Long multiplication

Long multiplication
You are encouraged to solve this task according to the task description, using any language you may know.

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

Haskell

<lang haskell>digits :: Integer -> [Integer] digits = map (fromIntegral.digitToInt) . show

lZZ = inits $ repeat 0

table f = map . flip (map . f)

polymul = ((map sum . transpose . zipWith (++) lZZ) .) . table (*)

longmult = (foldl1 ((+) . (10 *)) .) . (. digits) . polymul . digits</lang> Output: <lang haskell>*Main> (2^64) `longmult` (2^64) 340282366920938463463374607431768211456</lang>

J

   (([+10x*])/@|.@(,.&.":@[+//.@(*/),.&.":@]))/ ,~2x^64
340282366920938463463374607431768211456

• digits: ,.&.": y

   ,.&.": 123
1 2 3

• polynomial multiplication: x (+//.@(*/)) y ref. [1]

   1 2 3 (+//.@(*/)) 1 2 3
1 4 10 12 9

• building the decimal result: ([+10x*])/|. y

   ([+10x*])/|. 1 4 10 12 9
15129

or using the primitive dyad #. instead of ([+10x*])/@|.

   (10x #.,.&.":@[+//.@(*/),.&.":@])/ ,~2x^64
340282366920938463463374607431768211456

Perl

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

1. 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>

Python

Works with: Python version 3.0

Translation of: Perl

<lang python>#!/usr/bin/env python

def add_with_carry(result, addend, addendpos):

   while True:
       while len(result) < addendpos + 1:
           result.append(0)
       addend_result = str(int(addend) + int(result[addendpos]))
       addend_digits = list(addend_result)
       result[addendpos] = addend_digits.pop()

       if not addend_digits:
           break
       addend = addend_digits.pop()
       addendpos += 1

def longhand_multiplication(multiplicand, multiplier):

   result = []
   for multiplicand_offset, multiplicand_digit in enumerate(reversed(multiplicand)):
       for multiplier_offset, multiplier_digit in enumerate(reversed(multiplier), start=multiplicand_offset):
           multiplication_result = str(int(multiplicand_digit) * int(multiplier_digit))

           for addend_offset, result_digit_addend in enumerate(reversed(multiplication_result), start=multiplier_offset):
               add_with_carry(result, result_digit_addend, addend_offset)

   result.reverse()

   return .join(result)

if __name__ == "__main__":

   sixtyfour = "18446744073709551616"

   onetwentyeight = longhand_multiplication(sixtyfour, sixtyfour)
   print(onetwentyeight)</lang>

Shorter version:

Translation of: Haskell

<lang python>#!/usr/bin/env python

def digits(x):

   return [int(c) for c in str(x)]

def mult_table(xs, ys):

   return [[x * y for x in xs] for y in ys]

def polymul(xs, ys):

   return map(lambda *vs: sum(filter(None, vs)),
              *[[0] * i + zs for i, zs in enumerate(mult_table(xs, ys))])

def longmult(x, y):

   result = 0
   for v in polymul(digits(x), digits(y)):
       result = result * 10 + v
   return result

if __name__ == "__main__":

   print longmult(2**64, 2**64)</lang>