void
_fmpz_poly_pow_binomial(fmpz * res, const fmpz * poly, ulong e)
{
ulong i, f;
fmpz_t a, b, c;
*a = 1L;
*b = 1L;
*c = 1L;
fmpz_one(res);
fmpz_one(res + e);
for (i = 1UL, f = e - 1UL; i <= (e - 1UL) >> 1; i++, f--)
{
fmpz_mul(a, a, poly);
fmpz_mul(b, b, poly + 1);
fmpz_mul_ui(c, c, f + 1UL);
fmpz_divexact_ui(c, c, i);
fmpz_mul(res + i, b, c);
fmpz_mul(res + f, a, c);
}
if ((e & 1UL) == 0UL)
{
fmpz_mul(a, a, poly);
fmpz_mul(b, b, poly + 1);
fmpz_mul_ui(c, c, f + 1UL);
fmpz_divexact_ui(c, c, i);
fmpz_mul(res + i, b, c);
fmpz_mul(res + i, res + i, a);
i++, f--;
}
for ( ; i <= e; i++, f--)
{
fmpz_mul(a, a, poly);
fmpz_mul(b, b, poly + 1);
fmpz_mul(res + i, res + i, b);
fmpz_mul(res + f, res + f, a);
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
}
void
_fmpz_poly_revert_series_lagrange(fmpz * Qinv, const fmpz * Q, slong n)
{
slong i;
fmpz *R, *S, *T, *tmp;
if (n <= 2)
{
_fmpz_vec_set(Qinv, Q, n);
return;
}
R = _fmpz_vec_init(n - 1);
S = _fmpz_vec_init(n - 1);
T = _fmpz_vec_init(n - 1);
fmpz_zero(Qinv);
fmpz_set(Qinv + 1, Q + 1);
_fmpz_poly_inv_series(R, Q + 1, n - 1);
_fmpz_vec_set(S, R, n - 1);
for (i = 2; i < n; i++)
{
_fmpz_poly_mullow(T, S, n - 1, R, n - 1, n - 1);
fmpz_divexact_ui(Qinv + i, T + i - 1, i);
tmp = S; S = T; T = tmp;
}
_fmpz_vec_clear(R, n - 1);
_fmpz_vec_clear(S, n - 1);
_fmpz_vec_clear(T, n - 1);
}
void
_acb_poly_binomial_transform_basecase(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec)
{
slong n, k;
fmpz_t t;
fmpz_init(t);
for (n = 0; n < len; n++)
{
acb_zero(b + n);
for (k = 0; k < FLINT_MIN(n + 1, alen); k++)
{
if (k == 0)
{
fmpz_one(t);
}
else
{
fmpz_mul_si(t, t, -(n - k + 1));
fmpz_divexact_ui(t, t, k);
}
acb_addmul_fmpz(b + n, a + k, t, prec);
}
}
fmpz_clear(t);
}
void
fmpz_mat_scalar_divexact_ui_2arg(fmpz_mat_t R,mp_limb_t d)
{
fmpz* q=R->entries;
slong s=R->r * R->c;
for(;s--;q++)
fmpz_divexact_ui( q, q, d );
}
void
_fmpz_vec_scalar_divexact_ui(fmpz * vec1, const fmpz * vec2,
long len2, ulong c)
{
long i;
for (i = 0; i < len2; i++)
fmpz_divexact_ui(vec1 + i, vec2 + i, c);
}
void qsieve_ll_compute_C(qs_t qs_inf)
{
mp_limb_t A = qs_inf->A;
mp_limb_t B = qs_inf->B;
if ((mp_limb_signed_t) B < 0L) B = -B;
fmpz_set_ui(qs_inf->C, B);
fmpz_mul_ui(qs_inf->C, qs_inf->C, B);
fmpz_sub(qs_inf->C, qs_inf->C, qs_inf->kn);
fmpz_divexact_ui(qs_inf->C, qs_inf->C, A);
}
void
rising_difference_polynomial(fmpz * s, fmpz * c, ulong m)
{
long i, j, k;
fmpz_t t;
fmpz_init(t);
arith_stirling_number_1u_vec(s, m, m + 1);
for (k = 0; k < m; k++)
{
for (i = 0; i <= m - k - 1; i++)
{
fmpz_zero(c + m * k + i);
for (j = i + 1; j + k <= m; j++)
{
if (j == i + 1)
{
fmpz_bin_uiui(t, 1+i+k, k);
fmpz_mul_ui(t, t, m * (i+1));
}
else
{
fmpz_mul_ui(t, t, m * (k + j));
fmpz_divexact_ui(t, t, j - i);
}
fmpz_addmul(c + m * k + i, s + j + k, t);
}
}
}
fmpz_clear(t);
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("divexact_ui....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 100000; i++)
{
fmpz_t a, c;
mpz_t e, f, g;
ulong n;
fmpz_init(a);
fmpz_init(c);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
n = n_randtest_not_zero(state);
fmpz_mul_ui(c, a, n);
fmpz_get_mpz(e, c);
fmpz_divexact_ui(a, c, n);
mpz_divexact_ui(f, e, n);
fmpz_get_mpz(g, a);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
printf("FAIL1\n");
gmp_printf("n = %lu, e = %Zd, f = %Zd, g = %Zd\n", n, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(c);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
/* Test aliasing of a and c */
for (i = 0; i < 100000; i++)
{
fmpz_t a, c;
mpz_t d, f, g;
ulong n;
fmpz_init(a);
fmpz_init(c);
mpz_init(d);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
n = n_randtest_not_zero(state);
fmpz_mul_ui(c, a, n);
fmpz_get_mpz(d, c);
fmpz_divexact_ui(c, c, n);
mpz_divexact_ui(f, d, n);
fmpz_get_mpz(g, c);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
printf("FAIL:\n");
gmp_printf("d = %Zd, n = %lu, f = %Zd, g = %Zd\n", d, n, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(f);
mpz_clear(g);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
static void
__ramanujan_even_common_denom(fmpz * num, fmpz * den, long start, long n)
{
fmpz_t t, c, d, cden;
long j, k, m, mcase;
int prodsize;
if (start >= n)
return;
fmpz_init(t);
fmpz_init(c);
fmpz_init(d);
fmpz_init(cden);
/* Common denominator */
fmpz_primorial(cden, n + 1);
start += start % 2;
/* Convert initial values to common denominator */
for (k = 0; k < start; k += 2)
{
fmpz_divexact(t, cden, den + k);
fmpz_mul(num + k, num + k, t);
}
/* Ramanujan's recursive formula */
for (m = start; m < n; m += 2)
{
mcase = m % 6;
fmpz_mul_ui(num + m, cden, m + 3UL);
fmpz_divexact_ui(num + m, num + m, 3UL);
if (mcase == 4)
{
fmpz_neg(num + m, num + m);
fmpz_divexact_ui(num + m, num + m, 2UL);
}
/* All factors are strictly smaller than m + 4; choose prodsize such
that (m + 4)^prodsize fits in a signed long. */
{
#if FLINT64
if (m < 1444L) prodsize = 6;
else if (m < 2097148L) prodsize = 3;
else if (m < 3037000495L) prodsize = 2; /* not very likely... */
else abort();
#else
if (m < 32L) prodsize = 6;
else if (m < 1286L) prodsize = 3;
else if (m < 46336L) prodsize = 2;
else abort();
#endif
}
/* c = t = binomial(m+3, m) */
fmpz_set_ui(t, m + 1UL);
fmpz_mul_ui(t, t, m + 2UL);
fmpz_mul_ui(t, t, m + 3UL);
fmpz_divexact_ui(t, t, 6UL);
fmpz_set(c, t);
for (j = 6; j <= m; j += 6)
{
long r = m - j;
/* c = binomial(m+3, m-j); */
switch (prodsize)
{
case 2:
fmpz_mul_ui(c, c, (r+6)*(r+5));
fmpz_mul_ui(c, c, (r+4)*(r+3));
fmpz_mul_ui(c, c, (r+2)*(r+1));
fmpz_set_ui(d, (j+0)*(j+3));
fmpz_mul_ui(d, d, (j-2)*(j+2));
fmpz_mul_ui(d, d, (j-1)*(j+1));
fmpz_divexact(c, c, d);
break;
case 3:
fmpz_mul_ui(c, c, (r+6)*(r+5)*(r+4));
fmpz_mul_ui(c, c, (r+3)*(r+2)*(r+1));
fmpz_set_ui(d, (j+0)*(j+3)*(j-2));
fmpz_mul_ui(d, d, (j+2)*(j-1)*(j+1));
fmpz_divexact(c, c, d);
break;
case 6:
fmpz_mul_ui(c, c, (r+6)*(r+5)*(r+4)*(r+3)*(r+2)*(r+1));
fmpz_divexact_ui(c, c, (j+0)*(j+3)*(j-2)*(j+2)*(j-1)*(j+1));
break;
}
fmpz_submul(num + m, c, num + (m - j));
}
fmpz_divexact(num + m, num + m, t);
}
/* Convert to separate denominators */
for (k = 0; k < n; k += 2)
{
bernoulli_number_denom(den + k, k);
fmpz_divexact(t, cden, den + k);
fmpz_divexact(num + k, num + k, t);
}
fmpz_clear(t);
fmpz_clear(c);
fmpz_clear(d);
fmpz_clear(cden);
}