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/*
Copyright (C) 2019 D.H.J. Polymath
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"
static void
_arb_inv_si(arb_t res, slong a, slong prec)
{
arb_set_si(res, a);
arb_inv(res, res, prec);
}
static void
_arb_div_si_si(arb_t res, slong a, slong b, slong prec)
{
arb_set_si(res, a);
arb_div_si(res, res, b, prec);
}
static int
_arb_vec_overlaps(arb_srcptr a, arb_srcptr b, slong len)
{
slong i;
for (i = 0; i < len; i++)
{
if (!arb_overlaps(a + i, b + i))
{
return 0;
}
}
return 1;
}
static void
_check_containment(const char *name, const arb_t x, const char *s)
{
arb_t u;
slong prec = 300;
arb_init(u);
arb_set_str(u, s, prec);
if (!arb_contains(u, x))
{
flint_printf("FAIL: %s\n\n", name);
flint_printf("observed = "); arb_printn(x, 30, 0); flint_printf("\n\n");
flint_printf("expected = "); arb_printn(u, 30, 0); flint_printf("\n\n");
flint_abort();
}
arb_clear(u);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("platt_multieval....");
fflush(stdout);
flint_randinit(state);
/* Check a specific combination of parameter values that is relatively fast
* to evaluate and that has relatively tight bounds. */
{
slong A = 8;
slong B = 128;
slong N = A*B;
slong J = 1000;
slong K = 30;
slong sigma = 63;
slong prec = 128;
fmpz_t T;
arb_t h;
arb_ptr vec;
arb_init(h);
fmpz_init(T);
fmpz_set_si(T, 10000);
arb_set_d(h, 4.5);
/* Spot-check lemma bound containment
* in intervals calculated with PARI/GP. */
{
arb_t lem, xi, x, beta, t0;
slong i = 201;
slong k = 5;
slong wp = 300;
arb_init(lem);
arb_init(xi);
arb_init(x);
arb_init(t0);
arb_init(beta);
_arb_inv_si(xi, B, wp);
arb_mul_2exp_si(xi, xi, -1);
_arb_div_si_si(x, i, B, wp);
arb_set_fmpz(t0, T);
acb_dirichlet_platt_beta(beta, t0, wp);
acb_dirichlet_platt_lemma_32(lem, h, t0, x, wp);
_check_containment("Lemma 3.2", lem,
"[5.3526496753240991744e-1072334 +/- 2.55e-1072354]");
acb_dirichlet_platt_c_bound(lem, sigma, t0, h, k, wp);
_check_containment("Lemma A.3", lem,
"[1.3516642396389823078e+134 +/- 2.65e+114]");
acb_dirichlet_platt_lemma_A5(lem, B, h, k, wp);
_check_containment("Lemma A.5", lem,
"[1.0075390047893384632e-30 +/- 5.57e-51]");
acb_dirichlet_platt_lemma_A7(lem, sigma, t0, h, k, A, wp);
_check_containment("Lemma A.7", lem,
"[3.0406705491484062400e-505 +/- 1.57e-525]");
acb_dirichlet_platt_lemma_A9(lem, sigma, t0, h, A, wp);
_check_containment("Lemma A.9", lem,
"[6.8953211848420326275e-536 +/- 3.52e-556]");
acb_dirichlet_platt_lemma_A11(lem, t0, h, B, wp);
_check_containment("Lemma A.11", lem,
"[3.0825745863006335768e-42 +/- 3.68e-62]");
acb_dirichlet_platt_lemma_B1(lem, sigma, t0, h, J, wp);
_check_containment("Lemma B.1", lem,
"[8.5737638613320328274e-42 +/- 7.50e-63]");
acb_dirichlet_platt_lemma_B2(lem, K, h, xi, wp);
_check_containment("Lemma B.2", lem,
"[2.0748437544358592615e-44 +/- 4.76e-64]");
arb_clear(lem);
arb_clear(xi);
arb_clear(x);
arb_clear(t0);
arb_clear(beta);
}
/* Check a few random entries in the multieval vector. */
vec = _arb_vec_init(N);
acb_dirichlet_platt_multieval(vec, T, A, B, h, J, K, sigma, prec);
for (iter = 0; iter < 20; iter++)
{
arb_t t, r;
slong i = n_randint(state, N);
slong n = i - N/2;
arb_init(t);
arb_init(r);
_arb_div_si_si(t, n, A, prec);
arb_add_fmpz(t, t, T, prec);
acb_dirichlet_platt_scaled_lambda(r, t, prec);
if (!arb_overlaps(vec + i, r))
{
flint_printf("FAIL: overlap for hardcoded example\n\n");
flint_printf("i = %wd n = %wd\n\n", i, n);
flint_printf("vec[%wd] = ", i); arb_printn(vec + i, 30, 0); flint_printf("\n\n");
flint_printf("r = "); arb_printn(r, 30, 0); flint_printf("\n\n");
flint_abort();
}
arb_clear(t);
arb_clear(r);
}
fmpz_clear(T);
arb_clear(h);
_arb_vec_clear(vec, N);
}
for (iter = 0; iter < 10 * arb_test_multiplier(); iter++)
{
slong prec;
ulong A, B, N, J, K;
slong sigma, Tbits;
fmpz_t T;
arb_t h;
arb_ptr v1, v2;
/* better but slower limits are in parentheses below */
prec = 2 + n_randint(state, 300);
sigma = 1 + 2*(1 + n_randint(state, 100)); /* (200) */
J = 1 + n_randint(state, 100); /* (10000) */
K = 1 + n_randint(state, 20); /* (50) */
A = 1 + n_randint(state, 10);
B = 1 + n_randint(state, 10); /* (500) */
if (n_randint(state, 2))
A *= 2;
else
B *= 2;
N = A*B;
fmpz_init(T);
Tbits = 5 + n_randint(state, 15);
fmpz_set_ui(T, n_randtest_bits(state, Tbits));
arb_init(h);
arb_set_si(h, 1 + n_randint(state, 20000));
arb_div_si(h, h, 1000, prec);
v1 = _arb_vec_init(N);
v2 = _arb_vec_init(N);
acb_dirichlet_platt_scaled_lambda_vec(v1, T, A, B, prec);
acb_dirichlet_platt_multieval(v2, T, A, B, h, J, K, sigma, prec);
if (!_arb_vec_overlaps(v1, v2, N))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %wd prec = %wd\n\n", iter, prec);
flint_printf("sigma = %wd\n\n", sigma);
flint_printf("A = %wu B = %wu J = %wu K = %wu\n\n", A, B, J, K);
flint_printf("T = "); fmpz_print(T); flint_printf("\n\n");
flint_printf("h = "); arb_printn(h, 30, 0); flint_printf("\n\n");
flint_abort();
}
arb_clear(h);
fmpz_clear(T);
_arb_vec_clear(v1, N);
_arb_vec_clear(v2, N);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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