3.4 Comparison of Numbers

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.