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### 3.6 Arithmetic Operations

Emacs Lisp provides the traditional four arithmetic operations (addition, subtraction, multiplication, and division), as well as remainder and modulus functions, and functions to add or subtract 1. Except for `%`, each of these functions accepts both integer and floating-point arguments, and returns a floating-point number if any argument is floating point.

Emacs Lisp arithmetic functions do not check for integer overflow. Thus `(1+ 536870911)` may evaluate to −536870912, 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: / number &rest divisors

With one or more divisors, this function divides number by each divisor in divisors in turn, and returns the quotient. With no divisors, this function returns 1/number, i.e., the multiplicative inverse of number. Each argument may be a number or a marker.

If all the arguments are integers, the result is an integer, obtained by rounding the quotient towards zero after each division.

```          (/ 6 2)
⇒ 3
(/ 5 2)
⇒ 2
(/ 5.0 2)
⇒ 2.5
(/ 5 2.0)
⇒ 2.5
(/ 5.0 2.0)
⇒ 2.5
(/ 4.0)
⇒ 0.25
(/ 4)
⇒ 0
(/ 25 3 2)
⇒ 4
(/ -17 6)
⇒ -2
```

If you divide an integer by the integer 0, Emacs signals an `arith-error` error (see Errors). Floating-point division of a nonzero number by zero yields either positive or negative infinity (see Float Basics).

— Function: % dividend divisor

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

For any two integers dividend and divisor,

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

always equals dividend if divisor is nonzero.

```          (% 9 4)
⇒ 1
(% -9 4)
⇒ -1
(% 9 -4)
⇒ 1
(% -9 -4)
⇒ -1
```
— 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` permits floating-point arguments; it rounds the quotient downward (towards minus infinity) to an integer, and uses that quotient to compute the remainder.

If divisor is zero, `mod` signals an `arith-error` error if both arguments are integers, and returns a NaN otherwise.

```          (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 and to an `arith-error` if dividend is an integer and divisor is 0. For `floor`, see Numeric Conversions.