1Math::NumSeq::GolayRudiUnsSehrapCiornot(r3i)buted Perl DMoactuhm:e:nNtuamtSieoqn::GolayRudinShapiro(3)
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NAME

6       Math::NumSeq::GolayRudinShapiro -- parity of adjacent 11 bit pairs
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SYNOPSIS

9        use Math::NumSeq::GolayRudinShapiro;
10        my $seq = Math::NumSeq::GolayRudinShapiro->new;
11        my ($i, $value) = $seq->next;
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DESCRIPTION

14       This is the Golay/Rudin/Shapiro sequence of +1 or -1 according as an
15       even or odd number of adjacent 11 bit pairs in i.
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17           GRS(i) = (-1) ^ (count 11 bit pairs)
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19           starting from i=0
20           1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, ...
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22       The first -1 is at i=3 which is binary 11 with a single 11 bit pair,
23       then i=6 binary 110 likewise -1.  Later for example i=14 is binary 1110
24       which has two adjacent 11 pairs (overlapping pairs count), so value=1.
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26       The value is also the parity of the number of even-length runs of
27       1-bits in i.  An even length run has an odd number of 11 pairs, so each
28       of them is a -1 in the product.  An odd-length run of 1-bits is an even
29       number of 11 pairs so is +1 and has no effect on the result.
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31       Such a parity of even-length 1-bit runs and hence the GRS sequence
32       arises as the "dX,dY" change for each segment of the alternate paper
33       folding curve.  See "dX,dY" in Math::PlanePath::AlternatePaper.
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35   Values Type
36       Parameter "values_type => '0,1'" gives values 0 and 1, being the count
37       of adjacent 11s taken modulo 2, so 0 if even, 1 if odd.
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39           values_type => '0,1'
40           0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, ...
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FUNCTIONS

43       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
44       classes.
45
46       "$seq = Math::NumSeq::GolayRudinShapiro->new ()"
47       "$seq = Math::NumSeq::GolayRudinShapiro->new (values_type => $str)"
48           Create and return a new sequence object.  The "values_type"
49           parameter (a string) can be
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51               "1,-1"        1=even, -1=odd
52               "0,1"         0=even, 1=odd
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54   Random Access
55       "$value = $seq->ith($i)"
56           Return the $i'th value from the sequence, being +1 or -1 (or per
57           "values_type") according to the number of adjacent 11 bit pairs in
58           $i.
59
60       "$bool = $seq->pred($value)"
61           Return true if $value occurs in the sequence, which simply means
62           "$value == 1" or "$value == -1".  Or if "values_type=>'0,1'" then 0
63           or 1.
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SEE ALSO

66       Math::NumSeq, Math::NumSeq::GolayRudinShapiroCumulative,
67       Math::NumSeq::BaumSweet, Math::NumSeq::Fibbinary
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69       Math::PlanePath::AlternatePaper
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HOME PAGE

72       <http://user42.tuxfamily.org/math-numseq/index.html>
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LICENSE

75       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2017, 2019, 2020 Kevin
76       Ryde
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78       Math-NumSeq is free software; you can redistribute it and/or modify it
79       under the terms of the GNU General Public License as published by the
80       Free Software Foundation; either version 3, or (at your option) any
81       later version.
82
83       Math-NumSeq is distributed in the hope that it will be useful, but
84       WITHOUT ANY WARRANTY; without even the implied warranty of
85       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
86       General Public License for more details.
87
88       You should have received a copy of the GNU General Public License along
89       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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93perl v5.36.0                      2022-07-22Math::NumSeq::GolayRudinShapiro(3)
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