static uint32 get_initial_inv_sqrt(msieve_obj *obj, mpz_poly_t *alg_poly,
mpz_poly_t *prod, mpz_poly_t *isqrt_mod_q,
mpz_t q_out) {
/* find the prime q_out and the initial value of the
reciprocal square root of prod(x) mod q_out to use
for the Newton iteration */
uint32 i;
uint32 q, start_q;
alg_poly->degree++;
/* find a prime q for which mp_alg_poly mod q is
irreducible. The starting value to try was passed in */
start_q = mpz_get_ui(q_out);
for (i = 0; i < ISQRT_NUM_ATTEMPTS; i++) {
if (get_prime_for_sqrt(alg_poly, start_q + 1, &q)) {
if (start_q > 150) {
logprintf(obj, "warning: no irreducible prime "
"found, switching to small primes\n");
start_q = 50;
/* for octics, even mod 13 works and
is resonably fast */
if (alg_poly->degree > 6)
start_q = 12;
continue;
}
}
/* find the reciprocal square root mod q, or try
another q if this fails */
if (inv_sqrt_mod_q(isqrt_mod_q, prod,
alg_poly, q, &obj->seed1, &obj->seed2)) {
break;
}
start_q = q;
}
alg_poly->degree--;
if (i == ISQRT_NUM_ATTEMPTS) {
logprintf(obj, "error: cannot recover square root mod q\n");
return 0;
}
logprintf(obj, "initial square root is modulo %u\n", q);
mpz_set_ui(q_out, (unsigned long)q);
return 1;
}
static uint32 get_initial_inv_sqrt(msieve_obj *obj, mp_poly_t *mp_alg_poly,
gmp_poly_t *prod, gmp_poly_t *isqrt_mod_q,
mpz_t q_out) {
/* find the prime q_out and the initial value of the
reciprocal square root of prod(x) mod q_out to use
for the Newton iteration */
uint32 i, j;
uint32 q, start_q;
mp_poly_t mp_prod_mod_q;
mp_poly_t mp_isqrt_mod_q;
/* find a prime q for which mp_alg_poly mod q is
irreducible. The starting value to try was passed in */
start_q = mpz_get_ui(q_out);
for (i = 0; i < ISQRT_NUM_ATTEMPTS; i++) {
if (get_prime_for_sqrt(mp_alg_poly, start_q + 1, &q)) {
if (start_q > 150) {
logprintf(obj, "warning: no irreducible prime "
"found, switching to small primes\n");
start_q = 50;
/* for octics, even mod 13 works and
is resonably fast */
if (mp_alg_poly->degree > 6)
start_q = 12;
continue;
}
}
/* convert prod mod q to an mp_poly_t */
memset(&mp_prod_mod_q, 0, sizeof(mp_poly_t));
for (j = 0; j <= prod->degree; j++) {
signed_mp_t *coeff = mp_prod_mod_q.coeff + j;
uint32 r = mpz_fdiv_ui(prod->coeff[j],
(unsigned long)q);
coeff->sign = POSITIVE;
coeff->num.nwords = (r == 0) ? 0 : 1;
coeff->num.val[0] = r;
}
for (j = prod->degree; j; j--) {
signed_mp_t *coeff = mp_prod_mod_q.coeff + j;
if (!mp_is_zero(&coeff->num))
break;
}
mp_prod_mod_q.degree = j;
/* find the reciprocal square root mod q, or try
another q if this fails */
if (inv_sqrt_mod_q(&mp_isqrt_mod_q, &mp_prod_mod_q,
mp_alg_poly, q, &obj->seed1, &obj->seed2)) {
break;
}
start_q = q;
}
if (i == ISQRT_NUM_ATTEMPTS) {
logprintf(obj, "error: cannot recover square root mod q\n");
return 0;
}
/* initialize isqrt_mod_q */
mpz_set_ui(q_out, (unsigned long)q);
for (i = 0; i <= mp_isqrt_mod_q.degree; i++) {
signed_mp_t *coeff = mp_isqrt_mod_q.coeff + i;
mpz_set_ui(isqrt_mod_q->coeff[i],
(unsigned long)coeff->num.val[0]);
if (coeff->sign == NEGATIVE)
mpz_neg(isqrt_mod_q->coeff[i], isqrt_mod_q->coeff[i]);
}
isqrt_mod_q->degree = mp_isqrt_mod_q.degree;
logprintf(obj, "initial square root is modulo %u\n", q);
return 1;
}
