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1 /* Complex tangent function for a complex float type.
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2 Copyright (C) 1997-2018 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 __complex128
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23 ctanq (__complex128 x)
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24 {
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25 __complex128 res;
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26
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27 if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
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28 {
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29 if (isinfq (__imag__ x))
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30 {
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31 if (finiteq (__real__ x) && fabsq (__real__ x) > 1)
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32 {
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33 __float128 sinrx, cosrx;
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34 sincosq (__real__ x, &sinrx, &cosrx);
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35 __real__ res = copysignq (0, sinrx * cosrx);
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36 }
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37 else
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38 __real__ res = copysignq (0, __real__ x);
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39 __imag__ res = copysignq (1, __imag__ x);
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40 }
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41 else if (__real__ x == 0)
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42 {
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43 res = x;
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44 }
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45 else
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46 {
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47 __real__ res = nanq ("");
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48 if (__imag__ x == 0)
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49 __imag__ res = __imag__ x;
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50 else
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51 __imag__ res = nanq ("");
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52
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53 if (isinfq (__real__ x))
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54 feraiseexcept (FE_INVALID);
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55 }
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56 }
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57 else
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58 {
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59 __float128 sinrx, cosrx;
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60 __float128 den;
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61 const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
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62
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63 /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
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64 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
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65
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66 if (__glibc_likely (fabsq (__real__ x) > FLT128_MIN))
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67 {
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68 sincosq (__real__ x, &sinrx, &cosrx);
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69 }
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70 else
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71 {
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72 sinrx = __real__ x;
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73 cosrx = 1;
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74 }
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75
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76 if (fabsq (__imag__ x) > t)
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77 {
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78 /* Avoid intermediate overflow when the real part of the
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79 result may be subnormal. Ignoring negligible terms, the
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80 imaginary part is +/- 1, the real part is
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81 sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
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82 __float128 exp_2t = expq (2 * t);
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83
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84 __imag__ res = copysignq (1, __imag__ x);
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85 __real__ res = 4 * sinrx * cosrx;
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86 __imag__ x = fabsq (__imag__ x);
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87 __imag__ x -= t;
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88 __real__ res /= exp_2t;
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89 if (__imag__ x > t)
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90 {
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91 /* Underflow (original imaginary part of x has absolute
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92 value > 2t). */
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93 __real__ res /= exp_2t;
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94 }
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95 else
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96 __real__ res /= expq (2 * __imag__ x);
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97 }
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98 else
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99 {
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100 __float128 sinhix, coshix;
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101 if (fabsq (__imag__ x) > FLT128_MIN)
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102 {
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103 sinhix = sinhq (__imag__ x);
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104 coshix = coshq (__imag__ x);
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105 }
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106 else
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107 {
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108 sinhix = __imag__ x;
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109 coshix = 1;
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110 }
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112 if (fabsq (sinhix) > fabsq (cosrx) * FLT128_EPSILON)
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113 den = cosrx * cosrx + sinhix * sinhix;
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114 else
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115 den = cosrx * cosrx;
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116 __real__ res = sinrx * cosrx / den;
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117 __imag__ res = sinhix * coshix / den;
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118 }
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119 math_check_force_underflow_complex (res);
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120 }
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121
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122 return res;
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123 }
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