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[perl5.git] / lib / Math / Complex.t
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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';
20822f61 12 @INC = '../lib';
89d0527d 13}
5aabfad6 14
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15use Math::Complex;
16
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17use vars qw($VERSION);
18
19$VERSION = 1.91;
b42d0ec9 20
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21my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
22
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23$test = 0;
24$| = 1;
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25my @script = (
26 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' .
27 "\n\n"
28);
b42d0ec9 29my $eps = 1e-13;
89d0527d 30
d09ae4e6 31if ($^O eq 'unicos') { # For some reason root() produces very inaccurate
f3ff050f 32 $eps = 1e-10; # results in Cray UNICOS, and occasionally also
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33} # cos(), sin(), cosh(), sinh(). The division
34 # of doubles is the current suspect.
35
89d0527d 36while (<DATA>) {
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37 s/^\s+//;
38 next if $_ eq '' || /^\#/;
39 chomp;
40 $test_set = 0; # Assume not a test over a set of values
0e505df1 41 if (/^&(.+)/) {
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42 $op = $1;
43 next;
44 }
0e505df1 45 elsif (/^\{(.+)\}/) {
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46 set($1, \@set, \@val);
47 next;
48 }
49 elsif (s/^\|//) {
0c721ce2 50 $test_set = 1; # Requests we loop over the set...
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51 }
52 my @args = split(/:/);
0c721ce2 53 if ($test_set == 1) {
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54 my $i;
55 for ($i = 0; $i < @set; $i++) {
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56 # complex number
57 $target = $set[$i];
58 # textual value as found in set definition
59 $zvalue = $val[$i];
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60 test($zvalue, $target, @args);
61 }
62 } else {
63 test($op, undef, @args);
64 }
65}
66
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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);
16357284 78 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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79 print 'not ' unless Re($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));
16357284 88 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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89 print 'not ' unless (abs($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);
16357284 101 print "# $test Re(z) = ",$z->Re(), " Im(z) = ", $z->Im(), " z = $z\n";
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102 print 'not ' unless (arg($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
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123# test the divbyzeros
124
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125sub test_dbz {
126 for my $op (@_) {
127 $test++;
b42d0ec9 128 push(@script, <<EOT);
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129 eval '$op';
130 (\$bad) = (\$@ =~ /(.+)/);
131 print "# $test op = $op divbyzero? \$bad...\n";
132 print 'not ' unless (\$@ =~ /Division by zero/);
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133EOT
134 push(@script, qq(print "ok $test\\n";\n));
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135 }
136}
137
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138# test the logofzeros
139
140sub test_loz {
141 for my $op (@_) {
142 $test++;
b42d0ec9 143 push(@script, <<EOT);
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144 eval '$op';
145 (\$bad) = (\$@ =~ /(.+)/);
146 print "# $test op = $op logofzero? \$bad...\n";
147 print 'not ' unless (\$@ =~ /Logarithm of zero/);
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148EOT
149 push(@script, qq(print "ok $test\\n";\n));
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150 }
151}
152
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153test_dbz(
154 'i/0',
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155 'acot(0)',
156 'acot(+$i)',
157# 'acoth(-1)', # Log of zero.
158 'acoth(0)',
159 'acoth(+1)',
5cd24f17 160 'acsc(0)',
5cd24f17 161 'acsch(0)',
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162 'asec(0)',
163 'asech(0)',
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164 'atan($i)',
165# 'atanh(-1)', # Log of zero.
166 'atanh(+1)',
167 'cot(0)',
168 'coth(0)',
169 'csc(0)',
b42d0ec9 170 'csch(0)',
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171 );
172
173test_loz(
fb73857a 174 'log($zero)',
1fa12f56 175 'atan(-$i)',
b42d0ec9 176 'acot(-$i)',
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177 'atanh(-1)',
178 'acoth(-1)',
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179 );
180
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181# test the bad roots
182
183sub test_broot {
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184 for my $op (@_) {
185 $test++;
b42d0ec9 186 push(@script, <<EOT);
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187 eval 'root(2, $op)';
188 (\$bad) = (\$@ =~ /(.+)/);
189 print "# $test op = $op badroot? \$bad...\n";
1fa12f56 190 print 'not ' unless (\$@ =~ /root rank must be/);
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191EOT
192 push(@script, qq(print "ok $test\\n";\n));
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193 }
194}
195
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196test_broot(qw(-3 -2.1 0 0.99));
197
16357284 198sub test_display_format {
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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
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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;
476757f7 214 print "# j display_format polar?\n";
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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";
057216a3 274 print "not " unless "\$j" =~ /^-0(?:\\.5(?:0000\\d+)?|\\.49999\\d+)\\+0.86602540\\d+i\$/;
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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";
1ab88a68 283 print "not " unless "\$j" =~ /^\\[1,2\\.09439510\\d+\\]\$/;
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284 print "ok $test\n";
285
286 \$j->display_format('style' => 'cartesian', 'format' => '(%.5g)');
287EOS
476757f7 288
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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
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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 $test\n";
301EOS
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302}
303
304test_display_format();
305
89d0527d 306print "1..$test\n";
fe82cf6e 307eval join '', @script;
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308die $@ if $@;
309
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310sub abop {
311 my ($op) = @_;
312
313 push(@script, qq(print "# $op=\n";));
314}
315
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316sub test {
317 my ($op, $z, @args) = @_;
0e505df1 318 my ($baop) = 0;
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319 $test++;
320 my $i;
0e505df1 321 $baop = 1 if ($op =~ s/;=$//);
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322 for ($i = 0; $i < @args; $i++) {
323 $val = value($args[$i]);
fe82cf6e 324 push @script, "\$z$i = $val;\n";
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325 }
326 if (defined $z) {
327 $args = "'$op'"; # Really the value
0c721ce2 328 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
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329 push @script, "\$res = $try; ";
330 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
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331 } else {
332 my ($try, $args);
333 if (@args == 2) {
334 $try = "$op \$z0";
335 $args = "'$args[0]'";
336 } else {
337 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
338 $args = "'$args[0]', '$args[1]'";
339 }
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340 push @script, "\$res = $try; ";
341 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
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342 if (@args > 2 and $baop) { # binary assignment ops
343 $test++;
344 # check the op= works
345 push @script, <<EOB;
346{
fb73857a 347 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
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348
349 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
350
fb73857a 351 my \$zb = cplx(\$z1r, \$z1i);
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352
353 \$za $op= \$zb;
354 my (\$zbr, \$zbi) = \@{\$zb->cartesian};
355
356 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
357EOB
358 $test++;
359 # check that the rhs has not changed
360 push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
b42d0ec9 361 push @script, qq(print "ok $test\\n";\n);
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362 push @script, "}\n";
363 }
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364 }
365}
366
367sub set {
368 my ($set, $setref, $valref) = @_;
369 @{$setref} = ();
370 @{$valref} = ();
371 my @set = split(/;\s*/, $set);
372 my @res;
373 my $i;
374 for ($i = 0; $i < @set; $i++) {
375 push(@{$valref}, $set[$i]);
376 my $val = value($set[$i]);
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377 push @script, "\$s$i = $val;\n";
378 push @{$setref}, "\$s$i";
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379 }
380}
381
382sub value {
383 local ($_) = @_;
384 if (/^\s*\((.*),(.*)\)/) {
385 return "cplx($1,$2)";
386 }
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387 elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
388 return "cplx($1,0)";
389 }
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390 elsif (/^\s*\[(.*),(.*)\]/) {
391 return "cplxe($1,$2)";
392 }
393 elsif (/^\s*'(.*)'/) {
394 my $ex = $1;
395 $ex =~ s/\bz\b/$target/g;
396 $ex =~ s/\br\b/abs($target)/g;
397 $ex =~ s/\bt\b/arg($target)/g;
398 $ex =~ s/\ba\b/Re($target)/g;
399 $ex =~ s/\bb\b/Im($target)/g;
400 return $ex;
401 }
402 elsif (/^\s*"(.*)"/) {
403 return "\"$1\"";
404 }
405 return $_;
406}
407
408sub check {
409 my ($test, $try, $got, $expected, @z) = @_;
0c721ce2 410
16357284 411 print "# @_\n";
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412
413 if ("$got" eq "$expected"
414 ||
415 ($expected =~ /^-?\d/ && $got == $expected)
416 ||
417 (abs($got - $expected) < $eps)
418 ) {
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419 print "ok $test\n";
420 } else {
421 print "not ok $test\n";
422 my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
423 print "# '$try' expected: '$expected' got: '$got' for $args\n";
424 }
425}
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426
427sub addsq {
428 my ($z1, $z2) = @_;
429 return ($z1 + i*$z2) * ($z1 - i*$z2);
430}
431
432sub subsq {
433 my ($z1, $z2) = @_;
434 return ($z1 + $z2) * ($z1 - $z2);
435}
436
89d0527d 437__END__
0e505df1 438&+;=
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439(3,4):(3,4):(6,8)
440(-3,4):(3,-4):(0,0)
441(3,4):-3:(0,4)
4421:(4,2):(5,2)
443[2,0]:[2,pi]:(0,0)
444
445&++
446(2,1):(3,1)
447
0e505df1 448&-;=
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449(2,3):(-2,-3)
450[2,pi/2]:[2,-(pi)/2]
4512:[2,0]:(0,0)
452[3,0]:2:(1,0)
4533:(4,5):(-1,-5)
454(4,5):3:(1,5)
0e505df1 455(2,1):(3,5):(-1,-4)
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456
457&--
458(1,2):(0,2)
459[2,pi]:[3,pi]
460
0e505df1 461&*;=
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462(0,1):(0,1):(-1,0)
463(4,5):(1,0):(4,5)
464[2,2*pi/3]:(1,0):[2,2*pi/3]
4652:(0,1):(0,2)
466(0,1):3:(0,3)
467(0,1):(4,1):(-1,4)
468(2,1):(4,-1):(9,2)
469
0e505df1 470&/;=
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471(3,4):(3,4):(1,0)
472(4,-5):1:(4,-5)
4731:(0,1):(0,-1)
474(0,6):(0,2):(3,0)
475(9,2):(4,-1):(2,1)
476[4,pi]:[2,pi/2]:[2,pi/2]
477[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
478
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479&**;=
480(2,0):(3,0):(8,0)
481(3,0):(2,0):(9,0)
482(2,3):(4,0):(-119,-120)
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483(0,0):(1,0):(0,0)
484(0,0):(2,3):(0,0)
485(1,0):(0,0):(1,0)
486(1,0):(1,0):(1,0)
487(1,0):(2,3):(1,0)
488(2,3):(0,0):(1,0)
489(2,3):(1,0):(2,3)
2820d885 490(0,0):(0,0):(1,0)
0e505df1 491
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492&Re
493(3,4):3
494(-3,4):-3
495[1,pi/2]:0
496
497&Im
498(3,4):4
499(3,-4):-4
500[1,pi/2]:1
501
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502&abs
503(3,4):5
504(-3,4):5
505
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506&arg
507[2,0]:0
508[-2,0]:pi
509
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510&~
511(4,5):(4,-5)
512(-3,4):(-3,-4)
513[2,pi/2]:[2,-(pi)/2]
514
515&<
516(3,4):(1,2):0
517(3,4):(3,2):0
518(3,4):(3,8):1
519(4,4):(5,129):1
520
521&==
522(3,4):(4,5):0
523(3,4):(3,5):0
524(3,4):(2,4):0
525(3,4):(3,4):1
526
527&sqrt
0c721ce2 528-9:(0,3)
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529(-100,0):(0,10)
530(16,-30):(5,-3)
531
532&stringify_cartesian
533(-100,0):"-100"
534(0,1):"i"
535(4,-3):"4-3i"
536(4,0):"4"
537(-4,0):"-4"
538(-2,4):"-2+4i"
539(-2,-1):"-2-i"
540
541&stringify_polar
542[-1, 0]:"[1,pi]"
543[1, pi/3]:"[1,pi/3]"
544[6, -2*pi/3]:"[6,-2pi/3]"
545[0.5, -9*pi/11]:"[0.5,-9pi/11]"
546
547{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
548
549|'z + ~z':'2*Re(z)'
550|'z - ~z':'2*i*Im(z)'
551|'z * ~z':'abs(z) * abs(z)'
552
8c03c583 553{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
89d0527d 554
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555|'(root(z, 4))[1] ** 4':'z'
556|'(root(z, 5))[3] ** 5':'z'
557|'(root(z, 8))[7] ** 8':'z'
89d0527d 558|'abs(z)':'r'
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559|'acot(z)':'acotan(z)'
560|'acsc(z)':'acosec(z)'
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561|'acsc(z)':'asin(1 / z)'
562|'asec(z)':'acos(1 / z)'
89d0527d 563|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d 564|'cos(acos(z))':'z'
fb73857a 565|'addsq(cos(z), sin(z))':1
89d0527d 566|'cos(z)':'cosh(i*z)'
fb73857a 567|'subsq(cosh(z), sinh(z))':1
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568|'cot(acot(z))':'z'
569|'cot(z)':'1 / tan(z)'
570|'cot(z)':'cotan(z)'
571|'csc(acsc(z))':'z'
572|'csc(z)':'1 / sin(z)'
573|'csc(z)':'cosec(z)'
89d0527d 574|'exp(log(z))':'z'
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575|'exp(z)':'exp(a) * exp(i * b)'
576|'ln(z)':'log(z)'
577|'log(exp(z))':'z'
578|'log(z)':'log(r) + i*t'
89d0527d 579|'log10(z)':'log(z) / log(10)'
89d0527d 580|'logn(z, 2)':'log(z) / log(2)'
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581|'logn(z, 3)':'log(z) / log(3)'
582|'sec(asec(z))':'z'
583|'sec(z)':'1 / cos(z)'
584|'sin(asin(z))':'z'
585|'sin(i * z)':'i * sinh(z)'
586|'sqrt(z) * sqrt(z)':'z'
587|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
588|'tan(atan(z))':'z'
589|'z**z':'exp(z * log(z))'
89d0527d 590
0c721ce2 591{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d 592
89d0527d 593|'cosh(acosh(z))':'z'
0c721ce2
JH
594|'coth(acoth(z))':'z'
595|'coth(z)':'1 / tanh(z)'
596|'coth(z)':'cotanh(z)'
597|'csch(acsch(z))':'z'
598|'csch(z)':'1 / sinh(z)'
599|'csch(z)':'cosech(z)'
600|'sech(asech(z))':'z'
601|'sech(z)':'1 / cosh(z)'
602|'sinh(asinh(z))':'z'
89d0527d 603|'tanh(atanh(z))':'z'
89d0527d 604
0c721ce2 605{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d 606
89d0527d 607|'acos(cos(z)) ** 2':'z * z'
89d0527d 608|'acosh(cosh(z)) ** 2':'z * z'
0c721ce2
JH
609|'acoth(z)':'acotanh(z)'
610|'acoth(z)':'atanh(1 / z)'
611|'acsch(z)':'acosech(z)'
612|'acsch(z)':'asinh(1 / z)'
613|'asech(z)':'acosh(1 / z)'
614|'asin(sin(z))':'z'
615|'asinh(sinh(z))':'z'
616|'atan(tan(z))':'z'
89d0527d
RM
617|'atanh(tanh(z))':'z'
618
fb73857a
PP
619&log
620(-2.0,0):( 0.69314718055995, 3.14159265358979)
621(-1.0,0):( 0 , 3.14159265358979)
622(-0.5,0):( -0.69314718055995, 3.14159265358979)
623( 0.5,0):( -0.69314718055995, 0 )
624( 1.0,0):( 0 , 0 )
625( 2.0,0):( 0.69314718055995, 0 )
626
627&log
628( 2, 3):( 1.28247467873077, 0.98279372324733)
629(-2, 3):( 1.28247467873077, 2.15879893034246)
630(-2,-3):( 1.28247467873077, -2.15879893034246)
631( 2,-3):( 1.28247467873077, -0.98279372324733)
632
0c721ce2 633&sin
8c03c583
JH
634(-2.0,0):( -0.90929742682568, 0 )
635(-1.0,0):( -0.84147098480790, 0 )
636(-0.5,0):( -0.47942553860420, 0 )
637( 0.0,0):( 0 , 0 )
638( 0.5,0):( 0.47942553860420, 0 )
639( 1.0,0):( 0.84147098480790, 0 )
640( 2.0,0):( 0.90929742682568, 0 )
641
642&sin
0c721ce2
JH
643( 2, 3):( 9.15449914691143, -4.16890695996656)
644(-2, 3):( -9.15449914691143, -4.16890695996656)
645(-2,-3):( -9.15449914691143, 4.16890695996656)
646( 2,-3):( 9.15449914691143, 4.16890695996656)
647
648&cos
8c03c583
JH
649(-2.0,0):( -0.41614683654714, 0 )
650(-1.0,0):( 0.54030230586814, 0 )
651(-0.5,0):( 0.87758256189037, 0 )
652( 0.0,0):( 1 , 0 )
653( 0.5,0):( 0.87758256189037, 0 )
654( 1.0,0):( 0.54030230586814, 0 )
655( 2.0,0):( -0.41614683654714, 0 )
656
657&cos
0c721ce2
JH
658( 2, 3):( -4.18962569096881, -9.10922789375534)
659(-2, 3):( -4.18962569096881, 9.10922789375534)
660(-2,-3):( -4.18962569096881, -9.10922789375534)
661( 2,-3):( -4.18962569096881, 9.10922789375534)
662
663&tan
8c03c583
JH
664(-2.0,0):( 2.18503986326152, 0 )
665(-1.0,0):( -1.55740772465490, 0 )
666(-0.5,0):( -0.54630248984379, 0 )
667( 0.0,0):( 0 , 0 )
668( 0.5,0):( 0.54630248984379, 0 )
669( 1.0,0):( 1.55740772465490, 0 )
670( 2.0,0):( -2.18503986326152, 0 )
671
672&tan
0c721ce2
JH
673( 2, 3):( -0.00376402564150, 1.00323862735361)
674(-2, 3):( 0.00376402564150, 1.00323862735361)
675(-2,-3):( 0.00376402564150, -1.00323862735361)
676( 2,-3):( -0.00376402564150, -1.00323862735361)
677
678&sec
8c03c583
JH
679(-2.0,0):( -2.40299796172238, 0 )
680(-1.0,0):( 1.85081571768093, 0 )
681(-0.5,0):( 1.13949392732455, 0 )
682( 0.0,0):( 1 , 0 )
683( 0.5,0):( 1.13949392732455, 0 )
684( 1.0,0):( 1.85081571768093, 0 )
685( 2.0,0):( -2.40299796172238, 0 )
686
687&sec
0c721ce2
JH
688( 2, 3):( -0.04167496441114, 0.09061113719624)
689(-2, 3):( -0.04167496441114, -0.09061113719624)
690(-2,-3):( -0.04167496441114, 0.09061113719624)
691( 2,-3):( -0.04167496441114, -0.09061113719624)
692
693&csc
8c03c583
JH
694(-2.0,0):( -1.09975017029462, 0 )
695(-1.0,0):( -1.18839510577812, 0 )
696(-0.5,0):( -2.08582964293349, 0 )
697( 0.5,0):( 2.08582964293349, 0 )
698( 1.0,0):( 1.18839510577812, 0 )
699( 2.0,0):( 1.09975017029462, 0 )
700
701&csc
0c721ce2
JH
702( 2, 3):( 0.09047320975321, 0.04120098628857)
703(-2, 3):( -0.09047320975321, 0.04120098628857)
704(-2,-3):( -0.09047320975321, -0.04120098628857)
705( 2,-3):( 0.09047320975321, -0.04120098628857)
706
707&cot
8c03c583
JH
708(-2.0,0):( 0.45765755436029, 0 )
709(-1.0,0):( -0.64209261593433, 0 )
710(-0.5,0):( -1.83048772171245, 0 )
711( 0.5,0):( 1.83048772171245, 0 )
712( 1.0,0):( 0.64209261593433, 0 )
713( 2.0,0):( -0.45765755436029, 0 )
714
715&cot
0c721ce2
JH
716( 2, 3):( -0.00373971037634, -0.99675779656936)
717(-2, 3):( 0.00373971037634, -0.99675779656936)
718(-2,-3):( 0.00373971037634, 0.99675779656936)
719( 2,-3):( -0.00373971037634, 0.99675779656936)
720
721&asin
8c03c583
JH
722(-2.0,0):( -1.57079632679490, 1.31695789692482)
723(-1.0,0):( -1.57079632679490, 0 )
724(-0.5,0):( -0.52359877559830, 0 )
725( 0.0,0):( 0 , 0 )
726( 0.5,0):( 0.52359877559830, 0 )
727( 1.0,0):( 1.57079632679490, 0 )
728( 2.0,0):( 1.57079632679490, -1.31695789692482)
729
730&asin
0c721ce2
JH
731( 2, 3):( 0.57065278432110, 1.98338702991654)
732(-2, 3):( -0.57065278432110, 1.98338702991654)
733(-2,-3):( -0.57065278432110, -1.98338702991654)
734( 2,-3):( 0.57065278432110, -1.98338702991654)
735
736&acos
8c03c583
JH
737(-2.0,0):( 3.14159265358979, -1.31695789692482)
738(-1.0,0):( 3.14159265358979, 0 )
739(-0.5,0):( 2.09439510239320, 0 )
740( 0.0,0):( 1.57079632679490, 0 )
741( 0.5,0):( 1.04719755119660, 0 )
742( 1.0,0):( 0 , 0 )
743( 2.0,0):( 0 , 1.31695789692482)
744
745&acos
0c721ce2
JH
746( 2, 3):( 1.00014354247380, -1.98338702991654)
747(-2, 3):( 2.14144911111600, -1.98338702991654)
748(-2,-3):( 2.14144911111600, 1.98338702991654)
749( 2,-3):( 1.00014354247380, 1.98338702991654)
750
751&atan
8c03c583
JH
752(-2.0,0):( -1.10714871779409, 0 )
753(-1.0,0):( -0.78539816339745, 0 )
754(-0.5,0):( -0.46364760900081, 0 )
755( 0.0,0):( 0 , 0 )
756( 0.5,0):( 0.46364760900081, 0 )
757( 1.0,0):( 0.78539816339745, 0 )
758( 2.0,0):( 1.10714871779409, 0 )
759
760&atan
0c721ce2
JH
761( 2, 3):( 1.40992104959658, 0.22907268296854)
762(-2, 3):( -1.40992104959658, 0.22907268296854)
763(-2,-3):( -1.40992104959658, -0.22907268296854)
764( 2,-3):( 1.40992104959658, -0.22907268296854)
765
766&asec
8c03c583
JH
767(-2.0,0):( 2.09439510239320, 0 )
768(-1.0,0):( 3.14159265358979, 0 )
769(-0.5,0):( 3.14159265358979, -1.31695789692482)
770( 0.5,0):( 0 , 1.31695789692482)
771( 1.0,0):( 0 , 0 )
772( 2.0,0):( 1.04719755119660, 0 )
773
774&asec
0c721ce2
JH
775( 2, 3):( 1.42041072246703, 0.23133469857397)
776(-2, 3):( 1.72118193112276, 0.23133469857397)
777(-2,-3):( 1.72118193112276, -0.23133469857397)
778( 2,-3):( 1.42041072246703, -0.23133469857397)
779
780&acsc
8c03c583
JH
781(-2.0,0):( -0.52359877559830, 0 )
782(-1.0,0):( -1.57079632679490, 0 )
783(-0.5,0):( -1.57079632679490, 1.31695789692482)
784( 0.5,0):( 1.57079632679490, -1.31695789692482)
785( 1.0,0):( 1.57079632679490, 0 )
786( 2.0,0):( 0.52359877559830, 0 )
787
788&acsc
0c721ce2
JH
789( 2, 3):( 0.15038560432786, -0.23133469857397)
790(-2, 3):( -0.15038560432786, -0.23133469857397)
791(-2,-3):( -0.15038560432786, 0.23133469857397)
792( 2,-3):( 0.15038560432786, 0.23133469857397)
793
794&acot
8c03c583
JH
795(-2.0,0):( -0.46364760900081, 0 )
796(-1.0,0):( -0.78539816339745, 0 )
797(-0.5,0):( -1.10714871779409, 0 )
798( 0.5,0):( 1.10714871779409, 0 )
799( 1.0,0):( 0.78539816339745, 0 )
800( 2.0,0):( 0.46364760900081, 0 )
801
802&acot
0c721ce2
JH
803( 2, 3):( 0.16087527719832, -0.22907268296854)
804(-2, 3):( -0.16087527719832, -0.22907268296854)
805(-2,-3):( -0.16087527719832, 0.22907268296854)
806( 2,-3):( 0.16087527719832, 0.22907268296854)
807
808&sinh
8c03c583
JH
809(-2.0,0):( -3.62686040784702, 0 )
810(-1.0,0):( -1.17520119364380, 0 )
811(-0.5,0):( -0.52109530549375, 0 )
812( 0.0,0):( 0 , 0 )
813( 0.5,0):( 0.52109530549375, 0 )
814( 1.0,0):( 1.17520119364380, 0 )
815( 2.0,0):( 3.62686040784702, 0 )
816
817&sinh
0c721ce2
JH
818( 2, 3):( -3.59056458998578, 0.53092108624852)
819(-2, 3):( 3.59056458998578, 0.53092108624852)
820(-2,-3):( 3.59056458998578, -0.53092108624852)
821( 2,-3):( -3.59056458998578, -0.53092108624852)
822
823&cosh
8c03c583
JH
824(-2.0,0):( 3.76219569108363, 0 )
825(-1.0,0):( 1.54308063481524, 0 )
826(-0.5,0):( 1.12762596520638, 0 )
827( 0.0,0):( 1 , 0 )
828( 0.5,0):( 1.12762596520638, 0 )
829( 1.0,0):( 1.54308063481524, 0 )
830( 2.0,0):( 3.76219569108363, 0 )
831
832&cosh
0c721ce2
JH
833( 2, 3):( -3.72454550491532, 0.51182256998738)
834(-2, 3):( -3.72454550491532, -0.51182256998738)
835(-2,-3):( -3.72454550491532, 0.51182256998738)
836( 2,-3):( -3.72454550491532, -0.51182256998738)
837
838&tanh
8c03c583
JH
839(-2.0,0):( -0.96402758007582, 0 )
840(-1.0,0):( -0.76159415595576, 0 )
841(-0.5,0):( -0.46211715726001, 0 )
842( 0.0,0):( 0 , 0 )
843( 0.5,0):( 0.46211715726001, 0 )
844( 1.0,0):( 0.76159415595576, 0 )
845( 2.0,0):( 0.96402758007582, 0 )
846
847&tanh
0c721ce2
JH
848( 2, 3):( 0.96538587902213, -0.00988437503832)
849(-2, 3):( -0.96538587902213, -0.00988437503832)
850(-2,-3):( -0.96538587902213, 0.00988437503832)
851( 2,-3):( 0.96538587902213, 0.00988437503832)
852
853&sech
8c03c583
JH
854(-2.0,0):( 0.26580222883408, 0 )
855(-1.0,0):( 0.64805427366389, 0 )
856(-0.5,0):( 0.88681888397007, 0 )
857( 0.0,0):( 1 , 0 )
858( 0.5,0):( 0.88681888397007, 0 )
859( 1.0,0):( 0.64805427366389, 0 )
860( 2.0,0):( 0.26580222883408, 0 )
861
862&sech
0c721ce2
JH
863( 2, 3):( -0.26351297515839, -0.03621163655877)
864(-2, 3):( -0.26351297515839, 0.03621163655877)
865(-2,-3):( -0.26351297515839, -0.03621163655877)
866( 2,-3):( -0.26351297515839, 0.03621163655877)
867
868&csch
8c03c583
JH
869(-2.0,0):( -0.27572056477178, 0 )
870(-1.0,0):( -0.85091812823932, 0 )
871(-0.5,0):( -1.91903475133494, 0 )
872( 0.5,0):( 1.91903475133494, 0 )
873( 1.0,0):( 0.85091812823932, 0 )
874( 2.0,0):( 0.27572056477178, 0 )
875
876&csch
0c721ce2
JH
877( 2, 3):( -0.27254866146294, -0.04030057885689)
878(-2, 3):( 0.27254866146294, -0.04030057885689)
879(-2,-3):( 0.27254866146294, 0.04030057885689)
880( 2,-3):( -0.27254866146294, 0.04030057885689)
881
882&coth
8c03c583
JH
883(-2.0,0):( -1.03731472072755, 0 )
884(-1.0,0):( -1.31303528549933, 0 )
885(-0.5,0):( -2.16395341373865, 0 )
886( 0.5,0):( 2.16395341373865, 0 )
887( 1.0,0):( 1.31303528549933, 0 )
888( 2.0,0):( 1.03731472072755, 0 )
889
890&coth
0c721ce2
JH
891( 2, 3):( 1.03574663776500, 0.01060478347034)
892(-2, 3):( -1.03574663776500, 0.01060478347034)
893(-2,-3):( -1.03574663776500, -0.01060478347034)
894( 2,-3):( 1.03574663776500, -0.01060478347034)
895
896&asinh
8c03c583
JH
897(-2.0,0):( -1.44363547517881, 0 )
898(-1.0,0):( -0.88137358701954, 0 )
899(-0.5,0):( -0.48121182505960, 0 )
900( 0.0,0):( 0 , 0 )
901( 0.5,0):( 0.48121182505960, 0 )
902( 1.0,0):( 0.88137358701954, 0 )
903( 2.0,0):( 1.44363547517881, 0 )
904
905&asinh
0c721ce2
JH
906( 2, 3):( 1.96863792579310, 0.96465850440760)
907(-2, 3):( -1.96863792579310, 0.96465850440761)
908(-2,-3):( -1.96863792579310, -0.96465850440761)
909( 2,-3):( 1.96863792579310, -0.96465850440760)
910
911&acosh
9bc5fa8d 912(-2.0,0):( 1.31695789692482, 3.14159265358979)
8c03c583
JH
913(-1.0,0):( 0, 3.14159265358979)
914(-0.5,0):( 0, 2.09439510239320)
915( 0.0,0):( 0, 1.57079632679490)
916( 0.5,0):( 0, 1.04719755119660)
917( 1.0,0):( 0 , 0 )
918( 2.0,0):( 1.31695789692482, 0 )
919
920&acosh
0c721ce2 921( 2, 3):( 1.98338702991654, 1.00014354247380)
9bc5fa8d
JH
922(-2, 3):( 1.98338702991653, 2.14144911111600)
923(-2,-3):( 1.98338702991653, -2.14144911111600)
0c721ce2
JH
924( 2,-3):( 1.98338702991654, -1.00014354247380)
925
926&atanh
8c03c583
JH
927(-2.0,0):( -0.54930614433405, 1.57079632679490)
928(-0.5,0):( -0.54930614433405, 0 )
929( 0.0,0):( 0 , 0 )
930( 0.5,0):( 0.54930614433405, 0 )
931( 2.0,0):( 0.54930614433405, 1.57079632679490)
932
933&atanh
0c721ce2
JH
934( 2, 3):( 0.14694666622553, 1.33897252229449)
935(-2, 3):( -0.14694666622553, 1.33897252229449)
936(-2,-3):( -0.14694666622553, -1.33897252229449)
937( 2,-3):( 0.14694666622553, -1.33897252229449)
938
939&asech
8c03c583
JH
940(-2.0,0):( 0 , 2.09439510239320)
941(-1.0,0):( 0 , 3.14159265358979)
9bc5fa8d 942(-0.5,0):( 1.31695789692482, 3.14159265358979)
8c03c583
JH
943( 0.5,0):( 1.31695789692482, 0 )
944( 1.0,0):( 0 , 0 )
945( 2.0,0):( 0 , 1.04719755119660)
946
947&asech
0c721ce2 948( 2, 3):( 0.23133469857397, -1.42041072246703)
9bc5fa8d
JH
949(-2, 3):( 0.23133469857397, -1.72118193112276)
950(-2,-3):( 0.23133469857397, 1.72118193112276)
0c721ce2
JH
951( 2,-3):( 0.23133469857397, 1.42041072246703)
952
953&acsch
8c03c583
JH
954(-2.0,0):( -0.48121182505960, 0 )
955(-1.0,0):( -0.88137358701954, 0 )
956(-0.5,0):( -1.44363547517881, 0 )
957( 0.5,0):( 1.44363547517881, 0 )
958( 1.0,0):( 0.88137358701954, 0 )
959( 2.0,0):( 0.48121182505960, 0 )
960
961&acsch
0c721ce2
JH
962( 2, 3):( 0.15735549884499, -0.22996290237721)
963(-2, 3):( -0.15735549884499, -0.22996290237721)
964(-2,-3):( -0.15735549884499, 0.22996290237721)
965( 2,-3):( 0.15735549884499, 0.22996290237721)
966
967&acoth
8c03c583
JH
968(-2.0,0):( -0.54930614433405, 0 )
969(-0.5,0):( -0.54930614433405, 1.57079632679490)
970( 0.5,0):( 0.54930614433405, 1.57079632679490)
971( 2.0,0):( 0.54930614433405, 0 )
972
973&acoth
0c721ce2
JH
974( 2, 3):( 0.14694666622553, -0.23182380450040)
975(-2, 3):( -0.14694666622553, -0.23182380450040)
976(-2,-3):( -0.14694666622553, 0.23182380450040)
977( 2,-3):( 0.14694666622553, 0.23182380450040)
978
979# eof