Fix buggy numerics of tanh(complex) at inf #361

[zasdfgbnm]

Summary

Because:
lim[x->inf, tanh(x+iy)] = 1
lim[x->-inf, tanh(x+iy)] = -1

See also:
https://github.com/NVIDIA/libcudacxx/pull/210

[ldionne]

Thanks a lot for the patch, committing using your GitHub information (for attribution).

libcxx/include/complex

 
 template<class _Tp>
 complex<_Tp>
 tanh(const complex<_Tp>& __x)
 {
     if (__libcpp_isinf_or_builtin(__x.real()))
     {
         if (!__libcpp_isfinite_or_builtin(__x.imag()))
-            return complex<_Tp>(_Tp(1), _Tp(0));
-        return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
+            return complex<_Tp>(copysign(_Tp(1), __x.real()), _Tp(0));
+        return complex<_Tp>(copysign(_Tp(1), __x.real()), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
     }
     if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
         return __x;
     _Tp __2r(_Tp(2) * __x.real());
     _Tp __2i(_Tp(2) * __x.imag());
     _Tp __d(cosh(__2r) + cos(__2i));
     _Tp __2rsh(sinh(__2r));
     if (__libcpp_isinf_or_builtin(__2rsh) && __libcpp_isinf_or_builtin(__d))

libcxx/test/std/numerics/complex.number/complex.transcendentals/tanh.pass.cpp

for (unsigned i = 0; i < N; ++i)
         }
         else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
         else if (std::isinf(testcases[i].real()) && std::isfinite(testcases[i].imag()))
         {
-            assert(r.real() == 1);
-            assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(sin(2*testcases[i].imag())));
+          assert(r.real() == (testcases[i].real() > 0 ? 1 : -1));
+          assert(std::signbit(r.imag()) == std::signbit(sin(2 * testcases[i].imag())));
         }
         else if (std::isinf(testcases[i].real()) && std::isinf(testcases[i].imag()))
         {
-            assert(r.real() == 1);
-            assert(r.imag() == 0);
+          assert(r.real() == (testcases[i].real() > 0 ? 1 : -1));
         }
         else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
         {
-            assert(r.real() == 1);
-            assert(r.imag() == 0);
+          assert(r.real() == (testcases[i].real() > 0 ? 1 : -1));
         }
         else if (std::isnan(testcases[i].real()) && testcases[i].imag() == 0)
         {
             assert(std::isnan(r.real()));
             assert(r.imag() == 0);
             assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
         }
         else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))