source: vendor/perl/5.8.8/lib/Math/Trig.t

Last change on this file was 3181, checked in by bird, 18 years ago

perl 5.8.8
File size: 7.8 KB
Line 
1#!./perl
2
3#
4# Regression tests for the Math::Trig package
5#
6# The tests here are quite modest as the Math::Complex tests exercise
7# these interfaces quite vigorously.
8#
9# -- Jarkko Hietaniemi, April 1997
10
11BEGIN {
12 if ($ENV{PERL_CORE}) {
13 chdir 't' if -d 't';
14 @INC = '../lib';
15 }
16}
17
18use Math::Trig 1.03;
19
20my $pip2 = pi / 2;
21
22use strict;
23
24use vars qw($x $y $z);
25
26my $eps = 1e-11;
27
28if ($^O eq 'unicos') { # See lib/Math/Complex.pm and t/lib/complex.t.
29 $eps = 1e-10;
30}
31
32sub near ($$;$) {
33 my $e = defined $_[2] ? $_[2] : $eps;
34 print "# near? $_[0] $_[1] $e\n";
35 $_[1] ? (abs($_[0]/$_[1] - 1) < $e) : abs($_[0]) < $e;
36}
37
38print "1..49\n";
39
40$x = 0.9;
41print 'not ' unless (near(tan($x), sin($x) / cos($x)));
42print "ok 1\n";
43
44print 'not ' unless (near(sinh(2), 3.62686040784702));
45print "ok 2\n";
46
47print 'not ' unless (near(acsch(0.1), 2.99822295029797));
48print "ok 3\n";
49
50$x = asin(2);
51print 'not ' unless (ref $x eq 'Math::Complex');
52print "ok 4\n";
53
54# avoid using Math::Complex here
55$x =~ /^([^-]+)(-[^i]+)i$/;
56($y, $z) = ($1, $2);
57print 'not ' unless (near($y, 1.5707963267949) and
58 near($z, -1.31695789692482));
59print "ok 5\n";
60
61print 'not ' unless (near(deg2rad(90), pi/2));
62print "ok 6\n";
63
64print 'not ' unless (near(rad2deg(pi), 180));
65print "ok 7\n";
66
67use Math::Trig ':radial';
68
69{
70 my ($r,$t,$z) = cartesian_to_cylindrical(1,1,1);
71
72 print 'not ' unless (near($r, sqrt(2))) and
73 (near($t, deg2rad(45))) and
74 (near($z, 1));
75 print "ok 8\n";
76
77 ($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z);
78
79 print 'not ' unless (near($x, 1)) and
80 (near($y, 1)) and
81 (near($z, 1));
82 print "ok 9\n";
83
84 ($r,$t,$z) = cartesian_to_cylindrical(1,1,0);
85
86 print 'not ' unless (near($r, sqrt(2))) and
87 (near($t, deg2rad(45))) and
88 (near($z, 0));
89 print "ok 10\n";
90
91 ($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z);
92
93 print 'not ' unless (near($x, 1)) and
94 (near($y, 1)) and
95 (near($z, 0));
96 print "ok 11\n";
97}
98
99{
100 my ($r,$t,$f) = cartesian_to_spherical(1,1,1);
101
102 print 'not ' unless (near($r, sqrt(3))) and
103 (near($t, deg2rad(45))) and
104 (near($f, atan2(sqrt(2), 1)));
105 print "ok 12\n";
106
107 ($x,$y,$z) = spherical_to_cartesian($r, $t, $f);
108
109 print 'not ' unless (near($x, 1)) and
110 (near($y, 1)) and
111 (near($z, 1));
112 print "ok 13\n";
113
114 ($r,$t,$f) = cartesian_to_spherical(1,1,0);
115
116 print 'not ' unless (near($r, sqrt(2))) and
117 (near($t, deg2rad(45))) and
118 (near($f, deg2rad(90)));
119 print "ok 14\n";
120
121 ($x,$y,$z) = spherical_to_cartesian($r, $t, $f);
122
123 print 'not ' unless (near($x, 1)) and
124 (near($y, 1)) and
125 (near($z, 0));
126 print "ok 15\n";
127}
128
129{
130 my ($r,$t,$z) = cylindrical_to_spherical(spherical_to_cylindrical(1,1,1));
131
132 print 'not ' unless (near($r, 1)) and
133 (near($t, 1)) and
134 (near($z, 1));
135 print "ok 16\n";
136
137 ($r,$t,$z) = spherical_to_cylindrical(cylindrical_to_spherical(1,1,1));
138
139 print 'not ' unless (near($r, 1)) and
140 (near($t, 1)) and
141 (near($z, 1));
142 print "ok 17\n";
143}
144
145{
146 use Math::Trig 'great_circle_distance';
147
148 print 'not '
149 unless (near(great_circle_distance(0, 0, 0, pi/2), pi/2));
150 print "ok 18\n";
151
152 print 'not '
153 unless (near(great_circle_distance(0, 0, pi, pi), pi));
154 print "ok 19\n";
155
156 # London to Tokyo.
157 my @L = (deg2rad(-0.5), deg2rad(90 - 51.3));
158 my @T = (deg2rad(139.8),deg2rad(90 - 35.7));
159
160 my $km = great_circle_distance(@L, @T, 6378);
161
162 print 'not ' unless (near($km, 9605.26637021388));
163 print "ok 20\n";
164}
165
166{
167 my $R2D = 57.295779513082320876798154814169;
168
169 sub frac { $_[0] - int($_[0]) }
170
171 my $lotta_radians = deg2rad(1E+20, 1);
172 print "not " unless near($lotta_radians, 1E+20/$R2D);
173 print "ok 21\n";
174
175 my $negat_degrees = rad2deg(-1E20, 1);
176 print "not " unless near($negat_degrees, -1E+20*$R2D);
177 print "ok 22\n";
178
179 my $posit_degrees = rad2deg(-10000, 1);
180 print "not " unless near($posit_degrees, -10000*$R2D);
181 print "ok 23\n";
182}
183
184{
185 use Math::Trig 'great_circle_direction';
186
187 print 'not '
188 unless (near(great_circle_direction(0, 0, 0, pi/2), pi));
189 print "ok 24\n";
190
191# Retired test: Relies on atan2(0, 0), which is not portable.
192# print 'not '
193# unless (near(great_circle_direction(0, 0, pi, pi), -pi()/2));
194 print "ok 25\n";
195
196 my @London = (deg2rad( -0.167), deg2rad(90 - 51.3));
197 my @Tokyo = (deg2rad( 139.5), deg2rad(90 - 35.7));
198 my @Berlin = (deg2rad ( 13.417), deg2rad(90 - 52.533));
199 my @Paris = (deg2rad ( 2.333), deg2rad(90 - 48.867));
200
201 print 'not '
202 unless (near(rad2deg(great_circle_direction(@London, @Tokyo)),
203 31.791945393073));
204 print "ok 26\n";
205
206 print 'not '
207 unless (near(rad2deg(great_circle_direction(@Tokyo, @London)),
208 336.069766430326));
209 print "ok 27\n";
210
211 print 'not '
212 unless (near(rad2deg(great_circle_direction(@Berlin, @Paris)),
213 246.800348034667));
214
215 print "ok 28\n";
216
217 print 'not '
218 unless (near(rad2deg(great_circle_direction(@Paris, @Berlin)),
219 58.2079877553156));
220 print "ok 29\n";
221
222 use Math::Trig 'great_circle_bearing';
223
224 print 'not '
225 unless (near(rad2deg(great_circle_bearing(@Paris, @Berlin)),
226 58.2079877553156));
227 print "ok 30\n";
228
229 use Math::Trig 'great_circle_waypoint';
230 use Math::Trig 'great_circle_midpoint';
231
232 my ($lon, $lat);
233
234 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.0);
235
236 print 'not ' unless (near($lon, $London[0]));
237 print "ok 31\n";
238
239 print 'not ' unless (near($lat, $pip2 - $London[1]));
240 print "ok 32\n";
241
242 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 1.0);
243
244 print 'not ' unless (near($lon, $Tokyo[0]));
245 print "ok 33\n";
246
247 print 'not ' unless (near($lat, $pip2 - $Tokyo[1]));
248 print "ok 34\n";
249
250 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.5);
251
252 print 'not ' unless (near($lon, 1.55609593577679)); # 89.1577 E
253 print "ok 35\n";
254
255 print 'not ' unless (near($lat, 1.20296099733328)); # 68.9246 N
256 print "ok 36\n";
257
258 ($lon, $lat) = great_circle_midpoint(@London, @Tokyo);
259
260 print 'not ' unless (near($lon, 1.55609593577679)); # 89.1577 E
261 print "ok 37\n";
262
263 print 'not ' unless (near($lat, 1.20296099733328)); # 68.9246 N
264 print "ok 38\n";
265
266 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.25);
267
268 print 'not ' unless (near($lon, 0.516073562850837)); # 29.5688 E
269 print "ok 39\n";
270
271 print 'not ' unless (near($lat, 1.170565013391510)); # 67.0684 N
272 print "ok 40\n";
273 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.75);
274
275 print 'not ' unless (near($lon, 2.17494903805952)); # 124.6154 E
276 print "ok 41\n";
277
278 print 'not ' unless (near($lat, 0.952987032741305)); # 54.6021 N
279 print "ok 42\n";
280
281 use Math::Trig 'great_circle_destination';
282
283 my $dir1 = great_circle_direction(@London, @Tokyo);
284 my $dst1 = great_circle_distance(@London, @Tokyo);
285
286 ($lon, $lat) = great_circle_destination(@London, $dir1, $dst1);
287
288 print 'not ' unless (near($lon, $Tokyo[0]));
289 print "ok 43\n";
290
291 print 'not ' unless (near($lat, $pip2 - $Tokyo[1]));
292 print "ok 44\n";
293
294 my $dir2 = great_circle_direction(@Tokyo, @London);
295 my $dst2 = great_circle_distance(@Tokyo, @London);
296
297 ($lon, $lat) = great_circle_destination(@Tokyo, $dir2, $dst2);
298
299 print 'not ' unless (near($lon, $London[0]));
300 print "ok 45\n";
301
302 print 'not ' unless (near($lat, $pip2 - $London[1]));
303 print "ok 46\n";
304
305 my $dir3 = (great_circle_destination(@London, $dir1, $dst1))[2];
306
307 print 'not ' unless (near($dir3, 2.69379263839118)); # about 154.343 deg
308 print "ok 47\n";
309
310 my $dir4 = (great_circle_destination(@Tokyo, $dir2, $dst2))[2];
311
312 print 'not ' unless (near($dir4, 3.6993902625701)); # about 211.959 deg
313 print "ok 48\n";
314
315 print 'not ' unless (near($dst1, $dst2));
316 print "ok 49\n";
317}
318
319# eof
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