[libcxx-commits] [libcxx] [libcxx] makes `tanh(complex<float>)` work for large values (PR #122194)

Christopher Di Bella via libcxx-commits libcxx-commits at lists.llvm.org
Wed Jan 8 15:49:03 PST 2025


https://github.com/cjdb created https://github.com/llvm/llvm-project/pull/122194

By attempting to compute `sin(2x)` and `cos(2x)`, we were inadvertently producing `complex<float>(NaN, NaN)` for any `|x| > 2^127`, since `2x` would be computed as `inf`, and `sin(inf) == cos(inf) == NaN`.
    
This commit relies on trig identities to sidestep this issue and always produce a valid answer for large values of `tanh`. The test cases only handled `double`, so they have been expanded to test `float` and `long double` as well.

>From 3554b852e6cbcf47cff99d21f11860f29eedd341 Mon Sep 17 00:00:00 2001
From: Christopher Di Bella <cjdb at google.com>
Date: Mon, 6 Jan 2025 23:38:09 +0000
Subject: [PATCH 1/2] [libcxx] makes `tanh(complex<float>)` work for large
 values

By attempting to compute `sin(2x)` and `cos(2x)`, we were inadvertently
producing `complex<float>(NaN, NaN)` for any `|x| > 2^127`, since `2x`
would be computed as `inf`, and `sin(inf) == cos(inf) == NaN`.

This commit relies on trig identities to sidestep this issue and always
produce a valid answer for large values of `tanh`. The test cases only
handled `double`, so they have been expanded to test `float` and `long
double` as well.
---
 libcxx/include/complex                        |  40 +-
 .../test/std/numerics/complex.number/cases.h  | 355 +++++++++---------
 .../complex_divide_complex.pass.cpp           |  29 +-
 .../complex_times_complex.pass.cpp            |  25 +-
 .../complex.transcendentals/acos.pass.cpp     |  68 ++--
 .../complex.transcendentals/acosh.pass.cpp    |  63 ++--
 .../complex.transcendentals/asin.pass.cpp     |  55 +--
 .../complex.transcendentals/asinh.pass.cpp    |  61 +--
 .../complex.transcendentals/atan.pass.cpp     |  15 +-
 .../complex.transcendentals/atanh.pass.cpp    |  65 ++--
 .../complex.transcendentals/cos.pass.cpp      |  13 +-
 .../complex.transcendentals/cosh.pass.cpp     |  48 ++-
 .../complex.transcendentals/exp.pass.cpp      |  45 +--
 .../complex.transcendentals/log.pass.cpp      |  51 +--
 .../complex.transcendentals/log10.pass.cpp    |  11 +-
 .../pow_complex_complex.pass.cpp              |  11 +-
 .../pow_complex_scalar.pass.cpp               |  11 +-
 .../pow_scalar_complex.pass.cpp               |  11 +-
 .../complex.transcendentals/sin.pass.cpp      |  15 +-
 .../complex.transcendentals/sinh.pass.cpp     |  56 +--
 .../complex.transcendentals/sqrt.pass.cpp     |  65 +++-
 .../complex.transcendentals/tan.pass.cpp      |  15 +-
 .../complex.transcendentals/tanh.pass.cpp     |  47 ++-
 .../complex.value.ops/abs.pass.cpp            |  18 +-
 .../complex.value.ops/arg.pass.cpp            |  62 +--
 .../complex.value.ops/norm.pass.cpp           |  12 +-
 .../complex.value.ops/polar.pass.cpp          |  16 +-
 .../complex.value.ops/proj.pass.cpp           |  22 +-
 28 files changed, 757 insertions(+), 548 deletions(-)

diff --git a/libcxx/include/complex b/libcxx/include/complex
index df18159595b34d..5f425206100ce2 100644
--- a/libcxx/include/complex
+++ b/libcxx/include/complex
@@ -1236,6 +1236,36 @@ _LIBCPP_HIDE_FROM_ABI complex<_Tp> cosh(const complex<_Tp>& __x) {
 
 // tanh
 
+template<class _Tp>
+_LIBCPP_HIDE_FROM_ABI _Tp __sin2(const _Tp __x) noexcept
+{
+  static_assert(std::is_arithmetic<_Tp>::value, "requires an arithmetic type");
+  return 2 * std::sin(__x) * std::cos(__x);
+}
+
+template<class _Tp>
+_LIBCPP_HIDE_FROM_ABI _Tp __sinh2(const _Tp __x) noexcept
+{
+  static_assert(std::is_arithmetic<_Tp>::value, "requires an arithmetic type");
+  return 2 * std::sinh(__x) * std::cosh(__x);
+}
+
+template<class _Tp>
+_LIBCPP_HIDE_FROM_ABI _Tp __cos2(const _Tp __x) noexcept
+{
+  static_assert(std::is_arithmetic<_Tp>::value, "requires an arithmetic type");
+  const _Tp __cos = std::cos(__x);
+  return 2 * __cos * __cos - 1;
+}
+
+template<class _Tp>
+_LIBCPP_HIDE_FROM_ABI _Tp __cosh2(const _Tp __x) noexcept
+{
+  static_assert(std::is_arithmetic<_Tp>::value, "requires an arithmetic type");
+  const _Tp __cosh = std::cosh(__x);
+  return 2 * __cosh * __cosh - 1;
+}
+
 template <class _Tp>
 _LIBCPP_HIDE_FROM_ABI complex<_Tp> tanh(const complex<_Tp>& __x) {
   if (std::isinf(__x.real())) {
@@ -1245,13 +1275,11 @@ _LIBCPP_HIDE_FROM_ABI complex<_Tp> tanh(const complex<_Tp>& __x) {
   }
   if (std::isnan(__x.real()) && __x.imag() == 0)
     return __x;
-  _Tp __2r(_Tp(2) * __x.real());
-  _Tp __2i(_Tp(2) * __x.imag());
-  _Tp __d(std::cosh(__2r) + std::cos(__2i));
-  _Tp __2rsh(std::sinh(__2r));
+  _Tp __d(std::__cosh2(__x.real()) + std::__cos2(__x.imag()));
+  _Tp __2rsh(std::__sinh2(__x.real()));
   if (std::isinf(__2rsh) && std::isinf(__d))
-    return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1), __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
-  return complex<_Tp>(__2rsh / __d, std::sin(__2i) / __d);
+    return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1), __x.imag() > _Tp(0) ? _Tp(0) : _Tp(-0.));
+  return complex<_Tp>(__2rsh / __d, std::__sin2(__x.imag()) / __d);
 }
 
 // asin
diff --git a/libcxx/test/std/numerics/complex.number/cases.h b/libcxx/test/std/numerics/complex.number/cases.h
index b360e1423ff576..61096dd875fc4b 100644
--- a/libcxx/test/std/numerics/complex.number/cases.h
+++ b/libcxx/test/std/numerics/complex.number/cases.h
@@ -15,184 +15,190 @@
 
 #include <cassert>
 #include <complex>
+#include <limits>
 #include <type_traits>
 
 #include "test_macros.h"
 
-TEST_CONSTEXPR_CXX20 const std::complex<double> testcases[] =
+template<class T>
+TEST_CONSTEXPR_CXX20 const std::complex<T> testcases[] =
 {
-    std::complex<double>( 1.e-6,  1.e-6),
-    std::complex<double>(-1.e-6,  1.e-6),
-    std::complex<double>(-1.e-6, -1.e-6),
-    std::complex<double>( 1.e-6, -1.e-6),
-
-    std::complex<double>( 1.e+6,  1.e-6),
-    std::complex<double>(-1.e+6,  1.e-6),
-    std::complex<double>(-1.e+6, -1.e-6),
-    std::complex<double>( 1.e+6, -1.e-6),
-
-    std::complex<double>( 1.e-6,  1.e+6),
-    std::complex<double>(-1.e-6,  1.e+6),
-    std::complex<double>(-1.e-6, -1.e+6),
-    std::complex<double>( 1.e-6, -1.e+6),
-
-    std::complex<double>( 1.e+6,  1.e+6),
-    std::complex<double>(-1.e+6,  1.e+6),
-    std::complex<double>(-1.e+6, -1.e+6),
-    std::complex<double>( 1.e+6, -1.e+6),
-
-    std::complex<double>(-0, -1.e-6),
-    std::complex<double>(-0,  1.e-6),
-    std::complex<double>(-0,  1.e+6),
-    std::complex<double>(-0, -1.e+6),
-    std::complex<double>( 0, -1.e-6),
-    std::complex<double>( 0,  1.e-6),
-    std::complex<double>( 0,  1.e+6),
-    std::complex<double>( 0, -1.e+6),
-
-    std::complex<double>(-1.e-6, -0),
-    std::complex<double>( 1.e-6, -0),
-    std::complex<double>( 1.e+6, -0),
-    std::complex<double>(-1.e+6, -0),
-    std::complex<double>(-1.e-6,  0),
-    std::complex<double>( 1.e-6,  0),
-    std::complex<double>( 1.e+6,  0),
-    std::complex<double>(-1.e+6,  0),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(-2, std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(-1, std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(-0.5, std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(-0., std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(+0., std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(0.5, std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(1, std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(2, std::numeric_limits<double>::quiet_NaN()),
-    std::complex<double>(std::numeric_limits<double>::infinity(), std::numeric_limits<double>::quiet_NaN()),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), -std::numeric_limits<double>::infinity()),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), -std::numeric_limits<double>::infinity()),
-    std::complex<double>(-2, -std::numeric_limits<double>::infinity()),
-    std::complex<double>(-1, -std::numeric_limits<double>::infinity()),
-    std::complex<double>(-0.5, -std::numeric_limits<double>::infinity()),
-    std::complex<double>(-0., -std::numeric_limits<double>::infinity()),
-    std::complex<double>(+0., -std::numeric_limits<double>::infinity()),
-    std::complex<double>(0.5, -std::numeric_limits<double>::infinity()),
-    std::complex<double>(1, -std::numeric_limits<double>::infinity()),
-    std::complex<double>(2, -std::numeric_limits<double>::infinity()),
-    std::complex<double>(std::numeric_limits<double>::infinity(), -std::numeric_limits<double>::infinity()),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), -2),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), -2),
-    std::complex<double>(-2, -2),
-    std::complex<double>(-1, -2),
-    std::complex<double>(-0.5, -2),
-    std::complex<double>(-0., -2),
-    std::complex<double>(+0., -2),
-    std::complex<double>(0.5, -2),
-    std::complex<double>(1, -2),
-    std::complex<double>(2, -2),
-    std::complex<double>(std::numeric_limits<double>::infinity(), -2),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), -1),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), -1),
-    std::complex<double>(-2, -1),
-    std::complex<double>(-1, -1),
-    std::complex<double>(-0.5, -1),
-    std::complex<double>(-0., -1),
-    std::complex<double>(+0., -1),
-    std::complex<double>(0.5, -1),
-    std::complex<double>(1, -1),
-    std::complex<double>(2, -1),
-    std::complex<double>(std::numeric_limits<double>::infinity(), -1),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), -0.5),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), -0.5),
-    std::complex<double>(-2, -0.5),
-    std::complex<double>(-1, -0.5),
-    std::complex<double>(-0.5, -0.5),
-    std::complex<double>(-0., -0.5),
-    std::complex<double>(+0., -0.5),
-    std::complex<double>(0.5, -0.5),
-    std::complex<double>(1, -0.5),
-    std::complex<double>(2, -0.5),
-    std::complex<double>(std::numeric_limits<double>::infinity(), -0.5),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), -0.),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), -0.),
-    std::complex<double>(-2, -0.),
-    std::complex<double>(-1, -0.),
-    std::complex<double>(-0.5, -0.),
-    std::complex<double>(-0., -0.),
-    std::complex<double>(+0., -0.),
-    std::complex<double>(0.5, -0.),
-    std::complex<double>(1, -0.),
-    std::complex<double>(2, -0.),
-    std::complex<double>(std::numeric_limits<double>::infinity(), -0.),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), +0.),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), +0.),
-    std::complex<double>(-2, +0.),
-    std::complex<double>(-1, +0.),
-    std::complex<double>(-0.5, +0.),
-    std::complex<double>(-0., +0.),
-    std::complex<double>(+0., +0.),
-    std::complex<double>(0.5, +0.),
-    std::complex<double>(1, +0.),
-    std::complex<double>(2, +0.),
-    std::complex<double>(std::numeric_limits<double>::infinity(), +0.),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 0.5),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), 0.5),
-    std::complex<double>(-2, 0.5),
-    std::complex<double>(-1, 0.5),
-    std::complex<double>(-0.5, 0.5),
-    std::complex<double>(-0., 0.5),
-    std::complex<double>(+0., 0.5),
-    std::complex<double>(0.5, 0.5),
-    std::complex<double>(1, 0.5),
-    std::complex<double>(2, 0.5),
-    std::complex<double>(std::numeric_limits<double>::infinity(), 0.5),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 1),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), 1),
-    std::complex<double>(-2, 1),
-    std::complex<double>(-1, 1),
-    std::complex<double>(-0.5, 1),
-    std::complex<double>(-0., 1),
-    std::complex<double>(+0., 1),
-    std::complex<double>(0.5, 1),
-    std::complex<double>(1, 1),
-    std::complex<double>(2, 1),
-    std::complex<double>(std::numeric_limits<double>::infinity(), 1),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 2),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), 2),
-    std::complex<double>(-2, 2),
-    std::complex<double>(-1, 2),
-    std::complex<double>(-0.5, 2),
-    std::complex<double>(-0., 2),
-    std::complex<double>(+0., 2),
-    std::complex<double>(0.5, 2),
-    std::complex<double>(1, 2),
-    std::complex<double>(2, 2),
-    std::complex<double>(std::numeric_limits<double>::infinity(), 2),
-
-    std::complex<double>(std::numeric_limits<double>::quiet_NaN(), std::numeric_limits<double>::infinity()),
-    std::complex<double>(-std::numeric_limits<double>::infinity(), std::numeric_limits<double>::infinity()),
-    std::complex<double>(-2, std::numeric_limits<double>::infinity()),
-    std::complex<double>(-1, std::numeric_limits<double>::infinity()),
-    std::complex<double>(-0.5, std::numeric_limits<double>::infinity()),
-    std::complex<double>(-0., std::numeric_limits<double>::infinity()),
-    std::complex<double>(+0., std::numeric_limits<double>::infinity()),
-    std::complex<double>(0.5, std::numeric_limits<double>::infinity()),
-    std::complex<double>(1, std::numeric_limits<double>::infinity()),
-    std::complex<double>(2, std::numeric_limits<double>::infinity()),
-    std::complex<double>(std::numeric_limits<double>::infinity(), std::numeric_limits<double>::infinity())
+    std::complex<T>( 1.e-6,  1.e-6),
+    std::complex<T>(-1.e-6,  1.e-6),
+    std::complex<T>(-1.e-6, -1.e-6),
+    std::complex<T>( 1.e-6, -1.e-6),
+
+    std::complex<T>( 1.e+6,  1.e-6),
+    std::complex<T>(-1.e+6,  1.e-6),
+    std::complex<T>(-1.e+6, -1.e-6),
+    std::complex<T>( 1.e+6, -1.e-6),
+
+    std::complex<T>( 1.e-6,  1.e+6),
+    std::complex<T>(-1.e-6,  1.e+6),
+    std::complex<T>(-1.e-6, -1.e+6),
+    std::complex<T>( 1.e-6, -1.e+6),
+
+    std::complex<T>( 1.e+6,  1.e+6),
+    std::complex<T>(-1.e+6,  1.e+6),
+    std::complex<T>(-1.e+6, -1.e+6),
+    std::complex<T>( 1.e+6, -1.e+6),
+
+    std::complex<T>(-0, -1.e-6),
+    std::complex<T>(-0,  1.e-6),
+    std::complex<T>(-0,  1.e+6),
+    std::complex<T>(-0, -1.e+6),
+    std::complex<T>( 0, -1.e-6),
+    std::complex<T>( 0,  1.e-6),
+    std::complex<T>( 0,  1.e+6),
+    std::complex<T>( 0, -1.e+6),
+
+    std::complex<T>(-1.e-6, -0),
+    std::complex<T>( 1.e-6, -0),
+    std::complex<T>( 1.e+6, -0),
+    std::complex<T>(-1.e+6, -0),
+    std::complex<T>(-1.e-6,  0),
+    std::complex<T>( 1.e-6,  0),
+    std::complex<T>( 1.e+6,  0),
+    std::complex<T>(-1.e+6,  0),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(-2, std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(-1, std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(-0.5, std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(-0., std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(+0., std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(0.5, std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(1, std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(2, std::numeric_limits<T>::quiet_NaN()),
+    std::complex<T>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::quiet_NaN()),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), -std::numeric_limits<T>::infinity()),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), -std::numeric_limits<T>::infinity()),
+    std::complex<T>(-2, -std::numeric_limits<T>::infinity()),
+    std::complex<T>(-1, -std::numeric_limits<T>::infinity()),
+    std::complex<T>(-0.5, -std::numeric_limits<T>::infinity()),
+    std::complex<T>(-0., -std::numeric_limits<T>::infinity()),
+    std::complex<T>(+0., -std::numeric_limits<T>::infinity()),
+    std::complex<T>(0.5, -std::numeric_limits<T>::infinity()),
+    std::complex<T>(1, -std::numeric_limits<T>::infinity()),
+    std::complex<T>(2, -std::numeric_limits<T>::infinity()),
+    std::complex<T>(std::numeric_limits<T>::infinity(), -std::numeric_limits<T>::infinity()),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), -2),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), -2),
+    std::complex<T>(-2, -2),
+    std::complex<T>(-1, -2),
+    std::complex<T>(-0.5, -2),
+    std::complex<T>(-0., -2),
+    std::complex<T>(+0., -2),
+    std::complex<T>(0.5, -2),
+    std::complex<T>(1, -2),
+    std::complex<T>(2, -2),
+    std::complex<T>(std::numeric_limits<T>::infinity(), -2),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), -1),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), -1),
+    std::complex<T>(-2, -1),
+    std::complex<T>(-1, -1),
+    std::complex<T>(-0.5, -1),
+    std::complex<T>(-0., -1),
+    std::complex<T>(+0., -1),
+    std::complex<T>(0.5, -1),
+    std::complex<T>(1, -1),
+    std::complex<T>(2, -1),
+    std::complex<T>(std::numeric_limits<T>::infinity(), -1),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), -0.5),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), -0.5),
+    std::complex<T>(-2, -0.5),
+    std::complex<T>(-1, -0.5),
+    std::complex<T>(-0.5, -0.5),
+    std::complex<T>(-0., -0.5),
+    std::complex<T>(+0., -0.5),
+    std::complex<T>(0.5, -0.5),
+    std::complex<T>(1, -0.5),
+    std::complex<T>(2, -0.5),
+    std::complex<T>(std::numeric_limits<T>::infinity(), -0.5),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), -0.),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), -0.),
+    std::complex<T>(-2, -0.),
+    std::complex<T>(-1, -0.),
+    std::complex<T>(-0.5, -0.),
+    std::complex<T>(-0., -0.),
+    std::complex<T>(+0., -0.),
+    std::complex<T>(0.5, -0.),
+    std::complex<T>(1, -0.),
+    std::complex<T>(2, -0.),
+    std::complex<T>(std::numeric_limits<T>::infinity(), -0.),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), +0.),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), +0.),
+    std::complex<T>(-2, +0.),
+    std::complex<T>(-1, +0.),
+    std::complex<T>(-0.5, +0.),
+    std::complex<T>(-0., +0.),
+    std::complex<T>(+0., +0.),
+    std::complex<T>(0.5, +0.),
+    std::complex<T>(1, +0.),
+    std::complex<T>(2, +0.),
+    std::complex<T>(std::numeric_limits<T>::infinity(), +0.),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), 0.5),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), 0.5),
+    std::complex<T>(-2, 0.5),
+    std::complex<T>(-1, 0.5),
+    std::complex<T>(-0.5, 0.5),
+    std::complex<T>(-0., 0.5),
+    std::complex<T>(+0., 0.5),
+    std::complex<T>(0.5, 0.5),
+    std::complex<T>(1, 0.5),
+    std::complex<T>(2, 0.5),
+    std::complex<T>(std::numeric_limits<T>::infinity(), 0.5),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), 1),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), 1),
+    std::complex<T>(-2, 1),
+    std::complex<T>(-1, 1),
+    std::complex<T>(-0.5, 1),
+    std::complex<T>(-0., 1),
+    std::complex<T>(+0., 1),
+    std::complex<T>(0.5, 1),
+    std::complex<T>(1, 1),
+    std::complex<T>(2, 1),
+    std::complex<T>(std::numeric_limits<T>::infinity(), 1),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), 2),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), 2),
+    std::complex<T>(-2, 2),
+    std::complex<T>(-1, 2),
+    std::complex<T>(-0.5, 2),
+    std::complex<T>(-0., 2),
+    std::complex<T>(+0., 2),
+    std::complex<T>(0.5, 2),
+    std::complex<T>(1, 2),
+    std::complex<T>(2, 2),
+    std::complex<T>(std::numeric_limits<T>::infinity(), 2),
+
+    std::complex<T>(std::numeric_limits<T>::quiet_NaN(), std::numeric_limits<T>::infinity()),
+    std::complex<T>(-std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity()),
+    std::complex<T>(-2, std::numeric_limits<T>::infinity()),
+    std::complex<T>(-1, std::numeric_limits<T>::infinity()),
+    std::complex<T>(-0.5, std::numeric_limits<T>::infinity()),
+    std::complex<T>(-0., std::numeric_limits<T>::infinity()),
+    std::complex<T>(+0., std::numeric_limits<T>::infinity()),
+    std::complex<T>(0.5, std::numeric_limits<T>::infinity()),
+    std::complex<T>(1, std::numeric_limits<T>::infinity()),
+    std::complex<T>(2, std::numeric_limits<T>::infinity()),
+    std::complex<T>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity()),
+
+    std::complex<T>(std::numeric_limits<T>::max(), 1),
+    std::complex<T>(1, std::numeric_limits<T>::max()),
+    std::complex<T>(std::numeric_limits<T>::max(), std::numeric_limits<T>::max()),
 };
 
-enum {zero, non_zero, inf, NaN, non_zero_nan};
+enum {zero, non_zero, maximum_value, inf, NaN, non_zero_nan};
 
 template <class T, typename std::enable_if<std::is_floating_point<T>::value, int>::type = 0>
 TEST_CONSTEXPR_CXX20 bool test_isinf(T v) {
@@ -227,12 +233,15 @@ classify(const std::complex<T>& x)
             return NaN;
         return non_zero_nan;
     }
+    if (x.real() == std::numeric_limits<T>::max() || x.imag() == std::numeric_limits<T>::max())
+        return maximum_value;
     return non_zero;
 }
 
+template<class T>
 inline
 int
-classify(double x)
+classify(T x)
 {
     if (x == 0)
         return zero;
@@ -240,6 +249,8 @@ classify(double x)
         return inf;
     if (std::isnan(x))
         return NaN;
+    if (x == std::numeric_limits<T>::max())
+        return maximum_value;
     return non_zero;
 }
 
diff --git a/libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp
index d12dfd994b0ae9..9f4b139574b029 100644
--- a/libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp
@@ -34,24 +34,29 @@ test()
     return true;
 }
 
+template<class T>
 TEST_CONSTEXPR_CXX20
 bool
 test_edges()
 {
-  const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+  const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
   int classification[N];
   for (unsigned i=0; i < N; ++i)
-    classification[i] = classify(testcases[i]);
+    classification[i] = classify(testcases<T>[i]);
 
   for (unsigned i = 0; i < N; ++i) {
+    auto const x = testcases<T>[i];
     for (unsigned j = 0; j < N; ++j) {
-      std::complex<double> r = testcases[i] / testcases[j];
+      auto const y = testcases<T>[j];
+      std::complex<T> r = x / y;
       switch (classification[i]) {
       case zero:
         switch (classification[j]) {
         case zero:
           assert(classify(r) == NaN);
           break;
+        case maximum_value:
+          continue; // not tested
         case non_zero:
           assert(classify(r) == zero);
           break;
@@ -66,11 +71,15 @@ test_edges()
           break;
         }
         break;
+      case maximum_value:
+        continue; // not tested
       case non_zero:
         switch (classification[j]) {
         case zero:
           assert(classify(r) == inf);
           break;
+        case maximum_value:
+          continue; // not tested
         case non_zero:
           assert(classify(r) == non_zero);
           break;
@@ -90,6 +99,8 @@ test_edges()
         case zero:
           assert(classify(r) == inf);
           break;
+        case maximum_value:
+          continue; // not tested
         case non_zero:
           assert(classify(r) == inf);
           break;
@@ -109,6 +120,8 @@ test_edges()
         case zero:
           assert(classify(r) == NaN);
           break;
+        case maximum_value:
+          continue; // not tested
         case non_zero:
           assert(classify(r) == NaN);
           break;
@@ -128,6 +141,8 @@ test_edges()
         case zero:
           assert(classify(r) == inf);
           break;
+        case maximum_value:
+          continue; // not tested
         case non_zero:
           assert(classify(r) == NaN);
           break;
@@ -153,13 +168,17 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
 #if TEST_STD_VER > 17
     static_assert(test<float>());
     static_assert(test<double>());
     static_assert(test<long double>());
-    static_assert(test_edges());
+    static_assert(test_edges<float>());
+    static_assert(test_edges<double>());
+    static_assert(test_edges<long double>());
 #endif
 
     return 0;
diff --git a/libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp
index 817d6cdf492d30..ebc5f03e58ed98 100644
--- a/libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp
@@ -33,23 +33,26 @@ test()
 
 // test edges
 
+template<class T>
 TEST_CONSTEXPR_CXX20 bool test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     int classification[N];
     for (unsigned i=0; i < N; ++i)
-        classification[i] = classify(testcases[i]);
+        classification[i] = classify(testcases<T>[i]);
 
     for (unsigned i = 0; i < N; ++i)
     {
         for (unsigned j = 0; j < N; ++j)
         {
-            std::complex<double> r = testcases[i] * testcases[j];
+            std::complex<T> r = testcases<T>[i] * testcases<T>[j];
             switch (classification[i])
             {
             case zero:
                 switch (classification[j])
                 {
+                case maximum_value:
+                    continue; // not tested
                 case zero:
                 case non_zero:
                     assert(classify(r) == zero);
@@ -61,12 +64,16 @@ TEST_CONSTEXPR_CXX20 bool test_edges()
                     break;
                 }
                 break;
+            case maximum_value:
+                continue; // not tested
             case non_zero:
                 switch (classification[j])
                 {
                 case zero:
                     assert(classify(r) == zero);
                     break;
+                case maximum_value:
+                    continue; // not tested
                 case non_zero:
                     assert(classify(r) == non_zero);
                     break;
@@ -86,6 +93,8 @@ TEST_CONSTEXPR_CXX20 bool test_edges()
                 case NaN:
                     assert(classify(r) == NaN);
                     break;
+                case maximum_value:
+                    continue; // not tested
                 case non_zero:
                 case inf:
                 case non_zero_nan:
@@ -102,6 +111,8 @@ TEST_CONSTEXPR_CXX20 bool test_edges()
                 case inf:
                     assert(classify(r) == inf);
                     break;
+                case maximum_value:
+                    continue; // not tested
                 case zero:
                 case non_zero:
                 case NaN:
@@ -121,13 +132,17 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
 #if TEST_STD_VER > 17
     static_assert(test<float>());
     static_assert(test<double>());
     static_assert(test<long double>());
-    static_assert(test_edges());
+    static_assert(test_edges<float>());
+    static_assert(test_edges<double>());
+    static_assert(test_edges<long double>());
 #endif
 
   return 0;
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/acos.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/acos.pass.cpp
index 3158a3bc33d1c5..50756f8ff9a53c 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/acos.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/acos.pass.cpp
@@ -32,101 +32,109 @@ test()
     test(std::complex<T>(INFINITY, 1), std::complex<T>(0, -INFINITY));
 }
 
+template<class T>
 void test_edges()
 {
-    const double pi = std::atan2(+0., -0.);
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const T pi = std::atan2(+0., -0.);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = acos(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = acos(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
             is_about(r.real(), pi/2);
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) != std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) != std::signbit(r.imag()));
         }
-        else if (testcases[i].real() == 0 && std::isnan(testcases[i].imag()))
+        else if (testcases<T>[i].real() == 0 && std::isnan(testcases<T>[i].imag()))
         {
             is_about(r.real(), pi/2);
             assert(std::isnan(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             is_about(r.real(), pi/2);
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) != std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) != std::signbit(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && testcases[i].real() != 0 && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && testcases<T>[i].real() != 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isfinite(testcases<T>[i].imag()))
         {
             is_about(r.real(), pi);
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) != std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) != std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isfinite(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
             assert(!std::signbit(r.real()));
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) != std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) != std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isinf(testcases<T>[i].imag()))
         {
-            is_about(r.real(), 0.75 * pi);
+            is_about(r.real(), T(0.75) * pi);
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) != std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) != std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isinf(testcases<T>[i].imag()))
         {
-            is_about(r.real(), 0.25 * pi);
+            is_about(r.real(), T(0.25) * pi);
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) != std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) != std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isinf(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) != std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) != std::signbit(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (!std::signbit(testcases[i].real()) && !std::signbit(testcases[i].imag()))
+        else if (!std::signbit(testcases<T>[i].real()) && !std::signbit(testcases<T>[i].imag()))
         {
             assert(!std::signbit(r.real()));
             assert( std::signbit(r.imag()));
         }
-        else if (std::signbit(testcases[i].real()) && !std::signbit(testcases[i].imag()))
+        else if (std::signbit(testcases<T>[i].real()) && !std::signbit(testcases<T>[i].imag()))
         {
             assert(!std::signbit(r.real()));
             assert( std::signbit(r.imag()));
         }
-        else if (std::signbit(testcases[i].real()) && std::signbit(testcases[i].imag()))
+        else if (std::signbit(testcases<T>[i].real()) && std::signbit(testcases<T>[i].imag()))
         {
             assert(!std::signbit(r.real()));
             assert(!std::signbit(r.imag()));
         }
-        else if (!std::signbit(testcases[i].real()) && std::signbit(testcases[i].imag()))
+        else if (!std::signbit(testcases<T>[i].real()) && std::signbit(testcases<T>[i].imag()))
         {
             assert(!std::signbit(r.real()));
             assert(!std::signbit(r.imag()));
         }
+        else
+        {
+            assert(!std::isnan(r.real()));
+            assert(!std::isnan(r.imag()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
+        }
     }
 }
 
@@ -135,7 +143,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
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 424a3b1b82e1a0..ce580bdd507f80 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
@@ -32,103 +32,104 @@ test()
     test(std::complex<T>(INFINITY, 1), std::complex<T>(INFINITY, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const double pi = std::atan2(+0., -0.);
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const T pi = std::atan2(+0., -0.);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = acosh(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = acosh(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
             assert(!std::signbit(r.real()));
-            if (std::signbit(testcases[i].imag()))
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi/2);
             else
                 is_about(r.imag(),  pi/2);
         }
-        else if (testcases[i].real() == 1 && testcases[i].imag() == 0)
+        else if (testcases<T>[i].real() == 1 && testcases<T>[i].imag() == 0)
         {
             assert(r.real() == 0);
             assert(!std::signbit(r.real()));
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (testcases[i].real() == -1 && testcases[i].imag() == 0)
+        else if (testcases<T>[i].real() == -1 && testcases<T>[i].imag() == 0)
         {
             assert(r.real() == 0);
             assert(!std::signbit(r.real()));
-            if (std::signbit(testcases[i].imag()))
+            if (std::signbit(testcases<T>[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()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
-            if (std::signbit(testcases[i].imag()))
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi/2);
             else
                 is_about(r.imag(),  pi/2);
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
-            if (std::signbit(testcases[i].imag()))
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi);
             else
                 is_about(r.imag(),  pi);
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
-            if (std::signbit(testcases[i].imag()))
-                is_about(r.imag(), -0.75 * pi);
+            if (std::signbit(testcases<T>[i].imag()))
+                is_about(r.imag(), T(-0.75) * pi);
             else
-                is_about(r.imag(),  0.75 * pi);
+                is_about(r.imag(), T( 0.75) * pi);
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
-            if (std::signbit(testcases[i].imag()))
-                is_about(r.imag(), -0.25 * pi);
+            if (std::signbit(testcases<T>[i].imag()))
+                is_about(r.imag(), T(-0.25 * pi));
             else
-                is_about(r.imag(),  0.25 * pi);
+                is_about(r.imag(), T( 0.25 * pi));
         }
-        else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
@@ -136,7 +137,7 @@ void test_edges()
         else
         {
             assert(!std::signbit(r.real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
     }
 }
@@ -146,7 +147,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/asin.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/asin.pass.cpp
index 51da1c002a294c..4bd8b4fb186229 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/asin.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/asin.pass.cpp
@@ -32,79 +32,80 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(0, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const double pi = std::atan2(+0., -0.);
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const T pi = std::atan2(+0., -0.);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = asin(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = asin(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if ( testcases[i].real() == 0 && std::isnan(testcases[i].imag()))
+        else if ( testcases<T>[i].real() == 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
-            if (testcases[i].real() > 0)
+            if (testcases<T>[i].real() > 0)
                 is_about(r.real(),  pi/2);
             else
                 is_about(r.real(), - pi/2);
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
-            if (std::signbit(testcases[i].real()))
+            if (std::signbit(testcases<T>[i].real()))
                 is_about(r.real(), -pi/4);
             else
                 is_about(r.real(),  pi/4);
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].real()) != std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].real()) != std::signbit(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isinf(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
         else
         {
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
     }
 }
@@ -114,7 +115,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
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 b53509242c378e..80b2c440c4a890 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
@@ -32,88 +32,89 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(0, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const double pi = std::atan2(+0., -0.);
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const T pi = std::atan2(+0., -0.);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = asinh(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = asinh(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (testcases[i].real() == 0 && std::abs(testcases[i].imag()) == 1)
+        else if (testcases<T>[i].real() == 0 && std::abs(testcases<T>[i].imag()) == 1)
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
-            if (std::signbit(testcases[i].imag()))
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
+            if (std::signbit(testcases<T>[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()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
-            if (std::signbit(testcases[i].imag()))
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi/2);
             else
                 is_about(r.imag(),  pi/2);
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
-            if (std::signbit(testcases[i].imag()))
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi/4);
             else
                 is_about(r.imag(),  pi/4);
         }
-        else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && testcases[i].imag() == 0)
+        else if (std::isnan(testcases<T>[i].real()) && testcases<T>[i].imag() == 0)
         {
             assert(std::isnan(r.real()));
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
         else
         {
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
     }
 }
@@ -123,7 +124,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/atan.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/atan.pass.cpp
index f0c801649509d5..6901069d5e2848 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/atan.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/atan.pass.cpp
@@ -32,15 +32,16 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(0, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = atan(testcases[i]);
-        std::complex<double> t1(-imag(testcases[i]), real(testcases[i]));
-        std::complex<double> t2 = atanh(t1);
-        std::complex<double> z(imag(t2), -real(t2));
+        std::complex<T> r = atan(testcases<T>[i]);
+        std::complex<T> t1(-imag(testcases<T>[i]), real(testcases<T>[i]));
+        std::complex<T> t2 = atanh(t1);
+        std::complex<T> z(imag(t2), -real(t2));
         if (std::isnan(real(r)))
             assert(std::isnan(real(z)));
         else
@@ -63,7 +64,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/atanh.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/atanh.pass.cpp
index a126032bf8c240..2b8d79f21baf06 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/atanh.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/atanh.pass.cpp
@@ -32,92 +32,93 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(0, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const double pi = std::atan2(+0., -0.);
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const T pi = std::atan2(+0., -0.);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = atanh(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = atanh(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if ( testcases[i].real() == 0 && std::isnan(testcases[i].imag()))
+        else if ( testcases<T>[i].real() == 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::abs(testcases[i].real()) == 1 && testcases[i].imag() == 0)
+        else if (std::abs(testcases<T>[i].real()) == 1 && testcases<T>[i].imag() == 0)
         {
             assert(std::isinf(r.real()));
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
-            if (testcases[i].imag() > 0)
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
+            if (testcases<T>[i].imag() > 0)
                 is_about(r.imag(),  pi/2);
             else
                 is_about(r.imag(), -pi/2);
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
-            if (std::signbit(testcases[i].imag()))
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi/2);
             else
                 is_about(r.imag(),  pi/2);
         }
-        else if (std::isinf(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
-            if (std::signbit(testcases[i].imag()))
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi/2);
             else
                 is_about(r.imag(),  pi/2);
         }
-        else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
-            assert(std::signbit(testcases[i].real()) == std::signbit(r.real()));
-            if (std::signbit(testcases[i].imag()))
+            assert(std::signbit(testcases<T>[i].real()) == std::signbit(r.real()));
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi/2);
             else
                 is_about(r.imag(),  pi/2);
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
         else
         {
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
     }
 }
@@ -127,7 +128,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/cos.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/cos.pass.cpp
index 0571363de50c3b..922b0c87706b4c 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/cos.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/cos.pass.cpp
@@ -32,14 +32,15 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(1, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = cos(testcases[i]);
-        std::complex<double> t1(-imag(testcases[i]), real(testcases[i]));
-        std::complex<double> z = cosh(t1);
+        std::complex<T> r = cos(testcases<T>[i]);
+        std::complex<T> t1(-imag(testcases<T>[i]), real(testcases<T>[i]));
+        std::complex<T> z = cosh(t1);
         if (std::isnan(real(r)))
             assert(std::isnan(real(z)));
         else
@@ -62,7 +63,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/cosh.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/cosh.pass.cpp
index ad437bf44b996d..4fbec0cb6a6b00 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/cosh.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/cosh.pass.cpp
@@ -32,78 +32,86 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(1, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = cosh(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = cosh(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
             assert(r.real() == 1);
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (testcases[i].real() == 0 && std::isinf(testcases[i].imag()))
+        else if (testcases<T>[i].real() == 0 && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(r.imag() == 0);
         }
-        else if (testcases[i].real() == 0 && std::isnan(testcases[i].imag()))
+        else if (testcases<T>[i].real() == 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(r.imag() == 0);
         }
-        else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].imag() == 0)
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].imag() == 0)
         {
             assert(std::isinf(r.real()));
             assert(!std::signbit(r.real()));
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
-            assert(std::signbit(r.real()) == std::signbit(cos(testcases[i].imag())));
+            assert(std::signbit(r.real()) == std::signbit(cos(testcases<T>[i].imag())));
             assert(std::isinf(r.imag()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].real() * sin(testcases[i].imag())));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].real() * sin(testcases<T>[i].imag())));
         }
-        else if (std::isinf(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && testcases[i].imag() == 0)
+        else if (std::isnan(testcases<T>[i].real()) && testcases<T>[i].imag() == 0)
         {
             assert(std::isnan(r.real()));
             assert(r.imag() == 0);
         }
-        else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
+        else if (std::isfinite(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
+        {
+            assert(!std::isnan(r.real()));
+
+            bool const nan_okay = std::isinf(r.real()) && testcases<T>[i].imag() == 0; // inf * 0 == NaN
+            assert(!std::isnan(r.imag()) || nan_okay);
+        }
     }
 }
 
@@ -112,7 +120,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/exp.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/exp.pass.cpp
index 5c9574e6399d97..efc9b867ebe1ef 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/exp.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/exp.pass.cpp
@@ -32,79 +32,80 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(1, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = exp(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = exp(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
             assert(r.real() == 1.0);
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && testcases[i].imag() == 0)
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && testcases<T>[i].imag() == 0)
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isinf(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
             assert(r.imag() == 0);
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
             assert(r.imag() == 0);
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && testcases[i].imag() == 0)
+        else if (std::isnan(testcases<T>[i].real()) && testcases<T>[i].imag() == 0)
         {
             assert(std::isnan(r.real()));
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && testcases[i].imag() != 0)
+        else if (std::isnan(testcases<T>[i].real()) && testcases<T>[i].imag() != 0)
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isfinite(testcases[i].imag()) && std::abs(testcases[i].imag()) <= 1)
+        else if (std::isfinite(testcases<T>[i].imag()) && std::abs(testcases<T>[i].imag()) <= 1)
         {
             assert(!std::signbit(r.real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isinf(r.real()) && testcases[i].imag() == 0) {
+        else if (std::isinf(r.real()) && testcases<T>[i].imag() == 0) {
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
     }
 }
@@ -114,7 +115,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
     return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/log.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/log.pass.cpp
index 562d125e05323e..b1737f0de54ac4 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/log.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/log.pass.cpp
@@ -32,20 +32,21 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(-INFINITY, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const double pi = std::atan2(+0., -0.);
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const T pi = std::atan2(+0., -0.);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = log(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = log(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
-            if (std::signbit(testcases[i].real()))
+            if (std::signbit(testcases<T>[i].real()))
             {
                 assert(std::isinf(r.real()));
                 assert(r.real() < 0);
-                if (std::signbit(testcases[i].imag()))
+                if (std::signbit(testcases<T>[i].imag()))
                     is_about(r.imag(), -pi);
                 else
                     is_about(r.imag(), pi);
@@ -55,24 +56,24 @@ void test_edges()
                 assert(std::isinf(r.real()));
                 assert(r.real() < 0);
                 assert(r.imag() == 0);
-                assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+                assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
             }
         }
-        else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
-            if (testcases[i].imag() > 0)
+            if (testcases<T>[i].imag() > 0)
                 is_about(r.imag(), pi/2);
             else
                 is_about(r.imag(), -pi/2);
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()) && r.real() > 0);
             if (r.imag() > 0)
@@ -80,44 +81,44 @@ void test_edges()
             else
                 is_about(r.imag(), -pi);
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()) && r.real() > 0);
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (testcases[i].real() == 1 && testcases[i].imag() == 0)
+        else if (testcases<T>[i].real() == 1 && testcases<T>[i].imag() == 0)
         {
             assert(r.real() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (testcases[i].real() == 0 && testcases[i].imag() == 1)
+        else if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 1)
         {
             assert(r.real() == 0);
             is_about(r.imag(), pi/2);
         }
-        else if (testcases[i].real() == -1 && testcases[i].imag() == 0)
+        else if (testcases<T>[i].real() == -1 && testcases<T>[i].imag() == 0)
         {
             assert(r.real() == 0);
-            if (std::signbit(testcases[i].imag()))
+            if (std::signbit(testcases<T>[i].imag()))
                 is_about(r.imag(), -pi);
             else
                 is_about(r.imag(),  pi);
         }
-        else if (testcases[i].real() == 0 && testcases[i].imag() == -1)
+        else if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == -1)
         {
             assert(r.real() == 0);
             is_about(r.imag(), -pi/2);
         }
-        else if (std::isfinite(testcases[i].real()) && std::isfinite(testcases[i].imag()) && abs(testcases[i]) < 1)
+        else if (std::isfinite(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()) && abs(testcases<T>[i]) < 1)
         {
             assert( std::signbit(r.real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isfinite(testcases[i].imag()) && abs(testcases[i]) > 1)
+        else if (std::isfinite(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()) && abs(testcases<T>[i]) > 1)
         {
             assert(!std::signbit(r.real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
     }
 }
@@ -127,7 +128,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/log10.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/log10.pass.cpp
index 78818f0de15b2b..ae4fa59fb2c981 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/log10.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/log10.pass.cpp
@@ -32,13 +32,14 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(-INFINITY, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = log10(testcases[i]);
-        std::complex<double> z = log(testcases[i])/std::log(10);
+        std::complex<T> r = log10(testcases<T>[i]);
+        std::complex<T> z = log(testcases<T>[i])/std::log(T(10));
         if (std::isnan(real(r)))
             assert(std::isnan(real(z)));
         else
@@ -61,7 +62,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_complex_complex.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_complex_complex.pass.cpp
index 91754fac4d0a80..9bddbd0408a38d 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_complex_complex.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_complex_complex.pass.cpp
@@ -34,15 +34,16 @@ test()
     test(std::complex<T>(2, 3), std::complex<T>(2, 0), std::complex<T>(-5, 12));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
         for (unsigned j = 0; j < N; ++j)
         {
-            std::complex<double> r = pow(testcases[i], testcases[j]);
-            std::complex<double> z = exp(testcases[j] * log(testcases[i]));
+            std::complex<T> r = pow(testcases<T>[i], testcases<T>[j]);
+            std::complex<T> z = exp(testcases<T>[j] * log(testcases<T>[i]));
             if (std::isnan(real(r)))
                 assert(std::isnan(real(z)));
             else
@@ -66,7 +67,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_complex_scalar.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_complex_scalar.pass.cpp
index 4b1aef23281db1..1bbc211a09c3ae 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_complex_scalar.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_complex_scalar.pass.cpp
@@ -34,15 +34,16 @@ test()
     test(std::complex<T>(2, 3), T(2), std::complex<T>(-5, 12));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
         for (unsigned j = 0; j < N; ++j)
         {
-            std::complex<double> r = pow(testcases[i], real(testcases[j]));
-            std::complex<double> z = exp(std::complex<double>(real(testcases[j])) * log(testcases[i]));
+            std::complex<T> r = pow(testcases<T>[i], real(testcases<T>[j]));
+            std::complex<T> z = exp(std::complex<T>(real(testcases<T>[j])) * log(testcases<T>[i]));
             if (std::isnan(real(r)))
                 assert(std::isnan(real(z)));
             else
@@ -64,7 +65,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_scalar_complex.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_scalar_complex.pass.cpp
index 6022fddfaa7558..05bd55ef2a72a8 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_scalar_complex.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/pow_scalar_complex.pass.cpp
@@ -34,15 +34,16 @@ test()
     test(T(2), std::complex<T>(2), std::complex<T>(4));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
         for (unsigned j = 0; j < N; ++j)
         {
-            std::complex<double> r = pow(real(testcases[i]), testcases[j]);
-            std::complex<double> z = exp(testcases[j] * log(std::complex<double>(real(testcases[i]))));
+            std::complex<T> r = pow(real(testcases<T>[i]), testcases<T>[j]);
+            std::complex<T> z = exp(testcases<T>[j] * log(std::complex<T>(real(testcases<T>[i]))));
             if (std::isnan(real(r)))
                 assert(std::isnan(real(z)));
             else
@@ -64,7 +65,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sin.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sin.pass.cpp
index ceececa46f7cfd..d54c745781bee5 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sin.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sin.pass.cpp
@@ -32,15 +32,16 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(0, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = sin(testcases[i]);
-        std::complex<double> t1(-imag(testcases[i]), real(testcases[i]));
-        std::complex<double> t2 = sinh(t1);
-        std::complex<double> z(imag(t2), -real(t2));
+        std::complex<T> r = sin(testcases<T>[i]);
+        std::complex<T> t1(-imag(testcases<T>[i]), real(testcases<T>[i]));
+        std::complex<T> t2 = sinh(t1);
+        std::complex<T> z(imag(t2), -real(t2));
         if (std::isnan(real(r)))
             assert(std::isnan(real(z)));
         else
@@ -63,7 +64,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sinh.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sinh.pass.cpp
index 933ff71d8a09bb..62693f18b46225 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sinh.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sinh.pass.cpp
@@ -32,79 +32,89 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(0, 0));
 }
 
+#include <print>
+
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = sinh(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = sinh(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
             assert(r.real() == 0);
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (testcases[i].real() == 0 && std::isinf(testcases[i].imag()))
+        else if (testcases<T>[i].real() == 0 && std::isinf(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
             assert(std::isnan(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (testcases[i].real() == 0 && std::isnan(testcases[i].imag()))
+        else if (testcases<T>[i].real() == 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
             assert(std::isnan(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].imag() == 0)
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].imag() == 0)
         {
             assert(std::isinf(r.real()));
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real() * cos(testcases[i].imag())));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real() * cos(testcases<T>[i].imag())));
             assert(std::isinf(r.imag()));
-            assert(std::signbit(r.imag()) == std::signbit(sin(testcases[i].imag())));
+            assert(std::signbit(r.imag()) == std::signbit(sin(testcases<T>[i].imag())));
         }
-        else if (std::isinf(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && testcases[i].imag() == 0)
+        else if (std::isnan(testcases<T>[i].real()) && testcases<T>[i].imag() == 0)
         {
             assert(std::isnan(r.real()));
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
+        else if (std::isfinite(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
+        {
+            assert(!std::isnan(r.real()));
+
+            bool const nan_okay = std::isinf(r.real()) && testcases<T>[i].imag() == 0; // inf * 0 == NaN
+            assert(!std::isnan(r.imag()) || nan_okay);
+        }
     }
 }
 
@@ -113,7 +123,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sqrt.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sqrt.pass.cpp
index 12fd9a2c0440a1..1f2f9e9af4e576 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sqrt.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sqrt.pass.cpp
@@ -14,6 +14,7 @@
 
 #include <complex>
 #include <cassert>
+#include <type_traits>
 
 #include "test_macros.h"
 #include "../cases.h"
@@ -34,67 +35,91 @@ test()
     test(std::complex<T>(64, 0), std::complex<T>(8, 0));
 }
 
+// cosine calculations for std::arg terminate at different times based on the precision of T,
+// and can produce a very small negative number instead of a very small positive one, so we
+// should actually check that we're really close to zero instead of positive.
+template<class T>
+bool approaching_zero(const T value)
+{
+    auto in_range = [value](const T low, const T high) {
+        return low < value && value < high;
+    };
+    if constexpr (std::is_same_v<T, float>) {
+        return value == -0.0f || in_range(-4.38e-5f, 4.38e-5f);
+    }
+    else if constexpr (std::is_same_v<T, double>) {
+        return false;
+    }
+    else if constexpr (std::is_same_v<T, long double>) {
+        return value == -0.0f || in_range(-3.0e-17L, 3.0e-17L);
+    }
+    else {
+        std::abort();
+    }
+}
+
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = sqrt(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = sqrt(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
-            assert(!std::signbit(r.real()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(!std::signbit(r.real()) || approaching_zero(r.real()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
             assert(std::isinf(r.imag()));
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isfinite(testcases<T>[i].imag()))
         {
             assert(r.real() == 0);
             assert(!std::signbit(r.real()));
             assert(std::isinf(r.imag()));
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
             assert(r.imag() == 0);
-            assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag()));
+            assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() < 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isinf(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && testcases[i].real() > 0 && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && testcases<T>[i].real() > 0 && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isinf(r.real()));
             assert(r.real() > 0);
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && (std::isfinite(testcases[i].imag()) || std::isnan(testcases[i].imag())))
+        else if (std::isnan(testcases<T>[i].real()) && (std::isfinite(testcases<T>[i].imag()) || std::isnan(testcases<T>[i].imag())))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::signbit(testcases[i].imag()))
+        else if (std::signbit(testcases<T>[i].imag()))
         {
-            assert(!std::signbit(r.real()));
+            assert(!std::signbit(r.real()) || approaching_zero(r.real()));
             assert(std::signbit(r.imag()));
         }
         else
         {
-            assert(!std::signbit(r.real()));
+            assert(!std::signbit(r.real()) || approaching_zero(r.real()));
             assert(!std::signbit(r.imag()));
         }
     }
@@ -105,7 +130,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/tan.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/tan.pass.cpp
index 5c1f61ef644d3a..dc946a7808b628 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/tan.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/tan.pass.cpp
@@ -33,15 +33,16 @@ test()
     test(std::complex<T>(10000, -10000), std::complex<T>(0, -1));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = tan(testcases[i]);
-        std::complex<double> t1(-imag(testcases[i]), real(testcases[i]));
-        std::complex<double> t2 = tanh(t1);
-        std::complex<double> z(imag(t2), -real(t2));
+        std::complex<T> r = tan(testcases<T>[i]);
+        std::complex<T> t1(-imag(testcases<T>[i]), real(testcases<T>[i]));
+        std::complex<T> t2 = tanh(t1);
+        std::complex<T> z(imag(t2), -real(t2));
         if (std::isnan(real(r)))
             assert(std::isnan(real(z)));
         else
@@ -64,7 +65,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/tanh.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/tanh.pass.cpp
index f48cc88c6a38de..ebb27f82bf114f 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/tanh.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/tanh.pass.cpp
@@ -32,61 +32,68 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(0, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = tanh(testcases[i]);
-        if (testcases[i].real() == 0 && testcases[i].imag() == 0)
+        std::complex<T> r = tanh(testcases<T>[i]);
+        if (testcases<T>[i].real() == 0 && testcases<T>[i].imag() == 0)
         {
             assert(r.real() == 0);
-            assert(std::signbit(r.real()) == std::signbit(testcases[i].real()));
+            assert(std::signbit(r.real()) == std::signbit(testcases<T>[i].real()));
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isfinite(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isfinite(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isinf(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
-            assert(r.real() == (testcases[i].real() > 0 ? 1 : -1));
+            assert(r.real() == (testcases<T>[i].real() > 0 ? 1 : -1));
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(sin(2 * testcases[i].imag())));
+            assert(std::signbit(r.imag()) == std::signbit(sin(2 * testcases<T>[i].imag())));
         }
-        else if (std::isinf(testcases[i].real()) && std::isinf(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
         {
-            assert(r.real() == (testcases[i].real() > 0 ? 1 : -1));
+            assert(r.real() == (testcases<T>[i].real() > 0 ? 1 : -1));
             assert(r.imag() == 0);
         }
-        else if (std::isinf(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isinf(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
-            assert(r.real() == (testcases[i].real() > 0 ? 1 : -1));
+            assert(r.real() == (testcases<T>[i].real() > 0 ? 1 : -1));
             assert(r.imag() == 0);
         }
-        else if (std::isnan(testcases[i].real()) && testcases[i].imag() == 0)
+        else if (std::isnan(testcases<T>[i].real()) && testcases<T>[i].imag() == 0)
         {
             assert(std::isnan(r.real()));
             assert(r.imag() == 0);
-            assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag()));
+            assert(std::signbit(r.imag()) == std::signbit(testcases<T>[i].imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isfinite(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
-        else if (std::isnan(testcases[i].real()) && std::isnan(testcases[i].imag()))
+        else if (std::isnan(testcases<T>[i].real()) && std::isnan(testcases<T>[i].imag()))
         {
             assert(std::isnan(r.real()));
             assert(std::isnan(r.imag()));
         }
+        else if (std::isfinite(testcases<T>[i].real()) && std::isfinite(testcases<T>[i].imag()))
+        {
+            [[maybe_unused]] auto const x = testcases<T>[i];
+            assert(!std::isnan(r.real()));
+            assert(!std::isnan(r.imag()));
+        }
     }
 }
 
@@ -95,7 +102,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/abs.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/abs.pass.cpp
index d5ed2a6ba148cf..486596c2e923a4 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/abs.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/abs.pass.cpp
@@ -26,18 +26,26 @@ test()
     assert(abs(z) == 5);
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        double r = abs(testcases[i]);
-        switch (classify(testcases[i]))
+        T r = abs(testcases<T>[i]);
+        switch (classify(testcases<T>[i]))
         {
         case zero:
             assert(r == 0);
             assert(!std::signbit(r));
             break;
+        case maximum_value: {
+            // It appears that `max<float> + relatively_small_number == max<float>`, so we check to
+            // make sure that abs was actually effective before asserting that it should be infinity.
+            bool const ineffective_abs = (testcases<T>[i].real() + testcases<T>[i].imag()) == r;
+            assert((std::isinf(r) && r > 0) || ineffective_abs);
+            break;
+        }
         case non_zero:
             assert(std::isfinite(r) && r > 0);
             break;
@@ -59,7 +67,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/arg.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/arg.pass.cpp
index 49c54372a8e002..6367f20a635953 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/arg.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/arg.pass.cpp
@@ -26,45 +26,47 @@ test()
     assert(arg(z) == 0);
 }
 
+template<class T>
 void test_edges()
 {
-    const double pi = std::atan2(+0., -0.);
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const T pi = std::atan2(T(+0.), T(-0.));
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        double r = arg(testcases[i]);
-        if (std::isnan(testcases[i].real()) || std::isnan(testcases[i].imag()))
+        T r = arg(testcases<T>[i]);
+        if (std::isnan(testcases<T>[i].real()) || std::isnan(testcases<T>[i].imag()))
             assert(std::isnan(r));
         else
         {
-            switch (classify(testcases[i]))
+            switch (classify(testcases<T>[i]))
             {
             case zero:
-                if (std::signbit(testcases[i].real()))
+                if (std::signbit(testcases<T>[i].real()))
                 {
-                    if (std::signbit(testcases[i].imag()))
+                    if (std::signbit(testcases<T>[i].imag()))
                         is_about(r, -pi);
                     else
                         is_about(r, pi);
                 }
                 else
                 {
-                    assert(std::signbit(testcases[i].imag()) == std::signbit(r));
+                    assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r));
                 }
                 break;
+            case maximum_value:
             case non_zero:
-                if (testcases[i].real() == 0)
+                if (testcases<T>[i].real() == 0)
                 {
-                    if (testcases[i].imag() < 0)
+                    if (testcases<T>[i].imag() < 0)
                         is_about(r, -pi/2);
                     else
                         is_about(r, pi/2);
                 }
-                else if (testcases[i].imag() == 0)
+                else if (testcases<T>[i].imag() == 0)
                 {
-                    if (testcases[i].real() < 0)
+                    if (testcases<T>[i].real() < 0)
                     {
-                        if (std::signbit(testcases[i].imag()))
+                        if (std::signbit(testcases<T>[i].imag()))
                             is_about(r, -pi);
                         else
                             is_about(r, pi);
@@ -72,37 +74,37 @@ void test_edges()
                     else
                     {
                         assert(r == 0);
-                        assert(std::signbit(testcases[i].imag()) == std::signbit(r));
+                        assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r));
                     }
                 }
-                else if (testcases[i].imag() > 0)
+                else if (testcases<T>[i].imag() > 0)
                     assert(r > 0);
                 else
                     assert(r < 0);
                 break;
             case inf:
-                if (std::isinf(testcases[i].real()) && std::isinf(testcases[i].imag()))
+                if (std::isinf(testcases<T>[i].real()) && std::isinf(testcases<T>[i].imag()))
                 {
-                    if (testcases[i].real() < 0)
+                    if (testcases<T>[i].real() < 0)
                     {
-                        if (testcases[i].imag() > 0)
-                            is_about(r, 0.75 * pi);
+                        if (testcases<T>[i].imag() > 0)
+                            is_about(r, T( 0.75) * pi);
                         else
-                            is_about(r, -0.75 * pi);
+                            is_about(r, T(-0.75) * pi);
                     }
                     else
                     {
-                        if (testcases[i].imag() > 0)
-                            is_about(r, 0.25 * pi);
+                        if (testcases<T>[i].imag() > 0)
+                            is_about(r, T( 0.25) * pi);
                         else
-                            is_about(r, -0.25 * pi);
+                            is_about(r, T(-0.25) * pi);
                     }
                 }
-                else if (std::isinf(testcases[i].real()))
+                else if (std::isinf(testcases<T>[i].real()))
                 {
-                    if (testcases[i].real() < 0)
+                    if (testcases<T>[i].real() < 0)
                     {
-                        if (std::signbit(testcases[i].imag()))
+                        if (std::signbit(testcases<T>[i].imag()))
                             is_about(r, -pi);
                         else
                             is_about(r, pi);
@@ -110,12 +112,12 @@ void test_edges()
                     else
                     {
                         assert(r == 0);
-                        assert(std::signbit(r) == std::signbit(testcases[i].imag()));
+                        assert(std::signbit(r) == std::signbit(testcases<T>[i].imag()));
                     }
                 }
                 else
                 {
-                    if (testcases[i].imag() < 0)
+                    if (testcases<T>[i].imag() < 0)
                         is_about(r, -pi/2);
                     else
                         is_about(r, pi/2);
@@ -131,7 +133,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/norm.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/norm.pass.cpp
index 6e6dc10f1928d3..b1a699e1113a3e 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/norm.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/norm.pass.cpp
@@ -26,13 +26,14 @@ test()
     assert(norm(z) == 25);
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        double r = norm(testcases[i]);
-        switch (classify(testcases[i]))
+        T r = norm(testcases<T>[i]);
+        switch (classify(testcases<T>[i]))
         {
         case zero:
             assert(r == 0);
@@ -41,6 +42,7 @@ void test_edges()
         case non_zero:
             assert(std::isfinite(r) && r > 0);
             break;
+        case maximum_value:
         case inf:
             assert(std::isinf(r) && r > 0);
             break;
@@ -59,7 +61,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/polar.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/polar.pass.cpp
index 2b9c764abb591b..343ba9dbc51b4f 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/polar.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/polar.pass.cpp
@@ -44,14 +44,15 @@ test()
     test(T(100), T(0), std::complex<T>(100, 0));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        double r = real(testcases[i]);
-        double theta = imag(testcases[i]);
-        std::complex<double> z = std::polar(r, theta);
+        T r = real(testcases<T>[i]);
+        T theta = imag(testcases<T>[i]);
+        std::complex<T> z = std::polar(r, theta);
         switch (classify(r))
         {
         case zero:
@@ -62,9 +63,10 @@ void test_edges()
             }
             else
             {
-                assert(z == std::complex<double>());
+                assert(z == std::complex<T>());
             }
             break;
+        case maximum_value:
         case non_zero:
             if (std::signbit(r) || classify(theta) == inf || classify(theta) == NaN)
             {
@@ -108,7 +110,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/proj.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/proj.pass.cpp
index e118613b8dd31e..d523d49d8cdc87 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/proj.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/proj.pass.cpp
@@ -35,28 +35,30 @@ test()
     test(std::complex<T>(-1, -2), std::complex<T>(-1, -2));
 }
 
+template<class T>
 void test_edges()
 {
-    const unsigned N = sizeof(testcases) / sizeof(testcases[0]);
+    const unsigned N = sizeof(testcases<T>) / sizeof(testcases<T>[0]);
     for (unsigned i = 0; i < N; ++i)
     {
-        std::complex<double> r = proj(testcases[i]);
-        switch (classify(testcases[i]))
+        std::complex<T> r = proj(testcases<T>[i]);
+        switch (classify(testcases<T>[i]))
         {
         case zero:
         case non_zero:
-            assert(r == testcases[i]);
-            assert(std::signbit(real(r)) == std::signbit(real(testcases[i])));
-            assert(std::signbit(imag(r)) == std::signbit(imag(testcases[i])));
+        case maximum_value:
+            assert(r == testcases<T>[i]);
+            assert(std::signbit(real(r)) == std::signbit(real(testcases<T>[i])));
+            assert(std::signbit(imag(r)) == std::signbit(imag(testcases<T>[i])));
             break;
         case inf:
             assert(std::isinf(real(r)) && real(r) > 0);
             assert(imag(r) == 0);
-            assert(std::signbit(imag(r)) == std::signbit(imag(testcases[i])));
+            assert(std::signbit(imag(r)) == std::signbit(imag(testcases<T>[i])));
             break;
         case NaN:
         case non_zero_nan:
-            assert(classify(r) == classify(testcases[i]));
+            assert(classify(r) == classify(testcases<T>[i]));
             break;
         }
     }
@@ -67,7 +69,9 @@ int main(int, char**)
     test<float>();
     test<double>();
     test<long double>();
-    test_edges();
+    test_edges<float>();
+    test_edges<double>();
+    test_edges<long double>();
 
   return 0;
 }

>From 976a6937eb347c68371a321de843a9dbc03d969c Mon Sep 17 00:00:00 2001
From: Christopher Di Bella <cjdb at google.com>
Date: Wed, 8 Jan 2025 23:45:09 +0000
Subject: [PATCH 2/2] adds tests for lowest floating-point values

---
 libcxx/test/std/numerics/complex.number/cases.h | 17 ++++++++++++++++-
 .../complex.ops/complex_divide_complex.pass.cpp |  8 +++++++-
 .../complex.ops/complex_times_complex.pass.cpp  |  7 ++++++-
 .../complex.transcendentals/sinh.pass.cpp       |  2 --
 .../complex.transcendentals/sqrt.pass.cpp       | 11 +++++++++--
 .../complex.value.ops/abs.pass.cpp              |  9 ++++++++-
 .../complex.value.ops/arg.pass.cpp              |  1 +
 .../complex.value.ops/norm.pass.cpp             |  1 +
 .../complex.value.ops/polar.pass.cpp            |  1 +
 .../complex.value.ops/proj.pass.cpp             |  1 +
 10 files changed, 50 insertions(+), 8 deletions(-)

diff --git a/libcxx/test/std/numerics/complex.number/cases.h b/libcxx/test/std/numerics/complex.number/cases.h
index 61096dd875fc4b..37d327450311ae 100644
--- a/libcxx/test/std/numerics/complex.number/cases.h
+++ b/libcxx/test/std/numerics/complex.number/cases.h
@@ -194,11 +194,22 @@ TEST_CONSTEXPR_CXX20 const std::complex<T> testcases[] =
     std::complex<T>(std::numeric_limits<T>::infinity(), std::numeric_limits<T>::infinity()),
 
     std::complex<T>(std::numeric_limits<T>::max(), 1),
+    std::complex<T>(std::numeric_limits<T>::max(), -1),
+    std::complex<T>(std::numeric_limits<T>::lowest(), 1),
+    std::complex<T>(std::numeric_limits<T>::lowest(), -1),
+
     std::complex<T>(1, std::numeric_limits<T>::max()),
+    std::complex<T>(1, std::numeric_limits<T>::lowest()),
+    std::complex<T>(-1, std::numeric_limits<T>::max()),
+    std::complex<T>(-1, std::numeric_limits<T>::lowest()),
+
     std::complex<T>(std::numeric_limits<T>::max(), std::numeric_limits<T>::max()),
+    std::complex<T>(std::numeric_limits<T>::max(), std::numeric_limits<T>::lowest()),
+    std::complex<T>(std::numeric_limits<T>::lowest(), std::numeric_limits<T>::max()),
+    std::complex<T>(std::numeric_limits<T>::lowest(), std::numeric_limits<T>::lowest()),
 };
 
-enum {zero, non_zero, maximum_value, inf, NaN, non_zero_nan};
+enum {zero, non_zero, lowest_value, maximum_value, inf, NaN, non_zero_nan};
 
 template <class T, typename std::enable_if<std::is_floating_point<T>::value, int>::type = 0>
 TEST_CONSTEXPR_CXX20 bool test_isinf(T v) {
@@ -235,6 +246,8 @@ classify(const std::complex<T>& x)
     }
     if (x.real() == std::numeric_limits<T>::max() || x.imag() == std::numeric_limits<T>::max())
         return maximum_value;
+    if (x.real() == std::numeric_limits<T>::lowest() || x.imag() == std::numeric_limits<T>::lowest())
+        return lowest_value;
     return non_zero;
 }
 
@@ -251,6 +264,8 @@ classify(T x)
         return NaN;
     if (x == std::numeric_limits<T>::max())
         return maximum_value;
+    if (x == std::numeric_limits<T>::lowest())
+        return lowest_value;
     return non_zero;
 }
 
diff --git a/libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp
index 9f4b139574b029..bc0bdd0ec261dd 100644
--- a/libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp
@@ -12,7 +12,7 @@
 //   complex<T>
 //   operator/(const complex<T>& lhs, const complex<T>& rhs); // constexpr in C++20
 
-// ADDITIONAL_COMPILE_FLAGS(has-fconstexpr-steps): -fconstexpr-steps=2000000
+// ADDITIONAL_COMPILE_FLAGS(has-fconstexpr-steps): -fconstexpr-steps=2131685
 
 #include <cassert>
 #include <complex>
@@ -55,6 +55,7 @@ test_edges()
         case zero:
           assert(classify(r) == NaN);
           break;
+        case lowest_value:
         case maximum_value:
           continue; // not tested
         case non_zero:
@@ -71,6 +72,7 @@ test_edges()
           break;
         }
         break;
+      case lowest_value:
       case maximum_value:
         continue; // not tested
       case non_zero:
@@ -78,6 +80,7 @@ test_edges()
         case zero:
           assert(classify(r) == inf);
           break;
+        case lowest_value:
         case maximum_value:
           continue; // not tested
         case non_zero:
@@ -99,6 +102,7 @@ test_edges()
         case zero:
           assert(classify(r) == inf);
           break;
+        case lowest_value:
         case maximum_value:
           continue; // not tested
         case non_zero:
@@ -120,6 +124,7 @@ test_edges()
         case zero:
           assert(classify(r) == NaN);
           break;
+        case lowest_value:
         case maximum_value:
           continue; // not tested
         case non_zero:
@@ -141,6 +146,7 @@ test_edges()
         case zero:
           assert(classify(r) == inf);
           break;
+        case lowest_value:
         case maximum_value:
           continue; // not tested
         case non_zero:
diff --git a/libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp
index ebc5f03e58ed98..11256f651ffa78 100644
--- a/libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp
@@ -12,7 +12,7 @@
 //   complex<T>
 //   operator*(const complex<T>& lhs, const complex<T>& rhs); // constexpr in C++20
 
-// ADDITIONAL_COMPILE_FLAGS(has-fconstexpr-steps): -fconstexpr-steps=2000000
+// ADDITIONAL_COMPILE_FLAGS(has-fconstexpr-steps): -fconstexpr-steps=2131685
 
 #include <complex>
 #include <cassert>
@@ -51,6 +51,7 @@ TEST_CONSTEXPR_CXX20 bool test_edges()
             case zero:
                 switch (classification[j])
                 {
+                case lowest_value:
                 case maximum_value:
                     continue; // not tested
                 case zero:
@@ -64,6 +65,7 @@ TEST_CONSTEXPR_CXX20 bool test_edges()
                     break;
                 }
                 break;
+            case lowest_value:
             case maximum_value:
                 continue; // not tested
             case non_zero:
@@ -72,6 +74,7 @@ TEST_CONSTEXPR_CXX20 bool test_edges()
                 case zero:
                     assert(classify(r) == zero);
                     break;
+                case lowest_value:
                 case maximum_value:
                     continue; // not tested
                 case non_zero:
@@ -93,6 +96,7 @@ TEST_CONSTEXPR_CXX20 bool test_edges()
                 case NaN:
                     assert(classify(r) == NaN);
                     break;
+                case lowest_value:
                 case maximum_value:
                     continue; // not tested
                 case non_zero:
@@ -111,6 +115,7 @@ TEST_CONSTEXPR_CXX20 bool test_edges()
                 case inf:
                     assert(classify(r) == inf);
                     break;
+                case lowest_value:
                 case maximum_value:
                     continue; // not tested
                 case zero:
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sinh.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sinh.pass.cpp
index 62693f18b46225..d98b1736930634 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sinh.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sinh.pass.cpp
@@ -32,8 +32,6 @@ test()
     test(std::complex<T>(0, 0), std::complex<T>(0, 0));
 }
 
-#include <print>
-
 template<class T>
 void test_edges()
 {
diff --git a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sqrt.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sqrt.pass.cpp
index 1f2f9e9af4e576..64181649e8ba87 100644
--- a/libcxx/test/std/numerics/complex.number/complex.transcendentals/sqrt.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.transcendentals/sqrt.pass.cpp
@@ -114,12 +114,19 @@ void test_edges()
         }
         else if (std::signbit(testcases<T>[i].imag()))
         {
-            assert(!std::signbit(r.real()) || approaching_zero(r.real()));
+            // FIXME(https://github.com/llvm/llvm-project/issues/122172): move `expected_pass` into
+            // assert once #122172 is fixed.
+            const bool expected_pass = !std::signbit(r.real()) || approaching_zero(r.real());
+            assert((i != 156 || std::is_same<T, double>::value) ? expected_pass : !expected_pass);
             assert(std::signbit(r.imag()));
         }
         else
         {
-            assert(!std::signbit(r.real()) || approaching_zero(r.real()));
+
+            // FIXME(https://github.com/llvm/llvm-project/issues/122172): move `expected_pass` into
+            // assert once #122172 is fixed.
+            const bool expected_pass = !std::signbit(r.real()) || approaching_zero(r.real());
+            assert((i != 155 || std::is_same<T, double>::value) ? expected_pass : !expected_pass);
             assert(!std::signbit(r.imag()));
         }
     }
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/abs.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/abs.pass.cpp
index 486596c2e923a4..90e7aed7e2a486 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/abs.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/abs.pass.cpp
@@ -39,10 +39,17 @@ void test_edges()
             assert(r == 0);
             assert(!std::signbit(r));
             break;
+        case lowest_value: {
+            // It appears that `lowest<float> - relatively_small_number == lowest<float>`, so we check to
+            // make sure that abs was actually effective before asserting that it should be infinity.
+            bool const ineffective_abs = testcases<T>[i].real() + testcases<T>[i].imag() == -r;
+            assert((std::isinf(r) && r > 0) || ineffective_abs);
+            break;
+        }
         case maximum_value: {
             // It appears that `max<float> + relatively_small_number == max<float>`, so we check to
             // make sure that abs was actually effective before asserting that it should be infinity.
-            bool const ineffective_abs = (testcases<T>[i].real() + testcases<T>[i].imag()) == r;
+            bool const ineffective_abs = testcases<T>[i].real() + testcases<T>[i].imag() == r;
             assert((std::isinf(r) && r > 0) || ineffective_abs);
             break;
         }
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/arg.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/arg.pass.cpp
index 6367f20a635953..2d7fa5c64fb516 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/arg.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/arg.pass.cpp
@@ -53,6 +53,7 @@ void test_edges()
                     assert(std::signbit(testcases<T>[i].imag()) == std::signbit(r));
                 }
                 break;
+            case lowest_value:
             case maximum_value:
             case non_zero:
                 if (testcases<T>[i].real() == 0)
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/norm.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/norm.pass.cpp
index b1a699e1113a3e..2589e8ba6d9d47 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/norm.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/norm.pass.cpp
@@ -42,6 +42,7 @@ void test_edges()
         case non_zero:
             assert(std::isfinite(r) && r > 0);
             break;
+        case lowest_value:
         case maximum_value:
         case inf:
             assert(std::isinf(r) && r > 0);
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/polar.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/polar.pass.cpp
index 343ba9dbc51b4f..69f282d666c0b1 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/polar.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/polar.pass.cpp
@@ -66,6 +66,7 @@ void test_edges()
                 assert(z == std::complex<T>());
             }
             break;
+        case lowest_value:
         case maximum_value:
         case non_zero:
             if (std::signbit(r) || classify(theta) == inf || classify(theta) == NaN)
diff --git a/libcxx/test/std/numerics/complex.number/complex.value.ops/proj.pass.cpp b/libcxx/test/std/numerics/complex.number/complex.value.ops/proj.pass.cpp
index d523d49d8cdc87..e4b67b21ae5b30 100644
--- a/libcxx/test/std/numerics/complex.number/complex.value.ops/proj.pass.cpp
+++ b/libcxx/test/std/numerics/complex.number/complex.value.ops/proj.pass.cpp
@@ -46,6 +46,7 @@ void test_edges()
         {
         case zero:
         case non_zero:
+        case lowest_value:
         case maximum_value:
             assert(r == testcases<T>[i]);
             assert(std::signbit(real(r)) == std::signbit(real(testcases<T>[i])));



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