Commit | Line | Data |
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89d0527d RM |
1 | #!./perl |
2 | ||
fb73857a | 3 | # $RCSfile: complex.t,v $ |
89d0527d | 4 | # |
5aabfad6 | 5 | # Regression tests for the Math::Complex pacakge |
fb73857a | 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 | |
89d0527d RM |
14 | BEGIN { |
15 | chdir 't' if -d 't'; | |
16 | @INC = '../lib'; | |
17 | } | |
5aabfad6 | 18 | |
89d0527d RM |
19 | use Math::Complex; |
20 | ||
fb73857a | 21 | my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val); |
22 | ||
89d0527d RM |
23 | $test = 0; |
24 | $| = 1; | |
fb73857a | 25 | my @script = ( |
26 | 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' . | |
27 | "\n\n" | |
28 | ); | |
5aabfad6 | 29 | my $eps = 1e-11; |
89d0527d RM |
30 | |
31 | while (<DATA>) { | |
0c721ce2 JH |
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 (/^&(.+)/) { |
89d0527d RM |
37 | $op = $1; |
38 | next; | |
39 | } | |
0e505df1 | 40 | elsif (/^\{(.+)\}/) { |
89d0527d RM |
41 | set($1, \@set, \@val); |
42 | next; | |
43 | } | |
44 | elsif (s/^\|//) { | |
0c721ce2 | 45 | $test_set = 1; # Requests we loop over the set... |
89d0527d RM |
46 | } |
47 | my @args = split(/:/); | |
0c721ce2 | 48 | if ($test_set == 1) { |
89d0527d RM |
49 | my $i; |
50 | for ($i = 0; $i < @set; $i++) { | |
0c721ce2 JH |
51 | # complex number |
52 | $target = $set[$i]; | |
53 | # textual value as found in set definition | |
54 | $zvalue = $val[$i]; | |
89d0527d RM |
55 | test($zvalue, $target, @args); |
56 | } | |
57 | } else { | |
58 | test($op, undef, @args); | |
59 | } | |
60 | } | |
61 | ||
5cd24f17 | 62 | # test the divbyzeros |
63 | ||
0e505df1 JH |
64 | sub 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)); |
0e505df1 JH |
72 | } |
73 | } | |
74 | ||
8c03c583 JH |
75 | # test the logofzeros |
76 | ||
77 | sub 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)); |
8c03c583 JH |
85 | } |
86 | } | |
87 | ||
88 | my $minusi = cplx(0, -1); | |
89 | ||
5cd24f17 | 90 | test_dbz( |
91 | 'i/0', | |
92 | # 'tan(pi/2)', # may succeed thanks to floating point inaccuracies | |
93 | # 'sec(pi/2)', # may succeed thanks to floating point inaccuracies | |
94 | 'csc(0)', | |
95 | 'cot(0)', | |
96 | 'atan(i)', | |
8c03c583 | 97 | 'atan($minusi)', |
5cd24f17 | 98 | 'asec(0)', |
99 | 'acsc(0)', | |
100 | 'acot(i)', | |
8c03c583 | 101 | 'acot($minusi)', |
5cd24f17 | 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)', | |
8c03c583 JH |
109 | 'acoth(1)', |
110 | ); | |
111 | ||
fb73857a | 112 | my $zero = cplx(0, 0); |
113 | ||
8c03c583 | 114 | test_loz( |
fb73857a | 115 | 'log($zero)', |
8c03c583 JH |
116 | 'atanh(-1)', |
117 | 'acoth(-1)', | |
5cd24f17 | 118 | ); |
119 | ||
0e505df1 JH |
120 | # test the 0**0 |
121 | ||
122 | sub 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)); |
0e505df1 JH |
129 | } |
130 | ||
131 | test_ztz; | |
132 | ||
133 | # test the bad roots | |
134 | ||
135 | sub test_broot { | |
5cd24f17 | 136 | for my $op (@_) { |
137 | $test++; | |
138 | ||
0e505df1 JH |
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 $test\\n";\n)); |
5cd24f17 | 143 | } |
144 | } | |
145 | ||
0e505df1 JH |
146 | test_broot(qw(-3 -2.1 0 0.99)); |
147 | ||
89d0527d | 148 | print "1..$test\n"; |
fe82cf6e | 149 | eval join '', @script; |
89d0527d RM |
150 | die $@ if $@; |
151 | ||
0e505df1 JH |
152 | sub abop { |
153 | my ($op) = @_; | |
154 | ||
155 | push(@script, qq(print "# $op=\n";)); | |
156 | } | |
157 | ||
89d0527d RM |
158 | sub test { |
159 | my ($op, $z, @args) = @_; | |
0e505df1 | 160 | my ($baop) = 0; |
89d0527d RM |
161 | $test++; |
162 | my $i; | |
0e505df1 | 163 | $baop = 1 if ($op =~ s/;=$//); |
89d0527d RM |
164 | for ($i = 0; $i < @args; $i++) { |
165 | $val = value($args[$i]); | |
fe82cf6e | 166 | push @script, "\$z$i = $val;\n"; |
89d0527d RM |
167 | } |
168 | if (defined $z) { | |
169 | $args = "'$op'"; # Really the value | |
0c721ce2 | 170 | $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0"; |
fe82cf6e CS |
171 | push @script, "\$res = $try; "; |
172 | push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n"; | |
89d0527d RM |
173 | } else { |
174 | my ($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 | } | |
fe82cf6e CS |
182 | push @script, "\$res = $try; "; |
183 | push @script, "check($test, '$try', \$res, \$z$#args, $args);\n"; | |
0e505df1 JH |
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)); |
0e505df1 JH |
190 | |
191 | my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0); | |
192 | ||
fb73857a | 193 | my \$zb = cplx(\$z1r, \$z1i); |
0e505df1 JH |
194 | |
195 | \$za $op= \$zb; | |
196 | my (\$zbr, \$zbi) = \@{\$zb->cartesian}; | |
197 | ||
198 | check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args); | |
199 | EOB | |
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 $test\\n";\n); |
0e505df1 JH |
204 | push @script, "}\n"; |
205 | } | |
89d0527d RM |
206 | } |
207 | } | |
208 | ||
209 | sub set { | |
210 | my ($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[$i]); | |
fe82cf6e CS |
219 | push @script, "\$s$i = $val;\n"; |
220 | push @{$setref}, "\$s$i"; | |
89d0527d RM |
221 | } |
222 | } | |
223 | ||
224 | sub value { | |
225 | local ($_) = @_; | |
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 $_; | |
245 | } | |
246 | ||
247 | sub check { | |
248 | my ($test, $try, $got, $expected, @z) = @_; | |
0c721ce2 JH |
249 | |
250 | # print "# @_\n"; | |
251 | ||
252 | if ("$got" eq "$expected" | |
253 | || | |
254 | ($expected =~ /^-?\d/ && $got == $expected) | |
255 | || | |
256 | (abs($got - $expected) < $eps) | |
257 | ) { | |
89d0527d RM |
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 $args\n"; | |
263 | } | |
264 | } | |
fb73857a | 265 | |
266 | sub addsq { | |
267 | my ($z1, $z2) = @_; | |
268 | return ($z1 + i*$z2) * ($z1 - i*$z2); | |
269 | } | |
270 | ||
271 | sub subsq { | |
272 | my ($z1, $z2) = @_; | |
273 | return ($z1 + $z2) * ($z1 - $z2); | |
274 | } | |
275 | ||
89d0527d | 276 | __END__ |
0e505df1 | 277 | &+;= |
89d0527d RM |
278 | (3,4):(3,4):(6,8) |
279 | (-3,4):(3,-4):(0,0) | |
280 | (3,4):-3:(0,4) | |
281 | 1:(4,2):(5,2) | |
282 | [2,0]:[2,pi]:(0,0) | |
283 | ||
284 | &++ | |
285 | (2,1):(3,1) | |
286 | ||
0e505df1 | 287 | &-;= |
89d0527d RM |
288 | (2,3):(-2,-3) |
289 | [2,pi/2]:[2,-(pi)/2] | |
290 | 2:[2,0]:(0,0) | |
291 | [3,0]:2:(1,0) | |
292 | 3:(4,5):(-1,-5) | |
293 | (4,5):3:(1,5) | |
0e505df1 | 294 | (2,1):(3,5):(-1,-4) |
89d0527d RM |
295 | |
296 | &-- | |
297 | (1,2):(0,2) | |
298 | [2,pi]:[3,pi] | |
299 | ||
0e505df1 | 300 | &*;= |
89d0527d RM |
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] | |
304 | 2:(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 | &/;= |
89d0527d RM |
310 | (3,4):(3,4):(1,0) |
311 | (4,-5):1:(4,-5) | |
312 | 1:(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 | ||
0e505df1 JH |
318 | &**;= |
319 | (2,0):(3,0):(8,0) | |
320 | (3,0):(2,0):(9,0) | |
321 | (2,3):(4,0):(-119,-120) | |
ace5de91 GS |
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 | |
0c721ce2 JH |
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 | ||
89d0527d RM |
340 | &abs |
341 | (3,4):5 | |
342 | (-3,4):5 | |
343 | ||
0c721ce2 JH |
344 | &arg |
345 | [2,0]:0 | |
346 | [-2,0]:pi | |
347 | ||
89d0527d RM |
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) |
89d0527d RM |
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 JH |
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' |
0c721ce2 JH |
397 | |'acot(z)':'acotan(z)' |
398 | |'acsc(z)':'acosec(z)' | |
fb73857a | 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 JH |
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 JH |
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 JH |
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' | |
89d0527d RM |
455 | |'atanh(tanh(z))':'z' |
456 | ||
fb73857a | 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 |
8c03c583 JH |
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 JH |
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 JH |
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 JH |
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 JH |
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 JH |
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 | |
8c03c583 JH |
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 |