zz_pInfoT::zz_pInfoT(long NewP, long maxroot)
{
if (maxroot < 0) LogicError("zz_pContext: maxroot may not be negative");
if (NewP <= 1) LogicError("zz_pContext: p must be > 1");
if (NumBits(NewP) > NTL_SP_NBITS) ResourceError("zz_pContext: modulus too big");
ZZ P, B, M, M1, MinusM;
long n, i;
long q, t;
p = NewP;
pinv = 1/double(p);
p_info = 0;
conv(P, p);
sqr(B, P);
LeftShift(B, B, maxroot+NTL_FFTFudge);
set(M);
n = 0;
while (M <= B) {
UseFFTPrime(n);
q = GetFFTPrime(n);
n++;
mul(M, M, q);
}
if (n > 4) LogicError("zz_pInit: too many primes");
NumPrimes = n;
PrimeCnt = n;
MaxRoot = CalcMaxRoot(q);
if (maxroot < MaxRoot)
MaxRoot = maxroot;
negate(MinusM, M);
MinusMModP = rem(MinusM, p);
CoeffModP.SetLength(n);
x.SetLength(n);
u.SetLength(n);
for (i = 0; i < n; i++) {
q = GetFFTPrime(i);
div(M1, M, q);
t = rem(M1, q);
t = InvMod(t, q);
if (NTL_zz_p_QUICK_CRT) mul(M1, M1, t);
CoeffModP[i] = rem(M1, p);
x[i] = ((double) t)/((double) q);
u[i] = t;
}
}
zz_pInfoT::zz_pInfoT(INIT_FFT_TYPE, FFTPrimeInfo *info)
{
p = info->q;
pinv = info->qinv;
p_info = info;
NumPrimes = 1;
PrimeCnt = 0;
MaxRoot = CalcMaxRoot(p);
}
NTL_CLIENT
// It is assumed that m,q,context, and root are already set. If root is set
// to zero, it will be computed by the compRoots() method. Then rInv is
// computed as the inverse of root.
zz_pContext BuildContext(long p, long maxroot) {
if (maxroot <= CalcMaxRoot(p))
return zz_pContext(INIT_USER_FFT, p);
else
return zz_pContext(p, maxroot);
}
void InitFFTPrimeInfo(FFTPrimeInfo& info, long q, long w, long bigtab)
{
double qinv = 1/((double) q);
long mr = CalcMaxRoot(q);
info.q = q;
info.qinv = qinv;
info.zz_p_context = 0;
info.RootTable.SetLength(mr+1);
info.RootInvTable.SetLength(mr+1);
info.TwoInvTable.SetLength(mr+1);
info.TwoInvPreconTable.SetLength(mr+1);
long *rt = &info.RootTable[0];
long *rit = &info.RootInvTable[0];
long *tit = &info.TwoInvTable[0];
mulmod_precon_t *tipt = &info.TwoInvPreconTable[0];
long j;
long t;
rt[mr] = w;
for (j = mr-1; j >= 0; j--)
rt[j] = MulMod(rt[j+1], rt[j+1], q);
rit[mr] = InvMod(w, q);
for (j = mr-1; j >= 0; j--)
rit[j] = MulMod(rit[j+1], rit[j+1], q);
t = InvMod(2, q);
tit[0] = 1;
for (j = 1; j <= mr; j++)
tit[j] = MulMod(tit[j-1], t, q);
for (j = 0; j <= mr; j++)
tipt[j] = PrepMulModPrecon(tit[j], q, qinv);
info.bigtab = bigtab;
}
zz_pInfoT::zz_pInfoT(INIT_USER_FFT_TYPE, long q)
{
long w;
if (!IsFFTPrime(q, w)) LogicError("invalid user supplied prime");
p = q;
pinv = 1/((double) q);
p_info_owner.make();
p_info = p_info_owner.get();
bool bigtab = false;
#ifdef NTL_FFT_BIGTAB
bigtab = true;
#endif
InitFFTPrimeInfo(*p_info, q, w, bigtab);
NumPrimes = 1;
PrimeCnt = 0;
MaxRoot = CalcMaxRoot(p);
}
zz_pInfoT::zz_pInfoT(long Index)
{
ref_count = 1;
index = Index;
if (index < 0)
Error("bad FFT prime index");
// allows non-consecutive indices...I'm not sure why
while (NumFFTPrimes < index)
UseFFTPrime(NumFFTPrimes);
UseFFTPrime(index);
p = FFTPrime[index];
pinv = FFTPrimeInv[index];
NumPrimes = 1;
PrimeCnt = 0;
MaxRoot = CalcMaxRoot(p);
}
void ZZ_p::DoInstall()
{
SmartPtr<ZZ_pTmpSpaceT> tmps = 0;
do { // NOTE: thread safe lazy init
Lazy<ZZ_pFFTInfoT>::Builder builder(ZZ_pInfo->FFTInfo);
if (!builder()) break;
UniquePtr<ZZ_pFFTInfoT> FFTInfo;
FFTInfo.make();
ZZ B, M, M1, M2, M3;
long n, i;
long q, t;
mulmod_t qinv;
sqr(B, ZZ_pInfo->p);
LeftShift(B, B, NTL_FFTMaxRoot+NTL_FFTFudge);
// FIXME: the following is quadratic time...would
// be nice to get a faster solution...
// One could estimate the # of primes by summing logs,
// then multiply using a tree-based multiply, then
// adjust up or down...
// Assuming IEEE floating point, the worst case estimate
// for error guarantees a correct answer +/- 1 for
// numprimes up to 2^25...for sure we won't be
// using that many primes...we can certainly put in
// a sanity check, though.
// If I want a more accuaruate summation (with using Kahan,
// which has some portability issues), I could represent
// numbers as x = a + f, where a is integer and f is the fractional
// part. Summing in this representation introduces an *absolute*
// error of 2 epsilon n, which is just as good as Kahan
// for this application.
// same strategy could also be used in the ZZX HomMul routine,
// if we ever want to make that subquadratic
set(M);
n = 0;
while (M <= B) {
UseFFTPrime(n);
q = GetFFTPrime(n);
n++;
mul(M, M, q);
}
FFTInfo->NumPrimes = n;
FFTInfo->MaxRoot = CalcMaxRoot(q);
double fn = double(n);
if (8.0*fn*(fn+48) > NTL_FDOUBLE_PRECISION)
ResourceError("modulus too big");
if (8.0*fn*(fn+48) <= NTL_FDOUBLE_PRECISION/double(NTL_SP_BOUND))
FFTInfo->QuickCRT = true;
else
FFTInfo->QuickCRT = false;
// FIXME: some of this stuff does not need to be initialized
// at all if FFTInfo->crt_struct.special()
FFTInfo->x.SetLength(n);
FFTInfo->u.SetLength(n);
FFTInfo->uqinv.SetLength(n);
FFTInfo->rem_struct.init(n, ZZ_pInfo->p, GetFFTPrime);
FFTInfo->crt_struct.init(n, ZZ_pInfo->p, GetFFTPrime);
if (!FFTInfo->crt_struct.special()) {
ZZ qq, rr;
DivRem(qq, rr, M, ZZ_pInfo->p);
NegateMod(FFTInfo->MinusMModP, rr, ZZ_pInfo->p);
for (i = 0; i < n; i++) {
q = GetFFTPrime(i);
qinv = GetFFTPrimeInv(i);
long tt = rem(qq, q);
mul(M2, ZZ_pInfo->p, tt);
add(M2, M2, rr);
div(M2, M2, q); // = (M/q) rem p
div(M1, M, q);
t = rem(M1, q);
t = InvMod(t, q);
mul(M3, M2, t);
rem(M3, M3, ZZ_pInfo->p);
FFTInfo->crt_struct.insert(i, M3);
FFTInfo->x[i] = ((double) t)/((double) q);
FFTInfo->u[i] = t;
FFTInfo->uqinv[i] = PrepMulModPrecon(FFTInfo->u[i], q, qinv);
}
}
tmps = MakeSmart<ZZ_pTmpSpaceT>();
tmps->crt_tmp_vec.fetch(FFTInfo->crt_struct);
tmps->rem_tmp_vec.fetch(FFTInfo->rem_struct);
builder.move(FFTInfo);
} while (0);
if (!tmps) {
const ZZ_pFFTInfoT *FFTInfo = ZZ_pInfo->FFTInfo.get();
tmps = MakeSmart<ZZ_pTmpSpaceT>();
tmps->crt_tmp_vec.fetch(FFTInfo->crt_struct);
tmps->rem_tmp_vec.fetch(FFTInfo->rem_struct);
}
ZZ_pTmpSpace = tmps;
}
zz_pContext BuildContext(long p, long maxroot) {
if (maxroot <= CalcMaxRoot(p))
return zz_pContext(INIT_USER_FFT, p);
else
return zz_pContext(p, maxroot);
}
newNTL_START_IMPL
zz_pInfoT::zz_pInfoT(long NewP, long maxroot)
{
ref_count = 1;
if (maxroot < 0) Error("zz_pContext: maxroot may not be negative");
if (NewP <= 1) Error("zz_pContext: p must be > 1");
if (NumBits(NewP) > newNTL_SP_NBITS) Error("zz_pContext: modulus too big");
ZZ P, B, M, M1, MinusM;
long n, i;
long q, t;
p = NewP;
pinv = 1/double(p);
index = -1;
conv(P, p);
sqr(B, P);
LeftShift(B, B, maxroot+newNTL_FFTFudge);
set(M);
n = 0;
while (M <= B) {
UseFFTPrime(n);
q = FFTPrime[n];
n++;
mul(M, M, q);
}
if (n > 4) Error("zz_pInit: too many primes");
NumPrimes = n;
PrimeCnt = n;
MaxRoot = CalcMaxRoot(q);
if (maxroot < MaxRoot)
MaxRoot = maxroot;
negate(MinusM, M);
MinusMModP = rem(MinusM, p);
if (!(CoeffModP = (long *) newNTL_MALLOC(n, sizeof(long), 0)))
Error("out of space");
if (!(x = (double *) newNTL_MALLOC(n, sizeof(double), 0)))
Error("out of space");
if (!(u = (long *) newNTL_MALLOC(n, sizeof(long), 0)))
Error("out of space");
for (i = 0; i < n; i++) {
q = FFTPrime[i];
div(M1, M, q);
t = rem(M1, q);
t = InvMod(t, q);
mul(M1, M1, t);
CoeffModP[i] = rem(M1, p);
x[i] = ((double) t)/((double) q);
u[i] = t;
}
}
void ZZ_pInfoT::init()
{
ZZ B, M, M1, M2, M3;
long n, i;
long q, t;
initialized = 1;
sqr(B, p);
LeftShift(B, B, NTL_FFTMaxRoot+NTL_FFTFudge);
set(M);
n = 0;
while (M <= B) {
UseFFTPrime(n);
q = FFTPrime[n];
n++;
mul(M, M, q);
}
NumPrimes = n;
MaxRoot = CalcMaxRoot(q);
double fn = double(n);
if (8.0*fn*(fn+32) > NTL_FDOUBLE_PRECISION)
Error("modulus too big");
if (8.0*fn*(fn+32) > NTL_FDOUBLE_PRECISION/double(NTL_SP_BOUND))
QuickCRT = 0;
else
QuickCRT = 1;
if (!(x = (double *) NTL_MALLOC(n, sizeof(double), 0)))
Error("out of space");
if (!(u = (long *) NTL_MALLOC(n, sizeof(long), 0)))
Error("out of space");
ZZ_p_rem_struct_init(&rem_struct, n, p, FFTPrime);
ZZ_p_crt_struct_init(&crt_struct, n, p, FFTPrime);
if (ZZ_p_crt_struct_special(crt_struct)) return;
ZZ qq, rr;
DivRem(qq, rr, M, p);
NegateMod(MinusMModP, rr, p);
for (i = 0; i < n; i++) {
q = FFTPrime[i];
long tt = rem(qq, q);
mul(M2, p, tt);
add(M2, M2, rr);
div(M2, M2, q); // = (M/q) rem p
div(M1, M, q);
t = rem(M1, q);
t = InvMod(t, q);
mul(M3, M2, t);
rem(M3, M3, p);
ZZ_p_crt_struct_insert(crt_struct, i, M3);
x[i] = ((double) t)/((double) q);
u[i] = t;
}
}
void UseFFTPrime(long index)
{
long numprimes = FFTTables_store.length();
if (index < 0 || index > numprimes)
Error("invalid FFT prime index");
if (index < numprimes) return;
// index == numprimes
long q, w;
NextFFTPrime(q, w);
double qinv = 1/((double) q);
long mr = CalcMaxRoot(q);
FFTTables_store.SetLength(numprimes+1);
FFTTables = FFTTables_store.elts();
FFTPrimeInfo& info = FFTTables[numprimes];
info.q = q;
info.qinv = qinv;
info.RootTable.SetLength(mr+1);
info.RootInvTable.SetLength(mr+1);
info.TwoInvTable.SetLength(mr+1);
info.TwoInvPreconTable.SetLength(mr+1);
long *rt = &info.RootTable[0];
long *rit = &info.RootInvTable[0];
long *tit = &info.TwoInvTable[0];
mulmod_precon_t *tipt = &info.TwoInvPreconTable[0];
long j;
long t;
rt[mr] = w;
for (j = mr-1; j >= 0; j--)
rt[j] = MulMod(rt[j+1], rt[j+1], q);
rit[mr] = InvMod(w, q);
for (j = mr-1; j >= 0; j--)
rit[j] = MulMod(rit[j+1], rit[j+1], q);
t = InvMod(2, q);
tit[0] = 1;
for (j = 1; j <= mr; j++)
tit[j] = MulMod(tit[j-1], t, q);
for (j = 0; j <= mr; j++)
tipt[j] = PrepMulModPrecon(tit[j], q, qinv);
// initialize data structures for the legacy inteface
NumFFTPrimes = FFTTables_store.length();
FFTPrime_store.SetLength(NumFFTPrimes);
FFTPrime = FFTPrime_store.elts();
FFTPrime[NumFFTPrimes-1] = q;
FFTPrimeInv_store.SetLength(NumFFTPrimes);
FFTPrimeInv = FFTPrimeInv_store.elts();
FFTPrimeInv[NumFFTPrimes-1] = qinv;
}
