🚀 go-pugleaf

Henry Baker (hbaker@netcom.com) wrote:
: To summarize, the 'correct' mod is one that produces remainders that follow
: the _divisor_, and therefore the 'correct' quotient is the _floor_ function.

In other words, computers should be programmed to flunk number theory and 
group theory, not to mention trigonometry (I'd love to see what you think 
a sine curve looks like around the vertical axis). Wonderful.

The point of arithmetic modulo n is that the same cycle of numbers 
repeats ad infinitum from 0 to (n - 1). It doesn't switch gears at zero. 
And "remainder" is defined as the unique NON-NEGATIVE number greater than 
equal to 0 but less than the divisor that is left over when the product 
of the divisor and some integer (quotient) is subtracted from the dividend.

These definitions of modulus and remainder are well founded and old, and
are useful in a large number of fields. (Quick: if there had been clocks
as we know them back then, what number would the little hand have been on
ten minutes before the opening moment of January 1 of the year 1: 10 or
2?) These concepts weren't just first invented to make life convenient 
for programmers, and the software industry shouldn't pretend to own these 
concepts any more than they should expect to use a non-standard 
definition for addition or cosine.

Certainly there are occasions when what you want for your programming 
task is the other way around, but that is a different function.