1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
|
# 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/>.
package Math::PlanePath::WythoffDifference;
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 xy_is_visited => 1;
use Math::PlanePath::WythoffArray;
my $wythoff = Math::PlanePath::WythoffArray->new;
sub n_to_xy {
my ($self, $n) = @_;
### WythoffDifference 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;
}
# f1+f0 > i
# f0 > i-f1
# check i-f1 as the stopping point, so that if i=UV_MAX then won't
# overflow a UV trying to get to f1>=i
#
my @fibs;
{
my $f0 = ($n * 0); # inherit bignum 0
my $f1 = $f0 + 1; # inherit bignum 1
while ($f0 <= $n-$f1) {
($f1,$f0) = ($f1+$f0,$f1);
push @fibs, $f1; # starting $fibs[0]=1
}
}
### @fibs
my $orig_n = $n;
# indices into fib[] which are the Fibonaccis adding up to $n
my @indices;
for (my $i = $#fibs; $i >= 0; $i--) {
### at: "n=$n f=".$fibs[$i]
if ($n >= $fibs[$i]) {
push @indices, $i;
$n -= $fibs[$i];
### sub: "$fibs[$i] to n=$n"
--$i;
}
}
### @indices
my $y = 0;
my $shift;
my $x;
my $low = $indices[-1];
if ($low % 2) {
# odd trailing zeros
$x = ($low+1)/2;
$shift = $low + 2;
pop @indices;
} else {
# even trailing zeros
$x = 0;
$shift = 1;
if ($low == 0) {
pop @indices;
} else {
$y = -1;
}
}
foreach my $i (@indices) {
### y add: "ishift=".($i-$shift)." fib=".$fibs[$i-$shift]
$y += $fibs[$i-$shift];
}
### $y
return ($x, $y);
}
# 6 | 11 28 73 191 500
# 5 | 9 23 60 157 411
# 4 | 8 20 52 136 356
# 3 | 6 15 39 102 267
# 2 | 4 10 26 68 178
# 1 | 3 7 18 47 123
# 0 | 1 2 5 13 34
# +-------------------
# 0 1 2 3 4
# 9 | 100100 10001010 1000101000 100010100000 10001010000000
# 8 | 100001 10000010 1000001000 100000100000 10000010000000
# 7 | 10101 1010010 101001000 10100100000 1010010000000
# 6 | 10100 1001010 100101000 10010100000 1001010000000
# 5 | 10001 1000010 100001000 10000100000 1000010000000
# 4 | 10000 101010 10101000 1010100000 101010000000
# 3 | 1001 100010 10001000 1000100000 100010000000
# 2 | 101 10010 1001000 100100000 10010000000
# 1 | 100 1010 101000 10100000 1010000000
# 0 | 1 10 1000 100000 10000000
# +--------------------------------------------------------
# 0 1 2 3 4
sub xy_to_n {
my ($self, $x, $y) = @_;
$x = round_nearest ($x);
if ($x == 0) {
my $n1 = $wythoff->xy_to_n(1,$y);
if ($n1) {
$n1 -= $wythoff->xy_to_n(0,$y);
}
return $n1;
}
return $wythoff->xy_to_n(2*$x-1,$y);
}
# exact
sub rect_to_n_range {
my ($self, $x1,$y1, $x2,$y2) = @_;
### WythoffDifference 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 > $y2;
if ($x2 < 0 || $y2 < 0) {
### all outside first quadrant ...
return (1, 0);
}
# bottom left into first quadrant
if ($x1 < 0) { $x1 *= 0; }
if ($y1 < 0) { $y1 *= 0; }
return ($self->xy_to_n($x1,$y1), # bottom left
$self->xy_to_n($x2,$y2)); # top right
}
1;
__END__
|
