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);
}
/* 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;
}
