File Coverage

blib/lib/Math/NumSeq/SternDiatomic.pm

Criterion	Covered	Total	%
statement	67	68	98.5
branch	7	8	87.5
condition	1	3	33.3
subroutine	18	18	100.0
pod	6	6	100.0
total	99	103	96.1

# 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 .


# Edsgar Dijkstra
#    http://www.cs.utexas.edu/users/EWD/ewd05xx/EWD570.PDF
#    http://www.cs.utexas.edu/users/EWD/ewd05xx/EWD578.PDF

# Some Properties of a Function Studied by De Rham, Carlitz and Dijkstra and
# its Relation to the Eisenstein-Stern's Diatomic Sequence
# I. Urhiba, Math. Comm. 6 2001 181-198

# Lind stern summary
# An extension of Stern's diatomic sequence Duke Math J 36
# 1969 55-60


package Math::NumSeq::SternDiatomic;
use 5.004;
use strict;

use vars '$VERSION', '@ISA';
$VERSION = 71;
use Math::NumSeq;
@ISA = ('Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;

use Math::NumSeq::Fibonacci;
*_bit_split_hightolow = \&Math::NumSeq::Fibonacci::_bit_split_hightolow;

# uncomment this to run the ### lines
#use Smart::Comments;

# use constant name => Math::NumSeq::__('Stern Diatomic');
use constant description => Math::NumSeq::__('Stern\'s diatomic sequence.');
use constant default_i_start => 0;
use constant values_min => 0;
use constant characteristic_smaller => 1;
use constant characteristic_increasing => 0;
use constant characteristic_integer => 1;

#------------------------------------------------------------------------------
# cf A126606 - starting 0,2 gives 2*diatomic
#    A049455 - repeat 0..2^k
#    A049456 - extra 1 at end of each row
#    A174980 - type ([0,1],1), adding 1 extra at n=2^k
#    A049455,A049456 stern/farey tree
#    A070878 stern by rows
#    A070879 stern by rows
#    http://oeis.org/stern_brocot.html
#
# cf Michael Somos iteration in A002487
use constant oeis_anum => 'A002487';

#------------------------------------------------------------------------------

sub rewind {
  my ($self) = @_;
  $self->{'i'} = $self->i_start;
  $self->{'p'} = 0;
  $self->{'q'} = 1;
}
sub seek_to_i {
  my ($self, $i) = @_;
  $self->{'i'} = $i;
  ($self->{'p'},$self->{'q'}) = $self->ith_pair($i);
}

sub next {
  my ($self) = @_;
  my $p = $self->{'p'};
  my $q = $self->{'q'};
  $self->{'p'} = $q;
  $self->{'q'} = $p + $q - 2*($p % $q);
  return ($self->{'i'}++, $p);
}

sub ith {
  my ($self, $i) = @_;
  return ($self->ith_pair($i))[0];
}

# Return ($value[i], $value[i+1]).
sub ith_pair {
  my ($self, $i) = @_;
  ### SternDiatomic _ith_pair(): "$i"

  if ($i < 0) {
    if ($i < -1) {
      return (undef,undef);
    } else {
      return (undef,0);
    }
  }
  if (_is_infinite($i)) {  # don't loop forever if $value is +/-infinity
    return ($i,$i);
  }

  my $p = ($i * 0); # inherit bignum 0
  my $q = $p + 1;   # inherit bignum 1

  foreach my $bit (_bit_split_hightolow($i)) {
    if ($bit) {
      $p += $q;
    } else {
      $q += $p;
    }
    $i = int($i/2);
  }

  ### result: "$p, $q"
  return ($p,$q);
}

sub pred {
  my ($self, $value) = @_;
  ### SternDiatomic pred(): $value
  return ($value >= 0 && $value == int($value));
}

1;
__END__