int main(void) { int i, j, result; flint_rand_t state; flint_printf("get/set_coeff_acb...."); fflush(stdout); flint_randinit(state); for (i = 0; i < 100; i++) { acb_poly_t a; acb_t x1, x2; slong coeff, len; acb_poly_init(a); acb_init(x1); acb_init(x2); len = n_randint(state, 100) + 1; for (j = 0; j < 100; j++) { acb_randtest(x1, state, 2 + n_randint(state, 200), 10); coeff = n_randint(state, len); acb_poly_set_coeff_acb(a, coeff, x1); acb_poly_get_coeff_acb(x2, a, coeff); result = (acb_equal(x1, x2)); if (!result) { flint_printf("FAIL:\n"); flint_printf("x1 = "), acb_print(x1), flint_printf("\n"); flint_printf("x2 = "), acb_print(x2), flint_printf("\n"); flint_printf("coeff = %wd, length = %wd\n", coeff, len); flint_abort(); } } acb_clear(x1); acb_clear(x2); acb_poly_clear(a); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; }
int main(void) { int i, result; flint_rand_t state; printf("get_coeff_ptr...."); fflush(stdout); flint_randinit(state); for (i = 0; i < 1000; i++) { acb_poly_t A; acb_t a; long n = n_randint(state, 100); acb_poly_init(A); acb_poly_randtest(A, state, n_randint(state, 100), 100, 10); acb_init(a); acb_poly_get_coeff_acb(a, A, n); result = n < acb_poly_length(A) ? acb_equal(a, acb_poly_get_coeff_ptr(A, n)) : acb_poly_get_coeff_ptr(A, n) == NULL; if (!result) { printf("FAIL:\n"); printf("A = "), acb_poly_printd(A, 10), printf("\n\n"); printf("a = "), acb_print(a), printf("\n\n"); printf("n = %ld\n\n", n); abort(); } acb_poly_clear(A); acb_clear(a); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return 0; }
void acb_hypgeom_bessel_k_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec) { if (acb_is_int(nu)) { acb_poly_t nux, zx, rx; acb_poly_init(nux); acb_poly_init(zx); acb_poly_init(rx); acb_poly_set_coeff_acb(nux, 0, nu); acb_poly_set_coeff_si(nux, 1, 1); acb_poly_set_acb(zx, z); acb_hypgeom_bessel_k_0f1_series(rx, nux, zx, 1, prec); acb_poly_get_coeff_acb(res, rx, 0); acb_poly_clear(nux); acb_poly_clear(zx); acb_poly_clear(rx); } else { acb_t t, u, v, w; acb_struct b[2]; acb_init(t); acb_init(u); acb_init(v); acb_init(w); acb_init(b + 0); acb_init(b + 1); /* u = 0F1(1+nu), v = 0F1(1-nu) */ acb_mul(t, z, z, prec); acb_mul_2exp_si(t, t, -2); acb_add_ui(b, nu, 1, prec); acb_one(b + 1); acb_hypgeom_pfq_direct(u, NULL, 0, b, 2, t, -1, prec); acb_sub_ui(b, nu, 1, prec); acb_neg(b, b); acb_hypgeom_pfq_direct(v, NULL, 0, b, 2, t, -1, prec); /* v = v * gamma(nu) / (z/2)^nu */ acb_mul_2exp_si(t, z, -1); acb_pow(t, t, nu, prec); acb_gamma(w, nu, prec); acb_mul(v, v, w, prec); acb_div(v, v, t, prec); /* u = u * t * pi / (gamma(nu) * nu * sin(pi nu)) */ acb_mul(u, u, t, prec); acb_const_pi(t, prec); acb_mul(u, u, t, prec); acb_sin_pi(t, nu, prec); acb_mul(t, t, w, prec); acb_mul(t, t, nu, prec); acb_div(u, u, t, prec); acb_sub(res, v, u, prec); acb_mul_2exp_si(res, res, -1); acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(w); acb_clear(b + 0); acb_clear(b + 1); } }
void _acb_hypgeom_2f1_transform_limit(acb_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t c, const acb_poly_t z, int which, slong prec) { acb_poly_t ba, ca, cb, cab, ac1, bc1, ab1, ba1, w, t, u, v, s; acb_t tt; acb_poly_init(ba); acb_poly_init(ca); acb_poly_init(cb); acb_poly_init(cab); acb_poly_init(ac1); acb_poly_init(bc1); acb_poly_init(ab1); acb_poly_init(ba1); acb_poly_init(w); acb_poly_init(t); acb_poly_init(u); acb_poly_init(v); acb_poly_init(s); acb_init(tt); acb_poly_add_si(s, z, -1, prec); /* s = 1 - z */ acb_poly_neg(s, s); acb_poly_sub(ba, b, a, prec); /* ba = b - a */ acb_poly_sub(ca, c, a, prec); /* ca = c - a */ acb_poly_sub(cb, c, b, prec); /* cb = c - b */ acb_poly_sub(cab, ca, b, prec); /* cab = c - a - b */ acb_poly_add_si(ac1, ca, -1, prec); acb_poly_neg(ac1, ac1); /* ac1 = a - c + 1 */ acb_poly_add_si(bc1, cb, -1, prec); acb_poly_neg(bc1, bc1); /* bc1 = b - c + 1 */ acb_poly_add_si(ab1, ba, -1, prec); acb_poly_neg(ab1, ab1); /* ab1 = a - b + 1 */ acb_poly_add_si(ba1, ba, 1, prec); /* ba1 = b - a + 1 */ /* t = left term, u = right term (DLMF 15.8.1 - 15.8.5) */ if (which == 2) { acb_poly_inv_series(w, z, 2, prec); /* w = 1/z */ acb_hypgeom_2f1_series_direct(t, a, ac1, ab1, w, 1, 2, prec); acb_hypgeom_2f1_series_direct(u, b, bc1, ba1, w, 1, 2, prec); } else if (which == 3) { acb_poly_inv_series(w, s, 2, prec); /* w = 1/(1-z) */ acb_hypgeom_2f1_series_direct(t, a, cb, ab1, w, 1, 2, prec); acb_hypgeom_2f1_series_direct(u, b, ca, ba1, w, 1, 2, prec); } else if (which == 4) { acb_poly_set(w, s); /* w = 1-z */ acb_poly_add(v, ac1, b, prec); /* v = a+b-c+1 */ acb_hypgeom_2f1_series_direct(t, a, b, v, w, 1, 2, prec); acb_poly_add_si(v, cab, 1, prec); /* v = c-a-b+1 */ acb_hypgeom_2f1_series_direct(u, ca, cb, v, w, 1, 2, prec); } else if (which == 5) { acb_poly_inv_series(w, z, 2, prec); /* w = 1-1/z */ acb_poly_neg(w, w); acb_poly_add_si(w, w, 1, prec); acb_poly_add(v, ac1, b, prec); /* v = a+b-c+1 */ acb_hypgeom_2f1_series_direct(t, a, ac1, v, w, 1, 2, prec); acb_poly_add_si(v, cab, 1, prec); /* v = c-a-b+1 */ acb_poly_add_si(u, a, -1, prec); /* u = 1-a */ acb_poly_neg(u, u); acb_hypgeom_2f1_series_direct(u, ca, u, v, w, 1, 2, prec); } else { flint_printf("invalid transformation!\n"); flint_abort(); } /* gamma factors */ acb_poly_rgamma_series(v, a, 2, prec); acb_poly_mullow(u, u, v, 2, prec); acb_poly_rgamma_series(v, ca, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_rgamma_series(v, b, 2, prec); if (which == 2 || which == 3) acb_poly_mullow(t, t, v, 2, prec); else acb_poly_mullow(u, u, v, 2, prec); acb_poly_rgamma_series(v, cb, 2, prec); if (which == 2 || which == 3) acb_poly_mullow(u, u, v, 2, prec); else acb_poly_mullow(t, t, v, 2, prec); if (which == 2 || which == 3) { if (which == 2) acb_poly_neg(s, z); /* -z, otherwise 1-z since before */ acb_poly_neg(v, a); acb_poly_pow_series(v, s, v, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_neg(v, b); acb_poly_pow_series(v, s, v, 2, prec); acb_poly_mullow(u, u, v, 2, prec); } else { acb_poly_pow_series(v, s, cab, 2, prec); acb_poly_mullow(u, u, v, 2, prec); if (which == 5) { acb_poly_neg(v, a); acb_poly_pow_series(v, z, v, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_neg(v, ca); acb_poly_pow_series(v, z, v, 2, prec); acb_poly_mullow(u, u, v, 2, prec); } } acb_poly_sub(t, t, u, prec); if (which == 2 || which == 3) acb_poly_sin_pi_series(v, ba, 2, prec); else acb_poly_sin_pi_series(v, cab, 2, prec); acb_poly_get_coeff_acb(tt, t, 1); acb_poly_get_coeff_acb(res, v, 1); acb_div(res, tt, res, prec); acb_const_pi(tt, prec); acb_mul(res, res, tt, prec); acb_poly_clear(ba); acb_poly_clear(ca); acb_poly_clear(cb); acb_poly_clear(cab); acb_poly_clear(ac1); acb_poly_clear(bc1); acb_poly_clear(ab1); acb_poly_clear(ba1); acb_poly_clear(w); acb_poly_clear(t); acb_poly_clear(u); acb_poly_clear(v); acb_poly_clear(s); acb_clear(tt); }
void acb_hypgeom_u_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, long prec) { if (acb_is_int(b)) { acb_poly_t aa, bb, zz; acb_poly_init(aa); acb_poly_init(bb); acb_poly_init(zz); acb_poly_set_acb(aa, a); acb_poly_set_coeff_acb(bb, 0, b); acb_poly_set_coeff_si(bb, 1, 1); acb_poly_set_acb(zz, z); acb_hypgeom_u_1f1_series(zz, aa, bb, zz, 1, prec); acb_poly_get_coeff_acb(res, zz, 0); acb_poly_clear(aa); acb_poly_clear(bb); acb_poly_clear(zz); } else { acb_t t, u, v; acb_struct aa[3]; acb_init(t); acb_init(u); acb_init(v); acb_init(aa + 0); acb_init(aa + 1); acb_init(aa + 2); acb_set(aa, a); acb_set(aa + 1, b); acb_one(aa + 2); acb_hypgeom_pfq_direct(u, aa, 1, aa + 1, 2, z, -1, prec); acb_sub(aa, a, b, prec); acb_add_ui(aa, aa, 1, prec); acb_sub_ui(aa + 1, b, 2, prec); acb_neg(aa + 1, aa + 1); acb_hypgeom_pfq_direct(v, aa, 1, aa + 1, 2, z, -1, prec); acb_sub_ui(aa + 1, b, 1, prec); /* rgamma(a-b+1) * gamma(1-b) * u */ acb_rgamma(t, aa, prec); acb_mul(u, u, t, prec); acb_neg(t, aa + 1); acb_gamma(t, t, prec); acb_mul(u, u, t, prec); /* rgamma(a) * gamma(b-1) * z^(1-b) * v */ acb_rgamma(t, a, prec); acb_mul(v, v, t, prec); acb_gamma(t, aa + 1, prec); acb_mul(v, v, t, prec); acb_neg(t, aa + 1); acb_pow(t, z, t, prec); acb_mul(v, v, t, prec); acb_add(res, u, v, prec); acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(aa + 0); acb_clear(aa + 1); acb_clear(aa + 2); } }