---
title: "Response To Day_Of_Week"
type: "article"
slug: "response-to-day_of_week"
url: "http://localhost/article/response-to-day_of_week/"
markdown_url: "http://localhost/article/response-to-day_of_week.md"
published_at: "2025-12-18T18:29:31+00:00"
modified_at: "2026-06-21T23:36:29+00:00"
featured_image:
  url: "http://localhost/wp-content/uploads/2022/04/20230809-041332.jpg"
excerpt: "While playing around with the function on paper there appears to be a slight error. I am sure that I will not be the first to see this but I will attempt to explain anyway. The year part of the function Y + Y/4 - Y/100 + Y/400 is correct taking into account leap years,…"
category:
  - name: "QL Hacker's Journal"
    slug: "ql-hackers-journal"
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  - name: "Full Text"
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  - name: "QL"
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  - name: "Superbasic (programming language)"
    slug: "superbasic-programming-language"
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model:
  - name: "Sinclair QL"
    slug: "sinclair-ql"
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publication_r:
  id: 33686
  title: "QL Hacker’s Journal"
  type: "periodical"
  url: "http://localhost/periodical/ql-hackers-journal/"
authors: "John Southern"
issue: "23"
issues_articles:
  - id: 61559
    title: "QL Hacker’s Journal 23"
    type: "issue"
    url: "http://localhost/issue/ql-hackers-journal-23/"
pubdate: "January 1996"
archive_link: true
---

# Response To Day_Of_Week

While playing around with the function on paper there appears to be a slight error. I am sure that I will not be the first to see this but I will attempt to explain anyway.

The year part of the function Y + Y/4 – Y/100 + Y/400 is correct taking into account leap years, centuries and leap centuries. The month part however, 2*m + 3*(m+1)/5, is fine in most cases except for the way rounding occurs.

Consider 20 June 1995. We get:

```
   30+2*6+3*7/5+1995+1995/4-1995/100+1995/400
   
   30+12+4.2+1995+498.75-19.95+4.9875
   
   2524.9875
```

The Modulus 7 of this is 4.9875. Rounded up to give 5, which equals Friday.

Now consider 2 July 1995. We get:

```
   2+2*7+3*8/5+1995+1995/4-1995/100+1995/400
   
   2+14+4.8+1995+498.75+4.9875
   
   2499.5875
```

The Modulus 7 of this is 0.5875. Rounded up this give us 1, which equals Monday. This should be 0 for Sunday.

To correct this could I suggest the following function instead:

```
   DEFine FuNction day_of_week$(d,m,y)
      LOCal a
      
      IF m=1 OR m=2 THEN
         m=m+12
	 d=d-1
      END IF

      a = INT((d+2.6*m+y+y/4-y/100+y/400+0.8125) MOD 7)
   
      IF a = 0 THEN RETurn "Sunday"
      IF a = 1 THEN RETurn "Monday"
      IF a = 2 THEN RETurn "Tuesday"
      IF a = 3 THEN RETurn "Wednesday"
      IF a = 4 THEN RETurn "Thursday"
      IF a = 5 THEN RETurn "Friday"
      IF a = 6 THEN RETurn "Saturday"
   
   END DEFine
```

The 2.6*m is for the offset each month required due to months not being made up of an exact number of weeks. The 0.8125 is the initial adjustment to set Sundays correctly.