Difference between mod and rem in Clojure

Question

I could not understand the difference between these two (mod & rem) functions.

Answer 1

Clojuredoc's example for rem describes the difference:

;; rem and mod are commonly used to get the remainder.
;; mod means Gaussian mod, so the result is always
;; non-negative.  Don't confuse it with ANSI C's %
;; operator, which despite being pronounced
;; 'mod' actually implements rem, i.e. -10 % 3 = -1.

user=> (mod -10 3)
2

user=> (rem -10 3)
-1

Answer 2

mod returns the difference of the first number, and the biggest integer (possibly negative) multiple of the second number that is less than the first number:
rem is just the remainder.

For example (rem -4 3) => -1 no surprise here: -4 divided by 3 is -1 with -1 "left over".
But weirdness happens if we use mod: (mod -4 3) => 2:

• The greatest integer multiple of 3 less than -4 is -6.
• -4 minus -6 is 2.

So even though they usually act similarly, mod does not return the remainder, it does something more specific.

You might find these clojuredocs examples helpful.