Closes bpo-28292: Implemented Calendar.itermonthdays3() and itermonthdays4(). (#4079)

Calendar.itermonthdates() will now consistently raise an exception when a date falls outside of the 0001-01-01 through 9999-12-31 range. To support applications that cannot tolerate such exceptions, the new methods itermonthdays3() and itermonthdays4() are added. The new methods return tuples and are not restricted by the range supported by datetime.date.

Thanks @serhiy-storchaka for suggesting the itermonthdays4() method and for the review.
diff --git a/Lib/calendar.py b/Lib/calendar.py
index 0218e2d..fb594e0 100644
--- a/Lib/calendar.py
+++ b/Lib/calendar.py
@@ -126,6 +126,24 @@
     return day1, ndays
 
 
+def monthlen(year, month):
+    return mdays[month] + (month == February and isleap(year))
+
+
+def prevmonth(year, month):
+    if month == 1:
+        return year-1, 12
+    else:
+        return year, month-1
+
+
+def nextmonth(year, month):
+    if month == 12:
+        return year+1, 1
+    else:
+        return year, month+1
+
+
 class Calendar(object):
     """
     Base calendar class. This class doesn't do any formatting. It simply
@@ -157,28 +175,8 @@
         values and will always iterate through complete weeks, so it will yield
         dates outside the specified month.
         """
-        date = datetime.date(year, month, 1)
-        # Go back to the beginning of the week
-        days = (date.weekday() - self.firstweekday) % 7
-        date -= datetime.timedelta(days=days)
-        oneday = datetime.timedelta(days=1)
-        while True:
-            yield date
-            try:
-                date += oneday
-            except OverflowError:
-                # Adding one day could fail after datetime.MAXYEAR
-                break
-            if date.month != month and date.weekday() == self.firstweekday:
-                break
-
-    def itermonthdays2(self, year, month):
-        """
-        Like itermonthdates(), but will yield (day number, weekday number)
-        tuples. For days outside the specified month the day number is 0.
-        """
-        for i, d in enumerate(self.itermonthdays(year, month), self.firstweekday):
-            yield d, i % 7
+        for y, m, d in self.itermonthdays3(year, month):
+            yield datetime.date(y, m, d)
 
     def itermonthdays(self, year, month):
         """
@@ -192,6 +190,40 @@
         days_after = (self.firstweekday - day1 - ndays) % 7
         yield from repeat(0, days_after)
 
+    def itermonthdays2(self, year, month):
+        """
+        Like itermonthdates(), but will yield (day number, weekday number)
+        tuples. For days outside the specified month the day number is 0.
+        """
+        for i, d in enumerate(self.itermonthdays(year, month), self.firstweekday):
+            yield d, i % 7
+
+    def itermonthdays3(self, year, month):
+        """
+        Like itermonthdates(), but will yield (year, month, day) tuples.  Can be
+        used for dates outside of datetime.date range.
+        """
+        day1, ndays = monthrange(year, month)
+        days_before = (day1 - self.firstweekday) % 7
+        days_after = (self.firstweekday - day1 - ndays) % 7
+        y, m = prevmonth(year, month)
+        end = monthlen(y, m) + 1
+        for d in range(end-days_before, end):
+            yield y, m, d
+        for d in range(1, ndays + 1):
+            yield year, month, d
+        y, m = nextmonth(year, month)
+        for d in range(1, days_after + 1):
+            yield y, m, d
+
+    def itermonthdays4(self, year, month):
+        """
+        Like itermonthdates(), but will yield (year, month, day, day_of_week) tuples.
+        Can be used for dates outside of datetime.date range.
+        """
+        for i, (y, m, d) in enumerate(self.itermonthdays3(year, month)):
+            yield y, m, d, (self.firstweekday + i) % 7
+
     def monthdatescalendar(self, year, month):
         """
         Return a matrix (list of lists) representing a month's calendar.