[libc++] Use _Complex for multiplication and division of complex floating point types

[philnik]

Summary

This significantly simplifies the implementation and improves the codegen. The only downside is that the accuracy can be marginally worse, but that is up to the compiler to decide with this change, which means is can be controlled by compiler flags.

[philnik]

Try to fix CI

[Mordante]

Can you modify the CI file to run with a limited number of configurations, but enable all platform.

Also fix the non floating point test to be fixed.

That way I can get a better view of the impact of the changes.

libcxx/test/std/numerics/complex.number/complex.member.ops/divide_equal_complex.pass.cpp

29–30

I would like to test with an epsion and not >=.
I think the values used in the test should give an exact result.

[Mordante]

Please verify nan and inf etc are tested otherwise test whether they change.

[ldionne]

I think this is the right approach to implement floating-point complex. We should let the compiler do the work whenever we can. If the result is "not good enough", then that's something we should take to the compiler folks (probably compiler-rt) instead.

Also, this is how libstdc++ implements their std::complex operations, so it's not like we're doing something crazy here. The need to change tests makes me a tiny bit uncomfortable, but in reality I think the tests should have been written that way from the start -- comparing floating point values for equality is a well known anti pattern.

So this roughly looks good to me but I'd like to see again after updating with the comments and green CI.

libcxx/test/std/numerics/complex.number/complex.member.ops/divide_equal_complex.pass.cpp

29–30

Yeah we should define a function to describe the fact that the value is "equal" (or "within the tolerance") instead of explicitly checking >= and <=.

libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp

15

Is this still required? Applies here and in the other complex tests I guess.

[philnik]

Address comments

[philnik]

Try to fix CI

[ldionne]

@mstorsjo Do you know what's the state of things for compiler-rt on Windows?

To summarize the issue, it seems like we are missing __muldc3 and __mulsc3 on Windows, which should be provided in compiler-rt (from https://buildkite.com/llvm-project/libcxx-ci/builds/29818#018aa944-7c19-4abf-8476-4b506918c33a).

[mstorsjo]

In D155312#4651731, @ldionne wrote:

@mstorsjo Do you know what's the state of things for compiler-rt on Windows?

In MinGW configs, compiler-rt is alive and well and everything works - and those configs work fine in that CI run.

To summarize the issue, it seems like we are missing __muldc3 and __mulsc3 on Windows, which should be provided in compiler-rt (from https://buildkite.com/llvm-project/libcxx-ci/builds/29818#018aa944-7c19-4abf-8476-4b506918c33a).

Indeed; in clang-cl configs, compiler-rt builtins aren't linked. This is the same issue as the helpers for __int128_t that also are missing that we've run into in a few places. There were some efforts to work on this (with some discussion threads on Discourse in the last few months) with @thieta, @rnk, @hans and others.

libcxx/include/cmath

 template <class _A1>
 _LIBCPP_INLINE_VISIBILITY
 _LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
 __constexpr_isfinite(_A1 __lcpp_x) _NOEXCEPT
 {
     return __builtin_isfinite(__lcpp_x);
 }
 
-_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI float __constexpr_copysign(float __x, float __y) _NOEXCEPT {
-    return __builtin_copysignf(__x, __y);
-}
-
-_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI double __constexpr_copysign(double __x, double __y) _NOEXCEPT {
-    return __builtin_copysign(__x, __y);
-}
-
-_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI long double
-__constexpr_copysign(long double __x, long double __y) _NOEXCEPT {
-    return __builtin_copysignl(__x, __y);
-}
-
-template <class _A1, class _A2>
-_LIBCPP_CONSTEXPR inline _LIBCPP_HIDE_FROM_ABI
-    typename std::__enable_if_t<std::is_arithmetic<_A1>::value && std::is_arithmetic<_A2>::value,
-                                std::__promote<_A1, _A2> >::type
-    __constexpr_copysign(_A1 __x, _A2 __y) _NOEXCEPT {
-    typedef typename std::__promote<_A1, _A2>::type __result_type;
-    static_assert((!(std::_IsSame<_A1, __result_type>::value && std::_IsSame<_A2, __result_type>::value)), "");
-    return __builtin_copysign((__result_type)__x, (__result_type)__y);
-}
-
-inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float __constexpr_fabs(float __x) _NOEXCEPT {
-    return __builtin_fabsf(__x);
-}
-
-inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double __constexpr_fabs(double __x) _NOEXCEPT {
-    return __builtin_fabs(__x);
-}
-
-inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double __constexpr_fabs(long double __x) _NOEXCEPT {
-    return __builtin_fabsl(__x);
-}
-
-template <class _Tp, __enable_if_t<is_integral<_Tp>::value, int> = 0>
-_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double __constexpr_fabs(_Tp __x) _NOEXCEPT {
-    return __builtin_fabs(static_cast<double>(__x));
-}
-
-inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 float __constexpr_fmax(float __x, float __y) _NOEXCEPT {
-#if !__has_constexpr_builtin(__builtin_fmaxf)
-  if (__libcpp_is_constant_evaluated()) {
-    if (std::__constexpr_isnan(__x))
-      return __y;
-    if (std::__constexpr_isnan(__y))
-      return __x;
-    return __x < __y ? __y : __x;
-  }
-#endif
-  return __builtin_fmaxf(__x, __y);
-}
-
-inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 double __constexpr_fmax(double __x, double __y) _NOEXCEPT {
-#if !__has_constexpr_builtin(__builtin_fmax)
-  if (__libcpp_is_constant_evaluated()) {
-    if (std::__constexpr_isnan(__x))
-      return __y;
-    if (std::__constexpr_isnan(__y))
-      return __x;
-    return __x < __y ? __y : __x;
-  }
-#endif
-  return __builtin_fmax(__x, __y);
-}
-
-inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 long double
-__constexpr_fmax(long double __x, long double __y) _NOEXCEPT {
-#if !__has_constexpr_builtin(__builtin_fmaxl)
-  if (__libcpp_is_constant_evaluated()) {
-    if (std::__constexpr_isnan(__x))
-      return __y;
-    if (std::__constexpr_isnan(__y))
-      return __x;
-    return __x < __y ? __y : __x;
-  }
-#endif
-  return __builtin_fmaxl(__x, __y);
-}
-
-template <class _Tp, class _Up, __enable_if_t<is_arithmetic<_Tp>::value && is_arithmetic<_Up>::value, int> = 0>
-_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __promote<_Tp, _Up>::type
-__constexpr_fmax(_Tp __x, _Up __y) _NOEXCEPT {
-  using __result_type = typename __promote<_Tp, _Up>::type;
-  return std::__constexpr_fmax(static_cast<__result_type>(__x), static_cast<__result_type>(__y));
-}
-
-template <class _Tp>
-_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp __constexpr_logb(_Tp __x) {
-#if !__has_constexpr_builtin(__builtin_logb)
-  if (__libcpp_is_constant_evaluated()) {
-    if (__x == _Tp(0)) {
-      // raise FE_DIVBYZERO
-      return -numeric_limits<_Tp>::infinity();
-    }
-
-    if (std::__constexpr_isinf(__x))
-      return numeric_limits<_Tp>::infinity();
-
-    if (std::__constexpr_isnan(__x))
-      return numeric_limits<_Tp>::quiet_NaN();
-
-    __x = std::__constexpr_fabs(__x);
-    unsigned long long __exp = 0;
-    while (__x >= numeric_limits<_Tp>::radix) {
-      __x /= numeric_limits<_Tp>::radix;
-      __exp += 1;
-    }
-    return _Tp(__exp);
-  }
-#endif // !__has_constexpr_builtin(__builtin_logb)
-  return __builtin_logb(__x);
-}
-
-template <class _Tp>
-_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Tp __constexpr_scalbn(_Tp __x, int __exp) {
-#if !__has_constexpr_builtin(__builtin_scalbln)
-  if (__libcpp_is_constant_evaluated()) {
-    if (__x == _Tp(0))
-      return __x;
-
-    if (std::__constexpr_isinf(__x))
-      return __x;
-
-    if (__exp == _Tp(0))
-      return __x;
-
-    if (std::__constexpr_isnan(__x))
-      return numeric_limits<_Tp>::quiet_NaN();
-
-    _Tp __mult(1);
-    if (__exp > 0) {
-      __mult = numeric_limits<_Tp>::radix;
-      --__exp;
-    } else {
-      ++__exp;
-      __exp = -__exp;
-      __mult /= numeric_limits<_Tp>::radix;
-    }
-
-    while (__exp > 0) {
-      if (!(__exp & 1)) {
-        __mult *= __mult;
-        __exp >>= 1;
-      } else {
-        __x *= __mult;
-        --__exp;
-      }
-    }
-    return __x;
-  }
-#endif // !__has_constexpr_builtin(__builtin_scalbln)
-  return __builtin_scalbn(__x, __exp);
-}
-
 #if _LIBCPP_STD_VER >= 20
 template <typename _Fp>
 _LIBCPP_HIDE_FROM_ABI constexpr
 _Fp __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept {
     if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0))
         return __t * __b + (1 - __t) * __a;
 
     if (__t == 1) return __b;

libcxx/include/complex

 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
 #endif
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 template<class _Tp> class _LIBCPP_TEMPLATE_VIS complex;
 
-template<class _Tp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
-template<class _Tp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
+template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0>
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
+operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
+
+template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0>
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
+operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
+
+template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0>
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
+operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
+
+template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0>
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
+operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
 
 template<class _Tp>
 class _LIBCPP_TEMPLATE_VIS complex
 {
 public:
     typedef _Tp value_type;
 private:
     value_type __re_;
template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c)
             *this = *this / complex(__c.real(), __c.imag());
             return *this;
         }
 };
 
 template<> class _LIBCPP_TEMPLATE_VIS complex<double>;
 template<> class _LIBCPP_TEMPLATE_VIS complex<long double>;
 
+struct __from_builtin_tag {};
+
+template <class _Tp>
+using __complex_t =
+    __conditional_t<is_same<_Tp, float>::value,
+                    _Complex float,
+                    __conditional_t<is_same<_Tp, double>::value, _Complex double, _Complex long double> >;
+
+template <class _Tp>
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR __complex_t<_Tp> __make_complex(_Tp __re, _Tp __im) {
+#if __has_builtin(__builtin_complex)
+  return __builtin_complex(__re, __im);
+#else
+  return __complex_t<_Tp>{__re, __im};
+#endif
+}
+
 template<>
 class _LIBCPP_TEMPLATE_VIS complex<float>
 {
     float __re_;
     float __im_;
 public:
     typedef float value_type;
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f)
         : __re_(__re), __im_(__im) {}
+
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(__from_builtin_tag, _Complex float __v)
+        : __re_(__real__ __v), __im_(__imag__ __v) {}
+
     _LIBCPP_INLINE_VISIBILITY
     explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
     _LIBCPP_INLINE_VISIBILITY
     explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;}
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;}
 
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex float __builtin() const { return std::__make_complex(__re_, __im_); }
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex float __f) {
+        __re_ = __real__ __f;
+        __im_ = __imag__ __f;
+    }
+
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (float __re)
         {__re_ = __re; __im_ = value_type(); return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(float __re) {__re_ += __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(float __re) {__re_ -= __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
 
     template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c)

 {
     double __re_;
     double __im_;
 public:
     typedef double value_type;
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0)
         : __re_(__re), __im_(__im) {}
+
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(__from_builtin_tag, _Complex double __v)
+        : __re_(__real__ __v), __im_(__imag__ __v) {}
+
     _LIBCPP_INLINE_VISIBILITY
     _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
     _LIBCPP_INLINE_VISIBILITY
     explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;}
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;}
 
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex double __builtin() const {
+            return std::__make_complex(__re_, __im_);
+    }
+
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex double __f) {
+            __re_ = __real__ __f;
+            __im_ = __imag__ __f;
+    }
+
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (double __re)
         {__re_ = __re; __im_ = value_type(); return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(double __re) {__re_ += __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(double __re) {__re_ -= __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
 
     template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c)

 {
     long double __re_;
     long double __im_;
 public:
     typedef long double value_type;
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
         : __re_(__re), __im_(__im) {}
+
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(__from_builtin_tag, _Complex long double __v)
+        : __re_(__real__ __v), __im_(__imag__ __v) {}
+
     _LIBCPP_INLINE_VISIBILITY
     _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
     _LIBCPP_INLINE_VISIBILITY
     _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
 
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;}
 
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex long double __builtin() const {
+            return std::__make_complex(__re_, __im_);
+    }
+
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex long double __f) {
+            __re_ = __real__ __f;
+            __im_ = __imag__ __f;
+    }
+
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (long double __re)
         {__re_ = __re; __im_ = value_type(); return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(long double __re) {__re_ += __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(long double __re) {__re_ -= __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
     _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
 
     template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c)

 complex<_Tp>
 operator-(const _Tp& __x, const complex<_Tp>& __y)
 {
     complex<_Tp> __t(-__y);
     __t += __x;
     return __t;
 }
 
-template<class _Tp>
+template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> >
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
+operator*(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) {
+  return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() * __rhs.__builtin());
+}
+
+template<class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> >
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
 operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
 {
     _Tp __a = __z.real();
     _Tp __b = __z.imag();
     _Tp __c = __w.real();
     _Tp __d = __w.imag();
 
-    // Avoid floating point operations that are invalid during constant evaluation
-    if (__libcpp_is_constant_evaluated()) {
-        bool __z_zero = __a == _Tp(0) && __b == _Tp(0);
-        bool __w_zero = __c == _Tp(0) && __d == _Tp(0);
-        bool __z_inf = std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b);
-        bool __w_inf = std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d);
-        bool __z_nan = !__z_inf && (
-            (std::__constexpr_isnan(__a) && std::__constexpr_isnan(__b))
-            || (std::__constexpr_isnan(__a) && __b == _Tp(0))
-            || (__a == _Tp(0) && std::__constexpr_isnan(__b))
-        );
-        bool __w_nan = !__w_inf && (
-            (std::__constexpr_isnan(__c) && std::__constexpr_isnan(__d))
-            || (std::__constexpr_isnan(__c) && __d == _Tp(0))
-            || (__c == _Tp(0) && std::__constexpr_isnan(__d))
-        );
-        if (__z_nan || __w_nan) {
-            return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
-        }
-        if (__z_inf || __w_inf) {
-            if (__z_zero || __w_zero) {
-                return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
-            }
-            return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity()));
-        }
-        bool __z_nonzero_nan = !__z_inf && !__z_nan && (std::__constexpr_isnan(__a) || std::__constexpr_isnan(__b));
-        bool __w_nonzero_nan = !__w_inf && !__w_nan && (std::__constexpr_isnan(__c) || std::__constexpr_isnan(__d));
-        if (__z_nonzero_nan || __w_nonzero_nan) {
-            return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
-        }
-    }
-
-    _Tp __ac = __a * __c;
-    _Tp __bd = __b * __d;
-    _Tp __ad = __a * __d;
-    _Tp __bc = __b * __c;
-    _Tp __x = __ac - __bd;
-    _Tp __y = __ad + __bc;
-    if (std::__constexpr_isnan(__x) && std::__constexpr_isnan(__y))
-    {
-        bool __recalc = false;
-        if (std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b))
-        {
-            __a = std::__constexpr_copysign(std::__constexpr_isinf(__a) ? _Tp(1) : _Tp(0), __a);
-            __b = std::__constexpr_copysign(std::__constexpr_isinf(__b) ? _Tp(1) : _Tp(0), __b);
-            if (std::__constexpr_isnan(__c))
-                __c = std::__constexpr_copysign(_Tp(0), __c);
-            if (std::__constexpr_isnan(__d))
-                __d = std::__constexpr_copysign(_Tp(0), __d);
-            __recalc = true;
-        }
-        if (std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d))
-        {
-            __c = std::__constexpr_copysign(std::__constexpr_isinf(__c) ? _Tp(1) : _Tp(0), __c);
-            __d = std::__constexpr_copysign(std::__constexpr_isinf(__d) ? _Tp(1) : _Tp(0), __d);
-            if (std::__constexpr_isnan(__a))
-                __a = std::__constexpr_copysign(_Tp(0), __a);
-            if (std::__constexpr_isnan(__b))
-                __b = std::__constexpr_copysign(_Tp(0), __b);
-            __recalc = true;
-        }
-        if (!__recalc && (std::__constexpr_isinf(__ac) || std::__constexpr_isinf(__bd) ||
-                          std::__constexpr_isinf(__ad) || std::__constexpr_isinf(__bc)))
-        {
-            if (std::__constexpr_isnan(__a))
-                __a = std::__constexpr_copysign(_Tp(0), __a);
-            if (std::__constexpr_isnan(__b))
-                __b = std::__constexpr_copysign(_Tp(0), __b);
-            if (std::__constexpr_isnan(__c))
-                __c = std::__constexpr_copysign(_Tp(0), __c);
-            if (std::__constexpr_isnan(__d))
-                __d = std::__constexpr_copysign(_Tp(0), __d);
-            __recalc = true;
-        }
-        if (__recalc)
-        {
-            __x = _Tp(INFINITY) * (__a * __c - __b * __d);
-            __y = _Tp(INFINITY) * (__a * __d + __b * __c);
-        }
-    }
-    return complex<_Tp>(__x, __y);
+    return complex<_Tp>((__a * __c) - (__b * __d), (__a * __d) + (__b * __c));
 }
 
 template<class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20
 complex<_Tp>
 operator*(const complex<_Tp>& __x, const _Tp& __y)
 {
     complex<_Tp> __t(__x);
     __t *= __y;
     return __t;
 }
 
 template<class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20
 complex<_Tp>
 operator*(const _Tp& __x, const complex<_Tp>& __y)
 {
     complex<_Tp> __t(__y);
     __t *= __x;
     return __t;
 }
 
-template<class _Tp>
+template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> >
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
+operator/(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) {
+  return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() / __rhs.__builtin());
+}
+
+template<class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> >
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
 operator/(const complex<_Tp>& __z, const complex<_Tp>& __w)
 {
-    int __ilogbw = 0;
     _Tp __a = __z.real();
     _Tp __b = __z.imag();
     _Tp __c = __w.real();
     _Tp __d = __w.imag();
-    _Tp __logbw = std::__constexpr_logb(std::__constexpr_fmax(std::__constexpr_fabs(__c), std::__constexpr_fabs(__d)));
-    if (std::__constexpr_isfinite(__logbw))
-    {
-        __ilogbw = static_cast<int>(__logbw);
-        __c = std::__constexpr_scalbn(__c, -__ilogbw);
-        __d = std::__constexpr_scalbn(__d, -__ilogbw);
-    }
-
-    // Avoid floating point operations that are invalid during constant evaluation
-    if (__libcpp_is_constant_evaluated()) {
-        bool __z_zero = __a == _Tp(0) && __b == _Tp(0);
-        bool __w_zero = __c == _Tp(0) && __d == _Tp(0);
-        bool __z_inf = std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b);
-        bool __w_inf = std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d);
-        bool __z_nan = !__z_inf && (
-            (std::__constexpr_isnan(__a) && std::__constexpr_isnan(__b))
-            || (std::__constexpr_isnan(__a) && __b == _Tp(0))
-            || (__a == _Tp(0) && std::__constexpr_isnan(__b))
-        );
-        bool __w_nan = !__w_inf && (
-            (std::__constexpr_isnan(__c) && std::__constexpr_isnan(__d))
-            || (std::__constexpr_isnan(__c) && __d == _Tp(0))
-            || (__c == _Tp(0) && std::__constexpr_isnan(__d))
-        );
-        if ((__z_nan || __w_nan) || (__z_inf && __w_inf)) {
-            return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
-        }
-        bool __z_nonzero_nan = !__z_inf && !__z_nan && (std::__constexpr_isnan(__a) || std::__constexpr_isnan(__b));
-        bool __w_nonzero_nan = !__w_inf && !__w_nan && (std::__constexpr_isnan(__c) || std::__constexpr_isnan(__d));
-        if (__z_nonzero_nan || __w_nonzero_nan) {
-            if (__w_zero) {
-                return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity()));
-            }
-            return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
-        }
-        if (__w_inf) {
-            return complex<_Tp>(_Tp(0), _Tp(0));
-        }
-        if (__z_inf) {
-            return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity()));
-        }
-        if (__w_zero) {
-            if (__z_zero) {
-                return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
-            }
-            return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity()));
-        }
-    }
 
     _Tp __denom = __c * __c + __d * __d;
-    _Tp __x = std::__constexpr_scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
-    _Tp __y = std::__constexpr_scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
-    if (std::__constexpr_isnan(__x) && std::__constexpr_isnan(__y))
-    {
-        if ((__denom == _Tp(0)) && (!std::__constexpr_isnan(__a) || !std::__constexpr_isnan(__b)))
-        {
-            __x = std::__constexpr_copysign(_Tp(INFINITY), __c) * __a;
-            __y = std::__constexpr_copysign(_Tp(INFINITY), __c) * __b;
-        } else if ((std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b)) && std::__constexpr_isfinite(__c) &&
-                   std::__constexpr_isfinite(__d)) {
-            __a = std::__constexpr_copysign(std::__constexpr_isinf(__a) ? _Tp(1) : _Tp(0), __a);
-            __b = std::__constexpr_copysign(std::__constexpr_isinf(__b) ? _Tp(1) : _Tp(0), __b);
-            __x = _Tp(INFINITY) * (__a * __c + __b * __d);
-            __y = _Tp(INFINITY) * (__b * __c - __a * __d);
-        } else if (std::__constexpr_isinf(__logbw) && __logbw > _Tp(0) && std::__constexpr_isfinite(__a) &&
-                   std::__constexpr_isfinite(__b)) {
-            __c = std::__constexpr_copysign(std::__constexpr_isinf(__c) ? _Tp(1) : _Tp(0), __c);
-            __d = std::__constexpr_copysign(std::__constexpr_isinf(__d) ? _Tp(1) : _Tp(0), __d);
-            __x = _Tp(0) * (__a * __c + __b * __d);
-            __y = _Tp(0) * (__b * __c - __a * __d);
-        }
-    }
-    return complex<_Tp>(__x, __y);
+    return complex<_Tp>((__a * __c + __b * __d) / __denom, (__b * __c - __a * __d) / __denom);
 }
 
 template<class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20
 complex<_Tp>
 operator/(const complex<_Tp>& __x, const _Tp& __y)
 {
     return complex<_Tp>(__x.real() / __y, __x.imag() / __y);

libcxx/test/std/numerics/complex.number/complex.member.ops/divide_equal_complex.pass.cpp

 //===----------------------------------------------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 
 // <complex>
 
 // complex& operator/=(const complex& rhs); // constexpr in C++20
 
-#include <complex>
 #include <cassert>
+#include <complex>
 
+#include "floating_pointer_helpers.h"
 #include "test_macros.h"
 
 template <class T>
 TEST_CONSTEXPR_CXX20
 bool
 test()
 {
     std::complex<T> c(-4, 7.5);
     const std::complex<T> c2(1.5, 2.5);
-    assert(c.real() == -4);
-    assert(c.imag() == 7.5);
+    assert(is_close(c.real(), T(-4)));
+    assert(is_close(c.imag(), T(7.5)));
     c /= c2;
-    assert(c.real() == 1.5);
-    assert(c.imag() == 2.5);
+    assert(is_close(c.real(), T(1.5)));
+    assert(is_close(c.imag(), T(2.5)));
     c /= c2;
-    assert(c.real() == 1);
-    assert(c.imag() == 0);
+    assert(is_close(c.real(), T(1)));
+    assert(is_close(c.imag(), T(0)));
 
     std::complex<T> c3;
 
     c3 = c;
     std::complex<int> ic (1,1);
     c3 /= ic;
-    assert(c3.real() == 0.5);
-    assert(c3.imag() == -0.5);
+    assert(is_close(c3.real(), T(0.5)));
+    assert(is_close(c3.imag(), T(-0.5)));
 
     c3 = c;
     std::complex<float> fc (1,1);
     c3 /= fc;
-    assert(c3.real() == 0.5);
-    assert(c3.imag() == -0.5);
+    assert(is_close(c3.real(), T(0.5)));
+    assert(is_close(c3.imag(), T(-0.5)));
     return true;
 }
 
 int main(int, char**)
 {
     test<float>();
     test<double>();
     test<long double>();

libcxx/test/std/numerics/complex.number/complex.ops/complex_divide_complex.pass.cpp

 //===----------------------------------------------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 
 // <complex>
 
 // template<class T>
 //   complex<T>
 //   operator/(const complex<T>& lhs, const complex<T>& rhs); // constexpr in C++20
 
-// ADDITIONAL_COMPILE_FLAGS(has-fconstexpr-steps): -fconstexpr-steps=5000000
+// ADDITIONAL_COMPILE_FLAGS(has-fconstexpr-steps): -fconstexpr-steps=2000000
 
-#include <complex>
 #include <cassert>
+#include <complex>
 
+#include "floating_pointer_helpers.h"
 #include "test_macros.h"
 #include "../cases.h"
 
 template <class T>
 TEST_CONSTEXPR_CXX20
 bool
 test()
 {
     const std::complex<T> lhs(-4.0, 7.5);
     const std::complex<T> rhs(1.5, 2.5);
-    assert(lhs / rhs == std::complex<T>(1.5, 2.5));
+    const std::complex<T> c = lhs / rhs;
+    assert(is_close(c.real(), T(1.5)));
+    assert(is_close(c.imag(), T(2.5)));
     return true;
 }
 
 TEST_CONSTEXPR_CXX20
 bool
 test_edges()
 {
   const unsigned N = sizeof(testcases) / sizeof(testcases[0]);

libcxx/test/std/numerics/complex.number/complex.ops/complex_times_complex.pass.cpp

 //===----------------------------------------------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 
 // <complex>
 
 // template<class T>
 //   complex<T>
 //   operator*(const complex<T>& lhs, const complex<T>& rhs); // constexpr in C++20
 
-// ADDITIONAL_COMPILE_FLAGS(has-fconstexpr-steps): -fconstexpr-steps=5000000
+// ADDITIONAL_COMPILE_FLAGS(has-fconstexpr-steps): -fconstexpr-steps=2000000
 
 #include <complex>
 #include <cassert>
 
 #include "test_macros.h"
 #include "../cases.h"
 
 template <class T>

libcxx/test/std/numerics/complex.number/complex.ops/scalar_divide_complex.pass.cpp

 
 template <class T>
 TEST_CONSTEXPR_CXX20
 bool
 test()
 {
     const T lhs(-8.5);
     const std::complex<T> rhs(1.5, 2.5);
-    assert(lhs / rhs == std::complex<T>(-1.5, 2.5));
+    const std::complex<T> c = lhs / rhs;
+    assert(c.real() >= T(-1.500000000000001));
+    assert(c.real() <= T(-1.499999999999999));
+    assert(c.imag() >= T(2.499999999999999));
+    assert(c.imag() <= T(2.500000000000001));
     return true;
 }
 
 int main(int, char**)
 {
     test<float>();
     test<double>();
     test<long double>();

libcxx/test/support/floating_pointer_helpers.h

+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef TEST_SUPPORT_FLOATING_POINT_HELPERS_H
+#define TEST_SUPPORT_FLOATING_POINT_HELPERS_H
+
+#include <limits>
+
+#include "test_macros.h"
+
+template <class T>
+TEST_CONSTEXPR_CXX20 bool is_close(T v, T comp) {
+  return v <= comp + std::numeric_limits<T>::epsilon() && v >= comp - std::numeric_limits<T>::epsilon();
+}
+
+#endif // TEST_SUPPORT_FLOATING_POINT_HELPERS_H