# Copyright 2010, 2011 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::ThueMorseEvil;
use 5.004;
use strict;
use List::Util 'max';
use Math::NumSeq;
use base 'Math::NumSeq';
use vars '$VERSION';
$VERSION = 38;
# FIXME: parameter for odd/even instead of sep series?
# ENHANCE-ME: maybe a radix parameter, modulo sum of digits
# bit count per example in perlfunc unpack()
# use constant name => Math::NumSeq::__('Thue-Morse Evil Numbers');
use constant description => Math::NumSeq::__('The Thue-Morse "evil" numbers, meaning numbers with an even number of 1s in their binary form (the opposite of the "odious"s).');
use constant oeis_anum => 'A001969'; # with even 1s
# df 'A026147'; # positions of 1s in evil
# cf A001285
# uncomment this to run the ### lines
#use Smart::Comments;
sub new {
my ($class, %options) = @_;
my $lo = $options{'lo'} || 0;
$lo = max ($lo, 0); # no negatives
# i initially the first $i < $lo satisfying pred(), but no further back
# than -1
my $i = $lo-1;
while ($i >= 0 && ! $class->pred($i)) {
$i--;
}
return bless { i => $i,
}, $class;
}
sub next {
my ($self) = @_;
my $i = $self->{'i'};
if (! ($i & 3)) {
### 0b...00 next same parity 0b...11 which is +3
return ($self->{'i'} += 3);
}
if (($i & 3) == 1) {
### 0b...01 next same parity 0b...10 which is +1
return ($self->{'i'} += 1);
}
if (($i & 6) == 2) {
### 0b...01. next same parity 0b...10. which is +2
return ($self->{'i'} += 2);
}
# search
until ($self->pred(++$i)) { }
return ($self->{'i'} = $i);
}
sub pred {
my ($self, $n) = @_;
return ! (1 & unpack('%32b*', pack('I', $n)));
}
1;
__END__