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acb_dirichlet_eta: finite results for intervals around s=1; test code

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This commit is contained in:
Fredrik Johansson 2016-10-15 21:24:27 +02:00
parent 10bc615ce5
commit 6668067cb2
2 changed files with 101 additions and 3 deletions
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36
acb_dirichlet/eta.c
View file

@ -14,10 +14,39 @@
void
acb_dirichlet_eta(acb_t res, const acb_t s, slong prec)
{
if (acb_is_one(s))
if (!acb_is_finite(s))
{
arb_const_log2(acb_realref(res), prec);
arb_zero(acb_imagref(res));
acb_indeterminate(res);
}
else if (arb_contains_si(acb_realref(s), 1) && arb_contains_zero(acb_imagref(s)))
{
if (acb_is_one(s))
{
arb_const_log2(acb_realref(res), prec);
arb_zero(acb_imagref(res));
}
else
{
mag_t m;
int is_real = acb_is_real(s);
mag_init(m);
/* Taylor coefficients at s = 1 are bounded by |c_k| < 1/4^k. */
acb_sub_ui(res, s, 1, prec);
acb_get_mag(m, res);
mag_mul_2exp_si(m, m, -2);
mag_geom_series(m, m, 1);
arb_const_log2(acb_realref(res), prec);
arb_zero(acb_imagref(res));
if (is_real)
arb_add_error_mag(acb_realref(res), m);
else
acb_add_error_mag(res, m);
mag_clear(m);
}
}
else
{
@ -34,3 +63,4 @@ acb_dirichlet_eta(acb_t res, const acb_t s, slong prec)
acb_clear(t);
}
}

68
acb_dirichlet/test/t-eta.c Normal file
View file

@ -0,0 +1,68 @@
/*
Copyright (C) 2016 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("eta....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 250 * arb_test_multiplier(); iter++)
{
acb_t z1, z2, s1, s2;
slong prec1, prec2;
acb_init(z1);
acb_init(z2);
acb_init(s1);
acb_init(s2);
acb_randtest(s1, state, 2 + n_randint(state, 100), 3);
acb_randtest(z1, state, 2 + n_randint(state, 100), 3);
acb_randtest(z2, state, 2 + n_randint(state, 100), 3);
prec1 = 2 + n_randint(state, 100);
prec2 = 2 + n_randint(state, 100);
acb_add(s2, s1, z1, prec2);
acb_sub(s2, s2, z1, prec2);
acb_dirichlet_eta(z1, s1, prec1);
acb_dirichlet_eta(z2, s2, prec2);
if (!acb_overlaps(z1, z2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("s1 = "); acb_printn(s1, 50, 0); flint_printf("\n\n");
flint_printf("s2 = "); acb_printn(s2, 50, 0); flint_printf("\n\n");
flint_printf("z1 = "); acb_printn(z1, 50, 0); flint_printf("\n\n");
flint_printf("z2 = "); acb_printn(z2, 50, 0); flint_printf("\n\n");
abort();
}
acb_clear(s1);
acb_clear(s2);
acb_clear(z1);
acb_clear(z2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}