% operator with negatives

[Brad Sherman]

--Quite distinct from the "%" is [not] a modulus operator discussion--.

For those wishing to implement a modulous function that behaves in 
a reasonable manner for all integers I offer the following notes
taken from a book by Knuth and others (title forgotten).

	To make "m mod n" well defined for any integer value, positive
	or negative start from the relation:
		m = n * floor(m/n) + m mod n
	producing:
		m mod n = m - n * floor(m/n)
	e.g.:
		 5 mod  3 =  5 -   3  * floor( 5 /  3 ) =  5 -   3  *   1  =  2
		-5 mod  3 = -5 -   3  * floor(-5 /  3 ) = -5 -   3  * (-2) =  1
		 5 mod -3 =  5 - (-3) * floor( 5 /(-3)) =  5 - (-3) * (-2) = -1
		-5 mod -3 = -5 - (-3) * floor(-5 /(-3)) = -5 - (-3) *   1  = -2

	Note that the result always matches the modulus in sign.  No
	no one has ever come up with a good name for "m" and they
	suggest (with no smiley in the text!) "modumor."

[Errors in the above are mine, not Knuth's, I'm sure.]
---------------------------------
	Brad Sherman (bks at alfa.berkeley.edu)
	"Mathematics is the queen of the sciences and number theory
	the queen of mathematics." -- C.F. Gauss