void Cmod<type>::iFFT(zpx &x, const zzv& y)const
{
FHE_TIMER_START;
zpBak bak; bak.save();
context.restore();
zp rt;
long m = getM();
// convert input to zpx format, initializing only the coeffs i s.t. (i,m)=1
x.rep.SetLength(m);
long i,j;
for (i=j=0; i<m; i++)
if (zMStar->inZmStar(i)) conv(x.rep[i], y[j++]);
x.normalize();
conv(rt, rInv); // convert rInv to zp format
BluesteinFFT(x, m, rt, *ipowers, ipowers_aux, *iRb, iRb_aux, *Ra); // call the FFT routine
// reduce the result mod (Phi_m(X),q) and copy to the output polynomial x
FHE_NTIMER_START("iFFT:division")
rem(x, x, *phimx); // out %= (Phi_m(X),q)
FHE_NTIMER_STOP("iFFT:division")
// normalize
zp mm_inv;
conv(mm_inv, m_inv);
x *= mm_inv;
FHE_TIMER_STOP;
}
void FFTHelper::FFT(const zz_pX& f, Vec<zz_p>& v) const
{
tmp = f;
BluesteinFFT(tmp, m, root, powers, powers_aux, Rb, Rb_aux, Ra);
v.SetLength(phim);
for (long i = 0, j = 0; i < m; i++)
if (coprime[i]) v[j++] = coeff(tmp, i);
}
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 FFTHelper::iFFT(zz_pX& f, const Vec<zz_p>& v, bool normalize) const
{
tmp.rep.SetLength(m);
for (long i = 0, j = 0; i < m; i++) {
if (coprime[i]) tmp.rep[i] = v[j++];
}
tmp.normalize();
BluesteinFFT(tmp, m, iroot, ipowers, ipowers_aux, iRb, iRb_aux, Ra);
rem(f, tmp, phimx);
if (normalize) f *= m_inv;
}
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));
}
void Cmod<zz,zp,zpx,zzv,fftrep,zpContext>::FFT(zzv &y, const ZZX& x) const
{
context.restore();
zp rt;
zpx in, out;
conv(in,x); // convert input to zpx format
conv(rt, root); // convert root to zp format
BluesteinFFT(out, in, getM(), rt, *powers, *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->phiM());
unsigned i,j;
for (i=j=0; i<getM(); i++)
if (zmStar->inZmStar(i)) y[j++] = rep(coeff(out,i));
}
void Cmod<type>::FFT(zzv &y, const ZZX& x) const
{
FHE_TIMER_START;
zpBak bak; bak.save();
context.restore();
zp rt;
zpx& tmp = getScratch();
conv(tmp,x); // convert input to zpx format
conv(rt, root); // convert root to zp format
BluesteinFFT(tmp, getM(), rt, *powers, powers_aux, *Rb, Rb_aux, *Ra); // 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));
FHE_TIMER_STOP;
}
void Cmod<zz,zp,zpx,zzv,fftrep,zpContext>::iFFT(ZZX &x, const zzv& y) const
{
context.restore();
zp rt;
zpx in, out, pwrs;
// convert input to zpx format, initializing only the coeffs i s.t. (i,m)=1
in.SetMaxLength(getM());
unsigned i,j;
for (i=j=0; i<getM(); i++)
if (zmStar->inZmStar(i)) SetCoeff(in, i, y[j++]);
in.normalize();
conv(rt, rInv); // convert rInv to zp format
BluesteinFFT(out, in, getM(), rt, *ipowers, *iRb); // call the FFT routine
out /= getM(); // normalization
// reduce the result mod (Phi_m(X),q) and copy to the output polynomial x
conv(in, zmStar->PhimX()); // convert Phi_m(X) to zpx format
rem(out, out, in); // out %= (Phi_m(X),q)
conv(x,out); // convert output to ZZX format
}
void Cmodulus::iFFT(zz_pX &x, const vec_long& y)const
{
FHE_TIMER_START;
zz_pBak bak; bak.save();
context.restore();
if (zMStar->getPow2()) {
// special case when m is a power of 2
long k = zMStar->getPow2();
long phim = (1L << (k-1));
long p = zz_p::modulus();
const zz_p *ipowers_p = (*ipowers).rep.elts();
const mulmod_precon_t *ipowers_aux_p = ipowers_aux.elts();
const long *yp = y.elts();
vec_long& tmp = Cmodulus::getScratch_vec_long();
tmp.SetLength(phim);
long *tmp_p = tmp.elts();
#ifdef FHE_OPENCL
AltFFTRev1(tmp_p, yp, k-1, *altFFTInfo);
#else
FFTRev1(tmp_p, yp, k-1, *zz_pInfo->p_info);
#endif
x.rep.SetLength(phim);
zz_p *xp = x.rep.elts();
for (long i = 0; i < phim; i++)
xp[i].LoopHole() = MulModPrecon(tmp_p[i], rep(ipowers_p[i]), p, ipowers_aux_p[i]);
x.normalize();
return;
}
zz_p rt;
long m = getM();
// convert input to zpx format, initializing only the coeffs i s.t. (i,m)=1
x.rep.SetLength(m);
long i,j;
for (i=j=0; i<m; i++)
if (zMStar->inZmStar(i)) x.rep[i].LoopHole() = y[j++]; // DIRT: y[j] already reduced
x.normalize();
conv(rt, rInv); // convert rInv to zp format
BluesteinFFT(x, m, rt, *ipowers, ipowers_aux, *iRb); // call the FFT routine
// reduce the result mod (Phi_m(X),q) and copy to the output polynomial x
{ FHE_NTIMER_START(iFFT_division);
rem(x, x, *phimx); // out %= (Phi_m(X),q)
}
// normalize
zz_p mm_inv;
conv(mm_inv, m_inv);
x *= mm_inv;
}
