File Coverage

blib/lib/Math/NumSeq/SqrtContinuedPeriod.pm

Criterion	Covered	Total	%
statement	51	53	96.2
branch	6	8	75.0
condition			n/a
subroutine	13	13	100.0
pod	1	1	100.0
total	71	75	94.6

# 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 .

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

use vars '$VERSION', '@ISA';
$VERSION = 72;

use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
        'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;

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


# use constant name => Math::NumSeq::__('Sqrt Continued Fraction Period');
use constant description => Math::NumSeq::__('Period of the continued fraction expansion of sqrt(i), or 0 for perfect squares (where the expansion is finite)');
use constant characteristic_count => 1;
use constant characteristic_smaller => 1;
use constant characteristic_increasing => 0;
use constant default_i_start => 1;
use constant values_min => 0;

# cf A097853 contfrac sqrt(n) period, or 1 if square
#    A054269 contfrac sqrt(prime(i)) period
#
use constant oeis_anum => 'A003285';  # sqrt period, or 0 if square

sub ith {
  my ($self, $i) = @_;
  ### SqrtContinuedPeriod ith(): $i

  if (_is_infinite($i)) {
    return $i;
  }
  if ($i <= 0) {
    return 0;
  }

  # initial a[1] = floor(sqrt(i)) = $root
  # then root + 1/x = sqrt(i)
  #      1/x = sqrt(i)-root
  #      x = 1/(sqrt(i)-root)
  #      x = (sqrt(i)+root)/(i-root*root)
  # so P = root
  #    Q = i - root*root
  #
  my $p = my $root = int(sqrt($i));
  my $q = $i - $root*$root;
  if ($q <= 0) {
    # perfect square
    return 0;
  }

  my %seen;
  my $count = 0;
  for (;;) {
    if ($seen{"$p,$q"}++) {
      return $count;
    }
    $count++;

    my $value = int (($root + $p) / $q);
    $p -= $value*$q;
    ($p, $q) = (-$p,
                ($i - $p*$p) / $q);

    ### assert: $p >= 0
    ### assert: $q > 0
    ### assert: $p <= $root
    ### assert: $q <= 2*$root+1
    ### assert: (($p*$p - $i) % $q) == 0
  }
}

1;
__END__