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(emacs-lisp-intro.info)Compute a Remainder

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Side Trip: Compute a Remainder
------------------------------

   In Lisp, the function for computing a remainder is `%'.  The
function returns the remainder of its first argument divided by its
second argument.  As it happens, `%' is a function in Emacs Lisp that
you cannot discover using `apropos': you find nothing if you type `M-x
apropos <RET> remainder <RET>'.  The only way to learn of the existence
of `%' is to read about it in a book such as this or in the Emacs Lisp
sources.  The `%' function is used in the code for
`rotate-yank-pointer', which is described in an appendix.  (Note: The
Body of `rotate-yank-pointer'.)

   You can try the `%' function by evaluating the following two
expressions:

     (% 7 5)
     
     (% 10 5)

The first expression returns 2 and the second expression returns 0.

   To test whether the returned value is zero or some other number, we
can use the `zerop' function.  This function returns `t' if its
argument, which must be a number, is zero.

     (zerop (% 7 5))
          => nil
     
     (zerop (% 10 5))
          => t

   Thus, the following expression will return `t' if the height of the
graph is evenly divisible by five:

     (zerop (% height 5))

(The value of `height', of course, can be found from `(apply 'max
numbers-list)'.)

   On the other hand, if the value of `height' is not a multiple of
five, we want to reset the value to the next higher multiple of five.
This is straightforward arithmetic using functions with which we are
already familiar.  First, we divide the value of `height' by five to
determine how many times five goes into the number.  Thus, five goes
into twelve twice.  If we add one to this quotient and multiply by
five, we will obtain the value of the next multiple of five that is
larger than the height.  Five goes into twelve twice.  Add one to two,
and multiply by five; the result is fifteen, which is the next multiple
of five that is higher than twelve.  The Lisp expression for this is:

     (* (1+ (/ height 5)) 5)

For example, if you evaluate the following, the result is 15:

     (* (1+ (/ 12 5)) 5)

   All through this discussion, we have been using `five' as the value
for spacing labels on the Y axis; but we may want to use some other
value.  For generality, we should replace `five' with a variable to
which we can assign a value.  The best name I can think of for this
variable is `Y-axis-label-spacing'.

   Using this term, and an `if' expression, we produce the following:

     (if (zerop (% height Y-axis-label-spacing))
         height
       ;; else
       (* (1+ (/ height Y-axis-label-spacing))
          Y-axis-label-spacing))

This expression returns the value of `height' itself if the height is
an even multiple of the value of the `Y-axis-label-spacing' or else it
computes and returns a value of `height' that is equal to the next
higher multiple of the value of the `Y-axis-label-spacing'.

   We can now include this expression in the `let' expression of the
`print-graph' function (after first setting the value of
`Y-axis-label-spacing'):

     (defvar Y-axis-label-spacing 5
       "Number of lines from one Y axis label to next.")
     
     ...
     (let* ((height (apply 'max numbers-list))
            (height-of-top-line
             (if (zerop (% height Y-axis-label-spacing))
                 height
               ;; else
               (* (1+ (/ height Y-axis-label-spacing))
                  Y-axis-label-spacing)))
            (symbol-width (length graph-blank))))
     ...

(Note use of the  `let*' function: the initial value of height is
computed once by the `(apply 'max numbers-list)' expression and then
the resulting value of  `height' is used to compute its final value.
Note: The `let*' expression, for more about `let*'.)