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1 /* Complex hyperbole tangent for __float128.
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2 Copyright (C) 1997-2012 Free Software Foundation, Inc.
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3 This file is part of the GNU C Library.
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4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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5
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6 The GNU C Library is free software; you can redistribute it and/or
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7 modify it under the terms of the GNU Lesser General Public
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8 License as published by the Free Software Foundation; either
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9 version 2.1 of the License, or (at your option) any later version.
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10
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11 The GNU C Library is distributed in the hope that it will be useful,
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12 but WITHOUT ANY WARRANTY; without even the implied warranty of
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13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 Lesser General Public License for more details.
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15
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16 You should have received a copy of the GNU Lesser General Public
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17 License along with the GNU C Library; if not, see
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18 <http://www.gnu.org/licenses/>. */
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19
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20 #include "quadmath-imp.h"
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21
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22 #ifdef HAVE_FENV_H
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23 # include <fenv.h>
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24 #endif
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25
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26
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27 __complex128
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28 ctanhq (__complex128 x)
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29 {
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30 __complex128 res;
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31
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32 if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
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33 {
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34 if (__quadmath_isinf_nsq (__real__ x))
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35 {
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36 __real__ res = copysignq (1.0Q, __real__ x);
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37 __imag__ res = copysignq (0.0Q, __imag__ x);
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38 }
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39 else if (__imag__ x == 0.0Q)
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40 {
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41 res = x;
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42 }
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43 else
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44 {
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45 __real__ res = nanq ("");
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46 __imag__ res = nanq ("");
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47
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48 #ifdef HAVE_FENV_H
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49 if (__quadmath_isinf_nsq (__imag__ x))
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50 feraiseexcept (FE_INVALID);
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51 #endif
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52 }
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53 }
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54 else
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55 {
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56 __float128 sinix, cosix;
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57 __float128 den;
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58 const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
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59 int icls = fpclassifyq (__imag__ x);
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60
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61 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
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62 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
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63
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64 if (__builtin_expect (icls != QUADFP_SUBNORMAL, 1))
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65 {
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66 sincosq (__imag__ x, &sinix, &cosix);
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67 }
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68 else
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69 {
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70 sinix = __imag__ x;
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71 cosix = 1.0Q;
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72 }
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73
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74 if (fabsq (__real__ x) > t)
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75 {
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76 /* Avoid intermediate overflow when the imaginary part of
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77 the result may be subnormal. Ignoring negligible terms,
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78 the real part is +/- 1, the imaginary part is
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79 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
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80 __float128 exp_2t = expq (2 * t);
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81
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82 __real__ res = copysignq (1.0, __real__ x);
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83 __imag__ res = 4 * sinix * cosix;
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84 __real__ x = fabsq (__real__ x);
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85 __real__ x -= t;
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86 __imag__ res /= exp_2t;
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87 if (__real__ x > t)
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88 {
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89 /* Underflow (original real part of x has absolute value
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90 > 2t). */
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91 __imag__ res /= exp_2t;
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92 }
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93 else
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94 __imag__ res /= expq (2 * __real__ x);
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95 }
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96 else
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97 {
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98 __float128 sinhrx, coshrx;
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99 if (fabsq (__real__ x) > FLT128_MIN)
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100 {
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101 sinhrx = sinhq (__real__ x);
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102 coshrx = coshq (__real__ x);
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103 }
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104 else
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105 {
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106 sinhrx = __real__ x;
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107 coshrx = 1.0Q;
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108 }
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109
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110 if (fabsq (sinhrx) > fabsq (cosix) * FLT128_EPSILON)
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111 den = sinhrx * sinhrx + cosix * cosix;
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112 else
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113 den = cosix * cosix;
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114 __real__ res = sinhrx * coshrx / den;
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115 __imag__ res = sinix * cosix / den;
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116 }
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117 }
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118
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119 return res;
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120 }
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