diff --git a/libcxx/include/complex b/libcxx/include/complex
--- a/libcxx/include/complex
+++ b/libcxx/include/complex
@@ -250,8 +250,21 @@
 
 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
@@ -315,6 +328,8 @@
 template<> class _LIBCPP_TEMPLATE_VIS complex<double>;
 template<> class _LIBCPP_TEMPLATE_VIS complex<long double>;
 
+struct __from_builtin_tag {};
+
 template<>
 class _LIBCPP_TEMPLATE_VIS complex<float>
 {
@@ -325,6 +340,10 @@
 
     _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
@@ -336,6 +355,12 @@
     _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 __builtin_complex(__re_, __im_); }
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR 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;}
@@ -383,6 +408,10 @@
 
     _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
@@ -394,6 +423,15 @@
     _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 __builtin_complex(__re_, __im_);
+    }
+
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR 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;}
@@ -441,6 +479,10 @@
 
     _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
@@ -452,6 +494,15 @@
     _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 __builtin_complex(__re_, __im_);
+    }
+
+    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR 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;}
@@ -581,7 +632,13 @@
     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)
 {
@@ -590,87 +647,7 @@
     _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>
@@ -693,7 +670,13 @@
     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)
 {
@@ -703,77 +686,13 @@
     _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()));
-        }
-    }
+    __ilogbw = static_cast<int>(__logbw);
+    __c = std::__constexpr_scalbn(__c, -__ilogbw);
+    __d = std::__constexpr_scalbn(__d, -__ilogbw);
 
     _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);
 }