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 (__FLT_ABI(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 (__FLT_ABI(signbit) (__real__ ret))
     ret = -ret;
 
   return ret;
-- 
2.35.3.windows.1