/* The error for eta(s) is bounded by 3/(3+sqrt(8))^n */
void
borwein_error(fmpr_t err, long n)
{
fmpr_sqrt_ui(err, 8, FMPRB_RAD_PREC, FMPR_RND_DOWN);
fmpr_add_ui(err, err, 3, FMPRB_RAD_PREC, FMPR_RND_DOWN);
fmpr_pow_sloppy_ui(err, err, n, FMPRB_RAD_PREC, FMPR_RND_DOWN);
fmpr_ui_div(err, 3, err, FMPRB_RAD_PREC, FMPR_RND_UP);
}
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;
}
slong
hypgeom_root_bound(const mag_t z, int r)
{
if (r == 0)
{
return 0;
}
else
{
fmpr_t t;
slong v;
fmpr_init(t);
mag_get_fmpr(t, z);
fmpr_root(t, t, r, MAG_BITS, FMPR_RND_UP);
fmpr_add_ui(t, t, 1, MAG_BITS, FMPR_RND_UP);
v = fmpr_get_si(t, FMPR_RND_UP);
fmpr_clear(t);
return v;
}
}
/* 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);
}