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 320