Sidharth Malhotra wrote:
> I encountered a problem with floating point arithmetic that I'm afraid
> may be causing greater calculation errors in my program. The program
> I'm writing calculates numerical solutions for ordinary differential
> equations (http://sid.cwru.edu/perl/euler.pl). What's happening is
> that floating point storage is not rounding off properly and down the
> line
> 2.4 + 0.025 = 2.42499999999999 instead of 2.425. You can easily spot
> the error in this short script:
>
> my $num = 1;
> my $add = 0.025;
> while ($num < 4) {
> $num += $add;
> print $count++ . " $num\n";
> }
> The resulting error in my particular differential equation is 2/10^15
> which is fine exept the the error gets compounded over a few hundred
> iterations. Does anyone have any suggestions for how to improve upon
> this? I do understand that there are accuracy limitations with floating
> pt. nums.
Numerical Computations is a very complicated and ugly obsession :-(
I'm quite only a hacker ;-(
But often, It's useful to avoid long iterations on sum.
E.g. the upon script could be written as:
my $num = 1;
my $add = 0.025;
while ($num < 4) {
$num = $add * ($count+1);
print $count++, " $num\n";
}
Another way is to round while calculations
if you exactly know how many digits your intermediate result have.
E.g. in the above example it's clear that in every step
$num has always the form \d\.\d{0,3}.
So you can reduce the little calculation error by rounding:
my $num = 1;
my $add = 0.025;
while ($num < 4) {
$num += $add;
# I add 0.0005 to $num -> rounding up
$num = int ((1000 * $num) + 5) / 1000;
print $count++, " $num\n";
}
Well, to say to truth, I can't really help.
But your adress (http://sid.cwru.edu/perl/euler.pl) brings a
read time out as I tried.
Best Wishes,
Andrea
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