int test_bernoulli_mod_p(unsigned long p)
{
unsigned long *res = (unsigned long*) flint_stack_alloc((p-1)/2);
if(!bernoulli_mod_p_mpz(res, p))
{
printf("Could not factor p = %d\n", p);
flint_stack_release();
return FALSE;
}
int result = verify_bernoulli_mod_p(res, p);
flint_stack_release();
return result;
}
void fmpz_tdiv(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp;
if (sizeb == 0)
{
printf("Error: division by zero!\n");
abort();
} else if (sizea < sizeb) // Todo: make this deal with sizea == sizeb but a < b
{
res[0] = 0;
} else
{
temp = (fmpz_t) flint_stack_alloc(sizeb);
mpn_tdiv_qr(res+1, temp, 0, a+1, sizea, b+1, sizeb);
res[0] = sizea - sizeb + 1;
if ((long) (a0 ^ b0) < 0) res[0] = -res[0];
flint_stack_release();
}
NORM(res);
}
// truncated multiplication for fmpz
void fmpz_mul_trunc(fmpz_t res, fmpz_t a, fmpz_t b, unsigned long trunc)
{
unsigned long sizea = FLINT_MIN(fmpz_size(a), trunc);
unsigned long sizeb = FLINT_MIN(fmpz_size(b), trunc);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
if ((sizea == 0) || (sizeb == 0)) {
res[0] = 0;
return;
}
if (trunc >= sizea + sizeb) {
mp_limb_t mslimb;
if (sizea >= sizeb) mslimb = F_mpn_mul(res+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(res+1, b+1, sizeb, a+1, sizea);
res[0] = sizea + sizeb - (mslimb == 0);
} else {
mp_limb_t mslimb;
fmpz_t temp = flint_stack_alloc(sizea + sizeb + 1);
if (sizea >= sizeb) mslimb = F_mpn_mul_trunc(temp+1, a+1, sizea, b+1, sizeb, trunc);
else mslimb = F_mpn_mul_trunc(temp+1, b+1, sizeb, a+1, sizea, trunc);
temp[0] = trunc;
if (UNLIKELY(!mslimb))
__fmpz_normalise(temp); // normalise if most significant limb == 0
fmpz_set(res, temp);
flint_stack_release();
}
if ((long) (a[0] ^ b[0]) < 0L) res[0] = -res[0];
}
void fmpz_addmul(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
fmpz_t temp;
mp_limb_t mslimb;
if (sizea && sizeb)
{
if (sizea + sizeb < 100)
{
temp = (fmpz_t) flint_stack_alloc_small(sizea + sizeb + 1);
if (sizea >= sizeb) mslimb = mpn_mul(temp+1, a+1, sizea, b+1, sizeb);
else mslimb = mpn_mul(temp+1, b+1, sizeb, a+1, sizea);
temp[0] = sizea + sizeb - (mslimb == 0);
if ((long) (a[0] ^ b[0]) < 0) temp[0] = -temp[0];
fmpz_add(res, res, temp);
flint_stack_release_small();
} else
{
temp = (fmpz_t) flint_stack_alloc(sizea + sizeb + 1);
if (sizea >= sizeb) mslimb = F_mpn_mul(temp+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(temp+1, b+1, sizeb, a+1, sizea);
temp[0] = sizea + sizeb - (mslimb == 0);
if ((long) (a[0] ^ b[0]) < 0) temp[0] = -temp[0];
fmpz_add(res, res, temp);
flint_stack_release();
}
}
}
void tiny_poly_clear(poly_t * poly_inf)
{
mpz_clear(poly_inf->C);
flint_stack_release(); // release all A_inv2B[i]
flint_stack_release(); // release soln1
flint_stack_release(); // release soln2
flint_stack_release(); // release A_inv
flint_stack_release(); // release inv_p2
flint_stack_release(); // release A_inv2B
flint_stack_release(); // release A_modp
flint_stack_release(); // release A_ind
flint_stack_release(); // release B_terms
}
void fmpz_mul(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp;
if ((sizea == 0) || (sizeb == 0))
{
res[0] = 0;
} else if (sizea + sizeb < 100)
{
temp = (fmpz_t) flint_stack_alloc_small(sizea + sizeb + 1);
if (sizea > sizeb) mslimb = mpn_mul(temp+1, a+1, sizea, b+1, sizeb);
else if (sizea == sizeb)
{
mpn_mul_n(temp+1, a+1, b+1, sizeb);
mslimb = temp[2*sizeb];
}
else mslimb = mpn_mul(temp+1, b+1, sizeb, a+1, sizea);
temp[0] = sizea + sizeb - (mslimb == 0);
F_mpn_copy(res, temp, temp[0]+1);
if ((long) (a0 ^ b0) < 0) res[0] = -res[0];
flint_stack_release_small();
} else if (sizea + sizeb < 2*FLINT_FFT_LIMBS_CROSSOVER)
{
temp = (fmpz_t) flint_stack_alloc(sizea + sizeb + 1);
if (sizea > sizeb) mslimb = mpn_mul(temp+1, a+1, sizea, b+1, sizeb);
else if (sizea == sizeb)
{
mpn_mul_n(temp+1, a+1, b+1, sizeb);
mslimb = temp[2*sizeb];
}
else mslimb = mpn_mul(temp+1, b+1, sizeb, a+1, sizea);
temp[0] = sizea + sizeb - (mslimb == 0);
F_mpn_copy(res, temp, temp[0]+1);
if ((long) (a0 ^ b0) < 0) res[0] = -res[0];
flint_stack_release();
} else
{
if (sizea >= sizeb) mslimb = F_mpn_mul(res+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(res+1, b+1, sizeb, a+1, sizea);
res[0] = sizea+sizeb - (mslimb == 0);
if ((long) (a0 ^ b0) < 0) res[0] = -res[0];
}
}
void fmpz_fdiv(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp;
if (sizeb == 0)
{
printf("Error: division by zero!\n");
abort();
} else if (sizea < sizeb) // Todo: make this deal with sizea == sizeb but a < b
{
if (((long) (a0 ^ b0) < 0L) && (a0))
{
res[0] = -1L;
res[1] = 1;
} else res[0] = 0;
return;
} else
{
temp = (fmpz_t) flint_stack_alloc(sizeb);
mpn_tdiv_qr(res+1, temp, 0, a+1, sizea, b+1, sizeb);
res[0] = sizea - sizeb + 1;
if ((long) (a0 ^ b0) < 0L) res[0] = -res[0];
NORM(res);
if ((long) (a0 ^ b0) < 0L)
{
unsigned long i = 0;
for (; i < sizeb; i++)
{
if (temp[i]) break;
}
if (i < sizeb)
{
fmpz_sub_ui_inplace(res, 1UL);
}
}
flint_stack_release();
}
}
void fmpz_gcd(fmpz_t output, fmpz_t x1, fmpz_t x2)
{
ulong size1 = FLINT_ABS(x1[0]);
ulong size2 = FLINT_ABS(x2[0]);
mpz_t m1, m2, m0, m_out;
m1->_mp_d = x1 + 1;
m2->_mp_d = x2 + 1;
m1->_mp_alloc = size1;
m1->_mp_size = size1;
m2->_mp_alloc = size2;
m2->_mp_size = size2;
ulong size_out = FLINT_MAX(size1, size2)+1;
m0->_mp_d = flint_stack_alloc(size_out);
m0->_mp_alloc = size_out;
m0->_mp_size = 0;
mpz_gcd(m0, m1, m2);
size_out = m0->_mp_size;
F_mpn_copy(output + 1, m0->_mp_d, size_out);
output[0] = size_out;
flint_stack_release();
}
void compute_B_terms(QS_t * qs_inf, poly_t * poly_inf)
{
unsigned long s = poly_inf->s;
unsigned long * A_ind = poly_inf->A_ind;
unsigned long * A_modp = poly_inf->A_modp;
unsigned long * B_terms = poly_inf->B_terms;
prime_t * factor_base = qs_inf->factor_base;
unsigned long limbs = qs_inf->prec+1;
unsigned long limbs2;
unsigned long * A = poly_inf->A;
unsigned long * B = poly_inf->B;
unsigned long p, i;
unsigned long * temp1 = (unsigned long *) flint_stack_alloc(limbs);
unsigned long temp;
mp_limb_t msl;
double pinv;
for (i = 0; i < s; i++)
{
p = factor_base[A_ind[i]].p;
pinv = z_precompute_inverse(p);
mpn_divmod_1(temp1 + 1, A + 1, A[0], p);
temp1[0] = A[0] - (temp1[A[0]] == 0);
A_modp[i] = (temp = mpn_mod_1(temp1 + 1, temp1[0], p));
temp = z_invert(temp, p);
temp = z_mulmod_precomp(temp, qs_inf->sqrts[A_ind[i]], p, pinv);
if (temp > p/2) temp = p - temp;
msl = mpn_mul_1(B_terms + i*limbs + 1, temp1 + 1, temp1[0], temp);
if (msl)
{
B_terms[i*limbs + temp1[0] + 1] = msl;
B_terms[i*limbs] = temp1[0] + 1;
}
else B_terms[i*limbs] = temp1[0];
#if B_TERMS
mpz_t temp;
mpz_init(temp);
fmpz_to_mpz(temp, B_terms + i*limbs);
gmp_printf("B_%ld = %Zd\n", i, temp);
mpz_clear(temp);
#endif
}
F_mpn_copy(B, B_terms, B_terms[0]+1); // Set B to the sum of the B terms
if (limbs > B_terms[0] + 1) F_mpn_clear(B + B_terms[0] + 1, limbs - B_terms[0] - 1);
for (i = 1; i < s; i++)
{
limbs2 = B_terms[i*limbs];
msl = mpn_add_n(B+1, B+1, B_terms + i*limbs + 1, limbs2);
if (msl) mpn_add_1(B + limbs2 + 1, B + limbs2 + 1, limbs - limbs2 - 1, msl);
}
B[0] = limbs - 1;
while (!B[B[0]] && B[0]) B[0]--;
#if B_TERMS
mpz_t temp2;
mpz_init(temp2);
fmpz_to_mpz(temp2, B);
gmp_printf("B = %Zd\n", temp2);
mpz_clear(temp2);
#endif
flint_stack_release(); // release temp1
}
void compute_A(QS_t * qs_inf, poly_t * poly_inf)
{
unsigned long min = poly_inf->min;
unsigned long span = poly_inf->span;
unsigned long s = poly_inf->s;
unsigned long * A_ind = poly_inf->A_ind;
unsigned long * A = poly_inf->A;
unsigned long * target_A = poly_inf->target_A;
unsigned long * current_A = (unsigned long *) flint_stack_alloc(qs_inf->prec+1);
unsigned long * diff = (unsigned long *) flint_stack_alloc(qs_inf->prec+1);
unsigned long * best_diff = (unsigned long *) flint_stack_alloc(qs_inf->prec+1);
prime_t * factor_base = qs_inf->factor_base;
unsigned long factor, p;
unsigned long best1, best2, best3;
unsigned long odds = s - 3;
mp_limb_t msl;
int taken;
long i, j, k;
A[0] = 1;
A[1] = 1;
for (i = 0; i < odds; i++) // Randomly choose the first s-3 prime factors of A with odd indices
{
do
{
taken = 0;
A_ind[i] = ((z_randint(span) + min) | 1);
if (A_ind[i] == min + span) A_ind[i] -= 2;
for (j = 0; j < i; j++)
{
if (A_ind[i] == A_ind[j]) taken = 1;
}
} while (taken);
msl = mpn_mul_1(A+1, A+1, A[0], factor_base[A_ind[i]].p);
if (msl) // Compute the product of these s-3 primes
{
A[A[0]+1] = msl;
A[0]++;
}
}
for (k = 0; k < 30; k++) // Now try 8 different sets of even index primes as the remaining factors
{
F_mpn_copy(current_A, A, A[0] + 1);
for (i = 0; i < 3; i++) // Randomly choose the last 3 prime factors of A with even indices
{
do
{
taken = 0;
A_ind[s-3+i] = ((z_randint(span) + min) & -2L);
if (A_ind[s-3+i] < min) A_ind[s-3+i] += 2;
for (j = 0; j < i; j++)
{
if (A_ind[s-3+i] == A_ind[s-3+j]) taken = 1;
}
} while (taken);
msl = mpn_mul_1(current_A+1, current_A+1, current_A[0], factor_base[A_ind[s-3+i]].p);
if (msl) // Compute the product of these s-3 primes and the odd indexed primes
{
current_A[current_A[0]+1] = msl;
current_A[0]++;
}
}
if (k == 0) // Just store the first difference as the best one
{
if (target_A[0] >= current_A[0]) // Compute the difference with the target A
{
msl = mpn_sub(best_diff+1, target_A+1, target_A[0], current_A+1, current_A[0]);
best_diff[0] = target_A[0];
}
else
{
msl = mpn_sub(best_diff+1, current_A+1, current_A[0], target_A+1, target_A[0]);
best_diff[0] = current_A[0];
}
if (msl) F_mpn_negate(best_diff+1, best_diff+1, best_diff[0]);
while ((!best_diff[best_diff[0]]) && (best_diff[0])) best_diff[0]--; // Normalise best_diff
best1 = A_ind[s-3];
best2 = A_ind[s-2];
best3 = A_ind[s-1];
continue;
}
if (target_A[0] >= current_A[0]) // Compute the difference with the target A
{
msl = mpn_sub(diff+1, target_A+1, target_A[0], current_A+1, current_A[0]);
diff[0] = target_A[0];
}
else
{
msl = mpn_sub(diff+1, current_A+1, current_A[0], target_A+1, target_A[0]);
diff[0] = current_A[0];
}
if (msl) F_mpn_negate(diff+1, diff+1, diff[0]);
while ((!diff[diff[0]]) && (diff[0])) diff[0]--; // Normalise diff
if ((diff[0] < best_diff[0]) || ((diff[0] == best_diff[0]) && (mpn_cmp(diff+1, best_diff+1, diff[0]) < 0))) // The new diff is better
{
F_mpn_copy(best_diff, diff, diff[0]+1);
best1 = A_ind[s-3];
best2 = A_ind[s-2];
best3 = A_ind[s-1];
}
}
A_ind[s-3] = best1; // Multiply A by the product of these 3 primes and store their indices
A_ind[s-2] = best2;
A_ind[s-1] = best3;
for (i = 0; i < 3; i++)
{
msl = mpn_mul_1(A+1, A+1, A[0], factor_base[A_ind[s+i-3]].p);
if (msl)
{
A[A[0]+1] = msl;
A[0]++;
}
}
#if POLY_A
mpz_t A_disp, targ_A;
mpz_init(A_disp);
mpz_init(targ_A);
fmpz_to_mpz(A_disp, A);
fmpz_to_mpz(targ_A, target_A);
gmp_printf("A = %Zd, target A = %Zd\n", A_disp, targ_A);
mpz_clear(A_disp);
mpz_clear(targ_A);
#endif
/*for (i = 0; i < s; i++)
{
p = factor_base[A_ind[i]].p;
poly_inf->inv_p2[i] = z_precompute_inverse(p*p);
} */
fmpz_to_mpz(poly_inf->A_mpz, A);
flint_stack_release(); // release current_A
flint_stack_release(); // release diff
flint_stack_release(); // release best_diff
}
void poly_clear(poly_t * poly_inf)
{
mpz_clear(poly_inf->A_mpz);
mpz_clear(poly_inf->B_mpz);
mpz_clear(poly_inf->C);
flint_stack_release(); // release all A_inv2B[i]
flint_stack_release(); // release posn1
flint_stack_release(); // release posn2
flint_stack_release(); // release soln1
flint_stack_release(); // release soln2
flint_stack_release(); // release A_inv
flint_stack_release(); // release inv_p2
flint_stack_release(); // release A_inv2B
flint_stack_release(); // release A_modp
flint_stack_release(); // release A_ind
flint_stack_release(); // release target_A
flint_stack_release(); // release A
flint_stack_release(); // release B_terms
flint_stack_release(); // release B
}
void sqrts_clear(void)
{
flint_stack_release();
}
int fmpz_divides(fmpz_t q, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
mp_limb_t mslimb;
fmpz_t temp;
if (sizeb == 0)
{
printf("Error: division by zero!\n");
abort();
} else if (sizea == 0)
{
q[0] = 0;
return 1;
} else if (sizea < sizeb)
{
return 0;
} else if (sizea == sizeb)
{
int cmp = fmpz_cmpabs(a, b);
if (cmp < 0) return 0;
if (cmp == 0)
{
if ((long) (a0 ^ b0) < 0L) q[0] = -1L;
else q[0] = 1L;
q[1] = 1;
return 1;
}
}
if (fmpz_is_one(b))
{
fmpz_set(q, a);
return 1;
}
if (fmpz_is_m1(b))
{
fmpz_neg(q, a);
return 1;
}
temp = (fmpz_t) flint_stack_alloc(sizeb + 2);
mpn_tdiv_qr(q+1, temp+1, 0, a+1, sizea, b+1, sizeb);
temp[0] = sizeb;
NORM(temp);
if (temp[0] != 0)
{
flint_stack_release();
return 0;
}
q[0] = sizea - sizeb + 1;
NORM(q);
if ((long) (a0 ^ b0) < 0L) q[0] = -q[0];
flint_stack_release();
return 1;
}
void fmpz_mod(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = b0;
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp, temp2;
if (sizeb == 0)
{
printf("Error: division by zero!\n");
abort();
} else if (sizea < sizeb)
{
if ((long) a0 < 0L)
{
temp = (fmpz_t) flint_stack_alloc(sizeb + 2);
fmpz_add(temp, a, b);
fmpz_set(res, temp);
flint_stack_release();
} else fmpz_set(res, a);
return;
} else if ((sizea == sizeb) && (fmpz_cmpabs(a, b) < 0L))
{
if (fmpz_sgn(a) < 0) fmpz_add(res, a, b);
else fmpz_set(res, a);
return;
} else
{
if (fmpz_is_one(b))
{
fmpz_set_ui(res, 0L);
return;
}
temp = (fmpz_t) flint_stack_alloc(sizea - sizeb + 1);
temp2 = (fmpz_t) flint_stack_alloc(sizeb + 2);
mpn_tdiv_qr(temp, temp2+1, 0, a+1, sizea, b+1, sizeb);
temp2[0] = sizeb;
NORM(temp2);
if (a0 < 0L)
{
unsigned long i = 0;
for (; i < sizeb; i++)
{
if (temp2[i+1]) break;
}
if (i < sizeb)
{
fmpz_sub(temp2, b, temp2);
}
fmpz_set(res, temp2);
} else fmpz_set(res, temp2);
flint_stack_release();
flint_stack_release();
}
}
void primes_clear(void)
{
flint_stack_release();
}
void sizes_clear(void)
{
flint_stack_release();
}
void fmpz_comb_init(fmpz_comb_t comb, ulong * primes, ulong num_primes)
{
ulong i, j, k;
comb->primes = primes;
comb->num_primes = num_primes;
ulong n = 0L;
while (num_primes > (1L<<n)) n++;
comb->n = n;
ulong num;
// create zn_poly modulus information
comb->mod = (zn_mod_t *) flint_heap_alloc_bytes(sizeof(zn_mod_t)*num_primes);
for (ulong i = 0; i < num_primes; i++)
zn_mod_init(comb->mod[i], primes[i]);
if (n == 0) return; // nothing to do
// allocate space for comb
comb->comb = (fmpz_t **) flint_heap_alloc(n);
j = (1L<<(n - 1));
ulong size = 2;
mp_limb_t * ptr;
for (i = 0; i < n; i++)
{
comb->comb[i] = (fmpz_t *) flint_heap_alloc(j);
ptr = (mp_limb_t *) flint_heap_alloc((1L<<n) + j);
for (k = 0; k < j; k++, ptr += (size + 1))
{
comb->comb[i][k] = ptr;
}
j/=2;
size*=2;
}
// allocate space for res
comb->res = (fmpz_t **) flint_heap_alloc(n);
j = (1L<<(n - 1));
size = 2;
for (i = 0; i < n; i++)
{
comb->res[i] = (fmpz_t *) flint_heap_alloc(j);
ptr = (mp_limb_t *) flint_heap_alloc((1L<<n) + j);
for (k = 0; k < j; k++, ptr += (size + 1))
{
comb->res[i][k] = ptr;
}
j/=2;
size*=2;
}
// compute products of pairs of primes and place in comb
for (i = 0, j = 0; i + 2 <= num_primes; i += 2, j++)
{
fmpz_set_ui(comb->comb[0][j], primes[i]);
fmpz_mul_ui(comb->comb[0][j], comb->comb[0][j], primes[i+1]);
}
if (i < num_primes) // in case number of primes is odd
{
fmpz_set_ui(comb->comb[0][j], primes[i]);
i+=2;
j++;
}
num = (1L<<n); // set the rest of the entries on that row of the comb to 1
for (; i < num; i += 2, j++)
{
fmpz_set_ui(comb->comb[0][j], 1L);
}
// compute rest of comb by multiplying in pairs
ulong log_comb = 1;
num /= 2;
while (num >= 2)
{
for (i = 0, j = 0; i < num; i += 2, j++)
{
fmpz_mul(comb->comb[log_comb][j], comb->comb[log_comb-1][i], comb->comb[log_comb-1][i+1]);
}
log_comb++;
num /= 2;
}
// compute inverses from pairs of primes
fmpz_t temp = (fmpz_t) flint_stack_alloc(2);
fmpz_t temp2 = (fmpz_t) flint_stack_alloc(2);
for (i = 0, j = 0; i + 2 <= num_primes; i += 2, j++)
{
fmpz_set_ui(temp, primes[i]);
fmpz_set_ui(temp2, primes[i+1]);
fmpz_invert(comb->res[0][j], temp, temp2);
}
flint_stack_release(); //temp2
flint_stack_release(); //temp
ulong log_res = 1;
num = (1L<<(n - 1));
// compute remaining inverses, each level combining pairs from the level below
while (log_res < n)
{
for (i = 0, j = 0; i < num; i += 2, j++)
{
fmpz_invert(comb->res[log_res][j], comb->comb[log_res-1][i], comb->comb[log_res-1][i+1]);
}
log_res++;
num /= 2;
}
}
void flint_stack_release_small(void)
{
flint_stack_release();
}