The handling of ISO week-calendar year specifiers (%G, %g) and ISO week
number (%V) was merged into a single _M_g_G_V function, as the latter
requires ISO year value, computed by the former.

The values for %U and %W, which are based on the number of days since the
first Sunday and Monday of the year respectively, are now expressed as an
offset from the existing _M_day_of_year field. This reduces redundant
computation. The required flags were also updated to only need _DayOfYear
and _Weekday.

The _M_g_G_V function uses _M_day_of_year to compute __idoy, the day of
the year for the nearest Thursday. This value is used to determine if the
ISO year is the previous year (__idoy <= 0), the current year, or a
later year (__idoy > 366/365). This avoids an expensive conversion from
local_days to year_month_day if __idoy <= 365. If the ISO calendar year
is unchanged, the __idoy value is be reused for weekday index computation.

libstdc++-v3/ChangeLog:

        * include/bits/chrono_io.h(__formatter_chrono::_M_parse): Update
        needed flags for %g, %G, %V, %U, %W.
        (__formatter_chrono::_M_format_to): Change how %V is handled.
        (__formatter_chrono::_M_g_G): Merged into _M_g_G_V.
        (__formatter_chrono::_M_g_G_V): Reworked from _M_g_G.
        (__formatter_chrono::_M_U_V_W): Changed into _M_U_V.
        (__formatter_chrono::_M_U_W): Reworked implementation.
        * testsuite/std/time/year_month_day/io.cc: New tests.
---
v2 fixes off by one mistake, caused bu _M_day_of_year being 1 based, so 7 day
is last day of first week, but floor<weeks> requires 0 based indexing.
Added test files to cover this cases.


 libstdc++-v3/include/bits/chrono_io.h         | 93 +++++++++++--------
 .../testsuite/std/time/year_month_day/io.cc   | 28 +++++-
 2 files changed, 80 insertions(+), 41 deletions(-)

diff --git a/libstdc++-v3/include/bits/chrono_io.h 
b/libstdc++-v3/include/bits/chrono_io.h
index 809d795cbf2..407fa66b218 100644
--- a/libstdc++-v3/include/bits/chrono_io.h
+++ b/libstdc++-v3/include/bits/chrono_io.h
@@ -573,9 +573,9 @@ namespace __format
 
          auto __finalize = [this, &__spec, &__def] {
            using enum _ChronoParts;
-            _ChronoParts __checked 
+           _ChronoParts __checked 
              = __spec._M_debug ? _YearMonthDay|_IndexedWeekday
-                               : _Month|_Weekday;
+                               : _Month|_Weekday;
            // n.b. for calendar types __def._M_needed contains only parts
            // copied from the input, remaining ones are computed, and thus ok
            __spec._M_needs_ok_check 
@@ -694,7 +694,8 @@ namespace __format
                  break;
                case 'g':
                case 'G':
-                 __needed = _LocalDays|_Weekday;
+               case 'V':
+                 __needed = _LocalDays|_Year|_DayOfYear|_Weekday;
                  break;
                case 'H':
                case 'I':
@@ -742,9 +743,8 @@ namespace __format
                  __allowed_mods = _Mod_O;
                  break;
                case 'U':
-               case 'V':
                case 'W':
-                 __needed = _LocalDays|_Year|_DayOfYear|_Weekday;
+                 __needed = _DayOfYear|_Weekday;
                  __allowed_mods = _Mod_O;
                  break;
                case 'x':
@@ -1148,7 +1148,8 @@ namespace __format
                  break;
                case 'g':
                case 'G':
-                 __out = _M_g_G(__t, std::move(__out), __c == 'G');
+               case 'V':
+                 __out = _M_g_G_V(__t, std::move(__out), __c);
                  break;
                case 'H':
                case 'I':
@@ -1190,9 +1191,8 @@ namespace __format
                  __out = _M_u_w(__t._M_weekday, std::move(__out), __c);
                  break;
                case 'U':
-               case 'V':
                case 'W':
-                 __out = _M_U_V_W(__t, std::move(__out), __c);
+                 __out = _M_U_W(__t, std::move(__out), __c);
                  break;
                case 'z':
                  __out = _M_z(__t._M_zone_offset, std::move(__out), 
(bool)__mod);
@@ -1442,18 +1442,47 @@ namespace __format
 
       template<typename _OutIter>
        _OutIter
-       _M_g_G(const _ChronoData<_CharT>& __t, _OutIter __out,
-              bool __full) const
+       _M_g_G_V(const _ChronoData<_CharT>& __t, _OutIter __out,
+               _CharT __conv) const
        {
-         // %g last two decimal digits of the ISO week-based year.
-         // %G ISO week-based year.
-         using namespace chrono;
-         auto __d = __t._M_ldays;
-         // Move to nearest Thursday:
-         __d -= (__t._M_weekday - Monday) - days(3);
+         // %g  last two decimal digits of the ISO week-based year.
+         // %G  ISO week-based year.
+         // %V  ISO week-based week number as a decimal number.
+         // %OV Locale's alternative numeric rep.
+       
          // ISO week-based year is the year that contains that Thursday:
-         year __y = year_month_day(__d).year();
-         return _M_C_y_Y(__y, std::move(__out), "yY"[__full]);
+         // ISO week of __t is number of weeks since January 1 of the ISO year.
+         
+         using namespace chrono;
+         const _CharT __yconv = "yY"[__conv == 'G'];
+         // Offset of the nearest Thursday:
+         const days __offset = (__t._M_weekday - Monday) - days(3);
+         // Day of year of nearest Thursday:
+         days __idoy = __t._M_day_of_year - __offset;
+         if (__idoy > days(0) && __idoy <= days(365)) [[likely]]
+           {
+             // Nearest Thrusday is in the same year as __t._M_year
+             if (__conv != 'V')
+               return _M_C_y_Y(__t._M_year, std::move(__out), __yconv);
+       
+             const auto __wi = chrono::floor<weeks>(__idoy - days(1)).count() 
+ 1;
+             return __format::__write(std::move(__out), _S_two_digits(__wi));
+           }
+
+         // Nearest Thursday as local days
+         const local_days __ild = __t._M_ldays - __offset;
+         // Nearest Thursday in previous year (__idoy <= 0), on a leap day
+         // of same year, or later year (__idoy >= 366)
+         const year __iyear = (__idoy <= days(0))
+                            ? __t._M_year - years(1)
+                            : year_month_day(__ild).year();
+         if (__conv != 'V')
+           return _M_C_y_Y(__iyear, std::move(__out), __yconv);
+ 
+         if (__iyear != __t._M_year) [[likely]]
+           __idoy = __ild - local_days(__iyear/January/0);
+         const auto __wi = chrono::floor<weeks>(__idoy - days(1)).count() + 1;
+         return __format::__write(std::move(__out), _S_two_digits(__wi));
        }
 
       template<typename _OutIter>
@@ -1710,35 +1739,19 @@ namespace __format
 
       template<typename _OutIter>
        _OutIter
-       _M_U_V_W(const _ChronoData<_CharT>& __t, _OutIter __out,
+       _M_U_W(const _ChronoData<_CharT>& __t, _OutIter __out,
                 _CharT __conv) const
        {
          // %U  Week number of the year as a decimal number, from first Sunday.
          // %OU Locale's alternative numeric rep.
-         // %V  ISO week-based week number as a decimal number.
-         // %OV Locale's alternative numeric rep.
          // %W  Week number of the year as a decimal number, from first Monday.
          // %OW Locale's alternative numeric rep.
+         
          using namespace chrono;
-
-         auto __d = __t._M_ldays;
-         local_days __first; // First day of week 1.
-         if (__conv == 'V') // W01 begins on Monday before first Thursday.
-           {
-             // Move to nearest Thursday:
-             __d -= (__t._M_weekday - Monday) - days(3);
-             // ISO week of __t is number of weeks since January 1 of the
-             // same year as that nearest Thursday.
-             __first = local_days(year_month_day(__d).year()/January/1);
-           }
-         else
-           {
-             const weekday __weekstart = __conv == 'U' ? Sunday : Monday;
-             __first = local_days(__t._M_year/January/__weekstart[1]);
-           }
-         auto __weeks = chrono::floor<weeks>(__d - __first);
-         __string_view __sv = _S_two_digits(__weeks.count() + 1);
-         return __format::__write(std::move(__out), __sv);
+         const weekday __weekstart = __conv == 'U' ? Sunday : Monday;
+         const days __offset = __t._M_weekday - __weekstart;
+         auto __weeks = chrono::floor<weeks>(__t._M_day_of_year - __offset - 
days(1));
+         return __format::__write(std::move(__out), 
_S_two_digits(__weeks.count() + 1));
        }
 
       template<typename _OutIter>
diff --git a/libstdc++-v3/testsuite/std/time/year_month_day/io.cc 
b/libstdc++-v3/testsuite/std/time/year_month_day/io.cc
index 7b09ff4b95a..0c5ddb02750 100644
--- a/libstdc++-v3/testsuite/std/time/year_month_day/io.cc
+++ b/libstdc++-v3/testsuite/std/time/year_month_day/io.cc
@@ -49,6 +49,12 @@ test_format()
   VERIFY( s == "Day 6 (Sat) of Week 00 of 2022" );
   s = std::format("Day {:%w (%a) of Week %U of %Y}", 2022y/January/2);
   VERIFY( s == "Day 0 (Sun) of Week 01 of 2022" );
+  s = std::format("Day {:%w (%a) of Week %U of %Y}", 2024y/January/1);
+  VERIFY( s == "Day 1 (Mon) of Week 00 of 2024" );
+  s = std::format("Day {:%w (%a) of Week %U of %Y}", 2024y/January/7);
+  VERIFY( s == "Day 0 (Sun) of Week 01 of 2024" );
+  s = std::format("Day {:%w (%a) of Week %U of %Y}", 2024y/January/8);
+  VERIFY( s == "Day 1 (Mon) of Week 01 of 2024" );
   s = std::format("Day {:%w (%a) of Week %U of %Y}", 2022y/Quindecember/20);
   VERIFY( s == "Day 1 (Mon) of Week 73 of 2022" );
   // %W: Week number for weeks starting on Monday
@@ -56,7 +62,13 @@ test_format()
   VERIFY( s == "Day 7 (Sun) of Week 00 of 2022" );
   s = std::format("Day {:%u (%a) of Week %W of %Y}", 2022y/January/3);
   VERIFY( s == "Day 1 (Mon) of Week 01 of 2022" );
-  s = std::format("Day {:%w (%a) of Week %U of %Y}", 2022y/Quindecember/20);
+  s = std::format("Day {:%w (%a) of Week %W of %Y}", 2019y/January/1);
+  VERIFY( s == "Day 2 (Tue) of Week 00 of 2019" );
+  s = std::format("Day {:%w (%a) of Week %W of %Y}", 2019y/January/7);
+  VERIFY( s == "Day 1 (Mon) of Week 01 of 2019" );
+  s = std::format("Day {:%w (%a) of Week %W of %Y}", 2019y/January/8);
+  VERIFY( s == "Day 2 (Tue) of Week 01 of 2019" );
+  s = std::format("Day {:%w (%a) of Week %W of %Y}", 2022y/Quindecember/20);
   VERIFY( s == "Day 1 (Mon) of Week 73 of 2022" );
 
   // %G: ISO week-calendar year (ISO 8601)
@@ -65,6 +77,8 @@ test_format()
   VERIFY( s == "1976-W53" );
   s = std::format("{:%G-W%V}", 1977y/1/2);
   VERIFY( s == "1976-W53" );
+  s = std::format("{:%G-W%V}", 1977y/1/3);
+  VERIFY( s == "1977-W01" );
   s = std::format("{:%G-W%V}", 1977y/12/31);
   VERIFY( s == "1977-W52" );
   s = std::format("{:%G-W%V}", 1978y/1/1);
@@ -83,6 +97,18 @@ test_format()
   VERIFY( s == "1980-W01" );
   s = std::format("{:%G-W%V}", 1980y/18/20);
   VERIFY( s == "1981-W26" );
+  s = std::format("{:%G-W%V}", 2021y/01/01);
+  VERIFY( s == "2020-W53" );
+  s = std::format("{:%G-W%V}", 2021y/01/07);
+  VERIFY( s == "2021-W01" );
+  s = std::format("{:%G-W%V}", 2021y/01/8);
+  VERIFY( s == "2021-W01" );
+  s = std::format("{:%G-W%V}", 2020y/13/01);
+  VERIFY( s == "2020-W53" );
+  s = std::format("{:%G-W%V}", 2020y/13/07);
+  VERIFY( s == "2021-W01" );
+  s = std::format("{:%G-W%V}", 2020y/13/8);
+  VERIFY( s == "2021-W01" );
 
   s = std::format("{:%x}", 2022y/December/19);
   VERIFY( s == "12/19/22" );
-- 
2.51.0

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