Math::Base - arithmetics with baseX integers (updated)

[shmem]

Another "Silly use for Perl" entry.

Anonymous Monk asked for a method for incrementing mixed letters and numbers recently, which particular need is satisfied with Math::Base36. Can we do better? I guess, yes.

use 5.10.0;
use Math::Base;

my $begin = Math::Base->new(36, 1009, 1); # base, number, is_encoded
my $end   = Math::Base->new(36, 1020, 1);
my $c     = Math::Base->new(36, 42);

say $c->encode($_) for $begin .. $end;

# 1009
# 100A
# 100B
# 100C
# ...
# 101X
# 101Y
# 101Z
# 1020

# also (with updated code below)
# my $x = Math::Base->new(36, 46664); # 1008 in base36
# say ++$x for 0..63; # output same as above

# Arithmetics with different encodings:

$p = Math::Base->new(8,777,1); # decimal 511
$z = Math::Base->new(36, 35);  # 'Z' as base36
say $z * $p;                   # 42735 (octal)
say $p * $z;                   # 'DST' (base36)

# Changing the string representation:

$s = Math::Base->new(16,18);
say $s;                        # 12
$s->rebase(18);
say $s;                        # 10
$s += 3;                       # 13
$s->rebase(2);
say $s;                        # 10101

# Get decimal value:

$xyz = Math::Base->new(64, 'XYZabc', 1);
say $xyz->num;                 # 36013230438

Far from complete, but fun enough yet. For me, that is... ;-)

<Reveal this spoiler or all spoilers in this node or all in this thread>

Update: Below is an updated version which handles negative numbers, implements missing operators and lets you define your own charset for baseX conversion, e.g. to calculate base3 with qw(a b c). Also, a method integer() is added which emulates use integer globally for all calculations, and some utility methods/functions.

<Reveal this spoiler>

Update: fixed some bugs

I'll eventually make it into a CPAN package proper.

[no_slogan]

This is a neat idea, but encode spins forever when $num is negative and returns an empty string when it's zero. You could do this:

    my $val = abs($num);
    do {
        push @ret, $chars[$val % $base];
        $val = int($val / $base);
    } while $val;
    push @ret, '-' if $num < 0;

But '-' is in the @chars array.

[shmem]

What I did is to mimic the behavior of sprintf and hex in encode(), i.e. roll over:

    $num = (~abs($num))+1 if $num < 0;

And the return line now reads:

       return join( '', reverse @ret) || 0;

I've updated the op with the new version. Thanks for your hints!

[no_slogan]

$num = int $num;
$num = (~abs($num))+1 if $num < 0;

You can get the same effect with $num |= 0; ...but... why? Why would you want two's complement behavior in other bases?

Truncating at $n bits is mathematically equivalent to:

$num %= 2 ** $n;

That's only meaningful for base-2. You can truncate at $n base-$b digits using this:

$num %= $b ** $n;

So -1 becomes 999999 in base-10 or 666666 in base-7. If you want, you can pick a big number of digits that still fits in a double-precision float like this:

$num %= $base ** int(36.73/log($base));

[shmem]

This is one of the reasons why I wrote Far from complete (besides missing pod, tests, you name it.)

The perl builtins suffer from negative integer flaws also. The format %x of sprintf expects a signed an unsigned integer, but nonetheless

say $f = sprintf "%x", -15;
say hex $f;
__END__
fffffffffffffff1
18446744073709551601

on a 64bit system. The object could get a sign flag set by the constructor which is honored by arithmetic operations, but the string representation would be ambiguous anyways if the string has a leading dash.

I'm not sure what to do about that. Perhaps limiting to unsigned integers is the way to go, and encode should croak if the number is negative; don't know yet.

update: unsigned, yes, that's the point; common typo. It is coerced into an unsigned. Thanks Anonymous Monk fo pointing out the glitch.

[no_slogan]

%x is clearly documented as taking an unsigned int in the page you link to.

[hdb]

Here is my favorite example:

use Math::Base;

my $one = Math::Base->new( 13, 6 );
my $two = Math::Base->new( 13, 9 );

print "$one times $two equals ", $one*$two, " base 13.\n";

[shmem]

Perfect for a mathematical challenge on facebook. As is 5 * 6 = 42
:-P