void
gamma_taylor_bound_remainder(fmpr_t err, const fmpr_t z, long n)
{
fmpr_t t, u;
gamma_taylor_bound_extend_cache(n + 1);
fmpr_init(t);
fmpr_init(u);
/* denominator: 1 - r(n+1) * z, rounded down */
fmpr_mul(t, gamma_taylor_bound_ratio_cache + n + 1,
z, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_one(u);
fmpr_sub(u, u, t, FMPRB_RAD_PREC, FMPR_RND_DOWN);
if (fmpr_sgn(u) <= 0)
{
fmpr_pos_inf(err);
}
else
{
fmpr_pow_sloppy_ui(t, z, n, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_mul_2exp_si(t, t, gamma_taylor_bound_mag_cache[n + 1]);
fmpr_div(err, t, u, FMPRB_RAD_PREC, FMPR_RND_UP);
}
fmpr_clear(t);
fmpr_clear(u);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rfac_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
fmpr_t x, y;
fmpz_t f;
mag_t xb;
ulong n;
fmpr_init(x);
fmpr_init(y);
fmpz_init(f);
mag_init(xb);
mag_randtest_special(xb, state, 80);
n = n_randtest(state) % 2000;
mag_rfac_ui(xb, n);
fmpz_fac_ui(f, n);
fmpr_one(x);
fmpr_div_fmpz(x, x, f, 2 * MAG_BITS, FMPR_RND_UP);
mag_get_fmpr(y, xb);
MAG_CHECK_BITS(xb)
if (!(fmpr_cmpabs(y, x) >= 0))
{
flint_printf("FAIL\n\n");
flint_printf("n = %wu\n\n", n);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpz_clear(f);
mag_clear(xb);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("binpow_uiui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpr_t x, y;
mag_t b;
ulong m, n;
fmpr_init(x);
fmpr_init(y);
mag_init(b);
m = n_randtest(state);
n = n_randtest(state);
fmpr_one(x);
fmpr_div_ui(x, x, m, 128, FMPR_RND_UP);
fmpr_add_ui(x, x, 1, 128, FMPR_RND_UP);
fmpr_pow_sloppy_ui(x, x, n, 128, FMPR_RND_UP);
mag_binpow_uiui(b, m, n);
mag_get_fmpr(y, b);
MAG_CHECK_BITS(b)
if (!(fmpr_cmpabs(x, y) <= 0))
{
flint_printf("FAIL\n\n");
flint_printf("m = %wu\n\n", m);
flint_printf("n = %wu\n\n", n);
flint_printf("x = "); fmpr_printd(x, 10); flint_printf("\n\n");
flint_printf("y = "); fmpr_printd(y, 10); flint_printf("\n\n");
flint_abort();
}
fmpr_clear(x);
fmpr_clear(y);
mag_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
/* Absolute value of rising factorial (could speed up once complex gamma is available). */
void
fmpcb_rfac_abs_ubound2(fmpr_t bound, const fmpcb_t s, ulong n, long prec)
{
fmpr_t term, t;
ulong k;
/* M(k) = (a+k)^2 + b^2
M(0) = a^2 + b^2
M(k+1) = M(k) + 2*a + (2*k+1)
*/
fmpr_init(t);
fmpr_init(term);
fmpr_one(bound);
/* M(0) = a^2 + b^2 */
fmprb_get_abs_ubound_fmpr(t, fmpcb_realref(s), prec);
fmpr_mul(term, t, t, prec, FMPR_RND_UP);
fmprb_get_abs_ubound_fmpr(t, fmpcb_imagref(s), prec);
fmpr_mul(t, t, t, prec, FMPR_RND_UP);
fmpr_add(term, term, t, prec, FMPR_RND_UP);
/* we add t = 2*a to each term. note that this can be signed;
we always want the most positive value */
fmpr_add(t, fmprb_midref(fmpcb_realref(s)),
fmprb_radref(fmpcb_realref(s)), prec, FMPR_RND_CEIL);
fmpr_mul_2exp_si(t, t, 1);
for (k = 0; k < n; k++)
{
fmpr_mul(bound, bound, term, prec, FMPR_RND_UP);
fmpr_add_ui(term, term, 2 * k + 1, prec, FMPR_RND_UP);
fmpr_add(term, term, t, prec, FMPR_RND_UP);
}
fmpr_sqrt(bound, bound, prec, FMPR_RND_UP);
fmpr_clear(t);
fmpr_clear(term);
}
void
fmprb_mat_det_inplace(fmprb_t det, fmprb_mat_t A, long prec)
{
long i, n, sign, rank;
n = fmprb_mat_nrows(A);
rank = fmprb_mat_gauss_partial(A, prec);
sign = (rank < 0) ? -1 : 1;
rank = FLINT_ABS(rank);
fmprb_set_si(det, sign);
for (i = 0; i < rank; i++)
fmprb_mul(det, det, fmprb_mat_entry(A, i, i), prec);
/* bound unreduced part using Hadamard's inequality */
if (rank < n)
{
fmpr_t t;
fmprb_t d;
fmpr_init(t);
fmprb_init(d);
fmpr_one(fmprb_radref(d));
for (i = rank; i < n; i++)
{
fmprb_vec_get_fmpr_2norm_squared_bound(t, A->rows[i] + rank,
n - rank, FMPRB_RAD_PREC);
fmpr_mul(fmprb_radref(d), fmprb_radref(d), t, FMPRB_RAD_PREC, FMPR_RND_UP);
}
fmpr_sqrt(fmprb_radref(d), fmprb_radref(d), FMPRB_RAD_PREC, FMPR_RND_UP);
fmprb_mul(det, det, d, prec);
fmprb_clear(d);
fmpr_clear(t);
}
}