[libc++][math.h] Add double overloads

[philnik]

Summary

This allows libc++ to work with libcs that don't provide a proper math.h implementation.

[ldionne]

Pinging some Clang folks to get a better understanding of how Clang builtins work (feel free to suggest other people, I'm shooting randomly based on a quick git blame): @fhahn @Izaron @aaron.ballman

@bcain also for freestanding questions

I have a few questions:

1. Which math functions does Clang define as builtin? Does it define all the overloads, or only the double one that's usually coming from the C library?
2. What do these builtins do, exactly? I assume they try to do something clever and then fall back to a library-provided implementation (and they assume there's a suitable C-linkage definition somewhere)?
3. Why are builtins that are not reserved identifiers (e.g. cos, sin) disabled in freestanding mode? I'm asking generally, I know cmath is not part of Freestanding per se.
4. More generally speaking, what's the purpose of -fno-builtins?

Sorry, this is kind of open-ended, but I feel like this is important to understand here.

Also, on a related but tangential note, @philnik and I were trying to wrap our heads around what's the purpose of compiler builtin headers. It looks like the order of includes in Clang (and GCC) is: C++ library headers > compiler builtin headers > C library headers. This is true on both Linux and Darwin, so it's not accidental, it's really by design. Now, some headers exist only in the builtin headers (e.g. <stdbool.h>), some only in the C library headers (e.g. <stdio.h>), and some in both (e.g. <stdint.h>). Can anyone shed light on the logic behind this?

Is any of this documented anywhere?

libcxx/include/math.h

546

Q: Is there any reason we are not using _LIBCPP_PREFERRED_OVERLOAD?

Answer: GCC does not support it.

Fair enough.

[Izaron]

I'll take __builtin_fmax as an example (but other builtins are fairly similar to it).

In D138629#3949782, @ldionne wrote:

1. Which math functions does Clang define as builtin? Does it define all the overloads, or only the double one that's usually coming from the C library?

The canonical builtin versions take doubles as arguments, but there are builtin versions for other types (float, half, long double, long long double), here is the list of builtins:
https://github.com/llvm/llvm-project/blob/410c1f6269779a01ad24909974eafb0f2e8d8cac/clang/include/clang/Basic/Builtins.def#L262-L266

2. What do these builtins do, exactly? I assume they try to do something clever and then fall back to a library-provided implementation (and they assume there's a suitable C-linkage definition somewhere)?

If we are inside a constexpr expression, some builtins can be calculated there, in this case Clang emulates the builtin's logic:
https://github.com/llvm/llvm-project/blob/e672f5126fcfca650534ee5fd81425df36c76eb6/clang/lib/AST/ExprConstant.cpp#L14060-L14076

If we are inside a runtime-calculated expression, then builtins are mapped to some other code. For example, __builtin_fmax is mapped into calling the llvm.maxnum.f64 intrinsic:
godbolt - https://godbolt.org/z/fboz3Phf8
intrinsics docs - https://releases.llvm.org/3.6.1/docs/LangRef.html#llvm-maxnum-intrinsic

4. More generally speaking, what's the purpose of -fno-builtins?

This is a loanword from GCC. GCC artificially treats some functions (alloca, cos, sin, ...) as builtins, because this way it might generate more effective code instead calling these functions directly.
From docs: https://gcc.gnu.org/onlinedocs/gcc/C-Dialect-Options.html

for instance, calls to alloca may become single instructions which adjust the stack directly, and calls to memcpy may become inline copy loops. The resulting code is often both smaller and faster, but since the function calls no longer appear as such, you cannot set a breakpoint on those calls, nor can you change the behavior of the functions by linking with a different library

The flag disables this behaviour.

[aaron.ballman]

In D138629#3949782, @ldionne wrote:

3. Why are builtins that are not reserved identifiers (e.g. cos, sin) disabled in freestanding mode? I'm asking generally, I know cmath is not part of Freestanding per se.

The user expectation is that freestanding mode is the minimal set of library facilities required by the language, so if the language doesn't require cos, then that identifier needs to remain available for the user to use for their own purposes. Sometimes this is so they can make their own replacement for whatever funky hardware they're on, but sometimes it's because the standard steals general purpose identifiers like tan (color name), floor (a noun), and f16subf32 (er...).

4. More generally speaking, what's the purpose of -fno-builtins?

To disable all builtins regardless of whether you're in freestanding mode or not. Sometimes the builtins do things you don't want them to do and so you want to disable them (perhaps you don't like the behavior of __builtin_memcpy for some reason), and sometimes the builtins expose names you want to use (https://godbolt.org/z/cMxzojcr1).

Sorry, this is kind of open-ended, but I feel like this is important to understand here.

No worries at all, these are great questions!

Also, on a related but tangential note, @philnik and I were trying to wrap our heads around what's the purpose of compiler builtin headers. It looks like the order of includes in Clang (and GCC) is: C++ library headers > compiler builtin headers > C library headers. This is true on both Linux and Darwin, so it's not accidental, it's really by design. Now, some headers exist only in the builtin headers (e.g. <stdbool.h>), some only in the C library headers (e.g. <stdio.h>), and some in both (e.g. <stdint.h>). Can anyone shed light on the logic behind this?

Is any of this documented anywhere?

I don't know if we document it anywhere, but my understanding of the situation is: there are headers the compiler has to provide because the compiler is the only thing that can implement it (think: stdarg.h), there are headers the compiler has to provide because they're in freestanding (think: stdbool.h), and finally there are all the rest of the headers which the compiler doesn't have to care about (think: stdio.h). Some header files do an include_next because the host header file may provide additional facilities (for example, limits.h may be extended by the POSIX headers).

[philnik]

In D138629#3954442, @aaron.ballman wrote:

4. More generally speaking, what's the purpose of -fno-builtins?

To disable all builtins regardless of whether you're in freestanding mode or not. Sometimes the builtins do things you don't want them to do and so you want to disable them (perhaps you don't like the behavior of __builtin_memcpy for some reason), and sometimes the builtins expose names you want to use (https://godbolt.org/z/cMxzojcr1).

__buitin_memcpy works the same whether -fno-builtins is used or not, right? It's just that memcpy doesn't behave like __builtin_memcpy?

[aaron.ballman]

In D138629#3960439, @philnik wrote:

In D138629#3954442, @aaron.ballman wrote:

4. More generally speaking, what's the purpose of -fno-builtins?

To disable all builtins regardless of whether you're in freestanding mode or not. Sometimes the builtins do things you don't want them to do and so you want to disable them (perhaps you don't like the behavior of __builtin_memcpy for some reason), and sometimes the builtins expose names you want to use (https://godbolt.org/z/cMxzojcr1).

__buitin_memcpy works the same whether -fno-builtins is used or not, right? It's just that memcpy doesn't behave like __builtin_memcpy?

Correct, sorry for being unclear.

[ldionne]

Thanks a lot @aaron.ballman and @Izaron for the additional context around builtins and builtin headers, this has been useful.

So this patch is effectively a no-op as far as we're concerned in a world with compiler builtins. However, it would make libc++ work when used in the following combination:

1. on top of a C library that does not provide these math functions, and
2. -fno-builtins is passed to the compiler

I think we want to do this, however I am having a hard time just LGTMing it because we are not currently validating anything wrt this patch. Can you please rebase to at least get a green CI run?

[philnik]

Rebased

[philnik]

Fix diff

[philnik]

Rebased

[ldionne]

libcxx/include/math.h

545

Can you add a comment explaining how this works? Obviously just need to have one comment for the whole file.

libcxx/include/math.h

 // abs
 //
 // handled in stdlib.h
 
 // div
 //
 // handled in stdlib.h
 
+// We have to provide double overloads for <math.h> to work on platforms that don't provide the full set of math
+// functions. To make the overload set work with multiple functions that take the same arguments, we make our overloads
+// templates. Functions are preferred over function templates during overload resolution, which means that our overload
+// will only be selected when the C library doesn't provide one.
+
 // acos
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       acos(float __x) _NOEXCEPT       {return __builtin_acosf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double acos(double __x) _NOEXCEPT {
+  return __builtin_acos(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double acos(long double __x) _NOEXCEPT {return __builtin_acosl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 acos(_A1 __x) _NOEXCEPT {return __builtin_acos((double)__x);}
 
 // asin
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       asin(float __x) _NOEXCEPT       {return __builtin_asinf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double asin(double __x) _NOEXCEPT {
+  return __builtin_asin(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double asin(long double __x) _NOEXCEPT {return __builtin_asinl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 asin(_A1 __x) _NOEXCEPT {return __builtin_asin((double)__x);}
 
 // atan
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       atan(float __x) _NOEXCEPT       {return __builtin_atanf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double atan(double __x) _NOEXCEPT {
+  return __builtin_atan(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double atan(long double __x) _NOEXCEPT {return __builtin_atanl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 atan(_A1 __x) _NOEXCEPT {return __builtin_atan((double)__x);}
 
 // atan2
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       atan2(float __y, float __x) _NOEXCEPT             {return __builtin_atan2f(__y, __x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double atan2(double __x, double __y) _NOEXCEPT {
+  return __builtin_atan2(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double atan2(long double __y, long double __x) _NOEXCEPT {return __builtin_atan2l(__y, __x);}
 #    endif
 
 template <class _A1, class _A2>
 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
 atan2(_A1 __y, _A2 __x) _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 ::atan2((__result_type)__y, (__result_type)__x);
 }
 
 // ceil
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       ceil(float __x) _NOEXCEPT       {return __builtin_ceilf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double ceil(double __x) _NOEXCEPT {
+  return __builtin_ceil(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double ceil(long double __x) _NOEXCEPT {return __builtin_ceill(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 ceil(_A1 __x) _NOEXCEPT {return __builtin_ceil((double)__x);}
 
 // cos
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       cos(float __x) _NOEXCEPT       {return __builtin_cosf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double cos(double __x) _NOEXCEPT {
+  return __builtin_cos(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double cos(long double __x) _NOEXCEPT {return __builtin_cosl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 cos(_A1 __x) _NOEXCEPT {return __builtin_cos((double)__x);}
 
 // cosh
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       cosh(float __x) _NOEXCEPT       {return __builtin_coshf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double cosh(double __x) _NOEXCEPT {
+  return __builtin_cosh(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double cosh(long double __x) _NOEXCEPT {return __builtin_coshl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 cosh(_A1 __x) _NOEXCEPT {return __builtin_cosh((double)__x);}
 
 // exp
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       exp(float __x) _NOEXCEPT       {return __builtin_expf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double exp(double __x) _NOEXCEPT {
+  return __builtin_exp(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double exp(long double __x) _NOEXCEPT {return __builtin_expl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 exp(_A1 __x) _NOEXCEPT {return __builtin_exp((double)__x);}
 
 // fabs
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       fabs(float __x) _NOEXCEPT       {return __builtin_fabsf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double fabs(double __x) _NOEXCEPT {
+  return __builtin_fabs(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double fabs(long double __x) _NOEXCEPT {return __builtin_fabsl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 fabs(_A1 __x) _NOEXCEPT {return __builtin_fabs((double)__x);}
 
 // floor
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       floor(float __x) _NOEXCEPT       {return __builtin_floorf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double floor(double __x) _NOEXCEPT {
+  return __builtin_floor(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double floor(long double __x) _NOEXCEPT {return __builtin_floorl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 floor(_A1 __x) _NOEXCEPT {return __builtin_floor((double)__x);}
 
 // fmod
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       fmod(float __x, float __y) _NOEXCEPT             {return __builtin_fmodf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double fmod(double __x, double __y) _NOEXCEPT {
+  return __builtin_fmod(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double fmod(long double __x, long double __y) _NOEXCEPT {return __builtin_fmodl(__x, __y);}
 #    endif
 
 template <class _A1, class _A2>
 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
 fmod(_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 ::fmod((__result_type)__x, (__result_type)__y);
 }
 
 // frexp
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       frexp(float __x, int* __e) _NOEXCEPT       {return __builtin_frexpf(__x, __e);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double frexp(double __x, int* __e) _NOEXCEPT {
+  return __builtin_frexp(__x, __e);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double frexp(long double __x, int* __e) _NOEXCEPT {return __builtin_frexpl(__x, __e);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 frexp(_A1 __x, int* __e) _NOEXCEPT {return __builtin_frexp((double)__x, __e);}
 
 // ldexp
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       ldexp(float __x, int __e) _NOEXCEPT       {return __builtin_ldexpf(__x, __e);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double ldexp(double __x, int __e) _NOEXCEPT {
+  return __builtin_ldexp(__x, __e);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double ldexp(long double __x, int __e) _NOEXCEPT {return __builtin_ldexpl(__x, __e);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 ldexp(_A1 __x, int __e) _NOEXCEPT {return __builtin_ldexp((double)__x, __e);}
 
 // log
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       log(float __x) _NOEXCEPT       {return __builtin_logf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double log(double __x) _NOEXCEPT {
+  return __builtin_log(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double log(long double __x) _NOEXCEPT {return __builtin_logl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 log(_A1 __x) _NOEXCEPT {return __builtin_log((double)__x);}
 
 // log10
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       log10(float __x) _NOEXCEPT       {return __builtin_log10f(__x);}
+
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double log10(double __x) _NOEXCEPT {
+  return __builtin_log10(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double log10(long double __x) _NOEXCEPT {return __builtin_log10l(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 log10(_A1 __x) _NOEXCEPT {return __builtin_log10((double)__x);}
 
 // modf
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       modf(float __x, float* __y) _NOEXCEPT             {return __builtin_modff(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double modf(double __x, double* __y) _NOEXCEPT {
+  return __builtin_modf(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double modf(long double __x, long double* __y) _NOEXCEPT {return __builtin_modfl(__x, __y);}
 #    endif
 
 // pow
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       pow(float __x, float __y) _NOEXCEPT             {return __builtin_powf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double pow(double __x, double __y) _NOEXCEPT {
+  return __builtin_pow(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double pow(long double __x, long double __y) _NOEXCEPT {return __builtin_powl(__x, __y);}
 #    endif
 
 template <class _A1, class _A2>
 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
 pow(_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 ::pow((__result_type)__x, (__result_type)__y);
 }
 
 // sin
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       sin(float __x) _NOEXCEPT       {return __builtin_sinf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double sin(double __x) _NOEXCEPT {
+  return __builtin_sin(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double sin(long double __x) _NOEXCEPT {return __builtin_sinl(__x);}
 #endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 sin(_A1 __x) _NOEXCEPT {return __builtin_sin((double)__x);}
 
 // sinh
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       sinh(float __x) _NOEXCEPT       {return __builtin_sinhf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double sinh(double __x) _NOEXCEPT {
+  return __builtin_sinh(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double sinh(long double __x) _NOEXCEPT {return __builtin_sinhl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 sinh(_A1 __x) _NOEXCEPT {return __builtin_sinh((double)__x);}
 
 // sqrt
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       sqrt(float __x) _NOEXCEPT       {return __builtin_sqrtf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double sqrt(double __x) _NOEXCEPT {
+  return __builtin_sqrt(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double sqrt(long double __x) _NOEXCEPT {return __builtin_sqrtl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 sqrt(_A1 __x) _NOEXCEPT {return __builtin_sqrt((double)__x);}
 
 // tan
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       tan(float __x) _NOEXCEPT       {return __builtin_tanf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double tan(double __x) _NOEXCEPT {
+  return __builtin_tan(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double tan(long double __x) _NOEXCEPT {return __builtin_tanl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 tan(_A1 __x) _NOEXCEPT {return __builtin_tan((double)__x);}
 
 // tanh
 
 #    if !defined(__sun__)
 inline _LIBCPP_HIDE_FROM_ABI float       tanh(float __x) _NOEXCEPT       {return __builtin_tanhf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double tanh(double __x) _NOEXCEPT {
+  return __builtin_tanh(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double tanh(long double __x) _NOEXCEPT {return __builtin_tanhl(__x);}
 #    endif
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 tanh(_A1 __x) _NOEXCEPT {return __builtin_tanh((double)__x);}
 
 // acosh
 
 inline _LIBCPP_HIDE_FROM_ABI float       acosh(float __x) _NOEXCEPT       {return __builtin_acoshf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double acosh(double __x) _NOEXCEPT {
+  return __builtin_acosh(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double acosh(long double __x) _NOEXCEPT {return __builtin_acoshl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 acosh(_A1 __x) _NOEXCEPT {return __builtin_acosh((double)__x);}
 
 // asinh
 
 inline _LIBCPP_HIDE_FROM_ABI float       asinh(float __x) _NOEXCEPT       {return __builtin_asinhf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double asinh(double __x) _NOEXCEPT {
+  return __builtin_asinh(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double asinh(long double __x) _NOEXCEPT {return __builtin_asinhl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 asinh(_A1 __x) _NOEXCEPT {return __builtin_asinh((double)__x);}
 
 // atanh
 
 inline _LIBCPP_HIDE_FROM_ABI float       atanh(float __x) _NOEXCEPT       {return __builtin_atanhf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double atanh(double __x) _NOEXCEPT {
+  return __builtin_atanh(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double atanh(long double __x) _NOEXCEPT {return __builtin_atanhl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 atanh(_A1 __x) _NOEXCEPT {return __builtin_atanh((double)__x);}
 
 // cbrt
 
 inline _LIBCPP_HIDE_FROM_ABI float       cbrt(float __x) _NOEXCEPT       {return __builtin_cbrtf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double cbrt(double __x) _NOEXCEPT {
+  return __builtin_cbrt(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double cbrt(long double __x) _NOEXCEPT {return __builtin_cbrtl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 cbrt(_A1 __x) _NOEXCEPT {return __builtin_cbrt((double)__x);}
 
 // copysign

 >::type
     copysign(_A1 __x, _A2 __y) _NOEXCEPT {
   return ::__libcpp_copysign(__x, __y);
 }
 
 // erf
 
 inline _LIBCPP_HIDE_FROM_ABI float       erf(float __x) _NOEXCEPT       {return __builtin_erff(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double erf(double __x) _NOEXCEPT {
+  return __builtin_erf(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double erf(long double __x) _NOEXCEPT {return __builtin_erfl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 erf(_A1 __x) _NOEXCEPT {return __builtin_erf((double)__x);}
 
 // erfc
 
 inline _LIBCPP_HIDE_FROM_ABI float       erfc(float __x) _NOEXCEPT       {return __builtin_erfcf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double erfc(double __x) _NOEXCEPT {
+  return __builtin_erfc(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double erfc(long double __x) _NOEXCEPT {return __builtin_erfcl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 erfc(_A1 __x) _NOEXCEPT {return __builtin_erfc((double)__x);}
 
 // exp2
 
 inline _LIBCPP_HIDE_FROM_ABI float       exp2(float __x) _NOEXCEPT       {return __builtin_exp2f(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double exp2(double __x) _NOEXCEPT {
+  return __builtin_exp2(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double exp2(long double __x) _NOEXCEPT {return __builtin_exp2l(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 exp2(_A1 __x) _NOEXCEPT {return __builtin_exp2((double)__x);}
 
 // expm1
 
 inline _LIBCPP_HIDE_FROM_ABI float       expm1(float __x) _NOEXCEPT       {return __builtin_expm1f(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double expm1(double __x) _NOEXCEPT {
+  return __builtin_expm1(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double expm1(long double __x) _NOEXCEPT {return __builtin_expm1l(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 expm1(_A1 __x) _NOEXCEPT {return __builtin_expm1((double)__x);}
 
 // fdim
 
 inline _LIBCPP_HIDE_FROM_ABI float       fdim(float __x, float __y) _NOEXCEPT             {return __builtin_fdimf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double fdim(double __x, double __y) _NOEXCEPT {
+  return __builtin_fdim(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double fdim(long double __x, long double __y) _NOEXCEPT {return __builtin_fdiml(__x, __y);}
 
 template <class _A1, class _A2>
 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
 fdim(_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 ::fdim((__result_type)__x, (__result_type)__y);
 }
 
 // fma
 
 inline _LIBCPP_HIDE_FROM_ABI float       fma(float __x, float __y, float __z) _NOEXCEPT
 {
     return __builtin_fmaf(__x, __y, __z);
 }
+
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double fma(double __x, double __y, double __z) _NOEXCEPT {
+  return __builtin_fma(__x, __y, __z);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double fma(long double __x, long double __y, long double __z) _NOEXCEPT
 {
     return __builtin_fmal(__x, __y, __z);
 }
 
 template <class _A1, class _A2, class _A3>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::__enable_if_t
static_assert((!(std::_IsSame<_A1, __result_type>::value &&
                      std::_IsSame<_A2, __result_type>::value &&
                      std::_IsSame<_A3, __result_type>::value)), "");
     return __builtin_fma((__result_type)__x, (__result_type)__y, (__result_type)__z);
 }
 
 // fmax
 
 inline _LIBCPP_HIDE_FROM_ABI float       fmax(float __x, float __y) _NOEXCEPT             {return __builtin_fmaxf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double fmax(double __x, double __y) _NOEXCEPT {
+  return __builtin_fmax(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double fmax(long double __x, long double __y) _NOEXCEPT {return __builtin_fmaxl(__x, __y);}
 
 template <class _A1, class _A2>
 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
 fmax(_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 ::fmax((__result_type)__x, (__result_type)__y);
 }
 
 // fmin
 
 inline _LIBCPP_HIDE_FROM_ABI float       fmin(float __x, float __y) _NOEXCEPT             {return __builtin_fminf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double fmin(double __x, double __y) _NOEXCEPT {
+  return __builtin_fmin(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double fmin(long double __x, long double __y) _NOEXCEPT {return __builtin_fminl(__x, __y);}
 
 template <class _A1, class _A2>
 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
 fmin(_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 ::fmin((__result_type)__x, (__result_type)__y);
 }
 
 // hypot
 
 inline _LIBCPP_HIDE_FROM_ABI float       hypot(float __x, float __y) _NOEXCEPT             {return __builtin_hypotf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y) _NOEXCEPT {
+  return __builtin_hypot(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y) _NOEXCEPT {return __builtin_hypotl(__x, __y);}
 
 template <class _A1, class _A2>
 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
 hypot(_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 ::hypot((__result_type)__x, (__result_type)__y);
 }
 
 // ilogb
 
 inline _LIBCPP_HIDE_FROM_ABI int ilogb(float __x) _NOEXCEPT       {return __builtin_ilogbf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double ilogb(double __x) _NOEXCEPT {
+  return __builtin_ilogb(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI int ilogb(long double __x) _NOEXCEPT {return __builtin_ilogbl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, int>::type
 ilogb(_A1 __x) _NOEXCEPT {return __builtin_ilogb((double)__x);}
 
 // lgamma
 
 inline _LIBCPP_HIDE_FROM_ABI float       lgamma(float __x) _NOEXCEPT       {return __builtin_lgammaf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double lgamma(double __x) _NOEXCEPT {
+  return __builtin_lgamma(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double lgamma(long double __x) _NOEXCEPT {return __builtin_lgammal(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 lgamma(_A1 __x) _NOEXCEPT {return __builtin_lgamma((double)__x);}
 
 // llrint
 
 inline _LIBCPP_HIDE_FROM_ABI long long llrint(float __x) _NOEXCEPT
 {
     return __builtin_llrintf(__x);
 }
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI long long llrint(double __x) _NOEXCEPT {
+  return __builtin_llrint(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long long llrint(long double __x) _NOEXCEPT
 {
     return __builtin_llrintl(__x);
 }
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, long long>::type
 llrint(_A1 __x) _NOEXCEPT
 {
     return __builtin_llrint((double)__x);
 }
 
 // llround
 
 inline _LIBCPP_HIDE_FROM_ABI long long llround(float __x) _NOEXCEPT
 {
     return __builtin_llroundf(__x);
 }
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI long long llround(double __x) _NOEXCEPT {
+  return __builtin_llround(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long long llround(long double __x) _NOEXCEPT
 {
     return __builtin_llroundl(__x);
 }
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, long long>::type
 llround(_A1 __x) _NOEXCEPT
 {
     return __builtin_llround((double)__x);
 }
 
 // log1p
 
 inline _LIBCPP_HIDE_FROM_ABI float       log1p(float __x) _NOEXCEPT       {return __builtin_log1pf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double log1p(double __x) _NOEXCEPT {
+  return __builtin_log1p(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double log1p(long double __x) _NOEXCEPT {return __builtin_log1pl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 log1p(_A1 __x) _NOEXCEPT {return __builtin_log1p((double)__x);}
 
 // log2
 
 inline _LIBCPP_HIDE_FROM_ABI float       log2(float __x) _NOEXCEPT       {return __builtin_log2f(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double log2(double __x) _NOEXCEPT {
+  return __builtin_log2(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double log2(long double __x) _NOEXCEPT {return __builtin_log2l(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 log2(_A1 __x) _NOEXCEPT {return __builtin_log2((double)__x);}
 
 // logb
 
 inline _LIBCPP_HIDE_FROM_ABI float       logb(float __x) _NOEXCEPT       {return __builtin_logbf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double logb(double __x) _NOEXCEPT {
+  return __builtin_logb(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double logb(long double __x) _NOEXCEPT {return __builtin_logbl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 logb(_A1 __x) _NOEXCEPT {return __builtin_logb((double)__x);}
 
 // lrint
 
 inline _LIBCPP_HIDE_FROM_ABI long lrint(float __x) _NOEXCEPT
 {
     return __builtin_lrintf(__x);
 }
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI long lrint(double __x) _NOEXCEPT {
+  return __builtin_lrint(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long lrint(long double __x) _NOEXCEPT
 {
     return __builtin_lrintl(__x);
 }
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, long>::type
 lrint(_A1 __x) _NOEXCEPT
 {
     return __builtin_lrint((double)__x);
 }
 
 // lround
 
 inline _LIBCPP_HIDE_FROM_ABI long lround(float __x) _NOEXCEPT
 {
     return __builtin_lroundf(__x);
 }
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI long lround(double __x) _NOEXCEPT {
+  return __builtin_lround(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long lround(long double __x) _NOEXCEPT
 {
     return __builtin_lroundl(__x);
 }
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, long>::type
 lround(_A1 __x) _NOEXCEPT
 {
     return __builtin_lround((double)__x);
 }
 
 // nan
 
 // nearbyint
 
 inline _LIBCPP_HIDE_FROM_ABI float       nearbyint(float __x) _NOEXCEPT       {return __builtin_nearbyintf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double nearbyint(double __x) _NOEXCEPT {
+  return __builtin_nearbyint(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double nearbyint(long double __x) _NOEXCEPT {return __builtin_nearbyintl(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 nearbyint(_A1 __x) _NOEXCEPT {return __builtin_nearbyint((double)__x);}
 
 // nextafter
 
 inline _LIBCPP_HIDE_FROM_ABI float       nextafter(float __x, float __y) _NOEXCEPT             {return __builtin_nextafterf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double nextafter(double __x, double __y) _NOEXCEPT {
+  return __builtin_nextafter(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double nextafter(long double __x, long double __y) _NOEXCEPT {return __builtin_nextafterl(__x, __y);}
 
 template <class _A1, class _A2>
 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
 nextafter(_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 ::nextafter((__result_type)__x, (__result_type)__y);
 }
 
 // nexttoward
 
 inline _LIBCPP_HIDE_FROM_ABI float       nexttoward(float __x, long double __y) _NOEXCEPT       {return __builtin_nexttowardf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double nexttoward(double __x, long double __y) _NOEXCEPT {
+  return __builtin_nexttoward(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double nexttoward(long double __x, long double __y) _NOEXCEPT {return __builtin_nexttowardl(__x, __y);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 nexttoward(_A1 __x, long double __y) _NOEXCEPT {return __builtin_nexttoward((double)__x, __y);}
 
 // remainder
 
 inline _LIBCPP_HIDE_FROM_ABI float       remainder(float __x, float __y) _NOEXCEPT             {return __builtin_remainderf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double remainder(double __x, double __y) _NOEXCEPT {
+  return __builtin_remainder(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double remainder(long double __x, long double __y) _NOEXCEPT {return __builtin_remainderl(__x, __y);}
 
 template <class _A1, class _A2>
 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
 remainder(_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 ::remainder((__result_type)__x, (__result_type)__y);
 }
 
 // remquo
 
 inline _LIBCPP_HIDE_FROM_ABI float       remquo(float __x, float __y, int* __z) _NOEXCEPT             {return __builtin_remquof(__x, __y, __z);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double remquo(double __x, double __y, int* __z) _NOEXCEPT {
+  return __builtin_remquo(__x, __y, __z);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double remquo(long double __x, long double __y, int* __z) _NOEXCEPT {return __builtin_remquol(__x, __y, __z);}
 
 template <class _A1, class _A2>
 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
 remquo(_A1 __x, _A2 __y, int* __z) _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 ::remquo((__result_type)__x, (__result_type)__y, __z);
 }
 
 // rint
 
 inline _LIBCPP_HIDE_FROM_ABI float       rint(float __x) _NOEXCEPT
 {
     return __builtin_rintf(__x);
 }
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double rint(double __x) _NOEXCEPT {
+  return __builtin_rint(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double rint(long double __x) _NOEXCEPT
 {
     return __builtin_rintl(__x);
 }
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 rint(_A1 __x) _NOEXCEPT
 {
     return __builtin_rint((double)__x);
 }
 
 // round
 
 inline _LIBCPP_HIDE_FROM_ABI float       round(float __x) _NOEXCEPT
 {
     return __builtin_round(__x);
 }
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double round(double __x) _NOEXCEPT {
+  return __builtin_round(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double round(long double __x) _NOEXCEPT
 {
     return __builtin_roundl(__x);
 }
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 round(_A1 __x) _NOEXCEPT
 {
     return __builtin_round((double)__x);
 }
 
 // scalbln
 
 inline _LIBCPP_HIDE_FROM_ABI float       scalbln(float __x, long __y) _NOEXCEPT       {return __builtin_scalblnf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double scalbln(double __x, long __y) _NOEXCEPT {
+  return __builtin_scalbln(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double scalbln(long double __x, long __y) _NOEXCEPT {return __builtin_scalblnl(__x, __y);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 scalbln(_A1 __x, long __y) _NOEXCEPT {return __builtin_scalbln((double)__x, __y);}
 
 // scalbn
 
 inline _LIBCPP_HIDE_FROM_ABI float       scalbn(float __x, int __y) _NOEXCEPT       {return __builtin_scalbnf(__x, __y);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double scalbn(double __x, int __y) _NOEXCEPT {
+  return __builtin_scalbn(__x, __y);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double scalbn(long double __x, int __y) _NOEXCEPT {return __builtin_scalbnl(__x, __y);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 scalbn(_A1 __x, int __y) _NOEXCEPT {return __builtin_scalbn((double)__x, __y);}
 
 // tgamma
 
 inline _LIBCPP_HIDE_FROM_ABI float       tgamma(float __x) _NOEXCEPT       {return __builtin_tgammaf(__x);}
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double tgamma(double __x) _NOEXCEPT {
+  return __builtin_tgamma(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double tgamma(long double __x) _NOEXCEPT {return __builtin_tgammal(__x);}
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type
 tgamma(_A1 __x) _NOEXCEPT {return __builtin_tgamma((double)__x);}
 
 // trunc
 
 inline _LIBCPP_HIDE_FROM_ABI float       trunc(float __x) _NOEXCEPT
 {
     return __builtin_trunc(__x);
 }
+
+template <class = int>
+_LIBCPP_HIDE_FROM_ABI double trunc(double __x) _NOEXCEPT {
+  return __builtin_trunc(__x);
+}
+
 inline _LIBCPP_HIDE_FROM_ABI long double trunc(long double __x) _NOEXCEPT
 {
     return __builtin_truncl(__x);
 }
 
 template <class _A1>
 inline _LIBCPP_HIDE_FROM_ABI
 typename std::enable_if<std::is_integral<_A1>::value, double>::type