1#!./perl 2 3# $RCSfile: complex.t,v $ 4# 5# Regression tests for the Math::Complex pacakge 6# -- Raphael Manfredi since Sep 1996 7# -- Jarkko Hietaniemi since Mar 1997 8# -- Daniel S. Lewart since Sep 1997 9 10BEGIN { 11 chdir 't' if -d 't'; 12 @INC = '../lib'; 13} 14 15use Math::Complex; 16 17use vars qw($VERSION); 18 19$VERSION = 1.92; 20 21my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val); 22 23$test = 0; 24$| = 1; 25my @script = ( 26 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' . 27 "\n\n" 28); 29my $eps = 1e-13; 30 31if ($^O eq 'unicos') { # For some reason root() produces very inaccurate 32 $eps = 1e-10; # results in Cray UNICOS, and occasionally also 33} # cos(), sin(), cosh(), sinh(). The division 34 # of doubles is the current suspect. 35 36while (<DATA>) { 37 s/^\s+//; 38 next if $_ eq '' || /^\#/; 39 chomp; 40 $test_set = 0; # Assume not a test over a set of values 41 if (/^&(.+)/) { 42 $op = $1; 43 next; 44 } 45 elsif (/^\{(.+)\}/) { 46 set($1, \@set, \@val); 47 next; 48 } 49 elsif (s/^\|//) { 50 $test_set = 1; # Requests we loop over the set... 51 } 52 my @args = split(/:/); 53 if ($test_set == 1) { 54 my $i; 55 for ($i = 0; $i < @set; $i++) { 56 # complex number 57 $target = $set[$i]; 58 # textual value as found in set definition 59 $zvalue = $val[$i]; 60 test($zvalue, $target, @args); 61 } 62 } else { 63 test($op, undef, @args); 64 } 65} 66 67# 68 69sub test_mutators { 70 my $op; 71 72 $test++; 73push(@script, <<'EOT'); 74{ 75 my $z = cplx( 1, 1); 76 $z->Re(2); 77 $z->Im(3); 78 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; 79 print 'not ' unless Re($z) == 2 and Im($z) == 3; 80EOT 81 push(@script, qq(print "ok $test\\n"}\n)); 82 83 $test++; 84push(@script, <<'EOT'); 85{ 86 my $z = cplx( 1, 1); 87 $z->abs(3 * sqrt(2)); 88 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; 89 print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and 90 (arg($z) - pi / 4 ) < $eps and 91 (Re($z) - 3 ) < $eps and 92 (Im($z) - 3 ) < $eps; 93EOT 94 push(@script, qq(print "ok $test\\n"}\n)); 95 96 $test++; 97push(@script, <<'EOT'); 98{ 99 my $z = cplx( 1, 1); 100 $z->arg(-3 / 4 * pi); 101 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n"; 102 print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and 103 (abs($z) - sqrt(2) ) < $eps and 104 (Re($z) + 1 ) < $eps and 105 (Im($z) + 1 ) < $eps; 106EOT 107 push(@script, qq(print "ok $test\\n"}\n)); 108} 109 110test_mutators(); 111 112my $constants = ' 113my $i = cplx(0, 1); 114my $pi = cplx(pi, 0); 115my $pii = cplx(0, pi); 116my $pip2 = cplx(pi/2, 0); 117my $zero = cplx(0, 0); 118'; 119 120push(@script, $constants); 121 122 123# test the divbyzeros 124 125sub test_dbz { 126 for my $op (@_) { 127 $test++; 128 push(@script, <<EOT); 129 eval '$op'; 130 (\$bad) = (\$@ =~ /(.+)/); 131 print "# $test op = $op divbyzero? \$bad...\n"; 132 print 'not ' unless (\$@ =~ /Division by zero/); 133EOT 134 push(@script, qq(print "ok $test\\n";\n)); 135 } 136} 137 138# test the logofzeros 139 140sub test_loz { 141 for my $op (@_) { 142 $test++; 143 push(@script, <<EOT); 144 eval '$op'; 145 (\$bad) = (\$@ =~ /(.+)/); 146 print "# $test op = $op logofzero? \$bad...\n"; 147 print 'not ' unless (\$@ =~ /Logarithm of zero/); 148EOT 149 push(@script, qq(print "ok $test\\n";\n)); 150 } 151} 152 153test_dbz( 154 'i/0', 155 'acot(0)', 156 'acot(+$i)', 157# 'acoth(-1)', # Log of zero. 158 'acoth(0)', 159 'acoth(+1)', 160 'acsc(0)', 161 'acsch(0)', 162 'asec(0)', 163 'asech(0)', 164 'atan($i)', 165# 'atanh(-1)', # Log of zero. 166 'atanh(+1)', 167 'cot(0)', 168 'coth(0)', 169 'csc(0)', 170 'csch(0)', 171 ); 172 173test_loz( 174 'log($zero)', 175 'atan(-$i)', 176 'acot(-$i)', 177 'atanh(-1)', 178 'acoth(-1)', 179 ); 180 181# test the bad roots 182 183sub test_broot { 184 for my $op (@_) { 185 $test++; 186 push(@script, <<EOT); 187 eval 'root(2, $op)'; 188 (\$bad) = (\$@ =~ /(.+)/); 189 print "# $test op = $op badroot? \$bad...\n"; 190 print 'not ' unless (\$@ =~ /root rank must be/); 191EOT 192 push(@script, qq(print "ok $test\\n";\n)); 193 } 194} 195 196test_broot(qw(-3 -2.1 0 0.99)); 197 198sub test_display_format { 199 $test++; 200 push @script, <<EOS; 201 print "# package display_format cartesian?\n"; 202 print "not " unless Math::Complex->display_format eq 'cartesian'; 203 print "ok $test\n"; 204EOS 205 206 push @script, <<EOS; 207 my \$j = (root(1,3))[1]; 208 209 \$j->display_format('polar'); 210EOS 211 212 $test++; 213 push @script, <<EOS; 214 print "# j display_format polar?\n"; 215 print "not " unless \$j->display_format eq 'polar'; 216 print "ok $test\n"; 217EOS 218 219 $test++; 220 push @script, <<EOS; 221 print "# j = \$j\n"; 222 print "not " unless "\$j" eq "[1,2pi/3]"; 223 print "ok $test\n"; 224 225 my %display_format; 226 227 %display_format = \$j->display_format; 228EOS 229 230 $test++; 231 push @script, <<EOS; 232 print "# display_format{style} polar?\n"; 233 print "not " unless \$display_format{style} eq 'polar'; 234 print "ok $test\n"; 235EOS 236 237 $test++; 238 push @script, <<EOS; 239 print "# keys %display_format == 2?\n"; 240 print "not " unless keys %display_format == 2; 241 print "ok $test\n"; 242 243 \$j->display_format('style' => 'cartesian', 'format' => '%.5f'); 244EOS 245 246 $test++; 247 push @script, <<EOS; 248 print "# j = \$j\n"; 249 print "not " unless "\$j" eq "-0.50000+0.86603i"; 250 print "ok $test\n"; 251 252 %display_format = \$j->display_format; 253EOS 254 255 $test++; 256 push @script, <<EOS; 257 print "# display_format{format} %.5f?\n"; 258 print "not " unless \$display_format{format} eq '%.5f'; 259 print "ok $test\n"; 260EOS 261 262 $test++; 263 push @script, <<EOS; 264 print "# keys %display_format == 3?\n"; 265 print "not " unless keys %display_format == 3; 266 print "ok $test\n"; 267 268 \$j->display_format('format' => undef); 269EOS 270 271 $test++; 272 push @script, <<EOS; 273 print "# j = \$j\n"; 274 print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/; 275 print "ok $test\n"; 276 277 \$j->display_format('style' => 'polar', 'polar_pretty_print' => 0); 278EOS 279 280 $test++; 281 push @script, <<EOS; 282 print "# j = \$j\n"; 283 print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/; 284 print "ok $test\n"; 285 286 \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)'); 287EOS 288 289 $test++; 290 push @script, <<EOS; 291 print "# j = \$j\n"; 292 print "not " unless "\$j" eq "(-0.5)+(0.86603)i"; 293 print "ok $test\n"; 294EOS 295 296 $test++; 297 push @script, <<EOS; 298 print "# j display_format cartesian?\n"; 299 print "not " unless \$j->display_format eq 'cartesian'; 300 print "ok $test\n"; 301EOS 302} 303 304test_display_format(); 305 306sub test_remake { 307 $test++; 308 push @script, <<EOS; 309 print "# remake 2+3i\n"; 310 my \$z = cplx('2+3i'); 311 print "not " unless \$z == Math::Complex->make(2,3); 312 print "ok $test\n"; 313EOS 314 315 $test++; 316 push @script, <<EOS; 317 print "# remake 3i\n"; 318 my \$z = Math::Complex->make('3i'); 319 print "not " unless \$z == cplx(0,3); 320 print "ok $test\n"; 321EOS 322 323 $test++; 324 push @script, <<EOS; 325 print "# remake [2,3]\n"; 326 my \$z = cplxe('[2,3]'); 327 print "not " unless \$z == Math::Complex->emake(2,3); 328 print "ok $test\n"; 329EOS 330 331 $test++; 332 push @script, <<EOS; 333 print "# remake [2]\n"; 334 my \$z = Math::Complex->emake('[2]'); 335 print "not " unless \$z == cplxe(2); 336 print "ok $test\n"; 337EOS 338} 339 340test_remake(); 341 342print "1..$test\n"; 343eval join '', @script; 344die $@ if $@; 345 346sub abop { 347 my ($op) = @_; 348 349 push(@script, qq(print "# $op=\n";)); 350} 351 352sub test { 353 my ($op, $z, @args) = @_; 354 my ($baop) = 0; 355 $test++; 356 my $i; 357 $baop = 1 if ($op =~ s/;=$//); 358 for ($i = 0; $i < @args; $i++) { 359 $val = value($args[$i]); 360 push @script, "\$z$i = $val;\n"; 361 } 362 if (defined $z) { 363 $args = "'$op'"; # Really the value 364 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0"; 365 push @script, "\$res = $try; "; 366 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n"; 367 } else { 368 my ($try, $args); 369 if (@args == 2) { 370 $try = "$op \$z0"; 371 $args = "'$args[0]'"; 372 } else { 373 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1"; 374 $args = "'$args[0]', '$args[1]'"; 375 } 376 push @script, "\$res = $try; "; 377 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n"; 378 if (@args > 2 and $baop) { # binary assignment ops 379 $test++; 380 # check the op= works 381 push @script, <<EOB; 382{ 383 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0)); 384 385 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0); 386 387 my \$zb = cplx(\$z1r, \$z1i); 388 389 \$za $op= \$zb; 390 my (\$zbr, \$zbi) = \@{\$zb->cartesian}; 391 392 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args); 393EOB 394 $test++; 395 # check that the rhs has not changed 396 push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i);); 397 push @script, qq(print "ok $test\\n";\n); 398 push @script, "}\n"; 399 } 400 } 401} 402 403sub set { 404 my ($set, $setref, $valref) = @_; 405 @{$setref} = (); 406 @{$valref} = (); 407 my @set = split(/;\s*/, $set); 408 my @res; 409 my $i; 410 for ($i = 0; $i < @set; $i++) { 411 push(@{$valref}, $set[$i]); 412 my $val = value($set[$i]); 413 push @script, "\$s$i = $val;\n"; 414 push @{$setref}, "\$s$i"; 415 } 416} 417 418sub value { 419 local ($_) = @_; 420 if (/^\s*\((.*),(.*)\)/) { 421 return "cplx($1,$2)"; 422 } 423 elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) { 424 return "cplx($1,0)"; 425 } 426 elsif (/^\s*\[(.*),(.*)\]/) { 427 return "cplxe($1,$2)"; 428 } 429 elsif (/^\s*'(.*)'/) { 430 my $ex = $1; 431 $ex =~ s/\bz\b/$target/g; 432 $ex =~ s/\br\b/abs($target)/g; 433 $ex =~ s/\bt\b/arg($target)/g; 434 $ex =~ s/\ba\b/Re($target)/g; 435 $ex =~ s/\bb\b/Im($target)/g; 436 return $ex; 437 } 438 elsif (/^\s*"(.*)"/) { 439 return "\"$1\""; 440 } 441 return $_; 442} 443 444sub check { 445 my ($test, $try, $got, $expected, @z) = @_; 446 447 print "# @_\n"; 448 449 if ("$got" eq "$expected" 450 || 451 ($expected =~ /^-?\d/ && $got == $expected) 452 || 453 (abs($got - $expected) < $eps) 454 ) { 455 print "ok $test\n"; 456 } else { 457 print "not ok $test\n"; 458 my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]"; 459 print "# '$try' expected: '$expected' got: '$got' for $args\n"; 460 } 461} 462 463sub addsq { 464 my ($z1, $z2) = @_; 465 return ($z1 + i*$z2) * ($z1 - i*$z2); 466} 467 468sub subsq { 469 my ($z1, $z2) = @_; 470 return ($z1 + $z2) * ($z1 - $z2); 471} 472 473__END__ 474&+;= 475(3,4):(3,4):(6,8) 476(-3,4):(3,-4):(0,0) 477(3,4):-3:(0,4) 4781:(4,2):(5,2) 479[2,0]:[2,pi]:(0,0) 480 481&++ 482(2,1):(3,1) 483 484&-;= 485(2,3):(-2,-3) 486[2,pi/2]:[2,-(pi)/2] 4872:[2,0]:(0,0) 488[3,0]:2:(1,0) 4893:(4,5):(-1,-5) 490(4,5):3:(1,5) 491(2,1):(3,5):(-1,-4) 492 493&-- 494(1,2):(0,2) 495[2,pi]:[3,pi] 496 497&*;= 498(0,1):(0,1):(-1,0) 499(4,5):(1,0):(4,5) 500[2,2*pi/3]:(1,0):[2,2*pi/3] 5012:(0,1):(0,2) 502(0,1):3:(0,3) 503(0,1):(4,1):(-1,4) 504(2,1):(4,-1):(9,2) 505 506&/;= 507(3,4):(3,4):(1,0) 508(4,-5):1:(4,-5) 5091:(0,1):(0,-1) 510(0,6):(0,2):(3,0) 511(9,2):(4,-1):(2,1) 512[4,pi]:[2,pi/2]:[2,pi/2] 513[2,pi/2]:[4,pi]:[0.5,-(pi)/2] 514 515&**;= 516(2,0):(3,0):(8,0) 517(3,0):(2,0):(9,0) 518(2,3):(4,0):(-119,-120) 519(0,0):(1,0):(0,0) 520(0,0):(2,3):(0,0) 521(1,0):(0,0):(1,0) 522(1,0):(1,0):(1,0) 523(1,0):(2,3):(1,0) 524(2,3):(0,0):(1,0) 525(2,3):(1,0):(2,3) 526(0,0):(0,0):(1,0) 527 528&Re 529(3,4):3 530(-3,4):-3 531[1,pi/2]:0 532 533&Im 534(3,4):4 535(3,-4):-4 536[1,pi/2]:1 537 538&abs 539(3,4):5 540(-3,4):5 541 542&arg 543[2,0]:0 544[-2,0]:pi 545 546&~ 547(4,5):(4,-5) 548(-3,4):(-3,-4) 549[2,pi/2]:[2,-(pi)/2] 550 551&< 552(3,4):(1,2):0 553(3,4):(3,2):0 554(3,4):(3,8):1 555(4,4):(5,129):1 556 557&== 558(3,4):(4,5):0 559(3,4):(3,5):0 560(3,4):(2,4):0 561(3,4):(3,4):1 562 563&sqrt 564-9:(0,3) 565(-100,0):(0,10) 566(16,-30):(5,-3) 567 568&stringify_cartesian 569(-100,0):"-100" 570(0,1):"i" 571(4,-3):"4-3i" 572(4,0):"4" 573(-4,0):"-4" 574(-2,4):"-2+4i" 575(-2,-1):"-2-i" 576 577&stringify_polar 578[-1, 0]:"[1,pi]" 579[1, pi/3]:"[1,pi/3]" 580[6, -2*pi/3]:"[6,-2pi/3]" 581[0.5, -9*pi/11]:"[0.5,-9pi/11]" 582 583{ (4,3); [3,2]; (-3,4); (0,2); [2,1] } 584 585|'z + ~z':'2*Re(z)' 586|'z - ~z':'2*i*Im(z)' 587|'z * ~z':'abs(z) * abs(z)' 588 589{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] } 590 591|'(root(z, 4))[1] ** 4':'z' 592|'(root(z, 5))[3] ** 5':'z' 593|'(root(z, 8))[7] ** 8':'z' 594|'abs(z)':'r' 595|'acot(z)':'acotan(z)' 596|'acsc(z)':'acosec(z)' 597|'acsc(z)':'asin(1 / z)' 598|'asec(z)':'acos(1 / z)' 599|'cbrt(z)':'cbrt(r) * exp(i * t/3)' 600|'cos(acos(z))':'z' 601|'addsq(cos(z), sin(z))':1 602|'cos(z)':'cosh(i*z)' 603|'subsq(cosh(z), sinh(z))':1 604|'cot(acot(z))':'z' 605|'cot(z)':'1 / tan(z)' 606|'cot(z)':'cotan(z)' 607|'csc(acsc(z))':'z' 608|'csc(z)':'1 / sin(z)' 609|'csc(z)':'cosec(z)' 610|'exp(log(z))':'z' 611|'exp(z)':'exp(a) * exp(i * b)' 612|'ln(z)':'log(z)' 613|'log(exp(z))':'z' 614|'log(z)':'log(r) + i*t' 615|'log10(z)':'log(z) / log(10)' 616|'logn(z, 2)':'log(z) / log(2)' 617|'logn(z, 3)':'log(z) / log(3)' 618|'sec(asec(z))':'z' 619|'sec(z)':'1 / cos(z)' 620|'sin(asin(z))':'z' 621|'sin(i * z)':'i * sinh(z)' 622|'sqrt(z) * sqrt(z)':'z' 623|'sqrt(z)':'sqrt(r) * exp(i * t/2)' 624|'tan(atan(z))':'z' 625|'z**z':'exp(z * log(z))' 626 627{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) } 628 629|'cosh(acosh(z))':'z' 630|'coth(acoth(z))':'z' 631|'coth(z)':'1 / tanh(z)' 632|'coth(z)':'cotanh(z)' 633|'csch(acsch(z))':'z' 634|'csch(z)':'1 / sinh(z)' 635|'csch(z)':'cosech(z)' 636|'sech(asech(z))':'z' 637|'sech(z)':'1 / cosh(z)' 638|'sinh(asinh(z))':'z' 639|'tanh(atanh(z))':'z' 640 641{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) } 642 643|'acos(cos(z)) ** 2':'z * z' 644|'acosh(cosh(z)) ** 2':'z * z' 645|'acoth(z)':'acotanh(z)' 646|'acoth(z)':'atanh(1 / z)' 647|'acsch(z)':'acosech(z)' 648|'acsch(z)':'asinh(1 / z)' 649|'asech(z)':'acosh(1 / z)' 650|'asin(sin(z))':'z' 651|'asinh(sinh(z))':'z' 652|'atan(tan(z))':'z' 653|'atanh(tanh(z))':'z' 654 655&log 656(-2.0,0):( 0.69314718055995, 3.14159265358979) 657(-1.0,0):( 0 , 3.14159265358979) 658(-0.5,0):( -0.69314718055995, 3.14159265358979) 659( 0.5,0):( -0.69314718055995, 0 ) 660( 1.0,0):( 0 , 0 ) 661( 2.0,0):( 0.69314718055995, 0 ) 662 663&log 664( 2, 3):( 1.28247467873077, 0.98279372324733) 665(-2, 3):( 1.28247467873077, 2.15879893034246) 666(-2,-3):( 1.28247467873077, -2.15879893034246) 667( 2,-3):( 1.28247467873077, -0.98279372324733) 668 669&sin 670(-2.0,0):( -0.90929742682568, 0 ) 671(-1.0,0):( -0.84147098480790, 0 ) 672(-0.5,0):( -0.47942553860420, 0 ) 673( 0.0,0):( 0 , 0 ) 674( 0.5,0):( 0.47942553860420, 0 ) 675( 1.0,0):( 0.84147098480790, 0 ) 676( 2.0,0):( 0.90929742682568, 0 ) 677 678&sin 679( 2, 3):( 9.15449914691143, -4.16890695996656) 680(-2, 3):( -9.15449914691143, -4.16890695996656) 681(-2,-3):( -9.15449914691143, 4.16890695996656) 682( 2,-3):( 9.15449914691143, 4.16890695996656) 683 684&cos 685(-2.0,0):( -0.41614683654714, 0 ) 686(-1.0,0):( 0.54030230586814, 0 ) 687(-0.5,0):( 0.87758256189037, 0 ) 688( 0.0,0):( 1 , 0 ) 689( 0.5,0):( 0.87758256189037, 0 ) 690( 1.0,0):( 0.54030230586814, 0 ) 691( 2.0,0):( -0.41614683654714, 0 ) 692 693&cos 694( 2, 3):( -4.18962569096881, -9.10922789375534) 695(-2, 3):( -4.18962569096881, 9.10922789375534) 696(-2,-3):( -4.18962569096881, -9.10922789375534) 697( 2,-3):( -4.18962569096881, 9.10922789375534) 698 699&tan 700(-2.0,0):( 2.18503986326152, 0 ) 701(-1.0,0):( -1.55740772465490, 0 ) 702(-0.5,0):( -0.54630248984379, 0 ) 703( 0.0,0):( 0 , 0 ) 704( 0.5,0):( 0.54630248984379, 0 ) 705( 1.0,0):( 1.55740772465490, 0 ) 706( 2.0,0):( -2.18503986326152, 0 ) 707 708&tan 709( 2, 3):( -0.00376402564150, 1.00323862735361) 710(-2, 3):( 0.00376402564150, 1.00323862735361) 711(-2,-3):( 0.00376402564150, -1.00323862735361) 712( 2,-3):( -0.00376402564150, -1.00323862735361) 713 714&sec 715(-2.0,0):( -2.40299796172238, 0 ) 716(-1.0,0):( 1.85081571768093, 0 ) 717(-0.5,0):( 1.13949392732455, 0 ) 718( 0.0,0):( 1 , 0 ) 719( 0.5,0):( 1.13949392732455, 0 ) 720( 1.0,0):( 1.85081571768093, 0 ) 721( 2.0,0):( -2.40299796172238, 0 ) 722 723&sec 724( 2, 3):( -0.04167496441114, 0.09061113719624) 725(-2, 3):( -0.04167496441114, -0.09061113719624) 726(-2,-3):( -0.04167496441114, 0.09061113719624) 727( 2,-3):( -0.04167496441114, -0.09061113719624) 728 729&csc 730(-2.0,0):( -1.09975017029462, 0 ) 731(-1.0,0):( -1.18839510577812, 0 ) 732(-0.5,0):( -2.08582964293349, 0 ) 733( 0.5,0):( 2.08582964293349, 0 ) 734( 1.0,0):( 1.18839510577812, 0 ) 735( 2.0,0):( 1.09975017029462, 0 ) 736 737&csc 738( 2, 3):( 0.09047320975321, 0.04120098628857) 739(-2, 3):( -0.09047320975321, 0.04120098628857) 740(-2,-3):( -0.09047320975321, -0.04120098628857) 741( 2,-3):( 0.09047320975321, -0.04120098628857) 742 743&cot 744(-2.0,0):( 0.45765755436029, 0 ) 745(-1.0,0):( -0.64209261593433, 0 ) 746(-0.5,0):( -1.83048772171245, 0 ) 747( 0.5,0):( 1.83048772171245, 0 ) 748( 1.0,0):( 0.64209261593433, 0 ) 749( 2.0,0):( -0.45765755436029, 0 ) 750 751&cot 752( 2, 3):( -0.00373971037634, -0.99675779656936) 753(-2, 3):( 0.00373971037634, -0.99675779656936) 754(-2,-3):( 0.00373971037634, 0.99675779656936) 755( 2,-3):( -0.00373971037634, 0.99675779656936) 756 757&asin 758(-2.0,0):( -1.57079632679490, 1.31695789692482) 759(-1.0,0):( -1.57079632679490, 0 ) 760(-0.5,0):( -0.52359877559830, 0 ) 761( 0.0,0):( 0 , 0 ) 762( 0.5,0):( 0.52359877559830, 0 ) 763( 1.0,0):( 1.57079632679490, 0 ) 764( 2.0,0):( 1.57079632679490, -1.31695789692482) 765 766&asin 767( 2, 3):( 0.57065278432110, 1.98338702991654) 768(-2, 3):( -0.57065278432110, 1.98338702991654) 769(-2,-3):( -0.57065278432110, -1.98338702991654) 770( 2,-3):( 0.57065278432110, -1.98338702991654) 771 772&acos 773(-2.0,0):( 3.14159265358979, -1.31695789692482) 774(-1.0,0):( 3.14159265358979, 0 ) 775(-0.5,0):( 2.09439510239320, 0 ) 776( 0.0,0):( 1.57079632679490, 0 ) 777( 0.5,0):( 1.04719755119660, 0 ) 778( 1.0,0):( 0 , 0 ) 779( 2.0,0):( 0 , 1.31695789692482) 780 781&acos 782( 2, 3):( 1.00014354247380, -1.98338702991654) 783(-2, 3):( 2.14144911111600, -1.98338702991654) 784(-2,-3):( 2.14144911111600, 1.98338702991654) 785( 2,-3):( 1.00014354247380, 1.98338702991654) 786 787&atan 788(-2.0,0):( -1.10714871779409, 0 ) 789(-1.0,0):( -0.78539816339745, 0 ) 790(-0.5,0):( -0.46364760900081, 0 ) 791( 0.0,0):( 0 , 0 ) 792( 0.5,0):( 0.46364760900081, 0 ) 793( 1.0,0):( 0.78539816339745, 0 ) 794( 2.0,0):( 1.10714871779409, 0 ) 795 796&atan 797( 2, 3):( 1.40992104959658, 0.22907268296854) 798(-2, 3):( -1.40992104959658, 0.22907268296854) 799(-2,-3):( -1.40992104959658, -0.22907268296854) 800( 2,-3):( 1.40992104959658, -0.22907268296854) 801 802&asec 803(-2.0,0):( 2.09439510239320, 0 ) 804(-1.0,0):( 3.14159265358979, 0 ) 805(-0.5,0):( 3.14159265358979, -1.31695789692482) 806( 0.5,0):( 0 , 1.31695789692482) 807( 1.0,0):( 0 , 0 ) 808( 2.0,0):( 1.04719755119660, 0 ) 809 810&asec 811( 2, 3):( 1.42041072246703, 0.23133469857397) 812(-2, 3):( 1.72118193112276, 0.23133469857397) 813(-2,-3):( 1.72118193112276, -0.23133469857397) 814( 2,-3):( 1.42041072246703, -0.23133469857397) 815 816&acsc 817(-2.0,0):( -0.52359877559830, 0 ) 818(-1.0,0):( -1.57079632679490, 0 ) 819(-0.5,0):( -1.57079632679490, 1.31695789692482) 820( 0.5,0):( 1.57079632679490, -1.31695789692482) 821( 1.0,0):( 1.57079632679490, 0 ) 822( 2.0,0):( 0.52359877559830, 0 ) 823 824&acsc 825( 2, 3):( 0.15038560432786, -0.23133469857397) 826(-2, 3):( -0.15038560432786, -0.23133469857397) 827(-2,-3):( -0.15038560432786, 0.23133469857397) 828( 2,-3):( 0.15038560432786, 0.23133469857397) 829 830&acot 831(-2.0,0):( -0.46364760900081, 0 ) 832(-1.0,0):( -0.78539816339745, 0 ) 833(-0.5,0):( -1.10714871779409, 0 ) 834( 0.5,0):( 1.10714871779409, 0 ) 835( 1.0,0):( 0.78539816339745, 0 ) 836( 2.0,0):( 0.46364760900081, 0 ) 837 838&acot 839( 2, 3):( 0.16087527719832, -0.22907268296854) 840(-2, 3):( -0.16087527719832, -0.22907268296854) 841(-2,-3):( -0.16087527719832, 0.22907268296854) 842( 2,-3):( 0.16087527719832, 0.22907268296854) 843 844&sinh 845(-2.0,0):( -3.62686040784702, 0 ) 846(-1.0,0):( -1.17520119364380, 0 ) 847(-0.5,0):( -0.52109530549375, 0 ) 848( 0.0,0):( 0 , 0 ) 849( 0.5,0):( 0.52109530549375, 0 ) 850( 1.0,0):( 1.17520119364380, 0 ) 851( 2.0,0):( 3.62686040784702, 0 ) 852 853&sinh 854( 2, 3):( -3.59056458998578, 0.53092108624852) 855(-2, 3):( 3.59056458998578, 0.53092108624852) 856(-2,-3):( 3.59056458998578, -0.53092108624852) 857( 2,-3):( -3.59056458998578, -0.53092108624852) 858 859&cosh 860(-2.0,0):( 3.76219569108363, 0 ) 861(-1.0,0):( 1.54308063481524, 0 ) 862(-0.5,0):( 1.12762596520638, 0 ) 863( 0.0,0):( 1 , 0 ) 864( 0.5,0):( 1.12762596520638, 0 ) 865( 1.0,0):( 1.54308063481524, 0 ) 866( 2.0,0):( 3.76219569108363, 0 ) 867 868&cosh 869( 2, 3):( -3.72454550491532, 0.51182256998738) 870(-2, 3):( -3.72454550491532, -0.51182256998738) 871(-2,-3):( -3.72454550491532, 0.51182256998738) 872( 2,-3):( -3.72454550491532, -0.51182256998738) 873 874&tanh 875(-2.0,0):( -0.96402758007582, 0 ) 876(-1.0,0):( -0.76159415595576, 0 ) 877(-0.5,0):( -0.46211715726001, 0 ) 878( 0.0,0):( 0 , 0 ) 879( 0.5,0):( 0.46211715726001, 0 ) 880( 1.0,0):( 0.76159415595576, 0 ) 881( 2.0,0):( 0.96402758007582, 0 ) 882 883&tanh 884( 2, 3):( 0.96538587902213, -0.00988437503832) 885(-2, 3):( -0.96538587902213, -0.00988437503832) 886(-2,-3):( -0.96538587902213, 0.00988437503832) 887( 2,-3):( 0.96538587902213, 0.00988437503832) 888 889&sech 890(-2.0,0):( 0.26580222883408, 0 ) 891(-1.0,0):( 0.64805427366389, 0 ) 892(-0.5,0):( 0.88681888397007, 0 ) 893( 0.0,0):( 1 , 0 ) 894( 0.5,0):( 0.88681888397007, 0 ) 895( 1.0,0):( 0.64805427366389, 0 ) 896( 2.0,0):( 0.26580222883408, 0 ) 897 898&sech 899( 2, 3):( -0.26351297515839, -0.03621163655877) 900(-2, 3):( -0.26351297515839, 0.03621163655877) 901(-2,-3):( -0.26351297515839, -0.03621163655877) 902( 2,-3):( -0.26351297515839, 0.03621163655877) 903 904&csch 905(-2.0,0):( -0.27572056477178, 0 ) 906(-1.0,0):( -0.85091812823932, 0 ) 907(-0.5,0):( -1.91903475133494, 0 ) 908( 0.5,0):( 1.91903475133494, 0 ) 909( 1.0,0):( 0.85091812823932, 0 ) 910( 2.0,0):( 0.27572056477178, 0 ) 911 912&csch 913( 2, 3):( -0.27254866146294, -0.04030057885689) 914(-2, 3):( 0.27254866146294, -0.04030057885689) 915(-2,-3):( 0.27254866146294, 0.04030057885689) 916( 2,-3):( -0.27254866146294, 0.04030057885689) 917 918&coth 919(-2.0,0):( -1.03731472072755, 0 ) 920(-1.0,0):( -1.31303528549933, 0 ) 921(-0.5,0):( -2.16395341373865, 0 ) 922( 0.5,0):( 2.16395341373865, 0 ) 923( 1.0,0):( 1.31303528549933, 0 ) 924( 2.0,0):( 1.03731472072755, 0 ) 925 926&coth 927( 2, 3):( 1.03574663776500, 0.01060478347034) 928(-2, 3):( -1.03574663776500, 0.01060478347034) 929(-2,-3):( -1.03574663776500, -0.01060478347034) 930( 2,-3):( 1.03574663776500, -0.01060478347034) 931 932&asinh 933(-2.0,0):( -1.44363547517881, 0 ) 934(-1.0,0):( -0.88137358701954, 0 ) 935(-0.5,0):( -0.48121182505960, 0 ) 936( 0.0,0):( 0 , 0 ) 937( 0.5,0):( 0.48121182505960, 0 ) 938( 1.0,0):( 0.88137358701954, 0 ) 939( 2.0,0):( 1.44363547517881, 0 ) 940 941&asinh 942( 2, 3):( 1.96863792579310, 0.96465850440760) 943(-2, 3):( -1.96863792579310, 0.96465850440761) 944(-2,-3):( -1.96863792579310, -0.96465850440761) 945( 2,-3):( 1.96863792579310, -0.96465850440760) 946 947&acosh 948(-2.0,0):( 1.31695789692482, 3.14159265358979) 949(-1.0,0):( 0, 3.14159265358979) 950(-0.5,0):( 0, 2.09439510239320) 951( 0.0,0):( 0, 1.57079632679490) 952( 0.5,0):( 0, 1.04719755119660) 953( 1.0,0):( 0 , 0 ) 954( 2.0,0):( 1.31695789692482, 0 ) 955 956&acosh 957( 2, 3):( 1.98338702991654, 1.00014354247380) 958(-2, 3):( 1.98338702991653, 2.14144911111600) 959(-2,-3):( 1.98338702991653, -2.14144911111600) 960( 2,-3):( 1.98338702991654, -1.00014354247380) 961 962&atanh 963(-2.0,0):( -0.54930614433405, 1.57079632679490) 964(-0.5,0):( -0.54930614433405, 0 ) 965( 0.0,0):( 0 , 0 ) 966( 0.5,0):( 0.54930614433405, 0 ) 967( 2.0,0):( 0.54930614433405, 1.57079632679490) 968 969&atanh 970( 2, 3):( 0.14694666622553, 1.33897252229449) 971(-2, 3):( -0.14694666622553, 1.33897252229449) 972(-2,-3):( -0.14694666622553, -1.33897252229449) 973( 2,-3):( 0.14694666622553, -1.33897252229449) 974 975&asech 976(-2.0,0):( 0 , 2.09439510239320) 977(-1.0,0):( 0 , 3.14159265358979) 978(-0.5,0):( 1.31695789692482, 3.14159265358979) 979( 0.5,0):( 1.31695789692482, 0 ) 980( 1.0,0):( 0 , 0 ) 981( 2.0,0):( 0 , 1.04719755119660) 982 983&asech 984( 2, 3):( 0.23133469857397, -1.42041072246703) 985(-2, 3):( 0.23133469857397, -1.72118193112276) 986(-2,-3):( 0.23133469857397, 1.72118193112276) 987( 2,-3):( 0.23133469857397, 1.42041072246703) 988 989&acsch 990(-2.0,0):( -0.48121182505960, 0 ) 991(-1.0,0):( -0.88137358701954, 0 ) 992(-0.5,0):( -1.44363547517881, 0 ) 993( 0.5,0):( 1.44363547517881, 0 ) 994( 1.0,0):( 0.88137358701954, 0 ) 995( 2.0,0):( 0.48121182505960, 0 ) 996 997&acsch 998( 2, 3):( 0.15735549884499, -0.22996290237721) 999(-2, 3):( -0.15735549884499, -0.22996290237721) 1000(-2,-3):( -0.15735549884499, 0.22996290237721) 1001( 2,-3):( 0.15735549884499, 0.22996290237721) 1002 1003&acoth 1004(-2.0,0):( -0.54930614433405, 0 ) 1005(-0.5,0):( -0.54930614433405, 1.57079632679490) 1006( 0.5,0):( 0.54930614433405, 1.57079632679490) 1007( 2.0,0):( 0.54930614433405, 0 ) 1008 1009&acoth 1010( 2, 3):( 0.14694666622553, -0.23182380450040) 1011(-2, 3):( -0.14694666622553, -0.23182380450040) 1012(-2,-3):( -0.14694666622553, 0.23182380450040) 1013( 2,-3):( 0.14694666622553, 0.23182380450040) 1014 1015# eof 1016