2016-10-02 16:48 GMT+02:00 David T. Lewis <lewis at mail.msen.com>:

> On Sat, Oct 01, 2016 at 08:19:27PM +0000, commits at source.squeak.org wrote:
> > Nicolas Cellier uploaded a new version of Kernel to project The Trunk:
> > http://source.squeak.org/trunk/Kernel-nice.1043.mcz
> >
> > ==================== Summary ====================
> >
> > Name: Kernel-nice.1043
> > Author: nice
> > Time: 1 October 2016, 10:19:12.37443 pm
> > UUID: d29f9c07-edc8-4add-9b99-e889fd2be32a
> > Ancestors: Kernel-nice.1042
> >
> > Fix (10 raisedTo: 600) nthRoot: 300.
> > It did incorrectly return 126.0 instead of 100.
> >
>
> Can you say anything about the underlying cause of this problem? I saw it
> in my 64-bit image, but not in my 32-bit image. The Kernel-nice.1042 update
> resolved the problem in my 64-bit image, but I find that when I revert
> to Kernel-tfel.1040, the problem does not come back. Strange...
>
> Thanks,
> Dave
>
> Hi Dave,
I don't see why there would be any difference between 32 and 64 bits image.
The problem lies in the Newton-Raphson algorithm:

xn+1 = xn - (f(xn)-y)/(f'(xn))

for f(x) = x^p, the convergence is very slow when p is high because
derivative is p*x^(p-1).
But we did store the integer part of decrement:

    delta := (guess * guessToTheNthMinusOne - self) //
(guessToTheNthMinusOne * aPositiveInteger).

Initial guess is 128, delta=2, then 126 delta<1, so the initial algorithm
was stuck.

So I truncated xn+1 instead of truncating the delta and iterated until
xn+1=xn.

But the correction above was wrong, because we can have guess and nextGuess
from each side of nth-root, and never reach an integer fix point, but
rather x(n+2)=x(n+1) - 1 and x(n+1) = x(n) + 1.
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