Grid_avx512.h
/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/simd/Grid_avx512.h
Copyright (C) 2015
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: neo <cossu@post.kek.jp>
Author: paboyle <paboyle@ph.ed.ac.uk>
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 */
#include <immintrin.h>
namespace Grid{
namespace Optimization {
union u512f {
__m512 v;
float f[16];
};
union u512d {
__m512d v;
double f[8];
};
struct Vsplat{
//Complex float
inline __m512 operator()(float a, float b){
return _mm512_set_ps(b,a,b,a,b,a,b,a,b,a,b,a,b,a,b,a);
}
// Real float
inline __m512 operator()(float a){
return _mm512_set1_ps(a);
}
//Complex double
inline __m512d operator()(double a, double b){
return _mm512_set_pd(b,a,b,a,b,a,b,a);
}
//Real double
inline __m512d operator()(double a){
return _mm512_set1_pd(a);
}
//Integer
inline __m512i operator()(Integer a){
return _mm512_set1_epi32(a);
}
};
struct Vstore{
//Float
inline void operator()(__m512 a, float* F){
_mm512_store_ps(F,a);
}
//Double
inline void operator()(__m512d a, double* D){
_mm512_store_pd(D,a);
}
//Integer
inline void operator()(__m512i a, Integer* I){
_mm512_store_si512((__m512i *)I,a);
}
};
struct Vstream{
//Float
inline void operator()(float * a, __m512 b){
_mm512_stream_ps(a,b);
// _mm512_store_ps(a,b);
}
//Double
inline void operator()(double * a, __m512d b){
_mm512_stream_pd(a,b);
// _mm512_store_pd(a,b);
}
};
struct Vset{
// Complex float
inline __m512 operator()(Grid::ComplexF *a){
return _mm512_set_ps(a[7].imag(),a[7].real(),a[6].imag(),a[6].real(),
a[5].imag(),a[5].real(),a[4].imag(),a[4].real(),
a[3].imag(),a[3].real(),a[2].imag(),a[2].real(),
a[1].imag(),a[1].real(),a[0].imag(),a[0].real());
}
// Complex double
inline __m512d operator()(Grid::ComplexD *a){
return _mm512_set_pd(a[3].imag(),a[3].real(),a[2].imag(),a[2].real(),
a[1].imag(),a[1].real(),a[0].imag(),a[0].real());
}
// Real float
inline __m512 operator()(float *a){
return _mm512_set_ps( a[15],a[14],a[13],a[12],a[11],a[10],a[9],a[8],
a[7],a[6],a[5],a[4],a[3],a[2],a[1],a[0]);
}
// Real double
inline __m512d operator()(double *a){
return _mm512_set_pd(a[7],a[6],a[5],a[4],a[3],a[2],a[1],a[0]);
}
// Integer
inline __m512i operator()(Integer *a){
return _mm512_set_epi32( a[15],a[14],a[13],a[12],a[11],a[10],a[9],a[8],
a[7],a[6],a[5],a[4],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 __m512 operator()(__m512 a, __m512 b){
return _mm512_add_ps(a,b);
}
//Complex/Real double
inline __m512d operator()(__m512d a, __m512d b){
return _mm512_add_pd(a,b);
}
//Integer
inline __m512i operator()(__m512i a, __m512i b){
return _mm512_add_epi32(a,b);
}
};
struct Sub{
//Complex/Real float
inline __m512 operator()(__m512 a, __m512 b){
return _mm512_sub_ps(a,b);
}
//Complex/Real double
inline __m512d operator()(__m512d a, __m512d b){
return _mm512_sub_pd(a,b);
}
//Integer
inline __m512i operator()(__m512i a, __m512i b){
return _mm512_sub_epi32(a,b);
}
};
// Note, we can beat the shuf overhead in chain with two temporaries
// Ar Ai , Br Bi, Ai Ar // one shuf
//tmpr Ar Br, Ai Bi // Mul/Mac/Mac
//tmpi Br Ai, Bi Ar // Mul/Mac/Mac
// add tmpi,shuf(tmpi)
// sub tmpr,shuf(tmpi)
// shuf(tmpr,tmpi). // Could drop/trade for write mask
// Gives
// 2mul,4 mac +add+sub = 8 flop type insns
// 3shuf + 2 (+shuf) = 5/6 simd perm and 1/2 the load.
struct MultRealPart{
inline __m512 operator()(__m512 a, __m512 b){
__m512 ymm0;
ymm0 = _mm512_moveldup_ps(a); // ymm0 <- ar ar,
return _mm512_mul_ps(ymm0,b); // ymm0 <- ar bi, ar br
}
inline __m512d operator()(__m512d a, __m512d b){
__m512d ymm0;
ymm0 = _mm512_shuffle_pd(a,a,0x00); // ymm0 <- ar ar, ar,ar b'00,00
return _mm512_mul_pd(ymm0,b); // ymm0 <- ar bi, ar br
}
};
struct MaddRealPart{
inline __m512 operator()(__m512 a, __m512 b, __m512 c){
__m512 ymm0 = _mm512_moveldup_ps(a); // ymm0 <- ar ar,
return _mm512_fmadd_ps( ymm0, b, c);
}
inline __m512d operator()(__m512d a, __m512d b, __m512d c){
__m512d ymm0 = _mm512_shuffle_pd( a, a, 0x00 );
return _mm512_fmadd_pd( ymm0, b, c);
}
};
struct MultComplex{
// Complex float
inline __m512 operator()(__m512 a, __m512 b){
// dup, dup, perm, mul, madd
__m512 a_real = _mm512_moveldup_ps( a ); // Ar Ar
__m512 a_imag = _mm512_movehdup_ps( a ); // Ai Ai
a_imag = _mm512_mul_ps( a_imag, _mm512_permute_ps( b, 0xB1 ) ); // (Ai, Ai) * (Bi, Br) = Ai Bi, Ai Br
return _mm512_fmaddsub_ps( a_real, b, a_imag ); // Ar Br , Ar Bi +- Ai Bi = ArBr-AiBi , ArBi+AiBr
}
// Complex double
inline __m512d operator()(__m512d a, __m512d b){
__m512d a_real = _mm512_shuffle_pd( a, a, 0x00 );
__m512d a_imag = _mm512_shuffle_pd( a, a, 0xFF );
a_imag = _mm512_mul_pd( a_imag, _mm512_permute_pd( b, 0x55 ) );
return _mm512_fmaddsub_pd( a_real, b, a_imag );
}
};
struct Mult{
inline void mac(__m512 &a, __m512 b, __m512 c){
a= _mm512_fmadd_ps( b, c, a);
}
inline void mac(__m512d &a, __m512d b, __m512d c){
a= _mm512_fmadd_pd( b, c, a);
}
// Real float
inline __m512 operator()(__m512 a, __m512 b){
return _mm512_mul_ps(a,b);
}
// Real double
inline __m512d operator()(__m512d a, __m512d b){
return _mm512_mul_pd(a,b);
}
// Integer
inline __m512i operator()(__m512i a, __m512i b){
return _mm512_mullo_epi32(a,b);
}
};
struct Div{
// Real float
inline __m512 operator()(__m512 a, __m512 b){
return _mm512_div_ps(a,b);
}
// Real double
inline __m512d operator()(__m512d a, __m512d b){
return _mm512_div_pd(a,b);
}
};
struct Conj{
// Complex single
inline __m512 operator()(__m512 in){
return _mm512_mask_sub_ps(in,0xaaaa,_mm512_setzero_ps(),in); // Zero out 0+real 0-imag
}
// Complex double
inline __m512d operator()(__m512d in){
return _mm512_mask_sub_pd(in, 0xaa,_mm512_setzero_pd(), in);
}
// do not define for integer input
};
struct TimesMinusI{
//Complex single
inline __m512 operator()(__m512 in, __m512 ret){
//__m512 tmp = _mm512_mask_sub_ps(in,0xaaaa,_mm512_setzero_ps(),in); // real -imag
//return _mm512_shuffle_ps(tmp,tmp,_MM_SELECT_FOUR_FOUR(2,3,1,0)); // 0x4E??
__m512 tmp = _mm512_shuffle_ps(in,in,_MM_SELECT_FOUR_FOUR(2,3,0,1));
return _mm512_mask_sub_ps(tmp,0xaaaa,_mm512_setzero_ps(),tmp);
}
//Complex double
inline __m512d operator()(__m512d in, __m512d ret){
//__m512d tmp = _mm512_mask_sub_pd(in,0xaa,_mm512_setzero_pd(),in); // real -imag
//return _mm512_shuffle_pd(tmp,tmp,0x55);
__m512d tmp = _mm512_shuffle_pd(in,in,0x55);
return _mm512_mask_sub_pd(tmp,0xaa,_mm512_setzero_pd(),tmp);
}
};
struct TimesI{
//Complex single
inline __m512 operator()(__m512 in, __m512 ret){
__m512 tmp = _mm512_shuffle_ps(in,in,_MM_SELECT_FOUR_FOUR(2,3,0,1));
return _mm512_mask_sub_ps(tmp,0x5555,_mm512_setzero_ps(),tmp);
}
//Complex double
inline __m512d operator()(__m512d in, __m512d ret){
__m512d tmp = _mm512_shuffle_pd(in,in,0x55);
return _mm512_mask_sub_pd(tmp,0x55,_mm512_setzero_pd(),tmp);
}
};
// Gpermute utilities consider coalescing into 1 Gpermute
struct Permute{
static inline __m512 Permute0(__m512 in){
return _mm512_shuffle_f32x4(in,in,_MM_SELECT_FOUR_FOUR(1,0,3,2));
};
static inline __m512 Permute1(__m512 in){
return _mm512_shuffle_f32x4(in,in,_MM_SELECT_FOUR_FOUR(2,3,0,1));
};
static inline __m512 Permute2(__m512 in){
return _mm512_shuffle_ps(in,in,_MM_SELECT_FOUR_FOUR(1,0,3,2));
};
static inline __m512 Permute3(__m512 in){
return _mm512_shuffle_ps(in,in,_MM_SELECT_FOUR_FOUR(2,3,0,1));
};
static inline __m512d Permute0(__m512d in){
return _mm512_shuffle_f64x2(in,in,_MM_SELECT_FOUR_FOUR(1,0,3,2));
};
static inline __m512d Permute1(__m512d in){
return _mm512_shuffle_f64x2(in,in,_MM_SELECT_FOUR_FOUR(2,3,0,1));
};
static inline __m512d Permute2(__m512d in){
return _mm512_shuffle_pd(in,in,0x55);
};
static inline __m512d Permute3(__m512d in){
return in;
};
};
#define USE_FP16
struct PrecisionChange {
static inline __m512i StoH (__m512 a,__m512 b) {
__m512i h;
#ifdef USE_FP16
__m256i ha = _mm512_cvtps_ph(a,0);
__m256i hb = _mm512_cvtps_ph(b,0);
h =(__m512i) _mm512_castps256_ps512((__m256)ha);
h =(__m512i) _mm512_insertf64x4((__m512d)h,(__m256d)hb,1);
#else
assert(0);
#endif
return h;
}
static inline void HtoS (__m512i h,__m512 &sa,__m512 &sb) {
#ifdef USE_FP16
sa = _mm512_cvtph_ps((__m256i)_mm512_extractf64x4_pd((__m512d)h,0));
sb = _mm512_cvtph_ps((__m256i)_mm512_extractf64x4_pd((__m512d)h,1));
#else
assert(0);
#endif
}
static inline __m512 DtoS (__m512d a,__m512d b) {
__m256 sa = _mm512_cvtpd_ps(a);
__m256 sb = _mm512_cvtpd_ps(b);
__m512 s = _mm512_castps256_ps512(sa);
s =(__m512) _mm512_insertf64x4((__m512d)s,(__m256d)sb,1);
return s;
}
static inline void StoD (__m512 s,__m512d &a,__m512d &b) {
a = _mm512_cvtps_pd((__m256)_mm512_extractf64x4_pd((__m512d)s,0));
b = _mm512_cvtps_pd((__m256)_mm512_extractf64x4_pd((__m512d)s,1));
}
static inline __m512i DtoH (__m512d a,__m512d b,__m512d c,__m512d d) {
__m512 sa,sb;
sa = DtoS(a,b);
sb = DtoS(c,d);
return StoH(sa,sb);
}
static inline void HtoD (__m512i h,__m512d &a,__m512d &b,__m512d &c,__m512d &d) {
__m512 sa,sb;
HtoS(h,sa,sb);
StoD(sa,a,b);
StoD(sb,c,d);
}
};
// On extracting face: Ah Al , Bh Bl -> Ah Bh, Al Bl
// On merging buffers: Ah,Bh , Al Bl -> Ah Al, Bh, Bl
// The operation is its own inverse
struct Exchange{
// 3210 ordering
static inline void Exchange0(__m512 &out1,__m512 &out2,__m512 in1,__m512 in2){
out1= _mm512_shuffle_f32x4(in1,in2,_MM_SELECT_FOUR_FOUR(1,0,1,0));
out2= _mm512_shuffle_f32x4(in1,in2,_MM_SELECT_FOUR_FOUR(3,2,3,2));
};
static inline void Exchange1(__m512 &out1,__m512 &out2,__m512 in1,__m512 in2){
out1= _mm512_shuffle_f32x4(in1,in2,_MM_SELECT_FOUR_FOUR(2,0,2,0));
out2= _mm512_shuffle_f32x4(in1,in2,_MM_SELECT_FOUR_FOUR(3,1,3,1));
out1= _mm512_shuffle_f32x4(out1,out1,_MM_SELECT_FOUR_FOUR(3,1,2,0)); /*AECG*/
out2= _mm512_shuffle_f32x4(out2,out2,_MM_SELECT_FOUR_FOUR(3,1,2,0)); /*AECG*/
};
static inline void Exchange2(__m512 &out1,__m512 &out2,__m512 in1,__m512 in2){
out1= _mm512_shuffle_ps(in1,in2,_MM_SELECT_FOUR_FOUR(1,0,1,0));
out2= _mm512_shuffle_ps(in1,in2,_MM_SELECT_FOUR_FOUR(3,2,3,2));
};
static inline void Exchange3(__m512 &out1,__m512 &out2,__m512 in1,__m512 in2){
out1= _mm512_shuffle_ps(in1,in2,_MM_SELECT_FOUR_FOUR(2,0,2,0));
out2= _mm512_shuffle_ps(in1,in2,_MM_SELECT_FOUR_FOUR(3,1,3,1));
out1= _mm512_shuffle_ps(out1,out1,_MM_SELECT_FOUR_FOUR(3,1,2,0)); /*AECG*/
out2= _mm512_shuffle_ps(out2,out2,_MM_SELECT_FOUR_FOUR(3,1,2,0)); /*AECG*/
};
static inline void Exchange0(__m512d &out1,__m512d &out2,__m512d in1,__m512d in2){
out1= _mm512_shuffle_f64x2(in1,in2,_MM_SELECT_FOUR_FOUR(1,0,1,0));
out2= _mm512_shuffle_f64x2(in1,in2,_MM_SELECT_FOUR_FOUR(3,2,3,2));
};
static inline void Exchange1(__m512d &out1,__m512d &out2,__m512d in1,__m512d in2){
out1= _mm512_shuffle_f64x2(in1,in2,_MM_SELECT_FOUR_FOUR(2,0,2,0));
out2= _mm512_shuffle_f64x2(in1,in2,_MM_SELECT_FOUR_FOUR(3,1,3,1));
out1= _mm512_shuffle_f64x2(out1,out1,_MM_SELECT_FOUR_FOUR(3,1,2,0)); /*AECG*/
out2= _mm512_shuffle_f64x2(out2,out2,_MM_SELECT_FOUR_FOUR(3,1,2,0)); /*AECG*/
};
static inline void Exchange2(__m512d &out1,__m512d &out2,__m512d in1,__m512d in2){
out1 = _mm512_shuffle_pd(in1,in2,0x00);
out2 = _mm512_shuffle_pd(in1,in2,0xFF);
};
static inline void Exchange3(__m512d &out1,__m512d &out2,__m512d in1,__m512d in2){
assert(0);
return;
};
};
struct Rotate{
static inline __m512 rotate(__m512 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;
case 4: return tRotate<4>(in);break;
case 5: return tRotate<5>(in);break;
case 6: return tRotate<6>(in);break;
case 7: return tRotate<7>(in);break;
case 8 : return tRotate<8>(in);break;
case 9 : return tRotate<9>(in);break;
case 10: return tRotate<10>(in);break;
case 11: return tRotate<11>(in);break;
case 12: return tRotate<12>(in);break;
case 13: return tRotate<13>(in);break;
case 14: return tRotate<14>(in);break;
case 15: return tRotate<15>(in);break;
default: assert(0);
}
}
static inline __m512d rotate(__m512d 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;
case 4: return tRotate<4>(in);break;
case 5: return tRotate<5>(in);break;
case 6: return tRotate<6>(in);break;
case 7: return tRotate<7>(in);break;
default: assert(0);
}
}
template<int n> static inline __m512 tRotate(__m512 in){
return (__m512)_mm512_alignr_epi32((__m512i)in,(__m512i)in,n);
};
template<int n> static inline __m512d tRotate(__m512d in){
return (__m512d)_mm512_alignr_epi64((__m512i)in,(__m512i)in,n);
};
};
//////////////////////////////////////////////
// Some Template specialization
// Hack for CLANG until mm512_reduce_add_ps etc... are implemented in GCC and Clang releases
#ifndef __INTEL_COMPILER
#warning "Slow reduction due to incomplete reduce intrinsics"
//Complex float Reduce
template<>
inline Grid::ComplexF Reduce<Grid::ComplexF, __m512>::operator()(__m512 in){
__m512 v1,v2;
v1=Optimization::Permute::Permute0(in); // avx 512; quad complex single
v1= _mm512_add_ps(v1,in);
v2=Optimization::Permute::Permute1(v1);
v1 = _mm512_add_ps(v1,v2);
v2=Optimization::Permute::Permute2(v1);
v1 = _mm512_add_ps(v1,v2);
u512f conv; conv.v = v1;
return Grid::ComplexF(conv.f[0],conv.f[1]);
}
//Real float Reduce
template<>
inline Grid::RealF Reduce<Grid::RealF, __m512>::operator()(__m512 in){
__m512 v1,v2;
v1 = Optimization::Permute::Permute0(in); // avx 512; octo-double
v1 = _mm512_add_ps(v1,in);
v2 = Optimization::Permute::Permute1(v1);
v1 = _mm512_add_ps(v1,v2);
v2 = Optimization::Permute::Permute2(v1);
v1 = _mm512_add_ps(v1,v2);
v2 = Optimization::Permute::Permute3(v1);
v1 = _mm512_add_ps(v1,v2);
u512f conv; conv.v=v1;
return conv.f[0];
}
//Complex double Reduce
template<>
inline Grid::ComplexD Reduce<Grid::ComplexD, __m512d>::operator()(__m512d in){
__m512d v1;
v1 = Optimization::Permute::Permute0(in); // sse 128; paired complex single
v1 = _mm512_add_pd(v1,in);
v1 = Optimization::Permute::Permute1(in); // sse 128; paired complex single
v1 = _mm512_add_pd(v1,in);
u512d conv; conv.v = v1;
return Grid::ComplexD(conv.f[0],conv.f[1]);
}
//Real double Reduce
template<>
inline Grid::RealD Reduce<Grid::RealD, __m512d>::operator()(__m512d in){
__m512d v1,v2;
v1 = Optimization::Permute::Permute0(in); // avx 512; quad double
v1 = _mm512_add_pd(v1,in);
v2 = Optimization::Permute::Permute1(v1);
v1 = _mm512_add_pd(v1,v2);
v2 = Optimization::Permute::Permute2(v1);
v1 = _mm512_add_pd(v1,v2);
u512d conv; conv.v = v1;
return conv.f[0];
}
//Integer Reduce
template<>
inline Integer Reduce<Integer, __m512i>::operator()(__m512i in){
// No full vector reduce, use AVX to add upper and lower halves of register
// and perform AVX reduction.
__m256i v1, v2, v3;
__m128i u1, u2, ret;
v1 = _mm512_castsi512_si256(in); // upper half
v2 = _mm512_extracti32x8_epi32(in, 1); // lower half
v3 = _mm256_add_epi32(v1, v2);
v1 = _mm256_hadd_epi32(v3, v3);
v2 = _mm256_hadd_epi32(v1, v1);
u1 = _mm256_castsi256_si128(v2) // upper half
u2 = _mm256_extracti128_si256(v2, 1); // lower half
ret = _mm_add_epi32(u1, u2);
return _mm_cvtsi128_si32(ret);
}
#else
//Complex float Reduce
template<>
inline Grid::ComplexF Reduce<Grid::ComplexF, __m512>::operator()(__m512 in){
return Grid::ComplexF(_mm512_mask_reduce_add_ps(0x5555, in),_mm512_mask_reduce_add_ps(0xAAAA, in));
}
//Real float Reduce
template<>
inline Grid::RealF Reduce<Grid::RealF, __m512>::operator()(__m512 in){
return _mm512_reduce_add_ps(in);
}
//Complex double Reduce
template<>
inline Grid::ComplexD Reduce<Grid::ComplexD, __m512d>::operator()(__m512d in){
return Grid::ComplexD(_mm512_mask_reduce_add_pd(0x55, in),_mm512_mask_reduce_add_pd(0xAA, in));
}
//Real double Reduce
template<>
inline Grid::RealD Reduce<Grid::RealD, __m512d>::operator()(__m512d in){
return _mm512_reduce_add_pd(in);
}
//Integer Reduce
template<>
inline Integer Reduce<Integer, __m512i>::operator()(__m512i in){
return _mm512_reduce_add_epi32(in);
}
#endif
}
//////////////////////////////////////////////////////////////////////////////////////
// Here assign types
typedef __m512i SIMD_Htype; // Single precision type
typedef __m512 SIMD_Ftype; // Single precision type
typedef __m512d SIMD_Dtype; // Double precision type
typedef __m512i SIMD_Itype; // Integer type
// prefecth
inline void v_prefetch0(int size, const char *ptr){
for(int i=0;i<size;i+=64){ // Define L1 linesize above
_mm_prefetch(ptr+i+4096,_MM_HINT_T1);
_mm_prefetch(ptr+i+512,_MM_HINT_T0);
}
}
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::Mult MultSIMD;
typedef Optimization::Div DivSIMD;
typedef Optimization::MultComplex MultComplexSIMD;
typedef Optimization::MultRealPart MultRealPartSIMD;
typedef Optimization::MaddRealPart MaddRealPartSIMD;
typedef Optimization::Conj ConjSIMD;
typedef Optimization::TimesMinusI TimesMinusISIMD;
typedef Optimization::TimesI TimesISIMD;
}
