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Postings from October 2003
On Tue, Oct 07, 2003 at 06:33:33PM -0400, Ed Allen Smith <easmith@beatrice.rutgers.edu> wrote:
>
> I'll change my earlier suggestion of how to handle this in Math::BigInt. I
> suggest changing the current code in _root from:
>
> # fit's into one Perl scalar, so result can be computed directly
> $x->[0] = int( $x->[0] ** (1 / $n->[0]) );
>
> to:
>
> if ($x->[0] == 0) {
> return 0;
> }
> # fits into one Perl scalar, so result can be computed directly
> my $temp = $x->[0] ** (1 / $n->[0]);
> my $a = int($temp);
> my $b = int($temp + (($temp > 0) ? 0.5 : -0.5));
> if ($a == $b) {
> $x->[0] = $a;
> } elsif (abs(($a**$n->[0]) - $x->[0]) > abs(($b**$n->[0]) - $x->[0])) {
> $x->[0] = $b;
> } else {
> $x->[0] = $a;
> }
> return $x;
>
> In other words, if adding 0.5 (equivalently, subtracting, if the result is
> negative) will give a more arithmetically correct result after truncating, do
> it; otherwise, don't. (It's likely that the same sort of thing would be
> helpful for the _sqrt function.)
That's basically just a form of rounding, only not based on just
rounding the result. It looks more to me as if the goal here is to
come up with the greatest result $a such that $a**$n->[0] <= $x->[0]
(not sure if that "greatest" or "<=" is meant to apply to absolute
values or not).
But your general method certainly works for that.
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