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disable perl malloc on UNICOS for now
[p5sagit/p5-mst-13.2.git] / t / lib / complex.t
CommitLineData
89d0527d 1#!./perl
2
fb73857a 3# $RCSfile: complex.t,v $
89d0527d 4#
5aabfad6 5# Regression tests for the Math::Complex pacakge
b42d0ec9 6# -- Raphael Manfredi since Sep 1996
7# -- Jarkko Hietaniemi since Mar 1997
8# -- Daniel S. Lewart since Sep 1997
5aabfad6 9
89d0527d 10BEGIN {
11 chdir 't' if -d 't';
12 @INC = '../lib';
13}
5aabfad6 14
89d0527d 15use Math::Complex;
16
b42d0ec9 17$VERSION = sprintf("%s", q$Id: complex.t,v 1.8 1998/02/05 16:03:39 jhi Exp $ =~ /(\d+\.d+)/);
18
fb73857a 19my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val);
20
89d0527d 21$test = 0;
22$| = 1;
fb73857a 23my @script = (
24 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' .
25 "\n\n"
26);
b42d0ec9 27my $eps = 1e-13;
89d0527d 28
29while (<DATA>) {
0c721ce2 30 s/^\s+//;
31 next if $_ eq '' || /^\#/;
32 chomp;
33 $test_set = 0; # Assume not a test over a set of values
0e505df1 34 if (/^&(.+)/) {
89d0527d 35 $op = $1;
36 next;
37 }
0e505df1 38 elsif (/^\{(.+)\}/) {
89d0527d 39 set($1, \@set, \@val);
40 next;
41 }
42 elsif (s/^\|//) {
0c721ce2 43 $test_set = 1; # Requests we loop over the set...
89d0527d 44 }
45 my @args = split(/:/);
0c721ce2 46 if ($test_set == 1) {
89d0527d 47 my $i;
48 for ($i = 0; $i < @set; $i++) {
0c721ce2 49 # complex number
50 $target = $set[$i];
51 # textual value as found in set definition
52 $zvalue = $val[$i];
89d0527d 53 test($zvalue, $target, @args);
54 }
55 } else {
56 test($op, undef, @args);
57 }
58}
59
b42d0ec9 60#
61
62sub test_mutators {
63 my $op;
64
65 $test++;
66push(@script, <<'EOT');
67{
68 my $z = cplx( 1, 1);
69 $z->Re(2);
70 $z->Im(3);
71 print 'not ' unless Re($z) == 2 and Im($z) == 3;
72EOT
73 push(@script, qq(print "ok $test\\n"}\n));
74
75 $test++;
76push(@script, <<'EOT');
77{
78 my $z = cplx( 1, 1);
79 $z->abs(3 * sqrt(2));
80 print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and
81 (arg($z) - pi / 4 ) < $eps and
82 (Re($z) - 3 ) < $eps and
83 (Im($z) - 3 ) < $eps;
84EOT
85 push(@script, qq(print "ok $test\\n"}\n));
86
87 $test++;
88push(@script, <<'EOT');
89{
90 my $z = cplx( 1, 1);
91 $z->arg(-3 / 4 * pi);
92 print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and
93 (abs($z) - sqrt(2) ) < $eps and
94 (Re($z) + 1 ) < $eps and
95 (Im($z) + 1 ) < $eps;
96EOT
97 push(@script, qq(print "ok $test\\n"}\n));
98}
99
100test_mutators();
101
102my $constants = '
103my $i = cplx(0, 1);
104my $pi = cplx(pi, 0);
105my $pii = cplx(0, pi);
106my $pip2 = cplx(pi/2, 0);
107my $zero = cplx(0, 0);
108';
109
110push(@script, $constants);
111
112
5cd24f17 113# test the divbyzeros
114
0e505df1 115sub test_dbz {
116 for my $op (@_) {
117 $test++;
118
b42d0ec9 119 push(@script, <<EOT);
120eval '$op';
121print 'not ' unless (\$@ =~ /Division by zero/);
122EOT
123 push(@script, qq(print "ok $test\\n";\n));
0e505df1 124 }
125}
126
8c03c583 127# test the logofzeros
128
129sub test_loz {
130 for my $op (@_) {
131 $test++;
132
b42d0ec9 133 push(@script, <<EOT);
134eval '$op';
135print 'not ' unless (\$@ =~ /Logarithm of zero/);
136EOT
137 push(@script, qq(print "ok $test\\n";\n));
8c03c583 138 }
139}
140
5cd24f17 141test_dbz(
142 'i/0',
b42d0ec9 143 'acot(0)',
144 'acot(+$i)',
145# 'acoth(-1)', # Log of zero.
146 'acoth(0)',
147 'acoth(+1)',
5cd24f17 148 'acsc(0)',
5cd24f17 149 'acsch(0)',
b42d0ec9 150 'asec(0)',
151 'asech(0)',
152 'atan(-$i)',
153 'atan($i)',
154# 'atanh(-1)', # Log of zero.
155 'atanh(+1)',
156 'cot(0)',
157 'coth(0)',
158 'csc(0)',
159 'tan($pip2)',
160 'csch(0)',
161 'tan($pip2)',
8c03c583 162 );
163
164test_loz(
fb73857a 165 'log($zero)',
b42d0ec9 166 'acot(-$i)',
8c03c583 167 'atanh(-1)',
168 'acoth(-1)',
5cd24f17 169 );
170
0e505df1 171# test the 0**0
172
173sub test_ztz {
b42d0ec9 174 $test++;
0e505df1 175
b42d0ec9 176 push(@script, <<'EOT');
177eval 'cplx(0)**cplx(0)';
178print 'not ' unless ($@ =~ /zero raised to the zeroth/);
179EOT
180 push(@script, qq(print "ok $test\\n";\n));
0e505df1 181}
182
183test_ztz;
184
185# test the bad roots
186
187sub test_broot {
5cd24f17 188 for my $op (@_) {
189 $test++;
190
b42d0ec9 191 push(@script, <<EOT);
192eval 'root(2, $op)';
193print 'not ' unless (\$@ =~ /root must be/);
194EOT
195 push(@script, qq(print "ok $test\\n";\n));
5cd24f17 196 }
197}
198
0e505df1 199test_broot(qw(-3 -2.1 0 0.99));
200
89d0527d 201print "1..$test\n";
fe82cf6e 202eval join '', @script;
89d0527d 203die $@ if $@;
204
0e505df1 205sub abop {
206 my ($op) = @_;
207
208 push(@script, qq(print "# $op=\n";));
209}
210
89d0527d 211sub test {
212 my ($op, $z, @args) = @_;
0e505df1 213 my ($baop) = 0;
89d0527d 214 $test++;
215 my $i;
0e505df1 216 $baop = 1 if ($op =~ s/;=$//);
89d0527d 217 for ($i = 0; $i < @args; $i++) {
218 $val = value($args[$i]);
fe82cf6e 219 push @script, "\$z$i = $val;\n";
89d0527d 220 }
221 if (defined $z) {
222 $args = "'$op'"; # Really the value
0c721ce2 223 $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0";
fe82cf6e 224 push @script, "\$res = $try; ";
225 push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n";
89d0527d 226 } else {
227 my ($try, $args);
228 if (@args == 2) {
229 $try = "$op \$z0";
230 $args = "'$args[0]'";
231 } else {
232 $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1";
233 $args = "'$args[0]', '$args[1]'";
234 }
fe82cf6e 235 push @script, "\$res = $try; ";
236 push @script, "check($test, '$try', \$res, \$z$#args, $args);\n";
0e505df1 237 if (@args > 2 and $baop) { # binary assignment ops
238 $test++;
239 # check the op= works
240 push @script, <<EOB;
241{
fb73857a 242 my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
0e505df1 243
244 my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
245
fb73857a 246 my \$zb = cplx(\$z1r, \$z1i);
0e505df1 247
248 \$za $op= \$zb;
249 my (\$zbr, \$zbi) = \@{\$zb->cartesian};
250
251 check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
252EOB
253 $test++;
254 # check that the rhs has not changed
255 push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i););
b42d0ec9 256 push @script, qq(print "ok $test\\n";\n);
0e505df1 257 push @script, "}\n";
258 }
89d0527d 259 }
260}
261
262sub set {
263 my ($set, $setref, $valref) = @_;
264 @{$setref} = ();
265 @{$valref} = ();
266 my @set = split(/;\s*/, $set);
267 my @res;
268 my $i;
269 for ($i = 0; $i < @set; $i++) {
270 push(@{$valref}, $set[$i]);
271 my $val = value($set[$i]);
fe82cf6e 272 push @script, "\$s$i = $val;\n";
273 push @{$setref}, "\$s$i";
89d0527d 274 }
275}
276
277sub value {
278 local ($_) = @_;
279 if (/^\s*\((.*),(.*)\)/) {
280 return "cplx($1,$2)";
281 }
b42d0ec9 282 elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) {
283 return "cplx($1,0)";
284 }
89d0527d 285 elsif (/^\s*\[(.*),(.*)\]/) {
286 return "cplxe($1,$2)";
287 }
288 elsif (/^\s*'(.*)'/) {
289 my $ex = $1;
290 $ex =~ s/\bz\b/$target/g;
291 $ex =~ s/\br\b/abs($target)/g;
292 $ex =~ s/\bt\b/arg($target)/g;
293 $ex =~ s/\ba\b/Re($target)/g;
294 $ex =~ s/\bb\b/Im($target)/g;
295 return $ex;
296 }
297 elsif (/^\s*"(.*)"/) {
298 return "\"$1\"";
299 }
300 return $_;
301}
302
303sub check {
304 my ($test, $try, $got, $expected, @z) = @_;
0c721ce2 305
306# print "# @_\n";
307
308 if ("$got" eq "$expected"
309 ||
310 ($expected =~ /^-?\d/ && $got == $expected)
311 ||
312 (abs($got - $expected) < $eps)
313 ) {
89d0527d 314 print "ok $test\n";
315 } else {
316 print "not ok $test\n";
317 my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]";
318 print "# '$try' expected: '$expected' got: '$got' for $args\n";
319 }
320}
fb73857a 321
322sub addsq {
323 my ($z1, $z2) = @_;
324 return ($z1 + i*$z2) * ($z1 - i*$z2);
325}
326
327sub subsq {
328 my ($z1, $z2) = @_;
329 return ($z1 + $z2) * ($z1 - $z2);
330}
331
89d0527d 332__END__
0e505df1 333&+;=
89d0527d 334(3,4):(3,4):(6,8)
335(-3,4):(3,-4):(0,0)
336(3,4):-3:(0,4)
3371:(4,2):(5,2)
338[2,0]:[2,pi]:(0,0)
339
340&++
341(2,1):(3,1)
342
0e505df1 343&-;=
89d0527d 344(2,3):(-2,-3)
345[2,pi/2]:[2,-(pi)/2]
3462:[2,0]:(0,0)
347[3,0]:2:(1,0)
3483:(4,5):(-1,-5)
349(4,5):3:(1,5)
0e505df1 350(2,1):(3,5):(-1,-4)
89d0527d 351
352&--
353(1,2):(0,2)
354[2,pi]:[3,pi]
355
0e505df1 356&*;=
89d0527d 357(0,1):(0,1):(-1,0)
358(4,5):(1,0):(4,5)
359[2,2*pi/3]:(1,0):[2,2*pi/3]
3602:(0,1):(0,2)
361(0,1):3:(0,3)
362(0,1):(4,1):(-1,4)
363(2,1):(4,-1):(9,2)
364
0e505df1 365&/;=
89d0527d 366(3,4):(3,4):(1,0)
367(4,-5):1:(4,-5)
3681:(0,1):(0,-1)
369(0,6):(0,2):(3,0)
370(9,2):(4,-1):(2,1)
371[4,pi]:[2,pi/2]:[2,pi/2]
372[2,pi/2]:[4,pi]:[0.5,-(pi)/2]
373
0e505df1 374&**;=
375(2,0):(3,0):(8,0)
376(3,0):(2,0):(9,0)
377(2,3):(4,0):(-119,-120)
ace5de91 378(0,0):(1,0):(0,0)
379(0,0):(2,3):(0,0)
380(1,0):(0,0):(1,0)
381(1,0):(1,0):(1,0)
382(1,0):(2,3):(1,0)
383(2,3):(0,0):(1,0)
384(2,3):(1,0):(2,3)
0e505df1 385
0c721ce2 386&Re
387(3,4):3
388(-3,4):-3
389[1,pi/2]:0
390
391&Im
392(3,4):4
393(3,-4):-4
394[1,pi/2]:1
395
89d0527d 396&abs
397(3,4):5
398(-3,4):5
399
0c721ce2 400&arg
401[2,0]:0
402[-2,0]:pi
403
89d0527d 404&~
405(4,5):(4,-5)
406(-3,4):(-3,-4)
407[2,pi/2]:[2,-(pi)/2]
408
409&<
410(3,4):(1,2):0
411(3,4):(3,2):0
412(3,4):(3,8):1
413(4,4):(5,129):1
414
415&==
416(3,4):(4,5):0
417(3,4):(3,5):0
418(3,4):(2,4):0
419(3,4):(3,4):1
420
421&sqrt
0c721ce2 422-9:(0,3)
89d0527d 423(-100,0):(0,10)
424(16,-30):(5,-3)
425
426&stringify_cartesian
427(-100,0):"-100"
428(0,1):"i"
429(4,-3):"4-3i"
430(4,0):"4"
431(-4,0):"-4"
432(-2,4):"-2+4i"
433(-2,-1):"-2-i"
434
435&stringify_polar
436[-1, 0]:"[1,pi]"
437[1, pi/3]:"[1,pi/3]"
438[6, -2*pi/3]:"[6,-2pi/3]"
439[0.5, -9*pi/11]:"[0.5,-9pi/11]"
440
441{ (4,3); [3,2]; (-3,4); (0,2); [2,1] }
442
443|'z + ~z':'2*Re(z)'
444|'z - ~z':'2*i*Im(z)'
445|'z * ~z':'abs(z) * abs(z)'
446
8c03c583 447{ (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] }
89d0527d 448
0c721ce2 449|'(root(z, 4))[1] ** 4':'z'
450|'(root(z, 5))[3] ** 5':'z'
451|'(root(z, 8))[7] ** 8':'z'
89d0527d 452|'abs(z)':'r'
0c721ce2 453|'acot(z)':'acotan(z)'
454|'acsc(z)':'acosec(z)'
fb73857a 455|'acsc(z)':'asin(1 / z)'
456|'asec(z)':'acos(1 / z)'
89d0527d 457|'cbrt(z)':'cbrt(r) * exp(i * t/3)'
89d0527d 458|'cos(acos(z))':'z'
fb73857a 459|'addsq(cos(z), sin(z))':1
89d0527d 460|'cos(z)':'cosh(i*z)'
fb73857a 461|'subsq(cosh(z), sinh(z))':1
0c721ce2 462|'cot(acot(z))':'z'
463|'cot(z)':'1 / tan(z)'
464|'cot(z)':'cotan(z)'
465|'csc(acsc(z))':'z'
466|'csc(z)':'1 / sin(z)'
467|'csc(z)':'cosec(z)'
89d0527d 468|'exp(log(z))':'z'
0c721ce2 469|'exp(z)':'exp(a) * exp(i * b)'
470|'ln(z)':'log(z)'
471|'log(exp(z))':'z'
472|'log(z)':'log(r) + i*t'
89d0527d 473|'log10(z)':'log(z) / log(10)'
89d0527d 474|'logn(z, 2)':'log(z) / log(2)'
0c721ce2 475|'logn(z, 3)':'log(z) / log(3)'
476|'sec(asec(z))':'z'
477|'sec(z)':'1 / cos(z)'
478|'sin(asin(z))':'z'
479|'sin(i * z)':'i * sinh(z)'
480|'sqrt(z) * sqrt(z)':'z'
481|'sqrt(z)':'sqrt(r) * exp(i * t/2)'
482|'tan(atan(z))':'z'
483|'z**z':'exp(z * log(z))'
89d0527d 484
0c721ce2 485{ (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) }
89d0527d 486
89d0527d 487|'cosh(acosh(z))':'z'
0c721ce2 488|'coth(acoth(z))':'z'
489|'coth(z)':'1 / tanh(z)'
490|'coth(z)':'cotanh(z)'
491|'csch(acsch(z))':'z'
492|'csch(z)':'1 / sinh(z)'
493|'csch(z)':'cosech(z)'
494|'sech(asech(z))':'z'
495|'sech(z)':'1 / cosh(z)'
496|'sinh(asinh(z))':'z'
89d0527d 497|'tanh(atanh(z))':'z'
89d0527d 498
0c721ce2 499{ (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) }
89d0527d 500
89d0527d 501|'acos(cos(z)) ** 2':'z * z'
89d0527d 502|'acosh(cosh(z)) ** 2':'z * z'
0c721ce2 503|'acoth(z)':'acotanh(z)'
504|'acoth(z)':'atanh(1 / z)'
505|'acsch(z)':'acosech(z)'
506|'acsch(z)':'asinh(1 / z)'
507|'asech(z)':'acosh(1 / z)'
508|'asin(sin(z))':'z'
509|'asinh(sinh(z))':'z'
510|'atan(tan(z))':'z'
89d0527d 511|'atanh(tanh(z))':'z'
512
fb73857a 513&log
514(-2.0,0):( 0.69314718055995, 3.14159265358979)
515(-1.0,0):( 0 , 3.14159265358979)
516(-0.5,0):( -0.69314718055995, 3.14159265358979)
517( 0.5,0):( -0.69314718055995, 0 )
518( 1.0,0):( 0 , 0 )
519( 2.0,0):( 0.69314718055995, 0 )
520
521&log
522( 2, 3):( 1.28247467873077, 0.98279372324733)
523(-2, 3):( 1.28247467873077, 2.15879893034246)
524(-2,-3):( 1.28247467873077, -2.15879893034246)
525( 2,-3):( 1.28247467873077, -0.98279372324733)
526
0c721ce2 527&sin
8c03c583 528(-2.0,0):( -0.90929742682568, 0 )
529(-1.0,0):( -0.84147098480790, 0 )
530(-0.5,0):( -0.47942553860420, 0 )
531( 0.0,0):( 0 , 0 )
532( 0.5,0):( 0.47942553860420, 0 )
533( 1.0,0):( 0.84147098480790, 0 )
534( 2.0,0):( 0.90929742682568, 0 )
535
536&sin
0c721ce2 537( 2, 3):( 9.15449914691143, -4.16890695996656)
538(-2, 3):( -9.15449914691143, -4.16890695996656)
539(-2,-3):( -9.15449914691143, 4.16890695996656)
540( 2,-3):( 9.15449914691143, 4.16890695996656)
541
542&cos
8c03c583 543(-2.0,0):( -0.41614683654714, 0 )
544(-1.0,0):( 0.54030230586814, 0 )
545(-0.5,0):( 0.87758256189037, 0 )
546( 0.0,0):( 1 , 0 )
547( 0.5,0):( 0.87758256189037, 0 )
548( 1.0,0):( 0.54030230586814, 0 )
549( 2.0,0):( -0.41614683654714, 0 )
550
551&cos
0c721ce2 552( 2, 3):( -4.18962569096881, -9.10922789375534)
553(-2, 3):( -4.18962569096881, 9.10922789375534)
554(-2,-3):( -4.18962569096881, -9.10922789375534)
555( 2,-3):( -4.18962569096881, 9.10922789375534)
556
557&tan
8c03c583 558(-2.0,0):( 2.18503986326152, 0 )
559(-1.0,0):( -1.55740772465490, 0 )
560(-0.5,0):( -0.54630248984379, 0 )
561( 0.0,0):( 0 , 0 )
562( 0.5,0):( 0.54630248984379, 0 )
563( 1.0,0):( 1.55740772465490, 0 )
564( 2.0,0):( -2.18503986326152, 0 )
565
566&tan
0c721ce2 567( 2, 3):( -0.00376402564150, 1.00323862735361)
568(-2, 3):( 0.00376402564150, 1.00323862735361)
569(-2,-3):( 0.00376402564150, -1.00323862735361)
570( 2,-3):( -0.00376402564150, -1.00323862735361)
571
572&sec
8c03c583 573(-2.0,0):( -2.40299796172238, 0 )
574(-1.0,0):( 1.85081571768093, 0 )
575(-0.5,0):( 1.13949392732455, 0 )
576( 0.0,0):( 1 , 0 )
577( 0.5,0):( 1.13949392732455, 0 )
578( 1.0,0):( 1.85081571768093, 0 )
579( 2.0,0):( -2.40299796172238, 0 )
580
581&sec
0c721ce2 582( 2, 3):( -0.04167496441114, 0.09061113719624)
583(-2, 3):( -0.04167496441114, -0.09061113719624)
584(-2,-3):( -0.04167496441114, 0.09061113719624)
585( 2,-3):( -0.04167496441114, -0.09061113719624)
586
587&csc
8c03c583 588(-2.0,0):( -1.09975017029462, 0 )
589(-1.0,0):( -1.18839510577812, 0 )
590(-0.5,0):( -2.08582964293349, 0 )
591( 0.5,0):( 2.08582964293349, 0 )
592( 1.0,0):( 1.18839510577812, 0 )
593( 2.0,0):( 1.09975017029462, 0 )
594
595&csc
0c721ce2 596( 2, 3):( 0.09047320975321, 0.04120098628857)
597(-2, 3):( -0.09047320975321, 0.04120098628857)
598(-2,-3):( -0.09047320975321, -0.04120098628857)
599( 2,-3):( 0.09047320975321, -0.04120098628857)
600
601&cot
8c03c583 602(-2.0,0):( 0.45765755436029, 0 )
603(-1.0,0):( -0.64209261593433, 0 )
604(-0.5,0):( -1.83048772171245, 0 )
605( 0.5,0):( 1.83048772171245, 0 )
606( 1.0,0):( 0.64209261593433, 0 )
607( 2.0,0):( -0.45765755436029, 0 )
608
609&cot
0c721ce2 610( 2, 3):( -0.00373971037634, -0.99675779656936)
611(-2, 3):( 0.00373971037634, -0.99675779656936)
612(-2,-3):( 0.00373971037634, 0.99675779656936)
613( 2,-3):( -0.00373971037634, 0.99675779656936)
614
615&asin
8c03c583 616(-2.0,0):( -1.57079632679490, 1.31695789692482)
617(-1.0,0):( -1.57079632679490, 0 )
618(-0.5,0):( -0.52359877559830, 0 )
619( 0.0,0):( 0 , 0 )
620( 0.5,0):( 0.52359877559830, 0 )
621( 1.0,0):( 1.57079632679490, 0 )
622( 2.0,0):( 1.57079632679490, -1.31695789692482)
623
624&asin
0c721ce2 625( 2, 3):( 0.57065278432110, 1.98338702991654)
626(-2, 3):( -0.57065278432110, 1.98338702991654)
627(-2,-3):( -0.57065278432110, -1.98338702991654)
628( 2,-3):( 0.57065278432110, -1.98338702991654)
629
630&acos
8c03c583 631(-2.0,0):( 3.14159265358979, -1.31695789692482)
632(-1.0,0):( 3.14159265358979, 0 )
633(-0.5,0):( 2.09439510239320, 0 )
634( 0.0,0):( 1.57079632679490, 0 )
635( 0.5,0):( 1.04719755119660, 0 )
636( 1.0,0):( 0 , 0 )
637( 2.0,0):( 0 , 1.31695789692482)
638
639&acos
0c721ce2 640( 2, 3):( 1.00014354247380, -1.98338702991654)
641(-2, 3):( 2.14144911111600, -1.98338702991654)
642(-2,-3):( 2.14144911111600, 1.98338702991654)
643( 2,-3):( 1.00014354247380, 1.98338702991654)
644
645&atan
8c03c583 646(-2.0,0):( -1.10714871779409, 0 )
647(-1.0,0):( -0.78539816339745, 0 )
648(-0.5,0):( -0.46364760900081, 0 )
649( 0.0,0):( 0 , 0 )
650( 0.5,0):( 0.46364760900081, 0 )
651( 1.0,0):( 0.78539816339745, 0 )
652( 2.0,0):( 1.10714871779409, 0 )
653
654&atan
0c721ce2 655( 2, 3):( 1.40992104959658, 0.22907268296854)
656(-2, 3):( -1.40992104959658, 0.22907268296854)
657(-2,-3):( -1.40992104959658, -0.22907268296854)
658( 2,-3):( 1.40992104959658, -0.22907268296854)
659
660&asec
8c03c583 661(-2.0,0):( 2.09439510239320, 0 )
662(-1.0,0):( 3.14159265358979, 0 )
663(-0.5,0):( 3.14159265358979, -1.31695789692482)
664( 0.5,0):( 0 , 1.31695789692482)
665( 1.0,0):( 0 , 0 )
666( 2.0,0):( 1.04719755119660, 0 )
667
668&asec
0c721ce2 669( 2, 3):( 1.42041072246703, 0.23133469857397)
670(-2, 3):( 1.72118193112276, 0.23133469857397)
671(-2,-3):( 1.72118193112276, -0.23133469857397)
672( 2,-3):( 1.42041072246703, -0.23133469857397)
673
674&acsc
8c03c583 675(-2.0,0):( -0.52359877559830, 0 )
676(-1.0,0):( -1.57079632679490, 0 )
677(-0.5,0):( -1.57079632679490, 1.31695789692482)
678( 0.5,0):( 1.57079632679490, -1.31695789692482)
679( 1.0,0):( 1.57079632679490, 0 )
680( 2.0,0):( 0.52359877559830, 0 )
681
682&acsc
0c721ce2 683( 2, 3):( 0.15038560432786, -0.23133469857397)
684(-2, 3):( -0.15038560432786, -0.23133469857397)
685(-2,-3):( -0.15038560432786, 0.23133469857397)
686( 2,-3):( 0.15038560432786, 0.23133469857397)
687
688&acot
8c03c583 689(-2.0,0):( -0.46364760900081, 0 )
690(-1.0,0):( -0.78539816339745, 0 )
691(-0.5,0):( -1.10714871779409, 0 )
692( 0.5,0):( 1.10714871779409, 0 )
693( 1.0,0):( 0.78539816339745, 0 )
694( 2.0,0):( 0.46364760900081, 0 )
695
696&acot
0c721ce2 697( 2, 3):( 0.16087527719832, -0.22907268296854)
698(-2, 3):( -0.16087527719832, -0.22907268296854)
699(-2,-3):( -0.16087527719832, 0.22907268296854)
700( 2,-3):( 0.16087527719832, 0.22907268296854)
701
702&sinh
8c03c583 703(-2.0,0):( -3.62686040784702, 0 )
704(-1.0,0):( -1.17520119364380, 0 )
705(-0.5,0):( -0.52109530549375, 0 )
706( 0.0,0):( 0 , 0 )
707( 0.5,0):( 0.52109530549375, 0 )
708( 1.0,0):( 1.17520119364380, 0 )
709( 2.0,0):( 3.62686040784702, 0 )
710
711&sinh
0c721ce2 712( 2, 3):( -3.59056458998578, 0.53092108624852)
713(-2, 3):( 3.59056458998578, 0.53092108624852)
714(-2,-3):( 3.59056458998578, -0.53092108624852)
715( 2,-3):( -3.59056458998578, -0.53092108624852)
716
717&cosh
8c03c583 718(-2.0,0):( 3.76219569108363, 0 )
719(-1.0,0):( 1.54308063481524, 0 )
720(-0.5,0):( 1.12762596520638, 0 )
721( 0.0,0):( 1 , 0 )
722( 0.5,0):( 1.12762596520638, 0 )
723( 1.0,0):( 1.54308063481524, 0 )
724( 2.0,0):( 3.76219569108363, 0 )
725
726&cosh
0c721ce2 727( 2, 3):( -3.72454550491532, 0.51182256998738)
728(-2, 3):( -3.72454550491532, -0.51182256998738)
729(-2,-3):( -3.72454550491532, 0.51182256998738)
730( 2,-3):( -3.72454550491532, -0.51182256998738)
731
732&tanh
8c03c583 733(-2.0,0):( -0.96402758007582, 0 )
734(-1.0,0):( -0.76159415595576, 0 )
735(-0.5,0):( -0.46211715726001, 0 )
736( 0.0,0):( 0 , 0 )
737( 0.5,0):( 0.46211715726001, 0 )
738( 1.0,0):( 0.76159415595576, 0 )
739( 2.0,0):( 0.96402758007582, 0 )
740
741&tanh
0c721ce2 742( 2, 3):( 0.96538587902213, -0.00988437503832)
743(-2, 3):( -0.96538587902213, -0.00988437503832)
744(-2,-3):( -0.96538587902213, 0.00988437503832)
745( 2,-3):( 0.96538587902213, 0.00988437503832)
746
747&sech
8c03c583 748(-2.0,0):( 0.26580222883408, 0 )
749(-1.0,0):( 0.64805427366389, 0 )
750(-0.5,0):( 0.88681888397007, 0 )
751( 0.0,0):( 1 , 0 )
752( 0.5,0):( 0.88681888397007, 0 )
753( 1.0,0):( 0.64805427366389, 0 )
754( 2.0,0):( 0.26580222883408, 0 )
755
756&sech
0c721ce2 757( 2, 3):( -0.26351297515839, -0.03621163655877)
758(-2, 3):( -0.26351297515839, 0.03621163655877)
759(-2,-3):( -0.26351297515839, -0.03621163655877)
760( 2,-3):( -0.26351297515839, 0.03621163655877)
761
762&csch
8c03c583 763(-2.0,0):( -0.27572056477178, 0 )
764(-1.0,0):( -0.85091812823932, 0 )
765(-0.5,0):( -1.91903475133494, 0 )
766( 0.5,0):( 1.91903475133494, 0 )
767( 1.0,0):( 0.85091812823932, 0 )
768( 2.0,0):( 0.27572056477178, 0 )
769
770&csch
0c721ce2 771( 2, 3):( -0.27254866146294, -0.04030057885689)
772(-2, 3):( 0.27254866146294, -0.04030057885689)
773(-2,-3):( 0.27254866146294, 0.04030057885689)
774( 2,-3):( -0.27254866146294, 0.04030057885689)
775
776&coth
8c03c583 777(-2.0,0):( -1.03731472072755, 0 )
778(-1.0,0):( -1.31303528549933, 0 )
779(-0.5,0):( -2.16395341373865, 0 )
780( 0.5,0):( 2.16395341373865, 0 )
781( 1.0,0):( 1.31303528549933, 0 )
782( 2.0,0):( 1.03731472072755, 0 )
783
784&coth
0c721ce2 785( 2, 3):( 1.03574663776500, 0.01060478347034)
786(-2, 3):( -1.03574663776500, 0.01060478347034)
787(-2,-3):( -1.03574663776500, -0.01060478347034)
788( 2,-3):( 1.03574663776500, -0.01060478347034)
789
790&asinh
8c03c583 791(-2.0,0):( -1.44363547517881, 0 )
792(-1.0,0):( -0.88137358701954, 0 )
793(-0.5,0):( -0.48121182505960, 0 )
794( 0.0,0):( 0 , 0 )
795( 0.5,0):( 0.48121182505960, 0 )
796( 1.0,0):( 0.88137358701954, 0 )
797( 2.0,0):( 1.44363547517881, 0 )
798
799&asinh
0c721ce2 800( 2, 3):( 1.96863792579310, 0.96465850440760)
801(-2, 3):( -1.96863792579310, 0.96465850440761)
802(-2,-3):( -1.96863792579310, -0.96465850440761)
803( 2,-3):( 1.96863792579310, -0.96465850440760)
804
805&acosh
8c03c583 806(-2.0,0):( -1.31695789692482, 3.14159265358979)
807(-1.0,0):( 0, 3.14159265358979)
808(-0.5,0):( 0, 2.09439510239320)
809( 0.0,0):( 0, 1.57079632679490)
810( 0.5,0):( 0, 1.04719755119660)
811( 1.0,0):( 0 , 0 )
812( 2.0,0):( 1.31695789692482, 0 )
813
814&acosh
0c721ce2 815( 2, 3):( 1.98338702991654, 1.00014354247380)
816(-2, 3):( -1.98338702991653, -2.14144911111600)
817(-2,-3):( -1.98338702991653, 2.14144911111600)
818( 2,-3):( 1.98338702991654, -1.00014354247380)
819
820&atanh
8c03c583 821(-2.0,0):( -0.54930614433405, 1.57079632679490)
822(-0.5,0):( -0.54930614433405, 0 )
823( 0.0,0):( 0 , 0 )
824( 0.5,0):( 0.54930614433405, 0 )
825( 2.0,0):( 0.54930614433405, 1.57079632679490)
826
827&atanh
0c721ce2 828( 2, 3):( 0.14694666622553, 1.33897252229449)
829(-2, 3):( -0.14694666622553, 1.33897252229449)
830(-2,-3):( -0.14694666622553, -1.33897252229449)
831( 2,-3):( 0.14694666622553, -1.33897252229449)
832
833&asech
8c03c583 834(-2.0,0):( 0 , 2.09439510239320)
835(-1.0,0):( 0 , 3.14159265358979)
836(-0.5,0):( -1.31695789692482, 3.14159265358979)
837( 0.5,0):( 1.31695789692482, 0 )
838( 1.0,0):( 0 , 0 )
839( 2.0,0):( 0 , 1.04719755119660)
840
841&asech
0c721ce2 842( 2, 3):( 0.23133469857397, -1.42041072246703)
843(-2, 3):( -0.23133469857397, 1.72118193112276)
844(-2,-3):( -0.23133469857397, -1.72118193112276)
845( 2,-3):( 0.23133469857397, 1.42041072246703)
846
847&acsch
8c03c583 848(-2.0,0):( -0.48121182505960, 0 )
849(-1.0,0):( -0.88137358701954, 0 )
850(-0.5,0):( -1.44363547517881, 0 )
851( 0.5,0):( 1.44363547517881, 0 )
852( 1.0,0):( 0.88137358701954, 0 )
853( 2.0,0):( 0.48121182505960, 0 )
854
855&acsch
0c721ce2 856( 2, 3):( 0.15735549884499, -0.22996290237721)
857(-2, 3):( -0.15735549884499, -0.22996290237721)
858(-2,-3):( -0.15735549884499, 0.22996290237721)
859( 2,-3):( 0.15735549884499, 0.22996290237721)
860
861&acoth
8c03c583 862(-2.0,0):( -0.54930614433405, 0 )
863(-0.5,0):( -0.54930614433405, 1.57079632679490)
864( 0.5,0):( 0.54930614433405, 1.57079632679490)
865( 2.0,0):( 0.54930614433405, 0 )
866
867&acoth
0c721ce2 868( 2, 3):( 0.14694666622553, -0.23182380450040)
869(-2, 3):( -0.14694666622553, -0.23182380450040)
870(-2,-3):( -0.14694666622553, 0.23182380450040)
871( 2,-3):( 0.14694666622553, 0.23182380450040)
872
873# eof
fb73857a 874
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