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mod, rem

mod, rem Function

Syntax:

mod number divisor → modulus

rem number divisor → remainder

Arguments and Values:

number—a real.

divisor—a real.

modulus, remainder—a real.

Description:

mod and rem are generalizations of the modulus and remainder functions respectively.

mod performs the operation floor on number and divisor and returns the remainder of the floor operation.

rem performs the operation truncate on number and divisor and returns the remainder of the truncate operation.

mod and rem are the modulus and remainder functions when number and divisor are integers.

Examples:

(rem -1 5) → -1 
(mod -1 5) → 4 
(mod 13 4) → 1 
(rem 13 4) → 1 
(mod -13 4) → 3 
(rem -13 4) → -1 
(mod 13 -4) → -3 
(rem 13 -4) → 1 
(mod -13 -4) → -1 
(rem -13 -4) → -1 
(mod 13.4 1) → 0.4 
(rem 13.4 1) → 0.4 
(mod -13.4 1) → 0.6 
(rem -13.4 1) → -0.4


See Also:

floor, truncate

Notes:

The result of mod is either zero or a real with the same sign as divisor.

Expanded Reference: mod, rem​

Basic modulus and remainder​

mod returns the remainder from floor division. rem returns the remainder from truncate division. They agree when both arguments have the same sign.

(mod 13 4)
=> 1
(rem 13 4)
=> 1
(mod 10 3)
=> 1
(rem 10 3)
=> 1

Difference with negative arguments​

mod and rem differ when the arguments have different signs. mod always returns a result with the same sign as the divisor. rem always returns a result with the same sign as the dividend.

(mod -1 5)
=> 4
(rem -1 5)
=> -1

(mod -13 4)
=> 3
(rem -13 4)
=> -1

(mod 13 -4)
=> -3
(rem 13 -4)
=> 1

(mod -13 -4)
=> -1
(rem -13 -4)
=> -1

Floating-point arguments​

mod and rem work with floating-point numbers as well.

(mod 13.4 1)
=> 0.39999962
(rem 13.4 1)
=> 0.39999962
(mod -13.4 1)
=> 0.6000004
(rem -13.4 1)
=> -0.39999962

Testing divisibility​

mod (or rem) with a result of zero means the dividend is evenly divisible by the divisor.

(zerop (mod 12 3))
=> T
(zerop (mod 12 5))
=> NIL

Cyclic indexing​

mod is commonly used to wrap an index around within a fixed range.

(defun cyclic-index (i n)
  (mod i n))

(cyclic-index 7 5)
=> 2
(cyclic-index -1 5)
=> 4
(cyclic-index 5 5)
=> 0