int
main (int argc, char **argv)
{
mpz_t op1, op2, ref;
int i, j, chain_len;
gmp_randstate_t rands;
mpz_t bs;
unsigned long bsi, size_range;
int reps = 200;
if (argc == 2)
reps = atoi (argv[1]);
tests_start ();
gmp_randinit_default(rands);
check_data ();
mpz_init (bs);
mpz_init (op1);
mpz_init (op2);
mpz_init (ref);
mpz_init (gcd1);
mpz_init (gcd2);
mpz_init (temp1);
mpz_init (temp2);
mpz_init (s);
mpz_init (t);
for (i = 0; i < reps; i++)
{
/* Generate plain operands with unknown gcd. These types of operands
have proven to trigger certain bugs in development versions of the
gcd code. The "hgcd->row[3].rsize > M" ASSERT is not triggered by
the division chain code below, but that is most likely just a result
of that other ASSERTs are triggered before it. */
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 16 + 2;
mpz_urandomb (bs, rands, size_range);
mpz_urandomb (op1, rands, mpz_get_ui (bs) + MIN_OPERAND_BITSIZE);
mpz_urandomb (bs, rands, size_range);
mpz_urandomb (op2, rands, mpz_get_ui (bs) + MIN_OPERAND_BITSIZE);
mpz_urandomb (bs, rands, 2);
bsi = mpz_get_ui (bs);
if ((bsi & 1) != 0)
mpz_neg (op1, op1);
if ((bsi & 2) != 0)
mpz_neg (op2, op2);
one_test (op1, op2, NULL, i);
/* Generate a division chain backwards, allowing otherwise unlikely huge
quotients. */
mpz_set_ui (op1, 0);
mpz_urandomb (bs, rands, 32);
mpz_urandomb (bs, rands, mpz_get_ui (bs) % 16 + 1);
mpz_rrandomb (op2, rands, mpz_get_ui (bs));
mpz_add_ui (op2, op2, 1);
mpz_set (ref, op2);
mpz_urandomb (bs, rands, 32);
chain_len = mpz_get_ui (bs) % 50;
for (j = 0; j < chain_len; j++)
{
mpz_urandomb (bs, rands, 32);
mpz_urandomb (bs, rands, mpz_get_ui (bs) % 12 + 1);
mpz_rrandomb (temp2, rands, mpz_get_ui (bs) + 1);
mpz_add_ui (temp2, temp2, 1);
mpz_mul (temp1, op2, temp2);
mpz_add (op1, op1, temp1);
/* Don't generate overly huge operands. */
if (SIZ (op1) > 1000)
break;
mpz_urandomb (bs, rands, 32);
mpz_urandomb (bs, rands, mpz_get_ui (bs) % 12 + 1);
mpz_rrandomb (temp2, rands, mpz_get_ui (bs) + 1);
mpz_add_ui (temp2, temp2, 1);
mpz_mul (temp1, op1, temp2);
mpz_add (op2, op2, temp1);
/* Don't generate overly huge operands. */
if (SIZ (op2) > 1000)
break;
}
one_test (op1, op2, ref, i);
}
mpz_clear (bs);
mpz_clear (op1);
mpz_clear (op2);
mpz_clear (ref);
mpz_clear (gcd1);
mpz_clear (gcd2);
mpz_clear (temp1);
mpz_clear (temp2);
mpz_clear (s);
mpz_clear (t);
gmp_randclear(rands);
tests_end ();
exit (0);
}
void mpz_sqrtmp_r
(mpz_ptr root, mpz_srcptr a, mpz_srcptr p)
{
/* ? a \neq 0 */
if (mpz_get_ui(a) != 0)
{
/* ? p = 3 (mod 4) */
if (mpz_congruent_ui_p(p, 3L, 4L))
{
mpz_t foo;
mpz_init_set(foo, p);
mpz_add_ui(foo, foo, 1L);
mpz_fdiv_q_2exp(foo, foo, 2L);
mpz_powm(root, a, foo, p);
mpz_clear(foo);
return;
}
/* ! p = 1 (mod 4) */
else
{
/* ! s = (p-1)/4 */
mpz_t s;
mpz_init_set(s, p);
mpz_sub_ui(s, s, 1L);
mpz_fdiv_q_2exp(s, s, 2L);
/* ? p = 5 (mod 8) */
if (mpz_congruent_ui_p(p, 5L, 8L))
{
mpz_t foo, b;
mpz_init(foo);
mpz_powm(foo, a, s, p);
mpz_init_set(b, p);
mpz_add_ui(b, b, 3L);
mpz_fdiv_q_2exp(b, b, 3L);
mpz_powm(root, a, b, p);
/* ? a^{(p-1)/4} = 1 (mod p) */
if (mpz_cmp_ui(foo, 1L) == 0)
{
mpz_clear(foo), mpz_clear(s), mpz_clear(b);
return;
}
/* ! a^{(p-1)/4} = -1 (mod p) */
else
{
do
mpz_wrandomm(b, p);
while (mpz_jacobi(b, p) != -1);
mpz_powm(b, b, s, p);
mpz_mul(root, root, b);
mpz_mod(root, root, p);
mpz_clear(foo), mpz_clear(s), mpz_clear(b);
return;
}
}
/* ! p = 1 (mod 8) */
else
{
mpz_t foo, bar, b, t;
mpz_init(foo), mpz_init(bar);
mpz_powm(foo, a, s, p);
/* while a^s = 1 (mod p) */
while (mpz_cmp_ui(foo, 1L) == 0)
{
/* ? s odd */
if (mpz_odd_p(s))
{
mpz_add_ui(s, s, 1L);
mpz_fdiv_q_2exp(s, s, 1L);
mpz_powm(root, a, s, p);
mpz_clear(foo), mpz_clear(s);
return;
}
/* ! s even */
else
{
mpz_fdiv_q_2exp(s, s, 1L);
}
mpz_powm(foo, a, s, p);
}
/* ! a^s = -1 (mod p) */
mpz_init(b);
do
mpz_wrandomm(b, p);
while (mpz_jacobi(b, p) != -1);
mpz_init_set(t, p);
mpz_sub_ui(t, t, 1L);
mpz_fdiv_q_2exp(t, t, 1L);
/* while s even */
while (mpz_even_p(s))
{
mpz_fdiv_q_2exp(s, s, 1L);
mpz_fdiv_q_2exp(t, t, 1L);
mpz_powm(foo, a, s, p);
mpz_powm(bar, b, t, p);
mpz_mul(foo, foo, bar);
mpz_mod(foo, foo, p);
mpz_set_si(bar, -1L);
/* ? a^s * b^t = -1 (mod p) */
if (mpz_congruent_p(foo, bar, p))
{
mpz_set(bar, p);
mpz_sub_ui(bar, bar, 1L);
mpz_fdiv_q_2exp(bar, bar, 1L);
mpz_add(t, t, bar);
}
}
mpz_add_ui(s, s, 1L);
mpz_fdiv_q_2exp(s, s, 1L);
mpz_fdiv_q_2exp(t, t, 1L);
mpz_powm(foo, a, s, p);
mpz_powm(bar, b, t, p);
mpz_mul(root, foo, bar);
mpz_mod(root, root, p);
mpz_clear(foo), mpz_clear(bar);
mpz_clear(s), mpz_clear(b), mpz_clear(t);
return;
}
}
}
/* error, return zero root */
mpz_set_ui(root, 0L);
}
/* get value as a ui, on the assumption it fits */
static int
e_mpq_get_ui_fits (mpq_srcptr q)
{
return mpz_get_ui (mpq_numref (q));
}
int
main (int argc, char **argv)
{
mpz_t base, exp, mod;
mpz_t r1, r2, base2;
mp_size_t base_size, exp_size, mod_size;
unsigned long int exp2;
int i;
int reps = 100;
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long bsi, size_range;
tests_start ();
rands = RANDS;
mpz_init (bs);
if (argc == 2)
reps = atoi (argv[1]);
mpz_init (base);
mpz_init (exp);
mpz_init (mod);
mpz_init (r1);
mpz_init (r2);
mpz_init (base2);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 18 + 2;
do /* Loop until mathematically well-defined. */
{
mpz_urandomb (bs, rands, size_range);
base_size = mpz_get_ui (bs);
mpz_rrandomb (base, rands, base_size);
mpz_urandomb (bs, rands, 6L);
exp_size = mpz_get_ui (bs);
mpz_rrandomb (exp, rands, exp_size);
exp2 = mpz_getlimbn (exp, (mp_size_t) 0);
}
while (mpz_cmp_ui (base, 0) == 0 && exp2 == 0);
do
{
mpz_urandomb (bs, rands, size_range);
mod_size = mpz_get_ui (bs);
mpz_rrandomb (mod, rands, mod_size);
}
while (mpz_cmp_ui (mod, 0) == 0);
mpz_urandomb (bs, rands, 2);
bsi = mpz_get_ui (bs);
if ((bsi & 1) != 0)
mpz_neg (base, base);
/* printf ("%ld %ld\n", SIZ (base), SIZ (mod)); */
#if 0
putc ('\n', stderr);
debug_mp (base, -16);
debug_mp (mod, -16);
#endif
mpz_powm_ui (r1, base, exp2, mod);
MPZ_CHECK_FORMAT (r1);
mpz_set_ui (r2, 1);
mpz_set (base2, base);
mpz_mod (r2, r2, mod); /* needed when exp==0 and mod==1 */
while (exp2 != 0)
{
if (exp2 % 2 != 0)
{
mpz_mul (r2, r2, base2);
mpz_mod (r2, r2, mod);
}
mpz_mul (base2, base2, base2);
mpz_mod (base2, base2, mod);
exp2 = exp2 / 2;
}
#if 0
debug_mp (r1, -16);
debug_mp (r2, -16);
#endif
if (mpz_cmp (r1, r2) != 0)
{
fprintf (stderr, "\ntest %d: Incorrect results for operands:\n", i);
debug_mp (base, -16);
debug_mp (exp, -16);
debug_mp (mod, -16);
fprintf (stderr, "mpz_powm_ui result:\n");
debug_mp (r1, -16);
fprintf (stderr, "reference result:\n");
debug_mp (r2, -16);
abort ();
}
}
mpz_clear (bs);
mpz_clear (base);
mpz_clear (exp);
mpz_clear (mod);
mpz_clear (r1);
mpz_clear (r2);
mpz_clear (base2);
tests_end ();
exit (0);
}
void filter_SPV(uint8 parity, uint8 *sieve, uint32 poly_id, uint32 bnum,
static_conf_t *sconf, dynamic_conf_t *dconf)
{
//we have flagged this sieve offset as likely to produce a relation
//nothing left to do now but check and see.
int i;
uint32 bound, tmp, prime, root1, root2;
int smooth_num;
sieve_fb *fb;
sieve_fb_compressed *fbc;
tiny_fb_element_siqs *fullfb_ptr, *fullfb = sconf->factor_base->tinylist;
uint8 logp, bits;
uint32 tmp1, tmp2, tmp3, tmp4, offset, report_num;
fullfb_ptr = fullfb;
if (parity)
{
fb = dconf->fb_sieve_n;
fbc = dconf->comp_sieve_n;
}
else
{
fb = dconf->fb_sieve_p;
fbc = dconf->comp_sieve_p;
}
//the minimum value for the current poly_a and poly_b occur at offset (-b + sqrt(N))/a
//make it slightly easier for a number to go through full trial division for
//nearby blocks, since these offsets are more likely to factor over the FB.
mpz_sub(dconf->gmptmp1, sconf->sqrt_n, dconf->curr_poly->mpz_poly_b);
mpz_tdiv_q(dconf->gmptmp1, dconf->gmptmp1, dconf->curr_poly->mpz_poly_a);
if (mpz_sgn(dconf->gmptmp1) < 0)
mpz_neg(dconf->gmptmp1, dconf->gmptmp1);
mpz_tdiv_q_2exp(dconf->gmptmp1, dconf->gmptmp1, sconf->qs_blockbits);
if (abs(bnum - mpz_get_ui(dconf->gmptmp1)) == 0)
dconf->tf_small_cutoff = sconf->tf_small_cutoff - 5;
else if (abs(bnum - mpz_get_ui(dconf->gmptmp1)) == 1)
dconf->tf_small_cutoff = sconf->tf_small_cutoff - 3;
else
dconf->tf_small_cutoff = sconf->tf_small_cutoff;
#ifdef QS_TIMING
gettimeofday(&qs_timing_start, NULL);
#endif
for (report_num = 0; report_num < dconf->num_reports; report_num++)
{
uint64 q64;
#ifdef USE_YAFU_TDIV
z32 *tmp32 = &dconf->Qvals32[report_num];
#endif
//this one qualifies to check further, log that fact.
dconf->num++;
smooth_num = -1;
//this one is close enough, compute
//Q(x)/a = (ax + b)^2 - N, where x is the sieve index
//Q(x)/a = (ax + 2b)x + c;
offset = (bnum << sconf->qs_blockbits) + dconf->reports[report_num];
//multiple precision arithmetic. all the qstmp's are a global hack
//but I don't want to Init/Free millions of times if I don't have to.
mpz_mul_2exp(dconf->gmptmp2, dconf->curr_poly->mpz_poly_b, 1);
mpz_mul_ui(dconf->gmptmp1, dconf->curr_poly->mpz_poly_a, offset);
if (parity)
mpz_sub(dconf->Qvals[report_num], dconf->gmptmp1, dconf->gmptmp2);
else
mpz_add(dconf->Qvals[report_num], dconf->gmptmp1, dconf->gmptmp2);
mpz_mul_ui(dconf->Qvals[report_num], dconf->Qvals[report_num], offset);
mpz_add(dconf->Qvals[report_num], dconf->Qvals[report_num], dconf->curr_poly->mpz_poly_c);
if (mpz_sgn(dconf->Qvals[report_num]) < 0)
{
mpz_neg(dconf->Qvals[report_num], dconf->Qvals[report_num]);
dconf->fb_offsets[report_num][++smooth_num] = 0;
}
//we have two signs to worry about. the sign of the offset tells us how to calculate ax + b, while
//the sign of Q(x) tells us how to factor Q(x) (with or without a factor of -1)
//the square root phase will need to know both. fboffset holds the sign of Q(x). the sign of the
//offset is stored standalone in the relation structure.
//compute the bound for small primes. if we can't find enough small
//primes, then abort the trial division early because it is likely to fail to
//produce even a partial relation.
bits = sieve[dconf->reports[report_num]];
bits = (255 - bits) + sconf->tf_closnuf + 1;
#ifdef USE_YAFU_TDIV
mpz_to_z32(dconf->Qvals[report_num], tmp32);
//take care of powers of two
while ((tmp32->val[0] & 0x1) == 0)
{
zShiftRight32_x(tmp32, tmp32, 1);
dconf->fb_offsets[report_num][++smooth_num] = 1;
bits++;
}
#else
//take care of powers of two
while (mpz_even_p(dconf->Qvals[report_num]))
{
//zShiftRight32_x(Q,Q,1);
mpz_tdiv_q_2exp(dconf->Qvals[report_num], dconf->Qvals[report_num], 1);
dconf->fb_offsets[report_num][++smooth_num] = 1;
bits++;
}
#endif
i=2;
//explicitly trial divide by small primes which we have not
//been sieving. because we haven't been sieving, their progressions
//have not been updated and thus we can't use the faster methods
//seen below. fortunately, there shouldn't be many of these to test
//to speed things up, use multiplication by inverse rather than
//division, and do things in batches of 4 so we can use
//the whole cache line at once (16 byte structure)
//do the small primes in optimized batches of 4
bound = (sconf->sieve_small_fb_start - 4);
while ((uint32)i < bound)
{
tmp1 = offset + fullfb_ptr->correction[i];
q64 = (uint64)tmp1 * (uint64)fullfb_ptr->small_inv[i];
tmp1 = q64 >> 32;
//at this point tmp1 is offset / prime
tmp1 = offset - tmp1 * fullfb_ptr->prime[i];
//now tmp1 is offset % prime
i++;
tmp2 = offset + fullfb_ptr->correction[i];
q64 = (uint64)tmp2 * (uint64)fullfb_ptr->small_inv[i];
tmp2 = q64 >> 32;
tmp2 = offset - tmp2 * fullfb_ptr->prime[i];
i++;
tmp3 = offset + fullfb_ptr->correction[i];
q64 = (uint64)tmp3 * (uint64)fullfb_ptr->small_inv[i];
tmp3 = q64 >> 32;
tmp3 = offset - tmp3 * fullfb_ptr->prime[i];
i++;
tmp4 = offset + fullfb_ptr->correction[i];
q64 = (uint64)tmp4 * (uint64)fullfb_ptr->small_inv[i];
tmp4 = q64 >> 32;
tmp4 = offset - tmp4 * fullfb_ptr->prime[i];
i -= 3;
root1 = fbc->root1[i];
root2 = fbc->root2[i];
if (tmp1 == root1 || tmp1 == root2)
{
prime = fbc->prime[i];
logp = fbc->logp[i];
DIVIDE_ONE_PRIME
}
i++;
root1 = fbc->root1[i];
root2 = fbc->root2[i];
if (tmp2 == root1 || tmp2 == root2)
{
prime = fbc->prime[i];
logp = fbc->logp[i];
DIVIDE_ONE_PRIME
}
i++;
root1 = fbc->root1[i];
root2 = fbc->root2[i];
if (tmp3 == root1 || tmp3 == root2)
{
prime = fbc->prime[i];
logp = fbc->logp[i];
DIVIDE_ONE_PRIME
}
void mpq_vec_to_digest(hash_t* digest, const mpq_t* vec) {
for(int i = 0; i < NUM_HASH_CHUNKS; i++){
digest->bit[i] = mpz_get_ui(mpq_numref(vec[i]));
//gmp_printf("Vec->Digest %Qd %Lu\n", vec[i], digest->bit[i]);
}
}
int
mpfi_sin (mpfi_ptr a, mpfi_srcptr b)
{
int inexact_left, inexact_right, inexact = 0;
mp_prec_t prec, prec_left, prec_right;
mpfr_t tmp;
mpz_t z, zmod4;
mpz_t quad_left, quad_right;
int ql_mod4, qr_mod4;
if (MPFI_NAN_P (b)) {
mpfr_set_nan (&(a->left));
mpfr_set_nan (&(a->right));
MPFR_RET_NAN;
}
if (MPFI_INF_P (b)) {
/* the two endpoints are the same infinite */
if ( mpfr_cmp (&(b->left), &(b->right)) == 0) {
mpfr_set_nan (&(a->left));
mpfr_set_nan (&(a->right));
MPFR_RET_NAN;
}
mpfr_set_si (&(a->left), -1, MPFI_RNDD);
mpfr_set_si (&(a->right), 1, MPFI_RNDU);
return 0;
}
mpz_init (quad_left);
mpz_init (quad_right);
mpz_init (z);
/* quad_left gives the quadrant where the left endpoint of b is */
/* quad_left = floor (2 b->left / pi) */
/* idem for quad_right and b->right */
prec_left = mpfi_quadrant (quad_left, &(b->left));
prec_right = mpfi_quadrant (quad_right, &(b->right));
/* if there is at least one period in b, then a = [-1, 1] */
mpz_sub (z, quad_right, quad_left);
if (mpz_cmp_ui (z, 4) >= 0) {
mpfr_set_si (&(a->left), -1, MPFI_RNDD);
mpfr_set_si (&(a->right), 1, MPFI_RNDU);
inexact = 0;
}
else {
/* there is less than one period in b */
/* let us discuss according to the position (quadrant) of the endpoints of b */
/* computing precision = maximal precision required to determine the */
/* relative position of the endpoints of b and of integer multiples of Pi / 2 */
prec = mpfi_get_prec (a);
if (prec_left > prec) prec = prec_left;
if (prec_right > prec) prec = prec_right;
mpz_add (z, quad_left, quad_right);
/* z = quad_right + quad_left */
mpz_init (zmod4);
/* qr_mod4 gives the quadrant where the right endpoint of b is */
/* qr_mod4 = floor (2 b->right / pi) mod 4 */
mpz_mod_ui (zmod4, quad_right, 4);
qr_mod4 = mpz_get_ui (zmod4);
/* quad_left gives the quadrant where the left endpoint of b is */
/* quad_left = floor (2 b->left / pi) mod 4 */
mpz_mod_ui (zmod4, quad_left, 4);
ql_mod4 = mpz_get_ui (zmod4);
switch (qr_mod4) {
case 0:
switch (ql_mod4) {
case 0:
case 3:
inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD);
inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU);
break;
case 1:
mpz_add_ui (z, z, 1);
if (mpfi_cmp_sym_pi (z, &(b->left), &(b->right), prec) >= 0)
inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU);
else
inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU);
inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD);
break;
case 2:
inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD);
inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU);
break;
}
break;
case 1:
switch (ql_mod4) {
case 0:
mpz_add_ui (z, z, 1);
if (mpfi_cmp_sym_pi (z, &(b->right), &(b->left), prec) >= 0)
inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD);
else
inexact_left = mpfr_sin (&(a->left), &(b->right), MPFI_RNDD);
inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU);
break;
case 1:
mpfr_init2 (tmp, mpfr_get_prec (&(a->left)));
inexact_left = mpfr_sin (tmp, &(b->right), MPFI_RNDD);
inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU);
mpfr_set (&(a->left), tmp, MPFI_RNDD); /* exact */
mpfr_clear (tmp);
break;
case 2:
inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD);
inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU);
break;
case 3:
inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD);
inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU);
break;
}
break;
case 2:
switch (ql_mod4) {
case 0:
inexact_left = mpfr_sin (&(a->left), &(b->right), MPFI_RNDD);
inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU);
break;
case 1:
case 2:
mpfr_init2 (tmp, mpfr_get_prec (&(a->left)));
inexact_left = mpfr_sin (tmp, &(b->right), MPFI_RNDD);
inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU);
mpfr_set (&(a->left), tmp, MPFI_RNDD); /* exact */
mpfr_clear (tmp);
break;
case 3:
mpz_add_ui (z, z, 1);
if (mpfi_cmp_sym_pi (z, &(b->left), &(b->right), prec) >= 0)
inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD);
else
inexact_left = mpfr_sin (&(a->left), &(b->right), MPFI_RNDD);
inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU);
break;
}
break;
case 3:
switch (ql_mod4) {
case 0:
inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD);
inexact_right = mpfr_set_si (&(a->right), 1, MPFI_RNDU);
break;
case 1:
inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU);
inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD);
break;
case 2:
mpz_add_ui (z, z, 1);
if (mpfi_cmp_sym_pi (z, &(b->right), &(b->left), prec) >= 0)
inexact_right = mpfr_sin (&(a->right), &(b->left), MPFI_RNDU);
else
inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU);
inexact_left = mpfr_set_si (&(a->left), -1, MPFI_RNDD);
break;
case 3:
inexact_left = mpfr_sin (&(a->left), &(b->left), MPFI_RNDD);
inexact_right = mpfr_sin (&(a->right), &(b->right), MPFI_RNDU);
break;
}
break;
}
if (inexact_left) inexact = 1;
if (inexact_right) inexact += 2;
mpz_clear (zmod4);
}
mpz_clear (quad_left);
mpz_clear (quad_right);
mpz_clear (z);
return inexact;
}
// Return a LookupData struct with relevant fields set for the given terminal
//
// Set lookup_data->index to -1 if no match, to match expected output of
// indexInTerminalGroup, which calls this function to perform the lookup.
//
// NOTE: This function assumes that terminals_size_ is accurate so we can
// iterate up to terminals_size_ entries from the start of the group
// (terminal_data_) without anything horrible happening. Otherwise, we should
// check the return values from ReadLineFromCharArray and ParseNonterminalLine
// to make sure they work correctly.
//
// Die on failure to parse source_ids
//
LookupData* SeenTerminalGroup::lookup(const char *terminal) const {
// just for debug output
char space[1024];
char *read_buffer = space;
LookupData *lookup_data = new LookupData;
mpz_init(lookup_data->index);
unsigned long int index = 0;
unsigned long int terminalsSize = mpz_get_ui(terminals_size_);
const char* current_data_position = group_data_start_;
size_t bytes_remaining = group_data_size_;
// Iterate over the group, looking for the input string
while(index < terminalsSize) {
unsigned int bytes_read;
grammartools::ReadLineFromCharArray2(current_data_position,
bytes_read);
// Parse the line
const char *read_terminal, *source_ids;
double probability;
// just for debug output
assert(bytes_read + 1 <= 1024);
strncpy(read_buffer, current_data_position, bytes_read);
read_buffer[bytes_read] = 0;
grammartools::ParseNonterminalLine(current_data_position, bytes_read, &read_terminal,
probability, &source_ids);
auto len = strlen(terminal);
if ((len == strlen(read_terminal)) && (strncmp(terminal, read_terminal, len) == 0)) {
lookup_data->parse_status = kCanParse;
if (probability_ != probability) {
fprintf(stderr,
"Probability of terminal group doesn't match in line %s in "
"SeenTerminalGroup::lookup (should be %f, found %f)!\n",
read_buffer, probability_, probability);
exit(EXIT_FAILURE);
}
lookup_data->probability = probability_;
// index is already set correctly
if (!grammartools::AddSourceIDsFromString(source_ids,
lookup_data->source_ids)) {
fprintf(stderr,
"Could not parse source ids %s in line %s in "
"SeenTerminalGroup::lookup!\n",
source_ids, read_buffer);
exit(EXIT_FAILURE);
}
mpz_set_ui(lookup_data->index, index);
return lookup_data;
}
// Increment counters
index++;
current_data_position += bytes_read;
bytes_remaining -= bytes_read;
}
// If we are here, then terminal was not found
lookup_data->parse_status = kTerminalNotFound;
lookup_data->probability = -1;
mpz_set_si(lookup_data->index, -1);
return lookup_data;
}
int main(void)
{
int i, result;
flint_rand_t state;
mp_limb_t d;
mpz_t d_m;
printf("is_prime....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 100000; i++) /* Test that primes pass the test */
{
mpz_init(d_m);
do
{
d = n_randtest(state) | 1;
mpz_set_ui(d_m, d);
mpz_nextprime(d_m, d_m);
d = mpz_get_ui(d_m);
} while (mpz_size(d_m) > 1);
result = n_is_prime(d);
if (!result)
{
printf("FAIL:\n");
printf("d = %lu is declared composite\n", d);
abort();
}
mpz_clear(d_m);
}
for (i = 0; i < 100000; i++) /* Test that composites do not pass */
{
mpz_init(d_m);
do
{
d = n_randtest(state) | 1;
if (d == 1UL) d++;
mpz_set_ui(d_m, d);
} while (mpz_probab_prime_p(d_m, 12));
result = !n_is_prime(d);
if (!result)
{
printf("FAIL:\n");
printf("d = %lu is declared prime\n", d);
abort();
}
mpz_clear(d_m);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
mpz_probab_prime_p (mpz_srcptr n, int reps)
{
mp_limb_t r;
mpz_t n2;
/* Handle small and negative n. */
if (mpz_cmp_ui (n, 1000000L) <= 0)
{
int is_prime;
if (mpz_cmpabs_ui (n, 1000000L) <= 0)
{
is_prime = isprime (mpz_get_ui (n));
return is_prime ? 2 : 0;
}
/* Negative number. Negate and fall out. */
PTR(n2) = PTR(n);
SIZ(n2) = -SIZ(n);
n = n2;
}
/* If n is now even, it is not a prime. */
if ((mpz_get_ui (n) & 1) == 0)
return 0;
#if defined (PP)
/* Check if n has small factors. */
#if defined (PP_INVERTED)
r = MPN_MOD_OR_PREINV_MOD_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) PP,
(mp_limb_t) PP_INVERTED);
#else
r = mpn_mod_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) PP);
#endif
if (r % 3 == 0
#if BITS_PER_MP_LIMB >= 4
|| r % 5 == 0
#endif
#if BITS_PER_MP_LIMB >= 8
|| r % 7 == 0
#endif
#if BITS_PER_MP_LIMB >= 16
|| r % 11 == 0 || r % 13 == 0
#endif
#if BITS_PER_MP_LIMB >= 32
|| r % 17 == 0 || r % 19 == 0 || r % 23 == 0 || r % 29 == 0
#endif
#if BITS_PER_MP_LIMB >= 64
|| r % 31 == 0 || r % 37 == 0 || r % 41 == 0 || r % 43 == 0
|| r % 47 == 0 || r % 53 == 0
#endif
)
{
return 0;
}
#endif /* PP */
/* Do more dividing. We collect small primes, using umul_ppmm, until we
overflow a single limb. We divide our number by the small primes product,
and look for factors in the remainder. */
{
unsigned long int ln2;
unsigned long int q;
mp_limb_t p1, p0, p;
unsigned int primes[15];
int nprimes;
nprimes = 0;
p = 1;
ln2 = mpz_sizeinbase (n, 2); /* FIXME: tune this limit */
for (q = PP_FIRST_OMITTED; q < ln2; q += 2)
{
if (isprime (q))
{
umul_ppmm (p1, p0, p, q);
if (p1 != 0)
{
r = MPN_MOD_OR_MODEXACT_1_ODD (PTR(n), (mp_size_t) SIZ(n), p);
while (--nprimes >= 0)
if (r % primes[nprimes] == 0)
{
ASSERT_ALWAYS (mpn_mod_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) primes[nprimes]) == 0);
return 0;
}
p = q;
nprimes = 0;
}
else
{
p = p0;
}
primes[nprimes++] = q;
}
}
}
/* Perform a number of Miller-Rabin tests. */
return mpz_millerrabin (n, reps);
}
int
main (int argc, char **argv)
{
mpz_t dividend;
mpz_t quotient, remainder;
mpz_t quotient2, remainder2;
mpz_t temp;
mp_size_t dividend_size;
unsigned long divisor;
int i;
int reps = 10000;
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long bsi, size_range;
unsigned long r_rq, r_q, r_r, r;
tests_start ();
rands = RANDS;
mpz_init (bs);
if (argc == 2)
reps = atoi (argv[1]);
mpz_init (dividend);
mpz_init (quotient);
mpz_init (remainder);
mpz_init (quotient2);
mpz_init (remainder2);
mpz_init (temp);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 10 + 2; /* 0..2047 bit operands */
do
{
mpz_rrandomb (bs, rands, 64);
divisor = mpz_get_ui (bs);
}
while (divisor == 0);
mpz_urandomb (bs, rands, size_range);
dividend_size = mpz_get_ui (bs);
mpz_rrandomb (dividend, rands, dividend_size);
mpz_urandomb (bs, rands, 2);
bsi = mpz_get_ui (bs);
if ((bsi & 1) != 0)
mpz_neg (dividend, dividend);
/* printf ("%ld\n", SIZ (dividend)); */
r_rq = mpz_cdiv_qr_ui (quotient, remainder, dividend, divisor);
r_q = mpz_cdiv_q_ui (quotient2, dividend, divisor);
r_r = mpz_cdiv_r_ui (remainder2, dividend, divisor);
r = mpz_cdiv_ui (dividend, divisor);
/* First determine that the quotients and remainders computed
with different functions are equal. */
if (mpz_cmp (quotient, quotient2) != 0)
dump_abort ("quotients from mpz_cdiv_qr_ui and mpz_cdiv_q_ui differ",
dividend, divisor);
if (mpz_cmp (remainder, remainder2) != 0)
dump_abort ("remainders from mpz_cdiv_qr_ui and mpz_cdiv_r_ui differ",
dividend, divisor);
/* Check if the sign of the quotient is correct. */
if (mpz_cmp_ui (quotient, 0) != 0)
if ((mpz_cmp_ui (quotient, 0) < 0)
!= (mpz_cmp_ui (dividend, 0) < 0))
dump_abort ("quotient sign wrong", dividend, divisor);
/* Check if the remainder has the opposite sign as the (positive) divisor
(quotient rounded towards minus infinity). */
if (mpz_cmp_ui (remainder, 0) != 0)
if (mpz_cmp_ui (remainder, 0) > 0)
dump_abort ("remainder sign wrong", dividend, divisor);
mpz_mul_ui (temp, quotient, divisor);
mpz_add (temp, temp, remainder);
if (mpz_cmp (temp, dividend) != 0)
dump_abort ("n mod d != n - [n/d]*d", dividend, divisor);
mpz_abs (remainder, remainder);
if (mpz_cmp_ui (remainder, divisor) >= 0)
dump_abort ("remainder greater than divisor", dividend, divisor);
if (mpz_cmp_ui (remainder, r_rq) != 0)
dump_abort ("remainder returned from mpz_cdiv_qr_ui is wrong",
dividend, divisor);
if (mpz_cmp_ui (remainder, r_q) != 0)
dump_abort ("remainder returned from mpz_cdiv_q_ui is wrong",
dividend, divisor);
if (mpz_cmp_ui (remainder, r_r) != 0)
dump_abort ("remainder returned from mpz_cdiv_r_ui is wrong",
dividend, divisor);
if (mpz_cmp_ui (remainder, r) != 0)
dump_abort ("remainder returned from mpz_cdiv_ui is wrong",
dividend, divisor);
}
mpz_clear (bs);
mpz_clear (dividend);
mpz_clear (quotient);
mpz_clear (remainder);
mpz_clear (quotient2);
mpz_clear (remainder2);
mpz_clear (temp);
tests_end ();
exit (0);
}
/* assuming slaves (workers)) are all homogenous, let them all do the calculations
regarding primes sieving, calculating the smoothness base and the modular roots */
int main(int argc, char **argv) {
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
MPI_Comm_size(MPI_COMM_WORLD, &mpi_group_size);
int len;
MPI_Get_processor_name(processor_name, &len);
gettimeofday(&start_global, NULL);
print_lib_version();
mpz_init(N);
mpz_t B;
mpz_init(B);
unsigned long int uBase;
int64_t nb_primes;
modular_root_t *modular_roots;
uint64_t i, j;
if (argc < 2) {
PRINT(my_rank, "usage: %s Number_to_factorize\n", argv[0]);
exit(2);
}
if (mpz_init_set_str(N, argv[1], 10) == -1) {
PRINT(my_rank, "Cannot load N %s\n", argv[1]);
exit(2);
}
mpz_t sqrtN, rem;
mpz_init(sqrtN);
mpz_init(rem);
mpz_sqrtrem(sqrtN, rem, N);
if (mpz_cmp_ui(rem, 0) != 0) /* if not perfect square, calculate the ceiling */
mpz_add_ui(sqrtN, sqrtN, 1);
else /* N is a perfect square, factored! */
{
PRINT(my_rank, "\n<<<[FACTOR]>>> %s\n", mpz_get_str(NULL, 10, sqrtN));
return 0;
}
if (mpz_probab_prime_p(N, 10) > 0) /* don't bother factoring */
{
PRINT(my_rank, "N:%s is prime\n", mpz_get_str(NULL, 10, N));
exit(0);
}
OPEN_LOG_FILE("freq");
//--------------------------------------------------------
// calculate the smoothness base for the given N
//--------------------------------------------------------
get_smoothness_base(B, N); /* if N is too small, the program will surely fail, please consider a pen and paper instead */
uBase = mpz_get_ui(B);
PRINT(my_rank, "n: %s\tBase: %s\n",
mpz_get_str(NULL, 10, N), mpz_get_str(NULL, 10, B));
//--------------------------------------------------------
// sieve primes that are less than the smoothness base using Eratosthenes sieve
//--------------------------------------------------------
START_TIMER();
nb_primes = sieve_primes_up_to((int64_t) (uBase));
PRINT(my_rank, "\tPrimes found %" PRId64 " [Smoothness Base %lu]\n",
nb_primes, uBase);
STOP_TIMER_PRINT_TIME("\tEratosthenes Sieving done");
//--------------------------------------------------------
// fill the primes array with primes to which n is a quadratic residue
//--------------------------------------------------------
START_TIMER();
primes = calloc(nb_primes, sizeof(int64_t));
nb_qr_primes = fill_primes_with_quadratic_residue(primes, N);
/*for(i=0; i<nb_qr_primes; i++)
PRINT(my_rank, "%" PRId64 "\n", primes[i]);*/
PRINT(my_rank, "\tN-Quadratic primes found %" PRId64 "\n", nb_qr_primes);
STOP_TIMER_PRINT_TIME("\tQuadratic prime filtering done");
//--------------------------------------------------------
// calculate modular roots
//--------------------------------------------------------
START_TIMER();
modular_roots = calloc(nb_qr_primes, sizeof(modular_root_t));
mpz_t tmp, r1, r2;
mpz_init(tmp);
mpz_init(r1);
mpz_init(r2);
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(tmp, (unsigned long) primes[i]);
mpz_sqrtm(r1, N, tmp); /* calculate the modular root */
mpz_neg(r2, r1); /* -q mod n */
mpz_mod(r2, r2, tmp);
modular_roots[i].root1 = mpz_get_ui(r1);
modular_roots[i].root2 = mpz_get_ui(r2);
}
mpz_clear(tmp);
mpz_clear(r1);
mpz_clear(r2);
STOP_TIMER_PRINT_TIME("Modular roots calculation done");
//--------------------------------------------------------
// ***** initialize the matrix *****
//--------------------------------------------------------
if (my_rank == 0) /* only the master have the matrix */
{
START_TIMER();
init_matrix(&matrix, nb_qr_primes + NB_VECTORS_OFFSET, nb_qr_primes);
mpz_init2(tmp_matrix_row, nb_qr_primes);
STOP_TIMER_PRINT_TIME("Matrix initialized");
}
//--------------------------------------------------------
// [Sieving] - everyones sieves including the master
//--------------------------------------------------------
START_TIMER();
mpz_t x, sieving_index, next_sieving_index, relative_start, global_step;
unsigned long ui_index, SIEVING_STEP = 50000; /* we sieve for 50000 elements at each loop */
int LOCAL_SIEVING_ROUNDS = 10; /* number of iterations a worker sieves before communicating results to the master */
unsigned long sieving_round = 0;
unsigned long nb_big_rounds = 0;
uint64_t p_pow;
smooth_number_t *x_squared;
x_squared = calloc(SIEVING_STEP, sizeof(smooth_number_t));
if (my_rank == 0)
smooth_numbers = calloc(nb_qr_primes + NB_VECTORS_OFFSET,
sizeof(smooth_number_t));
else
temp_slaves_smooth_numbers = calloc(500, sizeof(smooth_number_t));
/* TODO: this is not properly correct, using a linkedlist is better to keep track of temporary
* smooth numbers at the slaves nodes however it's pretty rare to find 500 smooth numbers in
* 50000 * 10 interval. */
mpz_init_set(x, sqrtN);
mpz_init(global_step);
mpz_init(relative_start);
mpz_init(sieving_index);
mpz_init(next_sieving_index);
mpz_t p;
mpz_init(p);
mpz_t str;
mpz_init_set(str, sieving_index);
PRINT(my_rank, "\n[%s] Sieving ...\n", processor_name);
//--------------------------------------------------------
// Init before sieving
//--------------------------------------------------------
for (i = 0; i < SIEVING_STEP; i++) {
mpz_init(x_squared[i].value_x);
mpz_init(x_squared[i].value_x_squared);
mpz_init2(x_squared[i].factors_vect, nb_qr_primes);
mpz_add_ui(x, x, 1);
}
int nb_smooth_per_round = 0;
char s[512];
//--------------------------------------------------------
// WHILE smooth numbers found less than the primes in the smooth base + NB_VECTORS_OFFSET for master
// Or master asked for more smooth numbers from slaves
//--------------------------------------------------------
while (1) {
mpz_set_ui(global_step, nb_big_rounds); /* calculates the coordinate where the workers start sieving from */
mpz_mul_ui(global_step, global_step, (unsigned long) mpi_group_size);
mpz_mul_ui(global_step, global_step, SIEVING_STEP);
mpz_mul_ui(global_step, global_step, LOCAL_SIEVING_ROUNDS);
mpz_add(global_step, global_step, sqrtN);
mpz_set_ui(relative_start, SIEVING_STEP);
mpz_mul_ui(relative_start, relative_start, LOCAL_SIEVING_ROUNDS);
mpz_mul_ui(relative_start, relative_start, (unsigned long) my_rank);
mpz_add(relative_start, relative_start, global_step);
mpz_set(sieving_index, relative_start);
mpz_set(next_sieving_index, relative_start);
for (sieving_round = 0; sieving_round < LOCAL_SIEVING_ROUNDS; /* each slave sieves for LOCAL_SIEVING_ROUNDS rounds */
sieving_round++) {
nb_smooth_per_round = 0;
mpz_set(x, next_sieving_index); /* sieve numbers from sieving_index to sieving_index + sieving_step */
mpz_set(sieving_index, next_sieving_index);
if (my_rank == 0) {
printf("\r");
printf(
"\t\tSieving at: %s30 <--> Smooth numbers found: %" PRId64 "/%" PRId64 "",
mpz_get_str(NULL, 10, sieving_index),
nb_global_smooth_numbers_found, nb_qr_primes);
fflush(stdout);
}
for (i = 0; i < SIEVING_STEP; i++) {
mpz_set(x_squared[i].value_x, x);
mpz_pow_ui(x_squared[i].value_x_squared, x, 2); /* calculate value_x_squared <- x²-n */
mpz_sub(x_squared[i].value_x_squared,
x_squared[i].value_x_squared, N);
mpz_clear(x_squared[i].factors_vect);
mpz_init2(x_squared[i].factors_vect, nb_qr_primes); /* reconstruct a new fresh 0ed vector of size nb_qr_primes bits */
mpz_add_ui(x, x, 1);
}
mpz_set(next_sieving_index, x);
//--------------------------------------------------------
// eliminate factors in the x_squared array, those who are 'destructed' to 1 are smooth
//--------------------------------------------------------
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(p, (unsigned long) primes[i]);
mpz_set(x, sieving_index);
/* get the first multiple of p that is directly larger that sieving_index
* Quadratic SIEVING: all elements from this number and in positions multiples of root1 and root2
* are also multiples of p */
get_sieving_start_index(x, x, p, modular_roots[i].root1);
mpz_set(str, x);
mpz_sub(x, x, sieving_index); /* x contains index of first number that is divisible by p */
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p); /* eliminate all factors of p */
if (p_pow & 1) /* mark bit if odd power of p exists in this x_squared[j] */
{
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
/* sieve next element located p steps from here */
}
/* same goes for root2 */
if (modular_roots[i].root2 == modular_roots[i].root1)
continue;
mpz_set(x, sieving_index);
get_sieving_start_index(x, x, p, modular_roots[i].root2);
mpz_set(str, x);
mpz_sub(x, x, sieving_index);
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p);
if (p_pow & 1) {
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
}
}
}
if (my_rank == 0) /* master gathers smooth numbers from slaves */
{
gather_smooth_numbers();
notify_slaves();
} else /* slaves send their smooth numbers to master */
{
send_smooth_numbers_to_master();
nb_global_smooth_numbers_found = get_server_notification();
}
if (nb_global_smooth_numbers_found >= nb_qr_primes + NB_VECTORS_OFFSET)
break;
nb_big_rounds++;
}
STOP_TIMER_PRINT_TIME("\nSieving DONE");
if (my_rank == 0) {
uint64_t t = 0;
//--------------------------------------------------------
//the matrix ready, start Gauss elimination. The Matrix is filled on the call of save_smooth_number()
//--------------------------------------------------------
START_TIMER();
gauss_elimination(&matrix);
STOP_TIMER_PRINT_TIME("\nGauss elimination done");
uint64_t row_index = nb_qr_primes + NB_VECTORS_OFFSET - 1; /* last row in the matrix */
int nb_linear_relations = 0;
mpz_t linear_relation_z, solution_z;
mpz_init(linear_relation_z);
mpz_init(solution_z);
get_matrix_row(linear_relation_z, &matrix, row_index--); /* get the last few rows in the Gauss eliminated matrix*/
while (mpz_cmp_ui(linear_relation_z, 0) == 0) {
nb_linear_relations++;
get_matrix_row(linear_relation_z, &matrix, row_index--);
}
PRINT(my_rank, "\tLinear dependent relations found : %d\n",
nb_linear_relations);
//--------------------------------------------------------
// Factor
//--------------------------------------------------------
//We use the last linear relation to reconstruct our solution
START_TIMER();
PRINT(my_rank, "%s", "\nFactorizing..\n");
mpz_t solution_X, solution_Y;
mpz_init(solution_X);
mpz_init(solution_Y);
/* we start testing from the first linear relation encountered in the matrix */
for (j = nb_linear_relations; j > 0; j--) {
PRINT(my_rank, "Trying %d..\n", nb_linear_relations - j + 1);
mpz_set_ui(solution_X, 1);
mpz_set_ui(solution_Y, 1);
get_identity_row(solution_z, &matrix,
nb_qr_primes + NB_VECTORS_OFFSET - j + 1);
for (i = 0; i < nb_qr_primes; i++) {
if (mpz_tstbit(solution_z, i)) {
mpz_mul(solution_X, solution_X, smooth_numbers[i].value_x);
mpz_mod(solution_X, solution_X, N); /* reduce x to modulo N */
mpz_mul(solution_Y, solution_Y,
smooth_numbers[i].value_x_squared);
/*TODO: handling huge stuff here, there is no modulo N like in the solution_X case!
* eliminate squares as long as you go*/
}
}
mpz_sqrt(solution_Y, solution_Y);
mpz_mod(solution_Y, solution_Y, N); /* y = sqrt(MUL(xi²-n)) mod N */
mpz_sub(solution_X, solution_X, solution_Y);
mpz_gcd(solution_X, solution_X, N);
if (mpz_cmp(solution_X, N) != 0 && mpz_cmp_ui(solution_X, 1) != 0) /* factor can be 1 or N, try another relation */
break;
}
mpz_cdiv_q(solution_Y, N, solution_X);
PRINT(my_rank, "\n>>>>>>>>>>> FACTORED %s =\n",
mpz_get_str(NULL, 10, N));
PRINT(
my_rank,
"\tFactor 1: %s \n\tFactor 2: %s",
mpz_get_str(NULL, 10, solution_X), mpz_get_str(NULL, 10, solution_Y));
sprintf(s, "\n>>>>>>>>>>> FACTORED %s =\n", mpz_get_str(NULL, 10, N));
APPEND_TO_LOG_FILE(s);
sprintf(s, "\tFactor 1: %s \n\tFactor 2: %s",
mpz_get_str(NULL, 10, solution_X),
mpz_get_str(NULL, 10, solution_Y));
APPEND_TO_LOG_FILE(s);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
sprintf(s, "****** TOTAL TIME: %.3f ms\n",
elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
APPEND_TO_LOG_FILE(s);
STOP_TIMER_PRINT_TIME("\nFactorizing done");
}
PRINT(my_rank, "%s", "\nCleaning memory..\n");
/********************** clear the x_squared array **********************/
for (i = 0; i < SIEVING_STEP; i++) {
mpz_clear(x_squared[i].value_x);
mpz_clear(x_squared[i].value_x_squared);
//free(x_squared[i].factors_exp);
mpz_clear(x_squared[i].factors_vect);
}
free(x_squared);
/********************** clear the x_squared array **********************/
free(modular_roots);
/********************** clear the smooth_numbers array **********************/
if (my_rank == 0) {
for (i = 0; i < nb_qr_primes + NB_VECTORS_OFFSET; i++) {
mpz_clear(smooth_numbers[i].value_x);
mpz_clear(smooth_numbers[i].value_x_squared);
mpz_clear(smooth_numbers[i].factors_vect);
//free(smooth_numbers[i].factors_exp);
}
free(smooth_numbers);
} else {
for (i = 0; i < 500; i++) {
mpz_clear(temp_slaves_smooth_numbers[i].value_x);
mpz_clear(temp_slaves_smooth_numbers[i].value_x_squared);
mpz_clear(temp_slaves_smooth_numbers[i].factors_vect);
}
free(temp_slaves_smooth_numbers);
}
/********************** clear the smooth_numbers array **********************/
free(primes);
/********************** clear mpz _t **********************/mpz_clear(B);
mpz_clear(N);
sqrtN, rem;
mpz_clear(x);
mpz_clear(sieving_index);
mpz_clear(next_sieving_index);
mpz_clear(p);
mpz_clear(str);
/********************** clear mpz _t **********************/
free_matrix(&matrix);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
PRINT(my_rank, "****** TOTAL TIME: %.3f ms\n",
elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
show_mem_usage();
MPI_Finalize();
return 0;
}
int main(void)
{
int i, result;
flint_rand_t state;
printf("is_oddprime_binary....");
fflush(stdout);
flint_randinit(state);
n_compute_primes(10000);
for (i = 0; i < 100000; i++) /* Test that primes pass the test */
{
mp_limb_t d;
mpz_t d_m;
mpz_init(d_m);
do
{
d = n_randint(state, flint_primes_cutoff) | 1;
if (d == 1UL) d += 2;
mpz_set_ui(d_m, d);
mpz_nextprime(d_m, d_m);
d = mpz_get_ui(d_m);
} while (d > flint_primes_cutoff);
result = n_is_oddprime_binary(d);
if (!result)
{
printf("FAIL:\n");
printf("d = %lu is declared composite\n", d);
abort();
}
mpz_clear(d_m);
}
for (i = 0; i < 100000; i++) /* Test that not too many composites pass */
{
mp_limb_t d;
mpz_t d_m;
mpz_init(d_m);
do
{
d = n_randint(state, flint_primes_cutoff) | 1;
mpz_set_ui(d_m, d);
} while ((mpz_probab_prime_p(d_m, 12)) || (d > flint_primes_cutoff));
result = !n_is_oddprime_binary(d);
if (!result)
{
printf("FAIL:\n");
printf("d = %lu is declared prime\n", d);
abort();
}
mpz_clear(d_m);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
void
check_all (mpz_ptr want, mpz_srcptr x_orig, mpz_srcptr y_orig)
{
mpz_t got, x, y;
int negx, negy, swap, inplace;
mpz_init (got);
mpz_init_set (x, x_orig);
mpz_init_set (y, y_orig);
for (swap = 0; swap < 2; swap++)
{
mpz_swap (x, y);
for (negx = 0; negx < 2; negx++)
{
mpz_neg (x, x);
for (negy = 0; negy < 2; negy++)
{
mpz_neg (y, y);
for (inplace = 0; inplace <= 1; inplace++)
{
if (inplace)
{ mpz_set (got, x); mpz_lcm (got, got, y); }
else
mpz_lcm (got, x, y);
MPZ_CHECK_FORMAT (got);
if (mpz_cmp (got, want) != 0)
{
printf ("mpz_lcm wrong, inplace=%d\n", inplace);
fail:
mpz_trace ("x", x);
mpz_trace ("y", y);
mpz_trace ("got", got);
mpz_trace ("want", want);
abort ();
}
if (mpz_fits_ulong_p (y))
{
unsigned long yu = mpz_get_ui (y);
if (inplace)
{ mpz_set (got, x); mpz_lcm_ui (got, got, yu); }
else
mpz_lcm_ui (got, x, yu);
if (mpz_cmp (got, want) != 0)
{
printf ("mpz_lcm_ui wrong, inplace=%d\n", inplace);
printf ("yu=%lu\n", yu);
goto fail;
}
}
}
}
}
}
mpz_clear (got);
mpz_clear (x);
mpz_clear (y);
}
int
main (int argc, char *argv[])
{
char *progname = argv[0];
mpz_t fr, to;
mpz_t fr2, to2;
unsigned long sieve_lim;
unsigned long est_n_primes;
unsigned char *s;
mpz_t tmp;
mpz_t siev_sqr_lim;
while (argc != 1)
{
if (strcmp (argv[1], "-c") == 0)
{
flag_count = 1;
argv++;
argc--;
}
else if (strcmp (argv[1], "-p") == 0)
{
flag_print = 2;
argv++;
argc--;
}
else if (strcmp (argv[1], "-g") == 0)
{
flag_maxgap = 1;
argv++;
argc--;
}
else
break;
}
if (flag_count || flag_maxgap)
flag_print--; /* clear unless an explicit -p */
mpz_init (fr);
mpz_init (to);
mpz_init (fr2);
mpz_init (to2);
if (argc == 3)
{
mpz_set_str (fr, argv[1], 0);
if (argv[2][0] == '+')
{
mpz_set_str (to, argv[2] + 1, 0);
mpz_add (to, to, fr);
}
else
mpz_set_str (to, argv[2], 0);
}
else if (argc == 2)
{
mpz_set_ui (fr, 0);
mpz_set_str (to, argv[1], 0);
}
else
{
fprintf (stderr, "usage: %s [-c] [-p] [-g] [from [+]]to\n", progname);
exit (1);
}
mpz_set (fr2, fr);
if (mpz_cmp_ui (fr2, 3) < 0)
{
mpz_set_ui (fr2, 2);
report (fr2);
mpz_set_ui (fr2, 3);
}
mpz_setbit (fr2, 0); /* make odd */
mpz_sub_ui (to2, to, 1);
mpz_setbit (to2, 0); /* make odd */
mpz_init (tmp);
mpz_init (siev_sqr_lim);
mpz_sqrt (tmp, to2);
#define SIEVE_LIMIT 10000000
if (mpz_cmp_ui (tmp, SIEVE_LIMIT) < 0)
{
sieve_lim = mpz_get_ui (tmp);
}
else
{
sieve_lim = SIEVE_LIMIT;
mpz_sub (tmp, to2, fr2);
if (mpz_cmp_ui (tmp, sieve_lim) < 0)
sieve_lim = mpz_get_ui (tmp); /* limit sieving for small ranges */
}
mpz_set_ui (siev_sqr_lim, sieve_lim + 1);
mpz_mul_ui (siev_sqr_lim, siev_sqr_lim, sieve_lim + 1);
est_n_primes = (size_t) (sieve_lim / log((double) sieve_lim) * 1.13) + 10;
primes = malloc (est_n_primes * sizeof primes[0]);
make_primelist (sieve_lim);
assert (est_n_primes >= n_primes);
#if DEBUG
printf ("sieve_lim = %lu\n", sieve_lim);
printf ("n_primes = %lu (3..%u)\n",
n_primes, primes[n_primes - 1].prime);
#endif
#define S (1 << 15) /* FIXME: Figure out L1 cache size */
s = malloc (S/2);
while (mpz_cmp (fr2, to2) <= 0)
{
unsigned long rsize;
rsize = S;
mpz_add_ui (tmp, fr2, rsize);
if (mpz_cmp (tmp, to2) > 0)
{
mpz_sub (tmp, to2, fr2);
rsize = mpz_get_ui (tmp) + 2;
}
#if DEBUG
printf ("Sieving region ["); mpz_out_str (stdout, 10, fr2);
printf (","); mpz_add_ui (tmp, fr2, rsize - 2);
mpz_out_str (stdout, 10, tmp); printf ("]\n");
#endif
sieve_region (s, fr2, rsize);
find_primes (s, fr2, rsize / 2, siev_sqr_lim);
mpz_add_ui (fr2, fr2, S);
}
free (s);
if (flag_count)
printf ("Pi(interval) = %lu\n", total_primes);
if (flag_maxgap)
printf ("max gap: %lu\n", maxgap);
return 0;
}
int
main (int argc, char **argv)
{
mpz_t x2;
mpz_t x, rem;
mpz_t temp, temp2;
mp_size_t x2_size;
int i;
int reps = 20000;
gmp_randstate_t rands;
mpz_t bs;
unsigned long size_range;
tests_start ();
gmp_randinit_default(rands);
mpz_init (bs);
if (argc == 2)
reps = atoi (argv[1]);
mpz_init (x2);
mpz_init (x);
mpz_init (rem);
mpz_init (temp);
mpz_init (temp2);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 12 + 2; /* 0..8191 bit operands */
mpz_urandomb (bs, rands, size_range);
x2_size = mpz_get_ui (bs);
mpz_rrandomb (x2, rands, x2_size);
/* printf ("%ld\n", SIZ (x2)); */
mpz_sqrtrem (x, rem, x2);
mpz_mul (temp, x, x);
/* Is square of result > argument? */
if (mpz_cmp (temp, x2) > 0)
dump_abort (x2, x, rem);
mpz_add_ui (temp2, x, 1);
mpz_mul (temp2, temp2, temp2);
/* Is square of (result + 1) <= argument? */
if (mpz_cmp (temp2, x2) <= 0)
dump_abort (x2, x, rem);
mpz_add (temp2, temp, rem);
/* Is the remainder wrong? */
if (mpz_cmp (x2, temp2) != 0)
dump_abort (x2, x, rem);
}
mpz_clear (bs);
mpz_clear (x2);
mpz_clear (x);
mpz_clear (rem);
mpz_clear (temp);
mpz_clear (temp2);
gmp_randclear(rands);
tests_end ();
exit (0);
}
int
main (int argc, char **argv)
{
mpz_t op1, op2;
mpz_t prod, quot;
mp_size_t size;
int i;
int reps = 20000;
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long bsi, size_range;
tests_start ();
rands = RANDS;
mp_trace_base = -16;
mpz_init (bs);
if (argc == 2)
reps = atoi (argv[1]);
mpz_init (op1);
mpz_init (op2);
mpz_init (prod);
mpz_init (quot);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 10 + 2; /* 0..2047 bit operands */
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (op1, rands, size);
do
{
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (op2, rands, size);
}
while (mpz_sgn (op2) == 0);
mpz_urandomb (bs, rands, 2);
bsi = mpz_get_ui (bs);
if ((bsi & 1) != 0)
mpz_neg (op1, op1);
if ((bsi & 2) != 0)
mpz_neg (op2, op2);
mpz_mul (prod, op1, op2);
mpz_divexact (quot, prod, op2);
MPZ_CHECK_FORMAT (quot);
if (mpz_cmp (quot, op1) != 0)
{
printf ("Wrong results:\n");
mpz_trace (" got ", quot);
mpz_trace (" want ", op1);
mpz_trace (" dividend", prod);
mpz_trace (" divisor ", op2);
abort ();
}
}
mpz_clear (bs);
mpz_clear (op1);
mpz_clear (op2);
mpz_clear (prod);
mpz_clear (quot);
tests_end ();
exit (0);
}
int main(long argc, char *argv[])
{
if(argc != 4)
{
printf("Three arguments required\n");
printf("Usage: test6 a b c calculates pi(a*b^c)\n");
exit(1);
}
//Legacy GMP code below; the input must fit in a 64 bit unsigned integer
mpz_t n;
mpz_init(n);
mpz_ui_pow_ui(n,atol(argv[2]), atol(argv[3]));
mpz_mul_ui(n, n, atol(argv[1]));
uint64_t n2 = mpz_get_ui(n);
uint64_t* s = malloc((n2/64+3)*sizeof(uint64_t));
assert(s != NULL);
//for wheel mod 6
uint64_t word1 = 0x28A28A28A28A28A2;
uint64_t word2 = 0xA28A28A28A28A28A;
uint64_t word3 = 0x8A28A28A28A28A28;
uint64_t k;
for(k=0; k <= n2/64; k+=3)
{
s[k]=word1;
s[k+1]=word2;
s[k+2]=word3;
}
uint64_t sieve_to=floor(sqrt(n2));
uint64_t i,j;
i=5; //5 is the first number which is relatively prime to 6
int next = 4; //If i%6 = 5 then add 2 to i; if i%6 = 1 then add 4 to i;
while (i<=sieve_to)
{
next = 6 - next; //Alternate jumps of 2 and 4 to move through all the numbers congruent to +/- 1 mod 6
if(TEST(s,i)!=0) //Only sieve by primes
{
for(j=i*i; j<=n2; j+= 6*i) CLEAR(s,j); //since i*i is always 1 (mod 6), this sieves out all the multiples of i congruent to 1 (mod 6)
for(j=i*(i + next); j<=n2; j+= 6*i) CLEAR(s,j); //i*(i+next) is the first multiple of i which exceeds i*i and is congruent to -1 (mod 6)
}
i += next; //Advance pointer to the next number which is congruent to +/- 1
}
s[0] &= (~0 - 0xF); //Remove sieve entries for numbers less than 5;
s[0] += 0xC; //Put in the correct entries; 2 and 3 are prime, 1100b = 4d + 8d = 12d = 0xC
#if 0
for(i=0; i<=n2; i++)
if(TEST(s,i)>0) printf("%" PRIu64 "\n",i);
#endif
//Note ridiculous macro format required to print unit64_t without generating a compiler warning
printf("%" PRIu64 "\n", count_bits(s,0,n2));
return(0);
}
static PyObject *
GMPy_Integer_Pow(PyObject *b, PyObject *e, PyObject *m, CTXT_Object *context)
{
MPZ_Object *result = NULL, *tempb = NULL, *tempe = NULL, *tempm = NULL;
int has_mod;
/* Try to parse the modulus value first. */
if (m == Py_None) {
has_mod = 0;
}
else {
has_mod = 1;
if (!IS_INTEGER(m)) {
Py_RETURN_NOTIMPLEMENTED;
}
else {
if (!(tempm = GMPy_MPZ_From_Integer(m, context))) {
goto err;
}
}
}
result = GMPy_MPZ_New(context);
tempb = GMPy_MPZ_From_Integer(b, context);
tempe = GMPy_MPZ_From_Integer(e, context);
if (!tempb || !tempe || !result) {
goto err;
}
if (!has_mod) {
/* When no modulo is present, the exponent must fit in unsigned long.
*/
unsigned long el;
if (mpz_sgn(tempe->z) < 0) {
VALUE_ERROR("pow() exponent cannot be negative");
goto err;
}
if (!mpz_fits_ulong_p(tempe->z)) {
VALUE_ERROR("pow() outrageous exponent");
goto err;
}
el = mpz_get_ui(tempe->z);
mpz_pow_ui(result->z, tempb->z, el);
}
else {
/* Modulo is present. */
int sign;
mpz_t mm, base, exp;
sign = mpz_sgn(tempm->z);
if (sign == 0) {
VALUE_ERROR("pow() 3rd argument cannot be 0");
goto err;
}
mpz_inoc(mm);
mpz_abs(mm, tempm->z);
/* A negative exponent is allowed if inverse exists. */
if (mpz_sgn(tempe->z) < 0) {
mpz_inoc(base);
mpz_inoc(exp);
if (!mpz_invert(base, tempb->z, mm)) {
VALUE_ERROR("pow() base not invertible");
mpz_cloc(base);
mpz_cloc(exp);
mpz_cloc(mm);
goto err;
}
else {
mpz_abs(exp, tempe->z);
}
mpz_powm(result->z, base, exp, mm);
mpz_cloc(base);
mpz_cloc(exp);
}
else {
mpz_powm(result->z, tempb->z, tempe->z, mm);
}
mpz_cloc(mm);
/* Python uses a rather peculiar convention for negative modulos
* If the modulo is negative, result should be in the interval
* m < r <= 0 .
*/
if ((sign < 0) && (mpz_sgn(MPZ(result)) > 0)) {
mpz_add(result->z, result->z, tempm->z);
}
}
Py_XDECREF((PyObject*)tempb);
Py_XDECREF((PyObject*)tempe);
Py_XDECREF((PyObject*)tempm);
return (PyObject*)result;
err:
Py_XDECREF((PyObject*)tempb);
Py_XDECREF((PyObject*)tempe);
Py_XDECREF((PyObject*)tempm);
Py_DECREF((PyObject*)result);
return NULL;
}
num_t
num_int_part_sel(pseltype_t op_type, num_t hi, num_t lo, num_t a)
{
num_t r, m;
unsigned long mask_shl, lo_ui;
r = num_new_z(N_TEMP, NULL);
m = num_new_z(N_TEMP, NULL);
a = num_new_z(N_TEMP, a);
hi = num_new_z(N_TEMP, hi);
if (lo != NULL)
lo = num_new_z(N_TEMP, lo);
switch (op_type) {
case PSEL_SINGLE:
lo = num_new_z(N_TEMP, hi);
break;
case PSEL_FRANGE:
break;
case PSEL_DRANGE:
if (mpz_cmp_si(Z(lo), 0L) < 0) {
yyxerror("low index of part select operation must be "
"positive");
return NULL;
}
mpz_sub_ui(Z(lo), Z(lo), 1UL);
mpz_sub(Z(lo), Z(hi), Z(lo));
break;
}
if (mpz_cmp_si(Z(hi), 0L) < 0) {
yyxerror("high index of part select operation must be "
"positive");
return NULL;
}
if (mpz_cmp_si(Z(lo), 0L) < 0) {
yyxerror("low index of part select operation must be "
"positive");
return NULL;
}
if (!mpz_fits_ulong_p(Z(hi))) {
yyxerror("high index of part select operation needs to fit "
"into an unsigned long C datatype");
return NULL;
}
if (!mpz_fits_ulong_p(Z(lo))) {
yyxerror("low index of part select operation needs to fit "
"into an unsigned long C datatype");
return NULL;
}
lo_ui = mpz_get_ui(Z(lo));
mask_shl = 1 + (mpz_get_ui(Z(hi)) - lo_ui);
/*
* We do the part sel by:
* (1) shifting right by 'lo'
* (2) anding with ((1 << mask_shl)-1)
*/
mpz_div_2exp(Z(r), Z(a), lo_ui);
mpz_set_ui(Z(m), 1UL);
mpz_mul_2exp(Z(m), Z(m), mask_shl);
mpz_sub_ui(Z(m), Z(m), 1UL);
mpz_and(Z(r), Z(r), Z(m));
return r;
}
int
main (int argc, char **argv)
{
mpz_t dividend, divisor;
mpz_t quotient, remainder;
mpz_t quotient2, remainder2;
mpz_t temp;
mp_size_t dividend_size, divisor_size;
int i;
int reps = 1000;
gmp_randstate_t rands;
mpz_t bs;
unsigned long bsi, size_range;
tests_start ();
special_tests();
gmp_randinit_default(rands);
mpz_init (bs);
if (argc == 2)
reps = atoi (argv[1]);
mpz_init (dividend);
mpz_init (divisor);
mpz_init (quotient);
mpz_init (remainder);
mpz_init (quotient2);
mpz_init (remainder2);
mpz_init (temp);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 16 + 2; /* 0..131071 bit operands */
do
{
mpz_urandomb (bs, rands, size_range);
divisor_size = mpz_get_ui (bs);
mpz_rrandomb (divisor, rands, divisor_size);
}
while (mpz_sgn (divisor) == 0);
mpz_urandomb (bs, rands, size_range);
dividend_size = mpz_get_ui (bs) + divisor_size;
mpz_rrandomb (dividend, rands, dividend_size);
mpz_urandomb (bs, rands, 2);
bsi = mpz_get_ui (bs);
if ((bsi & 1) != 0)
mpz_neg (dividend, dividend);
if ((bsi & 2) != 0)
mpz_neg (divisor, divisor);
/* printf ("%ld %ld\n", SIZ (dividend), SIZ (divisor)); */
mpz_tdiv_qr (quotient, remainder, dividend, divisor);
mpz_tdiv_q (quotient2, dividend, divisor);
mpz_tdiv_r (remainder2, dividend, divisor);
/* First determine that the quotients and remainders computed
with different functions are equal. */
if (mpz_cmp (quotient, quotient2) != 0)
dump_abort (dividend, divisor);
if (mpz_cmp (remainder, remainder2) != 0)
dump_abort (dividend, divisor);
/* Check if the sign of the quotient is correct. */
if (mpz_cmp_ui (quotient, 0) != 0)
if ((mpz_cmp_ui (quotient, 0) < 0)
!= ((mpz_cmp_ui (dividend, 0) ^ mpz_cmp_ui (divisor, 0)) < 0))
dump_abort (dividend, divisor);
/* Check if the remainder has the same sign as the dividend
(quotient rounded towards 0). */
if (mpz_cmp_ui (remainder, 0) != 0)
if ((mpz_cmp_ui (remainder, 0) < 0) != (mpz_cmp_ui (dividend, 0) < 0))
dump_abort (dividend, divisor);
mpz_mul (temp, quotient, divisor);
mpz_add (temp, temp, remainder);
if (mpz_cmp (temp, dividend) != 0)
dump_abort (dividend, divisor);
mpz_abs (temp, divisor);
mpz_abs (remainder, remainder);
if (mpz_cmp (remainder, temp) >= 0)
dump_abort (dividend, divisor);
}
mpz_clear (bs);
mpz_clear (dividend);
mpz_clear (divisor);
mpz_clear (quotient);
mpz_clear (remainder);
mpz_clear (quotient2);
mpz_clear (remainder2);
mpz_clear (temp);
gmp_randclear(rands);
tests_end ();
exit (0);
}
void
check_random (int argc, char *argv[])
{
gmp_randstate_ptr rands = RANDS;
mpz_t a, c, d, ra, rc;
int i;
int want;
int reps = 10000;
mpz_t bs;
unsigned long size_range, size;
if (argc >= 2)
reps = atoi (argv[1]);
mpz_init (bs);
mpz_init (a);
mpz_init (c);
mpz_init (d);
mpz_init (ra);
mpz_init (rc);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 16 + 1; /* 0..65536 bit operands */
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (a, rands, size);
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 16 + 1; /* 0..65536 bit operands */
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (c, rands, size);
do
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 16 + 1; /* 0..65536 bit operands */
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (d, rands, size);
}
while (SIZ(d) == 0);
mpz_negrandom (a, rands);
MPZ_CHECK_FORMAT (a);
mpz_negrandom (c, rands);
MPZ_CHECK_FORMAT (c);
mpz_negrandom (d, rands);
mpz_fdiv_r (ra, a, d);
mpz_fdiv_r (rc, c, d);
want = (mpz_cmp (ra, rc) == 0);
check_one (a, c, d, want);
mpz_sub (ra, ra, rc);
mpz_sub (a, a, ra);
MPZ_CHECK_FORMAT (a);
check_one (a, c, d, 1);
if (! mpz_pow2abs_p (d))
{
refmpz_combit (a, urandom() % (8*GMP_LIMB_BITS));
check_one (a, c, d, 0);
}
}
mpz_clear (bs);
mpz_clear (a);
mpz_clear (c);
mpz_clear (d);
mpz_clear (ra);
mpz_clear (rc);
}
static bool bp_script_eval(parr *stack, const cstring *script,
const struct bp_tx *txTo, unsigned int nIn,
unsigned int flags, int nHashType)
{
struct const_buffer pc = { script->str, script->len };
struct const_buffer pend = { script->str + script->len, 0 };
struct const_buffer pbegincodehash = { script->str, script->len };
struct bscript_op op;
bool rc = false;
cstring *vfExec = cstr_new(NULL);
parr *altstack = parr_new(0, buffer_freep);
mpz_t bn, bn_Zero, bn_One;
mpz_init(bn);
mpz_init_set_ui(bn_Zero, 0);
mpz_init_set_ui(bn_One,1);
if (script->len > MAX_SCRIPT_SIZE)
goto out;
unsigned int nOpCount = 0;
bool fRequireMinimal = (flags & SCRIPT_VERIFY_MINIMALDATA) != 0;
struct bscript_parser bp;
bsp_start(&bp, &pc);
while (pc.p < pend.p) {
bool fExec = !count_false(vfExec);
if (!bsp_getop(&op, &bp))
goto out;
enum opcodetype opcode = op.op;
if (op.data.len > MAX_SCRIPT_ELEMENT_SIZE)
goto out;
if (opcode > OP_16 && ++nOpCount > MAX_OPS_PER_SCRIPT)
goto out;
if (disabled_op[opcode])
goto out;
if (fExec && 0 <= opcode && opcode <= OP_PUSHDATA4) {
if (fRequireMinimal && !CheckMinimalPush(&op.data, opcode))
goto out;
stack_push(stack, (struct buffer *) &op.data);
} else if (fExec || (OP_IF <= opcode && opcode <= OP_ENDIF))
switch (opcode) {
//
// Push value
//
case OP_1NEGATE:
case OP_1:
case OP_2:
case OP_3:
case OP_4:
case OP_5:
case OP_6:
case OP_7:
case OP_8:
case OP_9:
case OP_10:
case OP_11:
case OP_12:
case OP_13:
case OP_14:
case OP_15:
case OP_16:
mpz_set_si(bn, (int)opcode - (int)(OP_1 - 1));
stack_push_str(stack, bn_getvch(bn));
break;
//
// Control
//
case OP_NOP:
break;
case OP_CHECKLOCKTIMEVERIFY: {
if (!(flags & SCRIPT_VERIFY_CHECKLOCKTIMEVERIFY)) {
// not enabled; treat as a NOP2
if (flags & SCRIPT_VERIFY_DISCOURAGE_UPGRADABLE_NOPS)
goto out;
break;
}
if (stack->len < 1)
goto out;
// Note that elsewhere numeric opcodes are limited to
// operands in the range -2**31+1 to 2**31-1, however it is
// legal for opcodes to produce results exceeding that
// range. This limitation is implemented by CastToBigNum's
// default 4-byte limit.
//
// If we kept to that limit we'd have a year 2038 problem,
// even though the nLockTime field in transactions
// themselves is uint32 which only becomes meaningless
// after the year 2106.
//
// Thus as a special case we tell CastToBigNum to accept up
// to 5-byte bignums, which are good until 2**39-1, well
// beyond the 2**32-1 limit of the nLockTime field itself.
if (!CastToBigNum(bn, stacktop(stack, -1), fRequireMinimal, 5))
goto out;
// In the rare event that the argument may be < 0 due to
// some arithmetic being done first, you can always use
// 0 MAX CHECKLOCKTIMEVERIFY.
if (mpz_sgn(bn) < 0)
goto out;
uint64_t nLockTime = mpz_get_ui(bn);
// Actually compare the specified lock time with the transaction.
if (!CheckLockTime(nLockTime, txTo, nIn))
goto out;
break;
}
case OP_CHECKSEQUENCEVERIFY:
{
if (!(flags & SCRIPT_VERIFY_CHECKSEQUENCEVERIFY)) {
// not enabled; treat as a NOP3
if (flags & SCRIPT_VERIFY_DISCOURAGE_UPGRADABLE_NOPS)
goto out;
break;
}
if (stack->len < 1)
goto out;
// nSequence, like nLockTime, is a 32-bit unsigned integer
// field. See the comment in CHECKLOCKTIMEVERIFY regarding
// 5-byte numeric operands.
if (!CastToBigNum(bn, stacktop(stack, -1), fRequireMinimal, 5))
goto out;
// In the rare event that the argument may be < 0 due to
// some arithmetic being done first, you can always use
// 0 MAX CHECKSEQUENCEVERIFY.
if (mpz_sgn(bn) < 0)
goto out;
uint32_t nSequence = mpz_get_ui(bn);
// To provide for future soft-fork extensibility, if the
// operand has the disabled lock-time flag set,
// CHECKSEQUENCEVERIFY behaves as a NOP.
if ((nSequence & SEQUENCE_LOCKTIME_DISABLE_FLAG) != 0)
break;
// Compare the specified sequence number with the input.
if (!CheckSequence(nSequence, txTo, nIn))
goto out;
break;
}
case OP_NOP1: case OP_NOP4: case OP_NOP5:
case OP_NOP6: case OP_NOP7: case OP_NOP8: case OP_NOP9: case OP_NOP10:
if (flags & SCRIPT_VERIFY_DISCOURAGE_UPGRADABLE_NOPS)
goto out;
break;
case OP_IF:
case OP_NOTIF: {
// <expression> if [statements] [else [statements]] endif
bool fValue = false;
if (fExec) {
if (stack->len < 1)
goto out;
struct buffer *vch = stacktop(stack, -1);
fValue = CastToBool(vch);
if (opcode == OP_NOTIF)
fValue = !fValue;
popstack(stack);
}
uint8_t vc = (uint8_t) fValue;
cstr_append_c(vfExec, vc);
break;
}
case OP_ELSE: {
if (vfExec->len == 0)
goto out;
uint8_t *v = (uint8_t *) &vfExec->str[vfExec->len - 1];
*v = !(*v);
break;
}
case OP_ENDIF:
if (vfExec->len == 0)
goto out;
cstr_erase(vfExec, vfExec->len - 1, 1);
break;
case OP_VERIFY: {
if (stack->len < 1)
goto out;
bool fValue = CastToBool(stacktop(stack, -1));
if (fValue)
popstack(stack);
else
goto out;
break;
}
case OP_RETURN:
goto out;
//
// Stack ops
//
case OP_TOALTSTACK:
if (stack->len < 1)
goto out;
stack_push(altstack, stacktop(stack, -1));
popstack(stack);
break;
case OP_FROMALTSTACK:
if (altstack->len < 1)
goto out;
stack_push(stack, stacktop(altstack, -1));
popstack(altstack);
break;
case OP_2DROP:
// (x1 x2 -- )
if (stack->len < 2)
goto out;
popstack(stack);
popstack(stack);
break;
case OP_2DUP: {
// (x1 x2 -- x1 x2 x1 x2)
if (stack->len < 2)
goto out;
struct buffer *vch1 = stacktop(stack, -2);
struct buffer *vch2 = stacktop(stack, -1);
stack_push(stack, vch1);
stack_push(stack, vch2);
break;
}
case OP_3DUP: {
// (x1 x2 x3 -- x1 x2 x3 x1 x2 x3)
if (stack->len < 3)
goto out;
struct buffer *vch1 = stacktop(stack, -3);
struct buffer *vch2 = stacktop(stack, -2);
struct buffer *vch3 = stacktop(stack, -1);
stack_push(stack, vch1);
stack_push(stack, vch2);
stack_push(stack, vch3);
break;
}
case OP_2OVER: {
// (x1 x2 x3 x4 -- x1 x2 x3 x4 x1 x2)
if (stack->len < 4)
goto out;
struct buffer *vch1 = stacktop(stack, -4);
struct buffer *vch2 = stacktop(stack, -3);
stack_push(stack, vch1);
stack_push(stack, vch2);
break;
}
case OP_2ROT: {
// (x1 x2 x3 x4 x5 x6 -- x3 x4 x5 x6 x1 x2)
if (stack->len < 6)
goto out;
struct buffer *vch1 = stack_take(stack, -6);
struct buffer *vch2 = stack_take(stack, -5);
parr_remove_range(stack, stack->len - 6, 2);
stack_push_nocopy(stack, vch1);
stack_push_nocopy(stack, vch2);
break;
}
case OP_2SWAP:
// (x1 x2 x3 x4 -- x3 x4 x1 x2)
if (stack->len < 4)
goto out;
stack_swap(stack, -4, -2);
stack_swap(stack, -3, -1);
break;
case OP_IFDUP: {
// (x - 0 | x x)
if (stack->len < 1)
goto out;
struct buffer *vch = stacktop(stack, -1);
if (CastToBool(vch))
stack_push(stack, vch);
break;
}
case OP_DEPTH:
// -- stacksize
mpz_set_ui(bn, stack->len);
stack_push_str(stack, bn_getvch(bn));
break;
case OP_DROP:
// (x -- )
if (stack->len < 1)
goto out;
popstack(stack);
break;
case OP_DUP: {
// (x -- x x)
if (stack->len < 1)
goto out;
struct buffer *vch = stacktop(stack, -1);
stack_push(stack, vch);
break;
}
case OP_NIP:
// (x1 x2 -- x2)
if (stack->len < 2)
goto out;
parr_remove_idx(stack, stack->len - 2);
break;
case OP_OVER: {
// (x1 x2 -- x1 x2 x1)
if (stack->len < 2)
goto out;
struct buffer *vch = stacktop(stack, -2);
stack_push(stack, vch);
break;
}
case OP_PICK:
case OP_ROLL: {
// (xn ... x2 x1 x0 n - xn ... x2 x1 x0 xn)
// (xn ... x2 x1 x0 n - ... x2 x1 x0 xn)
if (stack->len < 2)
goto out;
int n = stackint(stack, -1, fRequireMinimal);
popstack(stack);
if (n < 0 || n >= (int)stack->len)
goto out;
struct buffer *vch = stacktop(stack, -n-1);
if (opcode == OP_ROLL) {
vch = buffer_copy(vch->p, vch->len);
parr_remove_idx(stack,
stack->len - n - 1);
stack_push_nocopy(stack, vch);
} else
stack_push(stack, vch);
break;
}
case OP_ROT: {
// (x1 x2 x3 -- x2 x3 x1)
// x2 x1 x3 after first swap
// x2 x3 x1 after second swap
if (stack->len < 3)
goto out;
stack_swap(stack, -3, -2);
stack_swap(stack, -2, -1);
break;
}
case OP_SWAP: {
// (x1 x2 -- x2 x1)
if (stack->len < 2)
goto out;
stack_swap(stack, -2, -1);
break;
}
case OP_TUCK: {
// (x1 x2 -- x2 x1 x2)
if (stack->len < 2)
goto out;
struct buffer *vch = stacktop(stack, -1);
stack_insert(stack, vch, -2);
break;
}
case OP_SIZE: {
// (in -- in size)
if (stack->len < 1)
goto out;
struct buffer *vch = stacktop(stack, -1);
mpz_set_ui(bn, vch->len);
stack_push_str(stack, bn_getvch(bn));
break;
}
case OP_EQUAL:
case OP_EQUALVERIFY: {
// (x1 x2 - bool)
if (stack->len < 2)
goto out;
struct buffer *vch1 = stacktop(stack, -2);
struct buffer *vch2 = stacktop(stack, -1);
bool fEqual = buffer_equal(vch1, vch2);
// OP_NOTEQUAL is disabled because it would be too easy to say
// something like n != 1 and have some wiseguy pass in 1 with extra
// zero bytes after it (numerically, 0x01 == 0x0001 == 0x000001)
//if (opcode == OP_NOTEQUAL)
// fEqual = !fEqual;
popstack(stack);
popstack(stack);
stack_push_str(stack, fEqual ? bn_getvch(bn_One) : bn_getvch(bn_Zero));
if (opcode == OP_EQUALVERIFY) {
if (fEqual)
popstack(stack);
else
goto out;
}
break;
}
//
// Numeric
//
case OP_1ADD:
case OP_1SUB:
case OP_NEGATE:
case OP_ABS:
case OP_NOT:
case OP_0NOTEQUAL: {
// (in -- out)
if (stack->len < 1)
goto out;
if (!CastToBigNum(bn, stacktop(stack, -1), fRequireMinimal, nDefaultMaxNumSize))
goto out;
switch (opcode)
{
case OP_1ADD:
mpz_add_ui(bn, bn, 1);
break;
case OP_1SUB:
mpz_sub_ui(bn, bn, 1);
break;
case OP_NEGATE:
mpz_neg(bn, bn);
break;
case OP_ABS:
mpz_abs(bn, bn);
break;
case OP_NOT:
mpz_set_ui(bn, mpz_sgn(bn) == 0 ? 1 : 0);
break;
case OP_0NOTEQUAL:
mpz_set_ui(bn, mpz_sgn(bn) == 0 ? 0 : 1);
break;
default:
// impossible
goto out;
}
popstack(stack);
stack_push_str(stack, bn_getvch(bn));
break;
}
case OP_ADD:
case OP_SUB:
case OP_BOOLAND:
case OP_BOOLOR:
case OP_NUMEQUAL:
case OP_NUMEQUALVERIFY:
case OP_NUMNOTEQUAL:
case OP_LESSTHAN:
case OP_GREATERTHAN:
case OP_LESSTHANOREQUAL:
case OP_GREATERTHANOREQUAL:
case OP_MIN:
case OP_MAX: {
// (x1 x2 -- out)
if (stack->len < 2)
goto out;
mpz_t bn1, bn2;
mpz_init(bn1);
mpz_init(bn2);
if (!CastToBigNum(bn1, stacktop(stack, -2), fRequireMinimal, nDefaultMaxNumSize) ||
!CastToBigNum(bn2, stacktop(stack, -1), fRequireMinimal, nDefaultMaxNumSize)) {
mpz_clear(bn1);
mpz_clear(bn2);
goto out;
}
switch (opcode)
{
case OP_ADD:
mpz_add(bn, bn1, bn2);
break;
case OP_SUB:
mpz_sub(bn, bn1, bn2);
break;
case OP_BOOLAND:
mpz_set_ui(bn,
!(mpz_sgn(bn1) == 0) && !(mpz_sgn(bn2) == 0) ?
1 : 0);
break;
case OP_BOOLOR:
mpz_set_ui(bn,
!(mpz_sgn(bn1) == 0) || !(mpz_sgn(bn2) == 0) ?
1 : 0);
break;
case OP_NUMEQUAL:
case OP_NUMEQUALVERIFY:
mpz_set_ui(bn,
mpz_cmp(bn1, bn2) == 0 ? 1 : 0);
break;
case OP_NUMNOTEQUAL:
mpz_set_ui(bn,
mpz_cmp(bn1, bn2) != 0 ? 1 : 0);
break;
case OP_LESSTHAN:
mpz_set_ui(bn,
mpz_cmp(bn1, bn2) < 0 ? 1 : 0);
break;
case OP_GREATERTHAN:
mpz_set_ui(bn,
mpz_cmp(bn1, bn2) > 0 ? 1 : 0);
break;
case OP_LESSTHANOREQUAL:
mpz_set_ui(bn,
mpz_cmp(bn1, bn2) <= 0 ? 1 : 0);
break;
case OP_GREATERTHANOREQUAL:
mpz_set_ui(bn,
mpz_cmp(bn1, bn2) >= 0 ? 1 : 0);
break;
case OP_MIN:
if (mpz_cmp(bn1, bn2) < 0)
mpz_set(bn, bn1);
else
mpz_set(bn, bn2);
break;
case OP_MAX:
if (mpz_cmp(bn1, bn2) > 0)
mpz_set(bn, bn1);
else
mpz_set(bn, bn2);
break;
default:
// impossible
break;
}
popstack(stack);
popstack(stack);
stack_push_str(stack, bn_getvch(bn));
mpz_clear(bn1);
mpz_clear(bn2);
if (opcode == OP_NUMEQUALVERIFY)
{
if (CastToBool(stacktop(stack, -1)))
popstack(stack);
else
goto out;
}
break;
}
case OP_WITHIN: {
// (x min max -- out)
if (stack->len < 3)
goto out;
mpz_t bn1, bn2, bn3;
mpz_init(bn1);
mpz_init(bn2);
mpz_init(bn3);
bool rc1 = CastToBigNum(bn1, stacktop(stack, -3), fRequireMinimal, nDefaultMaxNumSize);
bool rc2 = CastToBigNum(bn2, stacktop(stack, -2), fRequireMinimal, nDefaultMaxNumSize);
bool rc3 = CastToBigNum(bn3, stacktop(stack, -1), fRequireMinimal, nDefaultMaxNumSize);
bool fValue = (mpz_cmp(bn2, bn1) <= 0 &&
mpz_cmp(bn1, bn3) < 0);
popstack(stack);
popstack(stack);
popstack(stack);
stack_push_str(stack, fValue ? bn_getvch(bn_One) : bn_getvch(bn_Zero));
mpz_clear(bn1);
mpz_clear(bn2);
mpz_clear(bn3);
if (!rc1 || !rc2 || !rc3)
goto out;
break;
}
//
// Crypto
//
case OP_RIPEMD160:
case OP_SHA1:
case OP_SHA256:
case OP_HASH160:
case OP_HASH256: {
// (in -- hash)
if (stack->len < 1)
goto out;
struct buffer *vch = stacktop(stack, -1);
unsigned int hashlen;
unsigned char md[32];
switch (opcode) {
case OP_RIPEMD160:
hashlen = 20;
ripemd160(vch->p, vch->len, md);
break;
case OP_SHA1:
hashlen = 20;
sha1_Raw(vch->p, vch->len, md);
break;
case OP_SHA256:
hashlen = 32;
sha256_Raw(vch->p, vch->len, md);
break;
case OP_HASH160:
hashlen = 20;
bu_Hash160(md, vch->p, vch->len);
break;
case OP_HASH256:
hashlen = 32;
bu_Hash(md, vch->p, vch->len);
break;
default:
// impossible
goto out;
}
popstack(stack);
struct buffer buf = { md, hashlen };
stack_push(stack, &buf);
break;
}
case OP_CODESEPARATOR:
// Hash starts after the code separator
memcpy(&pbegincodehash, &pc, sizeof(pc));
break;
case OP_CHECKSIG:
case OP_CHECKSIGVERIFY: {
// (sig pubkey -- bool)
if (stack->len < 2)
goto out;
struct buffer *vchSig = stacktop(stack, -2);
struct buffer *vchPubKey = stacktop(stack, -1);
// Subset of script starting at the most recent codeseparator
cstring *scriptCode = cstr_new_buf(pbegincodehash.p,
pbegincodehash.len);
// Drop the signature, since there's no way for
// a signature to sign itself
string_find_del(scriptCode, vchSig);
if (!CheckSignatureEncoding(vchSig, flags) || !CheckPubKeyEncoding(vchPubKey, flags)) {
cstr_free(scriptCode, true);
goto out;
}
bool fSuccess = bp_checksig(vchSig, vchPubKey,
scriptCode,
txTo, nIn);
cstr_free(scriptCode, true);
popstack(stack);
popstack(stack);
stack_push_str(stack, fSuccess ? bn_getvch(bn_One) : bn_getvch(bn_Zero));
if (opcode == OP_CHECKSIGVERIFY)
{
if (fSuccess)
popstack(stack);
else
goto out;
}
break;
}
case OP_CHECKMULTISIG:
case OP_CHECKMULTISIGVERIFY: {
// ([sig ...] num_of_signatures [pubkey ...] num_of_pubkeys -- bool)
int i = 1;
if ((int)stack->len < i)
goto out;
int nKeysCount = stackint(stack, -i, fRequireMinimal);
if (nKeysCount < 0 || nKeysCount > MAX_PUBKEYS_PER_MULTISIG)
goto out;
nOpCount += nKeysCount;
if (nOpCount > MAX_OPS_PER_SCRIPT)
goto out;
int ikey = ++i;
i += nKeysCount;
if ((int)stack->len < i)
goto out;
int nSigsCount = stackint(stack, -i, fRequireMinimal);
if (nSigsCount < 0 || nSigsCount > nKeysCount)
goto out;
int isig = ++i;
i += nSigsCount;
if ((int)stack->len < i)
goto out;
// Subset of script starting at the most recent codeseparator
cstring *scriptCode = cstr_new_buf(pbegincodehash.p,
pbegincodehash.len);
// Drop the signatures, since there's no way for
// a signature to sign itself
int k;
for (k = 0; k < nSigsCount; k++)
{
struct buffer *vchSig =stacktop(stack, -isig-k);
string_find_del(scriptCode, vchSig);
}
bool fSuccess = true;
while (fSuccess && nSigsCount > 0)
{
struct buffer *vchSig = stacktop(stack, -isig);
struct buffer *vchPubKey = stacktop(stack, -ikey);
// Note how this makes the exact order of pubkey/signature evaluation
// distinguishable by CHECKMULTISIG NOT if the STRICTENC flag is set.
// See the script_(in)valid tests for details.
if (!CheckSignatureEncoding(vchSig, flags) || !CheckPubKeyEncoding(vchPubKey, flags)) {
cstr_free(scriptCode, true);
goto out;
}
// Check signature
bool fOk = bp_checksig(vchSig, vchPubKey,
scriptCode, txTo, nIn);
if (fOk) {
isig++;
nSigsCount--;
}
ikey++;
nKeysCount--;
// If there are more signatures left than keys left,
// then too many signatures have failed
if (nSigsCount > nKeysCount)
fSuccess = false;
}
cstr_free(scriptCode, true);
// Clean up stack of actual arguments
while (i-- > 1)
popstack(stack);
// A bug causes CHECKMULTISIG to consume one extra argument
// whose contents were not checked in any way.
//
// Unfortunately this is a potential source of mutability,
// so optionally verify it is exactly equal to zero prior
// to removing it from the stack.
if ((int)stack->len < 1)
goto out;
if ((flags & SCRIPT_VERIFY_NULLDUMMY) && stacktop(stack, -1)->len)
goto out;
popstack(stack);
stack_push_str(stack, fSuccess ? bn_getvch(bn_One) : bn_getvch(bn_Zero));
if (opcode == OP_CHECKMULTISIGVERIFY)
{
if (fSuccess)
popstack(stack);
else
goto out;
}
break;
}
default:
goto out;
}
// Size limits
if (stack->len + altstack->len > 1000)
goto out;
}
rc = (vfExec->len == 0 && bp.error == false);
out:
mpz_clears(bn, bn_Zero, bn_One, NULL);
parr_free(altstack, true);
cstr_free(vfExec, true);
return rc;
}
int
main (int argc, char **argv)
{
gmp_randstate_ptr rands;
unsigned long maxnbits, maxdbits, nbits, dbits;
mpz_t n, d, tz;
mp_size_t maxnn, maxdn, nn, dn, clearn, i;
mp_ptr np, dp, qp, rp;
mp_limb_t rh;
mp_limb_t t;
mp_limb_t dinv;
int count = COUNT;
mp_ptr scratch;
mp_limb_t ran;
mp_size_t alloc, itch;
mp_limb_t rran0, rran1, qran0, qran1;
TMP_DECL;
if (argc > 1)
{
char *end;
count = strtol (argv[1], &end, 0);
if (*end || count <= 0)
{
fprintf (stderr, "Invalid test count: %s.\n", argv[1]);
return 1;
}
}
maxdbits = MAX_DN;
maxnbits = MAX_NN;
tests_start ();
rands = RANDS;
mpz_init (n);
mpz_init (d);
mpz_init (tz);
maxnn = maxnbits / GMP_NUMB_BITS + 1;
maxdn = maxdbits / GMP_NUMB_BITS + 1;
TMP_MARK;
qp = TMP_ALLOC_LIMBS (maxnn + 2) + 1;
rp = TMP_ALLOC_LIMBS (maxnn + 2) + 1;
alloc = 1;
scratch = __GMP_ALLOCATE_FUNC_LIMBS (alloc);
for (test = 0; test < count;)
{
nbits = random_word (rands) % (maxnbits - GMP_NUMB_BITS) + 2 * GMP_NUMB_BITS;
if (maxdbits > nbits)
dbits = random_word (rands) % nbits + 1;
else
dbits = random_word (rands) % maxdbits + 1;
#if RAND_UNIFORM
#define RANDFUNC mpz_urandomb
#else
#define RANDFUNC mpz_rrandomb
#endif
do
{
RANDFUNC (n, rands, nbits);
do
{
RANDFUNC (d, rands, dbits);
}
while (mpz_sgn (d) == 0);
np = PTR (n);
dp = PTR (d);
nn = SIZ (n);
dn = SIZ (d);
}
while (nn < dn);
dp[0] |= 1;
mpz_urandomb (tz, rands, 32);
t = mpz_get_ui (tz);
if (t % 17 == 0)
dp[0] = GMP_NUMB_MAX;
switch ((int) t % 16)
{
case 0:
clearn = random_word (rands) % nn;
for (i = 0; i <= clearn; i++)
np[i] = 0;
break;
case 1:
mpn_sub_1 (np + nn - dn, dp, dn, random_word (rands));
break;
case 2:
mpn_add_1 (np + nn - dn, dp, dn, random_word (rands));
break;
}
test++;
binvert_limb (dinv, dp[0]);
rran0 = random_word (rands);
rran1 = random_word (rands);
qran0 = random_word (rands);
qran1 = random_word (rands);
qp[-1] = qran0;
qp[nn - dn + 1] = qran1;
rp[-1] = rran0;
ran = random_word (rands);
if ((double) (nn - dn) * dn < 1e5)
{
if (nn > dn)
{
/* Test mpn_sbpi1_bdiv_qr */
MPN_ZERO (qp, nn - dn);
MPN_ZERO (rp, dn);
MPN_COPY (rp, np, nn);
rh = mpn_sbpi1_bdiv_qr (qp, rp, nn, dp, dn, -dinv);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0);
check_one (qp, rp + nn - dn, rh, np, nn, dp, dn, "mpn_sbpi1_bdiv_qr");
}
if (nn > dn)
{
/* Test mpn_sbpi1_bdiv_q */
MPN_COPY (rp, np, nn);
MPN_ZERO (qp, nn - dn);
mpn_sbpi1_bdiv_q (qp, rp, nn - dn, dp, MIN(dn,nn-dn), -dinv);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0);
check_one (qp, NULL, 0, np, nn, dp, dn, "mpn_sbpi1_bdiv_q");
}
}
if (dn >= 4 && nn - dn >= 2)
{
/* Test mpn_dcpi1_bdiv_qr */
MPN_COPY (rp, np, nn);
MPN_ZERO (qp, nn - dn);
rh = mpn_dcpi1_bdiv_qr (qp, rp, nn, dp, dn, -dinv);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0);
check_one (qp, rp + nn - dn, rh, np, nn, dp, dn, "mpn_dcpi1_bdiv_qr");
}
if (dn >= 4 && nn - dn >= 2)
{
/* Test mpn_dcpi1_bdiv_q */
MPN_COPY (rp, np, nn);
MPN_ZERO (qp, nn - dn);
mpn_dcpi1_bdiv_q (qp, rp, nn - dn, dp, MIN(dn,nn-dn), -dinv);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0);
check_one (qp, NULL, 0, np, nn, dp, dn, "mpn_dcpi1_bdiv_q");
}
if (nn > dn)
{
/* Test mpn_bdiv_qr */
itch = mpn_bdiv_qr_itch (nn, dn);
if (itch + 1 > alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
MPN_ZERO (qp, nn - dn);
MPN_ZERO (rp, dn);
rp[dn] = rran1;
rh = mpn_bdiv_qr (qp, rp, np, nn, dp, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0); ASSERT_ALWAYS (rp[dn] == rran1);
check_one (qp, rp, rh, np, nn, dp, dn, "mpn_bdiv_qr");
}
if (nn - dn < 2 || dn < 2)
continue;
/* Test mpn_mu_bdiv_qr */
itch = mpn_mu_bdiv_qr_itch (nn, dn);
if (itch + 1 > alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
MPN_ZERO (qp, nn - dn);
MPN_ZERO (rp, dn);
rp[dn] = rran1;
rh = mpn_mu_bdiv_qr (qp, rp, np, nn, dp, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0); ASSERT_ALWAYS (rp[dn] == rran1);
check_one (qp, rp, rh, np, nn, dp, dn, "mpn_mu_bdiv_qr");
/* Test mpn_mu_bdiv_q */
itch = mpn_mu_bdiv_q_itch (nn, dn);
if (itch + 1 > alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
MPN_ZERO (qp, nn - dn + 1);
mpn_mu_bdiv_q (qp, np, nn - dn, dp, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
check_one (qp, NULL, 0, np, nn, dp, dn, "mpn_mu_bdiv_q");
}
__GMP_FREE_FUNC_LIMBS (scratch, alloc);
TMP_FREE;
mpz_clear (n);
mpz_clear (d);
mpz_clear (tz);
tests_end ();
return 0;
}
int
main (int argc, char **argv)
{
mpz_t op1, op2;
mp_size_t size;
int i;
int reps = 10000;
FILE *fp;
int base, base_out;
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long bsi, size_range;
size_t nread;
tests_start ();
rands = RANDS;
mpz_init (bs);
if (argc == 2)
reps = atoi (argv[1]);
mpz_init (op1);
mpz_init (op2);
fp = fopen (FILENAME, "w+");
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 10 + 2;
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (op1, rands, size);
mpz_urandomb (bs, rands, 1);
bsi = mpz_get_ui (bs);
if ((bsi & 1) != 0)
mpz_neg (op1, op1);
mpz_urandomb (bs, rands, 16);
bsi = mpz_get_ui (bs);
base = bsi % 62 + 1;
if (base == 1)
base = 0;
if (i % 2 == 0 && base <= 36)
base_out = -base;
else
base_out = base;
rewind (fp);
if (mpz_out_str (fp, base_out, op1) == 0
|| putc (' ', fp) == EOF
|| fflush (fp) != 0)
{
printf ("mpz_out_str write error\n");
abort ();
}
rewind (fp);
nread = mpz_inp_str (op2, fp, base);
if (nread == 0)
{
if (ferror (fp))
printf ("mpz_inp_str stream read error\n");
else
printf ("mpz_inp_str data conversion error\n");
abort ();
}
if (nread != ftell(fp))
{
printf ("mpz_inp_str nread doesn't match ftell\n");
printf (" nread %lu\n", (unsigned long) nread);
printf (" ftell %ld\n", ftell(fp));
abort ();
}
if (mpz_cmp (op1, op2))
{
printf ("ERROR\n");
printf ("op1 = "); debug_mp (op1, -16);
printf ("op2 = "); debug_mp (op2, -16);
printf ("base = %d\n", base);
abort ();
}
}
fclose (fp);
unlink (FILENAME);
mpz_clear (bs);
mpz_clear (op1);
mpz_clear (op2);
tests_end ();
exit (0);
}
static unsigned long get_int(void *a)
{
LTC_ARGCHK(a != NULL);
return mpz_get_ui(a);
}
u32_t*
mpz_trialdiv(mpz_t N,u32_t*pbuf,u32_t ncp,char*errmsg)
{
u32_t np,np1,i,e2,nlimb;
if(mpz_sgn(N)<=0){
if(mpz_sgn(N)==0)return pbuf;
mpz_neg(N,N);
}
if(mibuf_alloc<ncp){
if(mibuf_alloc> 0)free(mibuf);
mibuf_alloc= ncp;
mibuf= xmalloc(mibuf_alloc*sizeof(*mibuf));
}
e2= 0;
while((mpz_get_ui(N)%2)==0){
mpz_fdiv_q_2exp(N,N,1);
e2++;
}
nlimb= N[0]._mp_size;
if(lbuf_alloc<nlimb){
if(lbuf_alloc> 0)free(lbuf);
lbuf_alloc= nlimb;
lbuf= xmalloc(lbuf_alloc*sizeof(*lbuf));
}
memcpy(lbuf,N[0]._mp_d,nlimb*sizeof(*lbuf));
np= 0;
for(i= 0;i<ncp;i++){
mp_limb_t x,p,r;
p= pbuf[i];
x= mpqs_256_inv_table[(p&255)/2];
x= 2*x-p*x*x;
x= 2*x-p*x*x;
x= 2*x-p*x*x;
r= mpz_asm_td(p,x,lbuf,nlimb);
if(r!=0){
if(errmsg!=NULL)
Schlendrian("%s : %u does not divide\n",errmsg,pbuf[i]);
memcpy(lbuf,N[0]._mp_d,nlimb*sizeof(*lbuf));
continue;
}
while(lbuf[nlimb-1]==0)nlimb--;
if(errmsg==NULL)memcpy(N[0]._mp_d,lbuf,nlimb*sizeof(*lbuf));
mibuf[np]= x;
pbuf[np++]= p;
}
np1= np;
if(errmsg!=NULL)memcpy(N[0]._mp_d,lbuf,nlimb*sizeof(*lbuf));
for(i= 0;i<np1;i++){
mp_limb_t x,p,r;
p= pbuf[i];
x= mibuf[i];
for(;;){
r= mpz_asm_td(p,x,lbuf,nlimb);
if(r!=0){
memcpy(lbuf,N[0]._mp_d,nlimb*sizeof(*lbuf));
break;
}
while(lbuf[nlimb-1]==0)nlimb--;
memcpy(N[0]._mp_d,lbuf,nlimb*sizeof(*lbuf));
pbuf[np++]= p;
}
}
N[0]._mp_size= nlimb;
for(i= 0;i<e2;i++)
pbuf[np++]= 2;
return pbuf+np;
}/*:1*/
/* Find primes in region [fr,fr+rsize). Requires that fr is odd and that
rsize is even. The sieving array s should be aligned for "long int" and
have rsize/2 entries, rounded up to the nearest multiple of "long int". */
void
sieve_region (unsigned char *s, mpz_t fr, unsigned long rsize)
{
unsigned long ssize = rsize / 2;
unsigned long start, start2, prime;
unsigned long i;
mpz_t tmp;
mpz_init (tmp);
#if 0
/* initialize sieving array */
for (ii = 0; ii < (ssize + sizeof (long) - 1) / sizeof (long); ii++)
((long *) s) [ii] = ~0L;
#else
{
signed long k;
long *se = (long *) (s + ((ssize + sizeof (long) - 1) & -sizeof (long)));
for (k = -((ssize + sizeof (long) - 1) / sizeof (long)); k < 0; k++)
se[k] = ~0L;
}
#endif
for (i = 0; i < n_primes; i++)
{
prime = primes[i].prime;
if (primes[i].rem >= 0)
{
start2 = primes[i].rem;
}
else
{
mpz_set_ui (tmp, prime);
mpz_mul_ui (tmp, tmp, prime);
if (mpz_cmp (fr, tmp) <= 0)
{
mpz_sub (tmp, tmp, fr);
if (mpz_cmp_ui (tmp, 2 * ssize) > 0)
break; /* avoid overflow at next line, also speedup */
start = mpz_get_ui (tmp);
}
else
{
start = (prime - mpz_tdiv_ui (fr, prime)) % prime;
if (start % 2 != 0)
start += prime; /* adjust if even divisable */
}
start2 = start / 2;
}
#if 0
for (ii = start2; ii < ssize; ii += prime)
s[ii] = 0;
primes[i].rem = ii - ssize;
#else
{
signed long k;
unsigned char *se = s + ssize; /* point just beyond sieving range */
for (k = start2 - ssize; k < 0; k += prime)
se[k] = 0;
primes[i].rem = k;
}
#endif
}
mpz_clear (tmp);
}
int ecpp_test(unsigned long n)
{
mpz_t a, b,
x0, y0,
xt, yt,
tmp;
int z;
int is_prime = 0;
if (n <= USHRT_MAX)
{
return sieve_test(n);
}
mpz_init(a);
mpz_init(b);
mpz_init(x0);
mpz_init(y0);
mpz_init(xt);
mpz_init(yt);
mpz_init(tmp);
#ifdef DEBUG
gmp_fprintf(stderr, "\nTesting %d with ECPP...\n", n);
#endif /* DEBUG */
for (;;) /* keep trying while the curve order factoring fails */
{
for (;;) /* keep trying while n divides curve discriminant */
{
/* initialise a random point P = (x0, y0)
* and a random elliptic curve E(a, b): y^2 = x^3 + a*x + b
* with b expressed in terms of (a, x0, y0) so the point lies on the curve
*/
mpz_set_ui(a, rand() % n);
mpz_set_ui(x0, rand() % n);
mpz_set_ui(y0, rand() % n);
mpz_init(b);
mpz_mul(b, y0, y0);
mpz_mul(tmp, x0, x0);
mpz_submul(b, tmp, x0);
mpz_submul(b, a, x0);
mpz_mod_ui(b, b, n);
#ifdef DEBUG
gmp_fprintf(stderr, "\n\tn = %d\n", n);
gmp_fprintf(stderr, "\tE: y^2 = x^3 + %Zd * x + %Zd\n", a, b);
gmp_fprintf(stderr, "\tP = (%Zd,%Zd,1)\n", x0, y0);
#endif /* DEBUG */
/* the discriminant of the curve and n are required to be coprimes
* -- if not, then either
* A) n divides the discriminant -- a new curve must be generated
* B) n is composite and a proper factor is found -- the algorithm can
* terminate
*/
ec_discriminant(tmp, a, b);
#ifdef DEBUG
mpz_mod_ui(tmp, tmp, n);
gmp_fprintf(stderr, "\tdelta(E/GF(n)) = %Zd\n", tmp);
#endif /* DEBUG */
mpz_gcd_ui(tmp, tmp, n);
#ifdef DEBUG
gmp_fprintf(stderr, "\tgcd(delta, n) = %Zd\n", tmp);
#endif /* DEBUG */
if (0 == mpz_cmp_ui(tmp, 1))
{
break;
}
else if (0 != mpz_cmp_ui(tmp, n))
{
#ifdef DEBUG
gmp_fprintf(stderr, "\tfound a proper factor, %d is composite\n", n);
#endif /* DEBUG */
is_prime = 0;
goto cleanup_and_return;
}
}
/* P + P != 0, or a new curve is generated
*/
z = ec_add(xt, yt, x0, y0, 1, x0, y0, 1, n, a);
#ifdef DEBUG
gmp_fprintf(stderr, "\t2 * P = (%Zd,%Zd,%d)\n", xt, yt, z);
#endif /* DEBUG */
if (0 == z)
{
continue;
}
/* the curve order algorithm failing indicates n is composite
*/
if (!(ec_order(tmp, a, b, n)))
{
#ifdef DEBUG
gmp_fprintf(stderr,
"\tcurve order algorithm failed, %d must be composite\n", n);
#endif /* DEBUG */
is_prime = 0;
break;
}
#ifdef DEBUG
gmp_fprintf(stderr, "\t|E/GF(n)| = %Zd\n", tmp);
#endif /* DEBUG */
/* the curve order should be the multiple of 2 and a "probable prime" n --
* if the order is not even, a new curve is generated
*/
if (!mpz_even_p(tmp))
{
#ifdef DEBUG
gmp_fprintf(stderr, "\t|E/GF(n)| is odd, generating new curve...\n");
#endif /* DEBUG */
continue;
}
/* order * P = 0, or n is composite
*/
z = ec_times(xt, yt, x0, y0, 1, tmp, n, a);
#ifdef DEBUG
gmp_fprintf(stderr, "\t|E| * P = (%Zd,%Zd,%d)\n", xt, yt, z);
#endif /* DEBUG */
if (0 != z)
{
#ifdef DEBUG
gmp_fprintf(stderr, "\t|E| * P is non-zero, %d is composite\n", n);
#endif /* DEBUG */
is_prime = 0;
break;
}
/* at this point, order/2 being a prime implies n is a prime --
* a recursive call to ecpp_test is used to test order/2 for primality
*/
mpz_div_ui(tmp, tmp, 2);
if (ecpp_test(mpz_get_ui(tmp)))
{
is_prime = 1;
break;
}
}
cleanup_and_return:
mpz_clear(a);
mpz_clear(b);
mpz_clear(x0);
mpz_clear(y0);
mpz_clear(xt);
mpz_clear(yt);
mpz_clear(tmp);
return is_prime;
}
void
one_test (mpz_t op1, mpz_t op2, mpz_t ref, int i)
{
/*
printf ("%ld %ld %ld\n", SIZ (op1), SIZ (op2), SIZ (ref));
fflush (stdout);
*/
/*
fprintf (stderr, "op1="); debug_mp (op1, -16);
fprintf (stderr, "op2="); debug_mp (op2, -16);
*/
mpz_gcdext (gcd1, s, NULL, op1, op2);
if (ref && mpz_cmp (ref, gcd1) != 0)
{
fprintf (stderr, "ERROR in test %d\n", i);
fprintf (stderr, "mpz_gcdext returned incorrect result\n");
fprintf (stderr, "op1="); debug_mp (op1, -16);
fprintf (stderr, "op2="); debug_mp (op2, -16);
fprintf (stderr, "expected result:\n"); debug_mp (ref, -16);
fprintf (stderr, "mpz_gcdext returns:\n");debug_mp (gcd1, -16);
abort ();
}
if (!gcdext_valid_p(op1, op2, gcd1, s))
{
fprintf (stderr, "ERROR in test %d\n", i);
fprintf (stderr, "mpz_gcdext returned invalid result\n");
fprintf (stderr, "op1="); debug_mp (op1, -16);
fprintf (stderr, "op2="); debug_mp (op2, -16);
fprintf (stderr, "mpz_gcdext returns:\n");debug_mp (gcd1, -16);
abort ();
}
mpz_gcd (gcd2, op1, op2);
if (mpz_cmp (gcd2, gcd1) != 0)
{
fprintf (stderr, "ERROR in test %d\n", i);
fprintf (stderr, "mpz_gcd returned incorrect result\n");
fprintf (stderr, "op1="); debug_mp (op1, -16);
fprintf (stderr, "op2="); debug_mp (op2, -16);
fprintf (stderr, "expected result:\n"); debug_mp (gcd1, -16);
fprintf (stderr, "mpz_gcd returns:\n"); debug_mp (gcd2, -16);
abort ();
}
/* This should probably move to t-gcd_ui.c */
if (mpz_fits_ulong_p (op1) || mpz_fits_ulong_p (op2))
{
if (mpz_fits_ulong_p (op1))
mpz_gcd_ui (gcd2, op2, mpz_get_ui (op1));
else
mpz_gcd_ui (gcd2, op1, mpz_get_ui (op2));
if (mpz_cmp (gcd2, gcd1))
{
fprintf (stderr, "ERROR in test %d\n", i);
fprintf (stderr, "mpz_gcd_ui returned incorrect result\n");
fprintf (stderr, "op1="); debug_mp (op1, -16);
fprintf (stderr, "op2="); debug_mp (op2, -16);
fprintf (stderr, "expected result:\n"); debug_mp (gcd1, -16);
fprintf (stderr, "mpz_gcd_ui returns:\n"); debug_mp (gcd2, -16);
abort ();
}
}
mpz_gcdext (gcd2, temp1, temp2, op1, op2);
mpz_mul (temp1, temp1, op1);
mpz_mul (temp2, temp2, op2);
mpz_add (temp1, temp1, temp2);
if (mpz_cmp (gcd1, gcd2) != 0
|| mpz_cmp (gcd2, temp1) != 0)
{
fprintf (stderr, "ERROR in test %d\n", i);
fprintf (stderr, "mpz_gcdext returned incorrect result\n");
fprintf (stderr, "op1="); debug_mp (op1, -16);
fprintf (stderr, "op2="); debug_mp (op2, -16);
fprintf (stderr, "expected result:\n"); debug_mp (gcd1, -16);
fprintf (stderr, "mpz_gcdext returns:\n");debug_mp (gcd2, -16);
abort ();
}
}
