void Cmodulus::FFT(vec_long &y, const ZZX& x) const
{
FHE_TIMER_START;
zz_pBak bak; bak.save();
context.restore();
zz_pX& tmp = Cmodulus::getScratch_zz_pX();
{ FHE_NTIMER_START(FFT_remainder);
conv(tmp,x); // convert input to zpx format
}
if (!ALT_CRT && zMStar->getPow2()) {
// special case when m is a power of 2
long k = zMStar->getPow2();
long phim = (1L << (k-1));
long dx = deg(tmp);
long p = zz_p::modulus();
const zz_p *powers_p = (*powers).rep.elts();
const mulmod_precon_t *powers_aux_p = powers_aux.elts();
y.SetLength(phim);
long *yp = y.elts();
zz_p *tmp_p = tmp.rep.elts();
for (long i = 0; i <= dx; i++)
yp[i] = MulModPrecon(rep(tmp_p[i]), rep(powers_p[i]), p, powers_aux_p[i]);
for (long i = dx+1; i < phim; i++)
yp[i] = 0;
FFTFwd(yp, yp, k-1, *zz_pInfo->p_info);
return;
}
zz_p rt;
conv(rt, root); // convert root to zp format
BluesteinFFT(tmp, getM(), rt, *powers, powers_aux, *Rb); // call the FFT routine
// copy the result to the output vector y, keeping only the
// entries corresponding to primitive roots of unity
y.SetLength(zMStar->getPhiM());
long i,j;
long m = getM();
for (i=j=0; i<m; i++)
if (zMStar->inZmStar(i)) y[j++] = rep(coeff(tmp,i));
}
void Cmodulus::FFT_aux(vec_long &y, zz_pX& tmp) const
{
if (zMStar->getPow2()) {
// special case when m is a power of 2
long k = zMStar->getPow2();
long phim = (1L << (k-1));
long dx = deg(tmp);
long p = zz_p::modulus();
const zz_p *powers_p = (*powers).rep.elts();
const mulmod_precon_t *powers_aux_p = powers_aux.elts();
y.SetLength(phim);
long *yp = y.elts();
zz_p *tmp_p = tmp.rep.elts();
for (long i = 0; i <= dx; i++)
yp[i] = MulModPrecon(rep(tmp_p[i]), rep(powers_p[i]), p, powers_aux_p[i]);
for (long i = dx+1; i < phim; i++)
yp[i] = 0;
#ifdef FHE_OPENCL
AltFFTFwd(yp, yp, k-1, *altFFTInfo);
#else
FFTFwd(yp, yp, k-1, *zz_pInfo->p_info);
#endif
return;
}
zz_p rt;
conv(rt, root); // convert root to zp format
BluesteinFFT(tmp, getM(), rt, *powers, powers_aux, *Rb); // call the FFT routine
// copy the result to the output vector y, keeping only the
// entries corresponding to primitive roots of unity
y.SetLength(zMStar->getPhiM());
long i,j;
long m = getM();
for (i=j=0; i<m; i++)
if (zMStar->inZmStar(i)) y[j++] = rep(coeff(tmp,i));
}
/*! Forward real FFT */
void Fft::FftRealCcs(audio_real *X, audio_real *Sp)
{
FFTFwd(X, Sp, m_Spec, m_Buf);
}
int main()
{
#ifdef NTL_SPMM_ULL
if (sizeof(NTL_ULL_TYPE) < 2*sizeof(long)) {
printf("999999999999999 ");
print_flag();
return 0;
}
#endif
long n, k;
n = 200;
k = 10*NTL_ZZ_NBITS;
ZZ p;
RandomLen(p, k);
ZZ_p::init(p); // initialization
ZZ_pX f, g, h, r1, r2, r3;
random(g, n); // g = random polynomial of degree < n
random(h, n); // h = " "
random(f, n); // f = " "
SetCoeff(f, n); // Sets coefficient of X^n to 1
// For doing arithmetic mod f quickly, one must pre-compute
// some information.
ZZ_pXModulus F;
build(F, f);
PlainMul(r1, g, h); // this uses classical arithmetic
PlainRem(r1, r1, f);
MulMod(r2, g, h, F); // this uses the FFT
MulMod(r3, g, h, f); // uses FFT, but slower
// compare the results...
if (r1 != r2) {
printf("999999999999999 ");
print_flag();
return 0;
}
else if (r1 != r3) {
printf("999999999999999 ");
print_flag();
return 0;
}
double t;
long i, j;
long iter;
const int nprimes = 30;
const long L = 12;
const long N = 1L << L;
long r;
for (r = 0; r < nprimes; r++) UseFFTPrime(r);
vec_long aa[nprimes], AA[nprimes];
for (r = 0; r < nprimes; r++) {
aa[r].SetLength(N);
AA[r].SetLength(N);
for (i = 0; i < N; i++)
aa[r][i] = RandomBnd(GetFFTPrime(r));
FFTFwd(AA[r].elts(), aa[r].elts(), L, r);
FFTRev1(AA[r].elts(), AA[r].elts(), L, r);
}
iter = 1;
do {
t = GetTime();
for (j = 0; j < iter; j++) {
for (r = 0; r < nprimes; r++) {
long *AAp = AA[r].elts();
long *aap = aa[r].elts();
long q = GetFFTPrime(r);
mulmod_t qinv = GetFFTPrimeInv(r);
FFTFwd(AAp, aap, L, r);
FFTRev1(AAp, aap, L, r);
for (i = 0; i < N; i++) AAp[i] = NormalizedMulMod(AAp[i], aap[i], q, qinv);
}
}
t = GetTime() - t;
iter = 2*iter;
} while(t < 1);
iter = iter/2;
iter = long((1.5/t)*iter) + 1;
double tvec[5];
long w;
for (w = 0; w < 5; w++) {
t = GetTime();
for (j = 0; j < iter; j++) {
for (r = 0; r < nprimes; r++) {
long *AAp = AA[r].elts();
long *aap = aa[r].elts();
long q = GetFFTPrime(r);
mulmod_t qinv = GetFFTPrimeInv(r);
FFTFwd(AAp, aap, L, r);
FFTRev1(AAp, aap, L, r);
for (i = 0; i < N; i++) AAp[i] = NormalizedMulMod(AAp[i], aap[i], q, qinv);
}
}
t = GetTime() - t;
tvec[w] = t;
}
t = clean_data(tvec);
t = floor((t/iter)*1e13);
if (t < 0 || t >= 1e15)
printf("999999999999999 ");
else
printf("%015.0f ", t);
printf(" [%ld] ", iter);
print_flag();
return 0;
}