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(elisp)Comparison of Numbers

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Comparison of Numbers
=====================

   To test numbers for numerical equality, you should normally use `=',
not `eq'.  There can be many distinct floating point number 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.

   At present, each integer value has a unique Lisp object in Emacs
Lisp.  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 a good idea to use `=' if you can, even for
comparing integers, just in case we change the representation of
integers in a future Emacs version.

   Sometimes it is useful to compare numbers with `equal'; it 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.

   There is another wrinkle: because floating point arithmetic is not
exact, it is often a bad idea to check for equality of two 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 (and (= x 0) (= y 0))
           (< (/ (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 integer values.

 - Function: = number-or-marker1 number-or-marker2
     This function tests whether its arguments are numerically equal,
     and returns `t' if so, `nil' otherwise.

 - 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-marker1 number-or-marker2
     This function tests whether its first argument is strictly less
     than its second argument.  It returns `t' if so, `nil' otherwise.

 - Function: <= number-or-marker1 number-or-marker2
     This function tests whether its first argument is less than or
     equal to its second argument.  It returns `t' if so, `nil'
     otherwise.

 - Function: > number-or-marker1 number-or-marker2
     This function tests whether its first argument is strictly greater
     than its second argument.  It returns `t' if so, `nil' otherwise.

 - Function: >= number-or-marker1 number-or-marker2
     This function tests whether its first argument is greater than or
     equal to its second 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.  If any of the
     argument is floating-point, the value is returned as floating
     point, even if it was given as an integer.

          (max 20)
               => 20
          (max 1 2.5)
               => 2.5
          (max 1 3 2.5)
               => 3.0

 - Function: min number-or-marker &rest numbers-or-markers
     This function returns the smallest of its arguments.  If any of
     the argument is floating-point, the value is returned as floating
     point, even if it was given as an integer.

          (min -4 1)
               => -4

 - Function: abs number
     This function returns the absolute value of NUMBER.