commit fa9a85ee02f35a5cad90db5b7002d9a5f164d96e
author Mikhail Maltsev <mikhail.maltsev@arm.com> Mon Feb 19 15:41:36 2018 +0000
committer Mikhail Maltsev <mikhail.maltsev@arm.com> Mon Feb 19 15:41:36 2018 +0000
tree edf2485adc0bb6e3e6ebda6e20c2a4df7d9426d2
parent 2061b8f536f569c67b01118629168b2bb7b0acfa

[libcxx] Improve accuracy of complex asinh and acosh

Summary:
Currently std::asinh and std::acosh use std::pow to compute x^2. This
results in a significant error when computing e.g. asinh(i) or
acosh(-1).

This patch expresses x^2 directly via x.real() and x.imag(), like it
is done in libstdc++/glibc, and adds tests that checks the accuracy.

Reviewers: EricWF, mclow.lists

Reviewed By: mclow.lists

Subscribers: christof, cfe-commits

Differential Revision: https://reviews.llvm.org/D41629

llvm-svn: 325510
Cr-Mirrored-From: sso://chromium.googlesource.com/_direct/external/github.com/llvm/llvm-project
Cr-Mirrored-Commit: 477b5f688c80064753827693c16d49957d3a3a95

include/complex

diff --git a/include/complex b/include/complex
index c7c1cde..d692ee3 100644
--- a/include/complex
+++ b/include/complex
@@ -1125,6 +1125,17 @@
     return _VSTD::pow(result_type(__x), result_type(__y));
 }
 
+// __sqr, computes pow(x, 2)
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+__sqr(const complex<_Tp>& __x)
+{
+    return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()),
+                        _Tp(2) * __x.real() * __x.imag());
+}
+
 // asinh
 
 template<class _Tp>
@@ -1150,7 +1161,7 @@
     }
     if (__libcpp_isinf_or_builtin(__x.imag()))
         return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
-    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
+    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _Tp(1)));
     return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
 }
 
@@ -1184,7 +1195,7 @@
     }
     if (__libcpp_isinf_or_builtin(__x.imag()))
         return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
-    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
+    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
     return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
 }
 
@@ -1318,7 +1329,7 @@
         return complex<_Tp>(__pi/_Tp(2), -__x.imag());
     if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
         return complex<_Tp>(__pi/_Tp(2), -__x.imag());
-    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
+    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
     if (signbit(__x.imag()))
         return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
     return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));