static int check_for_factor2(mpz_t f, mpz_t inputn, mpz_t fmin, mpz_t n, int stage, mpz_t* sfacs, int* nsfacs, int degree)
{
int success, sfaci;
UV B1;
/* Use this so we don't modify their input value */
mpz_set(n, inputn);
if (mpz_cmp(n, fmin) <= 0) return 0;
#if 0
{
/* Straightforward trial division up to 3000. */
PRIME_ITERATOR(iter);
UV tf;
UV const trial_limit = 3000;
for (tf = 2; tf < trial_limit; tf = prime_iterator_next(&iter)) {
if (mpz_cmp_ui(n, tf*tf) < 0) break;
while (mpz_divisible_ui_p(n, tf))
mpz_divexact_ui(n, n, tf);
}
prime_iterator_destroy(&iter);
}
#else
/* Utilize GMP's fast gcd algorithms. Trial to 224737 with two gcds. */
mpz_tdiv_q_2exp(n, n, mpz_scan1(n, 0));
while (mpz_divisible_ui_p(n, 3)) mpz_divexact_ui(n, n, 3);
while (mpz_divisible_ui_p(n, 5)) mpz_divexact_ui(n, n, 5);
if (mpz_cmp(n, fmin) <= 0) return 0;
mpz_gcd(f, n, _gcd_small);
while (mpz_cmp_ui(f, 1) > 0) {
mpz_divexact(n, n, f);
mpz_gcd(f, n, _gcd_small);
}
if (mpz_cmp(n, fmin) <= 0) return 0;
mpz_gcd(f, n, _gcd_large);
while (mpz_cmp_ui(f, 1) > 0) {
mpz_divexact(n, n, f);
mpz_gcd(f, n, _gcd_large);
}
/* Quick stage 1 n-1 using a single big powm + gcd. */
if (stage == 0) {
if (mpz_cmp(n, fmin) <= 0) return 0;
mpz_set_ui(f, 2);
mpz_powm(f, f, _lcm_small, n);
mpz_sub_ui(f, f, 1);
mpz_gcd(f, f, n);
if (mpz_cmp_ui(f, 1) != 0 && mpz_cmp(f, n) != 0) {
mpz_divexact(n, n, f);
if (mpz_cmp(f, n) > 0)
mpz_set(n, f);
}
}
#endif
sfaci = 0;
success = 1;
while (success) {
UV nsize = mpz_sizeinbase(n, 2);
if (mpz_cmp(n, fmin) <= 0) return 0;
if (_GMP_is_prob_prime(n)) { mpz_set(f, n); return (mpz_cmp(f, fmin) > 0); }
success = 0;
B1 = 300 + 3 * nsize;
if (degree <= 2) B1 += nsize; /* D1 & D2 are cheap to prove. Encourage. */
if (degree <= 0) B1 += nsize; /* N-1 and N+1 are really cheap. */
if (degree > 20 && stage <= 1) B1 -= nsize; /* Less time on big polys. */
if (degree > 40) B1 -= nsize/2; /* Less time on big polys. */
if (stage >= 1) {
#ifdef USE_LIBECM
/* TODO: Tune stage 1 (PM1?) */
/* TODO: LIBECM in other stages */
if (!success) {
ecm_params params;
ecm_init(params);
params->method = ECM_ECM;
mpz_set_ui(params->B2, 10*B1);
mpz_set_ui(params->sigma, 0);
success = ecm_factor(f, n, B1/4, params);
ecm_clear(params);
if (mpz_cmp(f, n) == 0) success = 0;
}
#else
if (!success) success = _GMP_pminus1_factor(n, f, B1, 6*B1);
if (!success) success = _GMP_pplus1_factor(n, f, 0, B1/8, B1/8);
if (!success && nsize < 500) success = _GMP_pbrent_factor(n, f, nsize, 1024-nsize);
#endif
}
/* Try any factors found in previous stage 2+ calls */
while (!success && sfaci < *nsfacs) {
if (mpz_divisible_p(n, sfacs[sfaci])) {
mpz_set(f, sfacs[sfaci]);
success = 1;
}
sfaci++;
}
if (stage > 1 && !success) {
if (stage == 2) {
if (!success) success = _GMP_pbrent_factor(n, f, nsize-1, 8192);
if (!success) success = _GMP_pminus1_factor(n, f, 6*B1, 60*B1);
/* p+1 with different initial point and searching farther */
if (!success) success = _GMP_pplus1_factor(n, f, 1, B1/2, B1/2);
if (!success) success = _GMP_ecm_factor_projective(n, f, 250, 3);
} else if (stage == 3) {
if (!success) success = _GMP_pbrent_factor(n, f, nsize+1, 16384);
if (!success) success = _GMP_pminus1_factor(n, f, 60*B1, 600*B1);
/* p+1 with a third initial point and searching farther */
if (!success) success = _GMP_pplus1_factor(n, f, 2, 1*B1, 1*B1);
if (!success) success = _GMP_ecm_factor_projective(n, f, B1/4, 4);
} else if (stage == 4) {
if (!success) success = _GMP_pminus1_factor(n, f, 300*B1, 300*20*B1);
if (!success) success = _GMP_ecm_factor_projective(n, f, B1/2, 4);
} else if (stage >= 5) {
UV B = B1 * (stage-4) * (stage-4) * (stage-4);
if (!success) success = _GMP_ecm_factor_projective(n, f, B, 8+stage);
}
}
if (success) {
if (mpz_cmp_ui(f, 1) == 0 || mpz_cmp(f, n) == 0) {
gmp_printf("factoring %Zd resulted in factor %Zd\n", n, f);
croak("internal error in ECPP factoring");
}
/* Add the factor to the saved factors list */
if (stage > 1 && *nsfacs < MAX_SFACS) {
/* gmp_printf(" ***** adding factor %Zd ****\n", f); */
mpz_init_set(sfacs[*nsfacs], f);
nsfacs[0]++;
}
/* Is the factor f what we want? */
if ( mpz_cmp(f, fmin) > 0 && _GMP_is_prob_prime(f) ) return 1;
/* Divide out f */
mpz_divexact(n, n, f);
}
}
/* n is larger than fmin and not prime */
mpz_set(f, n);
return -1;
}
/* Set up for clever FPS, where the reduced n is remembered each time */
static int check_for_factor(mpz_t f, mpz_t inputn, mpz_t fmin, mpz_t n, long stage)
{
int success;
/* Use this so we don't modify their input value */
mpz_set(n, inputn);
if (mpz_cmp(n, fmin) <= 0) return 0;
if (stage == 1) {
/* simple trial division */
while (mpz_divisible_ui_p(n, 2)) mpz_divexact_ui(n, n, 2);
while (mpz_divisible_ui_p(n, 3)) mpz_divexact_ui(n, n, 3);
if (mpz_gcd_ui(NULL, n, 2850092245UL) != 1) {
while (mpz_divisible_ui_p(n, 5)) mpz_divexact_ui(n, n, 5);
while (mpz_divisible_ui_p(n, 7)) mpz_divexact_ui(n, n, 7);
while (mpz_divisible_ui_p(n, 11)) mpz_divexact_ui(n, n, 11);
while (mpz_divisible_ui_p(n, 13)) mpz_divexact_ui(n, n, 13);
while (mpz_divisible_ui_p(n, 17)) mpz_divexact_ui(n, n, 17);
while (mpz_divisible_ui_p(n, 19)) mpz_divexact_ui(n, n, 19);
while (mpz_divisible_ui_p(n, 41)) mpz_divexact_ui(n, n, 41);
while (mpz_divisible_ui_p(n, 43)) mpz_divexact_ui(n, n, 43);
}
if (mpz_gcd_ui(NULL, n, 2392308223UL) != 1) {
while (mpz_divisible_ui_p(n, 23)) mpz_divexact_ui(n, n, 23);
while (mpz_divisible_ui_p(n, 29)) mpz_divexact_ui(n, n, 29);
while (mpz_divisible_ui_p(n, 31)) mpz_divexact_ui(n, n, 31);
while (mpz_divisible_ui_p(n, 37)) mpz_divexact_ui(n, n, 37);
while (mpz_divisible_ui_p(n, 53)) mpz_divexact_ui(n, n, 53);
while (mpz_divisible_ui_p(n, 59)) mpz_divexact_ui(n, n, 59);
}
}
success = 1;
while (success) {
if (mpz_cmp(n, fmin) <= 0) return 0;
if (_GMP_is_prob_prime(n)) { mpz_set(f, n); return (mpz_cmp(f, fmin) > 0); }
success = 0;
if (stage == 1) {
/* We should probably do something like B1 = 10 * ndigits */
UV B1 = (mpz_sizeinbase(n, 2) > 1200) ? 6000 : 3000;
if (!success) success = _GMP_pminus1_factor(n, f, B1, 10*B1);
} else if (stage == 2) {
if (!success) success = _GMP_pminus1_factor(n, f, 10000, 200000);
if (!success) success = _GMP_ecm_factor_projective(n, f, 250, 4);
} else if (stage == 3) {
if (!success) success = _GMP_pminus1_factor(n, f, 40000, 800000);
if (!success) success = _GMP_ecm_factor_projective(n, f, 500, 4);
} else if (stage == 4) {
if (!success) success = _GMP_pminus1_factor(n, f, 100000, 5000000);
if (!success) success = _GMP_ecm_factor_projective(n, f, 1000, 10);
} else if (stage >= 5) {
UV B = 4000 * (stage-4) * (stage-4) * (stage-4);
if (!success) success = _GMP_ecm_factor_projective(n, f, B, 20);
}
if (success) {
if (mpz_cmp_ui(f, 1) == 0 || mpz_cmp(f, n) == 0) {
gmp_printf("factoring %Zd resulted in factor %Zd\n", n, f);
croak("internal error in ECPP factoring");
}
/* Is the factor f what we want? */
if ( mpz_cmp(f, fmin) > 0 && _GMP_is_prob_prime(f) ) return 1;
/* Divide out f */
mpz_divexact(n, n, f);
}
}
/* n is larger than fmin and not prime */
mpz_set(f, n);
return -1;
}
static int check_for_factor(mpz_t f, mpz_t inputn, mpz_t fmin, mpz_t n, int stage, mpz_t* sfacs, int* nsfacs, int degree)
{
int success, sfaci;
UV B1;
/* Use this so we don't modify their input value */
mpz_set(n, inputn);
if (mpz_cmp(n, fmin) <= 0) return 0;
#if 0
/* Use this to really encourage n-1 / n+1 proof types */
if (degree <= 0) {
if (stage == 1) return -1;
if (stage == 0) stage = 1;
}
#endif
/* Utilize GMP's fast gcd algorithms. Trial to 224737+ with two gcds. */
mpz_tdiv_q_2exp(n, n, mpz_scan1(n, 0));
while (mpz_divisible_ui_p(n, 3)) mpz_divexact_ui(n, n, 3);
while (mpz_divisible_ui_p(n, 5)) mpz_divexact_ui(n, n, 5);
if (mpz_cmp(n, fmin) <= 0) return 0;
mpz_gcd(f, n, _gcd_small);
while (mpz_cmp_ui(f, 1) > 0) {
mpz_divexact(n, n, f);
mpz_gcd(f, f, n);
}
if (mpz_cmp(n, fmin) <= 0) return 0;
mpz_gcd(f, n, _gcd_large);
while (mpz_cmp_ui(f, 1) > 0) {
mpz_divexact(n, n, f);
mpz_gcd(f, f, n);
}
sfaci = 0;
success = 1;
while (success) {
UV nsize = mpz_sizeinbase(n, 2);
const int do_pm1 = 1;
const int do_pp1 = 1;
const int do_pbr = 0;
const int do_ecm = 0;
if (mpz_cmp(n, fmin) <= 0) return 0;
if (is_bpsw_prime(n)) { mpz_set(f, n); return (mpz_cmp(f, fmin) > 0); }
success = 0;
B1 = 300 + 3 * nsize;
if (degree <= 2) B1 += nsize; /* D1 & D2 are cheap to prove. */
if (degree <= 0) B1 += 2*nsize; /* N-1 and N+1 are really cheap. */
if (degree > 20 && stage <= 1) B1 -= nsize; /* Less time on big polys. */
if (degree > 40) B1 -= nsize/2; /* Less time on big polys. */
if (stage == 0) {
/* A relatively small performance hit, makes slightly smaller proofs. */
if (nsize < 900 && degree <= 2) B1 *= 1.8;
/* We need to try a bit harder for the large sizes :( */
if (nsize > 1400) B1 *= 2;
if (nsize > 2000) B1 *= 2;
if (!success)
success = _GMP_pminus1_factor(n, f, 100+B1/8, 100+B1);
} else if (stage >= 1) {
/* P-1 */
if ((!success && do_pm1))
success = _GMP_pminus1_factor(n, f, B1, 6*B1);
/* Pollard's Rho */
if ((!success && do_pbr && nsize < 500))
success = _GMP_pbrent_factor(n, f, nsize % 53, 1000-nsize);
/* P+1 */
if ((!success && do_pp1)) {
UV ppB = (nsize < 2000) ? B1/4 : B1/16;
success = _GMP_pplus1_factor(n, f, 0, ppB, ppB);
}
if ((!success && do_ecm))
success = _GMP_ecm_factor_projective(n, f, 400, 2000, 1);
#ifdef USE_LIBECM
/* TODO: LIBECM in other stages */
/* Note: this will be substantially slower than our code for small sizes
* and the small B1/B2 values we're using. */
if (!success && degree <= 2 && nsize > 600) {
ecm_params params;
ecm_init(params);
params->method = ECM_ECM;
mpz_set_ui(params->B2, 10*B1);
mpz_set_ui(params->sigma, 0);
success = ecm_factor(f, n, B1/4, params);
ecm_clear(params);
if (mpz_cmp(f, n) == 0) success = 0;
if (success) { printf("ECM FOUND FACTOR\n"); }
}
#endif
}
/* Try any factors found in previous stage 2+ calls */
while (!success && sfaci < *nsfacs) {
if (mpz_divisible_p(n, sfacs[sfaci])) {
mpz_set(f, sfacs[sfaci]);
success = 1;
}
sfaci++;
}
if (stage > 1 && !success) {
if (stage == 2) {
/* if (!success) success = _GMP_pbrent_factor(n, f, nsize-1, 8192); */
if (!success) success = _GMP_pminus1_factor(n, f, 6*B1, 60*B1);
/* p+1 with different initial point and searching farther */
if (!success) success = _GMP_pplus1_factor(n, f, 1, B1/2, B1/2);
if (!success) success = _GMP_ecm_factor_projective(n, f, 250, 2500, 8);
} else if (stage == 3) {
if (!success) success = _GMP_pbrent_factor(n, f, nsize+1, 16384);
if (!success) success = _GMP_pminus1_factor(n, f, 60*B1, 600*B1);
/* p+1 with a third initial point and searching farther */
if (!success) success = _GMP_pplus1_factor(n, f, 2, 1*B1, 1*B1);
if (!success) success = _GMP_ecm_factor_projective(n, f, B1/4, B1*4, 5);
} else if (stage == 4) {
if (!success) success = _GMP_pminus1_factor(n, f, 300*B1, 300*20*B1);
if (!success) success = _GMP_ecm_factor_projective(n, f, B1/2, B1*8, 4);
} else if (stage >= 5) {
UV B = B1 * (stage-4) * (stage-4) * (stage-4);
if (!success) success = _GMP_ecm_factor_projective(n, f, B, 10*B, 8+stage);
}
}
if (success) {
if (mpz_cmp_ui(f, 1) == 0 || mpz_cmp(f, n) == 0) {
gmp_printf("factoring %Zd resulted in factor %Zd\n", n, f);
croak("internal error in ECPP factoring");
}
/* Add the factor to the saved factors list */
if (stage > 1 && *nsfacs < MAX_SFACS) {
/* gmp_printf(" ***** adding factor %Zd ****\n", f); */
mpz_init_set(sfacs[*nsfacs], f);
nsfacs[0]++;
}
/* Is the factor f what we want? */
if ( mpz_cmp(f, fmin) > 0 && is_bpsw_prime(f) ) return 1;
/* Divide out f */
mpz_divexact(n, n, f);
}
}
/* n is larger than fmin and not prime */
mpz_set(f, n);
return -1;
}
