# Copyright 2010, 2011, 2012 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::ThueMorse;
use 5.004;
use strict;
use List::Util 'max';
use Math::NumSeq;
use base 'Math::NumSeq';
use vars '$VERSION';
$VERSION = 38;
# ENHANCE-ME: maybe a radix parameter, modulo sum of digits
# bit count per example in perlfunc unpack()
use constant description => Math::NumSeq::__('Sum of the digits in the given radix, modulo that radix. Eg. for binary this is the bitwise parity.');
use Math::NumSeq::Base::Digits
'parameter_info_array'; # radix parameter
# use constant parameter_info_array => [{ name => 'parity',
# display => Math::NumSeq::__('Parity'),
# type => 'enum',
# choices => ['odd','even'],
# choices_display => [__('Odd'),__('Even')],
# description => Math::NumSeq::__('The parity odd or even to show for the sequence.'),
# }];
# use constant oeis_anum => 'A001969'; # with even 1s
# df 'A026147'; # positions of 1s in evil
# cf A001285
my @oeis_anum = (undef,
undef,
'A010060', # 2 binary
'A053838', # 3 ternary
'A053839', # 4
'A053840', # 5
'A053841', # 6
'A053842', # 7
'A053843', # 8
'A053844', # 9
);
sub oeis_anum {
my ($self) = @_;
return $oeis_anum[$self->{'radix'}];
}
# 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
my $odd = 1;
if (defined $options{'thue_morse_odd'}) {
$odd = $options{'thue_morse_odd'};
}
if ($options{'parity'} && $options{'parity'} eq 'even') {
$odd = 0;
}
my $self = bless { odd => $odd }, $class;
# i initially the first $i < $lo satisfying pred(), but no further back
# than -1
my $i = $lo-1;
while ($i >= 0 && ! $self->pred($i)) {
$i--;
}
$self->{'i'} = $i;
return $self;
}
sub next {
my ($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 $self->{'odd'} ^ !(1 & unpack('%32b*', pack('I', $n)));
}
1;
__END__