int main()
{
long p = 1000;
long d = 53;
arb_t a, b, x, t;
arb_init(a);
arb_init(b);
arb_init(x);
arb_init(t);
// a = 1 + 2 ^ -76
arb_set_str(a, "2", p);
arb_set_str(t, "-76", p);
arb_pow(a, a, t, p);
arb_set_str(t, "1", p);
arb_add(a, t, a, p);
printf("a = "); arb_printd(a, d); printf("\n");
// b = 4 ^ 38 + 0.5
arb_set_str(b, "0.5", p);
arb_ui_pow_ui(t, 4, 38, p);
arb_add(b, t, b, p);
printf("b = "); arb_printd(b, d); printf("\n");
// x = a ^ b
arb_pow(x, a, b, p);
printf("x = "); arb_printd(x, d); printf("\n");
arb_const_e(t, p);
printf("e = "); arb_printd(t, d); printf("\n");
arb_sub(t, x, t, p);
printf("x-e = "); arb_printd(t, d); printf("\n");
printf("Computed with arb-%s\n", arb_version);
arb_clear(a);
arb_clear(b);
arb_clear(x);
arb_clear(t);
}
static __inline__ void
zeta_coeff_k(zeta_bsplit_t S, slong k, slong n, slong s)
{
arb_set_si(S->D, 2 * (n + k));
arb_mul_si(S->D, S->D, n - k, ARF_PREC_EXACT);
arb_set_si(S->Q1, k + 1);
arb_mul_si(S->Q1, S->Q1, 2*k + 1, ARF_PREC_EXACT);
if (k == 0)
{
arb_zero(S->A);
arb_one(S->Q2);
}
else
{
arb_set_si(S->A, k % 2 ? 1 : -1);
arb_mul(S->A, S->A, S->Q1, ARF_PREC_EXACT);
arb_ui_pow_ui(S->Q2, k, s, ARF_PREC_EXACT);
}
arb_mul(S->Q3, S->Q1, S->Q2, ARF_PREC_EXACT);
arb_zero(S->B);
arb_set(S->C, S->Q1);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("bernoulli_poly_ui....");
fflush(stdout);
flint_randinit(state);
/* test multiplication theorem */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t x, t, res1, res2;
ulong n, m, k;
slong prec;
n = n_randint(state, 50);
m = 1 + n_randint(state, 5);
prec = 2 + n_randint(state, 200);
acb_init(x);
acb_init(t);
acb_init(res1);
acb_init(res2);
acb_randtest(x, state, 2 + n_randint(state, 200), 20);
acb_randtest(res1, state, 2 + n_randint(state, 200), 20);
acb_mul_ui(t, x, m, prec);
acb_bernoulli_poly_ui(res1, n, t, prec);
acb_zero(res2);
for (k = 0; k < m; k++)
{
acb_set_ui(t, k);
acb_div_ui(t, t, m, prec);
acb_add(t, t, x, prec);
acb_bernoulli_poly_ui(t, n, t, prec);
acb_add(res2, res2, t, prec);
}
if (n > 0)
{
arb_ui_pow_ui(acb_realref(t), m, n - 1, prec);
acb_mul_arb(res2, res2, acb_realref(t), prec);
}
else
{
acb_div_ui(res2, res2, m, prec);
}
if (!acb_overlaps(res1, res2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu, m = %wu\n\n", n, m);
flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n");
flint_printf("res1 = "); acb_printd(res1, 15); flint_printf("\n\n");
flint_printf("res2 = "); acb_printd(res2, 15); flint_printf("\n\n");
abort();
}
acb_clear(x);
acb_clear(t);
acb_clear(res1);
acb_clear(res2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
bernoulli_rev_init(bernoulli_rev_t iter, ulong nmax)
{
long j;
fmpz_t t;
arb_t x;
arf_t u;
int round1, round2;
long wp;
nmax -= (nmax % 2);
iter->n = nmax;
iter->alloc = 0;
if (nmax < BERNOULLI_REV_MIN)
return;
iter->prec = wp = bernoulli_global_prec(nmax);
iter->max_power = bernoulli_zeta_terms(nmax, iter->prec);
iter->alloc = iter->max_power + 1;
iter->powers = _fmpz_vec_init(iter->alloc);
fmpz_init(iter->pow_error);
arb_init(iter->prefactor);
arb_init(iter->two_pi_squared);
arb_init(x);
fmpz_init(t);
arf_init(u);
/* precompute powers */
for (j = 3; j <= iter->max_power; j += 2)
{
arb_ui_pow_ui(x, j, nmax, bernoulli_power_prec(j, nmax, wp));
arb_inv(x, x, bernoulli_power_prec(j, nmax, wp));
round1 = arf_get_fmpz_fixed_si(t, arb_midref(x), -wp);
fmpz_set(iter->powers + j, t);
/* error: the radius, plus two roundings */
arf_set_mag(u, arb_radref(x));
round2 = arf_get_fmpz_fixed_si(t, u, -wp);
fmpz_add_ui(t, t, (round1 != 0) + (round2 != 0));
if (fmpz_cmp(iter->pow_error, t) < 0)
fmpz_set(iter->pow_error, t);
}
/* precompute (2pi)^2 and 2*(n!)/(2pi)^n */
arb_fac_ui(iter->prefactor, nmax, wp);
arb_mul_2exp_si(iter->prefactor, iter->prefactor, 1);
arb_const_pi(x, wp);
arb_mul_2exp_si(x, x, 1);
arb_mul(iter->two_pi_squared, x, x, wp);
arb_pow_ui(x, iter->two_pi_squared, nmax / 2, wp);
arb_div(iter->prefactor, iter->prefactor, x, wp);
fmpz_clear(t);
arb_clear(x);
arf_clear(u);
}