Problems? Is your data what you think it is? PerlMonks

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

by shmem (Chancellor)
 on Aug 22, 2017 at 12:19 UTC ( #1197795=CUFP: print w/replies, xml ) Need Help??

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... ;-)

```package Math::Base;
use strict; use warnings;
'""' => \&encode,
'0+' => \&num,
'-'  => \&minus,
'*'  => \&mul,
'/'  => \&div,
);

my %hash;
my @chars     = (0..9,'A'..'Z','a'..'z',map{chr\$_}32..47,58..64,91..96
+);
@hash{@chars} = 0..\$#chars;

sub new {
my (\$class, \$base, \$value, \$encoded) = @_;
my \$self = bless [\$base, \$value], \$class;
\$self->decode if \$encoded;
\$self;
}

sub rebase { \$_[0]->[0] = \$_[1] }

sub num { shift->[1] }
sub minus {
my (\$self, \$other, \$swap) = @_;
my \$result = \$self->[1] - \$other;
\$result = -\$result if \$swap;
ref \$result ? \$result : bless [\$self->[0],\$result];
}
my (\$self, \$other, \$swap) = @_;
my \$result = \$self->[1] + \$other;
ref \$result ? \$result : bless [\$self->[0],\$result];
}
sub mul {
my (\$self, \$other, \$swap) = @_;
my \$result = \$self->[1] * \$other;
ref \$result ? \$result : bless [\$self->[0],\$result];
}
sub div {
my (\$self, \$other, \$swap) = @_;
my \$result = \$swap ? \$other / \$self->[1] : \$self->[1] / \$other;
int(ref \$result ? \$result : bless [\$self->[0],\$result]);
}

sub encode {
my \$self = shift;
my (\$base,\$num) = @\$self;
\$num = shift if \$_[0];
my (\$rem,@ret);
while (\$num) {
push @ret, \$chars[(\$rem = \$num % \$base)];
\$num -= \$rem;
\$num /= \$base;
}
return join '', reverse @ret;
}

sub decode {
my \$self = shift;
my (\$base, \$str) = @\$self;
\$str = shift if \$_[0];
my \$num = 0;
\$num = \$num * \$base + \$hash{\$_} for \$str =~ /./g;
\$self->[1] = \$num;
}
1;
__END__

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.

Update: fixed some bugs

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

perl -le'print map{pack c,(\$-++?1:13)+ord}split//,ESEL'

Replies are listed 'Best First'.
Re: Math::Base - arithmetics with baseX integers
by no_slogan (Deacon) on Aug 22, 2017 at 14:32 UTC
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.

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!

perl -le'print map{pack c,(\$-++?1:13)+ord}split//,ESEL'
\$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));

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.

perl -le'print map{pack c,(\$-++?1:13)+ord}split//,ESEL'
%x is clearly documented as taking an unsigned int in the page you link to.
Re: Math::Base - arithmetics with baseX integers
by hdb (Monsignor) on Aug 22, 2017 at 12:54 UTC

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";

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

perl -le'print map{pack c,(\$-++?1:13)+ord}split//,ESEL'

Create A New User
Node Status?
node history
Node Type: CUFP [id://1197795]
Front-paged by Arunbear
help
Chatterbox?
and all is quiet...

How do I use this? | Other CB clients
Other Users?
Others studying the Monastery: (8)
As of 2018-07-16 20:33 GMT
Sections?
Information?
Find Nodes?
Leftovers?
Voting Booth?
It has been suggested to rename Perl 6 in order to boost its marketing potential. Which name would you prefer?

Results (349 votes). Check out past polls.

Notices?