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1#!./perl
2
fb73857a 3# $RCSfile: complex.t,v $
89d0527d 4#
5aabfad6 5# Regression tests for the Math::Complex pacakge
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6# -- Raphael Manfredi since Sep 1996
7# -- Jarkko Hietaniemi since Mar 1997
8# -- Daniel S. Lewart since Sep 1997
5aabfad6 9
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10BEGIN {
11 chdir 't' if -d 't';
93430cb4 12 unshift @INC, '../lib';
89d0527d 13}
5aabfad6 14
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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
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19my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
20
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21$test = 0;
22$| = 1;
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23my @script = (
24 'my ($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
f3ff050f 30 $eps = 1e-10; # results in Cray UNICOS, and occasionally also
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31} # cos(), sin(), cosh(), sinh(). The division
32 # of doubles is the current suspect.
33
89d0527d 34while (<DATA>) {
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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 (/^&(.+)/) {
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40 $op = $1;
41 next;
42 }
0e505df1 43 elsif (/^\{(.+)\}/) {
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44 set($1, \@set, \@val);
45 next;
46 }
47 elsif (s/^\|//) {
0c721ce2 48 $test_set = 1; # Requests we loop over the set...
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49 }
50 my @args = split(/:/);
0c721ce2 51 if ($test_set == 1) {
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52 my $i;
53 for ($i = 0; $i < @set; $i++) {
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54 # complex number
55 $target = $set[$i];
56 # textual value as found in set definition
57 $zvalue = $val[$i];
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58 test($zvalue, $target, @args);
59 }
60 } else {
61 test($op, undef, @args);
62 }
63}
64
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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 = $z\n";
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77 print 'not ' unless Re($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 = $z\n";
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87 print 'not ' unless (abs($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 = $z\n";
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100 print 'not ' unless (arg($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
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121# test the divbyzeros
122
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123sub test_dbz {
124 for my $op (@_) {
125 $test++;
b42d0ec9 126 push(@script, <<EOT);
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127 eval '$op';
128 (\$bad) = (\$@ =~ /(.+)/);
129 print "# $test op = $op divbyzero? \$bad...\n";
130 print 'not ' unless (\$@ =~ /Division by zero/);
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131EOT
132 push(@script, qq(print "ok $test\\n";\n));
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133 }
134}
135
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136# test the logofzeros
137
138sub test_loz {
139 for my $op (@_) {
140 $test++;
b42d0ec9 141 push(@script, <<EOT);
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142 eval '$op';
143 (\$bad) = (\$@ =~ /(.+)/);
144 print "# $test op = $op logofzero? \$bad...\n";
145 print 'not ' unless (\$@ =~ /Logarithm of zero/);
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146EOT
147 push(@script, qq(print "ok $test\\n";\n));
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148 }
149}
150
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151test_dbz(
152 'i/0',
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153 'acot(0)',
154 'acot(+$i)',
155# 'acoth(-1)', # Log of zero.
156 'acoth(0)',
157 'acoth(+1)',
5cd24f17 158 'acsc(0)',
5cd24f17 159 'acsch(0)',
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160 'asec(0)',
161 'asech(0)',
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162 'atan($i)',
163# 'atanh(-1)', # Log of zero.
164 'atanh(+1)',
165 'cot(0)',
166 'coth(0)',
167 'csc(0)',
b42d0ec9 168 'csch(0)',
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169 );
170
171test_loz(
fb73857a 172 'log($zero)',
1fa12f56 173 'atan(-$i)',
b42d0ec9 174 'acot(-$i)',
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175 'atanh(-1)',
176 'acoth(-1)',
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177 );
178
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179# test the bad roots
180
181sub test_broot {
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182 for my $op (@_) {
183 $test++;
b42d0ec9 184 push(@script, <<EOT);
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185 eval 'root(2, $op)';
186 (\$bad) = (\$@ =~ /(.+)/);
187 print "# $test op = $op badroot? \$bad...\n";
1fa12f56 188 print 'not ' unless (\$@ =~ /root rank must be/);
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189EOT
190 push(@script, qq(print "ok $test\\n";\n));
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191 }
192}
193
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194test_broot(qw(-3 -2.1 0 0.99));
195
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196sub test_display_format {
197 push @script, <<EOS;
198 my \$j = (root(1,3))[1];
199
200 \$j->display_format('polar');
201EOS
202
203 $test++;
204 push @script, <<EOS;
205 print "# display_format polar?\n";
206 print "not " unless \$j->display_format eq 'polar';
207 print "ok $test\n";
208EOS
209
210 $test++;
211 push @script, <<EOS;
212 print "# j = \$j\n";
213 print "not " unless "\$j" eq "[1,2pi/3]";
214 print "ok $test\n";
215
216 my %display_format;
217
218 %display_format = \$j->display_format;
219EOS
220
221 $test++;
222 push @script, <<EOS;
223 print "# display_format{style} polar?\n";
224 print "not " unless \$display_format{style} eq 'polar';
225 print "ok $test\n";
226EOS
227
228 $test++;
229 push @script, <<EOS;
230 print "# keys %display_format == 2?\n";
231 print "not " unless keys %display_format == 2;
232 print "ok $test\n";
233
234 \$j->display_format('style' => 'cartesian', 'format' => '%.5f');
235EOS
236
237 $test++;
238 push @script, <<EOS;
239 print "# j = \$j\n";
240 print "not " unless "\$j" eq "-0.50000+0.86603i";
241 print "ok $test\n";
242
243 %display_format = \$j->display_format;
244EOS
245
246 $test++;
247 push @script, <<EOS;
248 print "# display_format{format} %.5f?\n";
249 print "not " unless \$display_format{format} eq '%.5f';
250 print "ok $test\n";
251EOS
252
253 $test++;
254 push @script, <<EOS;
255 print "# keys %display_format == 3?\n";
256 print "not " unless keys %display_format == 3;
257 print "ok $test\n";
258
259 \$j->display_format('format' => undef);
260EOS
261
262 $test++;
263 push @script, <<EOS;
264 print "# j = \$j\n";
057216a3 265 print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/;
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266 print "ok $test\n";
267
268 \$j->display_format('style' => 'polar', 'polar_pretty_print' => 0);
269EOS
270
271 $test++;
272 push @script, <<EOS;
273 print "# j = \$j\n";
1ab88a68 274 print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/;
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275 print "ok $test\n";
276
277 \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)');
278EOS
279 $test++;
280 push @script, <<EOS;
281 print "# j = \$j\n";
282 print "not " unless "\$j" eq "(-0.5)+(0.86603)i";
283 print "ok $test\n";
284EOS
285}
286
287test_display_format();
288
89d0527d 289print "1..$test\n";
fe82cf6e 290eval join '', @script;
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291die $@ if $@;
292
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293sub abop {
294 my ($op) = @_;
295
296 push(@script, qq(print "# $op=\n";));
297}
298
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299sub test {
300 my ($op, $z, @args) = @_;
0e505df1 301 my ($baop) = 0;
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302 $test++;
303 my $i;
0e505df1 304 $baop = 1 if ($op =~ s/;=$//);
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305 for ($i = 0; $i < @args; $i++) {
306 $val = value($args[$i]);
fe82cf6e 307 push @script, "\$z$i = $val;\n";
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308 }
309 if (defined $z) {
310 $args = "'$op'"; # Really the value
0c721ce2 311 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
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312 push @script, "\$res = $try; ";
313 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
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314 } else {
315 my ($try, $args);
316 if (@args == 2) {
317 $try = "$op \$z0";
318 $args = "'$args[0]'";
319 } else {
320 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
321 $args = "'$args[0]', '$args[1]'";
322 }
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323 push @script, "\$res = $try; ";
324 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
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325 if (@args > 2 and $baop) { # binary assignment ops
326 $test++;
327 # check the op= works
328 push @script, <<EOB;
329{
fb73857a 330 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
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331
332 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
333
fb73857a 334 my \$zb = cplx(\$z1r, \$z1i);
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335
336 \$za $op= \$zb;
337 my (\$zbr, \$zbi) = \@{\$zb->cartesian};
338
339 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
340EOB
341 $test++;
342 # check that the rhs has not changed
343 push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
b42d0ec9 344 push @script, qq(print "ok $test\\n";\n);
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345 push @script, "}\n";
346 }
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347 }
348}
349
350sub set {
351 my ($set, $setref, $valref) = @_;
352 @{$setref} = ();
353 @{$valref} = ();
354 my @set = split(/;\s*/, $set);
355 my @res;
356 my $i;
357 for ($i = 0; $i < @set; $i++) {
358 push(@{$valref}, $set[$i]);
359 my $val = value($set[$i]);
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360 push @script, "\$s$i = $val;\n";
361 push @{$setref}, "\$s$i";
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362 }
363}
364
365sub value {
366 local ($_) = @_;
367 if (/^\s*\((.*),(.*)\)/) {
368 return "cplx($1,$2)";
369 }
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370 elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
371 return "cplx($1,0)";
372 }
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373 elsif (/^\s*\[(.*),(.*)\]/) {
374 return "cplxe($1,$2)";
375 }
376 elsif (/^\s*'(.*)'/) {
377 my $ex = $1;
378 $ex =~ s/\bz\b/$target/g;
379 $ex =~ s/\br\b/abs($target)/g;
380 $ex =~ s/\bt\b/arg($target)/g;
381 $ex =~ s/\ba\b/Re($target)/g;
382 $ex =~ s/\bb\b/Im($target)/g;
383 return $ex;
384 }
385 elsif (/^\s*"(.*)"/) {
386 return "\"$1\"";
387 }
388 return $_;
389}
390
391sub check {
392 my ($test, $try, $got, $expected, @z) = @_;
0c721ce2 393
16357284 394 print "# @_\n";
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395
396 if ("$got" eq "$expected"
397 ||
398 ($expected =~ /^-?\d/ && $got == $expected)
399 ||
400 (abs($got - $expected) < $eps)
401 ) {
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402 print "ok $test\n";
403 } else {
404 print "not ok $test\n";
405 my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
406 print "# '$try' expected: '$expected' got: '$got' for $args\n";
407 }
408}
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409
410sub addsq {
411 my ($z1, $z2) = @_;
412 return ($z1 + i*$z2) * ($z1 - i*$z2);
413}
414
415sub subsq {
416 my ($z1, $z2) = @_;
417 return ($z1 + $z2) * ($z1 - $z2);
418}
419
89d0527d 420__END__
0e505df1 421&+;=
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422(3,4):(3,4):(6,8)
423(-3,4):(3,-4):(0,0)
424(3,4):-3:(0,4)
4251:(4,2):(5,2)
426[2,0]:[2,pi]:(0,0)
427
428&++
429(2,1):(3,1)
430
0e505df1 431&-;=
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432(2,3):(-2,-3)
433[2,pi/2]:[2,-(pi)/2]
4342:[2,0]:(0,0)
435[3,0]:2:(1,0)
4363:(4,5):(-1,-5)
437(4,5):3:(1,5)
0e505df1 438(2,1):(3,5):(-1,-4)
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439
440&--
441(1,2):(0,2)
442[2,pi]:[3,pi]
443
0e505df1 444&*;=
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445(0,1):(0,1):(-1,0)
446(4,5):(1,0):(4,5)
447[2,2*pi/3]:(1,0):[2,2*pi/3]
4482:(0,1):(0,2)
449(0,1):3:(0,3)
450(0,1):(4,1):(-1,4)
451(2,1):(4,-1):(9,2)
452
0e505df1 453&/;=
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454(3,4):(3,4):(1,0)
455(4,-5):1:(4,-5)
4561:(0,1):(0,-1)
457(0,6):(0,2):(3,0)
458(9,2):(4,-1):(2,1)
459[4,pi]:[2,pi/2]:[2,pi/2]
460[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
461
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462&**;=
463(2,0):(3,0):(8,0)
464(3,0):(2,0):(9,0)
465(2,3):(4,0):(-119,-120)
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466(0,0):(1,0):(0,0)
467(0,0):(2,3):(0,0)
468(1,0):(0,0):(1,0)
469(1,0):(1,0):(1,0)
470(1,0):(2,3):(1,0)
471(2,3):(0,0):(1,0)
472(2,3):(1,0):(2,3)
2820d885 473(0,0):(0,0):(1,0)
0e505df1 474
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475&Re
476(3,4):3
477(-3,4):-3
478[1,pi/2]:0
479
480&Im
481(3,4):4
482(3,-4):-4
483[1,pi/2]:1
484
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485&abs
486(3,4):5
487(-3,4):5
488
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489&arg
490[2,0]:0
491[-2,0]:pi
492
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493&~
494(4,5):(4,-5)
495(-3,4):(-3,-4)
496[2,pi/2]:[2,-(pi)/2]
497
498&<
499(3,4):(1,2):0
500(3,4):(3,2):0
501(3,4):(3,8):1
502(4,4):(5,129):1
503
504&==
505(3,4):(4,5):0
506(3,4):(3,5):0
507(3,4):(2,4):0
508(3,4):(3,4):1
509
510&sqrt
0c721ce2 511-9:(0,3)
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512(-100,0):(0,10)
513(16,-30):(5,-3)
514
515&stringify_cartesian
516(-100,0):"-100"
517(0,1):"i"
518(4,-3):"4-3i"
519(4,0):"4"
520(-4,0):"-4"
521(-2,4):"-2+4i"
522(-2,-1):"-2-i"
523
524&stringify_polar
525[-1, 0]:"[1,pi]"
526[1, pi/3]:"[1,pi/3]"
527[6, -2*pi/3]:"[6,-2pi/3]"
528[0.5, -9*pi/11]:"[0.5,-9pi/11]"
529
530{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
531
532|'z + ~z':'2*Re(z)'
533|'z - ~z':'2*i*Im(z)'
534|'z * ~z':'abs(z) * abs(z)'
535
8c03c583 536{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
89d0527d 537
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538|'(root(z, 4))[1] ** 4':'z'
539|'(root(z, 5))[3] ** 5':'z'
540|'(root(z, 8))[7] ** 8':'z'
89d0527d 541|'abs(z)':'r'
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542|'acot(z)':'acotan(z)'
543|'acsc(z)':'acosec(z)'
fb73857a
PP
544|'acsc(z)':'asin(1 / z)'
545|'asec(z)':'acos(1 / z)'
89d0527d 546|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d 547|'cos(acos(z))':'z'
fb73857a 548|'addsq(cos(z), sin(z))':1
89d0527d 549|'cos(z)':'cosh(i*z)'
fb73857a 550|'subsq(cosh(z), sinh(z))':1
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551|'cot(acot(z))':'z'
552|'cot(z)':'1 / tan(z)'
553|'cot(z)':'cotan(z)'
554|'csc(acsc(z))':'z'
555|'csc(z)':'1 / sin(z)'
556|'csc(z)':'cosec(z)'
89d0527d 557|'exp(log(z))':'z'
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558|'exp(z)':'exp(a) * exp(i * b)'
559|'ln(z)':'log(z)'
560|'log(exp(z))':'z'
561|'log(z)':'log(r) + i*t'
89d0527d 562|'log10(z)':'log(z) / log(10)'
89d0527d 563|'logn(z, 2)':'log(z) / log(2)'
0c721ce2
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564|'logn(z, 3)':'log(z) / log(3)'
565|'sec(asec(z))':'z'
566|'sec(z)':'1 / cos(z)'
567|'sin(asin(z))':'z'
568|'sin(i * z)':'i * sinh(z)'
569|'sqrt(z) * sqrt(z)':'z'
570|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
571|'tan(atan(z))':'z'
572|'z**z':'exp(z * log(z))'
89d0527d 573
0c721ce2 574{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d 575
89d0527d 576|'cosh(acosh(z))':'z'
0c721ce2
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577|'coth(acoth(z))':'z'
578|'coth(z)':'1 / tanh(z)'
579|'coth(z)':'cotanh(z)'
580|'csch(acsch(z))':'z'
581|'csch(z)':'1 / sinh(z)'
582|'csch(z)':'cosech(z)'
583|'sech(asech(z))':'z'
584|'sech(z)':'1 / cosh(z)'
585|'sinh(asinh(z))':'z'
89d0527d 586|'tanh(atanh(z))':'z'
89d0527d 587
0c721ce2 588{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d 589
89d0527d 590|'acos(cos(z)) ** 2':'z * z'
89d0527d 591|'acosh(cosh(z)) ** 2':'z * z'
0c721ce2
JH
592|'acoth(z)':'acotanh(z)'
593|'acoth(z)':'atanh(1 / z)'
594|'acsch(z)':'acosech(z)'
595|'acsch(z)':'asinh(1 / z)'
596|'asech(z)':'acosh(1 / z)'
597|'asin(sin(z))':'z'
598|'asinh(sinh(z))':'z'
599|'atan(tan(z))':'z'
89d0527d
RM
600|'atanh(tanh(z))':'z'
601
fb73857a
PP
602&log
603(-2.0,0):( 0.69314718055995, 3.14159265358979)
604(-1.0,0):( 0 , 3.14159265358979)
605(-0.5,0):( -0.69314718055995, 3.14159265358979)
606( 0.5,0):( -0.69314718055995, 0 )
607( 1.0,0):( 0 , 0 )
608( 2.0,0):( 0.69314718055995, 0 )
609
610&log
611( 2, 3):( 1.28247467873077, 0.98279372324733)
612(-2, 3):( 1.28247467873077, 2.15879893034246)
613(-2,-3):( 1.28247467873077, -2.15879893034246)
614( 2,-3):( 1.28247467873077, -0.98279372324733)
615
0c721ce2 616&sin
8c03c583
JH
617(-2.0,0):( -0.90929742682568, 0 )
618(-1.0,0):( -0.84147098480790, 0 )
619(-0.5,0):( -0.47942553860420, 0 )
620( 0.0,0):( 0 , 0 )
621( 0.5,0):( 0.47942553860420, 0 )
622( 1.0,0):( 0.84147098480790, 0 )
623( 2.0,0):( 0.90929742682568, 0 )
624
625&sin
0c721ce2
JH
626( 2, 3):( 9.15449914691143, -4.16890695996656)
627(-2, 3):( -9.15449914691143, -4.16890695996656)
628(-2,-3):( -9.15449914691143, 4.16890695996656)
629( 2,-3):( 9.15449914691143, 4.16890695996656)
630
631&cos
8c03c583
JH
632(-2.0,0):( -0.41614683654714, 0 )
633(-1.0,0):( 0.54030230586814, 0 )
634(-0.5,0):( 0.87758256189037, 0 )
635( 0.0,0):( 1 , 0 )
636( 0.5,0):( 0.87758256189037, 0 )
637( 1.0,0):( 0.54030230586814, 0 )
638( 2.0,0):( -0.41614683654714, 0 )
639
640&cos
0c721ce2
JH
641( 2, 3):( -4.18962569096881, -9.10922789375534)
642(-2, 3):( -4.18962569096881, 9.10922789375534)
643(-2,-3):( -4.18962569096881, -9.10922789375534)
644( 2,-3):( -4.18962569096881, 9.10922789375534)
645
646&tan
8c03c583
JH
647(-2.0,0):( 2.18503986326152, 0 )
648(-1.0,0):( -1.55740772465490, 0 )
649(-0.5,0):( -0.54630248984379, 0 )
650( 0.0,0):( 0 , 0 )
651( 0.5,0):( 0.54630248984379, 0 )
652( 1.0,0):( 1.55740772465490, 0 )
653( 2.0,0):( -2.18503986326152, 0 )
654
655&tan
0c721ce2
JH
656( 2, 3):( -0.00376402564150, 1.00323862735361)
657(-2, 3):( 0.00376402564150, 1.00323862735361)
658(-2,-3):( 0.00376402564150, -1.00323862735361)
659( 2,-3):( -0.00376402564150, -1.00323862735361)
660
661&sec
8c03c583
JH
662(-2.0,0):( -2.40299796172238, 0 )
663(-1.0,0):( 1.85081571768093, 0 )
664(-0.5,0):( 1.13949392732455, 0 )
665( 0.0,0):( 1 , 0 )
666( 0.5,0):( 1.13949392732455, 0 )
667( 1.0,0):( 1.85081571768093, 0 )
668( 2.0,0):( -2.40299796172238, 0 )
669
670&sec
0c721ce2
JH
671( 2, 3):( -0.04167496441114, 0.09061113719624)
672(-2, 3):( -0.04167496441114, -0.09061113719624)
673(-2,-3):( -0.04167496441114, 0.09061113719624)
674( 2,-3):( -0.04167496441114, -0.09061113719624)
675
676&csc
8c03c583
JH
677(-2.0,0):( -1.09975017029462, 0 )
678(-1.0,0):( -1.18839510577812, 0 )
679(-0.5,0):( -2.08582964293349, 0 )
680( 0.5,0):( 2.08582964293349, 0 )
681( 1.0,0):( 1.18839510577812, 0 )
682( 2.0,0):( 1.09975017029462, 0 )
683
684&csc
0c721ce2
JH
685( 2, 3):( 0.09047320975321, 0.04120098628857)
686(-2, 3):( -0.09047320975321, 0.04120098628857)
687(-2,-3):( -0.09047320975321, -0.04120098628857)
688( 2,-3):( 0.09047320975321, -0.04120098628857)
689
690&cot
8c03c583
JH
691(-2.0,0):( 0.45765755436029, 0 )
692(-1.0,0):( -0.64209261593433, 0 )
693(-0.5,0):( -1.83048772171245, 0 )
694( 0.5,0):( 1.83048772171245, 0 )
695( 1.0,0):( 0.64209261593433, 0 )
696( 2.0,0):( -0.45765755436029, 0 )
697
698&cot
0c721ce2
JH
699( 2, 3):( -0.00373971037634, -0.99675779656936)
700(-2, 3):( 0.00373971037634, -0.99675779656936)
701(-2,-3):( 0.00373971037634, 0.99675779656936)
702( 2,-3):( -0.00373971037634, 0.99675779656936)
703
704&asin
8c03c583
JH
705(-2.0,0):( -1.57079632679490, 1.31695789692482)
706(-1.0,0):( -1.57079632679490, 0 )
707(-0.5,0):( -0.52359877559830, 0 )
708( 0.0,0):( 0 , 0 )
709( 0.5,0):( 0.52359877559830, 0 )
710( 1.0,0):( 1.57079632679490, 0 )
711( 2.0,0):( 1.57079632679490, -1.31695789692482)
712
713&asin
0c721ce2
JH
714( 2, 3):( 0.57065278432110, 1.98338702991654)
715(-2, 3):( -0.57065278432110, 1.98338702991654)
716(-2,-3):( -0.57065278432110, -1.98338702991654)
717( 2,-3):( 0.57065278432110, -1.98338702991654)
718
719&acos
8c03c583
JH
720(-2.0,0):( 3.14159265358979, -1.31695789692482)
721(-1.0,0):( 3.14159265358979, 0 )
722(-0.5,0):( 2.09439510239320, 0 )
723( 0.0,0):( 1.57079632679490, 0 )
724( 0.5,0):( 1.04719755119660, 0 )
725( 1.0,0):( 0 , 0 )
726( 2.0,0):( 0 , 1.31695789692482)
727
728&acos
0c721ce2
JH
729( 2, 3):( 1.00014354247380, -1.98338702991654)
730(-2, 3):( 2.14144911111600, -1.98338702991654)
731(-2,-3):( 2.14144911111600, 1.98338702991654)
732( 2,-3):( 1.00014354247380, 1.98338702991654)
733
734&atan
8c03c583
JH
735(-2.0,0):( -1.10714871779409, 0 )
736(-1.0,0):( -0.78539816339745, 0 )
737(-0.5,0):( -0.46364760900081, 0 )
738( 0.0,0):( 0 , 0 )
739( 0.5,0):( 0.46364760900081, 0 )
740( 1.0,0):( 0.78539816339745, 0 )
741( 2.0,0):( 1.10714871779409, 0 )
742
743&atan
0c721ce2
JH
744( 2, 3):( 1.40992104959658, 0.22907268296854)
745(-2, 3):( -1.40992104959658, 0.22907268296854)
746(-2,-3):( -1.40992104959658, -0.22907268296854)
747( 2,-3):( 1.40992104959658, -0.22907268296854)
748
749&asec
8c03c583
JH
750(-2.0,0):( 2.09439510239320, 0 )
751(-1.0,0):( 3.14159265358979, 0 )
752(-0.5,0):( 3.14159265358979, -1.31695789692482)
753( 0.5,0):( 0 , 1.31695789692482)
754( 1.0,0):( 0 , 0 )
755( 2.0,0):( 1.04719755119660, 0 )
756
757&asec
0c721ce2
JH
758( 2, 3):( 1.42041072246703, 0.23133469857397)
759(-2, 3):( 1.72118193112276, 0.23133469857397)
760(-2,-3):( 1.72118193112276, -0.23133469857397)
761( 2,-3):( 1.42041072246703, -0.23133469857397)
762
763&acsc
8c03c583
JH
764(-2.0,0):( -0.52359877559830, 0 )
765(-1.0,0):( -1.57079632679490, 0 )
766(-0.5,0):( -1.57079632679490, 1.31695789692482)
767( 0.5,0):( 1.57079632679490, -1.31695789692482)
768( 1.0,0):( 1.57079632679490, 0 )
769( 2.0,0):( 0.52359877559830, 0 )
770
771&acsc
0c721ce2
JH
772( 2, 3):( 0.15038560432786, -0.23133469857397)
773(-2, 3):( -0.15038560432786, -0.23133469857397)
774(-2,-3):( -0.15038560432786, 0.23133469857397)
775( 2,-3):( 0.15038560432786, 0.23133469857397)
776
777&acot
8c03c583
JH
778(-2.0,0):( -0.46364760900081, 0 )
779(-1.0,0):( -0.78539816339745, 0 )
780(-0.5,0):( -1.10714871779409, 0 )
781( 0.5,0):( 1.10714871779409, 0 )
782( 1.0,0):( 0.78539816339745, 0 )
783( 2.0,0):( 0.46364760900081, 0 )
784
785&acot
0c721ce2
JH
786( 2, 3):( 0.16087527719832, -0.22907268296854)
787(-2, 3):( -0.16087527719832, -0.22907268296854)
788(-2,-3):( -0.16087527719832, 0.22907268296854)
789( 2,-3):( 0.16087527719832, 0.22907268296854)
790
791&sinh
8c03c583
JH
792(-2.0,0):( -3.62686040784702, 0 )
793(-1.0,0):( -1.17520119364380, 0 )
794(-0.5,0):( -0.52109530549375, 0 )
795( 0.0,0):( 0 , 0 )
796( 0.5,0):( 0.52109530549375, 0 )
797( 1.0,0):( 1.17520119364380, 0 )
798( 2.0,0):( 3.62686040784702, 0 )
799
800&sinh
0c721ce2
JH
801( 2, 3):( -3.59056458998578, 0.53092108624852)
802(-2, 3):( 3.59056458998578, 0.53092108624852)
803(-2,-3):( 3.59056458998578, -0.53092108624852)
804( 2,-3):( -3.59056458998578, -0.53092108624852)
805
806&cosh
8c03c583
JH
807(-2.0,0):( 3.76219569108363, 0 )
808(-1.0,0):( 1.54308063481524, 0 )
809(-0.5,0):( 1.12762596520638, 0 )
810( 0.0,0):( 1 , 0 )
811( 0.5,0):( 1.12762596520638, 0 )
812( 1.0,0):( 1.54308063481524, 0 )
813( 2.0,0):( 3.76219569108363, 0 )
814
815&cosh
0c721ce2
JH
816( 2, 3):( -3.72454550491532, 0.51182256998738)
817(-2, 3):( -3.72454550491532, -0.51182256998738)
818(-2,-3):( -3.72454550491532, 0.51182256998738)
819( 2,-3):( -3.72454550491532, -0.51182256998738)
820
821&tanh
8c03c583
JH
822(-2.0,0):( -0.96402758007582, 0 )
823(-1.0,0):( -0.76159415595576, 0 )
824(-0.5,0):( -0.46211715726001, 0 )
825( 0.0,0):( 0 , 0 )
826( 0.5,0):( 0.46211715726001, 0 )
827( 1.0,0):( 0.76159415595576, 0 )
828( 2.0,0):( 0.96402758007582, 0 )
829
830&tanh
0c721ce2
JH
831( 2, 3):( 0.96538587902213, -0.00988437503832)
832(-2, 3):( -0.96538587902213, -0.00988437503832)
833(-2,-3):( -0.96538587902213, 0.00988437503832)
834( 2,-3):( 0.96538587902213, 0.00988437503832)
835
836&sech
8c03c583
JH
837(-2.0,0):( 0.26580222883408, 0 )
838(-1.0,0):( 0.64805427366389, 0 )
839(-0.5,0):( 0.88681888397007, 0 )
840( 0.0,0):( 1 , 0 )
841( 0.5,0):( 0.88681888397007, 0 )
842( 1.0,0):( 0.64805427366389, 0 )
843( 2.0,0):( 0.26580222883408, 0 )
844
845&sech
0c721ce2
JH
846( 2, 3):( -0.26351297515839, -0.03621163655877)
847(-2, 3):( -0.26351297515839, 0.03621163655877)
848(-2,-3):( -0.26351297515839, -0.03621163655877)
849( 2,-3):( -0.26351297515839, 0.03621163655877)
850
851&csch
8c03c583
JH
852(-2.0,0):( -0.27572056477178, 0 )
853(-1.0,0):( -0.85091812823932, 0 )
854(-0.5,0):( -1.91903475133494, 0 )
855( 0.5,0):( 1.91903475133494, 0 )
856( 1.0,0):( 0.85091812823932, 0 )
857( 2.0,0):( 0.27572056477178, 0 )
858
859&csch
0c721ce2
JH
860( 2, 3):( -0.27254866146294, -0.04030057885689)
861(-2, 3):( 0.27254866146294, -0.04030057885689)
862(-2,-3):( 0.27254866146294, 0.04030057885689)
863( 2,-3):( -0.27254866146294, 0.04030057885689)
864
865&coth
8c03c583
JH
866(-2.0,0):( -1.03731472072755, 0 )
867(-1.0,0):( -1.31303528549933, 0 )
868(-0.5,0):( -2.16395341373865, 0 )
869( 0.5,0):( 2.16395341373865, 0 )
870( 1.0,0):( 1.31303528549933, 0 )
871( 2.0,0):( 1.03731472072755, 0 )
872
873&coth
0c721ce2
JH
874( 2, 3):( 1.03574663776500, 0.01060478347034)
875(-2, 3):( -1.03574663776500, 0.01060478347034)
876(-2,-3):( -1.03574663776500, -0.01060478347034)
877( 2,-3):( 1.03574663776500, -0.01060478347034)
878
879&asinh
8c03c583
JH
880(-2.0,0):( -1.44363547517881, 0 )
881(-1.0,0):( -0.88137358701954, 0 )
882(-0.5,0):( -0.48121182505960, 0 )
883( 0.0,0):( 0 , 0 )
884( 0.5,0):( 0.48121182505960, 0 )
885( 1.0,0):( 0.88137358701954, 0 )
886( 2.0,0):( 1.44363547517881, 0 )
887
888&asinh
0c721ce2
JH
889( 2, 3):( 1.96863792579310, 0.96465850440760)
890(-2, 3):( -1.96863792579310, 0.96465850440761)
891(-2,-3):( -1.96863792579310, -0.96465850440761)
892( 2,-3):( 1.96863792579310, -0.96465850440760)
893
894&acosh
9bc5fa8d 895(-2.0,0):( 1.31695789692482, 3.14159265358979)
8c03c583
JH
896(-1.0,0):( 0, 3.14159265358979)
897(-0.5,0):( 0, 2.09439510239320)
898( 0.0,0):( 0, 1.57079632679490)
899( 0.5,0):( 0, 1.04719755119660)
900( 1.0,0):( 0 , 0 )
901( 2.0,0):( 1.31695789692482, 0 )
902
903&acosh
0c721ce2 904( 2, 3):( 1.98338702991654, 1.00014354247380)
9bc5fa8d
JH
905(-2, 3):( 1.98338702991653, 2.14144911111600)
906(-2,-3):( 1.98338702991653, -2.14144911111600)
0c721ce2
JH
907( 2,-3):( 1.98338702991654, -1.00014354247380)
908
909&atanh
8c03c583
JH
910(-2.0,0):( -0.54930614433405, 1.57079632679490)
911(-0.5,0):( -0.54930614433405, 0 )
912( 0.0,0):( 0 , 0 )
913( 0.5,0):( 0.54930614433405, 0 )
914( 2.0,0):( 0.54930614433405, 1.57079632679490)
915
916&atanh
0c721ce2
JH
917( 2, 3):( 0.14694666622553, 1.33897252229449)
918(-2, 3):( -0.14694666622553, 1.33897252229449)
919(-2,-3):( -0.14694666622553, -1.33897252229449)
920( 2,-3):( 0.14694666622553, -1.33897252229449)
921
922&asech
8c03c583
JH
923(-2.0,0):( 0 , 2.09439510239320)
924(-1.0,0):( 0 , 3.14159265358979)
9bc5fa8d 925(-0.5,0):( 1.31695789692482, 3.14159265358979)
8c03c583
JH
926( 0.5,0):( 1.31695789692482, 0 )
927( 1.0,0):( 0 , 0 )
928( 2.0,0):( 0 , 1.04719755119660)
929
930&asech
0c721ce2 931( 2, 3):( 0.23133469857397, -1.42041072246703)
9bc5fa8d
JH
932(-2, 3):( 0.23133469857397, -1.72118193112276)
933(-2,-3):( 0.23133469857397, 1.72118193112276)
0c721ce2
JH
934( 2,-3):( 0.23133469857397, 1.42041072246703)
935
936&acsch
8c03c583
JH
937(-2.0,0):( -0.48121182505960, 0 )
938(-1.0,0):( -0.88137358701954, 0 )
939(-0.5,0):( -1.44363547517881, 0 )
940( 0.5,0):( 1.44363547517881, 0 )
941( 1.0,0):( 0.88137358701954, 0 )
942( 2.0,0):( 0.48121182505960, 0 )
943
944&acsch
0c721ce2
JH
945( 2, 3):( 0.15735549884499, -0.22996290237721)
946(-2, 3):( -0.15735549884499, -0.22996290237721)
947(-2,-3):( -0.15735549884499, 0.22996290237721)
948( 2,-3):( 0.15735549884499, 0.22996290237721)
949
950&acoth
8c03c583
JH
951(-2.0,0):( -0.54930614433405, 0 )
952(-0.5,0):( -0.54930614433405, 1.57079632679490)
953( 0.5,0):( 0.54930614433405, 1.57079632679490)
954( 2.0,0):( 0.54930614433405, 0 )
955
956&acoth
0c721ce2
JH
957( 2, 3):( 0.14694666622553, -0.23182380450040)
958(-2, 3):( -0.14694666622553, -0.23182380450040)
959(-2,-3):( -0.14694666622553, 0.23182380450040)
960( 2,-3):( 0.14694666622553, 0.23182380450040)
961
962# eof