Error, error, unsupported BITS_PER_MP_LIMB
#endif
int
mpz_kronecker_ui (mpz_srcptr a, unsigned long b)
{
mp_srcptr a_ptr = PTR(a);
mp_size_t a_size;
mp_limb_t a_rem;
int result_bit1;
a_size = SIZ(a);
if (a_size == 0)
return JACOBI_0U (b);
if (b > GMP_NUMB_MAX)
{
mp_limb_t blimbs[2];
mpz_t bz;
ALLOC(bz) = numberof (blimbs);
PTR(bz) = blimbs;
mpz_set_ui (bz, b);
return mpz_kronecker (a, bz);
}
if ((b & 1) != 0)
{
result_bit1 = JACOBI_ASGN_SU_BIT1 (a_size, b);
}
else
{
mp_limb_t a_low = a_ptr[0];
int twos;
if (b == 0)
return JACOBI_LS0 (a_low, a_size); /* (a/0) */
if (! (a_low & 1))
return 0; /* (even/even)=0 */
/* (a/2)=(2/a) for a odd */
count_trailing_zeros (twos, b);
b >>= twos;
result_bit1 = (JACOBI_TWOS_U_BIT1 (twos, a_low)
^ JACOBI_ASGN_SU_BIT1 (a_size, b));
}
if (b == 1)
return JACOBI_BIT1_TO_PN (result_bit1); /* (a/1)=1 for any a */
a_size = ABS(a_size);
/* (a/b) = (a mod b / b) */
JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size, b);
return mpn_jacobi_base (a_rem, (mp_limb_t) b, result_bit1);
}
int
mpz_si_kronecker (long a, mpz_srcptr b)
{
mp_srcptr b_ptr;
mp_limb_t b_low;
mp_size_t b_size;
mp_size_t b_abs_size;
mp_limb_t a_limb, b_rem;
unsigned twos;
int result_bit1;
#if GMP_NUMB_BITS < BITS_PER_ULONG
if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX)
{
mp_limb_t alimbs[2];
mpz_t az;
ALLOC(az) = numberof (alimbs);
PTR(az) = alimbs;
mpz_set_si (az, a);
return mpz_kronecker (az, b);
}
#endif
b_size = SIZ (b);
if (b_size == 0)
return JACOBI_S0 (a); /* (a/0) */
/* account for the effect of the sign of b, then ignore it */
result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size);
b_ptr = PTR(b);
b_low = b_ptr[0];
b_abs_size = ABS (b_size);
if ((b_low & 1) != 0)
{
/* b odd */
result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
a_limb = (unsigned long) ABS(a);
if ((a_limb & 1) == 0)
{
/* (0/b)=1 for b=+/-1, 0 otherwise */
if (a_limb == 0)
return (b_abs_size == 1 && b_low == 1);
/* a even, b odd */
count_trailing_zeros (twos, a_limb);
a_limb >>= twos;
/* (a*2^n/b) = (a/b) * twos(n,a) */
result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
}
}
int
mpz_kronecker_si (mpz_srcptr a, long b)
{
mp_srcptr a_ptr;
mp_size_t a_size;
mp_limb_t a_rem, b_limb;
int result_bit1;
a_size = SIZ(a);
if (a_size == 0)
return JACOBI_0S (b);
#if GMP_NUMB_BITS < BITS_PER_ULONG
if (b > GMP_NUMB_MAX || b < -GMP_NUMB_MAX)
{
mp_limb_t blimbs[2];
mpz_t bz;
ALLOC(bz) = numberof (blimbs);
PTR(bz) = blimbs;
mpz_set_si (bz, b);
return mpz_kronecker (a, bz);
}
#endif
result_bit1 = JACOBI_BSGN_SS_BIT1 (a_size, b);
b_limb = (unsigned long) ABS (b);
a_ptr = PTR(a);
if ((b_limb & 1) == 0)
{
mp_limb_t a_low = a_ptr[0];
int twos;
if (b_limb == 0)
return JACOBI_LS0 (a_low, a_size); /* (a/0) */
if (! (a_low & 1))
return 0; /* (even/even)=0 */
/* (a/2)=(2/a) for a odd */
count_trailing_zeros (twos, b_limb);
b_limb >>= twos;
result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, a_low);
}
int checkpoly_siqs(siqs_poly *poly, mpz_t n)
{
//check that b^2 == N mod a
//and that c == (b*b - n)/a
mpz_t t1,t2,t3,t4;
mpz_init(t1);
mpz_init(t2);
mpz_init(t3);
mpz_init(t4);
mpz_set(t1, n);
mpz_tdiv_r(t3, t1, poly->mpz_poly_a); //zDiv(&t1,&poly->poly_a,&t2,&t3);
mpz_mul(t2, poly->mpz_poly_b, poly->mpz_poly_b); //zMul(&poly->poly_b,&poly->poly_b,&t2);
mpz_tdiv_r(t4, t2, poly->mpz_poly_a); //zDiv(&t2,&poly->poly_a,&t1,&t4);
if (mpz_cmp(t3,t4) != 0)
{
printf("\nError in checkpoly: %s^2 !== N mod %s\n",
mpz_conv2str(&gstr1.s, 10, poly->mpz_poly_b),
mpz_conv2str(&gstr2.s, 10, poly->mpz_poly_a));
if (mpz_sgn(poly->mpz_poly_b) < 0)
printf("b is negative\n");
}
if (mpz_kronecker(n, poly->mpz_poly_a) != 1)
printf("\nError in checkpoly: (a|N) != 1\n");
mpz_mul(t2, poly->mpz_poly_b, poly->mpz_poly_b); //zMul(&poly->poly_b,&poly->poly_b,&t2);
mpz_sub(t2, t2, n);
mpz_tdiv_q(t4, t2, poly->mpz_poly_a); //zDiv(&t2,&poly->poly_a,&t1,&t4);
if (mpz_cmp(t4,poly->mpz_poly_c) != 0)
printf("\nError in checkpoly: c != (b^2 - n)/a\n");
mpz_clear(t1);
mpz_clear(t2);
mpz_clear(t3);
mpz_clear(t4);
return 0;
}
static PyObject *
GMPy_MPZ_Function_Kronecker(PyObject *self, PyObject *args)
{
MPZ_Object *tempx = NULL, *tempy = NULL;
long res;
if (PyTuple_GET_SIZE(args) != 2) {
TYPE_ERROR("kronecker() requires 'mpz','mpz' arguments");
return NULL;
}
if (!(tempx = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 0), NULL)) ||
!(tempy = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 1), NULL))) {
Py_XDECREF((PyObject*)tempx);
Py_XDECREF((PyObject*)tempy);
return NULL;
}
res = (long)(mpz_kronecker(tempx->z, tempy->z));
Py_DECREF((PyObject*)tempx);
Py_DECREF((PyObject*)tempy);
return PyIntOrLong_FromLong(res);
}
int
mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
{
mp_srcptr b_ptr;
mp_limb_t b_low;
int b_abs_size;
mp_limb_t b_rem;
int twos;
int result_bit1;
/* (a/-1)=1 when a>=0, so the sign of b is ignored */
b_abs_size = ABSIZ (b);
if (b_abs_size == 0)
return JACOBI_U0 (a); /* (a/0) */
if (a > GMP_NUMB_MAX)
{
mp_limb_t alimbs[2];
mpz_t az;
ALLOC(az) = numberof (alimbs);
PTR(az) = alimbs;
mpz_set_ui (az, a);
return mpz_kronecker (az, b);
}
b_ptr = PTR(b);
b_low = b_ptr[0];
result_bit1 = 0;
if (! (b_low & 1))
{
/* (0/b)=0 for b!=+/-1; and (even/even)=0 */
if (! (a & 1))
return 0;
/* a odd, b even
Establish shifted b_low with valid bit1 for the RECIP below. Zero
limbs stripped are accounted for, but zero bits on b_low are not
because they remain in {b_ptr,b_abs_size} for
JACOBI_MOD_OR_MODEXACT_1_ODD. */
JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
if (! (b_low & 1))
{
if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
{
/* need b_ptr[1] to get bit1 in b_low */
if (b_abs_size == 1)
{
/* (a/0x80...00) == (a/2)^(NUMB-1) */
if ((GMP_NUMB_BITS % 2) == 0)
{
/* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
when GMP_NUMB_BITS is even, so it's still 0. */
ASSERT (result_bit1 == 0);
result_bit1 = JACOBI_TWO_U_BIT1 (a);
}
return JACOBI_BIT1_TO_PN (result_bit1);
}
/* b_abs_size > 1 */
b_low = b_ptr[1] << 1;
}
else
{
count_trailing_zeros (twos, b_low);
b_low >>= twos;
}
}
}
else
{
if (a == 0) /* (0/b)=1 for b=+/-1, 0 otherwise */
/* See Cohen section 1.5.
* See http://www.math.vt.edu/people/brown/doc/sqrts.pdf
*/
int sqrtmod(mpz_t x, mpz_t a, mpz_t p,
mpz_t t, mpz_t q, mpz_t b, mpz_t z) /* 4 temp variables */
{
int r, e, m;
/* Easy cases from page 31 (or Menezes 3.36, 3.37) */
if (mpz_congruent_ui_p(p, 3, 4)) {
mpz_add_ui(t, p, 1);
mpz_tdiv_q_2exp(t, t, 2);
mpz_powm(x, a, t, p);
return verify_sqrt(x, a, p, t, q);
}
if (mpz_congruent_ui_p(p, 5, 8)) {
mpz_sub_ui(t, p, 1);
mpz_tdiv_q_2exp(t, t, 2);
mpz_powm(q, a, t, p);
if (mpz_cmp_si(q, 1) == 0) { /* s = a^((p+3)/8) mod p */
mpz_add_ui(t, p, 3);
mpz_tdiv_q_2exp(t, t, 3);
mpz_powm(x, a, t, p);
} else { /* s = 2a * (4a)^((p-5)/8) mod p */
mpz_sub_ui(t, p, 5);
mpz_tdiv_q_2exp(t, t, 3);
mpz_mul_ui(q, a, 4);
mpz_powm(x, q, t, p);
mpz_mul_ui(x, x, 2);
mpz_mulmod(x, x, a, p, x);
}
return verify_sqrt(x, a, p, t, q);
}
if (mpz_kronecker(a, p) != 1) {
/* Possible no solution exists. Check Euler criterion. */
mpz_sub_ui(t, p, 1);
mpz_tdiv_q_2exp(t, t, 1);
mpz_powm(x, a, t, p);
if (mpz_cmp_si(x, 1) != 0) {
mpz_set_ui(x, 0);
return 0;
}
}
mpz_sub_ui(q, p, 1);
e = mpz_scan1(q, 0); /* Remove 2^e from q */
mpz_tdiv_q_2exp(q, q, e);
mpz_set_ui(t, 2);
while (mpz_legendre(t, p) != -1) /* choose t "at random" */
mpz_add_ui(t, t, 1);
mpz_powm(z, t, q, p); /* Step 1 complete */
r = e;
mpz_powm(b, a, q, p);
mpz_add_ui(q, q, 1);
mpz_divexact_ui(q, q, 2);
mpz_powm(x, a, q, p); /* Done with q, will use it for y now */
while (mpz_cmp_ui(b, 1)) {
/* calculate how many times b^2 mod p == 1 */
mpz_set(t, b);
m = 0;
do {
mpz_powm_ui(t, t, 2, p);
m++;
} while (m < r && mpz_cmp_ui(t, 1));
if (m >= r) break;
mpz_ui_pow_ui(t, 2, r-m-1);
mpz_powm(t, z, t, p);
mpz_mulmod(x, x, t, p, x);
mpz_powm_ui(z, t, 2, p);
mpz_mulmod(b, b, z, p, b);
r = m;
}
return verify_sqrt(x, a, p, t, q);
}
