From:	"Tom St Denis" <tomstdenis AT yahoo DOT com>
Newsgroups:	comp.os.msdos.djgpp
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Subject:	Re: DJGPP reserves wrong int size
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Date:	Thu, 05 Jul 2001 00:47:17 GMT
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To:	djgpp AT delorie DOT com
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"Graaagh the Mighty" <invalid AT erehwon DOT invalid> wrote in message
news:3b4372cf DOT 92024930 AT news DOT primus DOT ca...
> On Wed, 04 Jul 2001 20:30:20 +0300, "Eli Zaretskii"
> <eliz AT is DOT elta DOT co DOT il> sat on a tribble, which squeaked:
>
> >In any decent course in numerical computation, the first lesson
> >teaches you that you cannot even solve a quadratic equation without
> >risking numerical pitfalls.
>
> Newton's method? That does division, iteratively. The quadratic
> formula? I doubt you'll have trouble with numerical instability except
> right on the threshold of zero.
>
> Now please stop spouting your "numerical wisdom" and give some real,
> usable information about what might cause what was observed, given
> that all I did was assign some numbers to some doubles/long doubles
> and perform a few arithmetic operations on them -- not even inside of
> a loop.

Actually Newtons method works well and gives the same results as a typical
libc implementation.

In one test I solved for cube roots via doubles and I got the exact same
results.

Also newtons method is quick.  Within 10 or so itterations the result is
essentially found.  You can get goot square roots for example very quickly.

Using 5 itterations of newtons method of the square root of 17 I get

4.1231067170

And from sqrt() I get

 4.1231056256

Where newtons method gets 0.0000010914 higher.  With 6 steps I get the same
#'s.  With about 15 steps I get the same results over a wide range of #'s

Tom

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