Long multiplication

In this task, explicitly implement long multiplication. This is one possible approach to arbitrary-precision integer algebra.

For output, display the result of 2^64 * 2^64. The decimal representation of 2^64 is:

18446744073709551616

The output of 2^64 * 2^64 is 2^128, and that is:

340282366920938463463374607431768211456

Perl

<lang perl>#!/usr/bin/perl -w use strict;

This should probably be done in a loop rather than be recursive.

sub add_with_carry {

 my $resultref = shift;
 my $addend = shift;
 my $addendpos = shift;

 push @$resultref, (0) while (scalar @$resultref < $addendpos + 1);
 my $addend_result = $addend + $resultref->[$addendpos];
 my @addend_digits = reverse split //, $addend_result;
 $resultref->[$addendpos] = shift @addend_digits;

 my $carry_digit = shift @addend_digits;
 &add_with_carry($resultref, $carry_digit, $addendpos + 1)
   if( defined $carry_digit )

}

sub longhand_multiplication {

 my @multiplicand = reverse split //, shift;
 my @multiplier = reverse split //, shift;
 my @result = ();
 my $multiplicand_offset = 0;
 foreach my $multiplicand_digit (@multiplicand)
 {
   my $multiplier_offset = $multiplicand_offset;
   foreach my $multiplier_digit (@multiplier)
   {
     my $multiplication_result = $multiplicand_digit * $multiplier_digit;
     my @result_digit_addend_list = reverse split //, $multiplication_result;

     my $addend_offset = $multiplier_offset;
     foreach my $result_digit_addend (@result_digit_addend_list)
     {
       &add_with_carry(\@result, $result_digit_addend, $addend_offset++)
     }

     ++$multiplier_offset;
   }

   ++$multiplicand_offset;
 }

 @result = reverse @result;

 return join , @result;

}

my $sixtyfour = "18446744073709551616";

my $onetwentyeight = &longhand_multiplication($sixtyfour, $sixtyfour); print "$onetwentyeight\n";</lang>