libstdc++: More efficient days from date

This patch reimplements std::chrono::year_month_day::_M_days_since_epoch()
which calculates the number of elapsed days since 1970/01/01.  The new
implementation is based on Proposition 6.2 of Neri and Schneider, "Euclidean
Affine Functions and Applications to Calendar Algorithms" available at
https://arxiv.org/abs/2102.06959.

The aforementioned paper benchmarks the implementation against several
counterparts, including libc++'s (which is identical to the current
implementation).  The results, shown in Figure 3, indicate the new algorithm is
1.7 times faster than the current one.

The patch adds a test which loops through all dates in [-32767/01/01,
32767/12/31], and for each of them, gets the number of days and compares the
result against its expected value. The latter is calculated using a much
simpler and easy to understand algorithm but which is also much slower.

The dates used in the test covers the full range of possible values
[time.cal.year.members].  Despite its completeness the test runs in matter of
seconds.

libstdc++-v3/ChangeLog:

	* include/std/chrono (year_month_day::_M_days_since_epoch):
	New implementation.
	* testsuite/std/time/year_month_day/4.cc: New test.

libstdc++-v3/include/std/chrono

@@ -2466,26 +2466,34 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
       const auto __d1 = __d0 + 1;
 
       return year_month_day{chrono::year{__y1 + __z2}, chrono::month{__m1},
-			    chrono::day{__d1}
-      };
+			    chrono::day{__d1}};
     }
 
-    // Days since 1970/01/01. Magic.
+    // Days since 1970/01/01.
+    // Proposition 6.2 of Neri and Schneider,
+    // "Euclidean Affine Functions and Applications to Calendar Algorithms".
+    // https://arxiv.org/abs/2102.06959
     constexpr days
     year_month_day::_M_days_since_epoch() const noexcept
     {
-      const auto __y = static_cast<int>(_M_y) - (_M_m <= February);
-      const auto __m = static_cast<unsigned>(_M_m);
-      const auto __d = static_cast<unsigned>(_M_d);
-      const auto __era = (__y >= 0 ? __y : __y - 399) / 400;
-      // Year of "era" [0, 399].
-      const auto __yoe = static_cast<unsigned>(__y - __era * 400);
-      // Day of year [0, 365].
-      const auto __doy = (153 * (__m > 2 ? __m - 3 : __m + 9) + 2) / 5 + __d - 1;
-      // Day of "era" [0, 146096].
-      const auto __doe = __yoe * 365 + __yoe / 4 - __yoe / 100 + __doy;
-      const auto __days = __era * 146097 + static_cast<int>(__doe) - 719468;
-      return days{__days};
+      auto constexpr __z2    = static_cast<uint32_t>(-1468000);
+      auto constexpr __r2_e3 = static_cast<uint32_t>(536895458);
+
+      const auto __y1 = static_cast<uint32_t>(static_cast<int>(_M_y)) - __z2;
+      const auto __m1 = static_cast<uint32_t>(_M_m);
+      const auto __d1 = static_cast<uint32_t>(_M_d);
+
+      const auto __j  = static_cast<uint32_t>(__m1 < 3);
+      const auto __y0 = __y1 - __j;
+      const auto __m0 = __j ? __m1 + 12 : __m1;
+      const auto __d0 = __d1 - 1;
+
+      const auto __q1 = __y0 / 100;
+      const auto __yc = 1461 * __y0 / 4 - __q1 + __q1 / 4;
+      const auto __mc = (979 *__m0 - 2919) / 32;
+      const auto __dc = __d0;
+
+      return days{static_cast<int32_t>(__yc + __mc + __dc - __r2_e3)};
     }
 
     // YEAR_MONTH_DAY_LAST

libstdc++-v3/testsuite/std/time/year_month_day/4.cc

@@ -0,0 +1,71 @@
+// { dg-options "-std=gnu++2a" }
+// { dg-do run { target c++2a } }
+
+// Copyright (C) 2021 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// Class year_month_day [time.cal.year_month_day]
+
+#include <chrono>
+#include <testsuite_hooks.h>
+
+// Slow but very clear way of advancing one day.
+constexpr void
+advance(std::chrono::year_month_day& ymd) noexcept {
+
+  using namespace std::chrono;
+
+  auto y = ymd.year();
+  auto m = ymd.month();
+  auto d = ymd.day();
+
+  if (d != year_month_day_last{year{y}, month_day_last{m}}.day())
+    ++d;
+  else {
+    d = day{1};
+    if (m != December)
+      ++m;
+    else {
+      m = January;
+      ++y;
+    }
+  }
+  ymd = year_month_day{y, m, d};
+}
+
+void test01()
+{
+  using namespace std::chrono;
+
+  // [-32767y/January/1d, 32767y/December/31d] maps to [-12687428, 11248737]
+
+  auto n   = days{-12687428};
+  auto ymd = -32767y/January/1d;
+  while (ymd < 32767y/December/31d) {
+    VERIFY( static_cast<sys_days>(ymd) == sys_days{n} );
+    ++n;
+    advance(ymd);
+  }
+  // One more for ymd = 32767y/December/31d and n = 11248737.
+  VERIFY( sys_days{days{11248737}} == static_cast<sys_days>(32767y/December/31d) );
+}
+
+int main()
+{
+  test01();
+  return 0;
+}