Optimize std::midpoint for integers

[jorgbrown]

Summary

Same idea as the current algorithm, that is, add (half of the difference between a and b) to a.

But we use a different technique for computing the difference: we compute b - a into a pair of integers that are named "sign_bit" and "diff". We have to use a pair because subtracting two 32-bit integers produces a 33-bit result.

Computing half of that is a simple matter of shifting diff right by 1, and adding sign_bit shifted left by 31. llvm knows how to do that with one instruction: shld.

The only tricky part is that if the difference is odd and negative, then shifting it by one isn't the same as dividing it by two - shifting a negative one produces a negative one, for example. So there's one more adjustment: if the sign bit and the low bit of diff are one, we add one.

For a demonstration of the codegen difference, see https://godbolt.org/z/7ar3K9 , which also has a built-in test.

include/numeric

 #if _LIBCPP_STD_VER > 17
 template <class _Tp>
 _LIBCPP_INLINE_VISIBILITY constexpr
 enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp>
 midpoint(_Tp __a, _Tp __b) noexcept
 _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK
 {
     using _Up = std::make_unsigned_t<_Tp>;
+    constexpr _Up __bitshift = std::numeric_limits<_Up>::digits - 1;
 
-    int __sign = 1;
-    _Up __m = __a;
-    _Up __M = __b;
-    if (__a > __b)
-    {
-        __sign = -1;
-        __m = __b;
-        __M = __a;
-    }
-     return __a + __sign * _Tp(_Up(__M-__m) >> 1);
+    _Up __diff = _Up(__b) - _Up(__a);
+    _Up __sign_bit = __b < __a;
+
+    _Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff);
+
+    return __a + __half_diff;
 }
 
 
 template <class _TPtr>
 _LIBCPP_INLINE_VISIBILITY constexpr
 enable_if_t<is_pointer_v<_TPtr>
              && is_object_v<remove_pointer_t<_TPtr>>
              && ! is_void_v<remove_pointer_t<_TPtr>>