/* Copyright (C) 2015 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 . */ #include "arb_hypgeom.h" #include "acb_hypgeom.h" void acb_hypgeom_ci_asymp(acb_t res, const acb_t z, slong prec) { acb_t t, u, w, v, one; acb_init(t); acb_init(u); acb_init(w); acb_init(v); acb_init(one); acb_one(one); acb_mul_onei(w, z); /* u = U(1,1,iz) */ acb_hypgeom_u_asymp(u, one, one, w, -1, prec); /* v = e^(-iz) */ acb_neg(v, w); acb_exp(v, v, prec); acb_mul(t, u, v, prec); if (acb_is_real(z)) { arb_div(acb_realref(t), acb_imagref(t), acb_realref(z), prec); arb_zero(acb_imagref(t)); acb_neg(t, t); } else { /* u = U(1,1,-iz) */ acb_neg(w, w); acb_hypgeom_u_asymp(u, one, one, w, -1, prec); acb_inv(v, v, prec); acb_submul(t, u, v, prec); acb_div(t, t, w, prec); acb_mul_2exp_si(t, t, -1); } if (arb_is_zero(acb_realref(z))) { if (arb_is_positive(acb_imagref(z))) { arb_const_pi(acb_imagref(t), prec); arb_mul_2exp_si(acb_imagref(t), acb_imagref(t), -1); } else if (arb_is_negative(acb_imagref(z))) { arb_const_pi(acb_imagref(t), prec); arb_mul_2exp_si(acb_imagref(t), acb_imagref(t), -1); arb_neg(acb_imagref(t), acb_imagref(t)); } else { acb_const_pi(u, prec); acb_mul_2exp_si(u, u, -1); arb_zero(acb_imagref(t)); arb_add_error(acb_imagref(t), acb_realref(u)); } } else { /* 0 if positive or positive imaginary pi if upper left quadrant (including negative real axis) -pi if lower left quadrant (including negative imaginary axis) */ if (arb_is_positive(acb_realref(z))) { /* do nothing */ } else if (arb_is_negative(acb_realref(z)) && arb_is_nonnegative(acb_imagref(z))) { acb_const_pi(u, prec); arb_add(acb_imagref(t), acb_imagref(t), acb_realref(u), prec); } else if (arb_is_nonpositive(acb_realref(z)) && arb_is_negative(acb_imagref(z))) { acb_const_pi(u, prec); arb_sub(acb_imagref(t), acb_imagref(t), acb_realref(u), prec); } else { /* add [-pi,pi] */ acb_const_pi(u, prec); arb_add_error(acb_imagref(t), acb_realref(u)); } } acb_swap(res, t); acb_clear(t); acb_clear(u); acb_clear(w); acb_clear(v); acb_clear(one); } void acb_hypgeom_ci_2f3(acb_t res, const acb_t z, slong prec) { acb_t a, t, u; acb_struct b[3]; acb_init(a); acb_init(b); acb_init(b + 1); acb_init(b + 2); acb_init(t); acb_init(u); acb_one(a); acb_set_ui(b, 2); acb_set(b + 1, b); acb_set_ui(b + 2, 3); acb_mul_2exp_si(b + 2, b + 2, -1); acb_mul(t, z, z, prec); acb_mul_2exp_si(t, t, -2); acb_neg(t, t); acb_hypgeom_pfq_direct(u, a, 1, b, 3, t, -1, prec); acb_mul(u, u, t, prec); acb_log(t, z, prec); acb_add(u, u, t, prec); arb_const_euler(acb_realref(t), prec); arb_add(acb_realref(u), acb_realref(u), acb_realref(t), prec); acb_swap(res, u); acb_clear(a); acb_clear(b); acb_clear(b + 1); acb_clear(b + 2); acb_clear(t); acb_clear(u); } void acb_hypgeom_ci(acb_t res, const acb_t z, slong prec) { if (acb_is_real(z) && arb_is_finite(acb_realref(z))) { if (arb_is_positive(acb_realref(z))) { arb_hypgeom_ci(acb_realref(res), acb_realref(z), prec); arb_zero(acb_imagref(res)); } else if (arb_is_negative(acb_realref(z))) { arb_neg(acb_realref(res), acb_realref(z)); arb_hypgeom_ci(acb_realref(res), acb_realref(res), prec); arb_const_pi(acb_imagref(res), prec); } else { acb_indeterminate(res); } return; } if (acb_hypgeom_u_use_asymp(z, prec)) acb_hypgeom_ci_asymp(res, z, prec); else acb_hypgeom_ci_2f3(res, z, prec); }