# Re: polynomials

• To: info-mcl@ministry.cambridge.apple.com
• Subject: Re: polynomials
• From: ses@tipper.oit.unc.edu (Simon E Spero)
• Date: 21 Feb 1994 18:05:19 GMT
• Newsgroups: comp.lang.lisp, comp.lang.lisp.mcl
• Organization: University of North Carolina, Chapel Hill
• References: <DELEEUW.94Feb20113309@galton.math.ucla.edu>
• Xref: news.cambridge.apple.com comp.lang.lisp:7168 comp.lang.lisp.mcl:4949

```In article <DELEEUW.94Feb20113309@galton.math.ucla.edu>,
Jan Deleeuw <deleeuw@galton.math.ucla.edu> wrote:
>Hello,

Here's one attempt at a faster version, which reverses the order
of coefficients. It uses iteration instead of recursion; the version
of poly that you posted wasn't tail recursive; you could make it
tail-recusive by passing an accumulator but iteration seemed a more natural
way of expressing this problem.

Be careful about changing the safety setting - remember 0.0 isn't a
double-float. For yet more efficiency, you could turn poly into a macro;
just backquote and comma the code computing result.

(defun poly-2 (var coefs)
"compute a polynomial in var using coefficients in coefs. Coefficients are
in decending order - (poly-2 x (1 2 3 4)) == x^3 + 2x^2 + 3x +4"
(declare (optimize  speed safety)
(double-float var))
(do* ((result 0.0d0 (+ c (* result var)))
(coefficients coefs (cdr coefficients))
(c (car coefficients) (or (and coefficients (car coefficients))
0.0d0)))
((null coefficients) result)
(declare (double-float result c))))
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```

• References:
• polynomials
• From: deleeuw@galton.math.ucla.edu (Jan Deleeuw)