Factorials of rational numbers up to 999.9

Microcebus has asked for the wisdom of the Perl Monks concerning the following question:

Dear wise Monks,

I found that useful script to calculate factorials of rational numbers:

# Pragmas.
use strict;

# Modules.
use bignum;
use Math::Complex;


# Global variables.
use vars qw($g $lanczos_coef);

$g = 7;
$lanczos_coef = [
        0.99999999999980993,
        676.5203681218851,
        -1259.1392167224028,
        771.32342877765313,
        -176.61502916214059,
        12.507343278686905,
        -0.13857109526572012,
        9.9843695780195716e-6,
        1.5056327351493116e-7
];

sub gamma_lanczos {
        my $z = shift;
        $z = Math::Complex->make($z);
        if (Re($z) < 0.5) {
                return pi / (sin(pi * $z) * gamma(1 - $z));
        } else {
                $z -= 1;
                my $x = $lanczos_coef->[0];
                foreach my $i (1 .. $g + 2) {
                        $x += $lanczos_coef->[$i] / ($z + $i);
                }
                my $t = $z + $g + 0.5;
                return sqrt(2 * pi) * $t ** ($z + 0.5) * exp(-$t) * $x
+;
        }
}


print gamma_lanczos(25.78), "\n";
system("pause");
[download]

But using it together with the bignum module returns the error message: Can't locate object method "_cartesian" via package "Math::BigInt". The Math::BigInt module is up to date. All I want to do is calculating factorials of rational numbers up to 999.9. Can someone help?

Comment on Factorials of rational numbers up to 999.9 Download Code

Replies are listed 'Best First'.
Re: Factorials of rational numbers up to 999.9 by Corion (Patriarch) on May 16, 2011 at 08:08 UTC
You are mixing Math::Compex and bignum. I'm not really sure that that's well-supported. Have you looked at removing the use of one or the other? I would assume that using only Math::Complex should be sufficient. A call to `->_cartesian()` is issued from within Math::Complex, so my guess is that somewhere somehow, methods from Math::Complex are issued against Math::BigInt objects that may or may not come from bignum. This may be a bug in Math::Complex, but I don't know.	[reply] [d/l]
Re^2: Factorials of rational numbers up to 999.9 by Microcebus (Beadle) on May 16, 2011 at 08:17 UTC
without using bignum the script works fine, but the factorials become #INF at 143!	[reply]
Re^3: Factorials of rational numbers up to 999.9 by Corion (Patriarch) on May 16, 2011 at 08:21 UTC
Most likely this is because not all elements in your calculations are Math::Complex objects, especially the constants. I would try to convert all elements to Math::Complex objects, or remove all Math::Complex calculations in favor of Math::BigInt. I'm not sure what part Math::Complex plays in your calculations. Maybe you can eliminate Math::Complex in favor of number pairs, `(Math::BigInt, Math::BigInt)`, to denote the real and imaginary parts.	[reply] [d/l]
Re: Factorials of rational numbers up to 999.9 by anonymized user 468275 (Curate) on May 16, 2011 at 12:09 UTC
On AIX, Perl v5.8.2, the message is clearer: Math::Complex::make: Cannot take real part of Math::BigFloat. And as I expected, it goes away, producing 7.61401993629603e+24, when the use bignum is removed. Math::Complex has no idea that you have invoked bignum and has incompatible methods for this type of data. Some obvious choices are: 1) override and rewrite all the required Complex methods to be bignum-aware (check if bignum is loaded in a new "new" method) or 2) settle for no bignum Update: or rewrite the gamma function from scratch using bignum, for reference: http://mathworld.wolfram.com/GammaFunction.html One world, one people	[reply]