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