diff --git a/libstdc++-v3/include/std/chrono b/libstdc++-v3/include/std/chrono index a826982803b7855bfdd6d8ce15b2be677c621efa..45e7d269e4b41a8f340e429357e805b1f2b337d4 100644 --- a/libstdc++-v3/include/std/chrono +++ b/libstdc++-v3/include/std/chrono @@ -835,29 +835,29 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION constexpr bool is_leap() const noexcept { - // Testing divisibility by 100 first gives better performance, that is, - // return (_M_y % 100 != 0 || _M_y % 400 == 0) && _M_y % 4 == 0; - - // It gets even faster if _M_y is in [-536870800, 536870999] - // (which is the case here) and _M_y % 100 is replaced by - // __is_multiple_of_100 below. + // Testing divisibility by 100 first gives better performance [1], i.e., + // return _M_y % 100 == 0 ? _M_y % 400 == 0 : _M_y % 16 == 0; + // Furthermore, if _M_y % 100 == 0, then _M_y % 400 == 0 is equivalent + // to _M_y % 16 == 0, so we can simplify it to + // return _M_y % 100 == 0 ? _M_y % 16 == 0 : _M_y % 4 == 0. // #1 + // Similarly, we can replace 100 with 25 (which is good since + // _M_y % 25 == 0 requires one fewer instruction than _M_y % 100 == 0 + // [2]): + // return _M_y % 25 == 0 ? _M_y % 16 == 0 : _M_y % 4 == 0. // #2 + // Indeed, first assume _M_y % 4 != 0. Then _M_y % 16 != 0 and hence, + // _M_y % 4 == 0 and _M_y % 16 == 0 are both false. Therefore, #2 + // returns false as it should (regardless of _M_y % 25.) Now assume + // _M_y % 4 == 0. In this case, _M_y % 25 == 0 if, and only if, + // _M_y % 100 == 0, that is, #1 and #2 are equivalent. Finally, #2 is + // equivalent to + // return (_M_y & (_M_y % 25 == 0 ? 15 : 3)) == 0. // References: // [1] https://github.com/cassioneri/calendar - // [2] https://accu.org/journals/overload/28/155/overload155.pdf#page=16 - - // Furthermore, if y%100 == 0, then y%400==0 is equivalent to y%16==0, - // so we can simplify it to (!mult_100 && y % 4 == 0) || y % 16 == 0, - // which is equivalent to (y & (mult_100 ? 15 : 3)) == 0. - // See https://gcc.gnu.org/pipermail/libstdc++/2021-June/052815.html - - constexpr uint32_t __multiplier = 42949673; - constexpr uint32_t __bound = 42949669; - constexpr uint32_t __max_dividend = 1073741799; - constexpr uint32_t __offset = __max_dividend / 2 / 100 * 100; - const bool __is_multiple_of_100 - = __multiplier * (_M_y + __offset) < __bound; - return (_M_y & (__is_multiple_of_100 ? 15 : 3)) == 0; + // [2] https://godbolt.org/z/55G8rn77e + // [3] https://gcc.gnu.org/pipermail/libstdc++/2021-June/052815.html + + return (_M_y & (_M_y % 25 == 0 ? 15 : 3)) == 0; } explicit constexpr