Commit | Line | Data |
89d0527d |
1 | #!./perl |
2 | |
3 | # $RCSfile$ |
4 | # |
5aabfad6 |
5 | # Regression tests for the Math::Complex pacakge |
6 | # -- Raphael Manfredi, September 1996 |
5cd24f17 |
7 | # -- Jarkko Hietaniemi, March-April 1997 |
5aabfad6 |
8 | |
89d0527d |
9 | BEGIN { |
10 | chdir 't' if -d 't'; |
11 | @INC = '../lib'; |
12 | } |
5aabfad6 |
13 | |
89d0527d |
14 | use Math::Complex; |
15 | |
16 | $test = 0; |
17 | $| = 1; |
fe82cf6e |
18 | @script = (); |
5aabfad6 |
19 | my $eps = 1e-11; |
89d0527d |
20 | |
21 | while (<DATA>) { |
0c721ce2 |
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 (/^&(.+)/) { |
89d0527d |
27 | $op = $1; |
28 | next; |
29 | } |
0e505df1 |
30 | elsif (/^\{(.+)\}/) { |
89d0527d |
31 | set($1, \@set, \@val); |
32 | next; |
33 | } |
34 | elsif (s/^\|//) { |
0c721ce2 |
35 | $test_set = 1; # Requests we loop over the set... |
89d0527d |
36 | } |
37 | my @args = split(/:/); |
0c721ce2 |
38 | if ($test_set == 1) { |
89d0527d |
39 | my $i; |
40 | for ($i = 0; $i < @set; $i++) { |
0c721ce2 |
41 | # complex number |
42 | $target = $set[$i]; |
43 | # textual value as found in set definition |
44 | $zvalue = $val[$i]; |
89d0527d |
45 | test($zvalue, $target, @args); |
46 | } |
47 | } else { |
48 | test($op, undef, @args); |
49 | } |
50 | } |
51 | |
5cd24f17 |
52 | # test the divbyzeros |
53 | |
0e505df1 |
54 | sub 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 | |
8c03c583 |
65 | # test the logofzeros |
66 | |
67 | sub 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 | |
78 | my $minusi = cplx(0, -1); |
79 | |
5cd24f17 |
80 | test_dbz( |
81 | 'i/0', |
82 | # 'tan(pi/2)', # may succeed thanks to floating point inaccuracies |
83 | # 'sec(pi/2)', # may succeed thanks to floating point inaccuracies |
84 | 'csc(0)', |
85 | 'cot(0)', |
86 | 'atan(i)', |
8c03c583 |
87 | 'atan($minusi)', |
5cd24f17 |
88 | 'asec(0)', |
89 | 'acsc(0)', |
90 | 'acot(i)', |
8c03c583 |
91 | 'acot($minusi)', |
5cd24f17 |
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)', |
8c03c583 |
99 | 'acoth(1)', |
100 | ); |
101 | |
102 | test_loz( |
103 | 'atanh(-1)', |
104 | 'acoth(-1)', |
5cd24f17 |
105 | ); |
106 | |
0e505df1 |
107 | # test the 0**0 |
108 | |
109 | sub 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 | |
118 | test_ztz; |
119 | |
120 | # test the bad roots |
121 | |
122 | sub test_broot { |
5cd24f17 |
123 | for my $op (@_) { |
124 | $test++; |
125 | |
0e505df1 |
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/);)); |
5cd24f17 |
129 | push(@script, qq(print "ok $test\n";)); |
130 | } |
131 | } |
132 | |
0e505df1 |
133 | test_broot(qw(-3 -2.1 0 0.99)); |
134 | |
89d0527d |
135 | print "1..$test\n"; |
fe82cf6e |
136 | eval join '', @script; |
89d0527d |
137 | die $@ if $@; |
138 | |
0e505df1 |
139 | sub abop { |
140 | my ($op) = @_; |
141 | |
142 | push(@script, qq(print "# $op=\n";)); |
143 | } |
144 | |
89d0527d |
145 | sub test { |
146 | my ($op, $z, @args) = @_; |
0e505df1 |
147 | my ($baop) = 0; |
89d0527d |
148 | $test++; |
149 | my $i; |
0e505df1 |
150 | $baop = 1 if ($op =~ s/;=$//); |
89d0527d |
151 | for ($i = 0; $i < @args; $i++) { |
152 | $val = value($args[$i]); |
fe82cf6e |
153 | push @script, "\$z$i = $val;\n"; |
89d0527d |
154 | } |
155 | if (defined $z) { |
156 | $args = "'$op'"; # Really the value |
0c721ce2 |
157 | $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0"; |
fe82cf6e |
158 | push @script, "\$res = $try; "; |
159 | push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n"; |
89d0527d |
160 | } else { |
161 | my ($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 | } |
fe82cf6e |
169 | push @script, "\$res = $try; "; |
170 | push @script, "check($test, '$try', \$res, \$z$#args, $args);\n"; |
0e505df1 |
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); |
186 | EOB |
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 $test\n";); |
191 | push @script, "}\n"; |
192 | } |
89d0527d |
193 | } |
194 | } |
195 | |
196 | sub set { |
197 | my ($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[$i]); |
fe82cf6e |
206 | push @script, "\$s$i = $val;\n"; |
207 | push @{$setref}, "\$s$i"; |
89d0527d |
208 | } |
209 | } |
210 | |
211 | sub value { |
212 | local ($_) = @_; |
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 $_; |
232 | } |
233 | |
234 | sub check { |
235 | my ($test, $try, $got, $expected, @z) = @_; |
0c721ce2 |
236 | |
237 | # print "# @_\n"; |
238 | |
239 | if ("$got" eq "$expected" |
240 | || |
241 | ($expected =~ /^-?\d/ && $got == $expected) |
242 | || |
243 | (abs($got - $expected) < $eps) |
244 | ) { |
89d0527d |
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 | &+;= |
89d0527d |
254 | (3,4):(3,4):(6,8) |
255 | (-3,4):(3,-4):(0,0) |
256 | (3,4):-3:(0,4) |
257 | 1:(4,2):(5,2) |
258 | [2,0]:[2,pi]:(0,0) |
259 | |
260 | &++ |
261 | (2,1):(3,1) |
262 | |
0e505df1 |
263 | &-;= |
89d0527d |
264 | (2,3):(-2,-3) |
265 | [2,pi/2]:[2,-(pi)/2] |
266 | 2:[2,0]:(0,0) |
267 | [3,0]:2:(1,0) |
268 | 3:(4,5):(-1,-5) |
269 | (4,5):3:(1,5) |
0e505df1 |
270 | (2,1):(3,5):(-1,-4) |
89d0527d |
271 | |
272 | &-- |
273 | (1,2):(0,2) |
274 | [2,pi]:[3,pi] |
275 | |
0e505df1 |
276 | &*;= |
89d0527d |
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] |
280 | 2:(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 | &/;= |
89d0527d |
286 | (3,4):(3,4):(1,0) |
287 | (4,-5):1:(4,-5) |
288 | 1:(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 | |
0e505df1 |
294 | &**;= |
295 | (2,0):(3,0):(8,0) |
296 | (3,0):(2,0):(9,0) |
297 | (2,3):(4,0):(-119,-120) |
ace5de91 |
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 | |
0c721ce2 |
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 | |
89d0527d |
316 | &abs |
317 | (3,4):5 |
318 | (-3,4):5 |
319 | |
0c721ce2 |
320 | &arg |
321 | [2,0]:0 |
322 | [-2,0]:pi |
323 | |
89d0527d |
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) |
89d0527d |
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 | |
0c721ce2 |
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' |
0c721ce2 |
373 | |'acot(z)':'acotan(z)' |
374 | |'acsc(z)':'acosec(z)' |
8c03c583 |
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)' |
0c721ce2 |
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' |
0c721ce2 |
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)' |
0c721ce2 |
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' |
0c721ce2 |
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' |
0c721ce2 |
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' |
89d0527d |
431 | |'atanh(tanh(z))':'z' |
432 | |
0c721ce2 |
433 | &sin |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
0c721ce2 |
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 |
8c03c583 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |