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; }