1/* Return arc tangent of complex float type. 2 Copyright (C) 1997-2018 Free Software Foundation, Inc. 3 This file is part of the GNU C Library. 4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. 5 6 The GNU C Library is free software; you can redistribute it and/or 7 modify it under the terms of the GNU Lesser General Public 8 License as published by the Free Software Foundation; either 9 version 2.1 of the License, or (at your option) any later version. 10 11 The GNU C Library is distributed in the hope that it will be useful, 12 but WITHOUT ANY WARRANTY; without even the implied warranty of 13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 14 Lesser General Public License for more details. 15 16 You should have received a copy of the GNU Lesser General Public 17 License along with the GNU C Library; if not, see 18 <http://www.gnu.org/licenses/>. */ 19 20#include "quadmath-imp.h" 21 22__complex128 23catanq (__complex128 x) 24{ 25 __complex128 res; 26 int rcls = fpclassifyq (__real__ x); 27 int icls = fpclassifyq (__imag__ x); 28 29 if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE)) 30 { 31 if (rcls == QUADFP_INFINITE) 32 { 33 __real__ res = copysignq (M_PI_2q, __real__ x); 34 __imag__ res = copysignq (0, __imag__ x); 35 } 36 else if (icls == QUADFP_INFINITE) 37 { 38 if (rcls >= QUADFP_ZERO) 39 __real__ res = copysignq (M_PI_2q, __real__ x); 40 else 41 __real__ res = nanq (""); 42 __imag__ res = copysignq (0, __imag__ x); 43 } 44 else if (icls == QUADFP_ZERO || icls == QUADFP_INFINITE) 45 { 46 __real__ res = nanq (""); 47 __imag__ res = copysignq (0, __imag__ x); 48 } 49 else 50 { 51 __real__ res = nanq (""); 52 __imag__ res = nanq (""); 53 } 54 } 55 else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)) 56 { 57 res = x; 58 } 59 else 60 { 61 if (fabsq (__real__ x) >= 16 / FLT128_EPSILON 62 || fabsq (__imag__ x) >= 16 / FLT128_EPSILON) 63 { 64 __real__ res = copysignq (M_PI_2q, __real__ x); 65 if (fabsq (__real__ x) <= 1) 66 __imag__ res = 1 / __imag__ x; 67 else if (fabsq (__imag__ x) <= 1) 68 __imag__ res = __imag__ x / __real__ x / __real__ x; 69 else 70 { 71 __float128 h = hypotq (__real__ x / 2, __imag__ x / 2); 72 __imag__ res = __imag__ x / h / h / 4; 73 } 74 } 75 else 76 { 77 __float128 den, absx, absy; 78 79 absx = fabsq (__real__ x); 80 absy = fabsq (__imag__ x); 81 if (absx < absy) 82 { 83 __float128 t = absx; 84 absx = absy; 85 absy = t; 86 } 87 88 if (absy < FLT128_EPSILON / 2) 89 { 90 den = (1 - absx) * (1 + absx); 91 if (den == 0) 92 den = 0; 93 } 94 else if (absx >= 1) 95 den = (1 - absx) * (1 + absx) - absy * absy; 96 else if (absx >= 0.75Q || absy >= 0.5Q) 97 den = -__quadmath_x2y2m1q (absx, absy); 98 else 99 den = (1 - absx) * (1 + absx) - absy * absy; 100 101 __real__ res = 0.5Q * atan2q (2 * __real__ x, den); 102 103 if (fabsq (__imag__ x) == 1 104 && fabsq (__real__ x) < FLT128_EPSILON * FLT128_EPSILON) 105 __imag__ res = (copysignq (0.5Q, __imag__ x) 106 * ((__float128) M_LN2q 107 - logq (fabsq (__real__ x)))); 108 else 109 { 110 __float128 r2 = 0, num, f; 111 112 if (fabsq (__real__ x) >= FLT128_EPSILON * FLT128_EPSILON) 113 r2 = __real__ x * __real__ x; 114 115 num = __imag__ x + 1; 116 num = r2 + num * num; 117 118 den = __imag__ x - 1; 119 den = r2 + den * den; 120 121 f = num / den; 122 if (f < 0.5Q) 123 __imag__ res = 0.25Q * logq (f); 124 else 125 { 126 num = 4 * __imag__ x; 127 __imag__ res = 0.25Q * log1pq (num / den); 128 } 129 } 130 } 131 132 math_check_force_underflow_complex (res); 133 } 134 135 return res; 136} 137