5 # Regression tests for the Math::Complex pacakge
6 # -- Raphael Manfredi, September 1996
7 # -- Jarkko Hietaniemi, March-April 1997
23 next if $_ eq '' || /^\#/;
25 $test_set = 0; # Assume not a test over a set of values
31 set($1, \@set, \@val);
35 $test_set = 1; # Requests we loop over the set...
37 my @args = split(/:/);
40 for ($i = 0; $i < @set; $i++) {
43 # textual value as found in set definition
45 test($zvalue, $target, @args);
48 test($op, undef, @args);
58 # push(@script, qq(print "# '$op'\n";));
59 push(@script, qq(eval '$op';));
60 push(@script, qq(print 'not ' unless (\$@ =~ /Division by zero/);));
61 push(@script, qq(print "ok $test\n";));
71 # push(@script, qq(print "# '$op'\n";));
72 push(@script, qq(eval '$op';));
73 push(@script, qq(print 'not ' unless (\$@ =~ /Logarithm of zero/);));
74 push(@script, qq(print "ok $test\n";));
78 my $minusi = cplx(0, -1);
82 # 'tan(pi/2)', # may succeed thanks to floating point inaccuracies
83 # 'sec(pi/2)', # may succeed thanks to floating point inaccuracies
92 # 'tanh(pi/2)', # may succeed thanks to floating point inaccuracies
93 # 'sech(pi/2)', # may succeed thanks to floating point inaccuracies
112 # push(@script, qq(print "# 0**0\n";));
113 push(@script, qq(eval 'cplx(0)**cplx(0)';));
114 push(@script, qq(print 'not ' unless (\$@ =~ /zero raised to the/);));
115 push(@script, qq(print "ok $test\n";));
126 # push(@script, qq(print "# root(2, $op)\n";));
127 push(@script, qq(eval 'root(2, $op)';));
128 push(@script, qq(print 'not ' unless (\$@ =~ /root must be/);));
129 push(@script, qq(print "ok $test\n";));
133 test_broot(qw(-3 -2.1 0 0.99));
136 eval join '', @script;
142 push(@script, qq(print "# $op=\n";));
146 my ($op, $z, @args) = @_;
150 $baop = 1 if ($op =~ s/;=$//);
151 for ($i = 0; $i < @args; $i++) {
152 $val = value($args[$i]);
153 push @script, "\$z$i = $val;\n";
156 $args = "'$op'"; # Really the value
157 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
158 push @script, "\$res = $try; ";
159 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
164 $args = "'$args[0]'";
166 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
167 $args = "'$args[0]', '$args[1]'";
169 push @script, "\$res = $try; ";
170 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
171 if (@args > 2 and $baop) { # binary assignment ops
173 # check the op= works
176 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
178 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
180 my \$zb = cplx(\$z1r, \$z1i);
183 my (\$zbr, \$zbi) = \@{\$zb->cartesian};
185 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
188 # check that the rhs has not changed
189 push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
190 push @script, qq(print "ok $test\n";);
197 my ($set, $setref, $valref) = @_;
200 my @set = split(/;\s*/, $set);
203 for ($i = 0; $i < @set; $i++) {
204 push(@{$valref}, $set[$i]);
205 my $val = value($set[$i]);
206 push @script, "\$s$i = $val;\n";
207 push @{$setref}, "\$s$i";
213 if (/^\s*\((.*),(.*)\)/) {
214 return "cplx($1,$2)";
216 elsif (/^\s*\[(.*),(.*)\]/) {
217 return "cplxe($1,$2)";
219 elsif (/^\s*'(.*)'/) {
221 $ex =~ s/\bz\b/$target/g;
222 $ex =~ s/\br\b/abs($target)/g;
223 $ex =~ s/\bt\b/arg($target)/g;
224 $ex =~ s/\ba\b/Re($target)/g;
225 $ex =~ s/\bb\b/Im($target)/g;
228 elsif (/^\s*"(.*)"/) {
235 my ($test, $try, $got, $expected, @z) = @_;
239 if ("$got" eq "$expected"
241 ($expected =~ /^-?\d/ && $got == $expected)
243 (abs($got - $expected) < $eps)
247 print "not ok $test\n";
248 my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
249 print "# '$try' expected: '$expected' got: '$got' for $args\n";
279 [2,2*pi/3]:(1,0):[2,2*pi/3]
291 [4,pi]:[2,pi/2]:[2,pi/2]
292 [2,pi/2]:[4,pi]:[0.5,-(pi)/2]
297 (2,3):(4,0):(-119,-120)
358 [6, -2*pi/3]:"[6,-2pi/3]"
359 [0.5, -9*pi/11]:"[0.5,-9pi/11]"
361 { (4,3); [3,2]; (-3,4); (0,2); [2,1] }
364 |'z - ~z':'2*i*Im(z)'
365 |'z * ~z':'abs(z) * abs(z)'
367 { (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
369 |'(root(z, 4))[1] ** 4':'z'
370 |'(root(z, 5))[3] ** 5':'z'
371 |'(root(z, 8))[7] ** 8':'z'
373 |'acot(z)':'acotan(z)'
374 |'acsc(z)':'acosec(z)'
375 |'abs(acsc(z))':'abs(asin(1 / z))'
376 |'abs(asec(z))':'abs(acos(1 / z))'
377 |'cbrt(z)':'cbrt(r) * exp(i * t/3)'
379 |'cos(z) ** 2 + sin(z) ** 2':1
380 |'cos(z)':'cosh(i*z)'
381 |'cosh(z) ** 2 - sinh(z) ** 2':1
383 |'cot(z)':'1 / tan(z)'
386 |'csc(z)':'1 / sin(z)'
389 |'exp(z)':'exp(a) * exp(i * b)'
392 |'log(z)':'log(r) + i*t'
393 |'log10(z)':'log(z) / log(10)'
394 |'logn(z, 2)':'log(z) / log(2)'
395 |'logn(z, 3)':'log(z) / log(3)'
397 |'sec(z)':'1 / cos(z)'
399 |'sin(i * z)':'i * sinh(z)'
400 |'sqrt(z) * sqrt(z)':'z'
401 |'sqrt(z)':'sqrt(r) * exp(i * t/2)'
403 |'z**z':'exp(z * log(z))'
405 { (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
407 |'cosh(acosh(z))':'z'
408 |'coth(acoth(z))':'z'
409 |'coth(z)':'1 / tanh(z)'
410 |'coth(z)':'cotanh(z)'
411 |'csch(acsch(z))':'z'
412 |'csch(z)':'1 / sinh(z)'
413 |'csch(z)':'cosech(z)'
414 |'sech(asech(z))':'z'
415 |'sech(z)':'1 / cosh(z)'
416 |'sinh(asinh(z))':'z'
417 |'tanh(atanh(z))':'z'
419 { (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
421 |'acos(cos(z)) ** 2':'z * z'
422 |'acosh(cosh(z)) ** 2':'z * z'
423 |'acoth(z)':'acotanh(z)'
424 |'acoth(z)':'atanh(1 / z)'
425 |'acsch(z)':'acosech(z)'
426 |'acsch(z)':'asinh(1 / z)'
427 |'asech(z)':'acosh(1 / z)'
429 |'asinh(sinh(z))':'z'
431 |'atanh(tanh(z))':'z'
434 (-2.0,0):( -0.90929742682568, 0 )
435 (-1.0,0):( -0.84147098480790, 0 )
436 (-0.5,0):( -0.47942553860420, 0 )
438 ( 0.5,0):( 0.47942553860420, 0 )
439 ( 1.0,0):( 0.84147098480790, 0 )
440 ( 2.0,0):( 0.90929742682568, 0 )
443 ( 2, 3):( 9.15449914691143, -4.16890695996656)
444 (-2, 3):( -9.15449914691143, -4.16890695996656)
445 (-2,-3):( -9.15449914691143, 4.16890695996656)
446 ( 2,-3):( 9.15449914691143, 4.16890695996656)
449 (-2.0,0):( -0.41614683654714, 0 )
450 (-1.0,0):( 0.54030230586814, 0 )
451 (-0.5,0):( 0.87758256189037, 0 )
453 ( 0.5,0):( 0.87758256189037, 0 )
454 ( 1.0,0):( 0.54030230586814, 0 )
455 ( 2.0,0):( -0.41614683654714, 0 )
458 ( 2, 3):( -4.18962569096881, -9.10922789375534)
459 (-2, 3):( -4.18962569096881, 9.10922789375534)
460 (-2,-3):( -4.18962569096881, -9.10922789375534)
461 ( 2,-3):( -4.18962569096881, 9.10922789375534)
464 (-2.0,0):( 2.18503986326152, 0 )
465 (-1.0,0):( -1.55740772465490, 0 )
466 (-0.5,0):( -0.54630248984379, 0 )
468 ( 0.5,0):( 0.54630248984379, 0 )
469 ( 1.0,0):( 1.55740772465490, 0 )
470 ( 2.0,0):( -2.18503986326152, 0 )
473 ( 2, 3):( -0.00376402564150, 1.00323862735361)
474 (-2, 3):( 0.00376402564150, 1.00323862735361)
475 (-2,-3):( 0.00376402564150, -1.00323862735361)
476 ( 2,-3):( -0.00376402564150, -1.00323862735361)
479 (-2.0,0):( -2.40299796172238, 0 )
480 (-1.0,0):( 1.85081571768093, 0 )
481 (-0.5,0):( 1.13949392732455, 0 )
483 ( 0.5,0):( 1.13949392732455, 0 )
484 ( 1.0,0):( 1.85081571768093, 0 )
485 ( 2.0,0):( -2.40299796172238, 0 )
488 ( 2, 3):( -0.04167496441114, 0.09061113719624)
489 (-2, 3):( -0.04167496441114, -0.09061113719624)
490 (-2,-3):( -0.04167496441114, 0.09061113719624)
491 ( 2,-3):( -0.04167496441114, -0.09061113719624)
494 (-2.0,0):( -1.09975017029462, 0 )
495 (-1.0,0):( -1.18839510577812, 0 )
496 (-0.5,0):( -2.08582964293349, 0 )
497 ( 0.5,0):( 2.08582964293349, 0 )
498 ( 1.0,0):( 1.18839510577812, 0 )
499 ( 2.0,0):( 1.09975017029462, 0 )
502 ( 2, 3):( 0.09047320975321, 0.04120098628857)
503 (-2, 3):( -0.09047320975321, 0.04120098628857)
504 (-2,-3):( -0.09047320975321, -0.04120098628857)
505 ( 2,-3):( 0.09047320975321, -0.04120098628857)
508 (-2.0,0):( 0.45765755436029, 0 )
509 (-1.0,0):( -0.64209261593433, 0 )
510 (-0.5,0):( -1.83048772171245, 0 )
511 ( 0.5,0):( 1.83048772171245, 0 )
512 ( 1.0,0):( 0.64209261593433, 0 )
513 ( 2.0,0):( -0.45765755436029, 0 )
516 ( 2, 3):( -0.00373971037634, -0.99675779656936)
517 (-2, 3):( 0.00373971037634, -0.99675779656936)
518 (-2,-3):( 0.00373971037634, 0.99675779656936)
519 ( 2,-3):( -0.00373971037634, 0.99675779656936)
522 (-2.0,0):( -1.57079632679490, 1.31695789692482)
523 (-1.0,0):( -1.57079632679490, 0 )
524 (-0.5,0):( -0.52359877559830, 0 )
526 ( 0.5,0):( 0.52359877559830, 0 )
527 ( 1.0,0):( 1.57079632679490, 0 )
528 ( 2.0,0):( 1.57079632679490, -1.31695789692482)
531 ( 2, 3):( 0.57065278432110, 1.98338702991654)
532 (-2, 3):( -0.57065278432110, 1.98338702991654)
533 (-2,-3):( -0.57065278432110, -1.98338702991654)
534 ( 2,-3):( 0.57065278432110, -1.98338702991654)
537 (-2.0,0):( 3.14159265358979, -1.31695789692482)
538 (-1.0,0):( 3.14159265358979, 0 )
539 (-0.5,0):( 2.09439510239320, 0 )
540 ( 0.0,0):( 1.57079632679490, 0 )
541 ( 0.5,0):( 1.04719755119660, 0 )
543 ( 2.0,0):( 0 , 1.31695789692482)
546 ( 2, 3):( 1.00014354247380, -1.98338702991654)
547 (-2, 3):( 2.14144911111600, -1.98338702991654)
548 (-2,-3):( 2.14144911111600, 1.98338702991654)
549 ( 2,-3):( 1.00014354247380, 1.98338702991654)
552 (-2.0,0):( -1.10714871779409, 0 )
553 (-1.0,0):( -0.78539816339745, 0 )
554 (-0.5,0):( -0.46364760900081, 0 )
556 ( 0.5,0):( 0.46364760900081, 0 )
557 ( 1.0,0):( 0.78539816339745, 0 )
558 ( 2.0,0):( 1.10714871779409, 0 )
561 ( 2, 3):( 1.40992104959658, 0.22907268296854)
562 (-2, 3):( -1.40992104959658, 0.22907268296854)
563 (-2,-3):( -1.40992104959658, -0.22907268296854)
564 ( 2,-3):( 1.40992104959658, -0.22907268296854)
567 (-2.0,0):( 2.09439510239320, 0 )
568 (-1.0,0):( 3.14159265358979, 0 )
569 (-0.5,0):( 3.14159265358979, -1.31695789692482)
570 ( 0.5,0):( 0 , 1.31695789692482)
572 ( 2.0,0):( 1.04719755119660, 0 )
575 ( 2, 3):( 1.42041072246703, 0.23133469857397)
576 (-2, 3):( 1.72118193112276, 0.23133469857397)
577 (-2,-3):( 1.72118193112276, -0.23133469857397)
578 ( 2,-3):( 1.42041072246703, -0.23133469857397)
581 (-2.0,0):( -0.52359877559830, 0 )
582 (-1.0,0):( -1.57079632679490, 0 )
583 (-0.5,0):( -1.57079632679490, 1.31695789692482)
584 ( 0.5,0):( 1.57079632679490, -1.31695789692482)
585 ( 1.0,0):( 1.57079632679490, 0 )
586 ( 2.0,0):( 0.52359877559830, 0 )
589 ( 2, 3):( 0.15038560432786, -0.23133469857397)
590 (-2, 3):( -0.15038560432786, -0.23133469857397)
591 (-2,-3):( -0.15038560432786, 0.23133469857397)
592 ( 2,-3):( 0.15038560432786, 0.23133469857397)
595 (-2.0,0):( -0.46364760900081, 0 )
596 (-1.0,0):( -0.78539816339745, 0 )
597 (-0.5,0):( -1.10714871779409, 0 )
598 ( 0.5,0):( 1.10714871779409, 0 )
599 ( 1.0,0):( 0.78539816339745, 0 )
600 ( 2.0,0):( 0.46364760900081, 0 )
603 ( 2, 3):( 0.16087527719832, -0.22907268296854)
604 (-2, 3):( -0.16087527719832, -0.22907268296854)
605 (-2,-3):( -0.16087527719832, 0.22907268296854)
606 ( 2,-3):( 0.16087527719832, 0.22907268296854)
609 (-2.0,0):( -3.62686040784702, 0 )
610 (-1.0,0):( -1.17520119364380, 0 )
611 (-0.5,0):( -0.52109530549375, 0 )
613 ( 0.5,0):( 0.52109530549375, 0 )
614 ( 1.0,0):( 1.17520119364380, 0 )
615 ( 2.0,0):( 3.62686040784702, 0 )
618 ( 2, 3):( -3.59056458998578, 0.53092108624852)
619 (-2, 3):( 3.59056458998578, 0.53092108624852)
620 (-2,-3):( 3.59056458998578, -0.53092108624852)
621 ( 2,-3):( -3.59056458998578, -0.53092108624852)
624 (-2.0,0):( 3.76219569108363, 0 )
625 (-1.0,0):( 1.54308063481524, 0 )
626 (-0.5,0):( 1.12762596520638, 0 )
628 ( 0.5,0):( 1.12762596520638, 0 )
629 ( 1.0,0):( 1.54308063481524, 0 )
630 ( 2.0,0):( 3.76219569108363, 0 )
633 ( 2, 3):( -3.72454550491532, 0.51182256998738)
634 (-2, 3):( -3.72454550491532, -0.51182256998738)
635 (-2,-3):( -3.72454550491532, 0.51182256998738)
636 ( 2,-3):( -3.72454550491532, -0.51182256998738)
639 (-2.0,0):( -0.96402758007582, 0 )
640 (-1.0,0):( -0.76159415595576, 0 )
641 (-0.5,0):( -0.46211715726001, 0 )
643 ( 0.5,0):( 0.46211715726001, 0 )
644 ( 1.0,0):( 0.76159415595576, 0 )
645 ( 2.0,0):( 0.96402758007582, 0 )
648 ( 2, 3):( 0.96538587902213, -0.00988437503832)
649 (-2, 3):( -0.96538587902213, -0.00988437503832)
650 (-2,-3):( -0.96538587902213, 0.00988437503832)
651 ( 2,-3):( 0.96538587902213, 0.00988437503832)
654 (-2.0,0):( 0.26580222883408, 0 )
655 (-1.0,0):( 0.64805427366389, 0 )
656 (-0.5,0):( 0.88681888397007, 0 )
658 ( 0.5,0):( 0.88681888397007, 0 )
659 ( 1.0,0):( 0.64805427366389, 0 )
660 ( 2.0,0):( 0.26580222883408, 0 )
663 ( 2, 3):( -0.26351297515839, -0.03621163655877)
664 (-2, 3):( -0.26351297515839, 0.03621163655877)
665 (-2,-3):( -0.26351297515839, -0.03621163655877)
666 ( 2,-3):( -0.26351297515839, 0.03621163655877)
669 (-2.0,0):( -0.27572056477178, 0 )
670 (-1.0,0):( -0.85091812823932, 0 )
671 (-0.5,0):( -1.91903475133494, 0 )
672 ( 0.5,0):( 1.91903475133494, 0 )
673 ( 1.0,0):( 0.85091812823932, 0 )
674 ( 2.0,0):( 0.27572056477178, 0 )
677 ( 2, 3):( -0.27254866146294, -0.04030057885689)
678 (-2, 3):( 0.27254866146294, -0.04030057885689)
679 (-2,-3):( 0.27254866146294, 0.04030057885689)
680 ( 2,-3):( -0.27254866146294, 0.04030057885689)
683 (-2.0,0):( -1.03731472072755, 0 )
684 (-1.0,0):( -1.31303528549933, 0 )
685 (-0.5,0):( -2.16395341373865, 0 )
686 ( 0.5,0):( 2.16395341373865, 0 )
687 ( 1.0,0):( 1.31303528549933, 0 )
688 ( 2.0,0):( 1.03731472072755, 0 )
691 ( 2, 3):( 1.03574663776500, 0.01060478347034)
692 (-2, 3):( -1.03574663776500, 0.01060478347034)
693 (-2,-3):( -1.03574663776500, -0.01060478347034)
694 ( 2,-3):( 1.03574663776500, -0.01060478347034)
697 (-2.0,0):( -1.44363547517881, 0 )
698 (-1.0,0):( -0.88137358701954, 0 )
699 (-0.5,0):( -0.48121182505960, 0 )
701 ( 0.5,0):( 0.48121182505960, 0 )
702 ( 1.0,0):( 0.88137358701954, 0 )
703 ( 2.0,0):( 1.44363547517881, 0 )
706 ( 2, 3):( 1.96863792579310, 0.96465850440760)
707 (-2, 3):( -1.96863792579310, 0.96465850440761)
708 (-2,-3):( -1.96863792579310, -0.96465850440761)
709 ( 2,-3):( 1.96863792579310, -0.96465850440760)
712 (-2.0,0):( -1.31695789692482, 3.14159265358979)
713 (-1.0,0):( 0, 3.14159265358979)
714 (-0.5,0):( 0, 2.09439510239320)
715 ( 0.0,0):( 0, 1.57079632679490)
716 ( 0.5,0):( 0, 1.04719755119660)
718 ( 2.0,0):( 1.31695789692482, 0 )
721 ( 2, 3):( 1.98338702991654, 1.00014354247380)
722 (-2, 3):( -1.98338702991653, -2.14144911111600)
723 (-2,-3):( -1.98338702991653, 2.14144911111600)
724 ( 2,-3):( 1.98338702991654, -1.00014354247380)
727 (-2.0,0):( -0.54930614433405, 1.57079632679490)
728 (-0.5,0):( -0.54930614433405, 0 )
730 ( 0.5,0):( 0.54930614433405, 0 )
731 ( 2.0,0):( 0.54930614433405, 1.57079632679490)
734 ( 2, 3):( 0.14694666622553, 1.33897252229449)
735 (-2, 3):( -0.14694666622553, 1.33897252229449)
736 (-2,-3):( -0.14694666622553, -1.33897252229449)
737 ( 2,-3):( 0.14694666622553, -1.33897252229449)
740 (-2.0,0):( 0 , 2.09439510239320)
741 (-1.0,0):( 0 , 3.14159265358979)
742 (-0.5,0):( -1.31695789692482, 3.14159265358979)
743 ( 0.5,0):( 1.31695789692482, 0 )
745 ( 2.0,0):( 0 , 1.04719755119660)
748 ( 2, 3):( 0.23133469857397, -1.42041072246703)
749 (-2, 3):( -0.23133469857397, 1.72118193112276)
750 (-2,-3):( -0.23133469857397, -1.72118193112276)
751 ( 2,-3):( 0.23133469857397, 1.42041072246703)
754 (-2.0,0):( -0.48121182505960, 0 )
755 (-1.0,0):( -0.88137358701954, 0 )
756 (-0.5,0):( -1.44363547517881, 0 )
757 ( 0.5,0):( 1.44363547517881, 0 )
758 ( 1.0,0):( 0.88137358701954, 0 )
759 ( 2.0,0):( 0.48121182505960, 0 )
762 ( 2, 3):( 0.15735549884499, -0.22996290237721)
763 (-2, 3):( -0.15735549884499, -0.22996290237721)
764 (-2,-3):( -0.15735549884499, 0.22996290237721)
765 ( 2,-3):( 0.15735549884499, 0.22996290237721)
768 (-2.0,0):( -0.54930614433405, 0 )
769 (-0.5,0):( -0.54930614433405, 1.57079632679490)
770 ( 0.5,0):( 0.54930614433405, 1.57079632679490)
771 ( 2.0,0):( 0.54930614433405, 0 )
774 ( 2, 3):( 0.14694666622553, -0.23182380450040)
775 (-2, 3):( -0.14694666622553, -0.23182380450040)
776 (-2,-3):( -0.14694666622553, 0.23182380450040)
777 ( 2,-3):( 0.14694666622553, 0.23182380450040)