Adding without Addition

Wasn't sure if this belongs here, or in Obfuscations.

Having once run:

use strict;
use warnings;
use Storable;

my (%table);
foreach my $i (0..9) {
  foreach my $j ($i..9) {
    $table{$i}{$j} = $table{$j}{$i} = $i + $j
  }
}

store \%table, 'addition_table';
[download]

I present to you: addition!

use strict;
use warnings;
use Storable;

my %table = %{retrieve('addition_table')};
my @problem = @ARGV;
my (%matrix);
foreach my $number (@problem) {
  my $log = 0;
  push @{$matrix{$log++}}, $_ for reverse (split //, $number);
}

my $col = 0;
while (exists $matrix{$col}) {
  my @column = @{$matrix{$col}};
  my $first = shift @column;
  while(scalar @column > 0) {
    my $second = shift @column;
    $first = $table{$first}{$second};
    if (length($first) > 1) {
      $first = substr($first,-1,1);
      push @{$matrix{$col + 1}}, 1;
    }
  }
  $matrix{$col++} = $first;
}  
printf "%s",$matrix{$col - $_} for (1..$col);
print "\n";
[download]

H:\perl>perl adder.pl 1
1

H:\perl>perl adder.pl 21 14 99 6 12
152

H:\perl>perl adder.pl 999999999999999999999999999999999999999999 1
1000000000000000000000000000000000000000000
[download]

Addition tables for other number systems are left as an exercise for the (extremely bored) reader. Vaguely apropos of Multiply Hex values. I started to write a program to do multiplication and realized I needed to figure out how to add first.

But God demonstrates His own love toward us, in that while we were yet sinners, Christ died for us. Romans 5:8 (NASB)

Comment on Adding without Addition Select or Download Code

Replies are listed 'Best First'.

Re: Adding without Addition
by pryrt (Abbot) on Feb 15, 2017 at 18:21 UTC

I had started down a similar path inspired by the same node, but focusing on hex -- and stopping abruptly when I got busy on more pressing ($work-related) issues :-). I built the times and addition tables, and had started on my addition subroutine... but this is as far as I got. Posted for entertainment value only. :-)

package HexMath;
# add or multiply hexadecimal
my (%times, %sums);

BEGIN {    # create tables
    for my $x ( 0 .. 15 ) {
        my $hx = sprintf '%x', $x;
        for my $y ( 0 .. 15 ) {
            my $hy = sprintf '%x', $y;
            next if exists $times{$hx}{$hy};
            $times{$hx}{$hy} = $times{$hy}{$hx} = sprintf '%x', $x*$y;
            $sums{$hx}{$hy} = $sums{$hy}{$hx} = sprintf '%x', $x+$y;
        }
    }

    printf "\n%4s: ", 'x ';
    printf "%4x ", $_ for 0..15;
    for my $x ( 0 .. 15 ) {
        my $hx = sprintf '%x', $x;

        printf "\n%4.4s: ", $hx;

        for my $y ( 0 .. 15 ) {
            my $hy = sprintf '%x', $y;
            printf '%4.4s ', $times{$hx}{$hy};
        }
    }
    print "\n";

    printf "\n%4s: ", '+ ';
    printf "%4x ", $_ for 0..15;
    for my $x ( 0 .. 15 ) {
        my $hx = sprintf '%x', $x;

        printf "\n%4.4s: ", $hx;

        for my $y ( 0 .. 15 ) {
            my $hy = sprintf '%x', $y;
            printf '%4.4s ', $sums{$hx}{$hy};
        }
    }
    print "\n";

}



sub add {
    my $answer = shift;
    while( defined(my $addend  = shift)) {
        substr($answer,0,0,'0'x(length($addend)-length($answer))) if l
+ength($answer) < length($addend);
        substr($addend,0,0,'0'x(length($answer)-length($addend))) if l
+ength($addend) < length($answer);
        print "$answer + $addend = ";

        my $c = 0;
        for my $hexit ( 1 .. length($addend) ) {
            my $x = lc substr($answer, -$hexit, 1);
            my $y = lc substr($addend, -$hexit, 1);
            my $s = $sums{$x}{$y};
            #my $u =
            printf "\n\t#%d: %s + %s = %s\n", $hexit, $x, $y, $s;
        }

        print "$answer\n"
    }
}

package main;
HexMath::add('a','b','cqcq','d');
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