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[perl5.git] / t / lib / complex.t
CommitLineData
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1#!./perl
2
3# $RCSfile$
4#
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5# Regression tests for the Math::Complex pacakge
6# -- Raphael Manfredi, September 1996
5cd24f17 7# -- Jarkko Hietaniemi, March-April 1997
5aabfad6 8
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9BEGIN {
10 chdir 't' if -d 't';
11 @INC = '../lib';
12}
5aabfad6 13
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14use Math::Complex;
15
16$test = 0;
17$| = 1;
fe82cf6e 18@script = ();
5aabfad6 19my $eps = 1e-11;
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20
21while (<DATA>) {
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22 s/^\s+//;
23 next if $_ eq '' || /^\#/;
24 chomp;
25 $test_set = 0; # Assume not a test over a set of values
0e505df1 26 if (/^&(.+)/) {
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27 $op = $1;
28 next;
29 }
0e505df1 30 elsif (/^\{(.+)\}/) {
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31 set($1, \@set, \@val);
32 next;
33 }
34 elsif (s/^\|//) {
0c721ce2 35 $test_set = 1; # Requests we loop over the set...
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36 }
37 my @args = split(/:/);
0c721ce2 38 if ($test_set == 1) {
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39 my $i;
40 for ($i = 0; $i < @set; $i++) {
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41 # complex number
42 $target = $set[$i];
43 # textual value as found in set definition
44 $zvalue = $val[$i];
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45 test($zvalue, $target, @args);
46 }
47 } else {
48 test($op, undef, @args);
49 }
50}
51
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52# test the divbyzeros
53
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54sub test_dbz {
55 for my $op (@_) {
56 $test++;
57
58# push(@script, qq(print "# '$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";));
62 }
63}
64
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65# test the logofzeros
66
67sub test_loz {
68 for my $op (@_) {
69 $test++;
70
71# push(@script, qq(print "# '$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";));
75 }
76}
77
78my $minusi = cplx(0, -1);
79
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80test_dbz(
81 'i/0',
82# 'tan(pi/2)', # may succeed thanks to floating point inaccuracies
83# 'sec(pi/2)', # may succeed thanks to floating point inaccuracies
84 'csc(0)',
85 'cot(0)',
86 'atan(i)',
8c03c583 87 'atan($minusi)',
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88 'asec(0)',
89 'acsc(0)',
90 'acot(i)',
8c03c583 91 'acot($minusi)',
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92# 'tanh(pi/2)', # may succeed thanks to floating point inaccuracies
93# 'sech(pi/2)', # may succeed thanks to floating point inaccuracies
94 'csch(0)',
95 'coth(0)',
96 'atanh(1)',
97 'asech(0)',
98 'acsch(0)',
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99 'acoth(1)',
100 );
101
102test_loz(
103 'atanh(-1)',
104 'acoth(-1)',
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105 );
106
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107# test the 0**0
108
109sub test_ztz {
110 $test++;
111
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";));
116}
117
118test_ztz;
119
120# test the bad roots
121
122sub test_broot {
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123 for my $op (@_) {
124 $test++;
125
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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/);));
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129 push(@script, qq(print "ok $test\n";));
130 }
131}
132
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133test_broot(qw(-3 -2.1 0 0.99));
134
89d0527d 135print "1..$test\n";
fe82cf6e 136eval join '', @script;
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137die $@ if $@;
138
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139sub abop {
140 my ($op) = @_;
141
142 push(@script, qq(print "# $op=\n";));
143}
144
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145sub test {
146 my ($op, $z, @args) = @_;
0e505df1 147 my ($baop) = 0;
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148 $test++;
149 my $i;
0e505df1 150 $baop = 1 if ($op =~ s/;=$//);
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151 for ($i = 0; $i < @args; $i++) {
152 $val = value($args[$i]);
fe82cf6e 153 push @script, "\$z$i = $val;\n";
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154 }
155 if (defined $z) {
156 $args = "'$op'"; # Really the value
0c721ce2 157 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
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158 push @script, "\$res = $try; ";
159 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
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160 } else {
161 my ($try, $args);
162 if (@args == 2) {
163 $try = "$op \$z0";
164 $args = "'$args[0]'";
165 } else {
166 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
167 $args = "'$args[0]', '$args[1]'";
168 }
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169 push @script, "\$res = $try; ";
170 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
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171 if (@args > 2 and $baop) { # binary assignment ops
172 $test++;
173 # check the op= works
174 push @script, <<EOB;
175{
176 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
177
178 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
179
180 my \$zb = cplx(\$z1r, \$z1i);
181
182 \$za $op= \$zb;
183 my (\$zbr, \$zbi) = \@{\$zb->cartesian};
184
185 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
186EOB
187 $test++;
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 $test\n";);
191 push @script, "}\n";
192 }
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193 }
194}
195
196sub set {
197 my ($set, $setref, $valref) = @_;
198 @{$setref} = ();
199 @{$valref} = ();
200 my @set = split(/;\s*/, $set);
201 my @res;
202 my $i;
203 for ($i = 0; $i < @set; $i++) {
204 push(@{$valref}, $set[$i]);
205 my $val = value($set[$i]);
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206 push @script, "\$s$i = $val;\n";
207 push @{$setref}, "\$s$i";
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208 }
209}
210
211sub value {
212 local ($_) = @_;
213 if (/^\s*\((.*),(.*)\)/) {
214 return "cplx($1,$2)";
215 }
216 elsif (/^\s*\[(.*),(.*)\]/) {
217 return "cplxe($1,$2)";
218 }
219 elsif (/^\s*'(.*)'/) {
220 my $ex = $1;
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;
226 return $ex;
227 }
228 elsif (/^\s*"(.*)"/) {
229 return "\"$1\"";
230 }
231 return $_;
232}
233
234sub check {
235 my ($test, $try, $got, $expected, @z) = @_;
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236
237# print "# @_\n";
238
239 if ("$got" eq "$expected"
240 ||
241 ($expected =~ /^-?\d/ && $got == $expected)
242 ||
243 (abs($got - $expected) < $eps)
244 ) {
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245 print "ok $test\n";
246 } else {
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";
250 }
251}
252__END__
0e505df1 253&+;=
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254(3,4):(3,4):(6,8)
255(-3,4):(3,-4):(0,0)
256(3,4):-3:(0,4)
2571:(4,2):(5,2)
258[2,0]:[2,pi]:(0,0)
259
260&++
261(2,1):(3,1)
262
0e505df1 263&-;=
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264(2,3):(-2,-3)
265[2,pi/2]:[2,-(pi)/2]
2662:[2,0]:(0,0)
267[3,0]:2:(1,0)
2683:(4,5):(-1,-5)
269(4,5):3:(1,5)
0e505df1 270(2,1):(3,5):(-1,-4)
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271
272&--
273(1,2):(0,2)
274[2,pi]:[3,pi]
275
0e505df1 276&*;=
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277(0,1):(0,1):(-1,0)
278(4,5):(1,0):(4,5)
279[2,2*pi/3]:(1,0):[2,2*pi/3]
2802:(0,1):(0,2)
281(0,1):3:(0,3)
282(0,1):(4,1):(-1,4)
283(2,1):(4,-1):(9,2)
284
0e505df1 285&/;=
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286(3,4):(3,4):(1,0)
287(4,-5):1:(4,-5)
2881:(0,1):(0,-1)
289(0,6):(0,2):(3,0)
290(9,2):(4,-1):(2,1)
291[4,pi]:[2,pi/2]:[2,pi/2]
292[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
293
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294&**;=
295(2,0):(3,0):(8,0)
296(3,0):(2,0):(9,0)
297(2,3):(4,0):(-119,-120)
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298(0,0):(1,0):(0,0)
299(0,0):(2,3):(0,0)
300(1,0):(0,0):(1,0)
301(1,0):(1,0):(1,0)
302(1,0):(2,3):(1,0)
303(2,3):(0,0):(1,0)
304(2,3):(1,0):(2,3)
0e505df1 305
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306&Re
307(3,4):3
308(-3,4):-3
309[1,pi/2]:0
310
311&Im
312(3,4):4
313(3,-4):-4
314[1,pi/2]:1
315
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316&abs
317(3,4):5
318(-3,4):5
319
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320&arg
321[2,0]:0
322[-2,0]:pi
323
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324&~
325(4,5):(4,-5)
326(-3,4):(-3,-4)
327[2,pi/2]:[2,-(pi)/2]
328
329&<
330(3,4):(1,2):0
331(3,4):(3,2):0
332(3,4):(3,8):1
333(4,4):(5,129):1
334
335&==
336(3,4):(4,5):0
337(3,4):(3,5):0
338(3,4):(2,4):0
339(3,4):(3,4):1
340
341&sqrt
0c721ce2 342-9:(0,3)
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343(-100,0):(0,10)
344(16,-30):(5,-3)
345
346&stringify_cartesian
347(-100,0):"-100"
348(0,1):"i"
349(4,-3):"4-3i"
350(4,0):"4"
351(-4,0):"-4"
352(-2,4):"-2+4i"
353(-2,-1):"-2-i"
354
355&stringify_polar
356[-1, 0]:"[1,pi]"
357[1, pi/3]:"[1,pi/3]"
358[6, -2*pi/3]:"[6,-2pi/3]"
359[0.5, -9*pi/11]:"[0.5,-9pi/11]"
360
361{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
362
363|'z + ~z':'2*Re(z)'
364|'z - ~z':'2*i*Im(z)'
365|'z * ~z':'abs(z) * abs(z)'
366
8c03c583 367{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
89d0527d 368
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369|'(root(z, 4))[1] ** 4':'z'
370|'(root(z, 5))[3] ** 5':'z'
371|'(root(z, 8))[7] ** 8':'z'
89d0527d 372|'abs(z)':'r'
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373|'acot(z)':'acotan(z)'
374|'acsc(z)':'acosec(z)'
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375|'abs(acsc(z))':'abs(asin(1 / z))'
376|'abs(asec(z))':'abs(acos(1 / z))'
89d0527d 377|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d 378|'cos(acos(z))':'z'
89d0527d 379|'cos(z) ** 2 + sin(z) ** 2':1
89d0527d 380|'cos(z)':'cosh(i*z)'
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381|'cosh(z) ** 2 - sinh(z) ** 2':1
382|'cot(acot(z))':'z'
383|'cot(z)':'1 / tan(z)'
384|'cot(z)':'cotan(z)'
385|'csc(acsc(z))':'z'
386|'csc(z)':'1 / sin(z)'
387|'csc(z)':'cosec(z)'
89d0527d 388|'exp(log(z))':'z'
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389|'exp(z)':'exp(a) * exp(i * b)'
390|'ln(z)':'log(z)'
391|'log(exp(z))':'z'
392|'log(z)':'log(r) + i*t'
89d0527d 393|'log10(z)':'log(z) / log(10)'
89d0527d 394|'logn(z, 2)':'log(z) / log(2)'
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395|'logn(z, 3)':'log(z) / log(3)'
396|'sec(asec(z))':'z'
397|'sec(z)':'1 / cos(z)'
398|'sin(asin(z))':'z'
399|'sin(i * z)':'i * sinh(z)'
400|'sqrt(z) * sqrt(z)':'z'
401|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
402|'tan(atan(z))':'z'
403|'z**z':'exp(z * log(z))'
89d0527d 404
0c721ce2 405{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d 406
89d0527d 407|'cosh(acosh(z))':'z'
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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'
89d0527d 417|'tanh(atanh(z))':'z'
89d0527d 418
0c721ce2 419{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d 420
89d0527d 421|'acos(cos(z)) ** 2':'z * z'
89d0527d 422|'acosh(cosh(z)) ** 2':'z * z'
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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)'
428|'asin(sin(z))':'z'
429|'asinh(sinh(z))':'z'
430|'atan(tan(z))':'z'
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431|'atanh(tanh(z))':'z'
432
0c721ce2 433&sin
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434(-2.0,0):( -0.90929742682568, 0 )
435(-1.0,0):( -0.84147098480790, 0 )
436(-0.5,0):( -0.47942553860420, 0 )
437( 0.0,0):( 0 , 0 )
438( 0.5,0):( 0.47942553860420, 0 )
439( 1.0,0):( 0.84147098480790, 0 )
440( 2.0,0):( 0.90929742682568, 0 )
441
442&sin
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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)
447
448&cos
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449(-2.0,0):( -0.41614683654714, 0 )
450(-1.0,0):( 0.54030230586814, 0 )
451(-0.5,0):( 0.87758256189037, 0 )
452( 0.0,0):( 1 , 0 )
453( 0.5,0):( 0.87758256189037, 0 )
454( 1.0,0):( 0.54030230586814, 0 )
455( 2.0,0):( -0.41614683654714, 0 )
456
457&cos
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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)
462
463&tan
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464(-2.0,0):( 2.18503986326152, 0 )
465(-1.0,0):( -1.55740772465490, 0 )
466(-0.5,0):( -0.54630248984379, 0 )
467( 0.0,0):( 0 , 0 )
468( 0.5,0):( 0.54630248984379, 0 )
469( 1.0,0):( 1.55740772465490, 0 )
470( 2.0,0):( -2.18503986326152, 0 )
471
472&tan
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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)
477
478&sec
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479(-2.0,0):( -2.40299796172238, 0 )
480(-1.0,0):( 1.85081571768093, 0 )
481(-0.5,0):( 1.13949392732455, 0 )
482( 0.0,0):( 1 , 0 )
483( 0.5,0):( 1.13949392732455, 0 )
484( 1.0,0):( 1.85081571768093, 0 )
485( 2.0,0):( -2.40299796172238, 0 )
486
487&sec
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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)
492
493&csc
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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 )
500
501&csc
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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)
506
507&cot
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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 )
514
515&cot
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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)
520
521&asin
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522(-2.0,0):( -1.57079632679490, 1.31695789692482)
523(-1.0,0):( -1.57079632679490, 0 )
524(-0.5,0):( -0.52359877559830, 0 )
525( 0.0,0):( 0 , 0 )
526( 0.5,0):( 0.52359877559830, 0 )
527( 1.0,0):( 1.57079632679490, 0 )
528( 2.0,0):( 1.57079632679490, -1.31695789692482)
529
530&asin
0c721ce2
JH
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)
535
536&acos
8c03c583
JH
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 )
542( 1.0,0):( 0 , 0 )
543( 2.0,0):( 0 , 1.31695789692482)
544
545&acos
0c721ce2
JH
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)
550
551&atan
8c03c583
JH
552(-2.0,0):( -1.10714871779409, 0 )
553(-1.0,0):( -0.78539816339745, 0 )
554(-0.5,0):( -0.46364760900081, 0 )
555( 0.0,0):( 0 , 0 )
556( 0.5,0):( 0.46364760900081, 0 )
557( 1.0,0):( 0.78539816339745, 0 )
558( 2.0,0):( 1.10714871779409, 0 )
559
560&atan
0c721ce2
JH
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)
565
566&asec
8c03c583
JH
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)
571( 1.0,0):( 0 , 0 )
572( 2.0,0):( 1.04719755119660, 0 )
573
574&asec
0c721ce2
JH
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)
579
580&acsc
8c03c583
JH
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 )
587
588&acsc
0c721ce2
JH
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)
593
594&acot
8c03c583
JH
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 )
601
602&acot
0c721ce2
JH
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)
607
608&sinh
8c03c583
JH
609(-2.0,0):( -3.62686040784702, 0 )
610(-1.0,0):( -1.17520119364380, 0 )
611(-0.5,0):( -0.52109530549375, 0 )
612( 0.0,0):( 0 , 0 )
613( 0.5,0):( 0.52109530549375, 0 )
614( 1.0,0):( 1.17520119364380, 0 )
615( 2.0,0):( 3.62686040784702, 0 )
616
617&sinh
0c721ce2
JH
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)
622
623&cosh
8c03c583
JH
624(-2.0,0):( 3.76219569108363, 0 )
625(-1.0,0):( 1.54308063481524, 0 )
626(-0.5,0):( 1.12762596520638, 0 )
627( 0.0,0):( 1 , 0 )
628( 0.5,0):( 1.12762596520638, 0 )
629( 1.0,0):( 1.54308063481524, 0 )
630( 2.0,0):( 3.76219569108363, 0 )
631
632&cosh
0c721ce2
JH
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)
637
638&tanh
8c03c583
JH
639(-2.0,0):( -0.96402758007582, 0 )
640(-1.0,0):( -0.76159415595576, 0 )
641(-0.5,0):( -0.46211715726001, 0 )
642( 0.0,0):( 0 , 0 )
643( 0.5,0):( 0.46211715726001, 0 )
644( 1.0,0):( 0.76159415595576, 0 )
645( 2.0,0):( 0.96402758007582, 0 )
646
647&tanh
0c721ce2
JH
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)
652
653&sech
8c03c583
JH
654(-2.0,0):( 0.26580222883408, 0 )
655(-1.0,0):( 0.64805427366389, 0 )
656(-0.5,0):( 0.88681888397007, 0 )
657( 0.0,0):( 1 , 0 )
658( 0.5,0):( 0.88681888397007, 0 )
659( 1.0,0):( 0.64805427366389, 0 )
660( 2.0,0):( 0.26580222883408, 0 )
661
662&sech
0c721ce2
JH
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)
667
668&csch
8c03c583
JH
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 )
675
676&csch
0c721ce2
JH
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)
681
682&coth
8c03c583
JH
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 )
689
690&coth
0c721ce2
JH
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)
695
696&asinh
8c03c583
JH
697(-2.0,0):( -1.44363547517881, 0 )
698(-1.0,0):( -0.88137358701954, 0 )
699(-0.5,0):( -0.48121182505960, 0 )
700( 0.0,0):( 0 , 0 )
701( 0.5,0):( 0.48121182505960, 0 )
702( 1.0,0):( 0.88137358701954, 0 )
703( 2.0,0):( 1.44363547517881, 0 )
704
705&asinh
0c721ce2
JH
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)
710
711&acosh
8c03c583
JH
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)
717( 1.0,0):( 0 , 0 )
718( 2.0,0):( 1.31695789692482, 0 )
719
720&acosh
0c721ce2
JH
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)
725
726&atanh
8c03c583
JH
727(-2.0,0):( -0.54930614433405, 1.57079632679490)
728(-0.5,0):( -0.54930614433405, 0 )
729( 0.0,0):( 0 , 0 )
730( 0.5,0):( 0.54930614433405, 0 )
731( 2.0,0):( 0.54930614433405, 1.57079632679490)
732
733&atanh
0c721ce2
JH
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)
738
739&asech
8c03c583
JH
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 )
744( 1.0,0):( 0 , 0 )
745( 2.0,0):( 0 , 1.04719755119660)
746
747&asech
0c721ce2
JH
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)
752
753&acsch
8c03c583
JH
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 )
760
761&acsch
0c721ce2
JH
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)
766
767&acoth
8c03c583
JH
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 )
772
773&acoth
0c721ce2
JH
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)
778
779# eof