Mercurial > mxe-octave

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

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
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
line wrap: on
line source

From 59fd6e6ab7c93545175fa6ff46532b7a80dbdbfb Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
Date: Sat, 23 Jul 2022 15:30:46 +0200
Subject: [PATCH 1/2] casinh: Use approximation for large input.

---
 mingw-w64-crt/complex/casinh.def.h | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/mingw-w64-crt/complex/casinh.def.h b/mingw-w64-crt/complex/casinh.def.h
index 050d885a0..cce2d864e 100644
--- a/mingw-w64-crt/complex/casinh.def.h
+++ b/mingw-w64-crt/complex/casinh.def.h
@@ -87,6 +87,27 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
   if (r_class == FP_ZERO && i_class == FP_ZERO)
     return z;
 
+  /* casinh(z) = log(z + sqrt(z*z + 1)) */
+
+  if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
+      || __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
+  {
+    /* For large z, z + sqrt(z*z + 1) is approximately 2*z.
+    Use that approximation to avoid overflow when squaring.
+    Additionally, use symmetries to perform the calculation in the first
+    quadrant. */
+    __real__ x = __FLT_ABI(fabs) (__real__ z);
+    __imag__ x = __FLT_ABI(fabs) (__imag__ z);
+    x = __FLT_ABI(clog) (x);
+    __real__ x += M_LN2;
+
+    /* adjust signs for input quadrant */
+    __real__ ret = __FLT_ABI(copysign) (__real__ x, __real__ z);
+    __imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
+
+    return ret;
+  }
+
   __real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) + __FLT_CST(1.0);
   __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;
 
-- 
2.35.3.windows.1

From 4b5a229573ca98a622cc15d20bd561dbaec9bbfc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
Date: Sat, 23 Jul 2022 18:01:29 +0200
Subject: [PATCH 2/2] cacosh: Use approximation for large input.

---
 mingw-w64-crt/complex/cacosh.def.h | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/mingw-w64-crt/complex/cacosh.def.h b/mingw-w64-crt/complex/cacosh.def.h
index f4ea2da07..a3edd5288 100644
--- a/mingw-w64-crt/complex/cacosh.def.h
+++ b/mingw-w64-crt/complex/cacosh.def.h
@@ -80,6 +80,27 @@ __FLT_ABI(cacosh) (__FLT_TYPE __complex__ z)
     return ret;
   }
 
+  /* cacosh(z) = log(z + sqrt(z*z - 1)) */
+
+  if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
+      || __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
+  {
+    /* For large z, z + sqrt(z*z - 1) is approximately 2*z.
+    Use that approximation to avoid overflow when squaring.
+    Additionally, use symmetries to perform the calculation in the positive
+    half plane. */
+    __real__ x = __real__ z;
+    __imag__ x = __FLT_ABI(fabs) (__imag__ z);
+    x = __FLT_ABI(clog) (x);
+    __real__ x += M_LN2;
+
+    /* adjust signs for input */
+    __real__ ret = __real__ x;
+    __imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
+
+    return ret;
+  }
+
   __real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) - __FLT_CST(1.0);
   __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;
 
-- 
2.35.3.windows.1

From 9fcac91fc50120a5e6acfa94ba0a917c7faf2306 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
Date: Fri, 5 Aug 2022 18:36:49 +0200
Subject: [PATCH] cacosh: Handle negative zero input

---
 mingw-w64-crt/complex/cacosh.def.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/mingw-w64-crt/complex/cacosh.def.h b/mingw-w64-crt/complex/cacosh.def.h
index 1f03befae..addf2958e 100644
--- a/mingw-w64-crt/complex/cacosh.def.h
+++ b/mingw-w64-crt/complex/cacosh.def.h
@@ -106,7 +106,7 @@ __FLT_ABI(cacosh) (__FLT_TYPE __complex__ z)
 
   x = __FLT_ABI(csqrt) (x);
 
-  if (__real__ z < __FLT_CST(0.0))
+  if (signbit (__real__ z))
     x = -x;
 
   __real__ x += __real__ z;
@@ -114,7 +114,7 @@ __FLT_ABI(cacosh) (__FLT_TYPE __complex__ z)
 
   ret = __FLT_ABI(clog) (x);
 
-  if (__real__ ret < __FLT_CST(0.0))
+  if (signbit (__real__ ret))
     ret = -ret;
 
   return ret;
-- 
2.35.3.windows.1

From cddd2eb87270f368d18f79a1070a36e4dc5464eb Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
Date: Mon, 8 Aug 2022 18:01:32 +0200
Subject: [PATCH 1/3] casinh: Use symmetries also for default case.

---
 mingw-w64-crt/complex/casinh.def.h | 47 +++++++++++++++++-------------
 1 file changed, 26 insertions(+), 21 deletions(-)

diff --git a/mingw-w64-crt/complex/casinh.def.h b/mingw-w64-crt/complex/casinh.def.h
index cce2d864e..40ff67579 100644
--- a/mingw-w64-crt/complex/casinh.def.h
+++ b/mingw-w64-crt/complex/casinh.def.h
@@ -47,6 +47,7 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
 {
   __complex__ __FLT_TYPE ret;
   __complex__ __FLT_TYPE x;
+  __FLT_TYPE arz, aiz;
   int r_class = fpclassify (__real__ z);
   int i_class = fpclassify (__imag__ z);
 
@@ -89,32 +90,36 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
 
   /* casinh(z) = log(z + sqrt(z*z + 1)) */
 
-  if (__FLT_ABI(fabs) (__real__ z) >= __FLT_CST(1.0)/__FLT_EPSILON
-      || __FLT_ABI(fabs) (__imag__ z) >= __FLT_CST(1.0)/__FLT_EPSILON)
+  /* Use symmetries to perform the calculation in the first quadrant. */
+  arz = __FLT_ABI(fabs) (__real__ z);
+  aiz = __FLT_ABI(fabs) (__imag__ z);
+
+  if (arz >= __FLT_CST(1.0)/__FLT_EPSILON
+      || aiz >= __FLT_CST(1.0)/__FLT_EPSILON)
   {
     /* For large z, z + sqrt(z*z + 1) is approximately 2*z.
-    Use that approximation to avoid overflow when squaring.
-    Additionally, use symmetries to perform the calculation in the first
-    quadrant. */
-    __real__ x = __FLT_ABI(fabs) (__real__ z);
-    __imag__ x = __FLT_ABI(fabs) (__imag__ z);
-    x = __FLT_ABI(clog) (x);
-    __real__ x += M_LN2;
-
-    /* adjust signs for input quadrant */
-    __real__ ret = __FLT_ABI(copysign) (__real__ x, __real__ z);
-    __imag__ ret = __FLT_ABI(copysign) (__imag__ x, __imag__ z);
-
-    return ret;
+    Use that approximation to avoid overflow when squaring. */
+    __real__ x = arz;
+    __imag__ x = aiz;
+    ret = __FLT_ABI(clog) (x);
+    __real__ ret += M_LN2;
   }
+  else
+  {
+    __real__ x = (arz - aiz) * (arz + aiz) + __FLT_CST(1.0);
+    __imag__ x = __FLT_CST(2.0) * arz * aiz;
+
+    x = __FLT_ABI(csqrt) (x);
 
-  __real__ x = (__real__ z - __imag__ z) * (__real__ z + __imag__ z) + __FLT_CST(1.0);
-  __imag__ x = __FLT_CST(2.0) * __real__ z * __imag__ z;
+    __real__ x += arz;
+    __imag__ x += aiz;
 
-  x = __FLT_ABI(csqrt) (x);
+    ret = __FLT_ABI(clog) (x);
+  }
 
-  __real__ x += __real__ z;
-  __imag__ x += __imag__ z;
+  /* adjust signs for input quadrant */
+  __real__ ret = __FLT_ABI(copysign) (__real__ ret, __real__ z);
+  __imag__ ret = __FLT_ABI(copysign) (__imag__ ret, __imag__ z);
 
-  return __FLT_ABI(clog) (x);
+  return ret;
 }
-- 
2.35.3.windows.1

From f309692d67674526ec9a87ecae527cb6c207cf93 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
Date: Mon, 8 Aug 2022 18:02:40 +0200
Subject: [PATCH 2/3] casinh: Use approximations for small real part and
 absolute imaginary part < 1

---
 mingw-w64-crt/complex/casinh.def.h | 31 ++++++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)

diff --git a/mingw-w64-crt/complex/casinh.def.h b/mingw-w64-crt/complex/casinh.def.h
index 40ff67579..8d61b1399 100644
--- a/mingw-w64-crt/complex/casinh.def.h
+++ b/mingw-w64-crt/complex/casinh.def.h
@@ -104,6 +104,37 @@ __FLT_ABI(casinh) (__FLT_TYPE __complex__ z)
     ret = __FLT_ABI(clog) (x);
     __real__ ret += M_LN2;
   }
+  else if (arz <= __FLT_EPSILON && aiz < __FLT_CST(1.0))
+  {
+    /* Taylor series expansion around arz=0 for z + sqrt(z*z + 1):
+    c = arz + sqrt(1-aiz^2) + i*(aiz + arz*aiz / sqrt(1-aiz^2)) + O(arz^2)
+    Identity: clog(c) = log(|c|) + i*arg(c)
+    For real part of result:
+    |c| = 1 + arz / sqrt(1-aiz^2) + O(arz^2)  (Taylor series expansion)
+    For imaginary part of result:
+    c = (arz + sqrt(1-aiz^2))/sqrt(1-aiz^2) * (sqrt(1-aiz^2) + i*aiz) + O(arz^6)
+    */
+    __FLT_TYPE s1maiz2 = __FLT_ABI(sqrt) ((__FLT_CST(1.0)+aiz)*(__FLT_CST(1.0)-aiz));
+    __real__ ret = __FLT_ABI(log1p) (arz / s1maiz2);
+    __imag__ ret = __FLT_ABI(atan2) (aiz, s1maiz2);
+  }
+  else if (arz*arz <= __FLT_EPSILON && aiz < __FLT_CST(1.0))
+  {
+    /* Taylor series expansion around arz=0 for z + sqrt(z*z + 1):
+    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)
+    Identity: clog(c) = log(|c|) + i*arg(c)
+    For real part of result:
+    |c| = 1 + arz / sqrt(1-aiz^2) + arz^2/(2*(1-aiz^2)) + O(arz^3)  (Taylor series expansion)
+    For imaginary part of result:
+    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)
+    */
+    __FLT_TYPE onemaiz2 = (__FLT_CST(1.0)+aiz)*(__FLT_CST(1.0)-aiz);
+    __FLT_TYPE s1maiz2 = __FLT_ABI(sqrt) (onemaiz2);
+    __FLT_TYPE arz2red = arz * arz / __FLT_CST(2.0) / s1maiz2;
+    __real__ ret = __FLT_ABI(log1p) ((arz + arz2red) / s1maiz2);
+    __imag__ ret = __FLT_ABI(atan2) (aiz * (s1maiz2 + arz),
+                                     onemaiz2 + arz*s1maiz2 + arz2red);
+  }
   else
   {
     __real__ x = (arz - aiz) * (arz + aiz) + __FLT_CST(1.0);
-- 
2.35.3.windows.1

From b2ad7c96b759e8bc3af504018b70c91c8b0f135c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
Date: Mon, 8 Aug 2022 18:03:49 +0200
Subject: [PATCH 3/3] catanh: Use approximations for small real part

---
 mingw-w64-crt/complex/catanh.def.h | 37 +++++++++++++++++++++++++-----
 1 file changed, 31 insertions(+), 6 deletions(-)

From 7589dfe1f5478a3ba7b93ea6dc28fc0ffd271f12 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Markus=20M=C3=BCtzel?= <markus.muetzel@gmx.de>
Date: Mon, 8 Aug 2022 18:26:20 +0200
Subject: [PATCH 3/3] catanh: Use approximations for small real part

---
 mingw-w64-crt/complex/catanh.def.h | 37 +++++++++++++++++++++++++-----
 1 file changed, 31 insertions(+), 6 deletions(-)

diff --git a/mingw-w64-crt/complex/catanh.def.h b/mingw-w64-crt/complex/catanh.def.h
index 68949d139..1d46d4dcd 100644
--- a/mingw-w64-crt/complex/catanh.def.h
+++ b/mingw-w64-crt/complex/catanh.def.h
@@ -75,17 +75,42 @@ __FLT_ABI(catanh) (__FLT_TYPE __complex__ z)
   if (r_class == FP_ZERO && i_class == FP_ZERO)
     return z;
 
+  /* catanh(z) = 1/2 * clog(1+z) - 1/2 * clog(1-z) = 1/2 * clog((1+z)/(1-z)) */
+
+  /* Use identity clog(c) = 1/2*log(|c|^2) + i*arg(c) to calculate real and
+  imaginary parts separately. */
+
+  /* real part */
+  /* |c|^2 = (Im(z)^2 + (1+Re(z))^2)/(Im(z)^2 + (1-Re(z))^2) */
   i2 = __imag__ z * __imag__ z;
 
-  n = __FLT_CST(1.0) + __real__ z;
-  n = i2 + n * n;
+  if (__FLT_ABI(fabs) (__real__ z) <= __FLT_EPSILON)
+  {
+    /* |c|^2 = 1 + 4*Re(z)/(1+Im(z)^2) + O(Re(z)^2)  (Taylor series) */
+    __real__ ret = __FLT_CST(0.25) *
+      __FLT_ABI(log1p) (__FLT_CST(4.0)*(__real__ z) / (__FLT_CST(1.0) + i2));
+  }
+  else if ((__real__ z)*(__real__ z) <= __FLT_EPSILON)
+  {
+    /* |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) */
+    d = __real__ z / (__FLT_CST(1.0) + i2);
+    __real__ ret = __FLT_CST(0.25) *
+      __FLT_ABI(log1p) (__FLT_CST(4.0) * d * (__FLT_CST(1.0) + __FLT_CST(2.0) * d));
+  }
+  else
+  {
+    n = __FLT_CST(1.0) + __real__ z;
+    n = i2 + n * n;
 
-  d = __FLT_CST(1.0) - __real__ z;
-  d = i2 + d * d;
+    d = __FLT_CST(1.0) - __real__ z;
+    d = i2 + d * d;
 
-  __real__ ret = __FLT_CST(0.25) * (__FLT_ABI(log) (n) - __FLT_ABI(log) (d));
+    __real__ ret = __FLT_CST(0.25) * (__FLT_ABI(log) (n) - __FLT_ABI(log) (d));
+  }
 
-  d = 1 - __real__ z * __real__ z - i2;
+  /* imaginary part */
+  /* z = (1 - Re(z)^2 - Im(z)^2 + 2i * Im(z) / ((1-Re(z))^2 + Im(z)^2) */
+  d = __FLT_CST(1.0) - __real__ z * __real__ z - i2;
 
   __imag__ ret = __FLT_CST(0.5) * __FLT_ABI(atan2) (__FLT_CST(2.0) * __imag__ z, d);
 
-- 
2.35.3.windows.1