#!/usr/bin/perl -w
# Copyright 2011, 2012, 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/>.
use 5.004;
use strict;
use Test;
plan tests => 26;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::DragonMidpoint;
# uncomment this to run the ### lines
# use Smart::Comments '###';
#------------------------------------------------------------------------------
# A090678 turn=1 straight=0, except A090678 has extra initial 1,1
MyOEIS::compare_values
(anum => 'A090678',
func => sub {
my ($count) = @_;
my @got = (1,1);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath=>'DragonMidpoint',
turn_type => 'LSR');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, abs($value);
}
return \@got;
});
#------------------------------------------------------------------------------
# A203175 figure boundary length to N=2^k-1
MyOEIS::compare_values
(anum => 'A203175',
name => 'boundary length',
max_value => 10_000,
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::DragonMidpoint->new;
my @got = (1,1,2);
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_n_to_figure_boundary($path, 2**$k-1);
}
return \@got;
});
#------------------------------------------------------------------------------
# A077860 -- Y at N=2^k, starting k=1 N=2
require Math::NumSeq::PlanePathN;
my $bigclass = Math::NumSeq::PlanePathN::_bigint();
# Re -(i+1)^k + i-1
{
require Math::Complex;
my $path = Math::PlanePath::DragonMidpoint->new;
my $b = Math::Complex->make(1,1);
foreach my $k (1 .. 10) {
my $n = 2**$k;
my ($x,$y) = $path->n_to_xy($n);
my $c = $b; foreach (1 .. $k) { $c *= $b; }
$c *= Math::Complex->make(0,-1);
$c += Math::Complex->make(-1,1);
ok ($c->Re, $x);
ok ($c->Im, $y);
# print $x,",";
# print $c->Re,",";
# print $c->Im,",";
}
}
MyOEIS::compare_values
(anum => 'A077860',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::DragonMidpoint->new;
my @got;
for (my $n = $bigclass->new(2); @got < $count; $n *= 2) {
my ($x,$y) = $path->n_to_xy($n);
push @got, $y;
}
return \@got;
});
#------------------------------------------------------------------------------
# A073089 -- abs(dY), so 1 if step vertical, 0 if horizontal
# with extra leading 0
MyOEIS::compare_values
(anum => 'A073089',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::DragonMidpoint->new;
my @got = (0);
my ($prev_x, $prev_y) = $path->n_to_xy (0);
for (my $n = $path->n_start + 1; @got < $count; $n++) {
my ($x, $y) = $path->n_to_xy ($n);
if ($x == $prev_x) {
push @got, 1; # vertical
} else {
push @got, 0; # horizontal
}
($prev_x,$prev_y) = ($x,$y);
}
return \@got;
});
# A073089_func vs b-file
MyOEIS::compare_values
(anum => 'A073089',
func => sub {
my ($count) = @_;
my @got;
for (my $n = 1; @got < $count; $n++) {
push @got, A073089_func($n);
}
return \@got;
});
# A073089_func vs path
{
my $path = Math::PlanePath::DragonMidpoint->new;
my ($prev_x, $prev_y) = $path->n_to_xy (0);
my $bad = 0;
foreach my $n (0 .. 0x2FFF) {
my ($x, $y) = $path->n_to_xy ($n);
my ($nx, $ny) = $path->n_to_xy ($n+1);
my $path_value = ($x == $nx
? 1 # vertical
: 0); # horizontal
my $a_value = A073089_func($n+2);
if ($path_value != $a_value) {
MyTestHelpers::diag ("diff n=$n path=$path_value acalc=$a_value");
MyTestHelpers::diag (" xy=$x,$y nxy=$nx,$ny");
last if ++$bad > 10;
}
}
ok ($bad, 0, "A073089_func()");
}
sub A073089_func {
my ($n) = @_;
### A073089_func: $n
for (;;) {
if ($n <= 1) { return 0; }
if (($n % 4) == 2) { return 0; }
if (($n % 8) == 7) { return 0; }
if (($n % 16) == 13) { return 0; }
if (($n % 4) == 0) { return 1; }
if (($n % 8) == 3) { return 1; }
if (($n % 16) == 5) { return 1; }
if (($n % 8) == 1) {
$n = ($n-1)/2+1; # 8n+1 -> 4n+1
next;
}
die "oops";
}
}
# absdy_bitwise() vs path
{
my $path = Math::PlanePath::DragonMidpoint->new;
my ($prev_x, $prev_y) = $path->n_to_xy (0);
my $bad = 0;
foreach my $n (0 .. 0x2FFF) {
my ($x, $y) = $path->n_to_xy ($n);
my ($nx, $ny) = $path->n_to_xy ($n+1);
my $path_value = ($x == $nx
? 1 # vertical
: 0); # horizontal
my $a_value = absdy_bitwise($n);
if ($path_value != $a_value) {
MyTestHelpers::diag ("diff n=$n path=$path_value acalc=$a_value");
MyTestHelpers::diag (" xy=$x,$y nxy=$nx,$ny");
last if ++$bad > 10;
}
}
ok ($bad, 0, "absdy_bitwise()");
}
sub absdy_bitwise {
my ($n) = @_;
return ($n & 1) ^ bit_above_lowest_zero($n);
}
sub bit_above_lowest_zero {
my ($n) = @_;
for (;;) {
if (($n % 2) == 0) {
last;
}
$n = int($n/2);
}
$n = int($n/2);
return ($n % 2);
}
#------------------------------------------------------------------------------
exit 0;