[gcc r11-7372] libstdc++: More efficient last day of month

[Jonathan Wakely]

https://gcc.gnu.org/g:8265ab07f3bbeb672488fdfc6418e0bce89dff9c

commit r11-7372-g8265ab07f3bbeb672488fdfc6418e0bce89dff9c
Author: Cassio Neri <cassio.neri@gmail.com>
Date:   Wed Feb 24 18:12:47 2021 +0000

    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.

Diff:
---
 libstdc++-v3/include/std/chrono | 24 ++++++++++++++++++------
 1 file changed, 18 insertions(+), 6 deletions(-)

diff --git a/libstdc++-v3/include/std/chrono b/libstdc++-v3/include/std/chrono
index 3ba35a5bc86..feb2c2a1fad 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