Re: Classic game LUNAR and G=1E-03

[Nama <forums6000@mac.com>]

On May 6, 12:45 am, -scooter- <scooter....@gmail.com> wrote:
> > Ok...that makes sense.
>
> > So one last question before I can say this port is finished:
>
> > According to the document here (http://www.atariarchives.org/
> > basicgames/showpage.php?page=106):
> > (Q-Q*Q/2-Q^3/3-Q^4/4-Q^5/5)
> > can be replaced by the notation
> > -Q*(1+Q*(1/2+Q*(1/3+Q*(1/4+Q/5))))
>
> > If that is the case, then what would be the replacement for:
> > (Q/2+Q^2/6+Q^3/12+Q^4/20+Q^5/30)
>
> Look up "Horner's Method" -- the quick and dirty explanation is that
> Horner's is a linear time evaluation method for polynomials. It allows
> you to avoid computing the exponents. However, there is a bug in that
> expression -- it shouldn't start with -Q.
>
> Q*(1-Q*(1/2-Q*(1/3-Q*(1/4-Q/5))))
> = Q-Q^2*(1/2-Q*(1/3-Q*(1/4-Q/5)))
> = Q-Q^2/2-Q^3*(1/3-Q*(1/4-Q/5))
> = Q-Q^2/2-Q^3/3-Q^4*(1/4-Q/5)
> = Q-Q^2/2-Q^3/3-Q^4/4-Q^5/5
>
> BTW: Horner's method still shows up frequently on the Computer Science
> Graduate Record Exam here in the US. And it's a favorite interview
> torture question of mine, along with the XOR hack.
>
> -scooter

So I should replace:

-Q*(1+Q*(1/2+Q*(1/3+Q*(1/4+Q/5))))

with

Q*(1-Q*(1/2-Q*(1/3-Q*(1/4-Q/5))))

?