#!/usr/bin/perl -w
# Copyright 2010, 2011, 2012, 2013, 2014, 2015 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath 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-PlanePath 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-PlanePath. If not, see <http://www.gnu.org/licenses/>.
use 5.004;
use strict;
use Test;
plan tests => 7;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::CCurve;
# uncomment this to run the ### lines
# use Smart::Comments '###';
my $path = Math::PlanePath::CCurve->new;
# return 0,1,2,3 turn
sub path_n_turn {
my ($path, $n) = @_;
my $prev_dir = path_n_dir ($path, $n-1);
my $dir = path_n_dir ($path, $n);
return ($dir - $prev_dir) % 4;
}
# return 0,1,2,3
sub path_n_dir {
my ($path, $n) = @_;
my ($dx,$dy) = $path->n_to_dxdy($n) or die "Oops, no point at ",$n;
return dxdy_to_dir4 ($dx, $dy);
}
# return 0,1,2,3, with Y reckoned increasing upwards
sub dxdy_to_dir4 {
my ($dx, $dy) = @_;
if ($dx > 0) { return 0; } # east
if ($dx < 0) { return 2; } # west
if ($dy > 0) { return 1; } # north
if ($dy < 0) { return 3; } # south
}
sub right_boundary {
my ($n_end) = @_;
return MyOEIS::path_boundary_length ($path, $n_end, side => 'right');
}
use Memoize;
Memoize::memoize('right_boundary');
#------------------------------------------------------------------------------
# A096268 - morphism turn 1=straight,0=not-straight
# but OFFSET=0 is turn at N=1, so "next turn"
MyOEIS::compare_values
(anum => 'A096268',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'CCurve',
turn_type => 'Straight');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
MyOEIS::compare_values
(anum => q{A096268},
func => sub {
my ($count) = @_;
my @got;
for (my $n = 0; @got < $count; $n++) {
push @got, count_low_1_bits($n) % 2;
}
return \@got;
});
MyOEIS::compare_values
(anum => q{A096268},
func => sub {
my ($count) = @_;
my @got;
for (my $n = 0; @got < $count; $n++) {
push @got, count_low_0_bits($n+1) % 2;
}
return \@got;
});
sub count_low_1_bits {
my ($n) = @_;
my $count = 0;
while ($n % 2) {
$count++;
$n = int($n/2);
}
return $count;
}
sub count_low_0_bits {
my ($n) = @_;
if ($n == 0) { die; }
my $count = 0;
until ($n % 2) {
$count++;
$n /= 2;
}
return $count;
}
#------------------------------------------------------------------------------
# A038503 etc counts of segments in direction
foreach my $elem ([0, 'A038503', 0],
[1, 'A038504', 0],
[2, 'A038505', 1],
[3, 'A000749', 0]) {
my ($dir, $anum, $initial_k) = @$elem;
MyOEIS::compare_values
(anum => $anum,
max_value => 100_000,
func => sub {
my ($count) = @_;
my @got;
my $n = $path->n_start;
my $total = 0;
my $k = $initial_k;
while (@got < $count) {
my $n_end = 2**$k;
for ( ; $n < $n_end; $n++) {
$total += (dxdy_to_dir4($path->n_to_dxdy($n)) == $dir);
}
push @got, $total;
$k++;
}
return \@got;
});
}
#------------------------------------------------------------------------------
# A007814 - count low 0s, is turn right - 1
MyOEIS::compare_values
(anum => 'A007814',
fixup => sub {
my ($bvalues) = @_;
@$bvalues = map {$_ % 4} @$bvalues;
},
func => sub {
my ($count) = @_;
my @got;
my $total_turn = 0;
for (my $n = $path->n_start + 1; @got < $count; $n++) {
push @got, (1 - path_n_turn($path,$n)) % 4; # negate to right
}
return \@got;
});
#------------------------------------------------------------------------------
# A003159 - positions ending even 0 bits is where turn either left or right
MyOEIS::compare_values
(anum => 'A003159',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'LSR');
my @got;
while (@got < $count) {
my ($i, $lsr) = $seq->next;
if ($lsr) { # left or right
push @got, $i;
}
}
return \@got;
});
# A036554 - positions ending odd 0 bits is where turn straight or reverse
MyOEIS::compare_values
(anum => 'A036554',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'LSR');
my @got;
while (@got < $count) {
my ($i, $lsr) = $seq->next;
if ($lsr == 0) { # straight
push @got, $i;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A027383 right boundary differences
# cf
# CCurve right boundary diffs even terms
# 6,14,30,62,126
# A000918 2^n - 2.
# CCurve right boundary diffs odd terms
# 10,22,46,94,190
# A033484 3*2^n - 2.
MyOEIS::compare_values
(anum => 'A027383',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (1);
for (my $k = 1; @got < $count; $k++) {
my $b1 = right_boundary(2**$k);
my $b2 = right_boundary(2**($k+1));
push @got, $b2 - $b1;
}
return \@got;
});
# A131064 right boundary odd powers, extra initial 1
MyOEIS::compare_values
(anum => 'A131064',
max_value => 50_000,
func => sub {
my ($count) = @_;
my @got = (1);
for (my $k = 1; @got < $count; $k++) {
my $boundary = right_boundary(2**(2*$k-1)); # 1,3,5,..
push @got, $boundary;
### at: "k=$k $boundary"
}
return \@got;
});
#------------------------------------------------------------------------------
# A035263 - morphism turn 0=straight, 1=not-straight
MyOEIS::compare_values
(anum => 'A035263',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'CCurve',
turn_type => 'LSR');
my @got;
for (my $n = 1; @got < $count; $n++) {
my ($i,$value) = $seq->next;
push @got, $value == 0 ? 0 : 1;
}
return \@got;
});
MyOEIS::compare_values
(anum => q{A035263},
func => sub {
my ($count) = @_;
my @got;
for (my $n = 1; @got < $count; $n++) {
push @got, (count_low_0_bits($n) + 1) % 2;
}
return \@got;
});
#------------------------------------------------------------------------------
# A104488 -- num Hamiltonian groups
# No, different at n=67 and more
#
# MyOEIS::compare_values
# (anum => 'A104488',
# func => sub {
# my ($count) = @_;
# require Math::NumSeq::PlanePathTurn;
# my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'CCurve',
# turn_type => 'Right');
# my @got = (0,0,0,0);;
# while (@got < $count) {
# my ($i,$value) = $seq->next;
# push @got, $value;
# }
# return \@got;
# });
#------------------------------------------------------------------------------
# A146559 - (i+1)^k is X+iY at N=2^k
# A009545 - Im
# A146559 X at N=2^k, being Re((i+1)^k)
# A009545 Y at N=2^k, being Im((i+1)^k)
require Math::NumSeq::PlanePathN;
my $bigclass = Math::NumSeq::PlanePathN::_bigint();
MyOEIS::compare_values
(anum => 'A146559',
func => sub {
my ($count) = @_;
my @got;
for (my $n = $bigclass->new(1); @got < $count; $n *= 2) {
my ($x,$y) = $path->n_to_xy($n);
push @got, $x;
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A009545',
func => sub {
my ($count) = @_;
my @got;
for (my $n = $bigclass->new(1); @got < $count; $n *= 2) {
my ($x,$y) = $path->n_to_xy($n);
push @got, $y;
}
return \@got;
});
#------------------------------------------------------------------------------
# A000120 - count 1 bits total turn
MyOEIS::compare_values
(anum => 'A000120',
fixup => sub {
my ($bvalues) = @_;
@$bvalues = map {$_ % 4} @$bvalues;
},
func => sub {
my ($count) = @_;
my @got = (0);
my $total_turn = 0;
for (my $n = $path->n_start + 1; @got < $count; $n++) {
$total_turn += path_n_turn($path,$n);
push @got, $total_turn % 4;
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;