Subject: date-week-day screws up prior to AD 1

From: Zefram <[email-masked]>
Date: Sat, 18 Mar 2017 23:45:28 +0000

Looking at day of the week, via SRFI-19's date-week-day:

scheme@(guile-user)> (use-modules (srfi srfi-19))
scheme@(guile-user)> (julian-day->date 1721426 0) 
$1 = #<date nanosecond: 0 second: 0 minute: 0 hour: 12 day: 1 month: 1 year: 1 zone-offset: 0>
scheme@(guile-user)> (date-week-day (julian-day->date 1721426 0))
$2 = 1
scheme@(guile-user)> (date-week-day (julian-day->date 1721425 0))
$3 = 6

The output for 0001-01-01, Monday, is correct.  The preceding day is
actually a Sunday, but Saturday was shown.  Looking at the code, this
bug arises for the same reason as the problem with date-year-day raised
in bug#26151.  The date-year value, of the weird zero-skipping year
numbering, is passed to an algorithm that obviously expects astronomical
year numbering.

Looking at the code also reveals a second problem: the algorithm is
written to perform divisions with quotient where it obviously needs
modulo.  This will manifest in erroneous computations for some earlier
years once the above is fixed.

-zefram