libstdc++: More efficient last day of month

This patch reimplements std::chrono::year_month_day_last:day() which yields the
last day of a particular month.  The current implementation uses a look-up table
implemented as an unsigned[12] array.  The new implementation instead
is based on
the fact that a month m in [1, 12], except for m == 2 (February), is
either 31 or
30 days long and m's length depends on two things: m's parity and whether m >= 8
or not. These two conditions are determined by the 0th and 3th bit of m and,
therefore, cheap and straightforward bit-twiddling can provide the right result.

Measurements in x86_64 [1] suggest a 10% performance boost.  Although this does
not seem to be huge, notice that measurements are done in hot L1 cache
conditions which might not be very representative of production runs. Also
freeing L1 cache from holding the look-up table might allow performance
improvements elsewhere.

References:
[1] https://github.com/cassioneri/calendar

libstdc++-v3/ChangeLog:

	* include/std/chrono (year_month_day_last:day): New
	implementation.

1 files changed, 18 insertions, 6 deletions

diff --git a/libstdc++-v3/include/std/chrono b/libstdc++-v3/include/std/chrono
index 3ba35a5..feb2c2a 100644
--- a/libstdc++-v3/include/std/chrono
+++ b/libstdc++-v3/include/std/chrono
@@ -1269,9 +1269,6 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
 
       inline constexpr unsigned __days_per_month[12]
 	= { 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };
-
-      inline constexpr unsigned __last_day[12]
-	= { 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };
     }
 
     // DAY
@@ -2576,9 +2573,24 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
       constexpr chrono::day
       day() const noexcept
       {
-	if (!_M_mdl.ok() || (month() == February && _M_y.is_leap()))
-	  return chrono::day{29};
-	return chrono::day{__detail::__last_day[unsigned(month()) - 1]};
+	const auto __m = static_cast<unsigned>(month());
+
+	// Excluding February, the last day of month __m is either 30 or 31 or,
+	// in another words, it is 30 + b = 30 | b, where b is in {0, 1}.
+
+	// If __m in {1, 3, 4, 5, 6, 7}, then b is 1 if, and only if __m is odd.
+	// Hence, b = __m & 1 = (__m ^ 0) & 1.
+
+	// If __m in {8, 9, 10, 11, 12}, then b is 1 if, and only if __m is even.
+	// Hence, b = (__m ^ 1) & 1.
+
+	// Therefore, b = (__m ^ c) & 1, where c = 0, if __m < 8, or c = 1 if
+	// __m >= 8, that is, c = __m >> 3.
+
+	// The above mathematically justifies this implementation whose
+	// performance does not depend on look-up tables being on the L1 cache.
+	return chrono::day{__m != 2 ? ((__m ^ (__m >> 3)) & 1) | 30
+				    : _M_y.is_leap() ? 29 : 28};
       }
 
       constexpr