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[perl5.git] / t / lib / complex.t
CommitLineData
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1#!./perl
2
fb73857a 3# $RCSfile: complex.t,v $
89d0527d 4#
5aabfad6 5# Regression tests for the Math::Complex pacakge
fb73857a
PP
6# -- Raphael Manfredi September 1996
7# -- Jarkko Hietaniemi March-October 1997
8# -- Daniel S. Lewart September-October 1997
9
10$VERSION = '1.05';
11
12# $Id: complex.t,v 1.1 1997/10/15 10:02:15 jhi Exp jhi $
5aabfad6 13
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14BEGIN {
15 chdir 't' if -d 't';
16 @INC = '../lib';
17}
5aabfad6 18
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19use Math::Complex;
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);
5aabfad6 29my $eps = 1e-11;
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30
31while (<DATA>) {
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32 s/^\s+//;
33 next if $_ eq '' || /^\#/;
34 chomp;
35 $test_set = 0; # Assume not a test over a set of values
0e505df1 36 if (/^&(.+)/) {
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37 $op = $1;
38 next;
39 }
0e505df1 40 elsif (/^\{(.+)\}/) {
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41 set($1, \@set, \@val);
42 next;
43 }
44 elsif (s/^\|//) {
0c721ce2 45 $test_set = 1; # Requests we loop over the set...
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46 }
47 my @args = split(/:/);
0c721ce2 48 if ($test_set == 1) {
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49 my $i;
50 for ($i = 0; $i < @set; $i++) {
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51 # complex number
52 $target = $set[$i];
53 # textual value as found in set definition
54 $zvalue = $val[$i];
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55 test($zvalue, $target, @args);
56 }
57 } else {
58 test($op, undef, @args);
59 }
60}
61
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62# test the divbyzeros
63
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64sub test_dbz {
65 for my $op (@_) {
66 $test++;
67
68# push(@script, qq(print "# '$op'\n";));
69 push(@script, qq(eval '$op';));
70 push(@script, qq(print 'not ' unless (\$@ =~ /Division by zero/);));
fb73857a 71 push(@script, qq( print "ok $test\\n";\n));
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72 }
73}
74
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75# test the logofzeros
76
77sub test_loz {
78 for my $op (@_) {
79 $test++;
80
81# push(@script, qq(print "# '$op'\n";));
82 push(@script, qq(eval '$op';));
83 push(@script, qq(print 'not ' unless (\$@ =~ /Logarithm of zero/);));
fb73857a 84 push(@script, qq( print "ok $test\\n";\n));
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85 }
86}
87
88my $minusi = cplx(0, -1);
89
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90test_dbz(
91 'i/0',
92# 'tan(pi/2)', # may succeed thanks to floating point inaccuracies
93# 'sec(pi/2)', # may succeed thanks to floating point inaccuracies
94 'csc(0)',
95 'cot(0)',
96 'atan(i)',
8c03c583 97 'atan($minusi)',
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98 'asec(0)',
99 'acsc(0)',
100 'acot(i)',
8c03c583 101 'acot($minusi)',
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102# 'tanh(pi/2)', # may succeed thanks to floating point inaccuracies
103# 'sech(pi/2)', # may succeed thanks to floating point inaccuracies
104 'csch(0)',
105 'coth(0)',
106 'atanh(1)',
107 'asech(0)',
108 'acsch(0)',
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109 'acoth(1)',
110 );
111
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112my $zero = cplx(0, 0);
113
8c03c583 114test_loz(
fb73857a 115 'log($zero)',
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116 'atanh(-1)',
117 'acoth(-1)',
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118 );
119
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120# test the 0**0
121
122sub test_ztz {
123 $test++;
124
125# push(@script, qq(print "# 0**0\n";));
126 push(@script, qq(eval 'cplx(0)**cplx(0)';));
127 push(@script, qq(print 'not ' unless (\$@ =~ /zero raised to the/);));
fb73857a 128 push(@script, qq( print "ok $test\\n";\n));
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129}
130
131test_ztz;
132
133# test the bad roots
134
135sub test_broot {
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136 for my $op (@_) {
137 $test++;
138
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139# push(@script, qq(print "# root(2, $op)\n";));
140 push(@script, qq(eval 'root(2, $op)';));
141 push(@script, qq(print 'not ' unless (\$@ =~ /root must be/);));
fb73857a 142 push(@script, qq( print "ok $test\\n";\n));
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143 }
144}
145
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146test_broot(qw(-3 -2.1 0 0.99));
147
89d0527d 148print "1..$test\n";
fe82cf6e 149eval join '', @script;
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150die $@ if $@;
151
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152sub abop {
153 my ($op) = @_;
154
155 push(@script, qq(print "# $op=\n";));
156}
157
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158sub test {
159 my ($op, $z, @args) = @_;
0e505df1 160 my ($baop) = 0;
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161 $test++;
162 my $i;
0e505df1 163 $baop = 1 if ($op =~ s/;=$//);
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164 for ($i = 0; $i < @args; $i++) {
165 $val = value($args[$i]);
fe82cf6e 166 push @script, "\$z$i = $val;\n";
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167 }
168 if (defined $z) {
169 $args = "'$op'"; # Really the value
0c721ce2 170 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
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171 push @script, "\$res = $try; ";
172 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
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173 } else {
174 my ($try, $args);
175 if (@args == 2) {
176 $try = "$op \$z0";
177 $args = "'$args[0]'";
178 } else {
179 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
180 $args = "'$args[0]', '$args[1]'";
181 }
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182 push @script, "\$res = $try; ";
183 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
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184 if (@args > 2 and $baop) { # binary assignment ops
185 $test++;
186 # check the op= works
187 push @script, <<EOB;
188{
fb73857a 189 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
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190
191 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
192
fb73857a 193 my \$zb = cplx(\$z1r, \$z1i);
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194
195 \$za $op= \$zb;
196 my (\$zbr, \$zbi) = \@{\$zb->cartesian};
197
198 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
199EOB
200 $test++;
201 # check that the rhs has not changed
202 push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
fb73857a 203 push @script, qq( print "ok $test\\n";\n);
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204 push @script, "}\n";
205 }
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206 }
207}
208
209sub set {
210 my ($set, $setref, $valref) = @_;
211 @{$setref} = ();
212 @{$valref} = ();
213 my @set = split(/;\s*/, $set);
214 my @res;
215 my $i;
216 for ($i = 0; $i < @set; $i++) {
217 push(@{$valref}, $set[$i]);
218 my $val = value($set[$i]);
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219 push @script, "\$s$i = $val;\n";
220 push @{$setref}, "\$s$i";
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221 }
222}
223
224sub value {
225 local ($_) = @_;
226 if (/^\s*\((.*),(.*)\)/) {
227 return "cplx($1,$2)";
228 }
229 elsif (/^\s*\[(.*),(.*)\]/) {
230 return "cplxe($1,$2)";
231 }
232 elsif (/^\s*'(.*)'/) {
233 my $ex = $1;
234 $ex =~ s/\bz\b/$target/g;
235 $ex =~ s/\br\b/abs($target)/g;
236 $ex =~ s/\bt\b/arg($target)/g;
237 $ex =~ s/\ba\b/Re($target)/g;
238 $ex =~ s/\bb\b/Im($target)/g;
239 return $ex;
240 }
241 elsif (/^\s*"(.*)"/) {
242 return "\"$1\"";
243 }
244 return $_;
245}
246
247sub check {
248 my ($test, $try, $got, $expected, @z) = @_;
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249
250# print "# @_\n";
251
252 if ("$got" eq "$expected"
253 ||
254 ($expected =~ /^-?\d/ && $got == $expected)
255 ||
256 (abs($got - $expected) < $eps)
257 ) {
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258 print "ok $test\n";
259 } else {
260 print "not ok $test\n";
261 my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
262 print "# '$try' expected: '$expected' got: '$got' for $args\n";
263 }
264}
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265
266sub addsq {
267 my ($z1, $z2) = @_;
268 return ($z1 + i*$z2) * ($z1 - i*$z2);
269}
270
271sub subsq {
272 my ($z1, $z2) = @_;
273 return ($z1 + $z2) * ($z1 - $z2);
274}
275
89d0527d 276__END__
0e505df1 277&+;=
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278(3,4):(3,4):(6,8)
279(-3,4):(3,-4):(0,0)
280(3,4):-3:(0,4)
2811:(4,2):(5,2)
282[2,0]:[2,pi]:(0,0)
283
284&++
285(2,1):(3,1)
286
0e505df1 287&-;=
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288(2,3):(-2,-3)
289[2,pi/2]:[2,-(pi)/2]
2902:[2,0]:(0,0)
291[3,0]:2:(1,0)
2923:(4,5):(-1,-5)
293(4,5):3:(1,5)
0e505df1 294(2,1):(3,5):(-1,-4)
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295
296&--
297(1,2):(0,2)
298[2,pi]:[3,pi]
299
0e505df1 300&*;=
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301(0,1):(0,1):(-1,0)
302(4,5):(1,0):(4,5)
303[2,2*pi/3]:(1,0):[2,2*pi/3]
3042:(0,1):(0,2)
305(0,1):3:(0,3)
306(0,1):(4,1):(-1,4)
307(2,1):(4,-1):(9,2)
308
0e505df1 309&/;=
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310(3,4):(3,4):(1,0)
311(4,-5):1:(4,-5)
3121:(0,1):(0,-1)
313(0,6):(0,2):(3,0)
314(9,2):(4,-1):(2,1)
315[4,pi]:[2,pi/2]:[2,pi/2]
316[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
317
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318&**;=
319(2,0):(3,0):(8,0)
320(3,0):(2,0):(9,0)
321(2,3):(4,0):(-119,-120)
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322(0,0):(1,0):(0,0)
323(0,0):(2,3):(0,0)
324(1,0):(0,0):(1,0)
325(1,0):(1,0):(1,0)
326(1,0):(2,3):(1,0)
327(2,3):(0,0):(1,0)
328(2,3):(1,0):(2,3)
0e505df1 329
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330&Re
331(3,4):3
332(-3,4):-3
333[1,pi/2]:0
334
335&Im
336(3,4):4
337(3,-4):-4
338[1,pi/2]:1
339
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340&abs
341(3,4):5
342(-3,4):5
343
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344&arg
345[2,0]:0
346[-2,0]:pi
347
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348&~
349(4,5):(4,-5)
350(-3,4):(-3,-4)
351[2,pi/2]:[2,-(pi)/2]
352
353&<
354(3,4):(1,2):0
355(3,4):(3,2):0
356(3,4):(3,8):1
357(4,4):(5,129):1
358
359&==
360(3,4):(4,5):0
361(3,4):(3,5):0
362(3,4):(2,4):0
363(3,4):(3,4):1
364
365&sqrt
0c721ce2 366-9:(0,3)
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367(-100,0):(0,10)
368(16,-30):(5,-3)
369
370&stringify_cartesian
371(-100,0):"-100"
372(0,1):"i"
373(4,-3):"4-3i"
374(4,0):"4"
375(-4,0):"-4"
376(-2,4):"-2+4i"
377(-2,-1):"-2-i"
378
379&stringify_polar
380[-1, 0]:"[1,pi]"
381[1, pi/3]:"[1,pi/3]"
382[6, -2*pi/3]:"[6,-2pi/3]"
383[0.5, -9*pi/11]:"[0.5,-9pi/11]"
384
385{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
386
387|'z + ~z':'2*Re(z)'
388|'z - ~z':'2*i*Im(z)'
389|'z * ~z':'abs(z) * abs(z)'
390
8c03c583 391{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
89d0527d 392
0c721ce2
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393|'(root(z, 4))[1] ** 4':'z'
394|'(root(z, 5))[3] ** 5':'z'
395|'(root(z, 8))[7] ** 8':'z'
89d0527d 396|'abs(z)':'r'
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JH
397|'acot(z)':'acotan(z)'
398|'acsc(z)':'acosec(z)'
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PP
399|'acsc(z)':'asin(1 / z)'
400|'asec(z)':'acos(1 / z)'
89d0527d 401|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d 402|'cos(acos(z))':'z'
fb73857a 403|'addsq(cos(z), sin(z))':1
89d0527d 404|'cos(z)':'cosh(i*z)'
fb73857a 405|'subsq(cosh(z), sinh(z))':1
0c721ce2
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406|'cot(acot(z))':'z'
407|'cot(z)':'1 / tan(z)'
408|'cot(z)':'cotan(z)'
409|'csc(acsc(z))':'z'
410|'csc(z)':'1 / sin(z)'
411|'csc(z)':'cosec(z)'
89d0527d 412|'exp(log(z))':'z'
0c721ce2
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413|'exp(z)':'exp(a) * exp(i * b)'
414|'ln(z)':'log(z)'
415|'log(exp(z))':'z'
416|'log(z)':'log(r) + i*t'
89d0527d 417|'log10(z)':'log(z) / log(10)'
89d0527d 418|'logn(z, 2)':'log(z) / log(2)'
0c721ce2
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419|'logn(z, 3)':'log(z) / log(3)'
420|'sec(asec(z))':'z'
421|'sec(z)':'1 / cos(z)'
422|'sin(asin(z))':'z'
423|'sin(i * z)':'i * sinh(z)'
424|'sqrt(z) * sqrt(z)':'z'
425|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
426|'tan(atan(z))':'z'
427|'z**z':'exp(z * log(z))'
89d0527d 428
0c721ce2 429{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d 430
89d0527d 431|'cosh(acosh(z))':'z'
0c721ce2
JH
432|'coth(acoth(z))':'z'
433|'coth(z)':'1 / tanh(z)'
434|'coth(z)':'cotanh(z)'
435|'csch(acsch(z))':'z'
436|'csch(z)':'1 / sinh(z)'
437|'csch(z)':'cosech(z)'
438|'sech(asech(z))':'z'
439|'sech(z)':'1 / cosh(z)'
440|'sinh(asinh(z))':'z'
89d0527d 441|'tanh(atanh(z))':'z'
89d0527d 442
0c721ce2 443{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d 444
89d0527d 445|'acos(cos(z)) ** 2':'z * z'
89d0527d 446|'acosh(cosh(z)) ** 2':'z * z'
0c721ce2
JH
447|'acoth(z)':'acotanh(z)'
448|'acoth(z)':'atanh(1 / z)'
449|'acsch(z)':'acosech(z)'
450|'acsch(z)':'asinh(1 / z)'
451|'asech(z)':'acosh(1 / z)'
452|'asin(sin(z))':'z'
453|'asinh(sinh(z))':'z'
454|'atan(tan(z))':'z'
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455|'atanh(tanh(z))':'z'
456
fb73857a
PP
457&log
458(-2.0,0):( 0.69314718055995, 3.14159265358979)
459(-1.0,0):( 0 , 3.14159265358979)
460(-0.5,0):( -0.69314718055995, 3.14159265358979)
461( 0.5,0):( -0.69314718055995, 0 )
462( 1.0,0):( 0 , 0 )
463( 2.0,0):( 0.69314718055995, 0 )
464
465&log
466( 2, 3):( 1.28247467873077, 0.98279372324733)
467(-2, 3):( 1.28247467873077, 2.15879893034246)
468(-2,-3):( 1.28247467873077, -2.15879893034246)
469( 2,-3):( 1.28247467873077, -0.98279372324733)
470
0c721ce2 471&sin
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472(-2.0,0):( -0.90929742682568, 0 )
473(-1.0,0):( -0.84147098480790, 0 )
474(-0.5,0):( -0.47942553860420, 0 )
475( 0.0,0):( 0 , 0 )
476( 0.5,0):( 0.47942553860420, 0 )
477( 1.0,0):( 0.84147098480790, 0 )
478( 2.0,0):( 0.90929742682568, 0 )
479
480&sin
0c721ce2
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481( 2, 3):( 9.15449914691143, -4.16890695996656)
482(-2, 3):( -9.15449914691143, -4.16890695996656)
483(-2,-3):( -9.15449914691143, 4.16890695996656)
484( 2,-3):( 9.15449914691143, 4.16890695996656)
485
486&cos
8c03c583
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487(-2.0,0):( -0.41614683654714, 0 )
488(-1.0,0):( 0.54030230586814, 0 )
489(-0.5,0):( 0.87758256189037, 0 )
490( 0.0,0):( 1 , 0 )
491( 0.5,0):( 0.87758256189037, 0 )
492( 1.0,0):( 0.54030230586814, 0 )
493( 2.0,0):( -0.41614683654714, 0 )
494
495&cos
0c721ce2
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496( 2, 3):( -4.18962569096881, -9.10922789375534)
497(-2, 3):( -4.18962569096881, 9.10922789375534)
498(-2,-3):( -4.18962569096881, -9.10922789375534)
499( 2,-3):( -4.18962569096881, 9.10922789375534)
500
501&tan
8c03c583
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502(-2.0,0):( 2.18503986326152, 0 )
503(-1.0,0):( -1.55740772465490, 0 )
504(-0.5,0):( -0.54630248984379, 0 )
505( 0.0,0):( 0 , 0 )
506( 0.5,0):( 0.54630248984379, 0 )
507( 1.0,0):( 1.55740772465490, 0 )
508( 2.0,0):( -2.18503986326152, 0 )
509
510&tan
0c721ce2
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511( 2, 3):( -0.00376402564150, 1.00323862735361)
512(-2, 3):( 0.00376402564150, 1.00323862735361)
513(-2,-3):( 0.00376402564150, -1.00323862735361)
514( 2,-3):( -0.00376402564150, -1.00323862735361)
515
516&sec
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517(-2.0,0):( -2.40299796172238, 0 )
518(-1.0,0):( 1.85081571768093, 0 )
519(-0.5,0):( 1.13949392732455, 0 )
520( 0.0,0):( 1 , 0 )
521( 0.5,0):( 1.13949392732455, 0 )
522( 1.0,0):( 1.85081571768093, 0 )
523( 2.0,0):( -2.40299796172238, 0 )
524
525&sec
0c721ce2
JH
526( 2, 3):( -0.04167496441114, 0.09061113719624)
527(-2, 3):( -0.04167496441114, -0.09061113719624)
528(-2,-3):( -0.04167496441114, 0.09061113719624)
529( 2,-3):( -0.04167496441114, -0.09061113719624)
530
531&csc
8c03c583
JH
532(-2.0,0):( -1.09975017029462, 0 )
533(-1.0,0):( -1.18839510577812, 0 )
534(-0.5,0):( -2.08582964293349, 0 )
535( 0.5,0):( 2.08582964293349, 0 )
536( 1.0,0):( 1.18839510577812, 0 )
537( 2.0,0):( 1.09975017029462, 0 )
538
539&csc
0c721ce2
JH
540( 2, 3):( 0.09047320975321, 0.04120098628857)
541(-2, 3):( -0.09047320975321, 0.04120098628857)
542(-2,-3):( -0.09047320975321, -0.04120098628857)
543( 2,-3):( 0.09047320975321, -0.04120098628857)
544
545&cot
8c03c583
JH
546(-2.0,0):( 0.45765755436029, 0 )
547(-1.0,0):( -0.64209261593433, 0 )
548(-0.5,0):( -1.83048772171245, 0 )
549( 0.5,0):( 1.83048772171245, 0 )
550( 1.0,0):( 0.64209261593433, 0 )
551( 2.0,0):( -0.45765755436029, 0 )
552
553&cot
0c721ce2
JH
554( 2, 3):( -0.00373971037634, -0.99675779656936)
555(-2, 3):( 0.00373971037634, -0.99675779656936)
556(-2,-3):( 0.00373971037634, 0.99675779656936)
557( 2,-3):( -0.00373971037634, 0.99675779656936)
558
559&asin
8c03c583
JH
560(-2.0,0):( -1.57079632679490, 1.31695789692482)
561(-1.0,0):( -1.57079632679490, 0 )
562(-0.5,0):( -0.52359877559830, 0 )
563( 0.0,0):( 0 , 0 )
564( 0.5,0):( 0.52359877559830, 0 )
565( 1.0,0):( 1.57079632679490, 0 )
566( 2.0,0):( 1.57079632679490, -1.31695789692482)
567
568&asin
0c721ce2
JH
569( 2, 3):( 0.57065278432110, 1.98338702991654)
570(-2, 3):( -0.57065278432110, 1.98338702991654)
571(-2,-3):( -0.57065278432110, -1.98338702991654)
572( 2,-3):( 0.57065278432110, -1.98338702991654)
573
574&acos
8c03c583
JH
575(-2.0,0):( 3.14159265358979, -1.31695789692482)
576(-1.0,0):( 3.14159265358979, 0 )
577(-0.5,0):( 2.09439510239320, 0 )
578( 0.0,0):( 1.57079632679490, 0 )
579( 0.5,0):( 1.04719755119660, 0 )
580( 1.0,0):( 0 , 0 )
581( 2.0,0):( 0 , 1.31695789692482)
582
583&acos
0c721ce2
JH
584( 2, 3):( 1.00014354247380, -1.98338702991654)
585(-2, 3):( 2.14144911111600, -1.98338702991654)
586(-2,-3):( 2.14144911111600, 1.98338702991654)
587( 2,-3):( 1.00014354247380, 1.98338702991654)
588
589&atan
8c03c583
JH
590(-2.0,0):( -1.10714871779409, 0 )
591(-1.0,0):( -0.78539816339745, 0 )
592(-0.5,0):( -0.46364760900081, 0 )
593( 0.0,0):( 0 , 0 )
594( 0.5,0):( 0.46364760900081, 0 )
595( 1.0,0):( 0.78539816339745, 0 )
596( 2.0,0):( 1.10714871779409, 0 )
597
598&atan
0c721ce2
JH
599( 2, 3):( 1.40992104959658, 0.22907268296854)
600(-2, 3):( -1.40992104959658, 0.22907268296854)
601(-2,-3):( -1.40992104959658, -0.22907268296854)
602( 2,-3):( 1.40992104959658, -0.22907268296854)
603
604&asec
8c03c583
JH
605(-2.0,0):( 2.09439510239320, 0 )
606(-1.0,0):( 3.14159265358979, 0 )
607(-0.5,0):( 3.14159265358979, -1.31695789692482)
608( 0.5,0):( 0 , 1.31695789692482)
609( 1.0,0):( 0 , 0 )
610( 2.0,0):( 1.04719755119660, 0 )
611
612&asec
0c721ce2
JH
613( 2, 3):( 1.42041072246703, 0.23133469857397)
614(-2, 3):( 1.72118193112276, 0.23133469857397)
615(-2,-3):( 1.72118193112276, -0.23133469857397)
616( 2,-3):( 1.42041072246703, -0.23133469857397)
617
618&acsc
8c03c583
JH
619(-2.0,0):( -0.52359877559830, 0 )
620(-1.0,0):( -1.57079632679490, 0 )
621(-0.5,0):( -1.57079632679490, 1.31695789692482)
622( 0.5,0):( 1.57079632679490, -1.31695789692482)
623( 1.0,0):( 1.57079632679490, 0 )
624( 2.0,0):( 0.52359877559830, 0 )
625
626&acsc
0c721ce2
JH
627( 2, 3):( 0.15038560432786, -0.23133469857397)
628(-2, 3):( -0.15038560432786, -0.23133469857397)
629(-2,-3):( -0.15038560432786, 0.23133469857397)
630( 2,-3):( 0.15038560432786, 0.23133469857397)
631
632&acot
8c03c583
JH
633(-2.0,0):( -0.46364760900081, 0 )
634(-1.0,0):( -0.78539816339745, 0 )
635(-0.5,0):( -1.10714871779409, 0 )
636( 0.5,0):( 1.10714871779409, 0 )
637( 1.0,0):( 0.78539816339745, 0 )
638( 2.0,0):( 0.46364760900081, 0 )
639
640&acot
0c721ce2
JH
641( 2, 3):( 0.16087527719832, -0.22907268296854)
642(-2, 3):( -0.16087527719832, -0.22907268296854)
643(-2,-3):( -0.16087527719832, 0.22907268296854)
644( 2,-3):( 0.16087527719832, 0.22907268296854)
645
646&sinh
8c03c583
JH
647(-2.0,0):( -3.62686040784702, 0 )
648(-1.0,0):( -1.17520119364380, 0 )
649(-0.5,0):( -0.52109530549375, 0 )
650( 0.0,0):( 0 , 0 )
651( 0.5,0):( 0.52109530549375, 0 )
652( 1.0,0):( 1.17520119364380, 0 )
653( 2.0,0):( 3.62686040784702, 0 )
654
655&sinh
0c721ce2
JH
656( 2, 3):( -3.59056458998578, 0.53092108624852)
657(-2, 3):( 3.59056458998578, 0.53092108624852)
658(-2,-3):( 3.59056458998578, -0.53092108624852)
659( 2,-3):( -3.59056458998578, -0.53092108624852)
660
661&cosh
8c03c583
JH
662(-2.0,0):( 3.76219569108363, 0 )
663(-1.0,0):( 1.54308063481524, 0 )
664(-0.5,0):( 1.12762596520638, 0 )
665( 0.0,0):( 1 , 0 )
666( 0.5,0):( 1.12762596520638, 0 )
667( 1.0,0):( 1.54308063481524, 0 )
668( 2.0,0):( 3.76219569108363, 0 )
669
670&cosh
0c721ce2
JH
671( 2, 3):( -3.72454550491532, 0.51182256998738)
672(-2, 3):( -3.72454550491532, -0.51182256998738)
673(-2,-3):( -3.72454550491532, 0.51182256998738)
674( 2,-3):( -3.72454550491532, -0.51182256998738)
675
676&tanh
8c03c583
JH
677(-2.0,0):( -0.96402758007582, 0 )
678(-1.0,0):( -0.76159415595576, 0 )
679(-0.5,0):( -0.46211715726001, 0 )
680( 0.0,0):( 0 , 0 )
681( 0.5,0):( 0.46211715726001, 0 )
682( 1.0,0):( 0.76159415595576, 0 )
683( 2.0,0):( 0.96402758007582, 0 )
684
685&tanh
0c721ce2
JH
686( 2, 3):( 0.96538587902213, -0.00988437503832)
687(-2, 3):( -0.96538587902213, -0.00988437503832)
688(-2,-3):( -0.96538587902213, 0.00988437503832)
689( 2,-3):( 0.96538587902213, 0.00988437503832)
690
691&sech
8c03c583
JH
692(-2.0,0):( 0.26580222883408, 0 )
693(-1.0,0):( 0.64805427366389, 0 )
694(-0.5,0):( 0.88681888397007, 0 )
695( 0.0,0):( 1 , 0 )
696( 0.5,0):( 0.88681888397007, 0 )
697( 1.0,0):( 0.64805427366389, 0 )
698( 2.0,0):( 0.26580222883408, 0 )
699
700&sech
0c721ce2
JH
701( 2, 3):( -0.26351297515839, -0.03621163655877)
702(-2, 3):( -0.26351297515839, 0.03621163655877)
703(-2,-3):( -0.26351297515839, -0.03621163655877)
704( 2,-3):( -0.26351297515839, 0.03621163655877)
705
706&csch
8c03c583
JH
707(-2.0,0):( -0.27572056477178, 0 )
708(-1.0,0):( -0.85091812823932, 0 )
709(-0.5,0):( -1.91903475133494, 0 )
710( 0.5,0):( 1.91903475133494, 0 )
711( 1.0,0):( 0.85091812823932, 0 )
712( 2.0,0):( 0.27572056477178, 0 )
713
714&csch
0c721ce2
JH
715( 2, 3):( -0.27254866146294, -0.04030057885689)
716(-2, 3):( 0.27254866146294, -0.04030057885689)
717(-2,-3):( 0.27254866146294, 0.04030057885689)
718( 2,-3):( -0.27254866146294, 0.04030057885689)
719
720&coth
8c03c583
JH
721(-2.0,0):( -1.03731472072755, 0 )
722(-1.0,0):( -1.31303528549933, 0 )
723(-0.5,0):( -2.16395341373865, 0 )
724( 0.5,0):( 2.16395341373865, 0 )
725( 1.0,0):( 1.31303528549933, 0 )
726( 2.0,0):( 1.03731472072755, 0 )
727
728&coth
0c721ce2
JH
729( 2, 3):( 1.03574663776500, 0.01060478347034)
730(-2, 3):( -1.03574663776500, 0.01060478347034)
731(-2,-3):( -1.03574663776500, -0.01060478347034)
732( 2,-3):( 1.03574663776500, -0.01060478347034)
733
734&asinh
8c03c583
JH
735(-2.0,0):( -1.44363547517881, 0 )
736(-1.0,0):( -0.88137358701954, 0 )
737(-0.5,0):( -0.48121182505960, 0 )
738( 0.0,0):( 0 , 0 )
739( 0.5,0):( 0.48121182505960, 0 )
740( 1.0,0):( 0.88137358701954, 0 )
741( 2.0,0):( 1.44363547517881, 0 )
742
743&asinh
0c721ce2
JH
744( 2, 3):( 1.96863792579310, 0.96465850440760)
745(-2, 3):( -1.96863792579310, 0.96465850440761)
746(-2,-3):( -1.96863792579310, -0.96465850440761)
747( 2,-3):( 1.96863792579310, -0.96465850440760)
748
749&acosh
8c03c583
JH
750(-2.0,0):( -1.31695789692482, 3.14159265358979)
751(-1.0,0):( 0, 3.14159265358979)
752(-0.5,0):( 0, 2.09439510239320)
753( 0.0,0):( 0, 1.57079632679490)
754( 0.5,0):( 0, 1.04719755119660)
755( 1.0,0):( 0 , 0 )
756( 2.0,0):( 1.31695789692482, 0 )
757
758&acosh
0c721ce2
JH
759( 2, 3):( 1.98338702991654, 1.00014354247380)
760(-2, 3):( -1.98338702991653, -2.14144911111600)
761(-2,-3):( -1.98338702991653, 2.14144911111600)
762( 2,-3):( 1.98338702991654, -1.00014354247380)
763
764&atanh
8c03c583
JH
765(-2.0,0):( -0.54930614433405, 1.57079632679490)
766(-0.5,0):( -0.54930614433405, 0 )
767( 0.0,0):( 0 , 0 )
768( 0.5,0):( 0.54930614433405, 0 )
769( 2.0,0):( 0.54930614433405, 1.57079632679490)
770
771&atanh
0c721ce2
JH
772( 2, 3):( 0.14694666622553, 1.33897252229449)
773(-2, 3):( -0.14694666622553, 1.33897252229449)
774(-2,-3):( -0.14694666622553, -1.33897252229449)
775( 2,-3):( 0.14694666622553, -1.33897252229449)
776
777&asech
8c03c583
JH
778(-2.0,0):( 0 , 2.09439510239320)
779(-1.0,0):( 0 , 3.14159265358979)
780(-0.5,0):( -1.31695789692482, 3.14159265358979)
781( 0.5,0):( 1.31695789692482, 0 )
782( 1.0,0):( 0 , 0 )
783( 2.0,0):( 0 , 1.04719755119660)
784
785&asech
0c721ce2
JH
786( 2, 3):( 0.23133469857397, -1.42041072246703)
787(-2, 3):( -0.23133469857397, 1.72118193112276)
788(-2,-3):( -0.23133469857397, -1.72118193112276)
789( 2,-3):( 0.23133469857397, 1.42041072246703)
790
791&acsch
8c03c583
JH
792(-2.0,0):( -0.48121182505960, 0 )
793(-1.0,0):( -0.88137358701954, 0 )
794(-0.5,0):( -1.44363547517881, 0 )
795( 0.5,0):( 1.44363547517881, 0 )
796( 1.0,0):( 0.88137358701954, 0 )
797( 2.0,0):( 0.48121182505960, 0 )
798
799&acsch
0c721ce2
JH
800( 2, 3):( 0.15735549884499, -0.22996290237721)
801(-2, 3):( -0.15735549884499, -0.22996290237721)
802(-2,-3):( -0.15735549884499, 0.22996290237721)
803( 2,-3):( 0.15735549884499, 0.22996290237721)
804
805&acoth
8c03c583
JH
806(-2.0,0):( -0.54930614433405, 0 )
807(-0.5,0):( -0.54930614433405, 1.57079632679490)
808( 0.5,0):( 0.54930614433405, 1.57079632679490)
809( 2.0,0):( 0.54930614433405, 0 )
810
811&acoth
0c721ce2
JH
812( 2, 3):( 0.14694666622553, -0.23182380450040)
813(-2, 3):( -0.14694666622553, -0.23182380450040)
814(-2,-3):( -0.14694666622553, 0.23182380450040)
815( 2,-3):( 0.14694666622553, 0.23182380450040)
816
817# eof
fb73857a 818