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Re: 1. warnings 2. optimizations

Sam writes:
>      1. Emacs compile buffer doesn't understand the CLISP warnings (they 
>      are not in the standard format like "file:line:message"). Is it 
>      possible to make CLISP compilation message more standard?

A better approach to the treatment of line numbers in CLISP would be
needed for this. But you can customize your ~/.emacs :

      ;; Meta-g :== Meta-x goto-line
      (global-set-key "\M-g" 'goto-line)

>      2. The following 3 functions compute factorial:
>      ...
>      I would expect more difference between fac0 and (fac1 and fac2) than  
>      between fac1 and fac2. And I definitely did not expect much difference 
>      between fac 1 and fac2.

fac0 and fac2 are the same algorithm (they multiply the same numbers in the
same order), just in a different look.

>      On a second thought... The reason must be that we get to the bignums 
>      faster with fac0 and fac2!

You are in the bignums nearly all the time (already after 15 multiplications
out of 10000). That cannot account for a 12% speedup. Think once more.
(Hint: In clisp, the time needed for the multiplication of a fixnum with
a bignum is proportional to the length (in bits) of the bignum and independent
of the smaller factor.)

You might then try these:

       (defun fac3 (n)
         (labels ((f (a b)
                    (case (- b a)
                      (1 b)
                      (2 (* (- b 1) b))
                      (3 (* (- b 2) (- b 1) b))
                      (4 (* (- b 3) (- b 2) (- b 1) b))
                      (t (let ((m (ash (+ a b) -1))) (* (f a m) (f m b))))
                 )) )
           (if (plusp n) (f 0 n) 1)
       ) )

       (defun fac4 (n) (! n))  ; this is unfair