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convolution.cc
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#include "convolution.h"
using namespace std;
using namespace utils;
namespace fftwpp {
#ifdef __SSE2__
const union uvec sse2_pm = {
{ 0x00000000,0x00000000,0x00000000,0x80000000 }
};
/*
const union uvec sse2_mp = {
{ 0x00000000,0x80000000,0x00000000,0x00000000 }
};
*/
const union uvec sse2_mm = {
{ 0x00000000,0x80000000,0x00000000,0x80000000 }
};
#endif
const double sqrt3=sqrt(3.0);
const double hsqrt3=0.5*sqrt3;
const Complex zeta3(-0.5,hsqrt3);
const double twopi=2.0*M_PI;
// Build zeta table, returning the floor of the square root of m.
unsigned int BuildZeta(double arg, unsigned int m,
Complex *&ZetaH, Complex *&ZetaL, unsigned int threads,
unsigned int s)
{
if(s == 0) s=(int) sqrt((double) m);
unsigned int t=m/s;
if(s*t < m) ++t;
ZetaH=ComplexAlign(t);
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(unsigned int a=0; a < t; ++a) {
double theta=s*a*arg;
ZetaH[a]=Complex(cos(theta),sin(theta));
}
ZetaL=ComplexAlign(s);
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(unsigned int b=0; b < s; ++b) {
double theta=b*arg;
ZetaL[b]=Complex(cos(theta),sin(theta));
}
return s;
}
unsigned int BuildZeta(unsigned int n, unsigned int m,
Complex *&ZetaH, Complex *&ZetaL, unsigned int threads,
unsigned int s)
{
return BuildZeta(twopi/n,m,ZetaH,ZetaL,threads,s);
}
void ImplicitConvolution::convolve(Complex **F, multiplier *pmult,
unsigned int i, unsigned int offset)
{
if(indexsize >= 1) index[indexsize-1]=i;
unsigned int C=max(A,B);
Complex *P[C];
for(unsigned int a=0; a < C; ++a)
P[a]=F[a]+offset;
// Backwards FFT (even indices):
for(unsigned int a=0; a < A; ++a) {
BackwardsO->fft(P[a],U[a]);
}
if(A >= B)
(*pmult)(U,m,indexsize,index,0,threads); // multiply even indices
switch(A) {
case 1: pretransform<pretransform1>(P); break;
case 2: pretransform<pretransform2>(P); break;
case 3: pretransform<pretransform3>(P); break;
case 4: pretransform<pretransform4>(P); break;
default: pretransform<general>(P);
}
if(A > B) { // U[A-1] is free
Complex *W[A];
W[A-1]=U[A-1];
for(unsigned int a=1; a < A; ++a)
W[a-1]=P[a];
for(unsigned int a=A; a-- > 0;) // Loop from A-1 to 0.
BackwardsO->fft(P[a],W[a]);
(*pmult)(W,m,indexsize,index,1,threads); // multiply odd indices
// Return to original space
Complex *lastW=W[A-1];
for(unsigned int b=0; b < B; ++b) {
Complex *Pb=P[b];
ForwardsO->fft(W[b],Pb);
ForwardsO->fft(U[b],lastW);
posttransform(Pb,lastW);
}
} else if(A < B) { // U[B-1] is free
Complex *W[B];
W[B-1]=U[B-1];
for(unsigned int b=1; b < B; ++b)
W[b-1]=P[b];
for(unsigned int a=A; a-- > 0;) // Loop from A-1 to 0.
BackwardsO->fft(P[a],W[a]);
(*pmult)(W,m,indexsize,index,1,threads); // multiply odd indices
// Return to original space
for(unsigned int b=0; b < B; ++b)
ForwardsO->fft(W[b],P[b]);
(*pmult)(U,m,indexsize,index,0,threads); // multiply even indices
Complex *f0=P[0];
Complex *u0=U[0];
Forwards->fft(u0);
posttransform(f0,u0);
for(unsigned int b=1; b < B; ++b) {
Complex *fb=P[b];
Complex *ub=U[b];
Complex *u0=U[0];
ForwardsO->fft(ub,u0);
posttransform(fb,u0);
}
} else { // A == B
// Backwards FFT (odd indices):
for(unsigned int a=0; a < A; ++a)
Backwards->fft(P[a]);
(*pmult)(P,m,indexsize,index,1,threads); //multiply odd indices
// Return to original space:
Complex *f0=P[0];
Complex *u0=U[0];
Forwards->fft(f0);
Forwards->fft(u0);
posttransform(f0,u0);
for(unsigned int b=1; b < B; ++b) {
Complex *fb=P[b];
Complex *ub=U[b];
Complex *u0=U[0];
Forwards->fft(fb);
ForwardsO->fft(ub,u0);
posttransform(fb,u0);
}
}
}
template<class T>
inline void ImplicitConvolution::
pretransform(Complex **F, unsigned int k, Vec& Zetak)
{
for(unsigned int a=0; a < A; ++a) {
Complex *fka=F[a]+k;
STORE(fka,ZMULT(Zetak,LOAD(fka)));
}
}
template<>
inline void ImplicitConvolution::
pretransform<pretransform1>(Complex **F, unsigned int k, Vec& Zetak)
{
Complex *fk0=F[0]+k;
Vec Fk0=LOAD(fk0);
STORE(fk0,ZMULT(Zetak,Fk0));
}
template<>
inline void ImplicitConvolution::
pretransform<pretransform2>(Complex **F, unsigned int k, Vec& Zetak)
{
Complex *fk0=F[0]+k;
Complex *fk1=F[1]+k;
Vec Fk0=LOAD(fk0);
Vec Fk1=LOAD(fk1);
STORE(fk0,ZMULT(Zetak,Fk0));
STORE(fk1,ZMULT(Zetak,Fk1));
}
template<>
inline void ImplicitConvolution::
pretransform<pretransform3>(Complex **F, unsigned int k, Vec& Zetak)
{
Complex *fk0=F[0]+k;
Complex *fk1=F[1]+k;
Complex *fk2=F[2]+k;
Vec Fk0=LOAD(fk0);
Vec Fk1=LOAD(fk1);
Vec Fk2=LOAD(fk2);
STORE(fk0,ZMULT(Zetak,Fk0));
STORE(fk1,ZMULT(Zetak,Fk1));
STORE(fk2,ZMULT(Zetak,Fk2));
}
template<>
inline void ImplicitConvolution::
pretransform<pretransform4>(Complex **F, unsigned int k, Vec& Zetak)
{
Complex *fk0=F[0]+k;
Complex *fk1=F[1]+k;
Complex *fk2=F[2]+k;
Complex *fk3=F[3]+k;
Vec Fk0=LOAD(fk0);
Vec Fk1=LOAD(fk1);
Vec Fk2=LOAD(fk2);
Vec Fk3=LOAD(fk3);
STORE(fk0,ZMULT(Zetak,Fk0));
STORE(fk1,ZMULT(Zetak,Fk1));
STORE(fk2,ZMULT(Zetak,Fk2));
STORE(fk3,ZMULT(Zetak,Fk3));
}
// multiply by root of unity to prepare for inverse FFT for odd modes
template<class T>
void ImplicitConvolution::pretransform(Complex **F)
{
PARALLEL(
for(unsigned int K=0; K < m; K += s) {
Complex *ZetaL0=ZetaL-K;
unsigned int stop=min(K+s,m);
Vec Zeta=LOAD(ZetaH+K/s);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
for(unsigned int k=K; k < stop; ++k) {
Vec Zetak=ZMULT(X,Y,LOAD(ZetaL0+k));
pretransform<T>(F,k,Zetak);
}
}
);
}
// multiply by root of unity to prepare and add for inverse FFT for odd modes
void ImplicitConvolution::posttransform(Complex *f, Complex *u)
{
PARALLEL(
for(unsigned int K=0; K < m; K += s) {
unsigned int stop=min(K+s,m);
Complex *ZetaL0=ZetaL-K;
Vec Zeta=LOAD(ZetaH+K/s);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
for(unsigned int k=K; k < stop; ++k) {
Vec Zetak=ZMULT(X,Y,LOAD(ZetaL0+k));
Complex *fki=f+k;
STORE(fki,ZCMULT(Zetak,LOAD(fki))+LOAD(u+k));
}
}
);
}
void ImplicitHConvolution::pretransform(Complex *F, Complex *f1c, Complex *U)
{
Vec Mhalf=LOAD2(-0.5);
Vec HSqrt3=LOAD2(hsqrt3);
double Re=0.0, Im=0.0;
unsigned int m1=m-1;
U[0]=compact ? F->re : F->re-F[m].re; // Nyquist
if(even) {
unsigned int a=1/s;
Vec Zeta=LOAD(ZetaH+a);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
Vec zeta1=ZMULT(X,Y,LOAD(ZetaL+1-s*a));
Vec Fa=LOAD(F+1);
Vec Fb=LOAD(F+m1);
Vec B=Fb*Mhalf+CONJ(Fa);
Fb *= HSqrt3;
Vec A=ZCMULT(zeta1,UNPACKL(B,Fb)); // Optimize?
B=ZCMULTI(zeta1,UNPACKH(B,Fb));
STORE(f1c,CONJ(A+B));
double re=F[c].re;
Re=2.0*re;
Im=re+sqrt3*F[c].im;
}
unsigned int c1=c+1;
unsigned int d=c1/2;
unsigned int a=c1/s;
Vec Zeta=LOAD(ZetaH+a);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
Vec Zetac1=ZMULT(X,Y,LOAD(ZetaL+c1-s*a));
PARALLEL(
for(unsigned int K=0; K <= d; K += s) {
Complex *ZetaL0=ZetaL-K;
unsigned int stop=min(K+s,d+1);
Vec Zeta=LOAD(ZetaH+K/s);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
Complex *fm=F+m;
Complex *fpc1=F+c1;
Complex *fmc1=fm-c1;
Complex *upc1=U+c1;
for(unsigned int k=max(1,K); k < stop; ++k) {
Vec zetak=ZMULT(X,Y,LOAD(ZetaL0+k));
Vec Zetak=ZCMULT(zetak,Zetac1);
Vec Fa=LOAD(F+k);
Vec FA=LOAD(fpc1-k);
Vec FB=LOAD(fmc1+k);
Vec Fb=LOAD(fm-k);
Vec b=Fb*Mhalf+CONJ(Fa);
STORE(F+k,Fa+CONJ(Fb));
Fb *= HSqrt3;
Vec a=ZCMULT(zetak,UNPACKL(b,Fb));
b=ZCMULTI(zetak,UNPACKH(b,Fb));
STORE(fmc1+k,CONJ(a+b));
STORE(U+k,a-b);
b=FB*Mhalf+CONJ(FA);
STORE(fpc1-k,FA+CONJ(FB));
FB *= HSqrt3;
a=ZCMULT(Zetak,UNPACKL(b,FB));
b=ZCMULTI(Zetak,UNPACKH(b,FB));
STORE(upc1-k,a-b);
STORE(fm-k,CONJ(a+b));
}
}
);
if(even) {
F[c]=Re;
U[c]=Im;
}
}
void ImplicitHConvolution::posttransform(Complex *F, const Complex& w,
Complex *U)
{
Vec Mhalf=LOAD2(-0.5);
Vec HSqrt3=LOAD2(hsqrt3);
unsigned int m1=m-1;
unsigned int c1=c+1;
unsigned int d=c1/2;
unsigned int a=c1/s;
Vec Zeta=LOAD(ZetaH+a);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
Vec Zetac1=ZMULT(X,Y,LOAD(ZetaL+c1-s*a));
if(even && m > 2) {
unsigned int a=1/s;
Vec Zeta=LOAD(ZetaH+a);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
Vec zeta1=ZMULT(X,Y,LOAD(ZetaL+1-s*a));
Vec Zeta1=ZCMULT(zeta1,Zetac1);
Complex *f0=F;
Vec F0=LOAD(f0+1);
Vec F1=ZCMULT(zeta1,LOAD(&w));
Vec F2=ZMULT(zeta1,LOAD(U+1));
Vec S=F1+F2;
F2=CONJ(F0+Mhalf*S)-HSqrt3*FLIP(F1-F2);
STORE(f0+1,F0+S);
F0=LOAD(f0+c);
F1=ZCMULT(Zeta1,LOAD(f0+m1));
STORE(f0+m1,F2);
F2=ZMULT(Zeta1,LOAD(U+c));
STORE(f0+c,F0+F1+F2);
}
unsigned int D=c-d;
PARALLEL(
for(unsigned int K=0; K <= D; K += s) {
Complex *ZetaL0=ZetaL-K;
unsigned int stop=min(K+s,D+1);
Vec Zeta=LOAD(ZetaH+K/s);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
Complex *fm=F+m;
Complex *fpc1=F+c1;
Complex *fmc1=fm-c1;
Complex *upc1=U+c1;
for(unsigned int k=max(even+1,K); k < stop; ++k) {
Vec zetak=ZMULT(X,Y,LOAD(ZetaL0+k));
Vec Zetak=ZCMULT(zetak,Zetac1);
Vec F0=LOAD(F+k);
Vec F1=ZCMULT(zetak,LOAD(fmc1+k));
Vec F2=ZMULT(zetak,LOAD(U+k));
Vec S=F1+F2;
F2=CONJ(F0+Mhalf*S)-HSqrt3*FLIP(F1-F2);
Vec FA=LOAD(fpc1-k);
Vec FB=ZCMULT(Zetak,LOAD(fm-k));
Vec FC=ZMULT(Zetak,LOAD(upc1-k));
Vec T=FB+FC;
STORE(F+k,F0+S);
STORE(fpc1-k,FA+T);
STORE(fmc1+k,CONJ(FA+Mhalf*T)-HSqrt3*FLIP(FB-FC));
STORE(fm-k,F2);
}
}
);
if(d == D+1) {
unsigned int a=d/s;
Vec Zeta=LOAD(ZetaH+a);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
Vec Zetak=ZMULT(X,Y,LOAD(ZetaL+d-s*a));
Vec F0=LOAD(F+d);
Vec F1=ZCMULT(Zetak,LOAD(d == 1 && even ? &w : F+m-d));
Vec F2=ZMULT(Zetak,LOAD(U+d));
Vec S=F1+F2;
STORE(F+d,F0+S);
STORE(F+m-d,CONJ(F0+Mhalf*S)-HSqrt3*FLIP(F1-F2));
}
}
void ImplicitHConvolution::convolve(Complex **F, realmultiplier *pmult,
unsigned int i, unsigned int offset)
{
if(indexsize >= 1) index[indexsize-1]=i;
// Set problem-size variables and pointers:
unsigned int C=max(A,B);
Complex *C0[C], *C1[C], *C2[C]; // inputs to complex2real FFTs
double *D0[C], *D1[C], *D2[C]; // outputs of complex2real FFTs
Complex **c0=C0, **c1=C1, **c2=C2;
double **d0=D0, **d1=D1, **d2=D2;
unsigned int start=m-1-c; // c-1 (c) for m=even (odd)
for(unsigned int a=0; a < C; ++a) {
Complex *f=F[a]+offset;
c0[a]=f;
c1[a]=f+start;
}
if(A != B) {
for(unsigned int a=0; a < C-1; ++a) {
d0[a]=(double *) c0[a+1];
d1[a]=(double *) c1[a+1];
}
if(A > B) {
d0[A-1]=(double *) U[A-1];
d1[A-1]=(double *) U[A-1];
d2=(double **) U;
for(unsigned int b=0; b < B; ++b)
c2[b]=U[b+1];
} else {
d0[B-1]=(double *) U[0];
d1[B-1]=(double *) U[0];
for(unsigned int b=0; b < B-1; ++b)
c2[b]=U[b+1];
c2[B-1]=U[0];
for(unsigned int b=0; b < B; ++b)
d2[b]=(double *) c2[b];
}
} else {
c2=U;
d0=(double **) c0;
d1=(double **) c1;
d2=(double **) c2;
}
// Complex-to-real FFTs and pmults:
double Re[B],Im[B];
// r=-1 (backwards):
if(A >= B) {
for(unsigned int a=0; a < A-1; ++a) {
pretransform(c0[a],w+a,U[A-1]);
cro->fft(U[A-1],U[a]);
}
pretransform(c0[A-1],w+A-1,U[A-1]);
cr->fft(U[A-1]);
(*pmult)((double **) U,m,indexsize,index,-1,threads);
} else {
for(unsigned int a=A; a-- > 0;) {// Loop from A-1 to 0.
pretransform(c0[a],w+a,U[a]);
cro->fft(U[a],d2[a]);
}
}
// r=0:
double T[A];
for(unsigned int a=A; a-- > 0;) { // Loop from A-1 to 0.
Complex *c0a=c0[a];
T[a]=c0a[0].re; // r=0, k=0
if(!compact)
c0a[0].re += 2.0*c0a[m].re; // Nyquist
crO->fft(c0a,d0[a]);
}
(*pmult)(d0,m,indexsize,index,0,threads);
for(unsigned int b=0; b < B; ++b) {
Complex *c0b=c0[b];
rcO->fft(d0[b],c0b);
if(!compact) c0b[m]=0.0; // Zero Nyquist mode, for Hermitian symmetry.
Complex z=c0[b][start]; // r=0, k=start
Re[b]=z.re;
Im[b]=z.im;
}
if(even) {
for(unsigned int a=C; a-- > 0;) { // Loop from C-1 to 0.
Complex *c1a=c1[a];
Complex tmp=w[a];
w[a].re=c1a[1].re; // r=0, k=c
c1a[1]=tmp; // r=1, k=1
}
}
// r=1:
for(unsigned int a=A; a-- > 0;) { // Loop from A-1 to 0.
Complex *c1a=c1[a];
c1a[0]=compact ? T[a] : T[a]-c1a[c+1].re; // r=1, k=0 with Nyquist
crO->fft(c1[a],d1[a]);
}
(*pmult)(d1,m,indexsize,index,1,threads);
for(unsigned int b=0; b < B; ++b) {
Complex *c1b=c1[b];
rcO->fft(d1[b],c1b); // r=1
if(even) {
double tmp=w[b].re;
w[b]=c1b[1]; // r=1, k=1
c1b[1]=tmp; // r=0, k=c
}
}
// r=-1 (forwards):
if(A > B) {
for(unsigned int b=0; b < B; ++b) {
rco->fft(d2[b],U[A-1]);
double R=c1[b][0].re;
c0[b][start]=Complex(Re[b],Im[b]); // r=0, k=c-1 (c) for m=even (odd)
c0[b][0]=c0[b][0].re+R+U[A-1][0].re;
posttransform(c0[b],w[b],U[A-1]);
}
} else {
if(A < B)
(*pmult)(d2,m,indexsize,index,-1,threads);
rc->fft(c2[0]);
double R=c1[0][0].re;
c0[0][start]=Complex(Re[0],Im[0]); // r=0, k=c-1 (c) for m=even (odd)
c0[0][0]=c0[0][0].re+R+c2[0][0].re;
posttransform(c0[0],w[0],c2[0]);
for(unsigned int b=1; b < B; ++b) {
rco->fft(d2[b],c2[0]);
double R=c1[b][0].re;
c0[b][start]=Complex(Re[b],Im[b]); // r=0, k=c-1 (c) for m=even (odd)
c0[b][0]=c0[b][0].re+R+c2[0][0].re;
posttransform(c0[b],w[b],c2[0]);
}
}
}
void fftpad::expand(Complex *f, Complex *u)
{
PARALLEL(
for(unsigned int K=0; K < m; K += s) {
Complex *ZetaL0=ZetaL-K;
unsigned int stop=min(K+s,m);
Vec H=LOAD(ZetaH+K/s);
for(unsigned int k=K; k < stop; ++k) {
Vec Zetak=ZMULT(H,LOAD(ZetaL0+k));
Vec X=UNPACKL(Zetak,Zetak);
Vec Y=CONJ(UNPACKH(Zetak,Zetak));
unsigned int kstride=k*stride;
Complex *fk=f+kstride;
Complex *uk=u+kstride;
for(unsigned int i=0; i < M; ++i)
STORE(uk+i,ZMULT(X,Y,LOAD(fk+i)));
}
}
);
}
void fftpad::backwards(Complex *f, Complex *u)
{
expand(f,u);
Backwards->fft(f);
Backwards->fft(u);
}
void fftpad::reduce(Complex *f, Complex *u)
{
PARALLEL(
for(unsigned int K=0; K < m; K += s) {
Complex *ZetaL0=ZetaL-K;
unsigned int stop=min(K+s,m);
Vec H=LOAD(ZetaH+K/s);
for(unsigned int k=K; k < stop; ++k) {
Vec Zetak=ZMULT(H,LOAD(ZetaL0+k));
Vec X=UNPACKL(Zetak,Zetak);
Vec Y=UNPACKH(CONJ(Zetak),Zetak);
unsigned int kstride=k*stride;
Complex *uk=u+kstride;
Complex *fk=f+kstride;
for(unsigned int i=0; i < M; ++i)
STORE(fk+i,LOAD(fk+i)+ZMULT(X,Y,LOAD(uk+i)));
}
}
);
}
void fftpad::forwards(Complex *f, Complex *u)
{
Forwards->fft(f);
Forwards->fft(u);
reduce(f,u);
}
void fft0pad::expand(Complex *f, Complex *u)
{
Complex *fm1stride=f+(m-1)*stride;
for(unsigned int i=0; i < M; ++i)
u[i]=fm1stride[i];
Vec Mhalf=LOAD2(-0.5);
Vec Mhsqrt3=LOAD2(-hsqrt3);
unsigned int stop=s;
for(unsigned int K=0; K < m; K += s) {
Complex *ZetaL0=ZetaL-K;
Vec H=LOAD(ZetaH+K/s);
for(unsigned int k=max(1,K); k < stop; ++k) {
Vec Zetak=ZMULT(H,LOAD(ZetaL0+k));
Vec X=UNPACKL(Zetak,Zetak);
Vec Y=CONJ(UNPACKH(Zetak,Zetak));
unsigned int kstride=k*stride;
Complex *uk=u+kstride;
Complex *fk=f+kstride;
Complex *fmk=fm1stride+kstride;
for(unsigned int i=0; i < M; ++i) {
Vec A=LOAD(fmk+i);
Vec B=LOAD(f+i);
Vec Z=B*Mhalf+A;
STORE(f+i,LOAD(fk+i));
STORE(fk+i,B+A);
B *= Mhsqrt3;
A=ZMULT(X,Y,UNPACKL(Z,B));
B=ZMULTI(X,Y,CONJ(UNPACKH(Z,B)));
STORE(fmk+i,A+B);
STORE(uk+i,CONJ(A-B));
}
}
stop=min(stop+s,m);
}
}
void fft0pad::Backwards1(Complex *f, Complex *u)
{
Complex *umstride=u+m*stride;
Complex *fm1stride=f+(m-1)*stride;
for(unsigned int i=0; i < M; ++i) {
umstride[i]=fm1stride[i]; // Store extra value here.
fm1stride[i]=u[i];
}
Backwards->fft(fm1stride);
}
void fft0pad::backwards(Complex *f, Complex *u)
{
expand(f,u);
Backwards->fft(f);
Backwards1(f,u);
Backwards->fft(u);
}
void fft0pad::reduce(Complex *f, Complex *u)
{
Complex *umstride=u+m*stride;
for(unsigned int i=0; i < M; ++i)
umstride[i]=umstride[i]+f[i]+u[i];
Vec Mhalf=LOAD2(-0.5);
Vec HSqrt3=LOAD2(hsqrt3);
Complex *fm1stride=f+(m-1)*stride;
unsigned int stop=s;
for(unsigned int K=0; K < m; K += s) {
Complex *ZetaL0=ZetaL-K;
Vec H=LOAD(ZetaH+K/s);
for(unsigned int k=max(1,K); k < stop; ++k) {
Vec Zetak=ZMULT(H,LOAD(ZetaL0+k));
Vec X=UNPACKL(Zetak,Zetak);
Vec Y=CONJ(UNPACKH(Zetak,Zetak));
unsigned int kstride=k*stride;
Complex *fk=f+kstride;
Complex *fm1k=fm1stride+kstride;
Complex *uk=u+kstride;
for(unsigned int i=0; i < M; ++i) {
Vec F0=LOAD(fk+i);
Vec F1=ZMULT(X,-Y,LOAD(fm1k+i));
Vec F2=ZMULT(X,Y,LOAD(uk+i));
Vec S=F1+F2;
STORE(fk+i-stride,F0+Mhalf*S+HSqrt3*ZMULTI(F1-F2));
STORE(fm1k+i,F0+S);
}
}
stop=min(stop+s,m);
}
for(unsigned int i=0; i < M; ++i)
fm1stride[i]=umstride[i];
}
void fft0pad::Forwards0(Complex *f)
{
Forwards->fft(f+(m-1)*stride);
}
void fft0pad::Forwards1(Complex *f, Complex *u)
{
Complex *umstride=u+m*stride;
unsigned int m1stride=(m-1)*stride;
Complex *fm1stride=f+m1stride;
for(unsigned int i=0; i < M; ++i) {
Complex temp=umstride[i];
umstride[i]=fm1stride[i];
fm1stride[i]=temp;
}
}
void fft0pad::forwards(Complex *f, Complex *u)
{
Forwards0(f);
Forwards1(f,u);
Forwards->fft(f);
Forwards->fft(u);
reduce(f,u);
}
void fft1pad::expand(Complex *f, Complex *u)
{
Complex *fmstride=f+m*stride;
for(unsigned int i=0; i < M; ++i) {
Complex Nyquist=f[i];
f[i]=fmstride[i]+2.0*Nyquist;
u[i]=fmstride[i] -= Nyquist;
}
Vec Mhalf=LOAD2(-0.5);
Vec Mhsqrt3=LOAD2(-hsqrt3);
unsigned int inc=s;
PARALLEL(
for(unsigned int K=0; K < m; K += inc) {
Complex *ZetaL0=ZetaL-K;
unsigned int stop=min(K+s,m);
Vec Zeta=LOAD(ZetaH+K/s);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
for(unsigned int k=max(1,K); k < stop; ++k) {
Vec zetak=ZMULT(X,Y,LOAD(ZetaL0+k));
unsigned int kstride=k*stride;
Complex *uk=u+kstride;
Complex *fk=f+kstride;
Complex *fmk=fmstride+kstride;
for(unsigned int i=0; i < M; ++i) {
Vec Fa=LOAD(fk+i);
Vec Fb=LOAD(fmk+i);
Vec B=Fa*Mhalf+Fb;
STORE(fk+i,Fa+Fb);
Fa *= Mhsqrt3;
Vec A=ZMULT(zetak,UNPACKL(B,Fa));
B=ZMULTI(zetak,UNPACKH(B,Fa));
STORE(fmk+i,A+B);
STORE(uk+i,CONJ(A-B));
}
}
}
);
}
void fft1pad::Backwards1(Complex *f, Complex *u)
{
Backwards->fft(f+m*stride);
}
void fft1pad::reduce(Complex *f, Complex *u)
{
Complex *fmstride=f+m*stride;
for(unsigned int i=0; i < M; ++i) {
Complex f0=f[i];
Complex f1=fmstride[i];
Complex f2=u[i];
f[i]=0.0; // Zero Nyquist mode, for Hermitian symmetry.
fmstride[i]=(f0+f1+f2);
}
Vec Mhalf=LOAD2(-0.5);
Vec HSqrt3=LOAD2(hsqrt3);
unsigned int inc=s;
PARALLEL(
for(unsigned int K=0; K < m; K += inc) {
Complex *ZetaL0=ZetaL-K;
unsigned int stop=min(K+s,m);
Vec Zeta=LOAD(ZetaH+K/s);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
for(unsigned int k=max(1,K); k < stop; ++k) {
Vec zetak=ZMULT(X,Y,LOAD(ZetaL0+k));
unsigned int kstride=k*stride;
Complex *fk=f+kstride;
Complex *fmk=fmstride+kstride;
Complex *uk=u+kstride;
for(unsigned int i=0; i < M; ++i) {
Vec F0=LOAD(fk+i);
Vec F1=ZCMULT(zetak,LOAD(fmk+i));
Vec F2=ZMULT(zetak,LOAD(uk+i));
Vec S=F1+F2;
STORE(fk+i,F0+Mhalf*S+HSqrt3*ZMULTI(F1-F2));
STORE(fmk+i,F0+S);
}
}
}
);
}
void fft1pad::Forwards0(Complex *f)
{
Forwards->fft(f+m*stride);
}
void fft1pad::Forwards1(Complex *f, Complex *u)
{
}
void fft1pad::forwards(Complex *f, Complex *u)
{
Forwards->fft(f);
Forwards->fft(f+m*stride);
Forwards->fft(u);
reduce(f,u);
}
// a[0][k]=sum_i a[i][k]*b[i][k]*c[i][k]
void ImplicitHTConvolution::mult(double *a, double *b, double **C,
unsigned int offset)
{
unsigned int twom=2*m;
if(M == 1) { // a[k]=a[k]*b[k]*c[k]
double *C0=C[0]+offset;
#ifdef __SSE2__
PARALLEL(
for(unsigned int k=0; k < twom; k += 2) {
double *ak=a+k;
STORE(ak,LOAD(ak)*LOAD(b+k)*LOAD(C0+k));
}
);
#else
PARALLEL(
for(unsigned int k=0; k < twom; ++k)
a[k] *= b[k]*C0[k];
);
#endif
} else if(M == 2) {
double *a1=a+stride;
double *b1=b+stride;
double *C0=C[0]+offset;
double *C1=C[1]+offset;
#ifdef __SSE2__
PARALLEL(
for(unsigned int k=0; k < twom; k += 2) {
double *ak=a+k;
STORE(ak,LOAD(ak)*LOAD(b+k)*LOAD(C0+k)+
LOAD(a1+k)*LOAD(b1+k)*LOAD(C1+k));
}
);
#else
PARALLEL(
for(unsigned int k=0; k < twom; ++k)
a[k]=a[k]*b[k]*C0[k]+a1[k]*b1[k]*C1[k];
);
#endif
} else if(M == 3) {
double *a1=a+stride;
double *a2=a1+stride;
double *b1=b+stride;
double *b2=b1+stride;
double *C0=C[0]+offset;
double *C1=C[1]+offset;
double *C2=C[2]+offset;
#ifdef __SSE2__
PARALLEL(
for(unsigned int k=0; k < twom; k += 2) {
double *ak=a+k;
STORE(ak,LOAD(ak)*LOAD(b+k)*LOAD(C0+k)+
LOAD(a1+k)*LOAD(b1+k)*LOAD(C1+k)+
LOAD(a2+k)*LOAD(b2+k)*LOAD(C2+k));
}
);
#else
PARALLEL(
for(unsigned int k=0; k < twom; ++k)
a[k]=a[k]*b[k]*C0[k]+a1[k]*b1[k]*C1[k]+a2[k]*b2[k]*C2[k];
);
#endif
} else {
double *A=a-offset;
double *B=b-offset;
double *C0=C[0];
unsigned int stop=twom+offset;
#ifdef __SSE2__
PARALLEL(
for(unsigned int k=offset; k < stop; k += 2) {
double *p=A+k;
double *q=B+k;
Vec sum=LOAD(p)*LOAD(q)*LOAD(C0+k);
for(unsigned int i=1; i < M; ++i) {
unsigned int istride=i*stride;
sum += LOAD(p+istride)*LOAD(q+istride)*LOAD(C[i]+k);
}
STORE(p,sum);
}
);
#else
PARALLEL(
for(unsigned int k=offset; k < stop; ++k) {
double *p=A+k;
double *q=B+k;
double sum=(*p)*(*q)*C0[k];
for(unsigned int i=1; i < M; ++i) {
unsigned int istride=i*stride;
sum += p[istride]*q[istride]*C[i][k];
}
*p=sum;
}
);
#endif
}
}
void ImplicitHTConvolution::convolve(Complex **F, Complex **G, Complex **H,
Complex *u, Complex *v, Complex **W,
unsigned int offset)
{
// 8M-3 of 8M FFTs are out-of-place
Complex *w=W[0];
unsigned int m1=m+1;
for(unsigned int i=0; i < M; ++i) {
Complex *fi=F[i]+offset;
Complex *gi=G[i]+offset;
Complex *hi=H[i]+offset;
unsigned int im1=i*m1;
Complex *ui=u+im1;
Complex *vi=v+im1;
Complex *wi=w+im1;
if(i+1 < M) {
ui += m1;
vi += m1;
wi += m1;
}
PARALLEL(
for(unsigned int K=0; K < m; K += s) {
Complex *ZetaL0=ZetaL-K;
unsigned int stop=min(K+s,m);
Vec Zeta=LOAD(ZetaH+K/s);
Vec X=UNPACKL(Zeta,Zeta);
Vec Y=CONJ(UNPACKH(Zeta,Zeta));
for(unsigned int k=K; k < stop; ++k) {
Vec Zetak=ZMULT(X,Y,LOAD(ZetaL0+k));
Vec Fk=LOAD(fi+k);
Vec Gk=LOAD(gi+k);
Vec Hk=LOAD(hi+k);
STORE(ui+k,ZMULT(Zetak,Fk));
STORE(vi+k,ZMULT(Zetak,Gk));
STORE(wi+k,ZMULT(Zetak,Hk));
}
}
);
ui[m]=0.0;
vi[m]=0.0;
wi[m]=0.0;