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 11use strict; 12use warnings; 13use Test::More tests => 157; 14 15use Math::Trig 1.18; 16use Math::Trig 1.18 qw(:pi Inf); 17 18our $vax_float = (pack("d",1) =~ /^[\x80\x10]\x40/); 19our $has_inf = !$vax_float; 20 21my $pip2 = pi / 2; 22 23use strict; 24 25our($x, $y, $z); 26 27my $eps = 1e-11; 28 29if ($^O eq 'unicos') { # See lib/Math/Complex.pm and t/lib/complex.t. 30 $eps = 1e-10; 31} 32 33sub near { 34 my $e = defined $_[2] ? $_[2] : $eps; 35 my $d = $_[1] ? abs($_[0]/$_[1] - 1) : abs($_[0]); 36 print "# near? $_[0] $_[1] : $d : $e\n"; 37 $_[1] ? ($d < $e) : abs($_[0]) < $e; 38} 39 40print "# Sanity checks\n"; 41 42ok(near(sin(1), 0.841470984807897)); 43ok(near(cos(1), 0.54030230586814)); 44ok(near(tan(1), 1.5574077246549)); 45 46ok(near(sec(1), 1.85081571768093)); 47ok(near(csc(1), 1.18839510577812)); 48ok(near(cot(1), 0.642092615934331)); 49 50ok(near(asin(1), 1.5707963267949)); 51ok(near(acos(1), 0)); 52ok(near(atan(1), 0.785398163397448)); 53 54ok(near(asec(1), 0)); 55ok(near(acsc(1), 1.5707963267949)); 56ok(near(acot(1), 0.785398163397448)); 57 58ok(near(sinh(1), 1.1752011936438)); 59ok(near(cosh(1), 1.54308063481524)); 60ok(near(tanh(1), 0.761594155955765)); 61 62ok(near(sech(1), 0.648054273663885)); 63ok(near(csch(1), 0.850918128239322)); 64ok(near(coth(1), 1.31303528549933)); 65 66ok(near(asinh(1), 0.881373587019543)); 67ok(near(acosh(1), 0)); 68ok(near(atanh(0.9), 1.47221948958322)); # atanh(1.0) would be an error. 69 70ok(near(asech(0.9), 0.467145308103262)); 71ok(near(acsch(2), 0.481211825059603)); 72ok(near(acoth(2), 0.549306144334055)); 73 74print "# Basics\n"; 75 76$x = 0.9; 77ok(near(tan($x), sin($x) / cos($x))); 78 79ok(near(sinh(2), 3.62686040784702)); 80 81ok(near(acsch(0.1), 2.99822295029797)); 82 83$x = asin(2); 84is(ref $x, 'Math::Complex'); 85 86# avoid using Math::Complex here 87$x =~ /^([^-]+)(-[^i]+)i$/; 88($y, $z) = ($1, $2); 89ok(near($y, 1.5707963267949)); 90ok(near($z, -1.31695789692482)); 91 92ok(near(deg2rad(90), pi/2)); 93 94ok(near(rad2deg(pi), 180)); 95 96use Math::Trig ':radial'; 97 98{ 99 my ($r,$t,$z) = cartesian_to_cylindrical(1,1,1); 100 101 ok(near($r, sqrt(2))); 102 ok(near($t, deg2rad(45))); 103 ok(near($z, 1)); 104 105 ($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z); 106 107 ok(near($x, 1)); 108 ok(near($y, 1)); 109 ok(near($z, 1)); 110 111 ($r,$t,$z) = cartesian_to_cylindrical(1,1,0); 112 113 ok(near($r, sqrt(2))); 114 ok(near($t, deg2rad(45))); 115 ok(near($z, 0)); 116 117 ($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z); 118 119 ok(near($x, 1)); 120 ok(near($y, 1)); 121 ok(near($z, 0)); 122} 123 124{ 125 my ($r,$t,$f) = cartesian_to_spherical(1,1,1); 126 127 ok(near($r, sqrt(3))); 128 ok(near($t, deg2rad(45))); 129 ok(near($f, atan2(sqrt(2), 1))); 130 131 ($x,$y,$z) = spherical_to_cartesian($r, $t, $f); 132 133 ok(near($x, 1)); 134 ok(near($y, 1)); 135 ok(near($z, 1)); 136 137 ($r,$t,$f) = cartesian_to_spherical(1,1,0); 138 139 ok(near($r, sqrt(2))); 140 ok(near($t, deg2rad(45))); 141 ok(near($f, deg2rad(90))); 142 143 ($x,$y,$z) = spherical_to_cartesian($r, $t, $f); 144 145 ok(near($x, 1)); 146 ok(near($y, 1)); 147 ok(near($z, 0)); 148} 149 150{ 151 my ($r,$t,$z) = cylindrical_to_spherical(spherical_to_cylindrical(1,1,1)); 152 153 ok(near($r, 1)); 154 ok(near($t, 1)); 155 ok(near($z, 1)); 156 157 ($r,$t,$z) = spherical_to_cylindrical(cylindrical_to_spherical(1,1,1)); 158 159 ok(near($r, 1)); 160 ok(near($t, 1)); 161 ok(near($z, 1)); 162} 163 164{ 165 use Math::Trig 'great_circle_distance'; 166 167 ok(near(great_circle_distance(0, 0, 0, pi/2), pi/2)); 168 169 ok(near(great_circle_distance(0, 0, pi, pi), pi)); 170 171 # London to Tokyo. 172 my @L = (deg2rad(-0.5), deg2rad(90 - 51.3)); 173 my @T = (deg2rad(139.8), deg2rad(90 - 35.7)); 174 175 my $km = great_circle_distance(@L, @T, 6378); 176 177 ok(near($km, 9605.26637021388)); 178} 179 180{ 181 my $R2D = 57.295779513082320876798154814169; 182 183 sub frac { $_[0] - int($_[0]) } 184 185 my $lotta_radians = deg2rad(1E+20, 1); 186 ok(near($lotta_radians, 1E+20/$R2D)); 187 188 my $negat_degrees = rad2deg(-1E20, 1); 189 ok(near($negat_degrees, -1E+20*$R2D)); 190 191 my $posit_degrees = rad2deg(-10000, 1); 192 ok(near($posit_degrees, -10000*$R2D)); 193} 194 195{ 196 use Math::Trig 'great_circle_direction'; 197 198 ok(near(great_circle_direction(0, 0, 0, pi/2), pi)); 199 200# Retired test: Relies on atan2(0, 0), which is not portable. 201# ok(near(great_circle_direction(0, 0, pi, pi), -pi()/2)); 202 203 my @London = (deg2rad( -0.167), deg2rad(90 - 51.3)); 204 my @Tokyo = (deg2rad( 139.5), deg2rad(90 - 35.7)); 205 my @Berlin = (deg2rad ( 13.417), deg2rad(90 - 52.533)); 206 my @Paris = (deg2rad ( 2.333), deg2rad(90 - 48.867)); 207 208 ok(near(rad2deg(great_circle_direction(@London, @Tokyo)), 209 31.791945393073)); 210 211 ok(near(rad2deg(great_circle_direction(@Tokyo, @London)), 212 336.069766430326)); 213 214 ok(near(rad2deg(great_circle_direction(@Berlin, @Paris)), 215 246.800348034667)); 216 217 ok(near(rad2deg(great_circle_direction(@Paris, @Berlin)), 218 58.2079877553156)); 219 220 use Math::Trig 'great_circle_bearing'; 221 222 ok(near(rad2deg(great_circle_bearing(@Paris, @Berlin)), 223 58.2079877553156)); 224 225 use Math::Trig 'great_circle_waypoint'; 226 use Math::Trig 'great_circle_midpoint'; 227 228 my ($lon, $lat); 229 230 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.0); 231 232 ok(near($lon, $London[0])); 233 234 ok(near($lat, $London[1])); 235 236 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 1.0); 237 238 ok(near($lon, $Tokyo[0])); 239 240 ok(near($lat, $Tokyo[1])); 241 242 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.5); 243 244 ok(near($lon, 1.55609593577679)); # 89.16 E 245 246 ok(near($lat, 0.36783532946162)); # 68.93 N 247 248 ($lon, $lat) = great_circle_midpoint(@London, @Tokyo); 249 250 ok(near($lon, 1.55609593577679)); # 89.16 E 251 252 ok(near($lat, 0.367835329461615)); # 68.93 N 253 254 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.25); 255 256 ok(near($lon, 0.516073562850837)); # 29.57 E 257 258 ok(near($lat, 0.400231313403387)); # 67.07 N 259 260 ($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.75); 261 262 ok(near($lon, 2.17494903805952)); # 124.62 E 263 264 ok(near($lat, 0.617809294053591)); # 54.60 N 265 266 use Math::Trig 'great_circle_destination'; 267 268 my $dir1 = great_circle_direction(@London, @Tokyo); 269 my $dst1 = great_circle_distance(@London, @Tokyo); 270 271 ($lon, $lat) = great_circle_destination(@London, $dir1, $dst1); 272 273 ok(near($lon, $Tokyo[0])); 274 275 ok(near($lat, $pip2 - $Tokyo[1])); 276 277 my $dir2 = great_circle_direction(@Tokyo, @London); 278 my $dst2 = great_circle_distance(@Tokyo, @London); 279 280 ($lon, $lat) = great_circle_destination(@Tokyo, $dir2, $dst2); 281 282 ok(near($lon, $London[0])); 283 284 ok(near($lat, $pip2 - $London[1])); 285 286 my $dir3 = (great_circle_destination(@London, $dir1, $dst1))[2]; 287 288 ok(near($dir3, 2.69379263839118)); # about 154.343 deg 289 290 my $dir4 = (great_circle_destination(@Tokyo, $dir2, $dst2))[2]; 291 292 ok(near($dir4, 3.6993902625701)); # about 211.959 deg 293 294 ok(near($dst1, $dst2)); 295} 296 297SKIP: { 298# With netbsd-vax (or any vax) there is neither Inf, nor 1e40. 299skip("different float range", 42) if $vax_float; 300skip("no inf", 42) unless $has_inf; 301 302print "# Infinity\n"; 303 304my $BigDouble = eval '1e40'; 305 306# E.g. netbsd-alpha core dumps on Inf arith without this. 307local $SIG{FPE} = sub { }; 308 309ok(Inf() > $BigDouble); # This passes in netbsd-alpha. 310ok(Inf() + $BigDouble > $BigDouble); # This coredumps in netbsd-alpha. 311ok(Inf() + $BigDouble == Inf()); 312ok(Inf() - $BigDouble > $BigDouble); 313ok(Inf() - $BigDouble == Inf()); 314ok(Inf() * $BigDouble > $BigDouble); 315ok(Inf() * $BigDouble == Inf()); 316ok(Inf() / $BigDouble > $BigDouble); 317ok(Inf() / $BigDouble == Inf()); 318 319ok(-Inf() < -$BigDouble); 320ok(-Inf() + $BigDouble < $BigDouble); 321ok(-Inf() + $BigDouble == -Inf()); 322ok(-Inf() - $BigDouble < -$BigDouble); 323ok(-Inf() - $BigDouble == -Inf()); 324ok(-Inf() * $BigDouble < -$BigDouble); 325ok(-Inf() * $BigDouble == -Inf()); 326ok(-Inf() / $BigDouble < -$BigDouble); 327ok(-Inf() / $BigDouble == -Inf()); 328 329print "# sinh/sech/cosh/csch/tanh/coth unto infinity\n"; 330 331ok(near(sinh(100), eval '1.3441e+43', 1e-3)); 332ok(near(sech(100), eval '7.4402e-44', 1e-3)); 333ok(near(cosh(100), eval '1.3441e+43', 1e-3)); 334ok(near(csch(100), eval '7.4402e-44', 1e-3)); 335ok(near(tanh(100), 1)); 336ok(near(coth(100), 1)); 337 338ok(near(sinh(-100), eval '-1.3441e+43', 1e-3)); 339ok(near(sech(-100), eval ' 7.4402e-44', 1e-3)); 340ok(near(cosh(-100), eval ' 1.3441e+43', 1e-3)); 341ok(near(csch(-100), eval '-7.4402e-44', 1e-3)); 342ok(near(tanh(-100), -1)); 343ok(near(coth(-100), -1)); 344 345cmp_ok(sinh(1e5), '==', Inf()); 346cmp_ok(sech(1e5), '==', 0); 347cmp_ok(cosh(1e5), '==', Inf()); 348cmp_ok(csch(1e5), '==', 0); 349cmp_ok(tanh(1e5), '==', 1); 350cmp_ok(coth(1e5), '==', 1); 351 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); 358 359} 360 361print "# great_circle_distance with small angles\n"; 362 363for my $e (qw(1e-2 1e-3 1e-4 1e-5)) { 364 # Can't assume == 0 because of floating point fuzz, 365 # but let's hope for at least < $e. 366 cmp_ok(great_circle_distance(0, $e, 0, $e), '<', $e, 367 "great_circle_distance(0, $e, 0, $e) < $e"); 368} 369 370for my $e (qw(1e-5 1e-6 1e-7 1e-8)) { 371 # Verify that the distance is positive for points close together. A poor 372 # algorithm is likely to give a distance of zero in some of these cases. 373 cmp_ok(great_circle_distance(2, 2, 2, 2+$e), '>', 0, 374 "great_circle_distance(2, 2, 2, " . (2+$e) . ") > 0"); 375} 376 377print "# asin_real, acos_real\n"; 378 379is(acos_real(-2.0), pi); 380is(acos_real(-1.0), pi); 381is(acos_real(-0.5), acos(-0.5)); 382is(acos_real( 0.0), acos( 0.0)); 383is(acos_real( 0.5), acos( 0.5)); 384is(acos_real( 1.0), 0); 385is(acos_real( 2.0), 0); 386 387is(asin_real(-2.0), -&pip2); 388is(asin_real(-1.0), -&pip2); 389is(asin_real(-0.5), asin(-0.5)); 390is(asin_real( 0.0), asin( 0.0)); 391is(asin_real( 0.5), asin( 0.5)); 392is(asin_real( 1.0), pip2); 393is(asin_real( 2.0), pip2); 394 395# eof 396