/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("gamma_upper...."); fflush(stdout); flint_randinit(state); /* special accuracy test -- see nemo #38 */ for (iter = 0; iter < 1000; iter++) { acb_t a, z, res; slong prec, goal; int regularized; acb_init(a); acb_init(z); acb_init(res); acb_set_si(a, n_randint(state, 100) - 50); do { acb_set_si(z, n_randint(state, 100) - 50); } while (acb_is_zero(z)); regularized = n_randint(state, 3); goal = 2 + n_randint(state, 4000); for (prec = 2 + n_randint(state, 1000); ; prec *= 2) { acb_hypgeom_gamma_upper(res, a, z, regularized, prec); if (acb_rel_accuracy_bits(res) > goal) break; if (prec > 10000) { printf("FAIL (convergence)\n"); flint_printf("regularized = %d\n\n", regularized); flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res = "); acb_printd(res, 30); flint_printf("\n\n"); abort(); } } acb_clear(a); acb_clear(z); acb_clear(res); } for (iter = 0; iter < 2000; iter++) { acb_t a0, a1, b, z, w0, w1, t, u; slong prec0, prec1; int regularized; acb_init(a0); acb_init(a1); acb_init(b); acb_init(z); acb_init(w0); acb_init(w1); acb_init(t); acb_init(u); regularized = n_randint(state, 3); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); acb_randtest_param(a0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_add_ui(a1, a0, 1, prec0); switch (n_randint(state, 4)) { case 0: acb_hypgeom_gamma_upper_asymp(w0, a0, z, regularized, prec0); break; case 1: acb_hypgeom_gamma_upper_1f1a(w0, a0, z, regularized, prec0); break; case 2: acb_hypgeom_gamma_upper_1f1b(w0, a0, z, regularized, prec0); break; default: acb_hypgeom_gamma_upper(w0, a0, z, regularized, prec0); } switch (n_randint(state, 4)) { case 0: acb_hypgeom_gamma_upper_asymp(w1, a0, z, regularized, prec1); break; case 1: acb_hypgeom_gamma_upper_1f1a(w1, a0, z, regularized, prec1); break; case 2: acb_hypgeom_gamma_upper_1f1b(w1, a0, z, regularized, prec1); break; default: acb_hypgeom_gamma_upper(w1, a0, z, regularized, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("a0 = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } switch (n_randint(state, 4)) { case 0: acb_hypgeom_gamma_upper_asymp(w1, a1, z, regularized, prec1); break; case 1: acb_hypgeom_gamma_upper_1f1a(w1, a1, z, regularized, prec1); break; case 2: acb_hypgeom_gamma_upper_1f1b(w1, a1, z, regularized, prec1); break; default: acb_hypgeom_gamma_upper(w1, a1, z, regularized, prec1); } if (regularized == 2) { acb_one(t); acb_neg(u, z); acb_exp(u, u, prec0); acb_mul(t, t, u, prec0); acb_mul(b, w1, z, prec0); acb_addmul(t, a0, w0, prec0); acb_sub(t, t, b, prec0); } else if (regularized == 1) { /* Q(a,z) + exp(-z) z^a / Gamma(a+1) - Q(a+1,z) = 0 */ acb_pow(t, z, a0, prec0); acb_rgamma(u, a1, prec0); acb_mul(t, t, u, prec0); acb_neg(u, z); acb_exp(u, u, prec0); acb_mul(t, t, u, prec0); acb_add(t, t, w0, prec0); acb_sub(t, t, w1, prec0); } else { /* a Gamma(a,z) + exp(-z) z^a - Gamma(a+1,z) = 0 */ acb_pow(t, z, a0, prec0); acb_neg(u, z); acb_exp(u, u, prec0); acb_mul(t, t, u, prec0); acb_addmul(t, a0, w0, prec0); acb_sub(t, t, w1, prec0); } if (!acb_contains_zero(t)) { flint_printf("FAIL: contiguous relation\n\n"); flint_printf("regularized = %d\n\n", regularized); flint_printf("a0 = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_clear(a0); acb_clear(a1); acb_clear(b); acb_clear(z); acb_clear(w0); acb_clear(w1); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }