2011-11-02 Richard B. Kreckel <kreckel@ginac.de>

	    Paolo Carlini  <paolo.carlini@oracle.com>

	PR libstdc++/50880
	* include/std/complex (__complex_acosh): Fix in a better way,
	use Kahan's formula.
	* include/tr1/complex (__complex_acosh): Likewise.

git-svn-id: svn+ssh://gcc.gnu.org/svn/gcc/trunk@180787 138bc75d-0d04-0410-961f-82ee72b054a4

diff --git a/libstdc++-v3/include/std/complex b/libstdc++-v3/include/std/complex
index 3c41b48..d742343 100644 (file)
--- a/libstdc++-v3/include/std/complex
+++ b/libstdc++-v3/include/std/complex
@@ -1686,14 +1686,9 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
     std::complex<_Tp>
     __complex_acosh(const std::complex<_Tp>& __z)
     {
-      std::complex<_Tp> __t((__z.real() - __z.imag())
-                           * (__z.real() + __z.imag()) - _Tp(1.0),
-                           _Tp(2.0) * __z.real() * __z.imag());
-      __t = std::sqrt(__t);
-      if (__z.real() < _Tp())
-       __t = -__t;
-
-      return std::log(__t + __z);
+      // Kahan's formula.
+      return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
+                                + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
     }
 
 #if _GLIBCXX_USE_C99_COMPLEX_TR1

diff --git a/libstdc++-v3/include/tr1/complex b/libstdc++-v3/include/tr1/complex
index d831eeb..689ea16 100644 (file)
--- a/libstdc++-v3/include/tr1/complex
+++ b/libstdc++-v3/include/tr1/complex
@@ -185,14 +185,9 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
     std::complex<_Tp>
     __complex_acosh(const std::complex<_Tp>& __z)
     {
-      std::complex<_Tp> __t((__z.real() - __z.imag())
-                           * (__z.real() + __z.imag()) - _Tp(1.0),
-                           _Tp(2.0) * __z.real() * __z.imag());
-      __t = std::sqrt(__t);
-      if (__z.real() < _Tp())
-       __t = -__t;
-
-      return std::log(__t + __z);
+      // Kahan's formula.
+      return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
+                                + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
     }
 
 #if _GLIBCXX_USE_C99_COMPLEX_TR1