NAME

Math::NoCarry - Perl extension for no-carry arithmetic

SYNOPSIS

        use Math::NoCarry qw(:all);
        my $sum        = add( 123, 456 );
        my $difference = subtract( 123, 456 );
        my $product    = multiply( 123, 456 );

DESCRIPTION

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:

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

        123
      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
    -------
      43878

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.

Functions

As of version 1.11, all of these functions are exportable on demand, or with the tag ":all" to get them all at once.

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 positive numbers A and B.

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

Returns false if either number is negative.

BUGS

•: none reported yet :)

TO DO

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.

SOURCE AVAILABILITY

This source is in GitHub:

        https://github.com/briandfoy/math-nocarry

AUTHOR

brian d foy, "<bdfoy@cpan.org>"

COPYRIGHT AND LICENSE

This program is free software; you can redistribute it and/or modify it under the terms of the Artistic License 2.0.

2021-01-16

perl v5.32.0