weekday-skip-days

name	weekday-skip-days
description	Compute weekdays correctly for calendars where some days (intercalary/epagomenal) are excluded from the weekday cycle. Use when implementing or debugging weekday logic with “skipped days”, “epagomenal”, “intercalary”, or “non-weekday” days.

Weekday Math With Skipped Days

Instructions

When a calendar defines a weekday cycle but explicitly excludes certain days (for example: intercalary days, mid-year days, festival-only epagomenal days), compute weekdays using the count of regular days that participate in the cycle—not using the raw day index.

1. Classify days

Identify, for the calendar rules you’re implementing:

• Which days are regular (weekday participates).
• Which days are skipped (weekday does not advance; you may still display a special label, but weekday progression must not include them).

Record your “skipped day set” in terms of the calendar’s internal indexing (e.g., specific dayIndex values within a year, or rule-based offsets like “the extra leap intercalary day”).

2. Use an anchored weekday

Find the weekday anchor (examples):

• Weekday of dayIndex = 0 (year start) is known.
• Weekday of a specific epoch date is known.

Let anchorWeekdayIndex be an integer in [0..6] for the weekday name order used by the calendar implementation.

3. Count only regular days

Compute how many days have elapsed since the anchor, but subtract any skipped days that occurred in that span:

regularDaysElapsed = totalDaysElapsed - skippedDaysInSpan

Then:

weekdayIndex = (anchorWeekdayIndex + regularDaysElapsed) % 7

4. Do not use dayIndex % 7 on skipped days

Avoid patterns like:

• weekdayNames[dayIndex % 7]
• weekdayNames[(dayIndex + k) % 7]

These implicitly advance weekdays across skipped days and will be wrong whenever skipped days occur between the anchor and the target date.

5. Output handling for skipped days

Choose a consistent display strategy and keep it stable:

• Option A: Show weekday as “(skipped)” for excluded days.
• Option B: Omit the weekday line entirely for excluded days.
• Option C: Show a special weekday label if the calendar defines one.

Regardless of display choice: the next regular day must resume weekday progression as if the skipped day did not exist.

6. Validate boundary conditions (tests)

Add/ensure tests at minimum:

• The day immediately before the first skipped day.
• Each skipped day itself (and leap-added skipped days).
• The day immediately after the last skipped day.
• The end of year case where a skipped day occurs just before the final day (this is where off-by-one weekday bugs often show up).

Also test with at least one leap-year (if leap days change which days are skipped).

7. Timezone day-boundary correctness

If your UI supports timezone offsets, ensure that:

• The date-to-dayIndex mapping uses the same local-midnight rule as other calendar systems (e.g., using the project’s faux-UTC + MIDNIGHT adjustment).
• Weekday progression uses the same resulting dayIndex / day boundary.

8. Negative years / historical dates

If the project supports BCE/negative years, ensure your modulus logic works for negative regularDaysElapsed (normalize with ((n % 7) + 7) % 7 style normalization).

Examples (patterns)

Compute weekday index from regular-days count

const weekdayIndex = ((anchorWeekdayIndex + regularDaysElapsed) % 7 + 7) % 7;
return weekdayNames[weekdayIndex];

Mark skipped day display without advancing

if (isSkippedDay) return `${specialDayLabel}\nWeekday: (skipped)`;
return `${specialDayLabel}\nWeekday: ${weekdayNames[weekdayIndex]}`;