void arb_hypgeom_legendre_q(arb_t res, const arb_t n, const arb_t m, const arb_t z, int type, slong prec) { acb_t t, u, v; acb_init(t); acb_init(u); acb_init(v); arb_set(acb_realref(t), n); arb_set(acb_realref(u), m); arb_set(acb_realref(v), z); acb_hypgeom_legendre_q(t, t, u, v, type, prec); if (acb_is_finite(t) && acb_is_real(t)) arb_swap(res, acb_realref(t)); else arb_indeterminate(res); acb_clear(t); acb_clear(u); acb_clear(v); }
int main(int argc, char *argv[]) { int function, i, numtests; slong prec, goal; double t, total, logtotal; acb_t a, b, c, z, r, s; acb_init(a); acb_init(b); acb_init(c); acb_init(z); acb_init(r); acb_init(s); /* J(0,pi x) I(0,pi x) K(0,pi x) */ for (function = 0; function < 3; function++) { total = 0.0; logtotal = 0.0; if (function < 2) numtests = 40; else numtests = 30; for (i = 0; i < numtests; i++) { // printf("%2d ", i + 1); fflush(stdout); TIMEIT_START prec = 96; for (;;) { if (function == 0) { acb_set_d_d(a, input_1f1[i][0], input_1f1[i][1]); acb_set_d_d(b, input_1f1[i][2], input_1f1[i][3]); acb_set_d_d(z, input_1f1[i][4], input_1f1[i][5]); acb_hypgeom_m(r, a, b, z, 0, prec); } else if (function == 1) { acb_set_d_d(a, input_1f1[i][0], input_1f1[i][1]); acb_set_d_d(b, input_1f1[i][2], input_1f1[i][3]); acb_set_d_d(z, input_1f1[i][4], input_1f1[i][5]); acb_hypgeom_u(r, a, b, z, prec); } else if (function == 2) { acb_set_d_d(a, input_2f1[i][0], input_2f1[i][1]); acb_set_d_d(b, input_2f1[i][2], input_2f1[i][3]); acb_set_d_d(c, input_2f1[i][4], input_2f1[i][5]); acb_set_d_d(z, input_2f1[i][6], input_2f1[i][7]); acb_hypgeom_2f1(r, a, b, c, z, 0, prec); } else { acb_set_d_d(a, input_2f1[i][0], input_2f1[i][1]); acb_set_d_d(b, input_2f1[i][2], input_2f1[i][3]); acb_set_d_d(c, input_2f1[i][4], input_2f1[i][5]); acb_set_d_d(z, input_2f1[i][6], input_2f1[i][7]); acb_mul_2exp_si(z, z, 1); acb_sub_ui(z, z, 1, prec); acb_neg(z, z); acb_hypgeom_legendre_q(r, a, c, z, 0, prec); } if (function == 3) { if (acb_rel_accuracy_bits(r) >= goal) break; } else { if (arb_can_round_arf(acb_realref(r), goal, ARF_RND_NEAR) && arb_can_round_arf(acb_imagref(r), goal, ARF_RND_NEAR)) break; } prec *= 2; } TIMEIT_STOP_VAL(t) total += t; logtotal += log(t); #if 1 printf("%8g, ", t); #else printf("%8ld %8g ", prec, t); _acb_print(r, 25); printf("\n"); #endif } printf("---------------------------------------------------------------\n"); printf("Mean %g s; geometric mean %g\n", total, exp(logtotal / numtests)); printf("---------------------------------------------------------------\n"); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(z); acb_clear(r); acb_clear(s); }
int main() { long iter; flint_rand_t state; printf("legendre_q...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t n, m, z, res1, res2; long prec1, prec2, ebits; acb_init(n); acb_init(m); acb_init(z); acb_init(res1); acb_init(res2); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); ebits = 1 + n_randint(state, 10); if (n_randint(state, 2)) { acb_set_si(m, n_randint(state, 20) - 10); acb_set_si(n, n_randint(state, 20) - 10); } else { acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits); acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits); } acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits); _acb_hypgeom_legendre_q_single(res1, n, m, z, prec1); _acb_hypgeom_legendre_q_double(res2, n, m, z, prec2); if (!acb_overlaps(res1, res2)) { printf("FAIL: consistency 1\n\n"); printf("iter = %ld, prec1 = %ld, prec2 = %ld\n\n", iter, prec1, prec2); printf("m = "); acb_printd(m, 30); printf("\n\n"); printf("n = "); acb_printd(n, 30); printf("\n\n"); printf("z = "); acb_printd(z, 30); printf("\n\n"); printf("res1 = "); acb_printd(res1, 30); printf("\n\n"); printf("res2 = "); acb_printd(res2, 30); printf("\n\n"); abort(); } acb_clear(n); acb_clear(m); acb_clear(z); acb_clear(res1); acb_clear(res2); } for (iter = 0; iter < 2000; iter++) { acb_t n, m, z, res1, res2, t, u; long prec1, prec2, ebits; int type; acb_init(n); acb_init(m); acb_init(z); acb_init(res1); acb_init(res2); acb_init(t); acb_init(u); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); ebits = 1 + n_randint(state, 10); if (n_randint(state, 2)) { acb_set_si(m, n_randint(state, 20) - 10); acb_set_si(n, n_randint(state, 20) - 10); } else { acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits); acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits); } acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits); type = n_randint(state, 2); acb_hypgeom_legendre_q(res1, n, m, z, type, prec1); acb_neg(t, m); acb_hypgeom_legendre_p(res2, n, t, z, type, prec2); acb_add(u, m, n, prec2); acb_add_ui(u, u, 1, prec2); acb_gamma(u, u, prec2); acb_mul(res2, res2, u, prec2); acb_sub(u, n, m, prec2); acb_add_ui(u, u, 1, prec2); acb_rgamma(u, u, prec2); acb_mul(res2, res2, u, prec2); acb_hypgeom_legendre_p(t, n, m, z, type, prec2); if (type == 0) { acb_cos_pi(u, m, prec2); acb_mul(t, t, u, prec2); } acb_sub(res2, t, res2, prec2); if (type == 1) { acb_exp_pi_i(t, m, prec2); acb_mul(res2, res2, t, prec2); } acb_sin_pi(t, m, prec2); if (acb_contains_zero(t)) acb_indeterminate(res2); else acb_div(res2, res2, t, prec2); acb_const_pi(t, prec2); acb_mul(res2, res2, t, prec2); acb_mul_2exp_si(res2, res2, -1); if (!acb_overlaps(res1, res2)) { printf("FAIL: consistency 2\n\n"); printf("iter = %ld, prec1 = %ld, prec2 = %ld\n\n", iter, prec1, prec2); printf("type = %d\n\n", type); printf("m = "); acb_printd(m, 30); printf("\n\n"); printf("n = "); acb_printd(n, 30); printf("\n\n"); printf("z = "); acb_printd(z, 30); printf("\n\n"); printf("res1 = "); acb_printd(res1, 30); printf("\n\n"); printf("res2 = "); acb_printd(res2, 30); printf("\n\n"); abort(); } acb_clear(n); acb_clear(m); acb_clear(z); acb_clear(res1); acb_clear(res2); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return EXIT_SUCCESS; }
void _acb_hypgeom_legendre_q_double(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec) { acb_t t, u, v; acb_init(t); acb_init(u); acb_init(v); if (acb_is_int(m)) { acb_sub_ui(t, z, 1, prec); acb_mul_2exp_si(u, m, -1); acb_pow(v, t, u, prec); acb_neg(t, t); acb_neg(u, u); acb_pow(t, t, u, prec); acb_mul(t, t, v, prec); acb_hypgeom_legendre_q(u, n, m, z, 0, prec); acb_mul(t, t, u, prec); acb_mul_2exp_si(u, m, -1); if (!acb_is_int(u)) acb_neg(t, t); acb_sub_ui(u, z, 1, prec); acb_sqrt(u, u, prec); acb_sub_ui(v, z, 1, prec); acb_neg(v, v); acb_rsqrt(v, v, prec); acb_mul(u, u, v, prec); acb_hypgeom_legendre_p(v, n, m, z, 1, prec); acb_mul(u, u, v, prec); acb_const_pi(v, prec); acb_mul(u, u, v, prec); acb_mul_2exp_si(u, u, -1); acb_sub(res, t, u, prec); } else { acb_sub(t, n, m, prec); acb_add_ui(t, t, 1, prec); acb_mul_2exp_si(u, m, 1); acb_rising(t, t, u, prec); acb_neg(u, m); acb_hypgeom_legendre_p(u, n, u, z, 1, prec); acb_mul(t, t, u, prec); acb_hypgeom_legendre_p(u, n, m, z, 1, prec); acb_sub(t, u, t, prec); acb_exp_pi_i(u, m, prec); acb_mul(t, t, u, prec); acb_sin_pi(u, m, prec); acb_div(t, t, u, prec); acb_const_pi(u, prec); acb_mul(t, t, u, prec); acb_mul_2exp_si(t, t, -1); acb_set(res, t); } acb_clear(t); acb_clear(u); acb_clear(v); }