#!/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;
use lib 't';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
# uncomment this to run the ### lines
#use Smart::Comments '###';
my $test_count = (tests => 447)[1];
plan tests => $test_count;
# version 1.14 for abs() overload
if (! eval 'use Number::Fraction 1.14; 1') {
MyTestHelpers::diag ('skip due to Number::Fraction 1.14 not available -- ',$@);
foreach (1 .. $test_count) {
skip ('due to no Number::Fraction', 1, 1);
}
exit 0;
}
MyTestHelpers::diag ('Number::Fraction version ', Number::Fraction->VERSION);
#------------------------------------------------------------------------------
# round_nearest()
use Math::PlanePath::Base::Generic 'round_nearest';
ok (round_nearest(Number::Fraction->new('-7/4')) == -2, 1);
ok (round_nearest(Number::Fraction->new('-3/2')) == -1, 1);
ok (round_nearest(Number::Fraction->new('-5/4')) == -1, 1);
ok (round_nearest(Number::Fraction->new('-3/4')) == -1, 1);
ok (round_nearest(Number::Fraction->new('-1/2')) == 0, 1);
ok (round_nearest(Number::Fraction->new('-1/4')) == 0, 1);
ok (round_nearest(Number::Fraction->new('1/4')) == 0, 1);
ok (round_nearest(Number::Fraction->new('5/4')) == 1, 1);
ok (round_nearest(Number::Fraction->new('3/2')) == 2, 1);
ok (round_nearest(Number::Fraction->new('7/4')) == 2, 1);
ok (round_nearest(Number::Fraction->new('2')) == 2, 1);
#------------------------------------------------------------------------------
# floor()
use Math::PlanePath::Base::Generic 'floor';
ok (floor(Number::Fraction->new('-7/4')) == -2, 1);
ok (floor(Number::Fraction->new('-3/2')) == -2, 1);
ok (floor(Number::Fraction->new('-5/4')) == -2, 1);
ok (floor(Number::Fraction->new('-3/4')) == -1, 1);
ok (floor(Number::Fraction->new('-1/2')) == -1, 1);
ok (floor(Number::Fraction->new('-1/4')) == -1, 1);
ok (floor(Number::Fraction->new('1/4')) == 0, 1);
ok (floor(Number::Fraction->new('3/4')) == 0, 1);
ok (floor(Number::Fraction->new('5/4')) == 1, 1);
ok (floor(Number::Fraction->new('3/2')) == 1, 1);
ok (floor(Number::Fraction->new('7/4')) == 1, 1);
ok (floor(Number::Fraction->new('2')) == 2, 1);
#------------------------------------------------------------------------------
# Rows
{
require Math::PlanePath::Rows;
my $width = 5;
my $path = Math::PlanePath::Rows->new (width => $width);
{
my $y = Number::Fraction->new(2) ** 20;
my $x = 4;
my $n = $y*$width + $x + 1;
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ($got_x == $x, 1, "got $got_x want $x");
ok ($got_y == $y);
my $got_n = $path->xy_to_n($x,$y);
ok ($got_n == $n, 1);
}
{
my $n = Number::Fraction->new('4/3');
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ("$got_x", '1/3');
ok ($got_y == 0, 1);
}
{
my $n = Number::Fraction->new('4/3') + 15;
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ("$got_x", '1/3');
ok ($got_y == 3, 1);
}
{
my $n = Number::Fraction->new('4/3') - 15;
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ("$got_x", '1/3');
ok ($got_y == -3, 1);
}
}
#------------------------------------------------------------------------------
# Diagonals
{
require Math::PlanePath::Diagonals;
my $path = Math::PlanePath::Diagonals->new;
{
my $x = Number::Fraction->new(2) ** 20 - 1;
my $n = ($x+1)*($x+2)/2; # triangular numbers on Y=0 horizontal
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ($got_x == $x, 1, "got $got_x want $x");
ok ($got_y == 0);
my $got_n = $path->xy_to_n($x,0);
ok ($got_n == $n, 1);
}
{
my $x = Number::Fraction->new(2) ** 20 - 1;
my $n = ($x+1)*($x+2)/2; # Y=0 horizontal
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ($got_x == $x, 1);
ok ($got_y == 0, 1);
my $got_n = $path->xy_to_n($x,0);
ok ($got_n == $n, 1);
}
{
my $y = Number::Fraction->new(2) ** 20 - 1;
my $n = $y*($y+1)/2 + 1; # X=0 vertical
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ($got_x == 0, 1);
ok ($got_y == $y, 1);
my $got_n = $path->xy_to_n(0,$y);
ok ($got_n, $n);
}
{
my $n = Number::Fraction->new(-1);
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ($got_x, undef);
ok ($got_y, undef);
}
{
my $n = Number::Fraction->new('1/2');
my ($got_x,$got_y) = $path->n_to_xy($n);
ok (!! $got_x->isa('Number::Fraction'), 1);
ok (!! $got_y->isa('Number::Fraction'), 1);
ok ($got_x == -0.5, 1);
ok ($got_y == 0.5, 1);
}
}
#------------------------------------------------------------------------------
### PeanoCurve ...
require Math::PlanePath::PeanoCurve;
{
my $path = Math::PlanePath::PeanoCurve->new;
require Number::Fraction;
my $n = Number::Fraction->new(9**5) + Number::Fraction->new('4/3');
my $want_x = Number::Fraction->new(3**5) + Number::Fraction->new('4/3');
my $want_y = Number::Fraction->new(3**5) - 1;
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ($got_x, $want_x);
ok ($got_y, $want_y);
}
#------------------------------------------------------------------------------
### ZOrderCurve ...
require Math::PlanePath::ZOrderCurve;
{
my $path = Math::PlanePath::ZOrderCurve->new;
require Number::Fraction;
my $n = Number::Fraction->new(4**5) + Number::Fraction->new('1/3');
$n->isa('Number::Fraction') || die "Oops, n not a BigRat";
my $want_x = Number::Fraction->new(2**5) + Number::Fraction->new('1/3');
my $want_y = 0;
my ($got_x,$got_y) = $path->n_to_xy($n);
ok ($got_x, $want_x);
ok ($got_y, $want_y);
}
#------------------------------------------------------------------------------
### round_down_pow() ...
use Math::PlanePath::Base::Digits 'round_down_pow';
{
my $orig = Number::Fraction->new(3) ** 20 + Number::Fraction->new('1/7');
my $n = Number::Fraction->new(3) ** 20 + Number::Fraction->new('1/7');
my ($pow,$exp) = round_down_pow($n,3);
ok ($n, $orig);
ok ($pow, Number::Fraction->new(3) ** 20);
ok ($exp, 20);
}
{
my $orig = Number::Fraction->new(3) ** 20;
my $n = Number::Fraction->new(3) ** 20;
my ($pow,$exp) = round_down_pow($n,3);
ok ($n, $orig);
ok ($pow, Number::Fraction->new(3) ** 20);
ok ($exp, 20);
}
#------------------------------------------------------------------------------
### Modules ...
my @modules = (
'HilbertSides',
'HilbertCurve',
'HilbertSpiral',
'CfracDigits,radix=1',
'CfracDigits',
'CfracDigits,radix=3',
'CfracDigits,radix=4',
'CfracDigits,radix=10',
'CfracDigits,radix=37',
'ChanTree',
'ChanTree,k=2',
'ChanTree,k=4',
'ChanTree,k=5',
'ChanTree,k=7',
'ChanTree,reduced=1',
'ChanTree,reduced=1,k=2',
'ChanTree,reduced=1,k=4',
'ChanTree,reduced=1,k=5',
'ChanTree,reduced=1,k=7',
'RationalsTree',
'RationalsTree,tree_type=L',
'RationalsTree,tree_type=HCS',
'FractionsTree',
'DekkingCurve',
'DekkingCentres',
'PyramidRows',
'PyramidRows,step=0',
'PyramidRows,step=1',
'PyramidRows,step=3',
'PyramidRows,step=37',
'PyramidRows,align=right',
'PyramidRows,align=right,step=0',
'PyramidRows,align=right,step=1',
'PyramidRows,align=right,step=3',
'PyramidRows,align=right,step=37',
'PyramidRows,align=left',
'PyramidRows,align=left,step=0',
'PyramidRows,align=left,step=1',
'PyramidRows,align=left,step=3',
'PyramidRows,align=left,step=37',
'GreekKeySpiral',
'GreekKeySpiral,turns=0',
'GreekKeySpiral,turns=1',
'GreekKeySpiral,turns=3',
'GreekKeySpiral,turns=4',
'GreekKeySpiral,turns=5',
'GreekKeySpiral,turns=6',
'GreekKeySpiral,turns=7',
'GreekKeySpiral,turns=8',
'GreekKeySpiral,turns=37',
'AlternatePaperMidpoint',
'AlternatePaperMidpoint,arms=2',
'AlternatePaperMidpoint,arms=3',
'AlternatePaperMidpoint,arms=4',
'AlternatePaperMidpoint,arms=5',
'AlternatePaperMidpoint,arms=6',
'AlternatePaperMidpoint,arms=7',
'AlternatePaperMidpoint,arms=8',
'AlternatePaper',
'AlternatePaper,arms=2',
'AlternatePaper,arms=3',
'AlternatePaper,arms=4',
'AlternatePaper,arms=5',
'AlternatePaper,arms=6',
'AlternatePaper,arms=7',
'AlternatePaper,arms=8',
'WythoffPreliminaryTriangle',
'WythoffArray',
'PowerArray',
'PowerArray,radix=3',
'PowerArray,radix=4',
'Diagonals',
'Diagonals,direction=up',
'DiagonalsOctant',
'DiagonalsOctant,direction=up',
'DiagonalsAlternating',
'TerdragonRounded',
'TerdragonRounded,arms=1',
'TerdragonRounded,arms=2',
'TerdragonRounded,arms=6',
'CCurve',
'R5DragonMidpoint',
'R5DragonMidpoint,arms=2',
'R5DragonMidpoint,arms=3',
'R5DragonMidpoint,arms=4',
'R5DragonCurve',
'R5DragonCurve,arms=2',
'R5DragonCurve,arms=3',
'R5DragonCurve,arms=4',
'DragonRounded',
'DragonMidpoint',
'DragonCurve',
'GrayCode',
'WunderlichSerpentine',
'WunderlichSerpentine,serpentine_type=100_000_000',
'WunderlichSerpentine,serpentine_type=000_000_001',
'WunderlichSerpentine,radix=2',
'WunderlichSerpentine,radix=4',
'WunderlichSerpentine,radix=5,serpentine_type=coil',
'CretanLabyrinth',
'TerdragonMidpoint',
'TerdragonMidpoint,arms=1',
'TerdragonMidpoint,arms=2',
'TerdragonMidpoint,arms=6',
'TerdragonCurve',
'TerdragonCurve,arms=1',
'TerdragonCurve,arms=2',
'TerdragonCurve,arms=6',
'OctagramSpiral',
'AnvilSpiral',
'AnvilSpiral,wider=1',
'AnvilSpiral,wider=2',
'AnvilSpiral,wider=9',
'AnvilSpiral,wider=17',
'AR2W2Curve',
'AR2W2Curve,start_shape=D2',
'AR2W2Curve,start_shape=B2',
'AR2W2Curve,start_shape=B1rev',
'AR2W2Curve,start_shape=D1rev',
'AR2W2Curve,start_shape=A2rev',
'BetaOmega',
'KochelCurve',
'CincoCurve',
'LTiling',
'LTiling,L_fill=ends',
'LTiling,L_fill=all',
'MPeaks', # but not across gap
'WunderlichMeander',
'FibonacciWordFractal',
# 'CornerReplicate', # not defined yet
'DigitGroups',
'PeanoCurve',
'ZOrderCurve',
'HIndexing',
'SierpinskiCurve',
'SierpinskiCurveStair',
'AztecDiamondRings', # but not across ring end
'DiamondArms',
'SquareArms',
'HexArms',
# 'UlamWarburton', # not really defined yet
# 'UlamWarburtonQuarter', # not really defined yet
'CellularRule54', # but not across gap
# 'CellularRule57', # but not across gap
# 'CellularRule57,mirror=1', # but not across gap
'CellularRule190', # but not across gap
'CellularRule190,mirror=1', # but not across gap
'Rows',
'Columns',
'SquareSpiral',
'DiamondSpiral',
'PentSpiral',
'PentSpiralSkewed',
'HexSpiral',
'HexSpiralSkewed',
'HeptSpiralSkewed',
'PyramidSpiral',
'TriangleSpiral',
'TriangleSpiralSkewed',
'TriangleSpiralSkewed,skew=right',
'TriangleSpiralSkewed,skew=up',
'TriangleSpiralSkewed,skew=down',
# 'SacksSpiral', # sin/cos
# 'TheodorusSpiral', # counting by N
# 'ArchimedeanChords', # counting by N
# 'VogelFloret', # sin/cos
'KnightSpiral',
'SierpinskiArrowheadCentres',
'SierpinskiArrowheadCentres,align=right',
'SierpinskiArrowheadCentres,align=left',
'SierpinskiArrowheadCentres,align=diagonal',
'SierpinskiArrowhead',
'SierpinskiArrowhead,align=right',
'SierpinskiArrowhead,align=left',
'SierpinskiArrowhead,align=diagonal',
# 'SierpinskiTriangle', # not really defined yet
'QuadricCurve',
'QuadricIslands',
'KochSquareflakes',
'KochSnowflakes',
'KochCurve',
'KochPeaks',
'FlowsnakeCentres',
'GosperReplicate',
'GosperSide',
'GosperIslands',
'Flowsnake',
# 'DivisibleColumns', # counting by N
# 'DivisibleColumns,divisor_type=proper',
# 'CoprimeColumns', # counting by N
# 'DiagonalRationals',# counting by N
# 'GcdRationals', # counting by N
# 'GcdRationals,pairs_order=rows_reverse',
# 'GcdRationals,pairs_order=diagonals_down',
# 'GcdRationals,pairs_order=diagonals_up',
# 'FactorRationals', # counting by N
# 'TriangularHypot', # counting by N
# 'TriangularHypot,points=odd',
# 'TriangularHypot,points=all',
# 'TriangularHypot,points=hex',
# 'TriangularHypot,points=hex_rotated',
# 'TriangularHypot,points=hex_centred',
'PythagoreanTree',
# 'Hypot', # searching by N
# 'HypotOctant', # searching by N
# 'PixelRings', # searching by N
# 'FilledRings', # searching by N
# 'MultipleRings', # sin/cos, maybe
'QuintetCentres',
'QuintetCurve',
'QuintetReplicate',
'SquareReplicate',
'ComplexPlus',
'ComplexPlus,realpart=3',
'ComplexMinus',
'ComplexMinus,realpart=3',
'ComplexRevolving',
'ImaginaryBase',
'ImaginaryHalf',
'CubicBase',
# 'File', # not applicable
'Corner',
'PyramidSides',
'Staircase',
'StaircaseAlternating',
'StaircaseAlternating,end_type=square',
);
my @classes = map {"Math::PlanePath::$_"} @modules;
sub module_parse {
my ($mod) = @_;
my ($class, @parameters) = split /,/, $mod;
return ("Math::PlanePath::$class",
map {/(.*?)=(.*)/ or die; ($1 => $2)} @parameters);
}
foreach my $module (@modules) {
### $module
my ($class, %parameters) = module_parse($module);
eval "require $class" or die;
my $path = $class->new (width => 23,
height => 17);
my $arms = $path->arms_count;
my $n = Number::Fraction->new(2**20) + 5;
if ($path->isa('Math::PlanePath::CellularRule190')) {
$n += 1; # not across gap
}
my $orig = Number::Fraction->new('1/3') + $n;
my $frac = Number::Fraction->new('1/3');
my $n_frac = $frac + $n;
my ($x1,$y1) = $path->n_to_xy($n);
### xy1: "$x1,$y1"
my ($x2,$y2) = $path->n_to_xy($n+$arms);
### xy2: "$x2,$y2"
my $dx = $x2 - $x1;
my $dy = $y2 - $y1;
### dxy: "$dx, $dy"
my $want_x = $frac * Number::Fraction->new ($dx) + $x1;
my $want_y = $frac * Number::Fraction->new ($dy) + $y1;
my ($x_frac,$y_frac) = $path->n_to_xy($n_frac);
### $x_frac
### $y_frac
ok ("$x_frac", "$want_x", "$module arms=$arms X frac at n=$n_frac");
ok ("$y_frac", "$want_y", "$module arms=$arms Y frac at n=$n_frac");
}
exit 0;