cmath: Support clang's -fdelayed-template-parsing

[dexonsmith]

Summary

r283051 added some functions to cmath (in namespace std) that have the same name as functions in math.h (in the global namespace). Clang's limited support for -fdelayed-template-parsing chokes on this. Rename the ones in cmath and their uses in complex and the test.

(Incidentally, I noticed that r283051 was optimizing the implementation of <complex>. I wonder why we have so much code in that header, instead of calling out to libc's already-optimized <complex.h> implementation?)

rdar://problem/32848355

[dexonsmith]

Ping! Hal, you committed r283051. Do you have a problem with this?

[hfinkel]

In D34578#801357, @dexonsmith wrote:

Ping! Hal, you committed r283051. Do you have a problem with this?

It looks like you're just renaming __libcpp_isnan and friends to __libcpp_isnan_or_builtin` and similar. LGTM

(Incidentally, I noticed that r283051 was optimizing the implementation of <complex>. I wonder why we have so much code in that header, instead of calling out to libc's already-optimized <complex.h> implementation?)

This is definitely worth looking at (especially given that we don't support complex of user-defined types with those functions). Would making complex<double> use _Complex double, and so on, be an API break? Would that matter?

[dexonsmith]

In D34578#801519, @hfinkel wrote:

In D34578#801357, @dexonsmith wrote:

Ping! Hal, you committed r283051. Do you have a problem with this?

It looks like you're just renaming __libcpp_isnan and friends to __libcpp_isnan_or_builtin` and similar. LGTM

Thanks; committed in r307357.

(Incidentally, I noticed that r283051 was optimizing the implementation of <complex>. I wonder why we have so much code in that header, instead of calling out to libc's already-optimized <complex.h> implementation?)

This is definitely worth looking at (especially given that we don't support complex of user-defined types with those functions). Would making complex<double> use _Complex double, and so on, be an API break? Would that matter?

I think paragraph 4 of complex.numbers (from n4640) effectively enforces that complex<T> and _Complex T are ABI-compatible.

libcxx/include/cmath

static_assert((!(is_same<_A1, __result_type>::value &&
                      is_same<_A3, __result_type>::value)), "");
     return hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z);
 }
 #endif
 
 template <class _A1>
 _LIBCPP_ALWAYS_INLINE
 _LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
-__libcpp_isnan(_A1 __lcpp_x) _NOEXCEPT
+__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
 {
 #if __has_builtin(__builtin_isnan)
     return __builtin_isnan(__lcpp_x);
 #else
     return isnan(__lcpp_x);
 #endif
 }
 
 template <class _A1>
 _LIBCPP_ALWAYS_INLINE
 _LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
-__libcpp_isnan(_A1 __lcpp_x) _NOEXCEPT
+__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
 {
     return isnan(__lcpp_x);
 }
 
 template <class _A1>
 _LIBCPP_ALWAYS_INLINE
 _LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
-__libcpp_isinf(_A1 __lcpp_x) _NOEXCEPT
+__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
 {
 #if __has_builtin(__builtin_isinf)
     return __builtin_isinf(__lcpp_x);
 #else
     return isinf(__lcpp_x);
 #endif
 }
 
 template <class _A1>
 _LIBCPP_ALWAYS_INLINE
 _LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
-__libcpp_isinf(_A1 __lcpp_x) _NOEXCEPT
+__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
 {
     return isinf(__lcpp_x);
 }
 
 template <class _A1>
 _LIBCPP_ALWAYS_INLINE
 _LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
-__libcpp_isfinite(_A1 __lcpp_x) _NOEXCEPT
+__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
 {
 #if __has_builtin(__builtin_isfinite)
     return __builtin_isfinite(__lcpp_x);
 #else
     return isfinite(__lcpp_x);
 #endif
 }
 
 template <class _A1>
 _LIBCPP_ALWAYS_INLINE
 _LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
-__libcpp_isfinite(_A1 __lcpp_x) _NOEXCEPT
+__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
 {
     return isfinite(__lcpp_x);
 }
 
 _LIBCPP_END_NAMESPACE_STD
 
 #endif  // _LIBCPP_CMATH

libcxx/include/complex

operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
     _Tp __c = __w.real();
     _Tp __d = __w.imag();
     _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 (__libcpp_isnan(__x) && __libcpp_isnan(__y))
+    if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
     {
         bool __recalc = false;
-        if (__libcpp_isinf(__a) || __libcpp_isinf(__b))
+        if (__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b))
         {
-            __a = copysign(__libcpp_isinf(__a) ? _Tp(1) : _Tp(0), __a);
-            __b = copysign(__libcpp_isinf(__b) ? _Tp(1) : _Tp(0), __b);
-            if (__libcpp_isnan(__c))
+            __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
+            __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
+            if (__libcpp_isnan_or_builtin(__c))
                 __c = copysign(_Tp(0), __c);
-            if (__libcpp_isnan(__d))
+            if (__libcpp_isnan_or_builtin(__d))
                 __d = copysign(_Tp(0), __d);
             __recalc = true;
         }
-        if (__libcpp_isinf(__c) || __libcpp_isinf(__d))
+        if (__libcpp_isinf_or_builtin(__c) || __libcpp_isinf_or_builtin(__d))
         {
-            __c = copysign(__libcpp_isinf(__c) ? _Tp(1) : _Tp(0), __c);
-            __d = copysign(__libcpp_isinf(__d) ? _Tp(1) : _Tp(0), __d);
-            if (__libcpp_isnan(__a))
+            __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
+            __d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
+            if (__libcpp_isnan_or_builtin(__a))
                 __a = copysign(_Tp(0), __a);
-            if (__libcpp_isnan(__b))
+            if (__libcpp_isnan_or_builtin(__b))
                 __b = copysign(_Tp(0), __b);
             __recalc = true;
         }
-        if (!__recalc && (__libcpp_isinf(__ac) || __libcpp_isinf(__bd) ||
-                          __libcpp_isinf(__ad) || __libcpp_isinf(__bc)))
+        if (!__recalc && (__libcpp_isinf_or_builtin(__ac) || __libcpp_isinf_or_builtin(__bd) ||
+                          __libcpp_isinf_or_builtin(__ad) || __libcpp_isinf_or_builtin(__bc)))
         {
-            if (__libcpp_isnan(__a))
+            if (__libcpp_isnan_or_builtin(__a))
                 __a = copysign(_Tp(0), __a);
-            if (__libcpp_isnan(__b))
+            if (__libcpp_isnan_or_builtin(__b))
                 __b = copysign(_Tp(0), __b);
-            if (__libcpp_isnan(__c))
+            if (__libcpp_isnan_or_builtin(__c))
                 __c = copysign(_Tp(0), __c);
-            if (__libcpp_isnan(__d))
+            if (__libcpp_isnan_or_builtin(__d))
                 __d = copysign(_Tp(0), __d);
             __recalc = true;
         }
         if (__recalc)
         {
             __x = _Tp(INFINITY) * (__a * __c - __b * __d);
             __y = _Tp(INFINITY) * (__a * __d + __b * __c);
         }

 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 = logb(fmax(fabs(__c), fabs(__d)));
-    if (__libcpp_isfinite(__logbw))
+    if (__libcpp_isfinite_or_builtin(__logbw))
     {
         __ilogbw = static_cast<int>(__logbw);
         __c = scalbn(__c, -__ilogbw);
         __d = scalbn(__d, -__ilogbw);
     }
     _Tp __denom = __c * __c + __d * __d;
     _Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
     _Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
-    if (__libcpp_isnan(__x) && __libcpp_isnan(__y))
+    if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
     {
-        if ((__denom == _Tp(0)) && (!__libcpp_isnan(__a) || !__libcpp_isnan(__b)))
+        if ((__denom == _Tp(0)) && (!__libcpp_isnan_or_builtin(__a) || !__libcpp_isnan_or_builtin(__b)))
         {
             __x = copysign(_Tp(INFINITY), __c) * __a;
             __y = copysign(_Tp(INFINITY), __c) * __b;
         }
-        else if ((__libcpp_isinf(__a) || __libcpp_isinf(__b)) && __libcpp_isfinite(__c) && __libcpp_isfinite(__d))
+        else if ((__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b)) && __libcpp_isfinite_or_builtin(__c) && __libcpp_isfinite_or_builtin(__d))
         {
-            __a = copysign(__libcpp_isinf(__a) ? _Tp(1) : _Tp(0), __a);
-            __b = copysign(__libcpp_isinf(__b) ? _Tp(1) : _Tp(0), __b);
+            __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
+            __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
             __x = _Tp(INFINITY) * (__a * __c + __b * __d);
             __y = _Tp(INFINITY) * (__b * __c - __a * __d);
         }
-        else if (__libcpp_isinf(__logbw) && __logbw > _Tp(0) && __libcpp_isfinite(__a) && __libcpp_isfinite(__b))
+        else if (__libcpp_isinf_or_builtin(__logbw) && __logbw > _Tp(0) && __libcpp_isfinite_or_builtin(__a) && __libcpp_isfinite_or_builtin(__b))
         {
-            __c = copysign(__libcpp_isinf(__c) ? _Tp(1) : _Tp(0), __c);
-            __d = copysign(__libcpp_isinf(__d) ? _Tp(1) : _Tp(0), __d);
+            __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
+            __d = copysign(__libcpp_isinf_or_builtin(__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);
 }
 
 template<class _Tp>

 
 // norm
 
 template<class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 norm(const complex<_Tp>& __c)
 {
-    if (__libcpp_isinf(__c.real()))
+    if (__libcpp_isinf_or_builtin(__c.real()))
         return abs(__c.real());
-    if (__libcpp_isinf(__c.imag()))
+    if (__libcpp_isinf_or_builtin(__c.imag()))
         return abs(__c.imag());
     return __c.real() * __c.real() + __c.imag() * __c.imag();
 }
 
 template <class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 typename __libcpp_complex_overload_traits<_Tp>::_ValueType
 norm(_Tp __re)

 // proj
 
 template<class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 complex<_Tp>
 proj(const complex<_Tp>& __c)
 {
     std::complex<_Tp> __r = __c;
-    if (__libcpp_isinf(__c.real()) || __libcpp_isinf(__c.imag()))
+    if (__libcpp_isinf_or_builtin(__c.real()) || __libcpp_isinf_or_builtin(__c.imag()))
         __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
     return __r;
 }
 
 template <class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 typename enable_if
 <
     is_floating_point<_Tp>::value,
     typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
 >::type
 proj(_Tp __re)
 {
-    if (__libcpp_isinf(__re))
+    if (__libcpp_isinf_or_builtin(__re))
         __re = abs(__re);
     return complex<_Tp>(__re);
 }
 
 template <class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 typename enable_if
 <
     is_integral<_Tp>::value,
     typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
 >::type
 proj(_Tp __re)
 {
     typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
     return _ComplexType(__re);
 }
 
 // polar
 
 template<class _Tp>
 complex<_Tp>
 polar(const _Tp& __rho, const _Tp& __theta = _Tp(0))
 {
-    if (__libcpp_isnan(__rho) || signbit(__rho))
+    if (__libcpp_isnan_or_builtin(__rho) || signbit(__rho))
         return complex<_Tp>(_Tp(NAN), _Tp(NAN));
-    if (__libcpp_isnan(__theta))
+    if (__libcpp_isnan_or_builtin(__theta))
     {
-        if (__libcpp_isinf(__rho))
+        if (__libcpp_isinf_or_builtin(__rho))
             return complex<_Tp>(__rho, __theta);
         return complex<_Tp>(__theta, __theta);
     }
-    if (__libcpp_isinf(__theta))
+    if (__libcpp_isinf_or_builtin(__theta))
     {
-        if (__libcpp_isinf(__rho))
+        if (__libcpp_isinf_or_builtin(__rho))
             return complex<_Tp>(__rho, _Tp(NAN));
         return complex<_Tp>(_Tp(NAN), _Tp(NAN));
     }
     _Tp __x = __rho * cos(__theta);
-    if (__libcpp_isnan(__x))
+    if (__libcpp_isnan_or_builtin(__x))
         __x = 0;
     _Tp __y = __rho * sin(__theta);
-    if (__libcpp_isnan(__y))
+    if (__libcpp_isnan_or_builtin(__y))
         __y = 0;
     return complex<_Tp>(__x, __y);
 }
 
 // log
 
 template<class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY

 }
 
 // sqrt
 
 template<class _Tp>
 complex<_Tp>
 sqrt(const complex<_Tp>& __x)
 {
-    if (__libcpp_isinf(__x.imag()))
+    if (__libcpp_isinf_or_builtin(__x.imag()))
         return complex<_Tp>(_Tp(INFINITY), __x.imag());
-    if (__libcpp_isinf(__x.real()))
+    if (__libcpp_isinf_or_builtin(__x.real()))
     {
         if (__x.real() > _Tp(0))
-            return complex<_Tp>(__x.real(), __libcpp_isnan(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
-        return complex<_Tp>(__libcpp_isnan(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
+            return complex<_Tp>(__x.real(), __libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
+        return complex<_Tp>(__libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
     }
     return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
 }
 
 // exp
 
 template<class _Tp>
 complex<_Tp>
 exp(const complex<_Tp>& __x)
 {
     _Tp __i = __x.imag();
-    if (__libcpp_isinf(__x.real()))
+    if (__libcpp_isinf_or_builtin(__x.real()))
     {
         if (__x.real() < _Tp(0))
         {
-            if (!__libcpp_isfinite(__i))
+            if (!__libcpp_isfinite_or_builtin(__i))
                 __i = _Tp(1);
         }
-        else if (__i == 0 || !__libcpp_isfinite(__i))
+        else if (__i == 0 || !__libcpp_isfinite_or_builtin(__i))
         {
-            if (__libcpp_isinf(__i))
+            if (__libcpp_isinf_or_builtin(__i))
                 __i = _Tp(NAN);
             return complex<_Tp>(__x.real(), __i);
         }
     }
-    else if (__libcpp_isnan(__x.real()) && __x.imag() == 0)
+    else if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
         return __x;
     _Tp __e = exp(__x.real());
     return complex<_Tp>(__e * cos(__i), __e * sin(__i));
 }
 
 // pow
 
 template<class _Tp>

 
 // asinh
 
 template<class _Tp>
 complex<_Tp>
 asinh(const complex<_Tp>& __x)
 {
     const _Tp __pi(atan2(+0., -0.));
-    if (__libcpp_isinf(__x.real()))
+    if (__libcpp_isinf_or_builtin(__x.real()))
     {
-        if (__libcpp_isnan(__x.imag()))
+        if (__libcpp_isnan_or_builtin(__x.imag()))
             return __x;
-        if (__libcpp_isinf(__x.imag()))
+        if (__libcpp_isinf_or_builtin(__x.imag()))
             return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
         return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
     }
-    if (__libcpp_isnan(__x.real()))
+    if (__libcpp_isnan_or_builtin(__x.real()))
     {
-        if (__libcpp_isinf(__x.imag()))
+        if (__libcpp_isinf_or_builtin(__x.imag()))
             return complex<_Tp>(__x.imag(), __x.real());
         if (__x.imag() == 0)
             return __x;
         return complex<_Tp>(__x.real(), __x.real());
     }
-    if (__libcpp_isinf(__x.imag()))
+    if (__libcpp_isinf_or_builtin(__x.imag()))
         return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
     complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
     return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
 }
 
 // acosh
 
 template<class _Tp>
 complex<_Tp>
 acosh(const complex<_Tp>& __x)
 {
     const _Tp __pi(atan2(+0., -0.));
-    if (__libcpp_isinf(__x.real()))
+    if (__libcpp_isinf_or_builtin(__x.real()))
     {
-        if (__libcpp_isnan(__x.imag()))
+        if (__libcpp_isnan_or_builtin(__x.imag()))
             return complex<_Tp>(abs(__x.real()), __x.imag());
-        if (__libcpp_isinf(__x.imag()))
+        if (__libcpp_isinf_or_builtin(__x.imag()))
         {
             if (__x.real() > 0)
                 return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
             else
                 return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
         }
         if (__x.real() < 0)
             return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
         return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
     }
-    if (__libcpp_isnan(__x.real()))
+    if (__libcpp_isnan_or_builtin(__x.real()))
     {
-        if (__libcpp_isinf(__x.imag()))
+        if (__libcpp_isinf_or_builtin(__x.imag()))
             return complex<_Tp>(abs(__x.imag()), __x.real());
         return complex<_Tp>(__x.real(), __x.real());
     }
-    if (__libcpp_isinf(__x.imag()))
+    if (__libcpp_isinf_or_builtin(__x.imag()))
         return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
     complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
     return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
 }
 
 // atanh
 
 template<class _Tp>
 complex<_Tp>
 atanh(const complex<_Tp>& __x)
 {
     const _Tp __pi(atan2(+0., -0.));
-    if (__libcpp_isinf(__x.imag()))
+    if (__libcpp_isinf_or_builtin(__x.imag()))
     {
         return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
     }
-    if (__libcpp_isnan(__x.imag()))
+    if (__libcpp_isnan_or_builtin(__x.imag()))
     {
-        if (__libcpp_isinf(__x.real()) || __x.real() == 0)
+        if (__libcpp_isinf_or_builtin(__x.real()) || __x.real() == 0)
             return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
         return complex<_Tp>(__x.imag(), __x.imag());
     }
-    if (__libcpp_isnan(__x.real()))
+    if (__libcpp_isnan_or_builtin(__x.real()))
     {
         return complex<_Tp>(__x.real(), __x.real());
     }
-    if (__libcpp_isinf(__x.real()))
+    if (__libcpp_isinf_or_builtin(__x.real()))
     {
         return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
     }
     if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
     {
         return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
     }
     complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
     return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
 }
 
 // sinh
 
 template<class _Tp>
 complex<_Tp>
 sinh(const complex<_Tp>& __x)
 {
-    if (__libcpp_isinf(__x.real()) && !__libcpp_isfinite(__x.imag()))
+    if (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
         return complex<_Tp>(__x.real(), _Tp(NAN));
-    if (__x.real() == 0 && !__libcpp_isfinite(__x.imag()))
+    if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
         return complex<_Tp>(__x.real(), _Tp(NAN));
-    if (__x.imag() == 0 && !__libcpp_isfinite(__x.real()))
+    if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__x.real()))
         return __x;
     return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
 }
 
 // cosh
 
 template<class _Tp>
 complex<_Tp>
 cosh(const complex<_Tp>& __x)
 {
-    if (__libcpp_isinf(__x.real()) && !__libcpp_isfinite(__x.imag()))
+    if (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
         return complex<_Tp>(abs(__x.real()), _Tp(NAN));
-    if (__x.real() == 0 && !__libcpp_isfinite(__x.imag()))
+    if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
         return complex<_Tp>(_Tp(NAN), __x.real());
     if (__x.real() == 0 && __x.imag() == 0)
         return complex<_Tp>(_Tp(1), __x.imag());
-    if (__x.imag() == 0 && !__libcpp_isfinite(__x.real()))
+    if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__x.real()))
         return complex<_Tp>(abs(__x.real()), __x.imag());
     return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
 }
 
 // tanh
 
 template<class _Tp>
 complex<_Tp>
 tanh(const complex<_Tp>& __x)
 {
-    if (__libcpp_isinf(__x.real()))
+    if (__libcpp_isinf_or_builtin(__x.real()))
     {
-        if (!__libcpp_isfinite(__x.imag()))
+        if (!__libcpp_isfinite_or_builtin(__x.imag()))
             return complex<_Tp>(_Tp(1), _Tp(0));
         return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
     }
-    if (__libcpp_isnan(__x.real()) && __x.imag() == 0)
+    if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
         return __x;
     _Tp __2r(_Tp(2) * __x.real());
     _Tp __2i(_Tp(2) * __x.imag());
     _Tp __d(cosh(__2r) + cos(__2i));
     _Tp __2rsh(sinh(__2r));
-    if (__libcpp_isinf(__2rsh) && __libcpp_isinf(__d))
+    if (__libcpp_isinf_or_builtin(__2rsh) && __libcpp_isinf_or_builtin(__d))
         return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
                             __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
     return  complex<_Tp>(__2rsh/__d, sin(__2i)/__d);
 }
 
 // asin
 
 template<class _Tp>
 complex<_Tp>
 asin(const complex<_Tp>& __x)
 {
     complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
     return complex<_Tp>(__z.imag(), -__z.real());
 }
 
 // acos
 
 template<class _Tp>
 complex<_Tp>
 acos(const complex<_Tp>& __x)
 {
     const _Tp __pi(atan2(+0., -0.));
-    if (__libcpp_isinf(__x.real()))
+    if (__libcpp_isinf_or_builtin(__x.real()))
     {
-        if (__libcpp_isnan(__x.imag()))
+        if (__libcpp_isnan_or_builtin(__x.imag()))
             return complex<_Tp>(__x.imag(), __x.real());
-        if (__libcpp_isinf(__x.imag()))
+        if (__libcpp_isinf_or_builtin(__x.imag()))
         {
             if (__x.real() < _Tp(0))
                 return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
             return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
         }
         if (__x.real() < _Tp(0))
             return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
         return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
     }
-    if (__libcpp_isnan(__x.real()))
+    if (__libcpp_isnan_or_builtin(__x.real()))
     {
-        if (__libcpp_isinf(__x.imag()))
+        if (__libcpp_isinf_or_builtin(__x.imag()))
             return complex<_Tp>(__x.real(), -__x.imag());
         return complex<_Tp>(__x.real(), __x.real());
     }
-    if (__libcpp_isinf(__x.imag()))
+    if (__libcpp_isinf_or_builtin(__x.imag()))
         return complex<_Tp>(__pi/_Tp(2), -__x.imag());
     if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
         return complex<_Tp>(__pi/_Tp(2), -__x.imag());
     complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
     if (signbit(__x.imag()))
         return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
     return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
 }

libcxx/test/libcxx/numerics/c.math/constexpr-fns.pass.cpp

 // This fails with gcc because __builtin_isnan and friends, which libcpp_isnan
 // and friends call, are not themselves constexpr-evaluatable.
 //
 // UNSUPPORTED: c++98, c++03
 // XFAIL: gcc
 
 #include <cmath>
 
-static_assert(std::__libcpp_isnan(0.) == false, "");
-static_assert(std::__libcpp_isinf(0.0) == false, "");
-static_assert(std::__libcpp_isfinite(0.0) == true, "");
+static_assert(std::__libcpp_isnan_or_builtin(0.) == false, "");
+static_assert(std::__libcpp_isinf_or_builtin(0.0) == false, "");
+static_assert(std::__libcpp_isfinite_or_builtin(0.0) == true, "");
 
 int main()
 {
 }

libcxx/test/libcxx/numerics/c.math/fdelayed-template-parsing.sh.cpp

+//===----------------------------------------------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// test that cmath builds with -fdelayed-template-parsing
+
+// REQUIRES: fdelayed-template-parsing
+
+// RUN: %build -fdelayed-template-parsing
+// RUN: %run
+
+#include <cmath>
+#include <cassert>
+
+#include "test_macros.h"
+
+int main() {
+  assert(std::isfinite(1.0));
+  assert(!std::isinf(1.0));
+  assert(!std::isnan(1.0));
+}
+
+using namespace std;

libcxx/utils/libcxx/test/config.py

def configure_features(self):
 
         if self.cxx.hasCompileFlag('-faligned-allocation'):
             self.config.available_features.add('-faligned-allocation')
         else:
             # FIXME remove this once more than just clang-4.0 support
             # C++17 aligned allocation.
             self.config.available_features.add('no-aligned-allocation')
 
+        if self.cxx.hasCompileFlag('-fdelayed-template-parsing'):
+            self.config.available_features.add('fdelayed-template-parsing')
+
         if self.get_lit_bool('has_libatomic', False):
             self.config.available_features.add('libatomic')
 
         macros = self.cxx.dumpMacros()
         if '__cpp_if_constexpr' not in macros:
             self.config.available_features.add('libcpp-no-if-constexpr')
 
         if '__cpp_structured_bindings' not in macros: