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9.6 Arithmetic Operations

SXEmacs 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 SXEmacs Lisp, arithmetic functions do not check for overflow. Thus `(1+ 134217727)` may evaluate to -134217728, depending on your hardware.

Function: 1+ number

This function returns number plus one. number may be a number, character or marker. Markers and characters are converted to integers.

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
```

Now that the `cl` package is always available from lisp code, a more convenient and natural way to increment a variable is `(incf foo)`.

Function: 1- number

This function returns number minus one. number may be a number, character or marker. Markers and characters are converted to integers.

Function: abs number

This returns the absolute value of number.

Function: + &rest numbers

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

If any of the arguments are characters or markers, they are first converted to integers.

```(+)
⇒ 0
(+ 1)
⇒ 1
(+ 1 2 3 4)
⇒ 10
```
Function: - &optional number &rest other-numbers

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 other-numbers from number, cumulatively. If there are no arguments, an error is signaled.

If any of the arguments are characters or markers, they are first converted to integers.

```(- 10 1 2 3 4)
⇒ 0
(- 10)
⇒ -10
(-)
⇒ 0
```
Function: * &rest numbers

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

If any of the arguments are characters or markers, they are first converted to integers.

```(*)
⇒ 1
(* 1)
⇒ 1
(* 1 2 3 4)
⇒ 24
```
Function: / dividend &rest divisors

The `/` function serves two purposes: inversion and division. When `/` has a single argument, the value is the inverse of the argument. When there are multiple arguments, `/` divides dividend by each of the divisors, cumulatively, returning the quotient. If there are no arguments, an error is signaled.

If none of the arguments are floats, then the result is an integer. 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 any of the arguments are characters or markers, they are first converted to integers.

If you divide by 0, an `arith-error` error is signaled. (See Errors.)

```(/ 6 2)
⇒ 3
```
```(/ 5 2)
⇒ 2
(/ 25 3 2)
⇒ 4
(/ 3.0)
⇒ 0.3333333333333333
(/ -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 Numeric Conversions.

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