<numeric>: Consider avoiding <limits> inclusion

[StephanTLavavej]

Currently, <numeric> includes <limits> in C++20 mode:

STL/stl/inc/numeric

Lines 13 to 15 in 46ae5f8

	#if _HAS_CXX20
	#include <limits>
	#endif // _HAS_CXX20

<limits> is a relatively large header (potentially affecting compiler throughput, i.e. slowing down builds), but our usage is very limited here - we just need floating-point min/max:

STL/stl/inc/numeric

Lines 640 to 641 in 46ae5f8

	if constexpr (is_floating_point_v<_Ty>) {
	constexpr _Ty _High_limit = (numeric_limits<_Ty>::max)() / 2;

STL/stl/inc/numeric

Line 675 in 46ae5f8

constexpr _Ty _Low_limit = (numeric_limits<_Ty>::min)() * 2;

<numeric> always includes <xutility> which includes <climits>:

STL/stl/inc/numeric

Line 11 in 46ae5f8

#include <xutility>

STL/stl/inc/xutility

Line 12 in 46ae5f8

#include <climits>

So <numeric> could directly use the classic macros:

STL/stl/inc/limits

Lines 872 to 878 in 46ae5f8

	_NODISCARD static constexpr float(min)() noexcept {
	return FLT_MIN;
	}
	_NODISCARD static constexpr float(max)() noexcept {
	return FLT_MAX;
	}

STL/stl/inc/limits

Lines 921 to 927 in 46ae5f8

	_NODISCARD static constexpr double(min)() noexcept {
	return DBL_MIN;
	}
	_NODISCARD static constexpr double(max)() noexcept {
	return DBL_MAX;
	}

STL/stl/inc/limits

Lines 970 to 976 in 46ae5f8

	_NODISCARD static constexpr long double(min)() noexcept {
	return LDBL_MIN;
	}
	_NODISCARD static constexpr long double(max)() noexcept {
	return LDBL_MAX;
	}

Specifically, the changes in <numeric> I'm envisioning are:

1. Stop including <limits>.
2. Define a helper variable template _Floating_min<_Ty>, specialized for float, double, and long double.
3. Similarly define _Floating_max<_Ty>.
4. Replace the numeric_limits calls with uses of the variable templates. Note that because users could theoretically pass volatile values, the uses should say remove_cv_t<_Ty>; numeric_limits was previously handling that:

STL/stl/inc/limits

Lines 108 to 118 in 46ae5f8

	template <class _Ty>
	class numeric_limits<const _Ty> : public numeric_limits<_Ty> { // numeric limits for const types
	};
	template <class _Ty>
	class numeric_limits<volatile _Ty> : public numeric_limits<_Ty> { // numeric limits for volatile types
	};
	template <class _Ty>
	class numeric_limits<const volatile _Ty> : public numeric_limits<_Ty> { // numeric limits for const volatile types
	};

[StephanTLavavej]

Casey Carter (@CaseyCarter) observed that there's another <limits> dependency that I forgot about, _Countr_zero, after we merged #665:

STL/stl/inc/numeric

Lines 566 to 568 in 46ae5f8

	#ifdef __cpp_lib_bitops // TRANSITION, VSO-1020212
	return static_cast<unsigned long>(_Countr_zero(_Mask));
	#else // ^^^ __cpp_lib_bitops / !__cpp_lib_bitops vvv

STL/stl/inc/limits

Lines 1015 to 1032 in 46ae5f8

	#ifdef __cpp_lib_bitops // TRANSITION, VSO-1020212
	template <class _Ty>
	inline constexpr bool _Is_standard_unsigned_integer =
	_Is_any_of_v<remove_cv_t<_Ty>, unsigned char, unsigned short, unsigned int, unsigned long, unsigned long long>;
	template <class _Ty, enable_if_t<_Is_standard_unsigned_integer<_Ty>, int> = 0>
	_NODISCARD constexpr int _Countr_zero(const _Ty _Val) noexcept {
	if (_Val == 0) {
	return numeric_limits<_Ty>::digits;
	}
	if constexpr (sizeof(_Ty) <= sizeof(unsigned int)) {
	return __builtin_ctz(_Val);
	} else {
	return __builtin_ctzll(_Val);
	}
	}
	#endif // __cpp_lib_bitops

This is also used by <bit>:

STL/stl/inc/bit

Lines 116 to 124 in 46ae5f8

	template <class _Ty, enable_if_t<_Is_standard_unsigned_integer<_Ty>, int> = 0>
	_NODISCARD constexpr int countr_zero(const _Ty _Val) noexcept {
	return _Countr_zero(_Val);
	}
	template <class _Ty, enable_if_t<_Is_standard_unsigned_integer<_Ty>, int> _Enabled = 0>
	_NODISCARD constexpr int countr_one(const _Ty _Val) noexcept {
	return _Countr_zero(static_cast<_Ty>(~_Val));
	}

We could move _Countr_zero up to <xtr1common>, after appropriately replacing the usage of numeric_limits<_Ty>::digits; hopefully that would improve throughput overall, but I'm not 100% certain.

[miscco]

My first candidate for the _Countr_zero Funktion actually was xtr1common but when I saw the limits usage I went for limits

[StephanTLavavej]

#795 has merged, so the analysis here needs to be updated.