This file is indexed.

/usr/share/perl5/Math/NoCarry.pm is in libmath-nocarry-perl 1.111-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
package Math::NoCarry;
use strict;

use warnings;
no warnings;

use Exporter qw(import);

use vars qw($VERSION @EXPORT_OK %EXPORT_TAGS);

@EXPORT_OK = qw(add subtract multiply);
%EXPORT_TAGS =  ( all => [ @EXPORT_OK ] );

$VERSION = '1.111';

=encoding utf8

=head1 NAME

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

=head1 SYNOPSIS

	use Math::NoCarry qw(:all);

	my $sum        = add( 123, 456 );

	my $difference = subtract( 123, 456 );

	my $product    = multiply( 123, 456 );

=head1 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:

	  1234
	+ 5678
	------
	  6802

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.

=head2 Functions

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

=over 4

=item multiply( A, B )

Returns the no carry product of A and B.

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

=cut

sub multiply {
	return $_[0] if $#_ < 1;

	@_ = map { $_ += 0 } @_;

	my $sign = ($_[0] > 0 and $_[1] < 0 ) ||
		($_[1] > 0 and $_[0] < 0 );

	my @p0 = reverse split //, abs $_[0];
	my @p1 = reverse split //, abs $_[1];

	my @m;

	foreach my $i ( 0 .. $#p0 ) {
		foreach my $j ( 0 .. $#p1 ) {
			push @m, ( ( $p1[$j] * $p0[$i] ) % 10 ) * ( 10**($i+$j) );
			}
		}

	while( @m > 1 ) {
		unshift @m, Math::NoCarry::add( shift @m, shift @m );
		}

	$m[0] *= -1 if $sign;

	return $m[0];
	}

=item 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.

=cut

sub add {
	return $_[0] if $#_ < 1;

	@_ = map { local $^W; $_ += 0 } @_;

	return unless( $_[0] >= 0 and $_[1] >= 0 );

	my @addends = map scalar reverse, @_;

	my $string = '';

	my $max = length $addends[0];
	$max = length $addends[1] if length $addends[1] > $max;

	for( my $i = 0; $i < $max ; $i++ ) {
		my @digits = map { local $^W = 0; substr( $_, $i, 1) or 0 } @addends;

		my $sum = ( $digits[0] + $digits[1] ) % 10;

		$string .= $sum;
		}

	$string =~ s/0*$//;

	$string = scalar reverse $string;

	return $string;
	}

=item 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.

=cut

sub subtract {
	return $_[0] if $#_ < 1;

	return unless( $_[0] >= 0 and $_[1] >= 0);

	my @addends = map scalar reverse, @_;

	my $string = '';

	my $max = length $addends[0];
	$max = length $addends[1] if length $addends[1] > $max;

	for( my $i = 0; $i < $max ; $i++ ) {
		my @digits = map { substr $_, $i, 1 } @addends;

		$digits[0] += 10 if $digits[0] < $digits[1];

		my $sum = ( $digits[0] - $digits[1] ) % 10;

		$string .= $sum;
		}

	return scalar reverse $string;
	}

1;

__END__

=back

=head1 BUGS

* none reported yet :)

=head1 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.

=head1 SOURCE AVAILABILITY

This source is in GitHub:

	https://github.com/briandfoy/Math-NoCarry

=head1 AUTHOR

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

=head1 COPYRIGHT AND LICENSE

Copyright © 2002-2016, brian d foy <bdfoy@cpan.org>. All rights reserved.

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

=cut