Author image brian d foy


Math::NoCarry - Perl extension for no carry arithmetic


        use Math::NoCarry;

        my $sum        = Math::NoCarry::add( 123, 456 );

        my $difference = Math::NoCarry::subtract( 123, 456 );

        my $product    = Math::NoCarry::multiply( 123, 456 );


No carry arithmetic doesn't allow you to carry digits to the next column. For example, if you add 8 and 4, you normally expect the answer to be 12, but that 1 digit is a carry. In no carry arithmetic you can't do that, so the sum of 8 and 4 is just 2. In effect, this is addition modulo 10 in each column. I discard all of the carry digits in this example:

        + 5678

For multiplication, the result of pair-wise multiplication of digits is the modulo 10 value of their normal, everyday multiplication.

      x 456
          8   6 x 3
         2    6 x 2
        6     6 x 1

         5    5 x 3
        0     5 x 2
       5      5 x 1

        2     4 x 3
       8      4 x 2
    + 4       4 x 1

Since multiplication and subtraction are actually types of additions, you can multiply and subtract like this as well.

No carry arithmetic is both associative and commutative.


This module does not export any functions.

multiply( A, B )

Returns the no carry product of A and B.

Return A if it is the only argument ( A x 1 );

add( A, B )

Returns the no carry sum of the positive numbers A and B.

Returns A if it is the only argument ( A + 0 )

Returns false if either number is negative.

subtract( A, B )

Returns the no carry difference of the postive numbers A and B.

Returns A if it is the only argument ( A - 0 )

Returns false if either number is negative.


* none reported yet :)


* this could be a full object package with overloaded +, *, and - operators

* it would be nice if i could give the functions more than two arguments.

* addition and subtraction don't do negative numbers.


This source is part of a SourceForge project which always has the latest sources in CVS, as well as all of the previous releases.

If, for some reason, I disappear from the world, one of the other members of the project can shepherd this module appropriately.


brian d foy, <>


Copyright (c) 2002-2007 brian d foy. All rights reserved.

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.