pd( + _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu)); +} +template <> +EIGEN_STRONG_INLINE Packet8d pcmp_lt_or_nan(const Packet8d& a, const Packet8d& b) { + __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_NGE_UQ); + return _mm512_castsi512_pd( + _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu)); +} + +template<> EIGEN_STRONG_INLINE Packet16f print<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_CUR_DIRECTION); } +template<> EIGEN_STRONG_INLINE Packet8d print<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_CUR_DIRECTION); } + +template<> EIGEN_STRONG_INLINE Packet16f pceil<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_TO_POS_INF); } +template<> EIGEN_STRONG_INLINE Packet8d pceil<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_TO_POS_INF); } + +template<> EIGEN_STRONG_INLINE Packet16f pfloor<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_TO_NEG_INF); } +template<> EIGEN_STRONG_INLINE Packet8d pfloor<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_TO_NEG_INF); } + +template <> +EIGEN_STRONG_INLINE Packet16i ptrue<Packet16i>(const Packet16i& /*a*/) { + return _mm512_set1_epi32(0xffffffffu); +} + +template <> +EIGEN_STRONG_INLINE Packet16f ptrue<Packet16f>(const Packet16f& a) { + return _mm512_castsi512_ps(ptrue<Packet16i>(_mm512_castps_si512(a))); +} + +template <> +EIGEN_STRONG_INLINE Packet8d ptrue<Packet8d>(const Packet8d& a) { + return _mm512_castsi512_pd(ptrue<Packet16i>(_mm512_castpd_si512(a))); +} + +template <> +EIGEN_STRONG_INLINE Packet16i pand<Packet16i>(const Packet16i& a, + const Packet16i& b) { + return _mm512_and_si512(a,b); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pand<Packet16f>(const Packet16f& a, + const Packet16f& b) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_and_ps(a, b); +#else + return _mm512_castsi512_ps(pand(_mm512_castps_si512(a),_mm512_castps_si512(b))); +#endif +} +template <> +EIGEN_STRONG_INLINE Packet8d pand<Packet8d>(const Packet8d& a, + const Packet8d& b) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_and_pd(a, b); +#else + Packet8d res = _mm512_undefined_pd(); + Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0); + Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0); + res = _mm512_insertf64x4(res, _mm256_and_pd(lane0_a, lane0_b), 0); + + Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1); + Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1); + return _mm512_insertf64x4(res, _mm256_and_pd(lane1_a, lane1_b), 1); +#endif +} + +template <> +EIGEN_STRONG_INLINE Packet16i por<Packet16i>(const Packet16i& a, const Packet16i& b) { + return _mm512_or_si512(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16f por<Packet16f>(const Packet16f& a, const Packet16f& b) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_or_ps(a, b); +#else + return _mm512_castsi512_ps(por(_mm512_castps_si512(a),_mm512_castps_si512(b))); +#endif +} + +template <> +EIGEN_STRONG_INLINE Packet8d por<Packet8d>(const Packet8d& a, + const Packet8d& b) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_or_pd(a, b); +#else + return _mm512_castsi512_pd(por(_mm512_castpd_si512(a),_mm512_castpd_si512(b))); +#endif +} + +template <> +EIGEN_STRONG_INLINE Packet16i pxor<Packet16i>(const Packet16i& a, const Packet16i& b) { + return _mm512_xor_si512(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pxor<Packet16f>(const Packet16f& a, const Packet16f& b) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_xor_ps(a, b); +#else + return _mm512_castsi512_ps(pxor(_mm512_castps_si512(a),_mm512_castps_si512(b))); +#endif +} + +template <> +EIGEN_STRONG_INLINE Packet8d pxor<Packet8d>(const Packet8d& a, const Packet8d& b) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_xor_pd(a, b); +#else + return _mm512_castsi512_pd(pxor(_mm512_castpd_si512(a),_mm512_castpd_si512(b))); +#endif +} + +template <> +EIGEN_STRONG_INLINE Packet16i pandnot<Packet16i>(const Packet16i& a, const Packet16i& b) { + return _mm512_andnot_si512(b, a); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pandnot<Packet16f>(const Packet16f& a, const Packet16f& b) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_andnot_ps(b, a); +#else + return _mm512_castsi512_ps(pandnot(_mm512_castps_si512(a),_mm512_castps_si512(b))); +#endif +} +template <> +EIGEN_STRONG_INLINE Packet8d pandnot<Packet8d>(const Packet8d& a,const Packet8d& b) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_andnot_pd(b, a); +#else + return _mm512_castsi512_pd(pandnot(_mm512_castpd_si512(a),_mm512_castpd_si512(b))); +#endif +} + +template<> EIGEN_STRONG_INLINE Packet16f pround<Packet16f>(const Packet16f& a) +{ + // Work-around for default std::round rounding mode. + const Packet16f mask = pset1frombits<Packet16f>(static_cast<numext::uint32_t>(0x80000000u)); + const Packet16f prev0dot5 = pset1frombits<Packet16f>(static_cast<numext::uint32_t>(0x3EFFFFFFu)); + return _mm512_roundscale_ps(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO); +} +template<> EIGEN_STRONG_INLINE Packet8d pround<Packet8d>(const Packet8d& a) +{ + // Work-around for default std::round rounding mode. + const Packet8d mask = pset1frombits<Packet8d>(static_cast<numext::uint64_t>(0x8000000000000000ull)); + const Packet8d prev0dot5 = pset1frombits<Packet8d>(static_cast<numext::uint64_t>(0x3FDFFFFFFFFFFFFFull)); + return _mm512_roundscale_pd(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO); +} + +template<int N> EIGEN_STRONG_INLINE Packet16i parithmetic_shift_right(Packet16i a) { + return _mm512_srai_epi32(a, N); +} + +template<int N> EIGEN_STRONG_INLINE Packet16i plogical_shift_right(Packet16i a) { + return _mm512_srli_epi32(a, N); +} + +template<int N> EIGEN_STRONG_INLINE Packet16i plogical_shift_left(Packet16i a) { + return _mm512_slli_epi32(a, N); +} + +template <> +EIGEN_STRONG_INLINE Packet16f pload<Packet16f>(const float* from) { + EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_ps(from); +} +template <> +EIGEN_STRONG_INLINE Packet8d pload<Packet8d>(const double* from) { + EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_pd(from); +} +template <> +EIGEN_STRONG_INLINE Packet16i pload<Packet16i>(const int* from) { + EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_si512( + reinterpret_cast<const __m512i*>(from)); +} + +template <> +EIGEN_STRONG_INLINE Packet16f ploadu<Packet16f>(const float* from) { + EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_ps(from); +} +template <> +EIGEN_STRONG_INLINE Packet8d ploadu<Packet8d>(const double* from) { + EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_pd(from); +} +template <> +EIGEN_STRONG_INLINE Packet16i ploadu<Packet16i>(const int* from) { + EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_si512( + reinterpret_cast<const __m512i*>(from)); +} + +template <> +EIGEN_STRONG_INLINE Packet16f ploadu<Packet16f>(const float* from, uint16_t umask) { + __mmask16 mask = static_cast<__mmask16>(umask); + EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_maskz_loadu_ps(mask, from); +} + +// Loads 8 floats from memory a returns the packet +// {a0, a0 a1, a1, a2, a2, a3, a3, a4, a4, a5, a5, a6, a6, a7, a7} +template <> +EIGEN_STRONG_INLINE Packet16f ploaddup<Packet16f>(const float* from) { + // an unaligned load is required here as there is no requirement + // on the alignment of input pointer 'from' + __m256i low_half = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from)); + __m512 even_elements = _mm512_castsi512_ps(_mm512_cvtepu32_epi64(low_half)); + __m512 pairs = _mm512_permute_ps(even_elements, _MM_SHUFFLE(2, 2, 0, 0)); + return pairs; +} + +#ifdef EIGEN_VECTORIZE_AVX512DQ +// FIXME: this does not look optimal, better load a Packet4d and shuffle... +// Loads 4 doubles from memory a returns the packet {a0, a0 a1, a1, a2, a2, a3, +// a3} +template <> +EIGEN_STRONG_INLINE Packet8d ploaddup<Packet8d>(const double* from) { + __m512d x = _mm512_setzero_pd(); + x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[0]), 0); + x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[1]), 1); + x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[2]), 2); + x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[3]), 3); + return x; +} +#else +template <> +EIGEN_STRONG_INLINE Packet8d ploaddup<Packet8d>(const double* from) { + __m512d x = _mm512_setzero_pd(); + x = _mm512_mask_broadcastsd_pd(x, 0x3<<0, _mm_load_sd(from+0)); + x = _mm512_mask_broadcastsd_pd(x, 0x3<<2, _mm_load_sd(from+1)); + x = _mm512_mask_broadcastsd_pd(x, 0x3<<4, _mm_load_sd(from+2)); + x = _mm512_mask_broadcastsd_pd(x, 0x3<<6, _mm_load_sd(from+3)); + return x; +} +#endif + +// Loads 4 floats from memory a returns the packet +// {a0, a0 a0, a0, a1, a1, a1, a1, a2, a2, a2, a2, a3, a3, a3, a3} +template <> +EIGEN_STRONG_INLINE Packet16f ploadquad<Packet16f>(const float* from) { + Packet16f tmp = _mm512_castps128_ps512(ploadu<Packet4f>(from)); + const Packet16i scatter_mask = _mm512_set_epi32(3,3,3,3, 2,2,2,2, 1,1,1,1, 0,0,0,0); + return _mm512_permutexvar_ps(scatter_mask, tmp); +} + +// Loads 2 doubles from memory a returns the packet +// {a0, a0 a0, a0, a1, a1, a1, a1} +template <> +EIGEN_STRONG_INLINE Packet8d ploadquad<Packet8d>(const double* from) { + __m256d lane0 = _mm256_set1_pd(*from); + __m256d lane1 = _mm256_set1_pd(*(from+1)); + __m512d tmp = _mm512_undefined_pd(); + tmp = _mm512_insertf64x4(tmp, lane0, 0); + return _mm512_insertf64x4(tmp, lane1, 1); +} + +template <> +EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet16f& from) { + EIGEN_DEBUG_ALIGNED_STORE _mm512_store_ps(to, from); +} +template <> +EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet8d& from) { + EIGEN_DEBUG_ALIGNED_STORE _mm512_store_pd(to, from); +} +template <> +EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet16i& from) { + EIGEN_DEBUG_ALIGNED_STORE _mm512_storeu_si512(reinterpret_cast<__m512i*>(to), + from); +} + +template <> +EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet16f& from) { + EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_ps(to, from); +} +template <> +EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet8d& from) { + EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_pd(to, from); +} +template <> +EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet16i& from) { + EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_si512( + reinterpret_cast<__m512i*>(to), from); +} +template <> +EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet16f& from, uint16_t umask) { + __mmask16 mask = static_cast<__mmask16>(umask); + EIGEN_DEBUG_UNALIGNED_STORE return _mm512_mask_storeu_ps(to, mask, from); +} + +template <> +EIGEN_DEVICE_FUNC inline Packet16f pgather<float, Packet16f>(const float* from, + Index stride) { + Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride)); + Packet16i stride_multiplier = + _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0); + Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier); + + return _mm512_i32gather_ps(indices, from, 4); +} +template <> +EIGEN_DEVICE_FUNC inline Packet8d pgather<double, Packet8d>(const double* from, + Index stride) { + Packet8i stride_vector = _mm256_set1_epi32(convert_index<int>(stride)); + Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0); + Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier); + + return _mm512_i32gather_pd(indices, from, 8); +} + +template <> +EIGEN_DEVICE_FUNC inline void pscatter<float, Packet16f>(float* to, + const Packet16f& from, + Index stride) { + Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride)); + Packet16i stride_multiplier = + _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0); + Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier); + _mm512_i32scatter_ps(to, indices, from, 4); +} +template <> +EIGEN_DEVICE_FUNC inline void pscatter<double, Packet8d>(double* to, + const Packet8d& from, + Index stride) { + Packet8i stride_vector = _mm256_set1_epi32(convert_index<int>(stride)); + Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0); + Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier); + _mm512_i32scatter_pd(to, indices, from, 8); +} + +template <> +EIGEN_STRONG_INLINE void pstore1<Packet16f>(float* to, const float& a) { + Packet16f pa = pset1<Packet16f>(a); + pstore(to, pa); +} +template <> +EIGEN_STRONG_INLINE void pstore1<Packet8d>(double* to, const double& a) { + Packet8d pa = pset1<Packet8d>(a); + pstore(to, pa); +} +template <> +EIGEN_STRONG_INLINE void pstore1<Packet16i>(int* to, const int& a) { + Packet16i pa = pset1<Packet16i>(a); + pstore(to, pa); +} + +template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); } +template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); } +template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); } + +template <> +EIGEN_STRONG_INLINE float pfirst<Packet16f>(const Packet16f& a) { + return _mm_cvtss_f32(_mm512_extractf32x4_ps(a, 0)); +} +template <> +EIGEN_STRONG_INLINE double pfirst<Packet8d>(const Packet8d& a) { + return _mm_cvtsd_f64(_mm256_extractf128_pd(_mm512_extractf64x4_pd(a, 0), 0)); +} +template <> +EIGEN_STRONG_INLINE int pfirst<Packet16i>(const Packet16i& a) { + return _mm_extract_epi32(_mm512_extracti32x4_epi32(a, 0), 0); +} + +template<> EIGEN_STRONG_INLINE Packet16f preverse(const Packet16f& a) +{ + return _mm512_permutexvar_ps(_mm512_set_epi32(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), a); +} + +template<> EIGEN_STRONG_INLINE Packet8d preverse(const Packet8d& a) +{ + return _mm512_permutexvar_pd(_mm512_set_epi32(0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7), a); +} + +template<> EIGEN_STRONG_INLINE Packet16f pabs(const Packet16f& a) +{ + // _mm512_abs_ps intrinsic not found, so hack around it + return _mm512_castsi512_ps(_mm512_and_si512(_mm512_castps_si512(a), _mm512_set1_epi32(0x7fffffff))); +} +template <> +EIGEN_STRONG_INLINE Packet8d pabs(const Packet8d& a) { + // _mm512_abs_ps intrinsic not found, so hack around it + return _mm512_castsi512_pd(_mm512_and_si512(_mm512_castpd_si512(a), + _mm512_set1_epi64(0x7fffffffffffffff))); +} + +template<> +EIGEN_STRONG_INLINE Packet16f pfrexp<Packet16f>(const Packet16f& a, Packet16f& exponent){ + return pfrexp_generic(a, exponent); +} + +// Extract exponent without existence of Packet8l. +template<> +EIGEN_STRONG_INLINE +Packet8d pfrexp_generic_get_biased_exponent(const Packet8d& a) { + const Packet8d cst_exp_mask = pset1frombits<Packet8d>(static_cast<uint64_t>(0x7ff0000000000000ull)); + #ifdef EIGEN_VECTORIZE_AVX512DQ + return _mm512_cvtepi64_pd(_mm512_srli_epi64(_mm512_castpd_si512(pand(a, cst_exp_mask)), 52)); + #else + return _mm512_cvtepi32_pd(_mm512_cvtepi64_epi32(_mm512_srli_epi64(_mm512_castpd_si512(pand(a, cst_exp_mask)), 52))); + #endif +} + +template<> +EIGEN_STRONG_INLINE Packet8d pfrexp<Packet8d>(const Packet8d& a, Packet8d& exponent) { + return pfrexp_generic(a, exponent); +} + +template<> EIGEN_STRONG_INLINE Packet16f pldexp<Packet16f>(const Packet16f& a, const Packet16f& exponent) { + return pldexp_generic(a, exponent); +} + +template<> EIGEN_STRONG_INLINE Packet8d pldexp<Packet8d>(const Packet8d& a, const Packet8d& exponent) { + // Clamp exponent to [-2099, 2099] + const Packet8d max_exponent = pset1<Packet8d>(2099.0); + const Packet8i e = _mm512_cvtpd_epi32(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent)); + + // Split 2^e into four factors and multiply. + const Packet8i bias = pset1<Packet8i>(1023); + Packet8i b = parithmetic_shift_right<2>(e); // floor(e/4) + + // 2^b + const Packet8i permute_idx = _mm256_setr_epi32(0, 4, 1, 5, 2, 6, 3, 7); + Packet8i hi = _mm256_permutevar8x32_epi32(padd(b, bias), permute_idx); + Packet8i lo = _mm256_slli_epi64(hi, 52); + hi = _mm256_slli_epi64(_mm256_srli_epi64(hi, 32), 52); + Packet8d c = _mm512_castsi512_pd(_mm512_inserti64x4(_mm512_castsi256_si512(lo), hi, 1)); + Packet8d out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b) + + // 2^(e - 3b) + b = psub(psub(psub(e, b), b), b); // e - 3b + hi = _mm256_permutevar8x32_epi32(padd(b, bias), permute_idx); + lo = _mm256_slli_epi64(hi, 52); + hi = _mm256_slli_epi64(_mm256_srli_epi64(hi, 32), 52); + c = _mm512_castsi512_pd(_mm512_inserti64x4(_mm512_castsi256_si512(lo), hi, 1)); + out = pmul(out, c); // a * 2^e + return out; +} + +#ifdef EIGEN_VECTORIZE_AVX512DQ +// AVX512F does not define _mm512_extractf32x8_ps to extract _m256 from _m512 +#define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT) \ + __m256 OUTPUT##_0 = _mm512_extractf32x8_ps(INPUT, 0); \ + __m256 OUTPUT##_1 = _mm512_extractf32x8_ps(INPUT, 1) +#else +#define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT) \ + __m256 OUTPUT##_0 = _mm256_insertf128_ps( \ + _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 0)), \ + _mm512_extractf32x4_ps(INPUT, 1), 1); \ + __m256 OUTPUT##_1 = _mm256_insertf128_ps( \ + _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 2)), \ + _mm512_extractf32x4_ps(INPUT, 3), 1); +#endif + +#ifdef EIGEN_VECTORIZE_AVX512DQ +#define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB) \ + OUTPUT = _mm512_insertf32x8(_mm512_castps256_ps512(INPUTA), INPUTB, 1); +#else +#define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB) \ + OUTPUT = _mm512_undefined_ps(); \ + OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 0), 0); \ + OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 1), 1); \ + OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 0), 2); \ + OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 1), 3); +#endif + +template <> +EIGEN_STRONG_INLINE float predux<Packet16f>(const Packet16f& a) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + __m256 lane0 = _mm512_extractf32x8_ps(a, 0); + __m256 lane1 = _mm512_extractf32x8_ps(a, 1); + Packet8f x = _mm256_add_ps(lane0, lane1); + return predux<Packet8f>(x); +#else + __m128 lane0 = _mm512_extractf32x4_ps(a, 0); + __m128 lane1 = _mm512_extractf32x4_ps(a, 1); + __m128 lane2 = _mm512_extractf32x4_ps(a, 2); + __m128 lane3 = _mm512_extractf32x4_ps(a, 3); + __m128 sum = _mm_add_ps(_mm_add_ps(lane0, lane1), _mm_add_ps(lane2, lane3)); + sum = _mm_hadd_ps(sum, sum); + sum = _mm_hadd_ps(sum, _mm_permute_ps(sum, 1)); + return _mm_cvtss_f32(sum); +#endif +} +template <> +EIGEN_STRONG_INLINE double predux<Packet8d>(const Packet8d& a) { + __m256d lane0 = _mm512_extractf64x4_pd(a, 0); + __m256d lane1 = _mm512_extractf64x4_pd(a, 1); + __m256d sum = _mm256_add_pd(lane0, lane1); + __m256d tmp0 = _mm256_hadd_pd(sum, _mm256_permute2f128_pd(sum, sum, 1)); + return _mm_cvtsd_f64(_mm256_castpd256_pd128(_mm256_hadd_pd(tmp0, tmp0))); +} + +template <> +EIGEN_STRONG_INLINE Packet8f predux_half_dowto4<Packet16f>(const Packet16f& a) { +#ifdef EIGEN_VECTORIZE_AVX512DQ + __m256 lane0 = _mm512_extractf32x8_ps(a, 0); + __m256 lane1 = _mm512_extractf32x8_ps(a, 1); + return _mm256_add_ps(lane0, lane1); +#else + __m128 lane0 = _mm512_extractf32x4_ps(a, 0); + __m128 lane1 = _mm512_extractf32x4_ps(a, 1); + __m128 lane2 = _mm512_extractf32x4_ps(a, 2); + __m128 lane3 = _mm512_extractf32x4_ps(a, 3); + __m128 sum0 = _mm_add_ps(lane0, lane2); + __m128 sum1 = _mm_add_ps(lane1, lane3); + return _mm256_insertf128_ps(_mm256_castps128_ps256(sum0), sum1, 1); +#endif +} +template <> +EIGEN_STRONG_INLINE Packet4d predux_half_dowto4<Packet8d>(const Packet8d& a) { + __m256d lane0 = _mm512_extractf64x4_pd(a, 0); + __m256d lane1 = _mm512_extractf64x4_pd(a, 1); + return _mm256_add_pd(lane0, lane1); +} + +template <> +EIGEN_STRONG_INLINE float predux_mul<Packet16f>(const Packet16f& a) { +//#ifdef EIGEN_VECTORIZE_AVX512DQ +#if 0 + Packet8f lane0 = _mm512_extractf32x8_ps(a, 0); + Packet8f lane1 = _mm512_extractf32x8_ps(a, 1); + Packet8f res = pmul(lane0, lane1); + res = pmul(res, _mm256_permute2f128_ps(res, res, 1)); + res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2))); + return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1)))); +#else + __m128 lane0 = _mm512_extractf32x4_ps(a, 0); + __m128 lane1 = _mm512_extractf32x4_ps(a, 1); + __m128 lane2 = _mm512_extractf32x4_ps(a, 2); + __m128 lane3 = _mm512_extractf32x4_ps(a, 3); + __m128 res = pmul(pmul(lane0, lane1), pmul(lane2, lane3)); + res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2))); + return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1)))); +#endif +} +template <> +EIGEN_STRONG_INLINE double predux_mul<Packet8d>(const Packet8d& a) { + __m256d lane0 = _mm512_extractf64x4_pd(a, 0); + __m256d lane1 = _mm512_extractf64x4_pd(a, 1); + __m256d res = pmul(lane0, lane1); + res = pmul(res, _mm256_permute2f128_pd(res, res, 1)); + return pfirst(pmul(res, _mm256_shuffle_pd(res, res, 1))); +} + +template <> +EIGEN_STRONG_INLINE float predux_min<Packet16f>(const Packet16f& a) { + __m128 lane0 = _mm512_extractf32x4_ps(a, 0); + __m128 lane1 = _mm512_extractf32x4_ps(a, 1); + __m128 lane2 = _mm512_extractf32x4_ps(a, 2); + __m128 lane3 = _mm512_extractf32x4_ps(a, 3); + __m128 res = _mm_min_ps(_mm_min_ps(lane0, lane1), _mm_min_ps(lane2, lane3)); + res = _mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2))); + return pfirst(_mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1)))); +} +template <> +EIGEN_STRONG_INLINE double predux_min<Packet8d>(const Packet8d& a) { + __m256d lane0 = _mm512_extractf64x4_pd(a, 0); + __m256d lane1 = _mm512_extractf64x4_pd(a, 1); + __m256d res = _mm256_min_pd(lane0, lane1); + res = _mm256_min_pd(res, _mm256_permute2f128_pd(res, res, 1)); + return pfirst(_mm256_min_pd(res, _mm256_shuffle_pd(res, res, 1))); +} + +template <> +EIGEN_STRONG_INLINE float predux_max<Packet16f>(const Packet16f& a) { + __m128 lane0 = _mm512_extractf32x4_ps(a, 0); + __m128 lane1 = _mm512_extractf32x4_ps(a, 1); + __m128 lane2 = _mm512_extractf32x4_ps(a, 2); + __m128 lane3 = _mm512_extractf32x4_ps(a, 3); + __m128 res = _mm_max_ps(_mm_max_ps(lane0, lane1), _mm_max_ps(lane2, lane3)); + res = _mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2))); + return pfirst(_mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1)))); +} + +template <> +EIGEN_STRONG_INLINE double predux_max<Packet8d>(const Packet8d& a) { + __m256d lane0 = _mm512_extractf64x4_pd(a, 0); + __m256d lane1 = _mm512_extractf64x4_pd(a, 1); + __m256d res = _mm256_max_pd(lane0, lane1); + res = _mm256_max_pd(res, _mm256_permute2f128_pd(res, res, 1)); + return pfirst(_mm256_max_pd(res, _mm256_shuffle_pd(res, res, 1))); +} + +template<> EIGEN_STRONG_INLINE bool predux_any(const Packet16f& x) +{ + Packet16i xi = _mm512_castps_si512(x); + __mmask16 tmp = _mm512_test_epi32_mask(xi,xi); + return !_mm512_kortestz(tmp,tmp); +} + + + +#define PACK_OUTPUT(OUTPUT, INPUT, INDEX, STRIDE) \ + EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[INDEX], INPUT[INDEX + STRIDE]); + +EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 16>& kernel) { + __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]); + __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]); + __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]); + __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]); + __m512 T4 = _mm512_unpacklo_ps(kernel.packet[4], kernel.packet[5]); + __m512 T5 = _mm512_unpackhi_ps(kernel.packet[4], kernel.packet[5]); + __m512 T6 = _mm512_unpacklo_ps(kernel.packet[6], kernel.packet[7]); + __m512 T7 = _mm512_unpackhi_ps(kernel.packet[6], kernel.packet[7]); + __m512 T8 = _mm512_unpacklo_ps(kernel.packet[8], kernel.packet[9]); + __m512 T9 = _mm512_unpackhi_ps(kernel.packet[8], kernel.packet[9]); + __m512 T10 = _mm512_unpacklo_ps(kernel.packet[10], kernel.packet[11]); + __m512 T11 = _mm512_unpackhi_ps(kernel.packet[10], kernel.packet[11]); + __m512 T12 = _mm512_unpacklo_ps(kernel.packet[12], kernel.packet[13]); + __m512 T13 = _mm512_unpackhi_ps(kernel.packet[12], kernel.packet[13]); + __m512 T14 = _mm512_unpacklo_ps(kernel.packet[14], kernel.packet[15]); + __m512 T15 = _mm512_unpackhi_ps(kernel.packet[14], kernel.packet[15]); + __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2)); + __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2)); + __m512 S4 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S5 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(3, 2, 3, 2)); + __m512 S6 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S7 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(3, 2, 3, 2)); + __m512 S8 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S9 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(3, 2, 3, 2)); + __m512 S10 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S11 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(3, 2, 3, 2)); + __m512 S12 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S13 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(3, 2, 3, 2)); + __m512 S14 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S15 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(3, 2, 3, 2)); + + EIGEN_EXTRACT_8f_FROM_16f(S0, S0); + EIGEN_EXTRACT_8f_FROM_16f(S1, S1); + EIGEN_EXTRACT_8f_FROM_16f(S2, S2); + EIGEN_EXTRACT_8f_FROM_16f(S3, S3); + EIGEN_EXTRACT_8f_FROM_16f(S4, S4); + EIGEN_EXTRACT_8f_FROM_16f(S5, S5); + EIGEN_EXTRACT_8f_FROM_16f(S6, S6); + EIGEN_EXTRACT_8f_FROM_16f(S7, S7); + EIGEN_EXTRACT_8f_FROM_16f(S8, S8); + EIGEN_EXTRACT_8f_FROM_16f(S9, S9); + EIGEN_EXTRACT_8f_FROM_16f(S10, S10); + EIGEN_EXTRACT_8f_FROM_16f(S11, S11); + EIGEN_EXTRACT_8f_FROM_16f(S12, S12); + EIGEN_EXTRACT_8f_FROM_16f(S13, S13); + EIGEN_EXTRACT_8f_FROM_16f(S14, S14); + EIGEN_EXTRACT_8f_FROM_16f(S15, S15); + + PacketBlock<Packet8f, 32> tmp; + + tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S4_0, 0x20); + tmp.packet[1] = _mm256_permute2f128_ps(S1_0, S5_0, 0x20); + tmp.packet[2] = _mm256_permute2f128_ps(S2_0, S6_0, 0x20); + tmp.packet[3] = _mm256_permute2f128_ps(S3_0, S7_0, 0x20); + tmp.packet[4] = _mm256_permute2f128_ps(S0_0, S4_0, 0x31); + tmp.packet[5] = _mm256_permute2f128_ps(S1_0, S5_0, 0x31); + tmp.packet[6] = _mm256_permute2f128_ps(S2_0, S6_0, 0x31); + tmp.packet[7] = _mm256_permute2f128_ps(S3_0, S7_0, 0x31); + + tmp.packet[8] = _mm256_permute2f128_ps(S0_1, S4_1, 0x20); + tmp.packet[9] = _mm256_permute2f128_ps(S1_1, S5_1, 0x20); + tmp.packet[10] = _mm256_permute2f128_ps(S2_1, S6_1, 0x20); + tmp.packet[11] = _mm256_permute2f128_ps(S3_1, S7_1, 0x20); + tmp.packet[12] = _mm256_permute2f128_ps(S0_1, S4_1, 0x31); + tmp.packet[13] = _mm256_permute2f128_ps(S1_1, S5_1, 0x31); + tmp.packet[14] = _mm256_permute2f128_ps(S2_1, S6_1, 0x31); + tmp.packet[15] = _mm256_permute2f128_ps(S3_1, S7_1, 0x31); + + // Second set of _m256 outputs + tmp.packet[16] = _mm256_permute2f128_ps(S8_0, S12_0, 0x20); + tmp.packet[17] = _mm256_permute2f128_ps(S9_0, S13_0, 0x20); + tmp.packet[18] = _mm256_permute2f128_ps(S10_0, S14_0, 0x20); + tmp.packet[19] = _mm256_permute2f128_ps(S11_0, S15_0, 0x20); + tmp.packet[20] = _mm256_permute2f128_ps(S8_0, S12_0, 0x31); + tmp.packet[21] = _mm256_permute2f128_ps(S9_0, S13_0, 0x31); + tmp.packet[22] = _mm256_permute2f128_ps(S10_0, S14_0, 0x31); + tmp.packet[23] = _mm256_permute2f128_ps(S11_0, S15_0, 0x31); + + tmp.packet[24] = _mm256_permute2f128_ps(S8_1, S12_1, 0x20); + tmp.packet[25] = _mm256_permute2f128_ps(S9_1, S13_1, 0x20); + tmp.packet[26] = _mm256_permute2f128_ps(S10_1, S14_1, 0x20); + tmp.packet[27] = _mm256_permute2f128_ps(S11_1, S15_1, 0x20); + tmp.packet[28] = _mm256_permute2f128_ps(S8_1, S12_1, 0x31); + tmp.packet[29] = _mm256_permute2f128_ps(S9_1, S13_1, 0x31); + tmp.packet[30] = _mm256_permute2f128_ps(S10_1, S14_1, 0x31); + tmp.packet[31] = _mm256_permute2f128_ps(S11_1, S15_1, 0x31); + + // Pack them into the output + PACK_OUTPUT(kernel.packet, tmp.packet, 0, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 1, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 2, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 3, 16); + + PACK_OUTPUT(kernel.packet, tmp.packet, 4, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 5, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 6, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 7, 16); + + PACK_OUTPUT(kernel.packet, tmp.packet, 8, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 9, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 10, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 11, 16); + + PACK_OUTPUT(kernel.packet, tmp.packet, 12, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 13, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 14, 16); + PACK_OUTPUT(kernel.packet, tmp.packet, 15, 16); +} +#define PACK_OUTPUT_2(OUTPUT, INPUT, INDEX, STRIDE) \ + EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[2 * INDEX], \ + INPUT[2 * INDEX + STRIDE]); + +EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 4>& kernel) { + __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]); + __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]); + __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]); + __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]); + + __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2)); + __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0)); + __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2)); + + EIGEN_EXTRACT_8f_FROM_16f(S0, S0); + EIGEN_EXTRACT_8f_FROM_16f(S1, S1); + EIGEN_EXTRACT_8f_FROM_16f(S2, S2); + EIGEN_EXTRACT_8f_FROM_16f(S3, S3); + + PacketBlock<Packet8f, 8> tmp; + + tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S1_0, 0x20); + tmp.packet[1] = _mm256_permute2f128_ps(S2_0, S3_0, 0x20); + tmp.packet[2] = _mm256_permute2f128_ps(S0_0, S1_0, 0x31); + tmp.packet[3] = _mm256_permute2f128_ps(S2_0, S3_0, 0x31); + + tmp.packet[4] = _mm256_permute2f128_ps(S0_1, S1_1, 0x20); + tmp.packet[5] = _mm256_permute2f128_ps(S2_1, S3_1, 0x20); + tmp.packet[6] = _mm256_permute2f128_ps(S0_1, S1_1, 0x31); + tmp.packet[7] = _mm256_permute2f128_ps(S2_1, S3_1, 0x31); + + PACK_OUTPUT_2(kernel.packet, tmp.packet, 0, 1); + PACK_OUTPUT_2(kernel.packet, tmp.packet, 1, 1); + PACK_OUTPUT_2(kernel.packet, tmp.packet, 2, 1); + PACK_OUTPUT_2(kernel.packet, tmp.packet, 3, 1); +} + +#define PACK_OUTPUT_SQ_D(OUTPUT, INPUT, INDEX, STRIDE) \ + OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX], 0); \ + OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX + STRIDE], 1); + +#define PACK_OUTPUT_D(OUTPUT, INPUT, INDEX, STRIDE) \ + OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX)], 0); \ + OUTPUT[INDEX] = \ + _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX) + STRIDE], 1); + +EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 4>& kernel) { + __m512d T0 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0); + __m512d T1 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0xff); + __m512d T2 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0); + __m512d T3 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0xff); + + PacketBlock<Packet4d, 8> tmp; + + tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0), + _mm512_extractf64x4_pd(T2, 0), 0x20); + tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0), + _mm512_extractf64x4_pd(T3, 0), 0x20); + tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0), + _mm512_extractf64x4_pd(T2, 0), 0x31); + tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0), + _mm512_extractf64x4_pd(T3, 0), 0x31); + + tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1), + _mm512_extractf64x4_pd(T2, 1), 0x20); + tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1), + _mm512_extractf64x4_pd(T3, 1), 0x20); + tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1), + _mm512_extractf64x4_pd(T2, 1), 0x31); + tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1), + _mm512_extractf64x4_pd(T3, 1), 0x31); + + PACK_OUTPUT_D(kernel.packet, tmp.packet, 0, 1); + PACK_OUTPUT_D(kernel.packet, tmp.packet, 1, 1); + PACK_OUTPUT_D(kernel.packet, tmp.packet, 2, 1); + PACK_OUTPUT_D(kernel.packet, tmp.packet, 3, 1); +} + +EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 8>& kernel) { + __m512d T0 = _mm512_unpacklo_pd(kernel.packet[0], kernel.packet[1]); + __m512d T1 = _mm512_unpackhi_pd(kernel.packet[0], kernel.packet[1]); + __m512d T2 = _mm512_unpacklo_pd(kernel.packet[2], kernel.packet[3]); + __m512d T3 = _mm512_unpackhi_pd(kernel.packet[2], kernel.packet[3]); + __m512d T4 = _mm512_unpacklo_pd(kernel.packet[4], kernel.packet[5]); + __m512d T5 = _mm512_unpackhi_pd(kernel.packet[4], kernel.packet[5]); + __m512d T6 = _mm512_unpacklo_pd(kernel.packet[6], kernel.packet[7]); + __m512d T7 = _mm512_unpackhi_pd(kernel.packet[6], kernel.packet[7]); + + PacketBlock<Packet4d, 16> tmp; + + tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0), + _mm512_extractf64x4_pd(T2, 0), 0x20); + tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0), + _mm512_extractf64x4_pd(T3, 0), 0x20); + tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0), + _mm512_extractf64x4_pd(T2, 0), 0x31); + tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0), + _mm512_extractf64x4_pd(T3, 0), 0x31); + + tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1), + _mm512_extractf64x4_pd(T2, 1), 0x20); + tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1), + _mm512_extractf64x4_pd(T3, 1), 0x20); + tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1), + _mm512_extractf64x4_pd(T2, 1), 0x31); + tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1), + _mm512_extractf64x4_pd(T3, 1), 0x31); + + tmp.packet[8] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 0), + _mm512_extractf64x4_pd(T6, 0), 0x20); + tmp.packet[9] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 0), + _mm512_extractf64x4_pd(T7, 0), 0x20); + tmp.packet[10] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 0), + _mm512_extractf64x4_pd(T6, 0), 0x31); + tmp.packet[11] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 0), + _mm512_extractf64x4_pd(T7, 0), 0x31); + + tmp.packet[12] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 1), + _mm512_extractf64x4_pd(T6, 1), 0x20); + tmp.packet[13] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 1), + _mm512_extractf64x4_pd(T7, 1), 0x20); + tmp.packet[14] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 1), + _mm512_extractf64x4_pd(T6, 1), 0x31); + tmp.packet[15] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 1), + _mm512_extractf64x4_pd(T7, 1), 0x31); + + PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 0, 8); + PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 1, 8); + PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 2, 8); + PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 3, 8); + + PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 4, 8); + PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 5, 8); + PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 6, 8); + PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 7, 8); +} +template <> +EIGEN_STRONG_INLINE Packet16f pblend(const Selector<16>& /*ifPacket*/, + const Packet16f& /*thenPacket*/, + const Packet16f& /*elsePacket*/) { + assert(false && "To be implemented"); + return Packet16f(); +} +template <> +EIGEN_STRONG_INLINE Packet8d pblend(const Selector<8>& ifPacket, + const Packet8d& thenPacket, + const Packet8d& elsePacket) { + __mmask8 m = (ifPacket.select[0] ) + | (ifPacket.select[1]<<1) + | (ifPacket.select[2]<<2) + | (ifPacket.select[3]<<3) + | (ifPacket.select[4]<<4) + | (ifPacket.select[5]<<5) + | (ifPacket.select[6]<<6) + | (ifPacket.select[7]<<7); + return _mm512_mask_blend_pd(m, elsePacket, thenPacket); +} + +// Packet math for Eigen::half +template<> EIGEN_STRONG_INLINE Packet16h pset1<Packet16h>(const Eigen::half& from) { + return _mm256_set1_epi16(from.x); +} + +template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet16h>(const Packet16h& from) { + return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm256_extract_epi16(from, 0))); +} + +template<> EIGEN_STRONG_INLINE Packet16h pload<Packet16h>(const Eigen::half* from) { + return _mm256_load_si256(reinterpret_cast<const __m256i*>(from)); +} + +template<> EIGEN_STRONG_INLINE Packet16h ploadu<Packet16h>(const Eigen::half* from) { + return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from)); +} + +template<> EIGEN_STRONG_INLINE void pstore<half>(Eigen::half* to, const Packet16h& from) { + // (void*) -> workaround clang warning: + // cast from 'Eigen::half *' to '__m256i *' increases required alignment from 2 to 32 + _mm256_store_si256((__m256i*)(void*)to, from); +} + +template<> EIGEN_STRONG_INLINE void pstoreu<half>(Eigen::half* to, const Packet16h& from) { + // (void*) -> workaround clang warning: + // cast from 'Eigen::half *' to '__m256i *' increases required alignment from 2 to 32 + _mm256_storeu_si256((__m256i*)(void*)to, from); +} + +template<> EIGEN_STRONG_INLINE Packet16h +ploaddup<Packet16h>(const Eigen::half* from) { + unsigned short a = from[0].x; + unsigned short b = from[1].x; + unsigned short c = from[2].x; + unsigned short d = from[3].x; + unsigned short e = from[4].x; + unsigned short f = from[5].x; + unsigned short g = from[6].x; + unsigned short h = from[7].x; + return _mm256_set_epi16(h, h, g, g, f, f, e, e, d, d, c, c, b, b, a, a); +} + +template<> EIGEN_STRONG_INLINE Packet16h +ploadquad(const Eigen::half* from) { + unsigned short a = from[0].x; + unsigned short b = from[1].x; + unsigned short c = from[2].x; + unsigned short d = from[3].x; + return _mm256_set_epi16(d, d, d, d, c, c, c, c, b, b, b, b, a, a, a, a); +} + +EIGEN_STRONG_INLINE Packet16f half2float(const Packet16h& a) { +#ifdef EIGEN_HAS_FP16_C + return _mm512_cvtph_ps(a); +#else + EIGEN_ALIGN64 half aux[16]; + pstore(aux, a); + float f0(aux[0]); + float f1(aux[1]); + float f2(aux[2]); + float f3(aux[3]); + float f4(aux[4]); + float f5(aux[5]); + float f6(aux[6]); + float f7(aux[7]); + float f8(aux[8]); + float f9(aux[9]); + float fa(aux[10]); + float fb(aux[11]); + float fc(aux[12]); + float fd(aux[13]); + float fe(aux[14]); + float ff(aux[15]); + + return _mm512_set_ps( + ff, fe, fd, fc, fb, fa, f9, f8, f7, f6, f5, f4, f3, f2, f1, f0); +#endif +} + +EIGEN_STRONG_INLINE Packet16h float2half(const Packet16f& a) { +#ifdef EIGEN_HAS_FP16_C + return _mm512_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC); +#else + EIGEN_ALIGN64 float aux[16]; + pstore(aux, a); + half h0(aux[0]); + half h1(aux[1]); + half h2(aux[2]); + half h3(aux[3]); + half h4(aux[4]); + half h5(aux[5]); + half h6(aux[6]); + half h7(aux[7]); + half h8(aux[8]); + half h9(aux[9]); + half ha(aux[10]); + half hb(aux[11]); + half hc(aux[12]); + half hd(aux[13]); + half he(aux[14]); + half hf(aux[15]); + + return _mm256_set_epi16( + hf.x, he.x, hd.x, hc.x, hb.x, ha.x, h9.x, h8.x, + h7.x, h6.x, h5.x, h4.x, h3.x, h2.x, h1.x, h0.x); +#endif +} + +template<> EIGEN_STRONG_INLINE Packet16h ptrue(const Packet16h& a) { + return ptrue(Packet8i(a)); +} + +template <> +EIGEN_STRONG_INLINE Packet16h pabs(const Packet16h& a) { + const __m256i sign_mask = _mm256_set1_epi16(static_cast<numext::uint16_t>(0x8000)); + return _mm256_andnot_si256(sign_mask, a); +} + +template <> +EIGEN_STRONG_INLINE Packet16h pmin<Packet16h>(const Packet16h& a, + const Packet16h& b) { + return float2half(pmin<Packet16f>(half2float(a), half2float(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16h pmax<Packet16h>(const Packet16h& a, + const Packet16h& b) { + return float2half(pmax<Packet16f>(half2float(a), half2float(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16h plset<Packet16h>(const half& a) { + return float2half(plset<Packet16f>(static_cast<float>(a))); +} + +template<> EIGEN_STRONG_INLINE Packet16h por(const Packet16h& a,const Packet16h& b) { + // in some cases Packet8i is a wrapper around __m256i, so we need to + // cast to Packet8i to call the correct overload. + return por(Packet8i(a),Packet8i(b)); +} +template<> EIGEN_STRONG_INLINE Packet16h pxor(const Packet16h& a,const Packet16h& b) { + return pxor(Packet8i(a),Packet8i(b)); +} +template<> EIGEN_STRONG_INLINE Packet16h pand(const Packet16h& a,const Packet16h& b) { + return pand(Packet8i(a),Packet8i(b)); +} +template<> EIGEN_STRONG_INLINE Packet16h pandnot(const Packet16h& a,const Packet16h& b) { + return pandnot(Packet8i(a),Packet8i(b)); +} + +template<> EIGEN_STRONG_INLINE Packet16h pselect(const Packet16h& mask, const Packet16h& a, const Packet16h& b) { + return _mm256_blendv_epi8(b, a, mask); +} + +template<> EIGEN_STRONG_INLINE Packet16h pround<Packet16h>(const Packet16h& a) { + return float2half(pround<Packet16f>(half2float(a))); +} + +template<> EIGEN_STRONG_INLINE Packet16h print<Packet16h>(const Packet16h& a) { + return float2half(print<Packet16f>(half2float(a))); +} + +template<> EIGEN_STRONG_INLINE Packet16h pceil<Packet16h>(const Packet16h& a) { + return float2half(pceil<Packet16f>(half2float(a))); +} + +template<> EIGEN_STRONG_INLINE Packet16h pfloor<Packet16h>(const Packet16h& a) { + return float2half(pfloor<Packet16f>(half2float(a))); +} + +template<> EIGEN_STRONG_INLINE Packet16h pcmp_eq(const Packet16h& a,const Packet16h& b) { + Packet16f af = half2float(a); + Packet16f bf = half2float(b); + return Pack32To16(pcmp_eq(af, bf)); +} + +template<> EIGEN_STRONG_INLINE Packet16h pcmp_le(const Packet16h& a,const Packet16h& b) { + return Pack32To16(pcmp_le(half2float(a), half2float(b))); +} + +template<> EIGEN_STRONG_INLINE Packet16h pcmp_lt(const Packet16h& a,const Packet16h& b) { + return Pack32To16(pcmp_lt(half2float(a), half2float(b))); +} + +template<> EIGEN_STRONG_INLINE Packet16h pcmp_lt_or_nan(const Packet16h& a,const Packet16h& b) { + return Pack32To16(pcmp_lt_or_nan(half2float(a), half2float(b))); +} + +template<> EIGEN_STRONG_INLINE Packet16h pconj(const Packet16h& a) { return a; } + +template<> EIGEN_STRONG_INLINE Packet16h pnegate(const Packet16h& a) { + Packet16h sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000)); + return _mm256_xor_si256(a, sign_mask); +} + +template<> EIGEN_STRONG_INLINE Packet16h padd<Packet16h>(const Packet16h& a, const Packet16h& b) { + Packet16f af = half2float(a); + Packet16f bf = half2float(b); + Packet16f rf = padd(af, bf); + return float2half(rf); +} + +template<> EIGEN_STRONG_INLINE Packet16h psub<Packet16h>(const Packet16h& a, const Packet16h& b) { + Packet16f af = half2float(a); + Packet16f bf = half2float(b); + Packet16f rf = psub(af, bf); + return float2half(rf); +} + +template<> EIGEN_STRONG_INLINE Packet16h pmul<Packet16h>(const Packet16h& a, const Packet16h& b) { + Packet16f af = half2float(a); + Packet16f bf = half2float(b); + Packet16f rf = pmul(af, bf); + return float2half(rf); +} + +template<> EIGEN_STRONG_INLINE Packet16h pdiv<Packet16h>(const Packet16h& a, const Packet16h& b) { + Packet16f af = half2float(a); + Packet16f bf = half2float(b); + Packet16f rf = pdiv(af, bf); + return float2half(rf); +} + +template<> EIGEN_STRONG_INLINE half predux<Packet16h>(const Packet16h& from) { + Packet16f from_float = half2float(from); + return half(predux(from_float)); +} + +template <> +EIGEN_STRONG_INLINE Packet8h predux_half_dowto4<Packet16h>(const Packet16h& a) { + Packet8h lane0 = _mm256_extractf128_si256(a, 0); + Packet8h lane1 = _mm256_extractf128_si256(a, 1); + return padd<Packet8h>(lane0, lane1); +} + +template<> EIGEN_STRONG_INLINE Eigen::half predux_max<Packet16h>(const Packet16h& a) { + Packet16f af = half2float(a); + float reduced = predux_max<Packet16f>(af); + return Eigen::half(reduced); +} + +template<> EIGEN_STRONG_INLINE Eigen::half predux_min<Packet16h>(const Packet16h& a) { + Packet16f af = half2float(a); + float reduced = predux_min<Packet16f>(af); + return Eigen::half(reduced); +} + +template<> EIGEN_STRONG_INLINE half predux_mul<Packet16h>(const Packet16h& from) { + Packet16f from_float = half2float(from); + return half(predux_mul(from_float)); +} + +template<> EIGEN_STRONG_INLINE Packet16h preverse(const Packet16h& a) +{ + __m128i m = _mm_setr_epi8(14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1); + return _mm256_insertf128_si256( + _mm256_castsi128_si256(_mm_shuffle_epi8(_mm256_extractf128_si256(a,1),m)), + _mm_shuffle_epi8(_mm256_extractf128_si256(a,0),m), 1); +} + +template<> EIGEN_STRONG_INLINE Packet16h pgather<Eigen::half, Packet16h>(const Eigen::half* from, Index stride) +{ + return _mm256_set_epi16( + from[15*stride].x, from[14*stride].x, from[13*stride].x, from[12*stride].x, + from[11*stride].x, from[10*stride].x, from[9*stride].x, from[8*stride].x, + from[7*stride].x, from[6*stride].x, from[5*stride].x, from[4*stride].x, + from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x); +} + +template<> EIGEN_STRONG_INLINE void pscatter<half, Packet16h>(half* to, const Packet16h& from, Index stride) +{ + EIGEN_ALIGN64 half aux[16]; + pstore(aux, from); + to[stride*0] = aux[0]; + to[stride*1] = aux[1]; + to[stride*2] = aux[2]; + to[stride*3] = aux[3]; + to[stride*4] = aux[4]; + to[stride*5] = aux[5]; + to[stride*6] = aux[6]; + to[stride*7] = aux[7]; + to[stride*8] = aux[8]; + to[stride*9] = aux[9]; + to[stride*10] = aux[10]; + to[stride*11] = aux[11]; + to[stride*12] = aux[12]; + to[stride*13] = aux[13]; + to[stride*14] = aux[14]; + to[stride*15] = aux[15]; +} + +EIGEN_STRONG_INLINE void +ptranspose(PacketBlock<Packet16h,16>& kernel) { + __m256i a = kernel.packet[0]; + __m256i b = kernel.packet[1]; + __m256i c = kernel.packet[2]; + __m256i d = kernel.packet[3]; + __m256i e = kernel.packet[4]; + __m256i f = kernel.packet[5]; + __m256i g = kernel.packet[6]; + __m256i h = kernel.packet[7]; + __m256i i = kernel.packet[8]; + __m256i j = kernel.packet[9]; + __m256i k = kernel.packet[10]; + __m256i l = kernel.packet[11]; + __m256i m = kernel.packet[12]; + __m256i n = kernel.packet[13]; + __m256i o = kernel.packet[14]; + __m256i p = kernel.packet[15]; + + __m256i ab_07 = _mm256_unpacklo_epi16(a, b); + __m256i cd_07 = _mm256_unpacklo_epi16(c, d); + __m256i ef_07 = _mm256_unpacklo_epi16(e, f); + __m256i gh_07 = _mm256_unpacklo_epi16(g, h); + __m256i ij_07 = _mm256_unpacklo_epi16(i, j); + __m256i kl_07 = _mm256_unpacklo_epi16(k, l); + __m256i mn_07 = _mm256_unpacklo_epi16(m, n); + __m256i op_07 = _mm256_unpacklo_epi16(o, p); + + __m256i ab_8f = _mm256_unpackhi_epi16(a, b); + __m256i cd_8f = _mm256_unpackhi_epi16(c, d); + __m256i ef_8f = _mm256_unpackhi_epi16(e, f); + __m256i gh_8f = _mm256_unpackhi_epi16(g, h); + __m256i ij_8f = _mm256_unpackhi_epi16(i, j); + __m256i kl_8f = _mm256_unpackhi_epi16(k, l); + __m256i mn_8f = _mm256_unpackhi_epi16(m, n); + __m256i op_8f = _mm256_unpackhi_epi16(o, p); + + __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07); + __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07); + __m256i efgh_03 = _mm256_unpacklo_epi32(ef_07, gh_07); + __m256i efgh_47 = _mm256_unpackhi_epi32(ef_07, gh_07); + __m256i ijkl_03 = _mm256_unpacklo_epi32(ij_07, kl_07); + __m256i ijkl_47 = _mm256_unpackhi_epi32(ij_07, kl_07); + __m256i mnop_03 = _mm256_unpacklo_epi32(mn_07, op_07); + __m256i mnop_47 = _mm256_unpackhi_epi32(mn_07, op_07); + + __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f); + __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f); + __m256i efgh_8b = _mm256_unpacklo_epi32(ef_8f, gh_8f); + __m256i efgh_cf = _mm256_unpackhi_epi32(ef_8f, gh_8f); + __m256i ijkl_8b = _mm256_unpacklo_epi32(ij_8f, kl_8f); + __m256i ijkl_cf = _mm256_unpackhi_epi32(ij_8f, kl_8f); + __m256i mnop_8b = _mm256_unpacklo_epi32(mn_8f, op_8f); + __m256i mnop_cf = _mm256_unpackhi_epi32(mn_8f, op_8f); + + __m256i abcdefgh_01 = _mm256_unpacklo_epi64(abcd_03, efgh_03); + __m256i abcdefgh_23 = _mm256_unpackhi_epi64(abcd_03, efgh_03); + __m256i ijklmnop_01 = _mm256_unpacklo_epi64(ijkl_03, mnop_03); + __m256i ijklmnop_23 = _mm256_unpackhi_epi64(ijkl_03, mnop_03); + __m256i abcdefgh_45 = _mm256_unpacklo_epi64(abcd_47, efgh_47); + __m256i abcdefgh_67 = _mm256_unpackhi_epi64(abcd_47, efgh_47); + __m256i ijklmnop_45 = _mm256_unpacklo_epi64(ijkl_47, mnop_47); + __m256i ijklmnop_67 = _mm256_unpackhi_epi64(ijkl_47, mnop_47); + __m256i abcdefgh_89 = _mm256_unpacklo_epi64(abcd_8b, efgh_8b); + __m256i abcdefgh_ab = _mm256_unpackhi_epi64(abcd_8b, efgh_8b); + __m256i ijklmnop_89 = _mm256_unpacklo_epi64(ijkl_8b, mnop_8b); + __m256i ijklmnop_ab = _mm256_unpackhi_epi64(ijkl_8b, mnop_8b); + __m256i abcdefgh_cd = _mm256_unpacklo_epi64(abcd_cf, efgh_cf); + __m256i abcdefgh_ef = _mm256_unpackhi_epi64(abcd_cf, efgh_cf); + __m256i ijklmnop_cd = _mm256_unpacklo_epi64(ijkl_cf, mnop_cf); + __m256i ijklmnop_ef = _mm256_unpackhi_epi64(ijkl_cf, mnop_cf); + + // NOTE: no unpacklo/hi instr in this case, so using permute instr. + __m256i a_p_0 = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x20); + __m256i a_p_1 = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x20); + __m256i a_p_2 = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x20); + __m256i a_p_3 = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x20); + __m256i a_p_4 = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x20); + __m256i a_p_5 = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x20); + __m256i a_p_6 = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x20); + __m256i a_p_7 = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x20); + __m256i a_p_8 = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x31); + __m256i a_p_9 = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x31); + __m256i a_p_a = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x31); + __m256i a_p_b = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x31); + __m256i a_p_c = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x31); + __m256i a_p_d = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x31); + __m256i a_p_e = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x31); + __m256i a_p_f = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x31); + + kernel.packet[0] = a_p_0; + kernel.packet[1] = a_p_1; + kernel.packet[2] = a_p_2; + kernel.packet[3] = a_p_3; + kernel.packet[4] = a_p_4; + kernel.packet[5] = a_p_5; + kernel.packet[6] = a_p_6; + kernel.packet[7] = a_p_7; + kernel.packet[8] = a_p_8; + kernel.packet[9] = a_p_9; + kernel.packet[10] = a_p_a; + kernel.packet[11] = a_p_b; + kernel.packet[12] = a_p_c; + kernel.packet[13] = a_p_d; + kernel.packet[14] = a_p_e; + kernel.packet[15] = a_p_f; +} + +EIGEN_STRONG_INLINE void +ptranspose(PacketBlock<Packet16h,8>& kernel) { + EIGEN_ALIGN64 half in[8][16]; + pstore<half>(in[0], kernel.packet[0]); + pstore<half>(in[1], kernel.packet[1]); + pstore<half>(in[2], kernel.packet[2]); + pstore<half>(in[3], kernel.packet[3]); + pstore<half>(in[4], kernel.packet[4]); + pstore<half>(in[5], kernel.packet[5]); + pstore<half>(in[6], kernel.packet[6]); + pstore<half>(in[7], kernel.packet[7]); + + EIGEN_ALIGN64 half out[8][16]; + + for (int i = 0; i < 8; ++i) { + for (int j = 0; j < 8; ++j) { + out[i][j] = in[j][2*i]; + } + for (int j = 0; j < 8; ++j) { + out[i][j+8] = in[j][2*i+1]; + } + } + + kernel.packet[0] = pload<Packet16h>(out[0]); + kernel.packet[1] = pload<Packet16h>(out[1]); + kernel.packet[2] = pload<Packet16h>(out[2]); + kernel.packet[3] = pload<Packet16h>(out[3]); + kernel.packet[4] = pload<Packet16h>(out[4]); + kernel.packet[5] = pload<Packet16h>(out[5]); + kernel.packet[6] = pload<Packet16h>(out[6]); + kernel.packet[7] = pload<Packet16h>(out[7]); +} + +EIGEN_STRONG_INLINE void +ptranspose(PacketBlock<Packet16h,4>& kernel) { + EIGEN_ALIGN64 half in[4][16]; + pstore<half>(in[0], kernel.packet[0]); + pstore<half>(in[1], kernel.packet[1]); + pstore<half>(in[2], kernel.packet[2]); + pstore<half>(in[3], kernel.packet[3]); + + EIGEN_ALIGN64 half out[4][16]; + + for (int i = 0; i < 4; ++i) { + for (int j = 0; j < 4; ++j) { + out[i][j] = in[j][4*i]; + } + for (int j = 0; j < 4; ++j) { + out[i][j+4] = in[j][4*i+1]; + } + for (int j = 0; j < 4; ++j) { + out[i][j+8] = in[j][4*i+2]; + } + for (int j = 0; j < 4; ++j) { + out[i][j+12] = in[j][4*i+3]; + } + } + + kernel.packet[0] = pload<Packet16h>(out[0]); + kernel.packet[1] = pload<Packet16h>(out[1]); + kernel.packet[2] = pload<Packet16h>(out[2]); + kernel.packet[3] = pload<Packet16h>(out[3]); +} + +template <> struct is_arithmetic<Packet16bf> { enum { value = true }; }; + +template <> +struct packet_traits<bfloat16> : default_packet_traits { + typedef Packet16bf type; + typedef Packet8bf half; + enum { + Vectorizable = 1, + AlignedOnScalar = 1, + size = 16, + HasHalfPacket = 1, + HasBlend = 0, + HasInsert = 1, + HasSin = EIGEN_FAST_MATH, + HasCos = EIGEN_FAST_MATH, +#if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT) +#ifdef EIGEN_VECTORIZE_AVX512DQ + HasLog = 1, // Currently fails test with bad accuracy. + HasLog1p = 1, + HasExpm1 = 1, + HasNdtri = 1, + HasBessel = 1, +#endif + HasExp = 1, + HasSqrt = EIGEN_FAST_MATH, + HasRsqrt = EIGEN_FAST_MATH, + HasTanh = EIGEN_FAST_MATH, + HasErf = EIGEN_FAST_MATH, +#endif + HasCmp = 1, + HasDiv = 1 + }; +}; + +template <> +struct unpacket_traits<Packet16bf> +{ + typedef bfloat16 type; + enum {size=16, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false}; + typedef Packet8bf half; +}; + +template <> +EIGEN_STRONG_INLINE Packet16bf pset1<Packet16bf>(const bfloat16& from) { + return _mm256_set1_epi16(from.value); +} + +template <> +EIGEN_STRONG_INLINE bfloat16 pfirst<Packet16bf>(const Packet16bf& from) { + bfloat16 t; + t.value = static_cast<unsigned short>(_mm256_extract_epi16(from, 0)); + return t; +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pload<Packet16bf>(const bfloat16* from) { + return _mm256_load_si256(reinterpret_cast<const __m256i*>(from)); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf ploadu<Packet16bf>(const bfloat16* from) { + return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from)); +} + +template <> +EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to, + const Packet16bf& from) { + _mm256_store_si256(reinterpret_cast<__m256i*>(to), from); +} + +template <> +EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to, + const Packet16bf& from) { + _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from); +} + +template<> EIGEN_STRONG_INLINE Packet16bf +ploaddup<Packet16bf>(const bfloat16* from) { + Packet16bf r; + unsigned short a = from[0].value; + unsigned short b = from[1].value; + unsigned short c = from[2].value; + unsigned short d = from[3].value; + unsigned short e = from[4].value; + unsigned short f = from[5].value; + unsigned short g = from[6].value; + unsigned short h = from[7].value; + return _mm256_set_epi16(h, h, g, g, f, f, e, e, d, d, c, c, b, b, a, a); +} + +template<> EIGEN_STRONG_INLINE Packet16bf +ploadquad(const bfloat16* from) { + Packet16bf r; + unsigned short a = from[0].value; + unsigned short b = from[1].value; + unsigned short c = from[2].value; + unsigned short d = from[3].value; + return _mm256_set_epi16(d, d, d, d, c, c, c, c, b, b, b, b, a, a, a, a); +} + +EIGEN_STRONG_INLINE Packet16f Bf16ToF32(const Packet16bf& a) { + return _mm512_castsi512_ps(_mm512_slli_epi32(_mm512_cvtepu16_epi32(a), 16)); +} + +// Convert float to bfloat16 according to round-to-nearest-even/denormals algorithm. +EIGEN_STRONG_INLINE Packet16bf F32ToBf16(const Packet16f& a) { + Packet16bf r; + +#if defined(EIGEN_VECTORIZE_AVX512BF16) && EIGEN_GNUC_AT_LEAST(10, 1) + // Since GCC 10.1 supports avx512bf16 and C style explicit cast + // (C++ static_cast is not supported yet), do converion via intrinsic + // and register path for performance. + r = (__m256i)(_mm512_cvtneps_pbh(a)); + +#else + __m512i t; + __m512i input = _mm512_castps_si512(a); + __m512i nan = _mm512_set1_epi32(0x7fc0); + + // uint32_t lsb = (input >> 16) & 1; + t = _mm512_and_si512(_mm512_srli_epi32(input, 16), _mm512_set1_epi32(1)); + // uint32_t rounding_bias = 0x7fff + lsb; + t = _mm512_add_epi32(t, _mm512_set1_epi32(0x7fff)); + // input += rounding_bias; + t = _mm512_add_epi32(t, input); + // input = input >> 16; + t = _mm512_srli_epi32(t, 16); + + // Check NaN before converting back to bf16 + __mmask16 mask = _mm512_cmp_ps_mask(a, a, _CMP_ORD_Q); + + t = _mm512_mask_blend_epi32(mask, nan, t); + // output.value = static_cast<uint16_t>(input); + r = _mm512_cvtepi32_epi16(t); +#endif // EIGEN_VECTORIZE_AVX512BF16 + + return r; +} + +template <> +EIGEN_STRONG_INLINE Packet16bf ptrue(const Packet16bf& a) { + return ptrue<Packet8i>(a); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf por(const Packet16bf& a, const Packet16bf& b) { + return por<Packet8i>(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pxor(const Packet16bf& a, const Packet16bf& b) { + return pxor<Packet8i>(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pand(const Packet16bf& a, const Packet16bf& b) { + return pand<Packet8i>(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pandnot(const Packet16bf& a, + const Packet16bf& b) { + return pandnot<Packet8i>(a, b); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pselect(const Packet16bf& mask, + const Packet16bf& a, + const Packet16bf& b) { + // Input mask is expected to be all 0/1, handle it with 8-bit + // intrinsic for performance. + return _mm256_blendv_epi8(b, a, mask); +} + +template<> EIGEN_STRONG_INLINE Packet16bf pround<Packet16bf>(const Packet16bf& a) +{ + return F32ToBf16(pround<Packet16f>(Bf16ToF32(a))); +} + +template<> EIGEN_STRONG_INLINE Packet16bf print<Packet16bf>(const Packet16bf& a) { + return F32ToBf16(print<Packet16f>(Bf16ToF32(a))); +} + +template<> EIGEN_STRONG_INLINE Packet16bf pceil<Packet16bf>(const Packet16bf& a) { + return F32ToBf16(pceil<Packet16f>(Bf16ToF32(a))); +} + +template<> EIGEN_STRONG_INLINE Packet16bf pfloor<Packet16bf>(const Packet16bf& a) { + return F32ToBf16(pfloor<Packet16f>(Bf16ToF32(a))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pcmp_eq(const Packet16bf& a, + const Packet16bf& b) { + return Pack32To16(pcmp_eq(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pcmp_le(const Packet16bf& a, + const Packet16bf& b) { + return Pack32To16(pcmp_le(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pcmp_lt(const Packet16bf& a, + const Packet16bf& b) { + return Pack32To16(pcmp_lt(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pcmp_lt_or_nan(const Packet16bf& a, + const Packet16bf& b) { + return Pack32To16(pcmp_lt_or_nan(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pnegate(const Packet16bf& a) { + Packet16bf sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000)); + return _mm256_xor_si256(a, sign_mask); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pconj(const Packet16bf& a) { + return a; +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pabs(const Packet16bf& a) { + const __m256i sign_mask = _mm256_set1_epi16(static_cast<numext::uint16_t>(0x8000)); + return _mm256_andnot_si256(sign_mask, a); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf padd<Packet16bf>(const Packet16bf& a, + const Packet16bf& b) { + return F32ToBf16(padd<Packet16f>(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf psub<Packet16bf>(const Packet16bf& a, + const Packet16bf& b) { + return F32ToBf16(psub<Packet16f>(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pmul<Packet16bf>(const Packet16bf& a, + const Packet16bf& b) { + return F32ToBf16(pmul<Packet16f>(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pdiv<Packet16bf>(const Packet16bf& a, + const Packet16bf& b) { + return F32ToBf16(pdiv<Packet16f>(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pmin<Packet16bf>(const Packet16bf& a, + const Packet16bf& b) { + return F32ToBf16(pmin<Packet16f>(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pmax<Packet16bf>(const Packet16bf& a, + const Packet16bf& b) { + return F32ToBf16(pmax<Packet16f>(Bf16ToF32(a), Bf16ToF32(b))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf plset<Packet16bf>(const bfloat16& a) { + return F32ToBf16(plset<Packet16f>(static_cast<float>(a))); +} + +template <> +EIGEN_STRONG_INLINE Packet8bf predux_half_dowto4<Packet16bf>(const Packet16bf& a) { + Packet8bf lane0 = _mm256_extractf128_si256(a, 0); + Packet8bf lane1 = _mm256_extractf128_si256(a, 1); + return padd<Packet8bf>(lane0, lane1); +} + +template <> +EIGEN_STRONG_INLINE bfloat16 predux<Packet16bf>(const Packet16bf& p) { + return static_cast<bfloat16>(predux<Packet16f>(Bf16ToF32(p))); +} + +template <> +EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet16bf>(const Packet16bf& from) { + return static_cast<bfloat16>(predux_mul<Packet16f>(Bf16ToF32(from))); +} + +template <> +EIGEN_STRONG_INLINE bfloat16 predux_min<Packet16bf>(const Packet16bf& from) { + return static_cast<bfloat16>(predux_min<Packet16f>(Bf16ToF32(from))); +} + +template <> +EIGEN_STRONG_INLINE bfloat16 predux_max<Packet16bf>(const Packet16bf& from) { + return static_cast<bfloat16>(predux_max<Packet16f>(Bf16ToF32(from))); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf preverse(const Packet16bf& a) { + __m256i m = _mm256_setr_epi8(14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1, + 14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1); + + Packet16bf res; + // Swap hi and lo first because shuffle is in 128-bit lanes. + res = _mm256_permute2x128_si256(a, a, 1); + // Shuffle 8-bit values in src within 2*128-bit lanes. + return _mm256_shuffle_epi8(res, m); +} + +template <> +EIGEN_STRONG_INLINE Packet16bf pgather<bfloat16, Packet16bf>(const bfloat16* from, + Index stride) { + return _mm256_set_epi16( + from[15*stride].value, from[14*stride].value, from[13*stride].value, from[12*stride].value, + from[11*stride].value, from[10*stride].value, from[9*stride].value, from[8*stride].value, + from[7*stride].value, from[6*stride].value, from[5*stride].value, from[4*stride].value, + from[3*stride].value, from[2*stride].value, from[1*stride].value, from[0*stride].value); +} + +template <> +EIGEN_STRONG_INLINE void pscatter<bfloat16, Packet16bf>(bfloat16* to, + const Packet16bf& from, + Index stride) { + EIGEN_ALIGN64 bfloat16 aux[16]; + pstore(aux, from); + to[stride*0] = aux[0]; + to[stride*1] = aux[1]; + to[stride*2] = aux[2]; + to[stride*3] = aux[3]; + to[stride*4] = aux[4]; + to[stride*5] = aux[5]; + to[stride*6] = aux[6]; + to[stride*7] = aux[7]; + to[stride*8] = aux[8]; + to[stride*9] = aux[9]; + to[stride*10] = aux[10]; + to[stride*11] = aux[11]; + to[stride*12] = aux[12]; + to[stride*13] = aux[13]; + to[stride*14] = aux[14]; + to[stride*15] = aux[15]; +} + +EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16bf,16>& kernel) { + __m256i a = kernel.packet[0]; + __m256i b = kernel.packet[1]; + __m256i c = kernel.packet[2]; + __m256i d = kernel.packet[3]; + __m256i e = kernel.packet[4]; + __m256i f = kernel.packet[5]; + __m256i g = kernel.packet[6]; + __m256i h = kernel.packet[7]; + __m256i i = kernel.packet[8]; + __m256i j = kernel.packet[9]; + __m256i k = kernel.packet[10]; + __m256i l = kernel.packet[11]; + __m256i m = kernel.packet[12]; + __m256i n = kernel.packet[13]; + __m256i o = kernel.packet[14]; + __m256i p = kernel.packet[15]; + + __m256i ab_07 = _mm256_unpacklo_epi16(a, b); + __m256i cd_07 = _mm256_unpacklo_epi16(c, d); + __m256i ef_07 = _mm256_unpacklo_epi16(e, f); + __m256i gh_07 = _mm256_unpacklo_epi16(g, h); + __m256i ij_07 = _mm256_unpacklo_epi16(i, j); + __m256i kl_07 = _mm256_unpacklo_epi16(k, l); + __m256i mn_07 = _mm256_unpacklo_epi16(m, n); + __m256i op_07 = _mm256_unpacklo_epi16(o, p); + + __m256i ab_8f = _mm256_unpackhi_epi16(a, b); + __m256i cd_8f = _mm256_unpackhi_epi16(c, d); + __m256i ef_8f = _mm256_unpackhi_epi16(e, f); + __m256i gh_8f = _mm256_unpackhi_epi16(g, h); + __m256i ij_8f = _mm256_unpackhi_epi16(i, j); + __m256i kl_8f = _mm256_unpackhi_epi16(k, l); + __m256i mn_8f = _mm256_unpackhi_epi16(m, n); + __m256i op_8f = _mm256_unpackhi_epi16(o, p); + + __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07); + __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07); + __m256i efgh_03 = _mm256_unpacklo_epi32(ef_07, gh_07); + __m256i efgh_47 = _mm256_unpackhi_epi32(ef_07, gh_07); + __m256i ijkl_03 = _mm256_unpacklo_epi32(ij_07, kl_07); + __m256i ijkl_47 = _mm256_unpackhi_epi32(ij_07, kl_07); + __m256i mnop_03 = _mm256_unpacklo_epi32(mn_07, op_07); + __m256i mnop_47 = _mm256_unpackhi_epi32(mn_07, op_07); + + __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f); + __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f); + __m256i efgh_8b = _mm256_unpacklo_epi32(ef_8f, gh_8f); + __m256i efgh_cf = _mm256_unpackhi_epi32(ef_8f, gh_8f); + __m256i ijkl_8b = _mm256_unpacklo_epi32(ij_8f, kl_8f); + __m256i ijkl_cf = _mm256_unpackhi_epi32(ij_8f, kl_8f); + __m256i mnop_8b = _mm256_unpacklo_epi32(mn_8f, op_8f); + __m256i mnop_cf = _mm256_unpackhi_epi32(mn_8f, op_8f); + + __m256i abcdefgh_01 = _mm256_unpacklo_epi64(abcd_03, efgh_03); + __m256i abcdefgh_23 = _mm256_unpackhi_epi64(abcd_03, efgh_03); + __m256i ijklmnop_01 = _mm256_unpacklo_epi64(ijkl_03, mnop_03); + __m256i ijklmnop_23 = _mm256_unpackhi_epi64(ijkl_03, mnop_03); + __m256i abcdefgh_45 = _mm256_unpacklo_epi64(abcd_47, efgh_47); + __m256i abcdefgh_67 = _mm256_unpackhi_epi64(abcd_47, efgh_47); + __m256i ijklmnop_45 = _mm256_unpacklo_epi64(ijkl_47, mnop_47); + __m256i ijklmnop_67 = _mm256_unpackhi_epi64(ijkl_47, mnop_47); + __m256i abcdefgh_89 = _mm256_unpacklo_epi64(abcd_8b, efgh_8b); + __m256i abcdefgh_ab = _mm256_unpackhi_epi64(abcd_8b, efgh_8b); + __m256i ijklmnop_89 = _mm256_unpacklo_epi64(ijkl_8b, mnop_8b); + __m256i ijklmnop_ab = _mm256_unpackhi_epi64(ijkl_8b, mnop_8b); + __m256i abcdefgh_cd = _mm256_unpacklo_epi64(abcd_cf, efgh_cf); + __m256i abcdefgh_ef = _mm256_unpackhi_epi64(abcd_cf, efgh_cf); + __m256i ijklmnop_cd = _mm256_unpacklo_epi64(ijkl_cf, mnop_cf); + __m256i ijklmnop_ef = _mm256_unpackhi_epi64(ijkl_cf, mnop_cf); + + // NOTE: no unpacklo/hi instr in this case, so using permute instr. + kernel.packet[0] = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x20); + kernel.packet[1] = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x20); + kernel.packet[2] = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x20); + kernel.packet[3] = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x20); + kernel.packet[4] = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x20); + kernel.packet[5] = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x20); + kernel.packet[6] = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x20); + kernel.packet[7] = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x20); + kernel.packet[8] = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x31); + kernel.packet[9] = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x31); + kernel.packet[10] = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x31); + kernel.packet[11] = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x31); + kernel.packet[12] = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x31); + kernel.packet[13] = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x31); + kernel.packet[14] = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x31); + kernel.packet[15] = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x31); +} + +EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16bf,4>& kernel) { + __m256i a = kernel.packet[0]; + __m256i b = kernel.packet[1]; + __m256i c = kernel.packet[2]; + __m256i d = kernel.packet[3]; + + __m256i ab_07 = _mm256_unpacklo_epi16(a, b); + __m256i cd_07 = _mm256_unpacklo_epi16(c, d); + __m256i ab_8f = _mm256_unpackhi_epi16(a, b); + __m256i cd_8f = _mm256_unpackhi_epi16(c, d); + + __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07); + __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07); + __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f); + __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f); + + // NOTE: no unpacklo/hi instr in this case, so using permute instr. + kernel.packet[0] = _mm256_permute2x128_si256(abcd_03, abcd_47, 0x20); + kernel.packet[1] = _mm256_permute2x128_si256(abcd_8b, abcd_cf, 0x20); + kernel.packet[2] = _mm256_permute2x128_si256(abcd_03, abcd_47, 0x31); + kernel.packet[3] = _mm256_permute2x128_si256(abcd_8b, abcd_cf, 0x31); +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_PACKET_MATH_AVX512_H diff --git a/Eigen/src/Core/arch/AVX512/TypeCasting.h b/Eigen/src/Core/arch/AVX512/TypeCasting.h new file mode 100644 index 0000000..3304127 --- /dev/null +++ b/Eigen/src/Core/arch/AVX512/TypeCasting.h @@ -0,0 +1,89 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2019 Rasmus Munk Larsen <rmlarsen@google.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_TYPE_CASTING_AVX512_H +#define EIGEN_TYPE_CASTING_AVX512_H + +namespace Eigen { + +namespace internal { + +template<> EIGEN_STRONG_INLINE Packet16i pcast<Packet16f, Packet16i>(const Packet16f& a) { + return _mm512_cvttps_epi32(a); +} + +template<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16i, Packet16f>(const Packet16i& a) { + return _mm512_cvtepi32_ps(a); +} + +template<> EIGEN_STRONG_INLINE Packet16i preinterpret<Packet16i, Packet16f>(const Packet16f& a) { + return _mm512_castps_si512(a); +} + +template<> EIGEN_STRONG_INLINE Packet16f preinterpret<Packet16f, Packet16i>(const Packet16i& a) { + return _mm512_castsi512_ps(a); +} + +template <> +struct type_casting_traits<half, float> { + enum { + VectorizedCast = 1, + SrcCoeffRatio = 1, + TgtCoeffRatio = 1 + }; +}; + +template<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16h, Packet16f>(const Packet16h& a) { + return half2float(a); +} + +template <> +struct type_casting_traits<float, half> { + enum { + VectorizedCast = 1, + SrcCoeffRatio = 1, + TgtCoeffRatio = 1 + }; +}; + +template<> EIGEN_STRONG_INLINE Packet16h pcast<Packet16f, Packet16h>(const Packet16f& a) { + return float2half(a); +} + +template <> +struct type_casting_traits<bfloat16, float> { + enum { + VectorizedCast = 1, + SrcCoeffRatio = 1, + TgtCoeffRatio = 1 + }; +}; + +template<> EIGEN_STRONG_INLINE Packet16f pcast<Packet16bf, Packet16f>(const Packet16bf& a) { + return Bf16ToF32(a); +} + +template <> +struct type_casting_traits<float, bfloat16> { + enum { + VectorizedCast = 1, + SrcCoeffRatio = 1, + TgtCoeffRatio = 1 + }; +}; + +template<> EIGEN_STRONG_INLINE Packet16bf pcast<Packet16f, Packet16bf>(const Packet16f& a) { + return F32ToBf16(a); +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_TYPE_CASTING_AVX512_H |