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(emacs-lisp-intro.info)Large buffer case

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What happens in a large buffer
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   In `beginning-of-buffer', the inner `if' expression tests whether
the size of the buffer is greater than 10,000 characters.  To do this,
it uses the `>' function and the `buffer-size' function.

   The line looks like this:

     (if (> (buffer-size) 10000)

When the buffer is large, the then-part of the `if' expression is
evaluated.  It reads like this (after formatting for easy reading):

     (*
       (prefix-numeric-value arg)
       (/ (buffer-size) 10))

This expression is a multiplication, with two arguments to the function
`*'.

   The first argument is `(prefix-numeric-value arg)'.  When `"P"' is
used as the argument for `interactive', the value passed to the
function as its argument is passed a "raw prefix argument", and not a
number.  (It is a number in a list.)  To perform the arithmetic, a
conversion is necessary, and `prefix-numeric-value' does the job.

   The second argument is `(/ (buffer-size) 10)'.  This expression
divides the numeric value of the buffer by ten.  This produces a number
that tells how many characters make up one tenth of the buffer size.
(In Lisp, `/' is used for division, just as `*' is used for
multiplication.)

   In the multiplication expression as a whole, this amount is
multiplied by the value of the prefix argument--the multiplication
looks like this:

     (* NUMERIC-VALUE-OF-PREFIX-ARG
        NUMBER-OF-CHARACTERS-IN-ONE-TENTH-OF-THE-BUFFER)

If, for example, the prefix argument is `7', the one-tenth value will
be multiplied by 7 to give a position 70% of the way through the buffer.

   The result of all this is that if the buffer is large, the
`goto-char' expression reads like this:

     (goto-char (* (prefix-numeric-value arg)
                   (/ (buffer-size) 10)))

   This puts the cursor where we want it.