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comparison src/mingw-w64-complex-inverse-trig.patch @ 6356:6f3c099c0d38

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mingw-w64: Use approximations for casinh if real part is small (bug #62332). * src/mingw-w64-complex-inverse-trig.patch: Use approximations for casinh if real part of input is small and the absolute imaginary part is smaller than 1.
author Markus Mützel <markus.muetzel@gmx.de>
date Sun, 07 Aug 2022 20:09:23 +0200
parents 9d1395334e68
children dc5ad8056086
comparison
equal deleted inserted replaced
6355:947f8511e9d1 6356:6f3c099c0d38
118 118
119 return ret; 119 return ret;
120 -- 120 --
121 2.35.3.windows.1 121 2.35.3.windows.1
122 122
123 From 98d5b204fe689ac35d348a1742723ec561a2c5f7 Mon Sep 17 00:00:00 2001
124 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
125 Date: Sun, 7 Aug 2022 13:21:29 +0200
126 Subject: [PATCH 1/2] casinh: Use symmetries also for default case.
127
128 ---
129 mingw-w64-crt/complex/casinh.def.h | 46 ++++++++++++++++--------------
130 1 file changed, 25 insertions(+), 21 deletions(-)
131
132 diff --git a/mingw-w64-crt/complex/casinh.def.h b/mingw-w64-crt/complex/casinh.def.h
133 index cce2d864e..d309e6392 100644
134 --- a/mingw-w64-crt/complex/casinh.def.h
135 +++ b/mingw-w64-crt/complex/casinh.def.h
136 @@ -89,32 +89,36 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
137
138 /* casinh(z) = log(z + sqrt(z*z + 1)) */
139
140 - if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
141 - || __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
142 + /* Use symmetries to perform the calculation in the first quadrant. */
143 + __FLT_TYPE arz = __FLT_ABI(fabs) (__real__ z);
144 + __FLT_TYPE aiz = __FLT_ABI(fabs) (__imag__ z);
145 +
146 + if (arz >= __FLT_CST(1.0)/__FLT_EPSILON
147 + || aiz >= __FLT_CST(1.0)/__FLT_EPSILON)
148 {
149 /* For large z, z + sqrt(z*z + 1) is approximately 2*z.
150 - Use that approximation to avoid overflow when squaring.
151 - Additionally, use symmetries to perform the calculation in the first
152 - quadrant. */
153 - __real__ x = __FLT_ABI(fabs) (__real__ z);
154 - __imag__ x = __FLT_ABI(fabs) (__imag__ z);
155 - x = __FLT_ABI(clog) (x);
156 - __real__ x += M_LN2;
157 -
158 - /* adjust signs for input quadrant */
159 - __real__ ret = __FLT_ABI(copysign) (__real__ x, __real__ z);
160 - __imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
161 -
162 - return ret;
163 + Use that approximation to avoid overflow when squaring. */
164 + __real__ x = arz;
165 + __imag__ x = aiz;
166 + ret = __FLT_ABI(clog) (x);
167 + __real__ ret += M_LN2;
168 }
169 + else
170 + {
171 + __real__ x = (arz - aiz) * (arz + aiz) + __FLT_CST(1.0);
172 + __imag__ x = __FLT_CST(2.0) * arz * aiz;
173 +
174 + x = __FLT_ABI(csqrt) (x);
175
176 - __real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) + __FLT_CST(1.0);
177 - __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;
178 + __real__ x += arz;
179 + __imag__ x += aiz;
180
181 - x = __FLT_ABI(csqrt) (x);
182 + ret = __FLT_ABI(clog) (x);
183 + }
184
185 - __real__ x += __real__ z;
186 - __imag__ x += __imag__ z;
187 + /* adjust signs for input quadrant */
188 + __real__ ret = __FLT_ABI(copysign) (__real__ ret, __real__ z);
189 + __imag__ ret = __FLT_ABI(copysign) (__imag__ ret, __imag__ z);
190
191 - return __FLT_ABI(clog) (x);
192 + return ret;
193 }
194 --
195 2.35.3.windows.1
196
197 From 099f1cd2d4261573d584aa415f47742fa977c773 Mon Sep 17 00:00:00 2001
198 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
199 Date: Sun, 7 Aug 2022 13:23:02 +0200
200 Subject: [PATCH 2/2] casinh: Use approximation for small real part and
201 absolute imaginary part < 1
202
203 ---
204 mingw-w64-crt/complex/casinh.def.h | 31 ++++++++++++++++++++++++++++++
205 1 file changed, 31 insertions(+)
206
207 From 575a070e3fb360fced10a458e72a298d3071c42e Mon Sep 17 00:00:00 2001
208 From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
209 Date: Sun, 7 Aug 2022 19:05:21 +0200
210 Subject: [PATCH 2/2] casinh: Use approximations for small real part and
211 absolute imaginary part < 1
212
213 ---
214 mingw-w64-crt/complex/casinh.def.h | 31 ++++++++++++++++++++++++++++++
215 1 file changed, 31 insertions(+)
216
217 diff --git a/mingw-w64-crt/complex/casinh.def.h b/mingw-w64-crt/complex/casinh.def.h
218 index d309e6392..a5447bfcd 100644
219 --- a/mingw-w64-crt/complex/casinh.def.h
220 +++ b/mingw-w64-crt/complex/casinh.def.h
221 @@ -103,6 +103,37 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
222 ret = __FLT_ABI(clog) (x);
223 __real__ ret += M_LN2;
224 }
225 + else if (arz*arz <= __FLT_EPSILON && aiz < __FLT_CST(1.0))
226 + {
227 + /* Taylor series expansion around arz=0 for z + sqrt(z*z + 1):
228 + 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)
229 + Identity: clog(c) = log(|c|) + i*arg(c)
230 + For real part of result:
231 + |c| = 1 + arz / sqrt(1-aiz^2) + arz^2/(2*(1-aiz^2)) + O(arz^3) (Taylor series expansion)
232 + For imaginary part of result:
233 + 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)
234 + */
235 + __FLT_TYPE onemaiz2 = (__FLT_CST(1.0)+aiz)*(__FLT_CST(1.0)-aiz);
236 + __FLT_TYPE s1maiz2 = __FLT_ABI(sqrt) (onemaiz2);
237 + __FLT_TYPE arz2red = arz * arz / __FLT_CST(2.0) / s1maiz2;
238 + __real__ ret = __FLT_ABI(log1p) ((arz + arz2red) / s1maiz2);
239 + __imag__ ret = __FLT_ABI(atan2) (aiz * (s1maiz2 + arz),
240 + onemaiz2 + arz*s1maiz2 + arz2red);
241 + }
242 + else if (arz <= __FLT_EPSILON && aiz < __FLT_CST(1.0))
243 + {
244 + /* Taylor series expansion around arz=0 for z + sqrt(z*z + 1):
245 + c = arz + sqrt(1-aiz^2) + i*(aiz + arz*aiz / sqrt(1-aiz^2)) + O(arz^2)
246 + Identity: clog(c) = log(|c|) + i*arg(c)
247 + For real part of result:
248 + |c| = 1 + arz / sqrt(1-aiz^2) + O(arz^2) (Taylor series expansion)
249 + For imaginary part of result:
250 + c = (arz + sqrt(1-aiz^2))/sqrt(1-aiz^2) * (sqrt(1-aiz^2) + i*aiz) + O(arz^6)
251 + */
252 + __FLT_TYPE s1maiz2 = __FLT_ABI(sqrt) ((__FLT_CST(1.0)+aiz)*(__FLT_CST(1.0)-aiz));
253 + __real__ ret = __FLT_ABI(log1p) (arz / s1maiz2);
254 + __imag__ ret = __FLT_ABI(atan2) (aiz, s1maiz2);
255 + }
256 else
257 {
258 __real__ x = (arz - aiz) * (arz + aiz) + __FLT_CST(1.0);
259 --
260 2.35.3.windows.1
261