( scratchpad ) -2 sqrt .
C{ 0.0 1.414213562373095 }
On Sun, Aug 10, 2008 at 10:15 AM, Kobi Lurie <[EMAIL PROTECTED]> wrote:
> nice, please note however that the sqrt cannot happen for negative numbers,
> so there is a need to check for that with an 'if'. (or possibly a case
> statement, so you can optimize-out the sqrt for 0)
> I also tried but it was pre cleave era :)
>
> see ya, kobi
>
>
> Slava Pestov wrote:
>
> > Hi all,
> >
> > For several years now, the quadratic formula has come up in
> > discussions of stack shuffling.
> >
> > All of the implementations that have come up, however, implemented the
> > naive formula:
> >
> > x =(*-b +/- sqrt(b^2-4ac))/(2a)
> >
> > The problem here is that if a and c are small, you're going to run
> > into accuracy problems. A better implementation is as follows, where
> > x_1 and x_2 are the roots:
> >
> > q = -1/2(b + sgn(b) * sqrt(b^2 - 4ac))
> > x_1 = q/a
> > x_2 = c/q
> >
> > This is from Numerical Recipes in C++, page 227.
> >
> > For fun, can anyone come up with a cleaner implementation of this?
> >
> > : discriminant ( c a b -- d )
> > sq -rot * 4 * - sqrt ; inline
> >
> > : q ( c a b -- q )
> > [ discriminant ] [ sgn ] [ ] tri
> > [ * ] dip + -0.5 * ; inline
> >
> > : roots ( c a q -- x1 x2 )
> > tuck [ / ] [ swap / ] 2bi* ; inline
> >
> > : quadratic ( c b a -- x1 x2 )
> > swap [ drop ] [ q ] 3bi roots ;
> >
> > For comparison, here is my original version:
> >
> > : monic ( c b a -- c' b' ) tuck [ / ] 2bi@ ;
> > : discriminant ( c b -- b d ) tuck sq 4 / swap - sqrt ;
> > : critical ( b d -- -b/2 d ) [ -2 / ] dip ;
> > : +- ( x y -- x+y x-y ) [ + ] [ - ] 2bi ;
> > : quadratic ( c b a -- alpha beta ) monic discriminant critical +- ;
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