# Copyright 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::CullenNumbers;
use 5.004;
use strict;
use vars '$VERSION', '@ISA';
$VERSION = 71;
use Math::NumSeq;
@ISA = ('Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('Cullen Numbers');
use constant description => Math::NumSeq::__('Cullen numbers n*2^n+1.');
use constant i_start => 0;
use constant values_min => 1;
use constant characteristic_increasing => 1;
use constant characteristic_integer => 1;
use constant oeis_anum => 'A002064';
# pow*i+1
my $uv_i_limit = do {
my $max = ~0;
my $limit = 1;
for (my $i = 1; $i < 1000; $i++) {
if ($i <= ($max-1) >> $i) {
$limit = $i;
} else {
last;
}
}
### max : $max
### cullen: (1<<$limit)*$limit+1
### assert: $limit*(1<<$limit)+1 <= $max
$limit
};
### $uv_i_limit
# or maybe ...
# (i+1)*2^(i+1) + 1
# = 2*(i+1)*2^i + 1
# = (2i+2)*2^i + 1
# = 2i*2^i + 2*2^i + 1
# = 2(i*2^i + 1) -2 + 2*2^i + 1
# = 2(i*2^i + 1) + 2*2^i - 1
sub rewind {
my ($self) = @_;
my $i = $self->{'i'} = $self->i_start;
$self->{'power'} = 2 ** $i;
}
sub _UNTESTED__seek_to_i {
my ($self, $i) = @_;
$self->{'i'} = $i;
if ($i >= $uv_i_limit) {
$i = Math::NumSeq::_to_bigint($i);
}
$self->{'power'} = 2 ** $i;
}
sub _UNTESTED__seek_to_value {
my ($self, $value) = @_;
$self->seek_to_i($self->value_to_i_ceil($value));
}
sub next {
my ($self) = @_;
my $i = $self->{'i'}++;
if ($i == $uv_i_limit) {
$self->{'power'} = Math::NumSeq::_to_bigint($self->{'power'});
}
my $value = $self->{'power'}*$i + 1;
$self->{'power'} *= 2;
return ($i, $value);
}
sub ith {
my ($self, $i) = @_;
return $i * 2**$i + 1;
}
sub pred {
my ($self, $value) = @_;
### CullenNumbers pred(): $value
{
my $int = int($value);
if ($value != $int) { return 0; }
$value = $int;
}
unless ($value >= 1
&& ($value % 2) == 1) {
return 0;
}
$value -= 1; # now seeking $value == $exp * 2**$exp
if (_is_infinite($value)) {
return 0;
}
my $exp = 0;
for (;;) {
if ($value <= $exp || $value % 2) {
return ($value == $exp);
}
$value = int($value/2);
$exp++;
}
}
use Math::NumSeq::WoodallNumbers;
*value_to_i_estimate = \&Math::NumSeq::WoodallNumbers::value_to_i_estimate;
1;
__END__
=for stopwords Ryde Cullen Math-NumSeq ie
=head1 NAME
Math::NumSeq::CullenNumbers -- Cullen numbers i*2^i+1
=head1 SYNOPSIS
use Math::NumSeq::CullenNumbers;
my $seq = Math::NumSeq::CullenNumbers->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
The Cullen numbers i*2^i+1 starting from i=0,
1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, ...
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::CullenNumbers-E<gt>new ()>
Create and return a new sequence object.
=back
=head2 Random Access
=over
=item C<$value = $seq-E<gt>ith($i)>
Return C<$i * 2**$i + 1>.
=item C<$bool = $seq-E<gt>pred($value)>
Return true if C<$value> is a Cullen number, ie. is equal to i*2^i+1 for
some i.
=item C<$i = $seq-E<gt>value_to_i_estimate($value)>
Return an estimate of the i corresponding to C<$value>.
=back
=head1 FORMULAS
=head2 Value to i Estimate
See L<Math::NumSeq::WoodallNumbers/Value to i Estimate>.
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::WoodallNumbers>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-numseq/index.html>
=head1 LICENSE
Copyright 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