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annotate src/mingw-w64-complex-inverse-trig.patch @ 6388:dbc29160e2b2

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mingw-w64: Update patch with changes applied upstream (bug #49091). * src/mingw-w64-complex-inverse-trig.patch: Use "signbit" macro correctly.
author Markus Mützel <markus.muetzel@gmx.de>
date Sat, 27 Aug 2022 13:05:12 +0200
parents dc5ad8056086
children
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0825abaf61a7 mingw-w64: Special case for large input for complex inverse trigonometric functions (bug #49091).
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1 From 59fd6e6ab7c93545175fa6ff46532b7a80dbdbfb Mon Sep 17 00:00:00 2001
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2 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
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3 Date: Sat, 23 Jul 2022 15:30:46 +0200
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4 Subject: [PATCH 1/2] casinh: Use approximation for large input.
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5
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6 ---
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7 mingw-w64-crt/complex/casinh.def.h | 21 +++++++++++++++++++++
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8 1 file changed, 21 insertions(+)
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9
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10 diff --git a/mingw-w64-crt/complex/casinh.def.h b/mingw-w64-crt/complex/casinh.def.h
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11 index 050d885a0..cce2d864e 100644
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12 --- a/mingw-w64-crt/complex/casinh.def.h
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13 +++ b/mingw-w64-crt/complex/casinh.def.h
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14 @@ -87,6 +87,27 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
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15 if (r_class == FP_ZERO && i_class == FP_ZERO)
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16 return z;
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17
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18 + /* casinh(z) = log(z + sqrt(z*z + 1)) */
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19 +
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20 + if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
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21 + || __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
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22 + {
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23 + /* For large z, z + sqrt(z*z + 1) is approximately 2*z.
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24 + Use that approximation to avoid overflow when squaring.
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25 + Additionally, use symmetries to perform the calculation in the first
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26 + quadrant. */
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27 + __real__ x = __FLT_ABI(fabs) (__real__ z);
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28 + __imag__ x = __FLT_ABI(fabs) (__imag__ z);
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29 + x = __FLT_ABI(clog) (x);
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30 + __real__ x += M_LN2;
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31 +
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32 + /* adjust signs for input quadrant */
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33 + __real__ ret = __FLT_ABI(copysign) (__real__ x, __real__ z);
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34 + __imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
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35 +
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36 + return ret;
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37 + }
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38 +
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39 __real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) + __FLT_CST(1.0);
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40 __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;
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41
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42 --
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43 2.35.3.windows.1
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44
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45 From 4b5a229573ca98a622cc15d20bd561dbaec9bbfc Mon Sep 17 00:00:00 2001
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46 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
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47 Date: Sat, 23 Jul 2022 18:01:29 +0200
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48 Subject: [PATCH 2/2] cacosh: Use approximation for large input.
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49
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50 ---
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51 mingw-w64-crt/complex/cacosh.def.h | 21 +++++++++++++++++++++
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52 1 file changed, 21 insertions(+)
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53
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54 diff --git a/mingw-w64-crt/complex/cacosh.def.h b/mingw-w64-crt/complex/cacosh.def.h
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55 index f4ea2da07..a3edd5288 100644
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56 --- a/mingw-w64-crt/complex/cacosh.def.h
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57 +++ b/mingw-w64-crt/complex/cacosh.def.h
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58 @@ -80,6 +80,27 @@ __FLT_ABI(cacosh) (__FLT_TYPE __complex__ z)
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59 return ret;
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60 }
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61
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62 + /* cacosh(z) = log(z + sqrt(z*z - 1)) */
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63 +
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64 + if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
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65 + || __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
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66 + {
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67 + /* For large z, z + sqrt(z*z - 1) is approximately 2*z.
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68 + Use that approximation to avoid overflow when squaring.
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69 + Additionally, use symmetries to perform the calculation in the positive
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70 + half plane. */
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71 + __real__ x = __real__ z;
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72 + __imag__ x = __FLT_ABI(fabs) (__imag__ z);
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73 + x = __FLT_ABI(clog) (x);
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74 + __real__ x += M_LN2;
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75 +
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76 + /* adjust signs for input */
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77 + __real__ ret = __real__ x;
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78 + __imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
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79 +
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80 + return ret;
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81 + }
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82 +
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83 __real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) - __FLT_CST(1.0);
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84 __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;
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85
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86 --
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87 2.35.3.windows.1
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88
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89 From 9fcac91fc50120a5e6acfa94ba0a917c7faf2306 Mon Sep 17 00:00:00 2001
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90 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
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91 Date: Fri, 5 Aug 2022 18:36:49 +0200
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92 Subject: [PATCH] cacosh: Handle negative zero input
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93
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94 ---
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95 mingw-w64-crt/complex/cacosh.def.h | 4 ++--
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96 1 file changed, 2 insertions(+), 2 deletions(-)
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97
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98 diff --git a/mingw-w64-crt/complex/cacosh.def.h b/mingw-w64-crt/complex/cacosh.def.h
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99 index 1f03befae..addf2958e 100644
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100 --- a/mingw-w64-crt/complex/cacosh.def.h
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101 +++ b/mingw-w64-crt/complex/cacosh.def.h
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102 @@ -106,7 +106,7 @@ __FLT_ABI(cacosh) (__FLT_TYPE __complex__ z)
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103
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104 x = __FLT_ABI(csqrt) (x);
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105
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106 - if (__real__ z < __FLT_CST(0.0))
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107 + if (signbit (__real__ z))
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108 x = -x;
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109
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110 __real__ x += __real__ z;
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111 @@ -114,7 +114,7 @@ __FLT_ABI(cacosh) (__FLT_TYPE __complex__ z)
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112
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113 ret = __FLT_ABI(clog) (x);
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114
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115 - if (__real__ ret < __FLT_CST(0.0))
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116 + if (signbit (__real__ ret))
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117 ret = -ret;
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118
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119 return ret;
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120 --
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121 2.35.3.windows.1
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122
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123 From cddd2eb87270f368d18f79a1070a36e4dc5464eb Mon Sep 17 00:00:00 2001
6356
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124 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
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125 Date: Mon, 8 Aug 2022 18:01:32 +0200
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126 Subject: [PATCH 1/3] casinh: Use symmetries also for default case.
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127
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128 ---
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129 mingw-w64-crt/complex/casinh.def.h | 47 +++++++++++++++++-------------
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130 1 file changed, 26 insertions(+), 21 deletions(-)
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131
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132 diff --git a/mingw-w64-crt/complex/casinh.def.h b/mingw-w64-crt/complex/casinh.def.h
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133 index cce2d864e..40ff67579 100644
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134 --- a/mingw-w64-crt/complex/casinh.def.h
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135 +++ b/mingw-w64-crt/complex/casinh.def.h
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136 @@ -47,6 +47,7 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
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137 {
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138 __complex__ __FLT_TYPE ret;
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139 __complex__ __FLT_TYPE x;
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140 + __FLT_TYPE arz, aiz;
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141 int r_class = fpclassify (__real__ z);
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142 int i_class = fpclassify (__imag__ z);
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143
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144 @@ -89,32 +90,36 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
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145
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146 /* casinh(z) = log(z + sqrt(z*z + 1)) */
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147
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148 - if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
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149 - || __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
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150 + /* Use symmetries to perform the calculation in the first quadrant. */
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151 + arz = __FLT_ABI(fabs) (__real__ z);
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152 + aiz = __FLT_ABI(fabs) (__imag__ z);
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153 +
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154 + if (arz >= __FLT_CST(1.0)/__FLT_EPSILON
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155 + || aiz >= __FLT_CST(1.0)/__FLT_EPSILON)
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156 {
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157 /* For large z, z + sqrt(z*z + 1) is approximately 2*z.
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158 - Use that approximation to avoid overflow when squaring.
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159 - Additionally, use symmetries to perform the calculation in the first
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160 - quadrant. */
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161 - __real__ x = __FLT_ABI(fabs) (__real__ z);
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162 - __imag__ x = __FLT_ABI(fabs) (__imag__ z);
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163 - x = __FLT_ABI(clog) (x);
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164 - __real__ x += M_LN2;
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165 -
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166 - /* adjust signs for input quadrant */
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167 - __real__ ret = __FLT_ABI(copysign) (__real__ x, __real__ z);
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168 - __imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
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169 -
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170 - return ret;
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171 + Use that approximation to avoid overflow when squaring. */
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172 + __real__ x = arz;
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173 + __imag__ x = aiz;
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174 + ret = __FLT_ABI(clog) (x);
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175 + __real__ ret += M_LN2;
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176 }
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177 + else
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178 + {
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179 + __real__ x = (arz - aiz) * (arz + aiz) + __FLT_CST(1.0);
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180 + __imag__ x = __FLT_CST(2.0) * arz * aiz;
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181 +
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182 + x = __FLT_ABI(csqrt) (x);
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183
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184 - __real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) + __FLT_CST(1.0);
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185 - __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;
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186 + __real__ x += arz;
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187 + __imag__ x += aiz;
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188
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189 - x = __FLT_ABI(csqrt) (x);
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190 + ret = __FLT_ABI(clog) (x);
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191 + }
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192
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193 - __real__ x += __real__ z;
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194 - __imag__ x += __imag__ z;
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195 + /* adjust signs for input quadrant */
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196 + __real__ ret = __FLT_ABI(copysign) (__real__ ret, __real__ z);
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197 + __imag__ ret = __FLT_ABI(copysign) (__imag__ ret, __imag__ z);
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198
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199 - return __FLT_ABI(clog) (x);
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200 + return ret;
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201 }
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202 --
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203 2.35.3.windows.1
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204
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205 From f309692d67674526ec9a87ecae527cb6c207cf93 Mon Sep 17 00:00:00 2001
6356
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206 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
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207 Date: Mon, 8 Aug 2022 18:02:40 +0200
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208 Subject: [PATCH 2/3] casinh: Use approximations for small real part and
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209 absolute imaginary part < 1
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210
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211 ---
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212 mingw-w64-crt/complex/casinh.def.h | 31 ++++++++++++++++++++++++++++++
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213 1 file changed, 31 insertions(+)
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214
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215 diff --git a/mingw-w64-crt/complex/casinh.def.h b/mingw-w64-crt/complex/casinh.def.h
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216 index 40ff67579..8d61b1399 100644
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217 --- a/mingw-w64-crt/complex/casinh.def.h
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218 +++ b/mingw-w64-crt/complex/casinh.def.h
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219 @@ -104,6 +104,37 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
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220 ret = __FLT_ABI(clog) (x);
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221 __real__ ret += M_LN2;
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222 }
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223 + else if (arz <= __FLT_EPSILON && aiz < __FLT_CST(1.0))
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224 + {
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225 + /* Taylor series expansion around arz=0 for z + sqrt(z*z + 1):
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226 + c = arz + sqrt(1-aiz^2) + i*(aiz + arz*aiz / sqrt(1-aiz^2)) + O(arz^2)
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227 + Identity: clog(c) = log(|c|) + i*arg(c)
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228 + For real part of result:
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229 + |c| = 1 + arz / sqrt(1-aiz^2) + O(arz^2) (Taylor series expansion)
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230 + For imaginary part of result:
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231 + c = (arz + sqrt(1-aiz^2))/sqrt(1-aiz^2) * (sqrt(1-aiz^2) + i*aiz) + O(arz^6)
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232 + */
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233 + __FLT_TYPE s1maiz2 = __FLT_ABI(sqrt) ((__FLT_CST(1.0)+aiz)*(__FLT_CST(1.0)-aiz));
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234 + __real__ ret = __FLT_ABI(log1p) (arz / s1maiz2);
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235 + __imag__ ret = __FLT_ABI(atan2) (aiz, s1maiz2);
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236 + }
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237 + else if (arz*arz <= __FLT_EPSILON && aiz < __FLT_CST(1.0))
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238 + {
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239 + /* Taylor series expansion around arz=0 for z + sqrt(z*z + 1):
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240 + c = arz + sqrt(1-aiz^2) + arz^2 / (2*(1-aiz^2)^(3/2)) + i*(aiz + arz*aiz / sqrt(1-aiz^2)) + O(arz^4)
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241 + Identity: clog(c) = log(|c|) + i*arg(c)
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242 + For real part of result:
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243 + |c| = 1 + arz / sqrt(1-aiz^2) + arz^2/(2*(1-aiz^2)) + O(arz^3) (Taylor series expansion)
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244 + For imaginary part of result:
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245 + c = 1/sqrt(1-aiz^2) * ((1-aiz^2) + arz*sqrt(1-aiz^2) + arz^2/(2*(1-aiz^2)) + i*aiz*(sqrt(1-aiz^2)+arz)) + O(arz^3)
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246 + */
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247 + __FLT_TYPE onemaiz2 = (__FLT_CST(1.0)+aiz)*(__FLT_CST(1.0)-aiz);
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248 + __FLT_TYPE s1maiz2 = __FLT_ABI(sqrt) (onemaiz2);
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249 + __FLT_TYPE arz2red = arz * arz / __FLT_CST(2.0) / s1maiz2;
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250 + __real__ ret = __FLT_ABI(log1p) ((arz + arz2red) / s1maiz2);
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251 + __imag__ ret = __FLT_ABI(atan2) (aiz * (s1maiz2 + arz),
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252 + onemaiz2 + arz*s1maiz2 + arz2red);
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253 + }
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254 else
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255 {
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256 __real__ x = (arz - aiz) * (arz + aiz) + __FLT_CST(1.0);
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257 --
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258 2.35.3.windows.1
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259
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260 From b2ad7c96b759e8bc3af504018b70c91c8b0f135c Mon Sep 17 00:00:00 2001
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261 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
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262 Date: Mon, 8 Aug 2022 18:03:49 +0200
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263 Subject: [PATCH 3/3] catanh: Use approximations for small real part
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264
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265 ---
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266 mingw-w64-crt/complex/catanh.def.h | 37 +++++++++++++++++++++++++-----
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267 1 file changed, 31 insertions(+), 6 deletions(-)
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268
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269 From 7589dfe1f5478a3ba7b93ea6dc28fc0ffd271f12 Mon Sep 17 00:00:00 2001
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270 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
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271 Date: Mon, 8 Aug 2022 18:26:20 +0200
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272 Subject: [PATCH 3/3] catanh: Use approximations for small real part
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273
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274 ---
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275 mingw-w64-crt/complex/catanh.def.h | 37 +++++++++++++++++++++++++-----
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276 1 file changed, 31 insertions(+), 6 deletions(-)
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277
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278 diff --git a/mingw-w64-crt/complex/catanh.def.h b/mingw-w64-crt/complex/catanh.def.h
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279 index 68949d139..1d46d4dcd 100644
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280 --- a/mingw-w64-crt/complex/catanh.def.h
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281 +++ b/mingw-w64-crt/complex/catanh.def.h
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282 @@ -75,17 +75,42 @@ __FLT_ABI(catanh) (__FLT_TYPE __complex__ z)
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283 if (r_class == FP_ZERO && i_class == FP_ZERO)
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284 return z;
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285
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286 + /* catanh(z) = 1/2 * clog(1+z) - 1/2 * clog(1-z) = 1/2 * clog((1+z)/(1-z)) */
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287 +
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288 + /* Use identity clog(c) = 1/2*log(|c|^2) + i*arg(c) to calculate real and
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289 + imaginary parts separately. */
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290 +
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291 + /* real part */
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292 + /* |c|^2 = (Im(z)^2 + (1+Re(z))^2)/(Im(z)^2 + (1-Re(z))^2) */
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293 i2 = __imag__ z * __imag__ z;
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294
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295 - n = __FLT_CST(1.0) + __real__ z;
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296 - n = i2 + n * n;
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297 + if (__FLT_ABI(fabs) (__real__ z) <= __FLT_EPSILON)
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298 + {
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299 + /* |c|^2 = 1 + 4*Re(z)/(1+Im(z)^2) + O(Re(z)^2) (Taylor series) */
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300 + __real__ ret = __FLT_CST(0.25) *
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301 + __FLT_ABI(log1p) (__FLT_CST(4.0)*(__real__ z) / (__FLT_CST(1.0) + i2));
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302 + }
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303 + else if ((__real__ z)*(__real__ z) <= __FLT_EPSILON)
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304 + {
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305 + /* |c|^2 = 1 + 4*Re(z)/(1+Im(z)^2) + 8*Re(z)^2/(1+Im(z)^2)^2 + O(Re(z)^3) (Taylor series) */
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306 + d = __real__ z / (__FLT_CST(1.0) + i2);
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307 + __real__ ret = __FLT_CST(0.25) *
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308 + __FLT_ABI(log1p) (__FLT_CST(4.0) * d * (__FLT_CST(1.0) + __FLT_CST(2.0) * d));
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309 + }
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310 + else
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311 + {
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312 + n = __FLT_CST(1.0) + __real__ z;
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313 + n = i2 + n * n;
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314
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315 - d = __FLT_CST(1.0) - __real__ z;
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316 - d = i2 + d * d;
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317 + d = __FLT_CST(1.0) - __real__ z;
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318 + d = i2 + d * d;
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319
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320 - __real__ ret = __FLT_CST(0.25) * (__FLT_ABI(log) (n) - __FLT_ABI(log) (d));
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321 + __real__ ret = __FLT_CST(0.25) * (__FLT_ABI(log) (n) - __FLT_ABI(log) (d));
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322 + }
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323
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324 - d = 1 - __real__ z * __real__ z - i2;
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325 + /* imaginary part */
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326 + /* z = (1 - Re(z)^2 - Im(z)^2 + 2i * Im(z) / ((1-Re(z))^2 + Im(z)^2) */
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327 + d = __FLT_CST(1.0) - __real__ z * __real__ z - i2;
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328
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329 __imag__ ret = __FLT_CST(0.5) * __FLT_ABI(atan2) (__FLT_CST(2.0) * __imag__ z, d);
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330
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331 --
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332 2.35.3.windows.1
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333