# 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::All;
use 5.004;
use strict;
use vars '$VERSION', '@ISA';
$VERSION = 70;
use Math::NumSeq;
@ISA = ('Math::NumSeq');
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('All Integers');
use constant description => Math::NumSeq::__('All integers 0,1,2,3,etc.');
use constant default_i_start => 0;
use constant characteristic_increasing => 1;
use constant characteristic_integer => 1;
# experimental i_start to get natural numbers ... probably not very important
# OEIS-Catalogue: A000027 i_start=1
# OEIS-Catalogue: A001477
my %oeis_anum = (0 => 'A001477', # non-negatives, starting 0
1 => 'A000027'); # natural numbers starting 1
sub oeis_anum {
my ($self) = @_;
return $oeis_anum{$self->i_start};
}
sub values_min {
my ($self) = @_;
return $self->i_start;
}
sub rewind {
my ($self) = @_;
$self->seek_to_i($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, $i);
}
sub ith {
my ($self, $i) = @_;
return $i;
}
sub pred {
my ($self, $value) = @_;
return ($value == int($value));
}
sub value_to_i {
my ($self, $value) = @_;
if ($value == int($value)) {
return $value;
}
return undef;
}
sub value_to_i_floor {
my ($self, $value) = @_;
return _floor($value);
}
sub value_to_i_ceil {
my ($self, $value) = @_;
return _ceil($value);
}
sub value_to_i_estimate {
my ($self, $value) = @_;
return int($value);
}
#------------------------------------------------------------------------------
# generic
# _floor() trying to work with BigRat/BigFloat too.
#
# For reference, POSIX::floor() in perl 5.12.4 is a bit bizarre on UV=64bit
# and NV=53bit double. UV=2^64-1 rounds up to NV=2^64 which floor() then
# returns, so floor() in fact increases the value of what was an integer
# already.
#
sub _floor {
my ($x) = @_;
### _floor(): "$x", $x
my $int = int($x);
if ($x == $int) {
### is an integer ...
return $x;
}
$x -= $int;
### frac: "$x"
if ($x >= 0) {
### frac is non-negative ...
return $int;
} else {
### frac is negative ...
return $int-1;
}
}
# _ceil() trying to work with BigRat/BigFloat too.
#
sub _ceil {
my ($x) = @_;
### _ceil(): "$x", $x
my $int = int($x);
if ($x == $int) {
### is an integer ...
return $x;
}
$x -= $int;
### frac: "$x"
if ($x > 0) {
### frac is positive ...
return $int+1;
} else {
### frac is non-negative ...
return $int;
}
}
1;
__END__
=for stopwords Ryde Math-NumSeq NumSeq
=head1 NAME
Math::NumSeq::All -- all integers
=head1 SYNOPSIS
use Math::NumSeq::All;
my $seq = Math::NumSeq::All->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
The non-negative integers 0,1,2,3,4, etc.
As a module this is trivial, but it helps put all integers into things using
NumSeq.
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::All-E<gt>new ()>
Create and return a new sequence object.
=item C<$i = $seq-E<gt>seek_to_value($value)>
Move the current i so that C<next()> will give C<$value> on the next call,
or ceil($value) if C<$value> is an integer.
=back
=head2 Random Access
=over
=item C<$value = $seq-E<gt>ith($i)>
Return C<$i>.
=item C<$bool = $seq-E<gt>pred($value)>
Return true if C<$value> is an integer.
=item C<$i = $seq-E<gt>value_to_i_ceil($value)>
=item C<$i = $seq-E<gt>value_to_i_floor($value)>
=item C<$i = $seq-E<gt>value_to_i_estimate($value)>
Return C<$value> rounded to the next higher or lower integer.
=back
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::Even>,
L<Math::NumSeq::Odd>
=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