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Quick pre-release fixes: clean up results in File::Spec::VMS and
[p5sagit/p5-mst-13.2.git] / t / lib / complex.t
CommitLineData
89d0527d 1#!./perl
2
fb73857a 3# $RCSfile: complex.t,v $
89d0527d 4#
5aabfad6 5# Regression tests for the Math::Complex pacakge
b42d0ec9 6# -- Raphael Manfredi since Sep 1996
7# -- Jarkko Hietaniemi since Mar 1997
8# -- Daniel S. Lewart since Sep 1997
5aabfad6 9
89d0527d 10BEGIN {
11 chdir 't' if -d 't';
93430cb4 12 unshift @INC, '../lib';
89d0527d 13}
5aabfad6 14
89d0527d 15use Math::Complex;
16
2820d885 17my $VERSION = sprintf("%s", q$Id: complex.t,v 1.9 1998/11/01 00:00:00 dsl Exp $ =~ /(\d+\.d+)/);
b42d0ec9 18
fb73857a 19my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
20
89d0527d 21$test = 0;
22$| = 1;
fb73857a 23my @script = (
24 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' .
25 "\n\n"
26);
b42d0ec9 27my $eps = 1e-13;
89d0527d 28
d09ae4e6 29if ($^O eq 'unicos') { # For some reason root() produces very inaccurate
30 $eps = 1e-11; # results in Cray UNICOS, and occasionally also
31} # cos(), sin(), cosh(), sinh(). The division
32 # of doubles is the current suspect.
33
89d0527d 34while (<DATA>) {
0c721ce2 35 s/^\s+//;
36 next if $_ eq '' || /^\#/;
37 chomp;
38 $test_set = 0; # Assume not a test over a set of values
0e505df1 39 if (/^&(.+)/) {
89d0527d 40 $op = $1;
41 next;
42 }
0e505df1 43 elsif (/^\{(.+)\}/) {
89d0527d 44 set($1, \@set, \@val);
45 next;
46 }
47 elsif (s/^\|//) {
0c721ce2 48 $test_set = 1; # Requests we loop over the set...
89d0527d 49 }
50 my @args = split(/:/);
0c721ce2 51 if ($test_set == 1) {
89d0527d 52 my $i;
53 for ($i = 0; $i < @set; $i++) {
0c721ce2 54 # complex number
55 $target = $set[$i];
56 # textual value as found in set definition
57 $zvalue = $val[$i];
89d0527d 58 test($zvalue, $target, @args);
59 }
60 } else {
61 test($op, undef, @args);
62 }
63}
64
b42d0ec9 65#
66
67sub test_mutators {
68 my $op;
69
70 $test++;
71push(@script, <<'EOT');
72{
73 my $z = cplx( 1, 1);
74 $z->Re(2);
75 $z->Im(3);
16357284 76 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
b42d0ec9 77 print 'not ' unless Re($z) == 2 and Im($z) == 3;
78EOT
79 push(@script, qq(print "ok $test\\n"}\n));
80
81 $test++;
82push(@script, <<'EOT');
83{
84 my $z = cplx( 1, 1);
85 $z->abs(3 * sqrt(2));
16357284 86 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
b42d0ec9 87 print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and
88 (arg($z) - pi / 4 ) < $eps and
89 (Re($z) - 3 ) < $eps and
90 (Im($z) - 3 ) < $eps;
91EOT
92 push(@script, qq(print "ok $test\\n"}\n));
93
94 $test++;
95push(@script, <<'EOT');
96{
97 my $z = cplx( 1, 1);
98 $z->arg(-3 / 4 * pi);
16357284 99 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
b42d0ec9 100 print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and
101 (abs($z) - sqrt(2) ) < $eps and
102 (Re($z) + 1 ) < $eps and
103 (Im($z) + 1 ) < $eps;
104EOT
105 push(@script, qq(print "ok $test\\n"}\n));
106}
107
108test_mutators();
109
110my $constants = '
111my $i = cplx(0, 1);
112my $pi = cplx(pi, 0);
113my $pii = cplx(0, pi);
114my $pip2 = cplx(pi/2, 0);
115my $zero = cplx(0, 0);
116';
117
118push(@script, $constants);
119
120
5cd24f17 121# test the divbyzeros
122
0e505df1 123sub test_dbz {
124 for my $op (@_) {
125 $test++;
b42d0ec9 126 push(@script, <<EOT);
16357284 127 eval '$op';
128 (\$bad) = (\$@ =~ /(.+)/);
129 print "# $test op = $op divbyzero? \$bad...\n";
130 print 'not ' unless (\$@ =~ /Division by zero/);
b42d0ec9 131EOT
132 push(@script, qq(print "ok $test\\n";\n));
0e505df1 133 }
134}
135
8c03c583 136# test the logofzeros
137
138sub test_loz {
139 for my $op (@_) {
140 $test++;
b42d0ec9 141 push(@script, <<EOT);
16357284 142 eval '$op';
143 (\$bad) = (\$@ =~ /(.+)/);
144 print "# $test op = $op logofzero? \$bad...\n";
145 print 'not ' unless (\$@ =~ /Logarithm of zero/);
b42d0ec9 146EOT
147 push(@script, qq(print "ok $test\\n";\n));
8c03c583 148 }
149}
150
5cd24f17 151test_dbz(
152 'i/0',
b42d0ec9 153 'acot(0)',
154 'acot(+$i)',
155# 'acoth(-1)', # Log of zero.
156 'acoth(0)',
157 'acoth(+1)',
5cd24f17 158 'acsc(0)',
5cd24f17 159 'acsch(0)',
b42d0ec9 160 'asec(0)',
161 'asech(0)',
162 'atan(-$i)',
163 'atan($i)',
164# 'atanh(-1)', # Log of zero.
165 'atanh(+1)',
166 'cot(0)',
167 'coth(0)',
168 'csc(0)',
169 'tan($pip2)',
170 'csch(0)',
171 'tan($pip2)',
8c03c583 172 );
173
174test_loz(
fb73857a 175 'log($zero)',
b42d0ec9 176 'acot(-$i)',
8c03c583 177 'atanh(-1)',
178 'acoth(-1)',
5cd24f17 179 );
180
0e505df1 181# test the bad roots
182
183sub test_broot {
5cd24f17 184 for my $op (@_) {
185 $test++;
b42d0ec9 186 push(@script, <<EOT);
16357284 187 eval 'root(2, $op)';
188 (\$bad) = (\$@ =~ /(.+)/);
189 print "# $test op = $op badroot? \$bad...\n";
190 print 'not ' unless (\$@ =~ /root must be/);
b42d0ec9 191EOT
192 push(@script, qq(print "ok $test\\n";\n));
5cd24f17 193 }
194}
195
0e505df1 196test_broot(qw(-3 -2.1 0 0.99));
197
16357284 198sub test_display_format {
199 push @script, <<EOS;
200 my \$j = (root(1,3))[1];
201
202 \$j->display_format('polar');
203EOS
204
205 $test++;
206 push @script, <<EOS;
207 print "# display_format polar?\n";
208 print "not " unless \$j->display_format eq 'polar';
209 print "ok $test\n";
210EOS
211
212 $test++;
213 push @script, <<EOS;
214 print "# j = \$j\n";
215 print "not " unless "\$j" eq "[1,2pi/3]";
216 print "ok $test\n";
217
218 my %display_format;
219
220 %display_format = \$j->display_format;
221EOS
222
223 $test++;
224 push @script, <<EOS;
225 print "# display_format{style} polar?\n";
226 print "not " unless \$display_format{style} eq 'polar';
227 print "ok $test\n";
228EOS
229
230 $test++;
231 push @script, <<EOS;
232 print "# keys %display_format == 2?\n";
233 print "not " unless keys %display_format == 2;
234 print "ok $test\n";
235
236 \$j->display_format('style' => 'cartesian', 'format' => '%.5f');
237EOS
238
239 $test++;
240 push @script, <<EOS;
241 print "# j = \$j\n";
242 print "not " unless "\$j" eq "-0.50000+0.86603i";
243 print "ok $test\n";
244
245 %display_format = \$j->display_format;
246EOS
247
248 $test++;
249 push @script, <<EOS;
250 print "# display_format{format} %.5f?\n";
251 print "not " unless \$display_format{format} eq '%.5f';
252 print "ok $test\n";
253EOS
254
255 $test++;
256 push @script, <<EOS;
257 print "# keys %display_format == 3?\n";
258 print "not " unless keys %display_format == 3;
259 print "ok $test\n";
260
261 \$j->display_format('format' => undef);
262EOS
263
264 $test++;
265 push @script, <<EOS;
09319b96 266 my \$dj = "\$j"; \$dj =~ s/(\\d{14})\\d+i/\$1i/;
267 print "# j = \$dj (truncated for display)\n";
268 print "not " unless \$dj eq "-0.5+0.86602540378443i";
16357284 269 print "ok $test\n";
270
271 \$j->display_format('style' => 'polar', 'polar_pretty_print' => 0);
272EOS
273
274 $test++;
275 push @script, <<EOS;
09319b96 276 my \$dj = "\$j"; \$dj =~ s/(\\d{12})\\d+\]/\$1]/;
277 print "# j = \$dj (truncated for display)\n";
278 print "not " unless \$dj eq "[1,2.094395102393]";
16357284 279 print "ok $test\n";
280
281 \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)');
282EOS
283 $test++;
284 push @script, <<EOS;
285 print "# j = \$j\n";
286 print "not " unless "\$j" eq "(-0.5)+(0.86603)i";
287 print "ok $test\n";
288EOS
289}
290
291test_display_format();
292
89d0527d 293print "1..$test\n";
fe82cf6e 294eval join '', @script;
89d0527d 295die $@ if $@;
296
0e505df1 297sub abop {
298 my ($op) = @_;
299
300 push(@script, qq(print "# $op=\n";));
301}
302
89d0527d 303sub test {
304 my ($op, $z, @args) = @_;
0e505df1 305 my ($baop) = 0;
89d0527d 306 $test++;
307 my $i;
0e505df1 308 $baop = 1 if ($op =~ s/;=$//);
89d0527d 309 for ($i = 0; $i < @args; $i++) {
310 $val = value($args[$i]);
fe82cf6e 311 push @script, "\$z$i = $val;\n";
89d0527d 312 }
313 if (defined $z) {
314 $args = "'$op'"; # Really the value
0c721ce2 315 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
fe82cf6e 316 push @script, "\$res = $try; ";
317 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
89d0527d 318 } else {
319 my ($try, $args);
320 if (@args == 2) {
321 $try = "$op \$z0";
322 $args = "'$args[0]'";
323 } else {
324 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
325 $args = "'$args[0]', '$args[1]'";
326 }
fe82cf6e 327 push @script, "\$res = $try; ";
328 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
0e505df1 329 if (@args > 2 and $baop) { # binary assignment ops
330 $test++;
331 # check the op= works
332 push @script, <<EOB;
333{
fb73857a 334 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
0e505df1 335
336 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
337
fb73857a 338 my \$zb = cplx(\$z1r, \$z1i);
0e505df1 339
340 \$za $op= \$zb;
341 my (\$zbr, \$zbi) = \@{\$zb->cartesian};
342
343 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
344EOB
345 $test++;
346 # check that the rhs has not changed
347 push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
b42d0ec9 348 push @script, qq(print "ok $test\\n";\n);
0e505df1 349 push @script, "}\n";
350 }
89d0527d 351 }
352}
353
354sub set {
355 my ($set, $setref, $valref) = @_;
356 @{$setref} = ();
357 @{$valref} = ();
358 my @set = split(/;\s*/, $set);
359 my @res;
360 my $i;
361 for ($i = 0; $i < @set; $i++) {
362 push(@{$valref}, $set[$i]);
363 my $val = value($set[$i]);
fe82cf6e 364 push @script, "\$s$i = $val;\n";
365 push @{$setref}, "\$s$i";
89d0527d 366 }
367}
368
369sub value {
370 local ($_) = @_;
371 if (/^\s*\((.*),(.*)\)/) {
372 return "cplx($1,$2)";
373 }
b42d0ec9 374 elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
375 return "cplx($1,0)";
376 }
89d0527d 377 elsif (/^\s*\[(.*),(.*)\]/) {
378 return "cplxe($1,$2)";
379 }
380 elsif (/^\s*'(.*)'/) {
381 my $ex = $1;
382 $ex =~ s/\bz\b/$target/g;
383 $ex =~ s/\br\b/abs($target)/g;
384 $ex =~ s/\bt\b/arg($target)/g;
385 $ex =~ s/\ba\b/Re($target)/g;
386 $ex =~ s/\bb\b/Im($target)/g;
387 return $ex;
388 }
389 elsif (/^\s*"(.*)"/) {
390 return "\"$1\"";
391 }
392 return $_;
393}
394
395sub check {
396 my ($test, $try, $got, $expected, @z) = @_;
0c721ce2 397
16357284 398 print "# @_\n";
0c721ce2 399
400 if ("$got" eq "$expected"
401 ||
402 ($expected =~ /^-?\d/ && $got == $expected)
403 ||
404 (abs($got - $expected) < $eps)
405 ) {
89d0527d 406 print "ok $test\n";
407 } else {
408 print "not ok $test\n";
409 my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
410 print "# '$try' expected: '$expected' got: '$got' for $args\n";
411 }
412}
fb73857a 413
414sub addsq {
415 my ($z1, $z2) = @_;
416 return ($z1 + i*$z2) * ($z1 - i*$z2);
417}
418
419sub subsq {
420 my ($z1, $z2) = @_;
421 return ($z1 + $z2) * ($z1 - $z2);
422}
423
89d0527d 424__END__
0e505df1 425&+;=
89d0527d 426(3,4):(3,4):(6,8)
427(-3,4):(3,-4):(0,0)
428(3,4):-3:(0,4)
4291:(4,2):(5,2)
430[2,0]:[2,pi]:(0,0)
431
432&++
433(2,1):(3,1)
434
0e505df1 435&-;=
89d0527d 436(2,3):(-2,-3)
437[2,pi/2]:[2,-(pi)/2]
4382:[2,0]:(0,0)
439[3,0]:2:(1,0)
4403:(4,5):(-1,-5)
441(4,5):3:(1,5)
0e505df1 442(2,1):(3,5):(-1,-4)
89d0527d 443
444&--
445(1,2):(0,2)
446[2,pi]:[3,pi]
447
0e505df1 448&*;=
89d0527d 449(0,1):(0,1):(-1,0)
450(4,5):(1,0):(4,5)
451[2,2*pi/3]:(1,0):[2,2*pi/3]
4522:(0,1):(0,2)
453(0,1):3:(0,3)
454(0,1):(4,1):(-1,4)
455(2,1):(4,-1):(9,2)
456
0e505df1 457&/;=
89d0527d 458(3,4):(3,4):(1,0)
459(4,-5):1:(4,-5)
4601:(0,1):(0,-1)
461(0,6):(0,2):(3,0)
462(9,2):(4,-1):(2,1)
463[4,pi]:[2,pi/2]:[2,pi/2]
464[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
465
0e505df1 466&**;=
467(2,0):(3,0):(8,0)
468(3,0):(2,0):(9,0)
469(2,3):(4,0):(-119,-120)
ace5de91 470(0,0):(1,0):(0,0)
471(0,0):(2,3):(0,0)
472(1,0):(0,0):(1,0)
473(1,0):(1,0):(1,0)
474(1,0):(2,3):(1,0)
475(2,3):(0,0):(1,0)
476(2,3):(1,0):(2,3)
2820d885 477(0,0):(0,0):(1,0)
0e505df1 478
0c721ce2 479&Re
480(3,4):3
481(-3,4):-3
482[1,pi/2]:0
483
484&Im
485(3,4):4
486(3,-4):-4
487[1,pi/2]:1
488
89d0527d 489&abs
490(3,4):5
491(-3,4):5
492
0c721ce2 493&arg
494[2,0]:0
495[-2,0]:pi
496
89d0527d 497&~
498(4,5):(4,-5)
499(-3,4):(-3,-4)
500[2,pi/2]:[2,-(pi)/2]
501
502&<
503(3,4):(1,2):0
504(3,4):(3,2):0
505(3,4):(3,8):1
506(4,4):(5,129):1
507
508&==
509(3,4):(4,5):0
510(3,4):(3,5):0
511(3,4):(2,4):0
512(3,4):(3,4):1
513
514&sqrt
0c721ce2 515-9:(0,3)
89d0527d 516(-100,0):(0,10)
517(16,-30):(5,-3)
518
519&stringify_cartesian
520(-100,0):"-100"
521(0,1):"i"
522(4,-3):"4-3i"
523(4,0):"4"
524(-4,0):"-4"
525(-2,4):"-2+4i"
526(-2,-1):"-2-i"
527
528&stringify_polar
529[-1, 0]:"[1,pi]"
530[1, pi/3]:"[1,pi/3]"
531[6, -2*pi/3]:"[6,-2pi/3]"
532[0.5, -9*pi/11]:"[0.5,-9pi/11]"
533
534{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
535
536|'z + ~z':'2*Re(z)'
537|'z - ~z':'2*i*Im(z)'
538|'z * ~z':'abs(z) * abs(z)'
539
8c03c583 540{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
89d0527d 541
0c721ce2 542|'(root(z, 4))[1] ** 4':'z'
543|'(root(z, 5))[3] ** 5':'z'
544|'(root(z, 8))[7] ** 8':'z'
89d0527d 545|'abs(z)':'r'
0c721ce2 546|'acot(z)':'acotan(z)'
547|'acsc(z)':'acosec(z)'
fb73857a 548|'acsc(z)':'asin(1 / z)'
549|'asec(z)':'acos(1 / z)'
89d0527d 550|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d 551|'cos(acos(z))':'z'
fb73857a 552|'addsq(cos(z), sin(z))':1
89d0527d 553|'cos(z)':'cosh(i*z)'
fb73857a 554|'subsq(cosh(z), sinh(z))':1
0c721ce2 555|'cot(acot(z))':'z'
556|'cot(z)':'1 / tan(z)'
557|'cot(z)':'cotan(z)'
558|'csc(acsc(z))':'z'
559|'csc(z)':'1 / sin(z)'
560|'csc(z)':'cosec(z)'
89d0527d 561|'exp(log(z))':'z'
0c721ce2 562|'exp(z)':'exp(a) * exp(i * b)'
563|'ln(z)':'log(z)'
564|'log(exp(z))':'z'
565|'log(z)':'log(r) + i*t'
89d0527d 566|'log10(z)':'log(z) / log(10)'
89d0527d 567|'logn(z, 2)':'log(z) / log(2)'
0c721ce2 568|'logn(z, 3)':'log(z) / log(3)'
569|'sec(asec(z))':'z'
570|'sec(z)':'1 / cos(z)'
571|'sin(asin(z))':'z'
572|'sin(i * z)':'i * sinh(z)'
573|'sqrt(z) * sqrt(z)':'z'
574|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
575|'tan(atan(z))':'z'
576|'z**z':'exp(z * log(z))'
89d0527d 577
0c721ce2 578{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d 579
89d0527d 580|'cosh(acosh(z))':'z'
0c721ce2 581|'coth(acoth(z))':'z'
582|'coth(z)':'1 / tanh(z)'
583|'coth(z)':'cotanh(z)'
584|'csch(acsch(z))':'z'
585|'csch(z)':'1 / sinh(z)'
586|'csch(z)':'cosech(z)'
587|'sech(asech(z))':'z'
588|'sech(z)':'1 / cosh(z)'
589|'sinh(asinh(z))':'z'
89d0527d 590|'tanh(atanh(z))':'z'
89d0527d 591
0c721ce2 592{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d 593
89d0527d 594|'acos(cos(z)) ** 2':'z * z'
89d0527d 595|'acosh(cosh(z)) ** 2':'z * z'
0c721ce2 596|'acoth(z)':'acotanh(z)'
597|'acoth(z)':'atanh(1 / z)'
598|'acsch(z)':'acosech(z)'
599|'acsch(z)':'asinh(1 / z)'
600|'asech(z)':'acosh(1 / z)'
601|'asin(sin(z))':'z'
602|'asinh(sinh(z))':'z'
603|'atan(tan(z))':'z'
89d0527d 604|'atanh(tanh(z))':'z'
605
fb73857a 606&log
607(-2.0,0):( 0.69314718055995, 3.14159265358979)
608(-1.0,0):( 0 , 3.14159265358979)
609(-0.5,0):( -0.69314718055995, 3.14159265358979)
610( 0.5,0):( -0.69314718055995, 0 )
611( 1.0,0):( 0 , 0 )
612( 2.0,0):( 0.69314718055995, 0 )
613
614&log
615( 2, 3):( 1.28247467873077, 0.98279372324733)
616(-2, 3):( 1.28247467873077, 2.15879893034246)
617(-2,-3):( 1.28247467873077, -2.15879893034246)
618( 2,-3):( 1.28247467873077, -0.98279372324733)
619
0c721ce2 620&sin
8c03c583 621(-2.0,0):( -0.90929742682568, 0 )
622(-1.0,0):( -0.84147098480790, 0 )
623(-0.5,0):( -0.47942553860420, 0 )
624( 0.0,0):( 0 , 0 )
625( 0.5,0):( 0.47942553860420, 0 )
626( 1.0,0):( 0.84147098480790, 0 )
627( 2.0,0):( 0.90929742682568, 0 )
628
629&sin
0c721ce2 630( 2, 3):( 9.15449914691143, -4.16890695996656)
631(-2, 3):( -9.15449914691143, -4.16890695996656)
632(-2,-3):( -9.15449914691143, 4.16890695996656)
633( 2,-3):( 9.15449914691143, 4.16890695996656)
634
635&cos
8c03c583 636(-2.0,0):( -0.41614683654714, 0 )
637(-1.0,0):( 0.54030230586814, 0 )
638(-0.5,0):( 0.87758256189037, 0 )
639( 0.0,0):( 1 , 0 )
640( 0.5,0):( 0.87758256189037, 0 )
641( 1.0,0):( 0.54030230586814, 0 )
642( 2.0,0):( -0.41614683654714, 0 )
643
644&cos
0c721ce2 645( 2, 3):( -4.18962569096881, -9.10922789375534)
646(-2, 3):( -4.18962569096881, 9.10922789375534)
647(-2,-3):( -4.18962569096881, -9.10922789375534)
648( 2,-3):( -4.18962569096881, 9.10922789375534)
649
650&tan
8c03c583 651(-2.0,0):( 2.18503986326152, 0 )
652(-1.0,0):( -1.55740772465490, 0 )
653(-0.5,0):( -0.54630248984379, 0 )
654( 0.0,0):( 0 , 0 )
655( 0.5,0):( 0.54630248984379, 0 )
656( 1.0,0):( 1.55740772465490, 0 )
657( 2.0,0):( -2.18503986326152, 0 )
658
659&tan
0c721ce2 660( 2, 3):( -0.00376402564150, 1.00323862735361)
661(-2, 3):( 0.00376402564150, 1.00323862735361)
662(-2,-3):( 0.00376402564150, -1.00323862735361)
663( 2,-3):( -0.00376402564150, -1.00323862735361)
664
665&sec
8c03c583 666(-2.0,0):( -2.40299796172238, 0 )
667(-1.0,0):( 1.85081571768093, 0 )
668(-0.5,0):( 1.13949392732455, 0 )
669( 0.0,0):( 1 , 0 )
670( 0.5,0):( 1.13949392732455, 0 )
671( 1.0,0):( 1.85081571768093, 0 )
672( 2.0,0):( -2.40299796172238, 0 )
673
674&sec
0c721ce2 675( 2, 3):( -0.04167496441114, 0.09061113719624)
676(-2, 3):( -0.04167496441114, -0.09061113719624)
677(-2,-3):( -0.04167496441114, 0.09061113719624)
678( 2,-3):( -0.04167496441114, -0.09061113719624)
679
680&csc
8c03c583 681(-2.0,0):( -1.09975017029462, 0 )
682(-1.0,0):( -1.18839510577812, 0 )
683(-0.5,0):( -2.08582964293349, 0 )
684( 0.5,0):( 2.08582964293349, 0 )
685( 1.0,0):( 1.18839510577812, 0 )
686( 2.0,0):( 1.09975017029462, 0 )
687
688&csc
0c721ce2 689( 2, 3):( 0.09047320975321, 0.04120098628857)
690(-2, 3):( -0.09047320975321, 0.04120098628857)
691(-2,-3):( -0.09047320975321, -0.04120098628857)
692( 2,-3):( 0.09047320975321, -0.04120098628857)
693
694&cot
8c03c583 695(-2.0,0):( 0.45765755436029, 0 )
696(-1.0,0):( -0.64209261593433, 0 )
697(-0.5,0):( -1.83048772171245, 0 )
698( 0.5,0):( 1.83048772171245, 0 )
699( 1.0,0):( 0.64209261593433, 0 )
700( 2.0,0):( -0.45765755436029, 0 )
701
702&cot
0c721ce2 703( 2, 3):( -0.00373971037634, -0.99675779656936)
704(-2, 3):( 0.00373971037634, -0.99675779656936)
705(-2,-3):( 0.00373971037634, 0.99675779656936)
706( 2,-3):( -0.00373971037634, 0.99675779656936)
707
708&asin
8c03c583 709(-2.0,0):( -1.57079632679490, 1.31695789692482)
710(-1.0,0):( -1.57079632679490, 0 )
711(-0.5,0):( -0.52359877559830, 0 )
712( 0.0,0):( 0 , 0 )
713( 0.5,0):( 0.52359877559830, 0 )
714( 1.0,0):( 1.57079632679490, 0 )
715( 2.0,0):( 1.57079632679490, -1.31695789692482)
716
717&asin
0c721ce2 718( 2, 3):( 0.57065278432110, 1.98338702991654)
719(-2, 3):( -0.57065278432110, 1.98338702991654)
720(-2,-3):( -0.57065278432110, -1.98338702991654)
721( 2,-3):( 0.57065278432110, -1.98338702991654)
722
723&acos
8c03c583 724(-2.0,0):( 3.14159265358979, -1.31695789692482)
725(-1.0,0):( 3.14159265358979, 0 )
726(-0.5,0):( 2.09439510239320, 0 )
727( 0.0,0):( 1.57079632679490, 0 )
728( 0.5,0):( 1.04719755119660, 0 )
729( 1.0,0):( 0 , 0 )
730( 2.0,0):( 0 , 1.31695789692482)
731
732&acos
0c721ce2 733( 2, 3):( 1.00014354247380, -1.98338702991654)
734(-2, 3):( 2.14144911111600, -1.98338702991654)
735(-2,-3):( 2.14144911111600, 1.98338702991654)
736( 2,-3):( 1.00014354247380, 1.98338702991654)
737
738&atan
8c03c583 739(-2.0,0):( -1.10714871779409, 0 )
740(-1.0,0):( -0.78539816339745, 0 )
741(-0.5,0):( -0.46364760900081, 0 )
742( 0.0,0):( 0 , 0 )
743( 0.5,0):( 0.46364760900081, 0 )
744( 1.0,0):( 0.78539816339745, 0 )
745( 2.0,0):( 1.10714871779409, 0 )
746
747&atan
0c721ce2 748( 2, 3):( 1.40992104959658, 0.22907268296854)
749(-2, 3):( -1.40992104959658, 0.22907268296854)
750(-2,-3):( -1.40992104959658, -0.22907268296854)
751( 2,-3):( 1.40992104959658, -0.22907268296854)
752
753&asec
8c03c583 754(-2.0,0):( 2.09439510239320, 0 )
755(-1.0,0):( 3.14159265358979, 0 )
756(-0.5,0):( 3.14159265358979, -1.31695789692482)
757( 0.5,0):( 0 , 1.31695789692482)
758( 1.0,0):( 0 , 0 )
759( 2.0,0):( 1.04719755119660, 0 )
760
761&asec
0c721ce2 762( 2, 3):( 1.42041072246703, 0.23133469857397)
763(-2, 3):( 1.72118193112276, 0.23133469857397)
764(-2,-3):( 1.72118193112276, -0.23133469857397)
765( 2,-3):( 1.42041072246703, -0.23133469857397)
766
767&acsc
8c03c583 768(-2.0,0):( -0.52359877559830, 0 )
769(-1.0,0):( -1.57079632679490, 0 )
770(-0.5,0):( -1.57079632679490, 1.31695789692482)
771( 0.5,0):( 1.57079632679490, -1.31695789692482)
772( 1.0,0):( 1.57079632679490, 0 )
773( 2.0,0):( 0.52359877559830, 0 )
774
775&acsc
0c721ce2 776( 2, 3):( 0.15038560432786, -0.23133469857397)
777(-2, 3):( -0.15038560432786, -0.23133469857397)
778(-2,-3):( -0.15038560432786, 0.23133469857397)
779( 2,-3):( 0.15038560432786, 0.23133469857397)
780
781&acot
8c03c583 782(-2.0,0):( -0.46364760900081, 0 )
783(-1.0,0):( -0.78539816339745, 0 )
784(-0.5,0):( -1.10714871779409, 0 )
785( 0.5,0):( 1.10714871779409, 0 )
786( 1.0,0):( 0.78539816339745, 0 )
787( 2.0,0):( 0.46364760900081, 0 )
788
789&acot
0c721ce2 790( 2, 3):( 0.16087527719832, -0.22907268296854)
791(-2, 3):( -0.16087527719832, -0.22907268296854)
792(-2,-3):( -0.16087527719832, 0.22907268296854)
793( 2,-3):( 0.16087527719832, 0.22907268296854)
794
795&sinh
8c03c583 796(-2.0,0):( -3.62686040784702, 0 )
797(-1.0,0):( -1.17520119364380, 0 )
798(-0.5,0):( -0.52109530549375, 0 )
799( 0.0,0):( 0 , 0 )
800( 0.5,0):( 0.52109530549375, 0 )
801( 1.0,0):( 1.17520119364380, 0 )
802( 2.0,0):( 3.62686040784702, 0 )
803
804&sinh
0c721ce2 805( 2, 3):( -3.59056458998578, 0.53092108624852)
806(-2, 3):( 3.59056458998578, 0.53092108624852)
807(-2,-3):( 3.59056458998578, -0.53092108624852)
808( 2,-3):( -3.59056458998578, -0.53092108624852)
809
810&cosh
8c03c583 811(-2.0,0):( 3.76219569108363, 0 )
812(-1.0,0):( 1.54308063481524, 0 )
813(-0.5,0):( 1.12762596520638, 0 )
814( 0.0,0):( 1 , 0 )
815( 0.5,0):( 1.12762596520638, 0 )
816( 1.0,0):( 1.54308063481524, 0 )
817( 2.0,0):( 3.76219569108363, 0 )
818
819&cosh
0c721ce2 820( 2, 3):( -3.72454550491532, 0.51182256998738)
821(-2, 3):( -3.72454550491532, -0.51182256998738)
822(-2,-3):( -3.72454550491532, 0.51182256998738)
823( 2,-3):( -3.72454550491532, -0.51182256998738)
824
825&tanh
8c03c583 826(-2.0,0):( -0.96402758007582, 0 )
827(-1.0,0):( -0.76159415595576, 0 )
828(-0.5,0):( -0.46211715726001, 0 )
829( 0.0,0):( 0 , 0 )
830( 0.5,0):( 0.46211715726001, 0 )
831( 1.0,0):( 0.76159415595576, 0 )
832( 2.0,0):( 0.96402758007582, 0 )
833
834&tanh
0c721ce2 835( 2, 3):( 0.96538587902213, -0.00988437503832)
836(-2, 3):( -0.96538587902213, -0.00988437503832)
837(-2,-3):( -0.96538587902213, 0.00988437503832)
838( 2,-3):( 0.96538587902213, 0.00988437503832)
839
840&sech
8c03c583 841(-2.0,0):( 0.26580222883408, 0 )
842(-1.0,0):( 0.64805427366389, 0 )
843(-0.5,0):( 0.88681888397007, 0 )
844( 0.0,0):( 1 , 0 )
845( 0.5,0):( 0.88681888397007, 0 )
846( 1.0,0):( 0.64805427366389, 0 )
847( 2.0,0):( 0.26580222883408, 0 )
848
849&sech
0c721ce2 850( 2, 3):( -0.26351297515839, -0.03621163655877)
851(-2, 3):( -0.26351297515839, 0.03621163655877)
852(-2,-3):( -0.26351297515839, -0.03621163655877)
853( 2,-3):( -0.26351297515839, 0.03621163655877)
854
855&csch
8c03c583 856(-2.0,0):( -0.27572056477178, 0 )
857(-1.0,0):( -0.85091812823932, 0 )
858(-0.5,0):( -1.91903475133494, 0 )
859( 0.5,0):( 1.91903475133494, 0 )
860( 1.0,0):( 0.85091812823932, 0 )
861( 2.0,0):( 0.27572056477178, 0 )
862
863&csch
0c721ce2 864( 2, 3):( -0.27254866146294, -0.04030057885689)
865(-2, 3):( 0.27254866146294, -0.04030057885689)
866(-2,-3):( 0.27254866146294, 0.04030057885689)
867( 2,-3):( -0.27254866146294, 0.04030057885689)
868
869&coth
8c03c583 870(-2.0,0):( -1.03731472072755, 0 )
871(-1.0,0):( -1.31303528549933, 0 )
872(-0.5,0):( -2.16395341373865, 0 )
873( 0.5,0):( 2.16395341373865, 0 )
874( 1.0,0):( 1.31303528549933, 0 )
875( 2.0,0):( 1.03731472072755, 0 )
876
877&coth
0c721ce2 878( 2, 3):( 1.03574663776500, 0.01060478347034)
879(-2, 3):( -1.03574663776500, 0.01060478347034)
880(-2,-3):( -1.03574663776500, -0.01060478347034)
881( 2,-3):( 1.03574663776500, -0.01060478347034)
882
883&asinh
8c03c583 884(-2.0,0):( -1.44363547517881, 0 )
885(-1.0,0):( -0.88137358701954, 0 )
886(-0.5,0):( -0.48121182505960, 0 )
887( 0.0,0):( 0 , 0 )
888( 0.5,0):( 0.48121182505960, 0 )
889( 1.0,0):( 0.88137358701954, 0 )
890( 2.0,0):( 1.44363547517881, 0 )
891
892&asinh
0c721ce2 893( 2, 3):( 1.96863792579310, 0.96465850440760)
894(-2, 3):( -1.96863792579310, 0.96465850440761)
895(-2,-3):( -1.96863792579310, -0.96465850440761)
896( 2,-3):( 1.96863792579310, -0.96465850440760)
897
898&acosh
8c03c583 899(-2.0,0):( -1.31695789692482, 3.14159265358979)
900(-1.0,0):( 0, 3.14159265358979)
901(-0.5,0):( 0, 2.09439510239320)
902( 0.0,0):( 0, 1.57079632679490)
903( 0.5,0):( 0, 1.04719755119660)
904( 1.0,0):( 0 , 0 )
905( 2.0,0):( 1.31695789692482, 0 )
906
907&acosh
0c721ce2 908( 2, 3):( 1.98338702991654, 1.00014354247380)
909(-2, 3):( -1.98338702991653, -2.14144911111600)
910(-2,-3):( -1.98338702991653, 2.14144911111600)
911( 2,-3):( 1.98338702991654, -1.00014354247380)
912
913&atanh
8c03c583 914(-2.0,0):( -0.54930614433405, 1.57079632679490)
915(-0.5,0):( -0.54930614433405, 0 )
916( 0.0,0):( 0 , 0 )
917( 0.5,0):( 0.54930614433405, 0 )
918( 2.0,0):( 0.54930614433405, 1.57079632679490)
919
920&atanh
0c721ce2 921( 2, 3):( 0.14694666622553, 1.33897252229449)
922(-2, 3):( -0.14694666622553, 1.33897252229449)
923(-2,-3):( -0.14694666622553, -1.33897252229449)
924( 2,-3):( 0.14694666622553, -1.33897252229449)
925
926&asech
8c03c583 927(-2.0,0):( 0 , 2.09439510239320)
928(-1.0,0):( 0 , 3.14159265358979)
929(-0.5,0):( -1.31695789692482, 3.14159265358979)
930( 0.5,0):( 1.31695789692482, 0 )
931( 1.0,0):( 0 , 0 )
932( 2.0,0):( 0 , 1.04719755119660)
933
934&asech
0c721ce2 935( 2, 3):( 0.23133469857397, -1.42041072246703)
936(-2, 3):( -0.23133469857397, 1.72118193112276)
937(-2,-3):( -0.23133469857397, -1.72118193112276)
938( 2,-3):( 0.23133469857397, 1.42041072246703)
939
940&acsch
8c03c583 941(-2.0,0):( -0.48121182505960, 0 )
942(-1.0,0):( -0.88137358701954, 0 )
943(-0.5,0):( -1.44363547517881, 0 )
944( 0.5,0):( 1.44363547517881, 0 )
945( 1.0,0):( 0.88137358701954, 0 )
946( 2.0,0):( 0.48121182505960, 0 )
947
948&acsch
0c721ce2 949( 2, 3):( 0.15735549884499, -0.22996290237721)
950(-2, 3):( -0.15735549884499, -0.22996290237721)
951(-2,-3):( -0.15735549884499, 0.22996290237721)
952( 2,-3):( 0.15735549884499, 0.22996290237721)
953
954&acoth
8c03c583 955(-2.0,0):( -0.54930614433405, 0 )
956(-0.5,0):( -0.54930614433405, 1.57079632679490)
957( 0.5,0):( 0.54930614433405, 1.57079632679490)
958( 2.0,0):( 0.54930614433405, 0 )
959
960&acoth
0c721ce2 961( 2, 3):( 0.14694666622553, -0.23182380450040)
962(-2, 3):( -0.14694666622553, -0.23182380450040)
963(-2,-3):( -0.14694666622553, 0.23182380450040)
964( 2,-3):( 0.14694666622553, 0.23182380450040)
965
966# eof
Unnamed repository; edit this file to name it for gitweb.