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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; use overload ( '""' => \&encode, '0+' => \&num, '-' => \&minus, '+' => \&add, '*' => \&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],$result]; } sub add { my ($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'

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