| lh | 9ed821d | 2023-04-07 01:36:19 -0700 | [diff] [blame^] | 1 | /* Complex tangent function for double. |
| 2 | Copyright (C) 1997-2015 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 <complex.h> |
| 21 | #include <fenv.h> |
| 22 | #include <math.h> |
| 23 | #include <math_private.h> |
| 24 | #include <float.h> |
| 25 | |
| 26 | __complex__ double |
| 27 | __ctan (__complex__ double x) |
| 28 | { |
| 29 | __complex__ double res; |
| 30 | |
| 31 | if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) |
| 32 | { |
| 33 | if (__isinf_ns (__imag__ x)) |
| 34 | { |
| 35 | __real__ res = __copysign (0.0, __real__ x); |
| 36 | __imag__ res = __copysign (1.0, __imag__ x); |
| 37 | } |
| 38 | else if (__real__ x == 0.0) |
| 39 | { |
| 40 | res = x; |
| 41 | } |
| 42 | else |
| 43 | { |
| 44 | __real__ res = __nan (""); |
| 45 | __imag__ res = __nan (""); |
| 46 | |
| 47 | if (__isinf_ns (__real__ x)) |
| 48 | feraiseexcept (FE_INVALID); |
| 49 | } |
| 50 | } |
| 51 | else |
| 52 | { |
| 53 | double sinrx, cosrx; |
| 54 | double den; |
| 55 | const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); |
| 56 | |
| 57 | /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) |
| 58 | = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ |
| 59 | |
| 60 | if (__glibc_likely (fabs (__real__ x) > DBL_MIN)) |
| 61 | { |
| 62 | __sincos (__real__ x, &sinrx, &cosrx); |
| 63 | } |
| 64 | else |
| 65 | { |
| 66 | sinrx = __real__ x; |
| 67 | cosrx = 1.0; |
| 68 | } |
| 69 | |
| 70 | if (fabs (__imag__ x) > t) |
| 71 | { |
| 72 | /* Avoid intermediate overflow when the real part of the |
| 73 | result may be subnormal. Ignoring negligible terms, the |
| 74 | imaginary part is +/- 1, the real part is |
| 75 | sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ |
| 76 | double exp_2t = __ieee754_exp (2 * t); |
| 77 | |
| 78 | __imag__ res = __copysign (1.0, __imag__ x); |
| 79 | __real__ res = 4 * sinrx * cosrx; |
| 80 | __imag__ x = fabs (__imag__ x); |
| 81 | __imag__ x -= t; |
| 82 | __real__ res /= exp_2t; |
| 83 | if (__imag__ x > t) |
| 84 | { |
| 85 | /* Underflow (original imaginary part of x has absolute |
| 86 | value > 2t). */ |
| 87 | __real__ res /= exp_2t; |
| 88 | } |
| 89 | else |
| 90 | __real__ res /= __ieee754_exp (2 * __imag__ x); |
| 91 | } |
| 92 | else |
| 93 | { |
| 94 | double sinhix, coshix; |
| 95 | if (fabs (__imag__ x) > DBL_MIN) |
| 96 | { |
| 97 | sinhix = __ieee754_sinh (__imag__ x); |
| 98 | coshix = __ieee754_cosh (__imag__ x); |
| 99 | } |
| 100 | else |
| 101 | { |
| 102 | sinhix = __imag__ x; |
| 103 | coshix = 1.0; |
| 104 | } |
| 105 | |
| 106 | if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON) |
| 107 | den = cosrx * cosrx + sinhix * sinhix; |
| 108 | else |
| 109 | den = cosrx * cosrx; |
| 110 | __real__ res = sinrx * cosrx / den; |
| 111 | __imag__ res = sinhix * coshix / den; |
| 112 | } |
| 113 | } |
| 114 | |
| 115 | return res; |
| 116 | } |
| 117 | weak_alias (__ctan, ctan) |
| 118 | #ifdef NO_LONG_DOUBLE |
| 119 | strong_alias (__ctan, __ctanl) |
| 120 | weak_alias (__ctan, ctanl) |
| 121 | #endif |