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annotate libquadmath/math/catanq.c @ 158:494b0b89df80 default tip

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Mon, 25 May 2020 18:13:55 +0900
parents 1830386684a0
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 /* Return arc tangent of 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 catanq (__complex128 x)
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24 {
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25 __complex128 res;
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26 int rcls = fpclassifyq (__real__ x);
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27 int icls = fpclassifyq (__imag__ x);
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28
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29 if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
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30 {
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31 if (rcls == QUADFP_INFINITE)
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32 {
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33 __real__ res = copysignq (M_PI_2q, __real__ x);
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34 __imag__ res = copysignq (0, __imag__ x);
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35 }
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36 else if (icls == QUADFP_INFINITE)
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37 {
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38 if (rcls >= QUADFP_ZERO)
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39 __real__ res = copysignq (M_PI_2q, __real__ x);
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40 else
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41 __real__ res = nanq ("");
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42 __imag__ res = copysignq (0, __imag__ x);
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43 }
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44 else if (icls == QUADFP_ZERO || icls == QUADFP_INFINITE)
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45 {
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46 __real__ res = nanq ("");
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47 __imag__ res = copysignq (0, __imag__ x);
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48 }
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49 else
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50 {
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51 __real__ res = nanq ("");
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52 __imag__ res = nanq ("");
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53 }
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54 }
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55 else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
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56 {
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57 res = x;
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58 }
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59 else
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60 {
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61 if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
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62 || fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
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63 {
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64 __real__ res = copysignq (M_PI_2q, __real__ x);
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65 if (fabsq (__real__ x) <= 1)
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66 __imag__ res = 1 / __imag__ x;
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67 else if (fabsq (__imag__ x) <= 1)
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68 __imag__ res = __imag__ x / __real__ x / __real__ x;
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69 else
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70 {
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71 __float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
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72 __imag__ res = __imag__ x / h / h / 4;
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73 }
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74 }
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75 else
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76 {
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77 __float128 den, absx, absy;
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78
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79 absx = fabsq (__real__ x);
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80 absy = fabsq (__imag__ x);
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81 if (absx < absy)
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82 {
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83 __float128 t = absx;
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84 absx = absy;
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85 absy = t;
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86 }
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87
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88 if (absy < FLT128_EPSILON / 2)
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89 {
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90 den = (1 - absx) * (1 + absx);
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91 if (den == 0)
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92 den = 0;
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93 }
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94 else if (absx >= 1)
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95 den = (1 - absx) * (1 + absx) - absy * absy;
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96 else if (absx >= 0.75Q || absy >= 0.5Q)
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97 den = -__quadmath_x2y2m1q (absx, absy);
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98 else
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99 den = (1 - absx) * (1 + absx) - absy * absy;
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100
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101 __real__ res = 0.5Q * atan2q (2 * __real__ x, den);
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102
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103 if (fabsq (__imag__ x) == 1
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104 && fabsq (__real__ x) < FLT128_EPSILON * FLT128_EPSILON)
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105 __imag__ res = (copysignq (0.5Q, __imag__ x)
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106 * ((__float128) M_LN2q
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107 - logq (fabsq (__real__ x))));
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108 else
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109 {
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110 __float128 r2 = 0, num, f;
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111
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112 if (fabsq (__real__ x) >= FLT128_EPSILON * FLT128_EPSILON)
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113 r2 = __real__ x * __real__ x;
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114
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115 num = __imag__ x + 1;
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116 num = r2 + num * num;
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117
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118 den = __imag__ x - 1;
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119 den = r2 + den * den;
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120
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121 f = num / den;
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122 if (f < 0.5Q)
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123 __imag__ res = 0.25Q * logq (f);
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124 else
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125 {
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126 num = 4 * __imag__ x;
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127 __imag__ res = 0.25Q * log1pq (num / den);
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128 }
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129 }
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130 }
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131
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132 math_check_force_underflow_complex (res);
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133 }
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134
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135 return res;
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136 }