To test numbers for numerical equality, you should normally use
`=`

instead of non-numeric comparison predicates like `eq`

,
`eql`

and `equal`

. Distinct floating-point and large
integer objects can be numerically equal. If you use `eq`

to
compare them, you test whether they are the same *object*; if you
use `eql`

or `equal`

, you test whether their values are
*indistinguishable*. In contrast, `=`

uses numeric
comparison, and sometimes returns `t`

when a non-numeric
comparison would return `nil`

and vice versa. See Floating-Point Basics.

In Emacs Lisp, if two fixnums are numerically equal, they are the
same Lisp object. That is, `eq`

is equivalent to `=`

on
fixnums. It is sometimes convenient to use `eq`

for comparing
an unknown value with a fixnum, because `eq`

does not report an
error if the unknown value is not a number—it accepts arguments of
any type. By contrast, `=`

signals an error if the arguments are
not numbers or markers. However, it is better programming practice to
use `=`

if you can, even for comparing integers.

Sometimes it is useful to compare numbers with `eql`

or `equal`

,
which treat two numbers as equal if they have the same data type (both
integers, or both floating point) and the same value. By contrast,
`=`

can treat an integer and a floating-point number as equal.
See Equality Predicates.

There is another wrinkle: because floating-point arithmetic is not exact, it is often a bad idea to check for equality of floating-point values. Usually it is better to test for approximate equality. Here’s a function to do this:

(defvar fuzz-factor 1.0e-6) (defun approx-equal (x y) (or (= x y) (< (/ (abs (- x y)) (max (abs x) (abs y))) fuzz-factor)))

- Function:
**=**`number-or-marker &rest number-or-markers`¶ This function tests whether all its arguments are numerically equal, and returns

`t`

if so,`nil`

otherwise.

- Function:
**eql**`value1 value2`¶ This function acts like

`eq`

except when both arguments are numbers. It compares numbers by type and numeric value, so that`(eql 1.0 1)`

returns`nil`

, but`(eql 1.0 1.0)`

and`(eql 1 1)`

both return`t`

. This can be used to compare large integers as well as small ones. Floating-point values with the same sign, exponent and fraction are`eql`

. This differs from numeric comparison:`(eql 0.0 -0.0)`

returns`nil`

and`(eql 0.0e+NaN 0.0e+NaN)`

returns`t`

, whereas`=`

does the opposite.

- Function:
**/=**`number-or-marker1 number-or-marker2`¶ This function tests whether its arguments are numerically equal, and returns

`t`

if they are not, and`nil`

if they are.

- Function:
**<**`number-or-marker &rest number-or-markers`¶ This function tests whether each argument is strictly less than the following argument. It returns

`t`

if so,`nil`

otherwise.

- Function:
**<=**`number-or-marker &rest number-or-markers`¶ This function tests whether each argument is less than or equal to the following argument. It returns

`t`

if so,`nil`

otherwise.

- Function:
**>**`number-or-marker &rest number-or-markers`¶ This function tests whether each argument is strictly greater than the following argument. It returns

`t`

if so,`nil`

otherwise.

- Function:
**>=**`number-or-marker &rest number-or-markers`¶ This function tests whether each argument is greater than or equal to the following argument. It returns

`t`

if so,`nil`

otherwise.

- Function:
**max**`number-or-marker &rest numbers-or-markers`¶ This function returns the largest of its arguments.

(max 20) ⇒ 20 (max 1 2.5) ⇒ 2.5 (max 1 3 2.5) ⇒ 3

- Function:
**min**`number-or-marker &rest numbers-or-markers`¶ This function returns the smallest of its arguments.

(min -4 1) ⇒ -4

- Function:
**abs**`number`¶ This function returns the absolute value of

`number`.