1 /* Return arc hyperbolic tangent for a 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 23 catanhq (__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 (icls == QUADFP_INFINITE) 32 { 33 __real__ res = copysignq (0, __real__ x); 34 __imag__ res = copysignq (M_PI_2q, __imag__ x); 35 } 36 else if (rcls == QUADFP_INFINITE || rcls == QUADFP_ZERO) 37 { 38 __real__ res = copysignq (0, __real__ x); 39 if (icls >= QUADFP_ZERO) 40 __imag__ res = copysignq (M_PI_2q, __imag__ x); 41 else 42 __imag__ res = nanq (""); 43 } 44 else 45 { 46 __real__ res = nanq (""); 47 __imag__ res = nanq (""); 48 } 49 } 50 else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)) 51 { 52 res = x; 53 } 54 else 55 { 56 if (fabsq (__real__ x) >= 16 / FLT128_EPSILON 57 || fabsq (__imag__ x) >= 16 / FLT128_EPSILON) 58 { 59 __imag__ res = copysignq (M_PI_2q, __imag__ x); 60 if (fabsq (__imag__ x) <= 1) 61 __real__ res = 1 / __real__ x; 62 else if (fabsq (__real__ x) <= 1) 63 __real__ res = __real__ x / __imag__ x / __imag__ x; 64 else 65 { 66 __float128 h = hypotq (__real__ x / 2, __imag__ x / 2); 67 __real__ res = __real__ x / h / h / 4; 68 } 69 } 70 else 71 { 72 if (fabsq (__real__ x) == 1 73 && fabsq (__imag__ x) < FLT128_EPSILON * FLT128_EPSILON) 74 __real__ res = (copysignq (0.5Q, __real__ x) 75 * ((__float128) M_LN2q 76 - logq (fabsq (__imag__ x)))); 77 else 78 { 79 __float128 i2 = 0; 80 if (fabsq (__imag__ x) >= FLT128_EPSILON * FLT128_EPSILON) 81 i2 = __imag__ x * __imag__ x; 82 83 __float128 num = 1 + __real__ x; 84 num = i2 + num * num; 85 86 __float128 den = 1 - __real__ x; 87 den = i2 + den * den; 88 89 __float128 f = num / den; 90 if (f < 0.5Q) 91 __real__ res = 0.25Q * logq (f); 92 else 93 { 94 num = 4 * __real__ x; 95 __real__ res = 0.25Q * log1pq (num / den); 96 } 97 } 98 99 __float128 absx, absy, den; 100 101 absx = fabsq (__real__ x); 102 absy = fabsq (__imag__ x); 103 if (absx < absy) 104 { 105 __float128 t = absx; 106 absx = absy; 107 absy = t; 108 } 109 110 if (absy < FLT128_EPSILON / 2) 111 { 112 den = (1 - absx) * (1 + absx); 113 if (den == 0) 114 den = 0; 115 } 116 else if (absx >= 1) 117 den = (1 - absx) * (1 + absx) - absy * absy; 118 else if (absx >= 0.75Q || absy >= 0.5Q) 119 den = -__quadmath_x2y2m1q (absx, absy); 120 else 121 den = (1 - absx) * (1 + absx) - absy * absy; 122 123 __imag__ res = 0.5Q * atan2q (2 * __imag__ x, den); 124 } 125 126 math_check_force_underflow_complex (res); 127 } 128 129 return res; 130 } 131