From e3a851a21bb69a4b18065dd859a724cfd984d8b3 Mon Sep 17 00:00:00 2001
From: Ulrich Drepper <drepper@gmail.com>
Date: Wed, 21 Dec 2011 22:08:12 -0500
Subject: [PATCH] Use Kahan's formula in cacosh

---
 ChangeLog        | 7 +++++++
 math/s_cacosh.c  | 5 +++++
 math/s_cacoshf.c | 6 ++++++
 math/s_cacoshl.c | 6 ++++++
 4 files changed, 24 insertions(+)

diff --git a/ChangeLog b/ChangeLog
index 1ccc3ddab0..4d2b1fcc98 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,10 @@
+2011-12-21  Ulrich Drepper  <drepper@gmail.com>
+
+	* math/s_cacosh.c: Use Kahan's formula if the subtraction could lead
+	to large cancellation.
+	* math/s_cacoshf.c: Likewise.
+	* math/s_cacoshl.c: Likewise.
+
 2011-11-18  Richard B. Kreckel  <kreckel@ginac.de>
 
 	[BZ #13305]
diff --git a/math/s_cacosh.c b/math/s_cacosh.c
index df5ce6945d..cb01ca87c5 100644
--- a/math/s_cacosh.c
+++ b/math/s_cacosh.c
@@ -65,6 +65,11 @@ __cacosh (__complex__ double x)
       __real__ res = 0.0;
       __imag__ res = __copysign (M_PI_2, __imag__ x);
     }
+  /* The factor 16 is just a guess.  */
+  else if (16.0 * fabs (__imag__ x) < fabs (__real__ x))
+    /* Kahan's formula which avoid cancellation through subtraction in
+       some cases.  */
+    res = 2.0 * __clog (__csqrt ((x + 1.0) / 2.0) + __csqrt ((x - 1.0) / 2.0));
   else
     {
       __complex__ double y;
diff --git a/math/s_cacoshf.c b/math/s_cacoshf.c
index aa4696f10b..fe046929e8 100644
--- a/math/s_cacoshf.c
+++ b/math/s_cacoshf.c
@@ -65,6 +65,12 @@ __cacoshf (__complex__ float x)
       __real__ res = 0.0;
       __imag__ res = __copysignf (M_PI_2, __imag__ x);
     }
+  /* The factor 16 is just a guess.  */
+  else if (16.0 * fabsf (__imag__ x) < fabsf (__real__ x))
+    /* Kahan's formula which avoid cancellation through subtraction in
+       some cases.  */
+    res = 2.0 * __clogf (__csqrtf ((x + 1.0) / 2.0)
+			 + __csqrtf ((x - 1.0) / 2.0));
   else
     {
       __complex__ float y;
diff --git a/math/s_cacoshl.c b/math/s_cacoshl.c
index b90b196959..84c2715d22 100644
--- a/math/s_cacoshl.c
+++ b/math/s_cacoshl.c
@@ -65,6 +65,12 @@ __cacoshl (__complex__ long double x)
       __real__ res = 0.0;
       __imag__ res = __copysignl (M_PI_2l, __imag__ x);
     }
+  /* The factor 16 is just a guess.  */
+  else if (16.0L * fabsl (__imag__ x) < fabsl (__real__ x))
+    /* Kahan's formula which avoid cancellation through subtraction in
+       some cases.  */
+    res = 2.0L * __clogl (__csqrtl ((x + 1.0L) / 2.0L)
+			  + __csqrtl ((x - 1.0L) / 2.0L));
   else
     {
       __complex__ long double y;