1 /* Complex hyperbolic tangent for float types. 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 ctanhq (__complex128 x) 24 { 25 __complex128 res; 26 27 if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x))) 28 { 29 if (isinfq (__real__ x)) 30 { 31 __real__ res = copysignq (1, __real__ x); 32 if (finiteq (__imag__ x) && fabsq (__imag__ x) > 1) 33 { 34 __float128 sinix, cosix; 35 sincosq (__imag__ x, &sinix, &cosix); 36 __imag__ res = copysignq (0, sinix * cosix); 37 } 38 else 39 __imag__ res = copysignq (0, __imag__ x); 40 } 41 else if (__imag__ x == 0) 42 { 43 res = x; 44 } 45 else 46 { 47 if (__real__ x == 0) 48 __real__ res = __real__ x; 49 else 50 __real__ res = nanq (""); 51 __imag__ res = nanq (""); 52 53 if (isinfq (__imag__ x)) 54 feraiseexcept (FE_INVALID); 55 } 56 } 57 else 58 { 59 __float128 sinix, cosix; 60 __float128 den; 61 const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2); 62 63 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y)) 64 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */ 65 66 if (__glibc_likely (fabsq (__imag__ x) > FLT128_MIN)) 67 { 68 sincosq (__imag__ x, &sinix, &cosix); 69 } 70 else 71 { 72 sinix = __imag__ x; 73 cosix = 1; 74 } 75 76 if (fabsq (__real__ x) > t) 77 { 78 /* Avoid intermediate overflow when the imaginary part of 79 the result may be subnormal. Ignoring negligible terms, 80 the real part is +/- 1, the imaginary part is 81 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ 82 __float128 exp_2t = expq (2 * t); 83 84 __real__ res = copysignq (1, __real__ x); 85 __imag__ res = 4 * sinix * cosix; 86 __real__ x = fabsq (__real__ x); 87 __real__ x -= t; 88 __imag__ res /= exp_2t; 89 if (__real__ x > t) 90 { 91 /* Underflow (original real part of x has absolute value 92 > 2t). */ 93 __imag__ res /= exp_2t; 94 } 95 else 96 __imag__ res /= expq (2 * __real__ x); 97 } 98 else 99 { 100 __float128 sinhrx, coshrx; 101 if (fabsq (__real__ x) > FLT128_MIN) 102 { 103 sinhrx = sinhq (__real__ x); 104 coshrx = coshq (__real__ x); 105 } 106 else 107 { 108 sinhrx = __real__ x; 109 coshrx = 1; 110 } 111 112 if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON) 113 den = sinhrx * sinhrx + cosix * cosix; 114 else 115 den = cosix * cosix; 116 __real__ res = sinhrx * coshrx / den; 117 __imag__ res = sinix * cosix / den; 118 } 119 math_check_force_underflow_complex (res); 120 } 121 122 return res; 123 } 124