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# Copyright 2013, 2014 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/>.
# A134561 triangle T(n,k) = k-th number whose Zeckendorf has exactly n terms
# 4180 5777 6387 6620 6709 6743 6756 6761 6763 6764 8361
# 1596 2206 2439 2528 2562 2575 2580 2582 2583 3193 3426
# 609 842 931 965 978 983 985 986 1219 1308 1342
# 232 321 355 368 373 375 376 465 499 512 517
# 88 122 135 140 142 143 177 190 195 197 198
# 33 46 51 53 54 67 72 74 75 80 82
# 12 17 19 20 25 27 28 30 31 32 38
# 4 6 7 9 10 11 14 15 16 18 22
# 1 2 3 5 8 13 21 34 55 89 144
# Y=1 Fibonacci
# Y=2 A095096
# X=1 first with Y many bits is Zeck 101010101
# A027941 Fib(2n+1)-1
# X=2 second with Y many bits is Zeck 1001010101 high 1, low 10101
# A005592 F(2n+1)+F(2n-1)-1
# X=3 third with Y many bits is Zeck 1010010101
# A005592 F(2n+1)+F(2n-1)-1
# X=4 fourth with Y many bits is Zeck 1010100101
package Math::PlanePath::ZeckendorfTerms;
use 5.004;
use strict;
use List::Util 'max';
use vars '$VERSION', '@ISA';
$VERSION = 117;
use Math::PlanePath;
@ISA = ('Math::PlanePath');
use Math::PlanePath::Base::Generic
'is_infinite',
'round_nearest';
# uncomment this to run the ### lines
# use Smart::Comments;
use constant class_x_negative => 0;
use constant class_y_negative => 0;
use constant y_minimum => 1;
use constant x_minimum => 1;
use Math::NumSeq::FibbinaryBitCount;
my $fbc = Math::NumSeq::FibbinaryBitCount->new;
my $next_n = 1;
my @n_to_x;
my @n_to_y;
my @yx_to_n;
sub _extend {
my ($self) = @_;
my $n = $next_n++;
my $y = $fbc->ith($n);
my $row = ($yx_to_n[$y] ||= []);
my $x = scalar(@$row) || 1;
$row->[$x] = $n;
$n_to_x[$n] = $x;
$n_to_y[$n] = $y;
}
sub n_to_xy {
my ($self, $n) = @_;
### ZeckendorfTerms n_to_xy(): $n
if ($n < 1) { return; }
if (is_infinite($n) || $n == 0) { return ($n,$n); }
{
# fractions on straight line ?
my $int = int($n);
if ($n != $int) {
my $frac = $n - $int; # inherit possible BigFloat/BigRat
my ($x1,$y1) = $self->n_to_xy($int);
my ($x2,$y2) = $self->n_to_xy($int+1);
my $dx = $x2-$x1;
my $dy = $y2-$y1;
return ($frac*$dx + $x1, $frac*$dy + $y1);
}
$n = $int;
}
my $y = $fbc->ith($n);
while ($next_n <= $n) {
_extend($self);
}
### $self
return ($n_to_x[$n], $n_to_y[$n]);
}
sub xy_to_n {
my ($self, $x, $y) = @_;
### ZeckendorfTerms xy_to_n(): "$x, $y"
$x = round_nearest ($x);
$y = round_nearest ($y);
if ($x < 1 || $y < 1) { return undef; }
if (is_infinite($x)) { return $x; }
if (is_infinite($y)) { return $y; }
for (;;) {
if (defined (my $n = $yx_to_n[$y][$x])) {
return $n;
}
_extend($self);
}
}
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### ZeckendorfTerms rect_to_n_range(): "$x1,$y1 $x2,$y2"
$x1 = round_nearest ($x1);
$y1 = round_nearest ($y1);
$x2 = round_nearest ($x2);
$y2 = round_nearest ($y2);
($x1,$x2) = ($x2,$x1) if $x1 > $x2;
($y1,$y2) = ($y2,$y1) if $y1 > $y2;
return (1, 10000);
# $self->xy_to_n($x2,$y2));
}
1;
__END__
=cut
# math-image --path=ZeckendorfTerms --output=numbers --all --size=60x14
=pod
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