Grid_sse4.h
/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/simd/Grid_sse4.h
Copyright (C) 2015
Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: neo <cossu@post.kek.jp>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/* END LEGAL */
//----------------------------------------------------------------------
/*! @file Grid_sse4.h
@brief Optimization libraries for SSE4 instructions set
Using intrinsics
*/
// Time-stamp: <2015-06-16 23:27:54 neo>
//----------------------------------------------------------------------
#include <pmmintrin.h>
namespace Grid {
namespace Optimization {
template<class vtype>
union uconv {
__m128 f;
vtype v;
};
union u128f {
__m128 v;
float f[4];
};
union u128d {
__m128d v;
double f[2];
};
struct Vsplat{
//Complex float
inline __m128 operator()(float a, float b){
return _mm_set_ps(b,a,b,a);
}
// Real float
inline __m128 operator()(float a){
return _mm_set_ps(a,a,a,a);
}
//Complex double
inline __m128d operator()(double a, double b){
return _mm_set_pd(b,a);
}
//Real double
inline __m128d operator()(double a){
return _mm_set_pd(a,a);
}
//Integer
inline __m128i operator()(Integer a){
return _mm_set1_epi32(a);
}
};
struct Vstore{
//Float
inline void operator()(__m128 a, float* F){
_mm_store_ps(F,a);
}
//Double
inline void operator()(__m128d a, double* D){
_mm_store_pd(D,a);
}
//Integer
inline void operator()(__m128i a, Integer* I){
_mm_store_si128((__m128i *)I,a);
}
};
struct Vstream{
//Float
inline void operator()(float * a, __m128 b){
_mm_stream_ps(a,b);
}
//Double
inline void operator()(double * a, __m128d b){
_mm_stream_pd(a,b);
}
};
struct Vset{
// Complex float
inline __m128 operator()(Grid::ComplexF *a){
return _mm_set_ps(a[1].imag(), a[1].real(),a[0].imag(),a[0].real());
}
// Complex double
inline __m128d operator()(Grid::ComplexD *a){
return _mm_set_pd(a[0].imag(),a[0].real());
}
// Real float
inline __m128 operator()(float *a){
return _mm_set_ps(a[3],a[2],a[1],a[0]);
}
// Real double
inline __m128d operator()(double *a){
return _mm_set_pd(a[1],a[0]);
}
// Integer
inline __m128i operator()(Integer *a){
return _mm_set_epi32(a[3],a[2],a[1],a[0]);
}
};
template <typename Out_type, typename In_type>
struct Reduce{
//Need templated class to overload output type
//General form must generate error if compiled
inline Out_type operator()(In_type in){
printf("Error, using wrong Reduce function\n");
exit(1);
return 0;
}
};
/////////////////////////////////////////////////////
// Arithmetic operations
/////////////////////////////////////////////////////
struct Sum{
//Complex/Real float
inline __m128 operator()(__m128 a, __m128 b){
return _mm_add_ps(a,b);
}
//Complex/Real double
inline __m128d operator()(__m128d a, __m128d b){
return _mm_add_pd(a,b);
}
//Integer
inline __m128i operator()(__m128i a, __m128i b){
return _mm_add_epi32(a,b);
}
};
struct Sub{
//Complex/Real float
inline __m128 operator()(__m128 a, __m128 b){
return _mm_sub_ps(a,b);
}
//Complex/Real double
inline __m128d operator()(__m128d a, __m128d b){
return _mm_sub_pd(a,b);
}
//Integer
inline __m128i operator()(__m128i a, __m128i b){
return _mm_sub_epi32(a,b);
}
};
struct MultRealPart{
inline __m128 operator()(__m128 a, __m128 b){
__m128 ymm0;
ymm0 = _mm_shuffle_ps(a,a,_MM_SELECT_FOUR_FOUR(2,2,0,0)); // ymm0 <- ar ar,
return _mm_mul_ps(ymm0,b); // ymm0 <- ar bi, ar br
}
inline __m128d operator()(__m128d a, __m128d b){
__m128d ymm0;
ymm0 = _mm_shuffle_pd(a,a,0x0); // ymm0 <- ar ar, ar,ar b'00,00
return _mm_mul_pd(ymm0,b); // ymm0 <- ar bi, ar br
}
};
struct MaddRealPart{
inline __m128 operator()(__m128 a, __m128 b, __m128 c){
__m128 ymm0 = _mm_shuffle_ps(a,a,_MM_SELECT_FOUR_FOUR(2,2,0,0)); // ymm0 <- ar ar,
return _mm_add_ps(_mm_mul_ps( ymm0, b),c);
}
inline __m128d operator()(__m128d a, __m128d b, __m128d c){
__m128d ymm0 = _mm_shuffle_pd( a, a, 0x0 );
return _mm_add_pd(_mm_mul_pd( ymm0, b),c);
}
};
struct MultComplex{
// Complex float
inline __m128 operator()(__m128 a, __m128 b){
__m128 ymm0,ymm1,ymm2;
ymm0 = _mm_shuffle_ps(a,a,_MM_SELECT_FOUR_FOUR(2,2,0,0)); // ymm0 <- ar ar,
ymm0 = _mm_mul_ps(ymm0,b); // ymm0 <- ar bi, ar br
ymm1 = _mm_shuffle_ps(b,b,_MM_SELECT_FOUR_FOUR(2,3,0,1)); // ymm1 <- br,bi
ymm2 = _mm_shuffle_ps(a,a,_MM_SELECT_FOUR_FOUR(3,3,1,1)); // ymm2 <- ai,ai
ymm1 = _mm_mul_ps(ymm1,ymm2); // ymm1 <- br ai, ai bi
return _mm_addsub_ps(ymm0,ymm1);
}
// Complex double
inline __m128d operator()(__m128d a, __m128d b){
__m128d ymm0,ymm1,ymm2;
ymm0 = _mm_shuffle_pd(a,a,0x0); // ymm0 <- ar ar,
ymm0 = _mm_mul_pd(ymm0,b); // ymm0 <- ar bi, ar br
ymm1 = _mm_shuffle_pd(b,b,0x1); // ymm1 <- br,bi b01
ymm2 = _mm_shuffle_pd(a,a,0x3); // ymm2 <- ai,ai b11
ymm1 = _mm_mul_pd(ymm1,ymm2); // ymm1 <- br ai, ai bi
return _mm_addsub_pd(ymm0,ymm1);
}
};
struct Mult{
inline void mac(__m128 &a, __m128 b, __m128 c){
a= _mm_add_ps(_mm_mul_ps(b,c),a);
}
inline void mac(__m128d &a, __m128d b, __m128d c){
a= _mm_add_pd(_mm_mul_pd(b,c),a);
}
// Real float
inline __m128 operator()(__m128 a, __m128 b){
return _mm_mul_ps(a,b);
}
// Real double
inline __m128d operator()(__m128d a, __m128d b){
return _mm_mul_pd(a,b);
}
// Integer
inline __m128i operator()(__m128i a, __m128i b){
return _mm_mullo_epi32(a,b);
}
};
struct Div{
// Real float
inline __m128 operator()(__m128 a, __m128 b){
return _mm_div_ps(a,b);
}
// Real double
inline __m128d operator()(__m128d a, __m128d b){
return _mm_div_pd(a,b);
}
};
struct Conj{
// Complex single
inline __m128 operator()(__m128 in){
return _mm_xor_ps(_mm_addsub_ps(_mm_setzero_ps(),in), _mm_set1_ps(-0.f));
}
// Complex double
inline __m128d operator()(__m128d in){
return _mm_xor_pd(_mm_addsub_pd(_mm_setzero_pd(),in), _mm_set1_pd(-0.f));//untested
}
// do not define for integer input
};
struct TimesMinusI{
//Complex single
inline __m128 operator()(__m128 in, __m128 ret){
__m128 tmp =_mm_addsub_ps(_mm_setzero_ps(),in); // r,-i
return _mm_shuffle_ps(tmp,tmp,_MM_SELECT_FOUR_FOUR(2,3,0,1));
}
//Complex double
inline __m128d operator()(__m128d in, __m128d ret){
__m128d tmp =_mm_addsub_pd(_mm_setzero_pd(),in); // r,-i
return _mm_shuffle_pd(tmp,tmp,0x1);
}
};
struct TimesI{
//Complex single
inline __m128 operator()(__m128 in, __m128 ret){
__m128 tmp =_mm_shuffle_ps(in,in,_MM_SELECT_FOUR_FOUR(2,3,0,1));
return _mm_addsub_ps(_mm_setzero_ps(),tmp); // r,-i
}
//Complex double
inline __m128d operator()(__m128d in, __m128d ret){
__m128d tmp = _mm_shuffle_pd(in,in,0x1);
return _mm_addsub_pd(_mm_setzero_pd(),tmp); // r,-i
}
};
struct Permute{
static inline __m128 Permute0(__m128 in){
return _mm_shuffle_ps(in,in,_MM_SELECT_FOUR_FOUR(1,0,3,2)); //AB CD -> CD AB
};
static inline __m128 Permute1(__m128 in){
return _mm_shuffle_ps(in,in,_MM_SELECT_FOUR_FOUR(2,3,0,1)); //AB CD -> BA DC
};
static inline __m128 Permute2(__m128 in){
return in;
};
static inline __m128 Permute3(__m128 in){
return in;
};
static inline __m128d Permute0(__m128d in){ //AB -> BA
return _mm_shuffle_pd(in,in,0x1);
};
static inline __m128d Permute1(__m128d in){
return in;
};
static inline __m128d Permute2(__m128d in){
return in;
};
static inline __m128d Permute3(__m128d in){
return in;
};
};
#define _my_alignr_epi32(a,b,n) _mm_alignr_epi8(a,b,(n*4)%16)
#define _my_alignr_epi64(a,b,n) _mm_alignr_epi8(a,b,(n*8)%16)
#ifdef SFW_FP16
struct Grid_half {
Grid_half(){}
Grid_half(uint16_t raw) : x(raw) {}
uint16_t x;
};
union FP32 {
unsigned int u;
float f;
};
// PAB - Lifted and adapted from Eigen, which is GPL V2
inline float sfw_half_to_float(Grid_half h) {
const FP32 magic = { 113 << 23 };
const unsigned int shifted_exp = 0x7c00 << 13; // exponent mask after shift
FP32 o;
o.u = (h.x & 0x7fff) << 13; // exponent/mantissa bits
unsigned int exp = shifted_exp & o.u; // just the exponent
o.u += (127 - 15) << 23; // exponent adjust
// handle exponent special cases
if (exp == shifted_exp) { // Inf/NaN?
o.u += (128 - 16) << 23; // extra exp adjust
} else if (exp == 0) { // Zero/Denormal?
o.u += 1 << 23; // extra exp adjust
o.f -= magic.f; // renormalize
}
o.u |= (h.x & 0x8000) << 16; // sign bit
return o.f;
}
inline Grid_half sfw_float_to_half(float ff) {
FP32 f; f.f = ff;
const FP32 f32infty = { 255 << 23 };
const FP32 f16max = { (127 + 16) << 23 };
const FP32 denorm_magic = { ((127 - 15) + (23 - 10) + 1) << 23 };
unsigned int sign_mask = 0x80000000u;
Grid_half o;
o.x = static_cast<unsigned short>(0x0u);
unsigned int sign = f.u & sign_mask;
f.u ^= sign;
// NOTE all the integer compares in this function can be safely
// compiled into signed compares since all operands are below
// 0x80000000. Important if you want fast straight SSE2 code
// (since there's no unsigned PCMPGTD).
if (f.u >= f16max.u) { // result is Inf or NaN (all exponent bits set)
o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf
} else { // (De)normalized number or zero
if (f.u < (113 << 23)) { // resulting FP16 is subnormal or zero
// use a magic value to align our 10 mantissa bits at the bottom of
// the float. as long as FP addition is round-to-nearest-even this
// just works.
f.f += denorm_magic.f;
// and one integer subtract of the bias later, we have our final float!
o.x = static_cast<unsigned short>(f.u - denorm_magic.u);
} else {
unsigned int mant_odd = (f.u >> 13) & 1; // resulting mantissa is odd
// update exponent, rounding bias part 1
f.u += ((unsigned int)(15 - 127) << 23) + 0xfff;
// rounding bias part 2
f.u += mant_odd;
// take the bits!
o.x = static_cast<unsigned short>(f.u >> 13);
}
}
o.x |= static_cast<unsigned short>(sign >> 16);
return o;
}
static inline __m128i Grid_mm_cvtps_ph(__m128 f,int discard) {
__m128i ret=(__m128i)_mm_setzero_ps();
float *fp = (float *)&f;
Grid_half *hp = (Grid_half *)&ret;
hp[0] = sfw_float_to_half(fp[0]);
hp[1] = sfw_float_to_half(fp[1]);
hp[2] = sfw_float_to_half(fp[2]);
hp[3] = sfw_float_to_half(fp[3]);
return ret;
}
static inline __m128 Grid_mm_cvtph_ps(__m128i h,int discard) {
__m128 ret=_mm_setzero_ps();
float *fp = (float *)&ret;
Grid_half *hp = (Grid_half *)&h;
fp[0] = sfw_half_to_float(hp[0]);
fp[1] = sfw_half_to_float(hp[1]);
fp[2] = sfw_half_to_float(hp[2]);
fp[3] = sfw_half_to_float(hp[3]);
return ret;
}
#else
#define Grid_mm_cvtps_ph _mm_cvtps_ph
#define Grid_mm_cvtph_ps _mm_cvtph_ps
#endif
struct PrecisionChange {
static inline __m128i StoH (__m128 a,__m128 b) {
__m128i ha = Grid_mm_cvtps_ph(a,0);
__m128i hb = Grid_mm_cvtps_ph(b,0);
__m128i h =(__m128i) _mm_shuffle_ps((__m128)ha,(__m128)hb,_MM_SELECT_FOUR_FOUR(1,0,1,0));
return h;
}
static inline void HtoS (__m128i h,__m128 &sa,__m128 &sb) {
sa = Grid_mm_cvtph_ps(h,0);
h = (__m128i)_my_alignr_epi32((__m128i)h,(__m128i)h,2);
sb = Grid_mm_cvtph_ps(h,0);
}
static inline __m128 DtoS (__m128d a,__m128d b) {
__m128 sa = _mm_cvtpd_ps(a);
__m128 sb = _mm_cvtpd_ps(b);
__m128 s = _mm_shuffle_ps(sa,sb,_MM_SELECT_FOUR_FOUR(1,0,1,0));
return s;
}
static inline void StoD (__m128 s,__m128d &a,__m128d &b) {
a = _mm_cvtps_pd(s);
s = (__m128)_my_alignr_epi32((__m128i)s,(__m128i)s,2);
b = _mm_cvtps_pd(s);
}
static inline __m128i DtoH (__m128d a,__m128d b,__m128d c,__m128d d) {
__m128 sa,sb;
sa = DtoS(a,b);
sb = DtoS(c,d);
return StoH(sa,sb);
}
static inline void HtoD (__m128i h,__m128d &a,__m128d &b,__m128d &c,__m128d &d) {
__m128 sa,sb;
HtoS(h,sa,sb);
StoD(sa,a,b);
StoD(sb,c,d);
}
};
struct Exchange{
// 3210 ordering
static inline void Exchange0(__m128 &out1,__m128 &out2,__m128 in1,__m128 in2){
out1= _mm_shuffle_ps(in1,in2,_MM_SELECT_FOUR_FOUR(1,0,1,0));
out2= _mm_shuffle_ps(in1,in2,_MM_SELECT_FOUR_FOUR(3,2,3,2));
};
static inline void Exchange1(__m128 &out1,__m128 &out2,__m128 in1,__m128 in2){
out1= _mm_shuffle_ps(in1,in2,_MM_SELECT_FOUR_FOUR(2,0,2,0)); /*ACEG*/
out2= _mm_shuffle_ps(in1,in2,_MM_SELECT_FOUR_FOUR(3,1,3,1)); /*BDFH*/
out1= _mm_shuffle_ps(out1,out1,_MM_SELECT_FOUR_FOUR(3,1,2,0)); /*AECG*/
out2= _mm_shuffle_ps(out2,out2,_MM_SELECT_FOUR_FOUR(3,1,2,0)); /*AECG*/
};
static inline void Exchange2(__m128 &out1,__m128 &out2,__m128 in1,__m128 in2){
assert(0);
return;
};
static inline void Exchange3(__m128 &out1,__m128 &out2,__m128 in1,__m128 in2){
assert(0);
return;
};
static inline void Exchange0(__m128d &out1,__m128d &out2,__m128d in1,__m128d in2){
out1= _mm_shuffle_pd(in1,in2,0x0);
out2= _mm_shuffle_pd(in1,in2,0x3);
};
static inline void Exchange1(__m128d &out1,__m128d &out2,__m128d in1,__m128d in2){
assert(0);
return;
};
static inline void Exchange2(__m128d &out1,__m128d &out2,__m128d in1,__m128d in2){
assert(0);
return;
};
static inline void Exchange3(__m128d &out1,__m128d &out2,__m128d in1,__m128d in2){
assert(0);
return;
};
};
struct Rotate{
static inline __m128 rotate(__m128 in,int n){
switch(n){
case 0: return tRotate<0>(in);break;
case 1: return tRotate<1>(in);break;
case 2: return tRotate<2>(in);break;
case 3: return tRotate<3>(in);break;
default: assert(0);
}
}
static inline __m128d rotate(__m128d in,int n){
switch(n){
case 0: return tRotate<0>(in);break;
case 1: return tRotate<1>(in);break;
default: assert(0);
}
}
template<int n> static inline __m128 tRotate(__m128 in){ return (__m128)_my_alignr_epi32((__m128i)in,(__m128i)in,n); };
template<int n> static inline __m128d tRotate(__m128d in){ return (__m128d)_my_alignr_epi64((__m128i)in,(__m128i)in,n); };
};
//////////////////////////////////////////////
// Some Template specialization
//Complex float Reduce
template<>
inline Grid::ComplexF Reduce<Grid::ComplexF, __m128>::operator()(__m128 in){
__m128 v1; // two complex
v1= Optimization::Permute::Permute0(in);
v1= _mm_add_ps(v1,in);
u128f conv; conv.v=v1;
return Grid::ComplexF(conv.f[0],conv.f[1]);
}
//Real float Reduce
template<>
inline Grid::RealF Reduce<Grid::RealF, __m128>::operator()(__m128 in){
__m128 v1,v2; // quad single
v1= Optimization::Permute::Permute0(in);
v1= _mm_add_ps(v1,in);
v2= Optimization::Permute::Permute1(v1);
v1 = _mm_add_ps(v1,v2);
u128f conv; conv.v=v1;
return conv.f[0];
}
//Complex double Reduce
template<>
inline Grid::ComplexD Reduce<Grid::ComplexD, __m128d>::operator()(__m128d in){
u128d conv; conv.v = in;
return Grid::ComplexD(conv.f[0],conv.f[1]);
}
//Real double Reduce
template<>
inline Grid::RealD Reduce<Grid::RealD, __m128d>::operator()(__m128d in){
__m128d v1;
v1 = Optimization::Permute::Permute0(in);
v1 = _mm_add_pd(v1,in);
u128d conv; conv.v = v1;
return conv.f[0];
}
//Integer Reduce
template<>
inline Integer Reduce<Integer, __m128i>::operator()(__m128i in){
__m128i v1 = _mm_hadd_epi32(in, in);
__m128i v2 = _mm_hadd_epi32(v1, v1);
return _mm_cvtsi128_si32(v2);
}
}
//////////////////////////////////////////////////////////////////////////////////////
// Here assign types
typedef __m128i SIMD_Htype; // Single precision type
typedef __m128 SIMD_Ftype; // Single precision type
typedef __m128d SIMD_Dtype; // Double precision type
typedef __m128i SIMD_Itype; // Integer type
// prefetch utilities
inline void v_prefetch0(int size, const char *ptr){};
inline void prefetch_HINT_T0(const char *ptr){
_mm_prefetch(ptr,_MM_HINT_T0);
}
// Function name aliases
typedef Optimization::Vsplat VsplatSIMD;
typedef Optimization::Vstore VstoreSIMD;
typedef Optimization::Vset VsetSIMD;
typedef Optimization::Vstream VstreamSIMD;
template <typename S, typename T> using ReduceSIMD = Optimization::Reduce<S,T>;
// Arithmetic operations
typedef Optimization::Sum SumSIMD;
typedef Optimization::Sub SubSIMD;
typedef Optimization::Div DivSIMD;
typedef Optimization::Mult MultSIMD;
typedef Optimization::MultComplex MultComplexSIMD;
typedef Optimization::MultRealPart MultRealPartSIMD;
typedef Optimization::MaddRealPart MaddRealPartSIMD;
typedef Optimization::Conj ConjSIMD;
typedef Optimization::TimesMinusI TimesMinusISIMD;
typedef Optimization::TimesI TimesISIMD;
}
