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3.4 Comparison of Numbers

To test numbers for numerical equality, you should normally use =, not eq. There can be many distinct floating-point objects with the same numeric value. If you use eq to compare them, then you test whether two values are the same object. By contrast, = compares only the numeric values of the objects.

In Emacs Lisp, each integer is a unique Lisp object. Therefore, eq is equivalent to = where integers are concerned. It is sometimes convenient to use eq for comparing an unknown value with an integer, 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 equal, which treats 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)))

Common Lisp note: Comparing numbers in Common Lisp always requires = because Common Lisp implements multi-word integers, and two distinct integer objects can have the same numeric value. Emacs Lisp can have just one integer object for any given value because it has a limited range of integers.
— 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.

— 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.