# Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde
# This file is part of Math-NumSeq.
#
# Math-NumSeq is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-NumSeq is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
package Math::NumSeq::Even;
use 5.004;
use strict;
use vars '$VERSION', '@ISA';
$VERSION = 71;
use Math::NumSeq;
@ISA = ('Math::NumSeq');
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('Even Integers');
use constant description => Math::NumSeq::__('The even integers 0, 2, 4, 6, 8, 10, etc.');
use constant i_start => 0;
use constant values_min => 0;
use constant characteristic_increasing => 1;
use constant characteristic_integer => 1;
# cf A007958 even with at least one odd digit
use constant oeis_anum => 'A005843'; # even 0,2,4
sub rewind {
my ($self) = @_;
$self->{'i'} = $self->i_start;
}
sub seek_to_i {
my ($self, $i) = @_;
$self->{'i'} = $i;
}
sub seek_to_value {
my ($self, $value) = @_;
$self->seek_to_i($self->value_to_i_ceil($value));
}
sub next {
my ($self) = @_;
my $i = $self->{'i'}++;
return ($i, 2*$i);
}
sub ith {
my ($self, $i) = @_;
return 2*$i;
}
sub pred {
my ($self, $value) = @_;
### Even pred(): $value
return ($value == int($value)
&& ($value % 2) == 0);
}
sub value_to_i {
my ($self, $value) = @_;
my $int = int($value);
if ($value == $int
&& ($int % 2) == 0) {
return $int/2;
}
return undef;
}
sub value_to_i_floor {
my ($self, $value) = @_;
if ($value < 0) {
my $i = int($value/2);
if (2*$i == $value) {
return $i;
} else {
return $i-1;
}
} else {
return int($value/2);
}
}
sub value_to_i_ceil {
my ($self, $value) = @_;
my $i = int($value/2);
if (2*$i < $value) {
return $i+1;
} else {
return $i;
}
}
sub value_to_i_estimate {
my ($self, $value) = @_;
return int($value/2);
}
1;
__END__
=for stopwords Ryde Math-NumSeq
=head1 NAME
Math::NumSeq::Even -- even integers
=head1 SYNOPSIS
use Math::NumSeq::Even;
my $seq = Math::NumSeq::Even->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
The even integers,
0, 2, 4, 6, 8, 10, ...
starting i=0
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::Even-E<gt>new ()>
Create and return a new sequence object.
=back
=head2 Iterating
=over
=item C<$seq-E<gt>seek_to_i($i)>
Move the current sequence position to C<$i>. The next call to C<next()>
will return C<$i> and corresponding value.
=item C<$seq-E<gt>seek_to_value($value)>
Move the current i so that C<next()> gives C<$value> on the next call, or if
C<$value> is an even integer then the next higher even.
=back
=head2 Random Access
=over
=item C<$value = $seq-E<gt>ith($i)>
Return C<2*$i>.
=item C<$bool = $seq-E<gt>pred($value)>
Return true if C<$value> is even.
=item C<$i = $seq-E<gt>value_to_i_ceil($value)>
=item C<$i = $seq-E<gt>value_to_i_floor($value)>
Return value/2 rounded up or down to the next integer.
=item C<$i = $seq-E<gt>value_to_i_estimate($value)>
Return an estimate of the i corresponding to C<$value>.
=back
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::Odd>,
L<Math::NumSeq::All>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-numseq/index.html>
=head1 LICENSE
Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde
Math-NumSeq is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
more details.
You should have received a copy of the GNU General Public License along with
Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
=cut