[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

2 files changed, 18 insertions, 0 deletions

diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp
index deb056d67de..5258bdc3a0f 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp
@@ -54,6 +54,15 @@ void test_edges()
             assert(r.imag() == 0);
             assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
         }
+        else if (testcases[i].real() == -1 && testcases[i].imag() == 0)
+        {
+            assert(r.real() == 0);
+            assert(!std::signbit(r.real()));
+            if (std::signbit(testcases[i].imag()))
+                is_about(r.imag(), -pi);
+            else
+                is_about(r.imag(),  pi);
+        }
         else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
         {
             assert(std::isinf(r.real()));
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp
index 3da56c32f19..cb9188d935a 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp
@@ -44,6 +44,15 @@ void test_edges()
             assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
             assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
         }
+        else if (testcases[i].real() == 0 && std::abs(testcases[i].imag()) == 1)
+        {
+            assert(r.real() == 0);
+            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            if (std::signbit(testcases[i].imag()))
+                is_about(r.imag(), -pi/2);
+            else
+                is_about(r.imag(),  pi/2);
+        }
         else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
         {
             assert(std::isinf(r.real()));