File Coverage

blib/lib/Math/NumSeq/DigitCount.pm

Criterion	Covered	Total	%
statement	71	73	97.2
branch	8	10	80.0
condition	1	3	33.3
subroutine	18	18	100.0
pod	3	3	100.0
total	101	107	94.3

# Copyright 2010, 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::DigitCount;
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;

use Math::NumSeq::Repdigits;
*_digit_split_lowtohigh = \&Math::NumSeq::Repdigits::_digit_split_lowtohigh;

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


# use constant name => Math::NumSeq::__('Digit Count');
use constant description => Math::NumSeq::__('How many of a given digit in each number, in a given radix, for example how many 1-bits in binary.');
use constant values_min => 0;
use constant default_i_start => 0;
use constant characteristic_count => 1;
use constant characteristic_smaller => 1;
use constant characteristic_increasing => 0;

use Math::NumSeq::Base::Digits;
use constant parameter_info_array =>
  [
   Math::NumSeq::Base::Digits->parameter_info_list(),
   {
    name        => 'digit',
    type        => 'integer',
    share_key   => 'digit-1',
    display     => Math::NumSeq::__('Digit'),
    default     => -1,
    minimum     => -1,
    width       => 2,
    description => Math::NumSeq::__('Digit to count, default -1 means radix-1.'),
   },
  ];

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

# cf A008687 - count 1s in twos-complement -n
#    A000788 - cumulative count 1-bits in 0 to n
#    A033093 - total count 0s in all bases 2 to n+1
#    A059015 - cumulative count 0-bits
#    A000788 - cumulative count 1-bits
#    A077266 - triangle of count 0s in bases 2 to n+1
#    A077268 - num bases with at least one 0

my @oeis_anum;  # $oeis_anum[radix]->[digit]
BEGIN {
  # cf A023416 treating "0" as a single digit zero
  $oeis_anum[0]->[2]->[0] = 'A080791'; # base 2 count 0s, start i=0
  $oeis_anum[0]->[2]->[1] = 'A000120'; # base 2 count 1s, start i=0
  # OEIS-Catalogue: A080791 radix=2 digit=0
  # OEIS-Catalogue: A000120 radix=2 digit=1

  $oeis_anum[1]->[3]->[0] = 'A077267'; # base 3 count 0s, start i=1
  $oeis_anum[0]->[3]->[1] = 'A062756'; # base 3 count 1s, start i=0
  $oeis_anum[0]->[3]->[2] = 'A081603'; # base 3 count 2s, start i=0
  # OEIS-Catalogue: A077267 radix=3 digit=0 i_start=1
  # OEIS-Catalogue: A062756 radix=3 digit=1
  # OEIS-Catalogue: A081603 radix=3 digit=2
  #
  # cf A081602 start i=0 but considers i=0 to have 1 zero, unlike other counts
  # $oeis_anum[0]->[3]->[0] = 'A081602'; # base 3 count 0s, start i=0
  # # OEIS-Catalogue: A081602 radix=3 digit=0

  $oeis_anum[0]->[4]->[0] = 'A160380'; # base 4 count 0s, start i=0
  $oeis_anum[0]->[4]->[1] = 'A160381'; # base 4 count 1s, start i=0
  $oeis_anum[0]->[4]->[2] = 'A160382'; # base 4 count 2s, start i=0
  $oeis_anum[0]->[4]->[3] = 'A160383'; # base 4 count 3s, start i=0
  # OEIS-Catalogue: A160380 radix=4 digit=0
  # OEIS-Catalogue: A160381 radix=4 digit=1
  # OEIS-Catalogue: A160382 radix=4 digit=2
  # OEIS-Catalogue: A160383 radix=4 digit=3

  # almost A055641 decimal count 9s, but it starts i=0 has 1 zero

  $oeis_anum[0]->[10]->[9] = 'A102683'; # base 10 count 9s, start i=0
  # OEIS-Catalogue: A102683 radix=10 digit=9
}
sub oeis_anum {
  my ($self) = @_;
  my $radix = $self->{'radix'};
  my $digit = $self->{'digit'};
  if ($digit == -1) {
    $digit = $radix-1;
  } elsif ($digit >= $radix) {
    return 'A000004'; # all zeros, starting i=0
  }
  return $oeis_anum[$self->i_start]->[$radix]->[$digit];
}

sub ith {
  my ($self, $i) = @_;
  $i = abs($i);
  if (_is_infinite ($i)) {
    return $i;
  }

  my $radix = $self->{'radix'};
  my $digit = $self->{'digit'};
  if ($digit == -1) { $digit = $radix - 1; }

  my $count = 0;
  foreach my $got_digit (_digit_split_lowtohigh($i, $radix)) {
    if ($got_digit == $digit) {
      $count++;
    }
  }
  return $count;
}

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

1;
__END__