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[perl5.git] / lib / Math / Trig.t
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1#!./perl
2
3#
4# Regression tests for the Math::Trig package
5#
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6# The tests here are quite modest as the Math::Complex tests exercise
7# these interfaces quite vigorously.
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8#
9# -- Jarkko Hietaniemi, April 1997
10
11BEGIN {
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12 if ($ENV{PERL_CORE}) {
13 chdir 't' if -d 't';
14 @INC = '../lib';
15 }
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16}
17
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18BEGIN {
19 eval { require Test::More };
20 if ($@) {
21 # We are willing to lose testing in e.g. 5.00504.
22 print "1..0 # No Test::More, skipping\n";
23 exit(0);
24 } else {
25 import Test::More;
26 }
27}
28
1515bec6 29plan(tests => 135);
affad850 30
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31use Math::Trig 1.09;
32use Math::Trig 1.09 qw(Inf);
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33
34my $pip2 = pi / 2;
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35
36use strict;
37
38use vars qw($x $y $z);
39
40my $eps = 1e-11;
41
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42if ($^O eq 'unicos') { # See lib/Math/Complex.pm and t/lib/complex.t.
43 $eps = 1e-10;
44}
45
5aabfad6 46sub near ($$;$) {
e64f0054 47 my $e = defined $_[2] ? $_[2] : $eps;
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48 my $d = $_[1] ? abs($_[0]/$_[1] - 1) : abs($_[0]);
49 print "# near? $_[0] $_[1] : $d : $e\n";
50 $_[1] ? ($d < $e) : abs($_[0]) < $e;
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51}
52
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53print "# Sanity checks\n";
54
55ok(near(sin(1), 0.841470984807897));
56ok(near(cos(1), 0.54030230586814));
57ok(near(tan(1), 1.5574077246549));
58
59ok(near(sec(1), 1.85081571768093));
60ok(near(csc(1), 1.18839510577812));
61ok(near(cot(1), 0.642092615934331));
62
63ok(near(asin(1), 1.5707963267949));
64ok(near(acos(1), 0));
65ok(near(atan(1), 0.785398163397448));
66
67ok(near(asec(1), 0));
68ok(near(acsc(1), 1.5707963267949));
69ok(near(acot(1), 0.785398163397448));
70
71ok(near(sinh(1), 1.1752011936438));
72ok(near(cosh(1), 1.54308063481524));
73ok(near(tanh(1), 0.761594155955765));
74
75ok(near(sech(1), 0.648054273663885));
76ok(near(csch(1), 0.850918128239322));
77ok(near(coth(1), 1.31303528549933));
78
79ok(near(asinh(1), 0.881373587019543));
80ok(near(acosh(1), 0));
81ok(near(atanh(0.9), 1.47221948958322)); # atanh(1.0) would be an error.
82
83ok(near(asech(0.9), 0.467145308103262));
84ok(near(acsch(2), 0.481211825059603));
85ok(near(acoth(2), 0.549306144334055));
86
87print "# Basics\n";
88
5aabfad6 89$x = 0.9;
affad850 90ok(near(tan($x), sin($x) / cos($x)));
5aabfad6 91
affad850 92ok(near(sinh(2), 3.62686040784702));
5aabfad6 93
affad850 94ok(near(acsch(0.1), 2.99822295029797));
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95
96$x = asin(2);
affad850 97is(ref $x, 'Math::Complex');
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98
99# avoid using Math::Complex here
100$x =~ /^([^-]+)(-[^i]+)i$/;
101($y, $z) = ($1, $2);
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102ok(near($y, 1.5707963267949));
103ok(near($z, -1.31695789692482));
5aabfad6 104
affad850 105ok(near(deg2rad(90), pi/2));
5aabfad6 106
affad850 107ok(near(rad2deg(pi), 180));
ace5de91 108
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109use Math::Trig ':radial';
110
111{
112 my ($r,$t,$z) = cartesian_to_cylindrical(1,1,1);
113
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114 ok(near($r, sqrt(2)));
115 ok(near($t, deg2rad(45)));
116 ok(near($z, 1));
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117
118 ($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z);
119
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120 ok(near($x, 1));
121 ok(near($y, 1));
122 ok(near($z, 1));
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123
124 ($r,$t,$z) = cartesian_to_cylindrical(1,1,0);
125
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126 ok(near($r, sqrt(2)));
127 ok(near($t, deg2rad(45)));
128 ok(near($z, 0));
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129
130 ($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z);
131
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132 ok(near($x, 1));
133 ok(near($y, 1));
134 ok(near($z, 0));
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135}
136
137{
138 my ($r,$t,$f) = cartesian_to_spherical(1,1,1);
139
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140 ok(near($r, sqrt(3)));
141 ok(near($t, deg2rad(45)));
142 ok(near($f, atan2(sqrt(2), 1)));
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143
144 ($x,$y,$z) = spherical_to_cartesian($r, $t, $f);
145
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146 ok(near($x, 1));
147 ok(near($y, 1));
148 ok(near($z, 1));
149
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150 ($r,$t,$f) = cartesian_to_spherical(1,1,0);
151
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152 ok(near($r, sqrt(2)));
153 ok(near($t, deg2rad(45)));
154 ok(near($f, deg2rad(90)));
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155
156 ($x,$y,$z) = spherical_to_cartesian($r, $t, $f);
157
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158 ok(near($x, 1));
159 ok(near($y, 1));
160 ok(near($z, 0));
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161}
162
163{
164 my ($r,$t,$z) = cylindrical_to_spherical(spherical_to_cylindrical(1,1,1));
165
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166 ok(near($r, 1));
167 ok(near($t, 1));
168 ok(near($z, 1));
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169
170 ($r,$t,$z) = spherical_to_cylindrical(cylindrical_to_spherical(1,1,1));
171
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172 ok(near($r, 1));
173 ok(near($t, 1));
174 ok(near($z, 1));
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175}
176
177{
9db5a202 178 use Math::Trig 'great_circle_distance';
d54bf66f 179
affad850 180 ok(near(great_circle_distance(0, 0, 0, pi/2), pi/2));
d54bf66f 181
affad850 182 ok(near(great_circle_distance(0, 0, pi, pi), pi));
d54bf66f 183
9db5a202 184 # London to Tokyo.
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185 my @L = (deg2rad(-0.5), deg2rad(90 - 51.3));
186 my @T = (deg2rad(139.8), deg2rad(90 - 35.7));
d54bf66f 187
9db5a202 188 my $km = great_circle_distance(@L, @T, 6378);
d54bf66f 189
affad850 190 ok(near($km, 9605.26637021388));
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191}
192
193{
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194 my $R2D = 57.295779513082320876798154814169;
195
196 sub frac { $_[0] - int($_[0]) }
197
9db5a202 198 my $lotta_radians = deg2rad(1E+20, 1);
affad850 199 ok(near($lotta_radians, 1E+20/$R2D));
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200
201 my $negat_degrees = rad2deg(-1E20, 1);
affad850 202 ok(near($negat_degrees, -1E+20*$R2D));
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203
204 my $posit_degrees = rad2deg(-10000, 1);
affad850 205 ok(near($posit_degrees, -10000*$R2D));
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206}
207
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208{
209 use Math::Trig 'great_circle_direction';
210
affad850 211 ok(near(great_circle_direction(0, 0, 0, pi/2), pi));
7e5f197a 212
bf5f1b4c 213# Retired test: Relies on atan2(0, 0), which is not portable.
affad850 214# ok(near(great_circle_direction(0, 0, pi, pi), -pi()/2));
7e5f197a 215
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216 my @London = (deg2rad( -0.167), deg2rad(90 - 51.3));
217 my @Tokyo = (deg2rad( 139.5), deg2rad(90 - 35.7));
218 my @Berlin = (deg2rad ( 13.417), deg2rad(90 - 52.533));
219 my @Paris = (deg2rad ( 2.333), deg2rad(90 - 48.867));
7e5f197a 220
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221 ok(near(rad2deg(great_circle_direction(@London, @Tokyo)),
222 31.791945393073));
bf5f1b4c 223
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224 ok(near(rad2deg(great_circle_direction(@Tokyo, @London)),
225 336.069766430326));
d139edd6 226
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227 ok(near(rad2deg(great_circle_direction(@Berlin, @Paris)),
228 246.800348034667));
d139edd6 229
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230 ok(near(rad2deg(great_circle_direction(@Paris, @Berlin)),
231 58.2079877553156));
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232
233 use Math::Trig 'great_circle_bearing';
234
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235 ok(near(rad2deg(great_circle_bearing(@Paris, @Berlin)),
236 58.2079877553156));
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237
238 use Math::Trig 'great_circle_waypoint';
239 use Math::Trig 'great_circle_midpoint';
240
241 my ($lon, $lat);
242
243 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.0);
244
affad850 245 ok(near($lon, $London[0]));
bf5f1b4c 246
618e05e9 247 ok(near($lat, $London[1]));
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248
249 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 1.0);
250
affad850 251 ok(near($lon, $Tokyo[0]));
bf5f1b4c 252
618e05e9 253 ok(near($lat, $Tokyo[1]));
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254
255 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.5);
256
618e05e9 257 ok(near($lon, 1.55609593577679)); # 89.16 E
bf5f1b4c 258
618e05e9 259 ok(near($lat, 0.36783532946162)); # 68.93 N
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260
261 ($lon, $lat) = great_circle_midpoint(@London, @Tokyo);
262
618e05e9 263 ok(near($lon, 1.55609593577679)); # 89.16 E
bf5f1b4c 264
618e05e9 265 ok(near($lat, 0.367835329461615)); # 68.93 N
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266
267 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.25);
268
618e05e9 269 ok(near($lon, 0.516073562850837)); # 29.57 E
affad850 270
618e05e9 271 ok(near($lat, 0.400231313403387)); # 67.07 N
bf5f1b4c 272
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273 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.75);
274
618e05e9 275 ok(near($lon, 2.17494903805952)); # 124.62 E
bf5f1b4c 276
618e05e9 277 ok(near($lat, 0.617809294053591)); # 54.60 N
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278
279 use Math::Trig 'great_circle_destination';
280
281 my $dir1 = great_circle_direction(@London, @Tokyo);
282 my $dst1 = great_circle_distance(@London, @Tokyo);
283
284 ($lon, $lat) = great_circle_destination(@London, $dir1, $dst1);
285
affad850 286 ok(near($lon, $Tokyo[0]));
bf5f1b4c 287
affad850 288 ok(near($lat, $pip2 - $Tokyo[1]));
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289
290 my $dir2 = great_circle_direction(@Tokyo, @London);
291 my $dst2 = great_circle_distance(@Tokyo, @London);
292
293 ($lon, $lat) = great_circle_destination(@Tokyo, $dir2, $dst2);
294
affad850 295 ok(near($lon, $London[0]));
bf5f1b4c 296
affad850 297 ok(near($lat, $pip2 - $London[1]));
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298
299 my $dir3 = (great_circle_destination(@London, $dir1, $dst1))[2];
300
affad850 301 ok(near($dir3, 2.69379263839118)); # about 154.343 deg
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302
303 my $dir4 = (great_circle_destination(@Tokyo, $dir2, $dst2))[2];
304
affad850 305 ok(near($dir4, 3.6993902625701)); # about 211.959 deg
bf5f1b4c 306
affad850 307 ok(near($dst1, $dst2));
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308}
309
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310print "# Infinity\n";
311
312my $BigDouble = 1e40;
313
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314local $SIG{FPE} = { }; # E.g. netbsd-alpha core dumps on Inf arith
315
316ok(Inf() > $BigDouble); # This passes in netbsd-alpha.
317ok(Inf() + $BigDouble > $BigDouble); # This coredumps.
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318ok(Inf() + $BigDouble == Inf());
319ok(Inf() - $BigDouble > $BigDouble);
320ok(Inf() - $BigDouble == Inf());
321ok(Inf() * $BigDouble > $BigDouble);
322ok(Inf() * $BigDouble == Inf());
323ok(Inf() / $BigDouble > $BigDouble);
324ok(Inf() / $BigDouble == Inf());
325
326ok(-Inf() < -$BigDouble);
327ok(-Inf() + $BigDouble < $BigDouble);
328ok(-Inf() + $BigDouble == -Inf());
329ok(-Inf() - $BigDouble < -$BigDouble);
330ok(-Inf() - $BigDouble == -Inf());
331ok(-Inf() * $BigDouble < -$BigDouble);
332ok(-Inf() * $BigDouble == -Inf());
333ok(-Inf() / $BigDouble < -$BigDouble);
334ok(-Inf() / $BigDouble == -Inf());
335
336print "# sinh/sech/cosh/csch/tanh/coth unto infinity\n";
337
338ok(near(sinh(100), 1.3441e+43, 1e-3));
339ok(near(sech(100), 7.4402e-44, 1e-3));
340ok(near(cosh(100), 1.3441e+43, 1e-3));
341ok(near(csch(100), 7.4402e-44, 1e-3));
342ok(near(tanh(100), 1));
343ok(near(coth(100), 1));
344
345ok(near(sinh(-100), -1.3441e+43, 1e-3));
346ok(near(sech(-100), 7.4402e-44, 1e-3));
347ok(near(cosh(-100), 1.3441e+43, 1e-3));
348ok(near(csch(-100), -7.4402e-44, 1e-3));
349ok(near(tanh(-100), -1));
350ok(near(coth(-100), -1));
351
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352cmp_ok(sinh(1e5), '==', Inf());
353cmp_ok(sech(1e5), '==', 0);
354cmp_ok(cosh(1e5), '==', Inf());
355cmp_ok(csch(1e5), '==', 0);
356cmp_ok(tanh(1e5), '==', 1);
357cmp_ok(coth(1e5), '==', 1);
358
359cmp_ok(sinh(-1e5), '==', -Inf());
360cmp_ok(sech(-1e5), '==', 0);
361cmp_ok(cosh(-1e5), '==', Inf());
362cmp_ok(csch(-1e5), '==', 0);
363cmp_ok(tanh(-1e5), '==', -1);
364cmp_ok(coth(-1e5), '==', -1);
1515bec6 365
5aabfad6 366# eof