#!./perl
#
# Regression tests for the Math::Trig package
#
# The tests here are quite modest as the Math::Complex tests exercise
# these interfaces quite vigorously.
#
# -- Jarkko Hietaniemi, April 1997
BEGIN {
if ($ENV{PERL_CORE}) {
chdir 't' if -d 't';
@INC = '../lib';
}
}
BEGIN {
eval { require Test::More };
if ($@) {
# We are willing to lose testing in e.g. 5.00504.
print "1..0 # No Test::More, skipping\n";
exit(0);
} else {
import Test::More;
}
}
plan(tests => 69);
use Math::Trig 1.03;
my $pip2 = pi / 2;
use strict;
use vars qw($x $y $z);
my $eps = 1e-11;
if ($^O eq 'unicos') { # See lib/Math/Complex.pm and t/lib/complex.t.
$eps = 1e-10;
}
sub near ($$;$) {
my $e = defined $_[2] ? $_[2] : $eps;
my $d = $_[1] ? abs($_[0]/$_[1] - 1) : abs($_[0]);
print "# near? $_[0] $_[1] : $d : $e\n";
$_[1] ? ($d < $e) : abs($_[0]) < $e;
}
$x = 0.9;
ok(near(tan($x), sin($x) / cos($x)));
ok(near(sinh(2), 3.62686040784702));
ok(near(acsch(0.1), 2.99822295029797));
$x = asin(2);
is(ref $x, 'Math::Complex');
# avoid using Math::Complex here
$x =~ /^([^-]+)(-[^i]+)i$/;
($y, $z) = ($1, $2);
ok(near($y, 1.5707963267949));
ok(near($z, -1.31695789692482));
ok(near(deg2rad(90), pi/2));
ok(near(rad2deg(pi), 180));
use Math::Trig ':radial';
{
my ($r,$t,$z) = cartesian_to_cylindrical(1,1,1);
ok(near($r, sqrt(2)));
ok(near($t, deg2rad(45)));
ok(near($z, 1));
($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z);
ok(near($x, 1));
ok(near($y, 1));
ok(near($z, 1));
($r,$t,$z) = cartesian_to_cylindrical(1,1,0);
ok(near($r, sqrt(2)));
ok(near($t, deg2rad(45)));
ok(near($z, 0));
($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z);
ok(near($x, 1));
ok(near($y, 1));
ok(near($z, 0));
}
{
my ($r,$t,$f) = cartesian_to_spherical(1,1,1);
ok(near($r, sqrt(3)));
ok(near($t, deg2rad(45)));
ok(near($f, atan2(sqrt(2), 1)));
($x,$y,$z) = spherical_to_cartesian($r, $t, $f);
ok(near($x, 1));
ok(near($y, 1));
ok(near($z, 1));
($r,$t,$f) = cartesian_to_spherical(1,1,0);
ok(near($r, sqrt(2)));
ok(near($t, deg2rad(45)));
ok(near($f, deg2rad(90)));
($x,$y,$z) = spherical_to_cartesian($r, $t, $f);
ok(near($x, 1));
ok(near($y, 1));
ok(near($z, 0));
}
{
my ($r,$t,$z) = cylindrical_to_spherical(spherical_to_cylindrical(1,1,1));
ok(near($r, 1));
ok(near($t, 1));
ok(near($z, 1));
($r,$t,$z) = spherical_to_cylindrical(cylindrical_to_spherical(1,1,1));
ok(near($r, 1));
ok(near($t, 1));
ok(near($z, 1));
}
{
use Math::Trig 'great_circle_distance';
ok(near(great_circle_distance(0, 0, 0, pi/2), pi/2));
ok(near(great_circle_distance(0, 0, pi, pi), pi));
# London to Tokyo.
my @L = (deg2rad(-0.5), deg2rad(90 - 51.3));
my @T = (deg2rad(139.8),deg2rad(90 - 35.7));
my $km = great_circle_distance(@L, @T, 6378);
ok(near($km, 9605.26637021388));
}
{
my $R2D = 57.295779513082320876798154814169;
sub frac { $_[0] - int($_[0]) }
my $lotta_radians = deg2rad(1E+20, 1);
ok(near($lotta_radians, 1E+20/$R2D));
my $negat_degrees = rad2deg(-1E20, 1);
ok(near($negat_degrees, -1E+20*$R2D));
my $posit_degrees = rad2deg(-10000, 1);
ok(near($posit_degrees, -10000*$R2D));
}
{
use Math::Trig 'great_circle_direction';
ok(near(great_circle_direction(0, 0, 0, pi/2), pi));
# Retired test: Relies on atan2(0, 0), which is not portable.
# ok(near(great_circle_direction(0, 0, pi, pi), -pi()/2));
my @London = (deg2rad( -0.167), deg2rad(90 - 51.3));
my @Tokyo = (deg2rad( 139.5), deg2rad(90 - 35.7));
my @Berlin = (deg2rad ( 13.417), deg2rad(90 - 52.533));
my @Paris = (deg2rad ( 2.333), deg2rad(90 - 48.867));
ok(near(rad2deg(great_circle_direction(@London, @Tokyo)),
31.791945393073));
ok(near(rad2deg(great_circle_direction(@Tokyo, @London)),
336.069766430326));
ok(near(rad2deg(great_circle_direction(@Berlin, @Paris)),
246.800348034667));
ok(near(rad2deg(great_circle_direction(@Paris, @Berlin)),
58.2079877553156));
use Math::Trig 'great_circle_bearing';
ok(near(rad2deg(great_circle_bearing(@Paris, @Berlin)),
58.2079877553156));
use Math::Trig 'great_circle_waypoint';
use Math::Trig 'great_circle_midpoint';
my ($lon, $lat);
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.0);
ok(near($lon, $London[0]));
ok(near($lat, $pip2 - $London[1]));
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 1.0);
ok(near($lon, $Tokyo[0]));
ok(near($lat, $pip2 - $Tokyo[1]));
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.5);
ok(near($lon, 1.55609593577679)); # 89.1577 E
ok(near($lat, 1.20296099733328)); # 68.9246 N
($lon, $lat) = great_circle_midpoint(@London, @Tokyo);
ok(near($lon, 1.55609593577679)); # 89.1577 E
ok(near($lat, 1.20296099733328)); # 68.9246 N
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.25);
ok(near($lon, 0.516073562850837)); # 29.5688 E
ok(near($lat, 1.170565013391510)); # 67.0684 N
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.75);
ok(near($lon, 2.17494903805952)); # 124.6154 E
ok(near($lat, 0.952987032741305)); # 54.6021 N
use Math::Trig 'great_circle_destination';
my $dir1 = great_circle_direction(@London, @Tokyo);
my $dst1 = great_circle_distance(@London, @Tokyo);
($lon, $lat) = great_circle_destination(@London, $dir1, $dst1);
ok(near($lon, $Tokyo[0]));
ok(near($lat, $pip2 - $Tokyo[1]));
my $dir2 = great_circle_direction(@Tokyo, @London);
my $dst2 = great_circle_distance(@Tokyo, @London);
($lon, $lat) = great_circle_destination(@Tokyo, $dir2, $dst2);
ok(near($lon, $London[0]));
ok(near($lat, $pip2 - $London[1]));
my $dir3 = (great_circle_destination(@London, $dir1, $dst1))[2];
ok(near($dir3, 2.69379263839118)); # about 154.343 deg
my $dir4 = (great_circle_destination(@Tokyo, $dir2, $dst2))[2];
ok(near($dir4, 3.6993902625701)); # about 211.959 deg
ok(near($dst1, $dst2));
}
# eof