mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
114 lines
3.6 KiB
C
114 lines
3.6 KiB
C
/*
|
|
Copyright (C) 2017 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 "arb_hypgeom.h"
|
|
|
|
int main()
|
|
{
|
|
slong iter;
|
|
flint_rand_t state;
|
|
|
|
flint_printf("legendre_p_ui_asymp....");
|
|
fflush(stdout);
|
|
|
|
flint_randinit(state);
|
|
|
|
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
|
|
{
|
|
arb_t x, r1, r1p, r2, r2p, r3, s;
|
|
ulong n;
|
|
slong prec1, prec2, K, K2, K3;
|
|
|
|
arb_init(x);
|
|
arb_init(r1);
|
|
arb_init(r1p);
|
|
arb_init(r2);
|
|
arb_init(r2p);
|
|
arb_init(r3);
|
|
arb_init(s);
|
|
|
|
n = n_randtest(state) % 500;
|
|
K = n_randint(state, 50);
|
|
K2 = n_randint(state, 500);
|
|
prec1 = 2 + n_randint(state, 1000);
|
|
prec2 = 2 + n_randint(state, 500);
|
|
|
|
arb_randtest(x, state, 2 + n_randint(state, 1000), 0);
|
|
arb_mul_2exp_si(x, x, -n_randint(state, 8));
|
|
if (n_randint(state, 2))
|
|
mag_zero(arb_radref(x));
|
|
|
|
arb_hypgeom_legendre_p_ui_asymp(r1, r1p, n, x, K, prec1);
|
|
|
|
arb_hypgeom_legendre_p_ui_one(r2, r2p, n, x, K2, prec2);
|
|
|
|
if (!arb_overlaps(r1, r2) || !arb_overlaps(r1p, r2p))
|
|
{
|
|
flint_printf("FAIL: overlap\n\n");
|
|
flint_printf("n = %wu, K = %wd\n\n", n, K);
|
|
flint_printf("x = "); arb_printn(x, 50, 0); flint_printf("\n\n");
|
|
flint_printf("r1 = "); arb_printn(r1, 50, 0); flint_printf("\n\n");
|
|
flint_printf("r2 = "); arb_printn(r2, 50, 0); flint_printf("\n\n");
|
|
flint_printf("r1p = "); arb_printn(r1p, 50, 0); flint_printf("\n\n");
|
|
flint_printf("r2p = "); arb_printn(r2p, 50, 0); flint_printf("\n\n");
|
|
flint_abort();
|
|
}
|
|
|
|
n = n_randtest(state);
|
|
if (n == UWORD_MAX) n--;
|
|
if (n == 0) n++;
|
|
K = n_randint(state, 50);
|
|
K2 = n_randint(state, 50);
|
|
K3 = n_randint(state, 50);
|
|
|
|
/* test (2n+1) x P_n(x) - n P_(n-1)(x) = (n+1) P_(n+1)(x) */
|
|
arb_hypgeom_legendre_p_ui_asymp(r1, NULL, n, x, K, prec2);
|
|
arb_mul(r1, r1, x, prec2);
|
|
arb_set_ui(r2, n);
|
|
arb_add_ui(r2, r2, n, prec2);
|
|
arb_add_ui(r2, r2, 1, prec2);
|
|
arb_mul(r1, r1, r2, prec2);
|
|
|
|
arb_hypgeom_legendre_p_ui_asymp(r2, NULL, n - 1, x, K2, prec2);
|
|
arb_mul_ui(r2, r2, n, prec2);
|
|
|
|
arb_hypgeom_legendre_p_ui_asymp(r3, NULL, n + 1, x, K3, prec2);
|
|
arb_mul_ui(r3, r3, n + 1, prec2);
|
|
|
|
arb_sub(s, r1, r2, prec2);
|
|
|
|
if (!arb_overlaps(s, r3))
|
|
{
|
|
flint_printf("FAIL: overlap (2)\n\n");
|
|
flint_printf("n = %wu, K = %wd, K2 = %wd, K3 = %wd\n\n", n, K, K2, K3);
|
|
flint_printf("x = "); arb_printn(x, 50, 0); flint_printf("\n\n");
|
|
flint_printf("r1 = "); arb_printn(r1, 50, 0); flint_printf("\n\n");
|
|
flint_printf("r2 = "); arb_printn(r2, 50, 0); flint_printf("\n\n");
|
|
flint_printf("s = "); arb_printn(s, 50, 0); flint_printf("\n\n");
|
|
flint_printf("r3 = "); arb_printn(r3, 50, 0); flint_printf("\n\n");
|
|
flint_abort();
|
|
}
|
|
|
|
arb_clear(x);
|
|
arb_clear(r1);
|
|
arb_clear(r1p);
|
|
arb_clear(r2);
|
|
arb_clear(r2p);
|
|
arb_clear(r3);
|
|
arb_clear(s);
|
|
}
|
|
|
|
flint_randclear(state);
|
|
flint_cleanup();
|
|
flint_printf("PASS\n");
|
|
return EXIT_SUCCESS;
|
|
}
|
|
|