void PlainResultant(ZZ_p& rres, const ZZ_pX& a, const ZZ_pX& b)
{
ZZ_p res;
if (IsZero(a) || IsZero(b))
clear(res);
else if (deg(a) == 0 && deg(b) == 0)
set(res);
else {
long d0, d1, d2;
ZZ_p lc;
set(res);
long n = max(deg(a),deg(b)) + 1;
ZZ_pX u(INIT_SIZE, n), v(INIT_SIZE, n);
ZZVec tmp(n, ZZ_p::ExtendedModulusSize());
u = a;
v = b;
for (;;) {
d0 = deg(u);
d1 = deg(v);
lc = LeadCoeff(v);
PlainRem(u, u, v, tmp);
swap(u, v);
d2 = deg(v);
if (d2 >= 0) {
power(lc, lc, d0-d2);
mul(res, res, lc);
if (d0 & d1 & 1) negate(res, res);
}
else {
if (d1 == 0) {
power(lc, lc, d0);
mul(res, res, lc);
}
else
clear(res);
break;
}
}
}
rres = res;
}
int main()
{
_newntl_gmp_hack = 0;
long n, k;
n = 200;
k = 10*newNTL_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;
long iter;
n = 1024;
k = 1024;
RandomLen(p, k);
ZZ_p::init(p);
ZZ_pX j1, j2, j3;
random(j1, n);
random(j2, n);
mul(j3, j1, j2);
iter = 1;
do {
t = GetTime();
for (i = 0; i < iter; i++) {
FFTMul(j3, j1, j2);
}
t = GetTime() - t;
iter = 2*iter;
} while(t < 1);
iter = iter/2;
iter = long((2/t)*iter) + 1;
double tvec[5];
long w;
for (w = 0; w < 5; w++) {
t = GetTime();
for (i = 0; i < iter; i++) {
FFTMul(j3, j1, j2);
}
t = GetTime() - t;
tvec[w] = t;
}
t = clean_data(tvec);
t = floor((t/iter)*1e12);
if (t < 0 || t >= 1e15)
printf("999999999999999 ");
else
printf("%015.0f ", t);
printf(" [%ld] ", iter);
print_flag();
return 0;
}
int main()
{
cerr << "This is NTL version " << NTL_VERSION << "\n";
cerr << "Basic Configuration Options:\n";
#ifdef NTL_STD_CXX
cerr << "NTL_STD_CXX\n";
#endif
#ifdef NTL_PSTD_NNS
cerr << "NTL_PSTD_NNS\n";
#endif
#ifdef NTL_PSTD_NHF
cerr << "NTL_PSTD_NHF\n";
#endif
#ifdef NTL_PSTD_NTN
cerr << "NTL_PSTD_NTN\n";
#endif
#ifdef NTL_GMP_LIP
cerr << "NTL_GMP_LIP\n";
#endif
#ifdef NTL_GMP_HACK
cerr << "NTL_GMP_HACK\n";
#endif
#ifdef NTL_GF2X_LIB
cerr << "NTL_GF2X_LIB\n";
#endif
#ifdef NTL_LONG_LONG_TYPE
cerr << "NTL_LONG_LONG_TYPE: ";
cerr << make_string(NTL_LONG_LONG_TYPE) << "\n";
#endif
#ifdef NTL_UNSIGNED_LONG_LONG_TYPE
cerr << "NTL_UNSIGNED_LONG_LONG_TYPE: ";
cerr << make_string(NTL_UNSIGNED_LONG_LONG_TYPE) << "\n";
#endif
#ifdef NTL_CXX_ONLY
cerr << "NTL_CXX_ONLY\n";
#endif
#ifdef NTL_X86_FIX
cerr << "NTL_X86_FIX\n";
#endif
#ifdef NTL_NO_X86_FIX
cerr << "NTL_NO_X86_FIX\n";
#endif
#ifdef NTL_NO_INIT_TRANS
cerr << "NTL_NO_INIT_TRANS\n";
#endif
#ifdef NTL_CLEAN_INT
cerr << "NTL_CLEAN_INT\n";
#endif
#ifdef NTL_CLEAN_PTR
cerr << "NTL_CLEAN_PTR\n";
#endif
#ifdef NTL_RANGE_CHECK
cerr << "NTL_RANGE_CHECK\n";
#endif
cerr << "\n";
cerr << "Resolution of double-word types:\n";
cerr << make_string(NTL_LL_TYPE) << "\n";
cerr << make_string(NTL_ULL_TYPE) << "\n";
cerr << "\n";
cerr << "Performance Options:\n";
#ifdef NTL_LONG_LONG
cerr << "NTL_LONG_LONG\n";
#endif
#ifdef NTL_AVOID_FLOAT
cerr << "NTL_AVOID_FLOAT\n";
#endif
#ifdef NTL_SPMM_UL
cerr << "NTL_SPMM_UL\n";
#endif
#ifdef NTL_SPMM_ULL
cerr << "NTL_SPMM_ULL\n";
#endif
#ifdef NTL_SPMM_ASM
cerr << "NTL_SPMM_ASM\n";
#endif
#ifdef NTL_AVOID_BRANCHING
cerr << "NTL_AVOID_BRANCHING\n";
#endif
#ifdef NTL_TBL_REM
cerr << "NTL_TBL_REM\n";
#endif
#ifdef NTL_GF2X_ALTCODE
cerr << "NTL_GF2X_ALTCODE\n";
#endif
#ifdef NTL_GF2X_ALTCODE1
cerr << "NTL_GF2X_ALTCODE1\n";
#endif
#ifdef NTL_GF2X_NOINLINE
cerr << "NTL_GF2X_NOINLINE\n";
#endif
cerr << "\n\n";
if (_ntl_gmp_hack)
cerr << "using GMP hack\n\n";
cerr << "running tests...";
long n, k;
n = 200;
k = 10*NTL_ZZ_NBITS;
ZZ p;
GenPrime(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
ZZ_p lc;
do {
random(lc);
} while (IsZero(lc));
SetCoeff(f, n, lc);
// 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) {
cerr << "r1 != r2!!\n";
return 1;
}
else if (r1 != r3) {
cerr << "r1 != r3!!\n";
return 1;
}
// small prime tests...I've made some changes in v5.3
// that should be checked on various platforms, so
// we might as well check them here.
if (SmallModulusTest(17, 1000)) {
cerr << "first SmallModulusTest failed!!\n";
return 1;
}
if (SmallModulusTest((1L << (NTL_SP_NBITS))-1, 1000)) {
cerr << "second SmallModulusTest failed!!\n";
return 1;
}
// Test gf2x code....
if (GF2X_test()) {
cerr << "GF2X test failed!\n";
return 1;
}
cerr << "OK\n";
ZZ x1, x2, x3, x4;
double t;
long i;
RandomLen(x1, 1024);
RandomBnd(x2, x1);
RandomBnd(x3, x1);
mul(x4, x2, x3);
t = GetTime();
for (i = 0; i < 100000; i++)
mul(x4, x2, x3);
t = GetTime()-t;
cerr << "time for 1024-bit mul: " << t*10 << "us";
if (_ntl_gmp_hack) {
_ntl_gmp_hack = 0;
mul(x4, x2, x3);
t = GetTime();
for (i = 0; i < 100000; i++)
mul(x4, x2, x3);
t = GetTime()-t;
cerr << " (" << (t*10) << "us without GMP)";
_ntl_gmp_hack = 1;
}
cerr << "\n";
rem(x2, x4, x1);
t = GetTime();
for (i = 0; i < 100000; i++)
rem(x2, x4, x1);
t = GetTime()-t;
cerr << "time for 2048/1024-bit rem: " << t*10 << "us";
if (_ntl_gmp_hack) {
_ntl_gmp_hack = 0;
rem(x2, x4, x1);
t = GetTime();
for (i = 0; i < 100000; i++)
rem(x2, x4, x1);
t = GetTime()-t;
cerr << " (" << (t*10) << "us without GMP)";
_ntl_gmp_hack = 1;
}
cerr << "\n";
GenPrime(p, 1024);
RandomBnd(x1, p);
if (IsZero(x1)) set(x1);
InvMod(x2, x1, p);
t = GetTime();
for (i = 0; i < 1000; i++)
InvMod(x2, x1, p);
t = GetTime()-t;
cerr << "time for 1024-bit modular inverse: " << t*1000 << "us";
if (_ntl_gmp_hack) {
_ntl_gmp_hack = 0;
InvMod(x2, x1, p);
t = GetTime();
for (i = 0; i < 1000; i++)
InvMod(x2, x1, p);
t = GetTime()-t;
cerr << " (" << (t*1000) << "us without GMP)";
_ntl_gmp_hack = 1;
}
cerr << "\n";
// test modulus switching
n = 1024;
k = 1024;
RandomLen(p, k);
ZZ_p::init(p);
ZZ_pInfo->check();
ZZ_pX j1, j2, j3;
random(j1, n);
random(j2, n);
t = GetTime();
for (i = 0; i < 20; i++) mul(j3, j1, j2);
t = GetTime()-t;
cerr << "time to multiply degree 1023 polynomials\n modulo a 1024-bit number: ";
cerr << (t/20) << "s";
if (_ntl_gmp_hack) {
_ntl_gmp_hack = 0;
ZZ_p::init(p);
ZZ_pInfo->check();
t = GetTime();
for (i = 0; i < 20; i++) mul(j3, j1, j2);
t = GetTime()-t;
cerr << " (" << (t/20) << "s without GMP)";
_ntl_gmp_hack = 1;
}
cerr << "\n";
GF2X_time();
return 0;
}
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;
}
int main()
{
#if (defined(NTL_CRT_ALTCODE) && !(defined(NTL_HAVE_LL_TYPE) && NTL_ZZ_NBITS == NTL_BITS_PER_LONG))
{
printf("999999999999999 ");
print_flag();
return 0;
}
#endif
SetSeed(ZZ(0));
long n, k;
n = 1024;
k = 30*NTL_SP_NBITS;
ZZ p;
RandomLen(p, k);
if (!IsOdd(p)) p++;
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;
long iter;
ZZ_pX a, b, c;
random(a, n);
random(b, n);
long da = deg(a);
long db = deg(b);
long dc = da + db;
long l = NextPowerOfTwo(dc+1);
FFTRep arep, brep, crep;
ToFFTRep(arep, a, l, 0, da);
ToFFTRep(brep, b, l, 0, db);
mul(crep, arep, brep);
ZZ_pXModRep modrep;
FromFFTRep(modrep, crep);
FromZZ_pXModRep(c, modrep, 0, dc);
iter = 1;
do {
t = GetTime();
for (i = 0; i < iter; i++) {
FromZZ_pXModRep(c, modrep, 0, dc);
}
t = GetTime() - t;
iter = 2*iter;
} while(t < 1);
iter = iter/2;
iter = long((3/t)*iter) + 1;
double tvec[5];
long w;
for (w = 0; w < 5; w++) {
t = GetTime();
for (i = 0; i < iter; i++) {
FromZZ_pXModRep(c, modrep, 0, dc);
}
t = GetTime() - t;
tvec[w] = t;
}
t = clean_data(tvec);
t = floor((t/iter)*1e12);
// The following is just to test some tuning Wizard logic --
// be sure to get rid of this!!
#if (defined(NTL_CRT_ALTCODE))
// t *= 1.12;
#endif
if (t < 0 || t >= 1e15)
printf("999999999999999 ");
else
printf("%015.0f ", t);
printf(" [%ld] ", iter);
print_flag();
return 0;
}