Arithmetic Operations

Emacs Lisp provides the traditional four arithmetic operations: addition, subtraction, multiplication, and division. Remainder and modulus functions supplement the division functions. The functions to add or subtract 1 are provided because they are traditional in Lisp and commonly used.

All of these functions except % return a floating point value if any argument is floating.

It is important to note that in Emacs Lisp, arithmetic functions do not check for overflow. Thus (1+ 134217727) may evaluate to -134217728, depending on your hardware.

Function: 1+ number-or-marker

This function returns number-or-marker plus 1. For example,

(setq foo 4)
     => 4
(1+ foo)
     => 5

This function is not analogous to the C operator ++---it does not increment a variable. It just computes a sum. Thus, if we continue,

foo
     => 4

If you want to increment the variable, you must use setq, like this:

(setq foo (1+ foo))
     => 5

Function: 1- number-or-marker

This function returns number-or-marker minus 1.

Function: + &rest numbers-or-markers

This function adds its arguments together. When given no arguments, + returns 0.

(+)
     => 0
(+ 1)
     => 1
(+ 1 2 3 4)
     => 10

Function: - &optional number-or-marker &rest more-numbers-or-markers

The - function serves two purposes: negation and subtraction. When - has a single argument, the value is the negative of the argument. When there are multiple arguments, - subtracts each of the more-numbers-or-markers from number-or-marker, cumulatively. If there are no arguments, the result is 0.

(- 10 1 2 3 4)
     => 0
(- 10)
     => -10
(-)
     => 0

Function: * &rest numbers-or-markers

This function multiplies its arguments together, and returns the product. When given no arguments, * returns 1.

(*)
     => 1
(* 1)
     => 1
(* 1 2 3 4)
     => 24

Function: / dividend divisor &rest divisors

This function divides dividend by divisor and returns the quotient. If there are additional arguments divisors, then it divides dividend by each divisor in turn. Each argument may be a number or a marker.

If all the arguments are integers, then the result is an integer too. This means the result has to be rounded. On most machines, the result is rounded towards zero after each division, but some machines may round differently with negative arguments. This is because the Lisp function / is implemented using the C division operator, which also permits machine-dependent rounding. As a practical matter, all known machines round in the standard fashion.

If you divide an integer by 0, an arith-error error is signaled. (See section Errors.) Floating point division by zero returns either infinity or a NaN if your machine supports IEEE floating point; otherwise, it signals an arith-error error.

(/ 6 2)
     => 3
(/ 5 2)
     => 2
(/ 5.0 2)
     => 2.5
(/ 5 2.0)
     => 2.5
(/ 5.0 2.0)
     => 2.5
(/ 25 3 2)
     => 4
(/ -17 6)
     => -2

The result of (/ -17 6) could in principle be -3 on some machines.

Function: % dividend divisor

This function returns the integer remainder after division of dividend by divisor. The arguments must be integers or markers.

For negative arguments, the remainder is in principle machine-dependent since the quotient is; but in practice, all known machines behave alike.

An arith-error results if divisor is 0.

(% 9 4)
     => 1
(% -9 4)
     => -1
(% 9 -4)
     => 1
(% -9 -4)
     => -1

For any two integers dividend and divisor,

(+ (% dividend divisor)
   (* (/ dividend divisor) divisor))

always equals dividend.

Function: mod dividend divisor

This function returns the value of dividend modulo divisor; in other words, the remainder after division of dividend by divisor, but with the same sign as divisor. The arguments must be numbers or markers.

Unlike %, mod returns a well-defined result for negative arguments. It also permits floating point arguments; it rounds the quotient downward (towards minus infinity) to an integer, and uses that quotient to compute the remainder.

An arith-error results if divisor is 0.

(mod 9 4)
     => 1
(mod -9 4)
     => 3
(mod 9 -4)
     => -3
(mod -9 -4)
     => -1
(mod 5.5 2.5)
     => .5

For any two numbers dividend and divisor,

(+ (mod dividend divisor)
   (* (floor dividend divisor) divisor))

always equals dividend, subject to rounding error if either argument is floating point. For floor, see section Numeric Conversions.

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