void
arb_zeta_ui_borwein_bsplit(arb_t x, ulong s, slong prec)
{
zeta_bsplit_t sum;
mag_t err;
slong wp, n;
/* zeta(0) = -1/2 */
if (s == 0)
{
arb_set_si(x, -1);
arb_mul_2exp_si(x, x, -1);
return;
}
if (s == 1)
{
flint_printf("zeta_ui_borwein_bsplit: zeta(1)");
abort();
}
n = prec / ERROR_B + 2;
wp = prec + 30;
zeta_bsplit_init(sum);
zeta_bsplit(sum, 0, n + 1, n, s, 0, wp);
/* A/Q3 - B/Q3 / (C/Q1) = (A*C - B*Q1) / (Q3*C) */
arb_mul(sum->A, sum->A, sum->C, wp);
arb_mul(sum->B, sum->B, sum->Q1, wp);
arb_sub(sum->A, sum->A, sum->B, wp);
arb_mul(sum->Q3, sum->Q3, sum->C, wp);
arb_div(sum->C, sum->A, sum->Q3, wp);
mag_init(err);
mag_borwein_error(err, n);
mag_add(arb_radref(sum->C), arb_radref(sum->C), err);
mag_clear(err);
/* convert from eta(s) to zeta(s) */
arb_div_2expm1_ui(x, sum->C, s - 1, wp);
arb_mul_2exp_si(x, x, s - 1);
zeta_bsplit_clear(sum);
}
int main()
{
long iter;
flint_rand_t state;
printf("div_2expm1_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
arb_t a, b, c;
ulong n;
long prec, acc1, acc2;
fmpz_t t;
arb_init(a);
arb_init(b);
arb_init(c);
fmpz_init(t);
prec = 2 + n_randint(state, 10000);
arb_randtest(a, state, 1 + n_randint(state, 10000), 10);
if (n_randint(state, 2))
n = 1 + (n_randtest(state) % (10 * prec));
else
n = n_randtest(state);
arb_div_2expm1_ui(b, a, n, prec);
arb_one(c);
if (n >= (1UL << (FLINT_BITS-1)))
{
arb_mul_2exp_si(c, c, (1UL << (FLINT_BITS-2)));
arb_mul_2exp_si(c, c, (1UL << (FLINT_BITS-2)));
arb_mul_2exp_si(c, c, n - (1UL << (FLINT_BITS-1)));
}
else
{
arb_mul_2exp_si(c, c, n);
}
arb_sub_ui(c, c, 1, prec);
arb_div(c, a, c, prec);
acc1 = arb_rel_accuracy_bits(a);
acc2 = arb_rel_accuracy_bits(b);
if (!arb_overlaps(b, c))
{
printf("FAIL: containment\n\n");
printf("n = %lu\n", n);
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
if (n > 0 && (acc2 < FLINT_MIN(prec, acc1) - 10) &&
!(acc1 == -ARF_PREC_EXACT && acc2 == -ARF_PREC_EXACT))
{
printf("FAIL: poor accuracy\n\n");
printf("prec=%ld, acc1=%ld, acc2=%ld\n\n", prec, acc1, acc2);
printf("n = %lu\n\n", n);
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
fmpz_clear(t);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
