Commit | Line | Data |
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 |
10 | BEGIN { |
11 | chdir 't' if -d 't'; |
12 | @INC = '../lib'; |
13 | } |
5aabfad6 |
14 | |
89d0527d |
15 | use Math::Complex; |
16 | |
2820d885 |
17 | my $VERSION = sprintf("%s", q$Id: complex.t,v 1.9 1998/11/01 00:00:00 dsl Exp $ =~ /(\d+\.d+)/); |
b42d0ec9 |
18 | |
fb73857a |
19 | my ($args, $op, $target, $test, $test_set, $try, $val, $zvalue, @set, @val); |
20 | |
89d0527d |
21 | $test = 0; |
22 | $| = 1; |
fb73857a |
23 | my @script = ( |
24 | 'my ($res, $s0,$s1,$s2,$s3,$s4,$s5,$s6,$s7,$s8,$s9,$s10, $z0,$z1,$z2);' . |
25 | "\n\n" |
26 | ); |
b42d0ec9 |
27 | my $eps = 1e-13; |
89d0527d |
28 | |
d09ae4e6 |
29 | if ($^O eq 'unicos') { # For some reason root() produces very inaccurate |
30 | $eps = 1e-11; # results in Cray UNICOS, and occasionally also |
31 | } # cos(), sin(), cosh(), sinh(). The division |
32 | # of doubles is the current suspect. |
33 | |
89d0527d |
34 | while (<DATA>) { |
0c721ce2 |
35 | s/^\s+//; |
36 | next if $_ eq '' || /^\#/; |
37 | chomp; |
38 | $test_set = 0; # Assume not a test over a set of values |
0e505df1 |
39 | if (/^&(.+)/) { |
89d0527d |
40 | $op = $1; |
41 | next; |
42 | } |
0e505df1 |
43 | elsif (/^\{(.+)\}/) { |
89d0527d |
44 | set($1, \@set, \@val); |
45 | next; |
46 | } |
47 | elsif (s/^\|//) { |
0c721ce2 |
48 | $test_set = 1; # Requests we loop over the set... |
89d0527d |
49 | } |
50 | my @args = split(/:/); |
0c721ce2 |
51 | if ($test_set == 1) { |
89d0527d |
52 | my $i; |
53 | for ($i = 0; $i < @set; $i++) { |
0c721ce2 |
54 | # complex number |
55 | $target = $set[$i]; |
56 | # textual value as found in set definition |
57 | $zvalue = $val[$i]; |
89d0527d |
58 | test($zvalue, $target, @args); |
59 | } |
60 | } else { |
61 | test($op, undef, @args); |
62 | } |
63 | } |
64 | |
b42d0ec9 |
65 | # |
66 | |
67 | sub test_mutators { |
68 | my $op; |
69 | |
70 | $test++; |
71 | push(@script, <<'EOT'); |
72 | { |
73 | my $z = cplx( 1, 1); |
74 | $z->Re(2); |
75 | $z->Im(3); |
76 | print 'not ' unless Re($z) == 2 and Im($z) == 3; |
77 | EOT |
78 | push(@script, qq(print "ok $test\\n"}\n)); |
79 | |
80 | $test++; |
81 | push(@script, <<'EOT'); |
82 | { |
83 | my $z = cplx( 1, 1); |
84 | $z->abs(3 * sqrt(2)); |
85 | print 'not ' unless (abs($z) - 3 * sqrt(2)) < $eps and |
86 | (arg($z) - pi / 4 ) < $eps and |
87 | (Re($z) - 3 ) < $eps and |
88 | (Im($z) - 3 ) < $eps; |
89 | EOT |
90 | push(@script, qq(print "ok $test\\n"}\n)); |
91 | |
92 | $test++; |
93 | push(@script, <<'EOT'); |
94 | { |
95 | my $z = cplx( 1, 1); |
96 | $z->arg(-3 / 4 * pi); |
97 | print 'not ' unless (arg($z) + 3 / 4 * pi) < $eps and |
98 | (abs($z) - sqrt(2) ) < $eps and |
99 | (Re($z) + 1 ) < $eps and |
100 | (Im($z) + 1 ) < $eps; |
101 | EOT |
102 | push(@script, qq(print "ok $test\\n"}\n)); |
103 | } |
104 | |
105 | test_mutators(); |
106 | |
107 | my $constants = ' |
108 | my $i = cplx(0, 1); |
109 | my $pi = cplx(pi, 0); |
110 | my $pii = cplx(0, pi); |
111 | my $pip2 = cplx(pi/2, 0); |
112 | my $zero = cplx(0, 0); |
113 | '; |
114 | |
115 | push(@script, $constants); |
116 | |
117 | |
5cd24f17 |
118 | # test the divbyzeros |
119 | |
0e505df1 |
120 | sub test_dbz { |
121 | for my $op (@_) { |
122 | $test++; |
123 | |
b42d0ec9 |
124 | push(@script, <<EOT); |
125 | eval '$op'; |
126 | print 'not ' unless (\$@ =~ /Division by zero/); |
127 | EOT |
128 | push(@script, qq(print "ok $test\\n";\n)); |
0e505df1 |
129 | } |
130 | } |
131 | |
8c03c583 |
132 | # test the logofzeros |
133 | |
134 | sub test_loz { |
135 | for my $op (@_) { |
136 | $test++; |
137 | |
b42d0ec9 |
138 | push(@script, <<EOT); |
139 | eval '$op'; |
140 | print 'not ' unless (\$@ =~ /Logarithm of zero/); |
141 | EOT |
142 | push(@script, qq(print "ok $test\\n";\n)); |
8c03c583 |
143 | } |
144 | } |
145 | |
5cd24f17 |
146 | test_dbz( |
147 | 'i/0', |
b42d0ec9 |
148 | 'acot(0)', |
149 | 'acot(+$i)', |
150 | # 'acoth(-1)', # Log of zero. |
151 | 'acoth(0)', |
152 | 'acoth(+1)', |
5cd24f17 |
153 | 'acsc(0)', |
5cd24f17 |
154 | 'acsch(0)', |
b42d0ec9 |
155 | 'asec(0)', |
156 | 'asech(0)', |
157 | 'atan(-$i)', |
158 | 'atan($i)', |
159 | # 'atanh(-1)', # Log of zero. |
160 | 'atanh(+1)', |
161 | 'cot(0)', |
162 | 'coth(0)', |
163 | 'csc(0)', |
164 | 'tan($pip2)', |
165 | 'csch(0)', |
166 | 'tan($pip2)', |
8c03c583 |
167 | ); |
168 | |
169 | test_loz( |
fb73857a |
170 | 'log($zero)', |
b42d0ec9 |
171 | 'acot(-$i)', |
8c03c583 |
172 | 'atanh(-1)', |
173 | 'acoth(-1)', |
5cd24f17 |
174 | ); |
175 | |
0e505df1 |
176 | # test the bad roots |
177 | |
178 | sub test_broot { |
5cd24f17 |
179 | for my $op (@_) { |
180 | $test++; |
181 | |
b42d0ec9 |
182 | push(@script, <<EOT); |
183 | eval 'root(2, $op)'; |
184 | print 'not ' unless (\$@ =~ /root must be/); |
185 | EOT |
186 | push(@script, qq(print "ok $test\\n";\n)); |
5cd24f17 |
187 | } |
188 | } |
189 | |
0e505df1 |
190 | test_broot(qw(-3 -2.1 0 0.99)); |
191 | |
89d0527d |
192 | print "1..$test\n"; |
fe82cf6e |
193 | eval join '', @script; |
89d0527d |
194 | die $@ if $@; |
195 | |
0e505df1 |
196 | sub abop { |
197 | my ($op) = @_; |
198 | |
199 | push(@script, qq(print "# $op=\n";)); |
200 | } |
201 | |
89d0527d |
202 | sub test { |
203 | my ($op, $z, @args) = @_; |
0e505df1 |
204 | my ($baop) = 0; |
89d0527d |
205 | $test++; |
206 | my $i; |
0e505df1 |
207 | $baop = 1 if ($op =~ s/;=$//); |
89d0527d |
208 | for ($i = 0; $i < @args; $i++) { |
209 | $val = value($args[$i]); |
fe82cf6e |
210 | push @script, "\$z$i = $val;\n"; |
89d0527d |
211 | } |
212 | if (defined $z) { |
213 | $args = "'$op'"; # Really the value |
0c721ce2 |
214 | $try = "abs(\$z0 - \$z1) <= $eps ? \$z1 : \$z0"; |
fe82cf6e |
215 | push @script, "\$res = $try; "; |
216 | push @script, "check($test, $args[0], \$res, \$z$#args, $args);\n"; |
89d0527d |
217 | } else { |
218 | my ($try, $args); |
219 | if (@args == 2) { |
220 | $try = "$op \$z0"; |
221 | $args = "'$args[0]'"; |
222 | } else { |
223 | $try = ($op =~ /^\w/) ? "$op(\$z0, \$z1)" : "\$z0 $op \$z1"; |
224 | $args = "'$args[0]', '$args[1]'"; |
225 | } |
fe82cf6e |
226 | push @script, "\$res = $try; "; |
227 | push @script, "check($test, '$try', \$res, \$z$#args, $args);\n"; |
0e505df1 |
228 | if (@args > 2 and $baop) { # binary assignment ops |
229 | $test++; |
230 | # check the op= works |
231 | push @script, <<EOB; |
232 | { |
fb73857a |
233 | my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0)); |
0e505df1 |
234 | |
235 | my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0); |
236 | |
fb73857a |
237 | my \$zb = cplx(\$z1r, \$z1i); |
0e505df1 |
238 | |
239 | \$za $op= \$zb; |
240 | my (\$zbr, \$zbi) = \@{\$zb->cartesian}; |
241 | |
242 | check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args); |
243 | EOB |
244 | $test++; |
245 | # check that the rhs has not changed |
246 | push @script, qq(print "not " unless (\$zbr == \$z1r and \$zbi == \$z1i);); |
b42d0ec9 |
247 | push @script, qq(print "ok $test\\n";\n); |
0e505df1 |
248 | push @script, "}\n"; |
249 | } |
89d0527d |
250 | } |
251 | } |
252 | |
253 | sub set { |
254 | my ($set, $setref, $valref) = @_; |
255 | @{$setref} = (); |
256 | @{$valref} = (); |
257 | my @set = split(/;\s*/, $set); |
258 | my @res; |
259 | my $i; |
260 | for ($i = 0; $i < @set; $i++) { |
261 | push(@{$valref}, $set[$i]); |
262 | my $val = value($set[$i]); |
fe82cf6e |
263 | push @script, "\$s$i = $val;\n"; |
264 | push @{$setref}, "\$s$i"; |
89d0527d |
265 | } |
266 | } |
267 | |
268 | sub value { |
269 | local ($_) = @_; |
270 | if (/^\s*\((.*),(.*)\)/) { |
271 | return "cplx($1,$2)"; |
272 | } |
b42d0ec9 |
273 | elsif (/^\s*([\-\+]?(?:\d+(\.\d+)?|\.\d+)(?:[e[\-\+]\d+])?)/) { |
274 | return "cplx($1,0)"; |
275 | } |
89d0527d |
276 | elsif (/^\s*\[(.*),(.*)\]/) { |
277 | return "cplxe($1,$2)"; |
278 | } |
279 | elsif (/^\s*'(.*)'/) { |
280 | my $ex = $1; |
281 | $ex =~ s/\bz\b/$target/g; |
282 | $ex =~ s/\br\b/abs($target)/g; |
283 | $ex =~ s/\bt\b/arg($target)/g; |
284 | $ex =~ s/\ba\b/Re($target)/g; |
285 | $ex =~ s/\bb\b/Im($target)/g; |
286 | return $ex; |
287 | } |
288 | elsif (/^\s*"(.*)"/) { |
289 | return "\"$1\""; |
290 | } |
291 | return $_; |
292 | } |
293 | |
294 | sub check { |
295 | my ($test, $try, $got, $expected, @z) = @_; |
0c721ce2 |
296 | |
297 | # print "# @_\n"; |
298 | |
299 | if ("$got" eq "$expected" |
300 | || |
301 | ($expected =~ /^-?\d/ && $got == $expected) |
302 | || |
303 | (abs($got - $expected) < $eps) |
304 | ) { |
89d0527d |
305 | print "ok $test\n"; |
306 | } else { |
307 | print "not ok $test\n"; |
308 | my $args = (@z == 1) ? "z = $z[0]" : "z0 = $z[0], z1 = $z[1]"; |
309 | print "# '$try' expected: '$expected' got: '$got' for $args\n"; |
310 | } |
311 | } |
fb73857a |
312 | |
313 | sub addsq { |
314 | my ($z1, $z2) = @_; |
315 | return ($z1 + i*$z2) * ($z1 - i*$z2); |
316 | } |
317 | |
318 | sub subsq { |
319 | my ($z1, $z2) = @_; |
320 | return ($z1 + $z2) * ($z1 - $z2); |
321 | } |
322 | |
89d0527d |
323 | __END__ |
0e505df1 |
324 | &+;= |
89d0527d |
325 | (3,4):(3,4):(6,8) |
326 | (-3,4):(3,-4):(0,0) |
327 | (3,4):-3:(0,4) |
328 | 1:(4,2):(5,2) |
329 | [2,0]:[2,pi]:(0,0) |
330 | |
331 | &++ |
332 | (2,1):(3,1) |
333 | |
0e505df1 |
334 | &-;= |
89d0527d |
335 | (2,3):(-2,-3) |
336 | [2,pi/2]:[2,-(pi)/2] |
337 | 2:[2,0]:(0,0) |
338 | [3,0]:2:(1,0) |
339 | 3:(4,5):(-1,-5) |
340 | (4,5):3:(1,5) |
0e505df1 |
341 | (2,1):(3,5):(-1,-4) |
89d0527d |
342 | |
343 | &-- |
344 | (1,2):(0,2) |
345 | [2,pi]:[3,pi] |
346 | |
0e505df1 |
347 | &*;= |
89d0527d |
348 | (0,1):(0,1):(-1,0) |
349 | (4,5):(1,0):(4,5) |
350 | [2,2*pi/3]:(1,0):[2,2*pi/3] |
351 | 2:(0,1):(0,2) |
352 | (0,1):3:(0,3) |
353 | (0,1):(4,1):(-1,4) |
354 | (2,1):(4,-1):(9,2) |
355 | |
0e505df1 |
356 | &/;= |
89d0527d |
357 | (3,4):(3,4):(1,0) |
358 | (4,-5):1:(4,-5) |
359 | 1:(0,1):(0,-1) |
360 | (0,6):(0,2):(3,0) |
361 | (9,2):(4,-1):(2,1) |
362 | [4,pi]:[2,pi/2]:[2,pi/2] |
363 | [2,pi/2]:[4,pi]:[0.5,-(pi)/2] |
364 | |
0e505df1 |
365 | &**;= |
366 | (2,0):(3,0):(8,0) |
367 | (3,0):(2,0):(9,0) |
368 | (2,3):(4,0):(-119,-120) |
ace5de91 |
369 | (0,0):(1,0):(0,0) |
370 | (0,0):(2,3):(0,0) |
371 | (1,0):(0,0):(1,0) |
372 | (1,0):(1,0):(1,0) |
373 | (1,0):(2,3):(1,0) |
374 | (2,3):(0,0):(1,0) |
375 | (2,3):(1,0):(2,3) |
2820d885 |
376 | (0,0):(0,0):(1,0) |
0e505df1 |
377 | |
0c721ce2 |
378 | &Re |
379 | (3,4):3 |
380 | (-3,4):-3 |
381 | [1,pi/2]:0 |
382 | |
383 | &Im |
384 | (3,4):4 |
385 | (3,-4):-4 |
386 | [1,pi/2]:1 |
387 | |
89d0527d |
388 | &abs |
389 | (3,4):5 |
390 | (-3,4):5 |
391 | |
0c721ce2 |
392 | &arg |
393 | [2,0]:0 |
394 | [-2,0]:pi |
395 | |
89d0527d |
396 | &~ |
397 | (4,5):(4,-5) |
398 | (-3,4):(-3,-4) |
399 | [2,pi/2]:[2,-(pi)/2] |
400 | |
401 | &< |
402 | (3,4):(1,2):0 |
403 | (3,4):(3,2):0 |
404 | (3,4):(3,8):1 |
405 | (4,4):(5,129):1 |
406 | |
407 | &== |
408 | (3,4):(4,5):0 |
409 | (3,4):(3,5):0 |
410 | (3,4):(2,4):0 |
411 | (3,4):(3,4):1 |
412 | |
413 | &sqrt |
0c721ce2 |
414 | -9:(0,3) |
89d0527d |
415 | (-100,0):(0,10) |
416 | (16,-30):(5,-3) |
417 | |
418 | &stringify_cartesian |
419 | (-100,0):"-100" |
420 | (0,1):"i" |
421 | (4,-3):"4-3i" |
422 | (4,0):"4" |
423 | (-4,0):"-4" |
424 | (-2,4):"-2+4i" |
425 | (-2,-1):"-2-i" |
426 | |
427 | &stringify_polar |
428 | [-1, 0]:"[1,pi]" |
429 | [1, pi/3]:"[1,pi/3]" |
430 | [6, -2*pi/3]:"[6,-2pi/3]" |
431 | [0.5, -9*pi/11]:"[0.5,-9pi/11]" |
432 | |
433 | { (4,3); [3,2]; (-3,4); (0,2); [2,1] } |
434 | |
435 | |'z + ~z':'2*Re(z)' |
436 | |'z - ~z':'2*i*Im(z)' |
437 | |'z * ~z':'abs(z) * abs(z)' |
438 | |
8c03c583 |
439 | { (0.5, 0); (-0.5, 0); (2,3); [3,2]; (-3,2); (0,2); 3; 1.2; (-3, 0); (-2, -1); [2,1] } |
89d0527d |
440 | |
0c721ce2 |
441 | |'(root(z, 4))[1] ** 4':'z' |
442 | |'(root(z, 5))[3] ** 5':'z' |
443 | |'(root(z, 8))[7] ** 8':'z' |
89d0527d |
444 | |'abs(z)':'r' |
0c721ce2 |
445 | |'acot(z)':'acotan(z)' |
446 | |'acsc(z)':'acosec(z)' |
fb73857a |
447 | |'acsc(z)':'asin(1 / z)' |
448 | |'asec(z)':'acos(1 / z)' |
89d0527d |
449 | |'cbrt(z)':'cbrt(r) * exp(i * t/3)' |
89d0527d |
450 | |'cos(acos(z))':'z' |
fb73857a |
451 | |'addsq(cos(z), sin(z))':1 |
89d0527d |
452 | |'cos(z)':'cosh(i*z)' |
fb73857a |
453 | |'subsq(cosh(z), sinh(z))':1 |
0c721ce2 |
454 | |'cot(acot(z))':'z' |
455 | |'cot(z)':'1 / tan(z)' |
456 | |'cot(z)':'cotan(z)' |
457 | |'csc(acsc(z))':'z' |
458 | |'csc(z)':'1 / sin(z)' |
459 | |'csc(z)':'cosec(z)' |
89d0527d |
460 | |'exp(log(z))':'z' |
0c721ce2 |
461 | |'exp(z)':'exp(a) * exp(i * b)' |
462 | |'ln(z)':'log(z)' |
463 | |'log(exp(z))':'z' |
464 | |'log(z)':'log(r) + i*t' |
89d0527d |
465 | |'log10(z)':'log(z) / log(10)' |
89d0527d |
466 | |'logn(z, 2)':'log(z) / log(2)' |
0c721ce2 |
467 | |'logn(z, 3)':'log(z) / log(3)' |
468 | |'sec(asec(z))':'z' |
469 | |'sec(z)':'1 / cos(z)' |
470 | |'sin(asin(z))':'z' |
471 | |'sin(i * z)':'i * sinh(z)' |
472 | |'sqrt(z) * sqrt(z)':'z' |
473 | |'sqrt(z)':'sqrt(r) * exp(i * t/2)' |
474 | |'tan(atan(z))':'z' |
475 | |'z**z':'exp(z * log(z))' |
89d0527d |
476 | |
0c721ce2 |
477 | { (1,1); [1,0.5]; (-2, -1); 2; -3; (-1,0.5); (0,0.5); 0.5; (2, 0); (-1, -2) } |
89d0527d |
478 | |
89d0527d |
479 | |'cosh(acosh(z))':'z' |
0c721ce2 |
480 | |'coth(acoth(z))':'z' |
481 | |'coth(z)':'1 / tanh(z)' |
482 | |'coth(z)':'cotanh(z)' |
483 | |'csch(acsch(z))':'z' |
484 | |'csch(z)':'1 / sinh(z)' |
485 | |'csch(z)':'cosech(z)' |
486 | |'sech(asech(z))':'z' |
487 | |'sech(z)':'1 / cosh(z)' |
488 | |'sinh(asinh(z))':'z' |
89d0527d |
489 | |'tanh(atanh(z))':'z' |
89d0527d |
490 | |
0c721ce2 |
491 | { (0.2,-0.4); [1,0.5]; -1.2; (-1,0.5); 0.5; (1.1, 0) } |
89d0527d |
492 | |
89d0527d |
493 | |'acos(cos(z)) ** 2':'z * z' |
89d0527d |
494 | |'acosh(cosh(z)) ** 2':'z * z' |
0c721ce2 |
495 | |'acoth(z)':'acotanh(z)' |
496 | |'acoth(z)':'atanh(1 / z)' |
497 | |'acsch(z)':'acosech(z)' |
498 | |'acsch(z)':'asinh(1 / z)' |
499 | |'asech(z)':'acosh(1 / z)' |
500 | |'asin(sin(z))':'z' |
501 | |'asinh(sinh(z))':'z' |
502 | |'atan(tan(z))':'z' |
89d0527d |
503 | |'atanh(tanh(z))':'z' |
504 | |
fb73857a |
505 | &log |
506 | (-2.0,0):( 0.69314718055995, 3.14159265358979) |
507 | (-1.0,0):( 0 , 3.14159265358979) |
508 | (-0.5,0):( -0.69314718055995, 3.14159265358979) |
509 | ( 0.5,0):( -0.69314718055995, 0 ) |
510 | ( 1.0,0):( 0 , 0 ) |
511 | ( 2.0,0):( 0.69314718055995, 0 ) |
512 | |
513 | &log |
514 | ( 2, 3):( 1.28247467873077, 0.98279372324733) |
515 | (-2, 3):( 1.28247467873077, 2.15879893034246) |
516 | (-2,-3):( 1.28247467873077, -2.15879893034246) |
517 | ( 2,-3):( 1.28247467873077, -0.98279372324733) |
518 | |
0c721ce2 |
519 | &sin |
8c03c583 |
520 | (-2.0,0):( -0.90929742682568, 0 ) |
521 | (-1.0,0):( -0.84147098480790, 0 ) |
522 | (-0.5,0):( -0.47942553860420, 0 ) |
523 | ( 0.0,0):( 0 , 0 ) |
524 | ( 0.5,0):( 0.47942553860420, 0 ) |
525 | ( 1.0,0):( 0.84147098480790, 0 ) |
526 | ( 2.0,0):( 0.90929742682568, 0 ) |
527 | |
528 | &sin |
0c721ce2 |
529 | ( 2, 3):( 9.15449914691143, -4.16890695996656) |
530 | (-2, 3):( -9.15449914691143, -4.16890695996656) |
531 | (-2,-3):( -9.15449914691143, 4.16890695996656) |
532 | ( 2,-3):( 9.15449914691143, 4.16890695996656) |
533 | |
534 | &cos |
8c03c583 |
535 | (-2.0,0):( -0.41614683654714, 0 ) |
536 | (-1.0,0):( 0.54030230586814, 0 ) |
537 | (-0.5,0):( 0.87758256189037, 0 ) |
538 | ( 0.0,0):( 1 , 0 ) |
539 | ( 0.5,0):( 0.87758256189037, 0 ) |
540 | ( 1.0,0):( 0.54030230586814, 0 ) |
541 | ( 2.0,0):( -0.41614683654714, 0 ) |
542 | |
543 | &cos |
0c721ce2 |
544 | ( 2, 3):( -4.18962569096881, -9.10922789375534) |
545 | (-2, 3):( -4.18962569096881, 9.10922789375534) |
546 | (-2,-3):( -4.18962569096881, -9.10922789375534) |
547 | ( 2,-3):( -4.18962569096881, 9.10922789375534) |
548 | |
549 | &tan |
8c03c583 |
550 | (-2.0,0):( 2.18503986326152, 0 ) |
551 | (-1.0,0):( -1.55740772465490, 0 ) |
552 | (-0.5,0):( -0.54630248984379, 0 ) |
553 | ( 0.0,0):( 0 , 0 ) |
554 | ( 0.5,0):( 0.54630248984379, 0 ) |
555 | ( 1.0,0):( 1.55740772465490, 0 ) |
556 | ( 2.0,0):( -2.18503986326152, 0 ) |
557 | |
558 | &tan |
0c721ce2 |
559 | ( 2, 3):( -0.00376402564150, 1.00323862735361) |
560 | (-2, 3):( 0.00376402564150, 1.00323862735361) |
561 | (-2,-3):( 0.00376402564150, -1.00323862735361) |
562 | ( 2,-3):( -0.00376402564150, -1.00323862735361) |
563 | |
564 | &sec |
8c03c583 |
565 | (-2.0,0):( -2.40299796172238, 0 ) |
566 | (-1.0,0):( 1.85081571768093, 0 ) |
567 | (-0.5,0):( 1.13949392732455, 0 ) |
568 | ( 0.0,0):( 1 , 0 ) |
569 | ( 0.5,0):( 1.13949392732455, 0 ) |
570 | ( 1.0,0):( 1.85081571768093, 0 ) |
571 | ( 2.0,0):( -2.40299796172238, 0 ) |
572 | |
573 | &sec |
0c721ce2 |
574 | ( 2, 3):( -0.04167496441114, 0.09061113719624) |
575 | (-2, 3):( -0.04167496441114, -0.09061113719624) |
576 | (-2,-3):( -0.04167496441114, 0.09061113719624) |
577 | ( 2,-3):( -0.04167496441114, -0.09061113719624) |
578 | |
579 | &csc |
8c03c583 |
580 | (-2.0,0):( -1.09975017029462, 0 ) |
581 | (-1.0,0):( -1.18839510577812, 0 ) |
582 | (-0.5,0):( -2.08582964293349, 0 ) |
583 | ( 0.5,0):( 2.08582964293349, 0 ) |
584 | ( 1.0,0):( 1.18839510577812, 0 ) |
585 | ( 2.0,0):( 1.09975017029462, 0 ) |
586 | |
587 | &csc |
0c721ce2 |
588 | ( 2, 3):( 0.09047320975321, 0.04120098628857) |
589 | (-2, 3):( -0.09047320975321, 0.04120098628857) |
590 | (-2,-3):( -0.09047320975321, -0.04120098628857) |
591 | ( 2,-3):( 0.09047320975321, -0.04120098628857) |
592 | |
593 | &cot |
8c03c583 |
594 | (-2.0,0):( 0.45765755436029, 0 ) |
595 | (-1.0,0):( -0.64209261593433, 0 ) |
596 | (-0.5,0):( -1.83048772171245, 0 ) |
597 | ( 0.5,0):( 1.83048772171245, 0 ) |
598 | ( 1.0,0):( 0.64209261593433, 0 ) |
599 | ( 2.0,0):( -0.45765755436029, 0 ) |
600 | |
601 | &cot |
0c721ce2 |
602 | ( 2, 3):( -0.00373971037634, -0.99675779656936) |
603 | (-2, 3):( 0.00373971037634, -0.99675779656936) |
604 | (-2,-3):( 0.00373971037634, 0.99675779656936) |
605 | ( 2,-3):( -0.00373971037634, 0.99675779656936) |
606 | |
607 | &asin |
8c03c583 |
608 | (-2.0,0):( -1.57079632679490, 1.31695789692482) |
609 | (-1.0,0):( -1.57079632679490, 0 ) |
610 | (-0.5,0):( -0.52359877559830, 0 ) |
611 | ( 0.0,0):( 0 , 0 ) |
612 | ( 0.5,0):( 0.52359877559830, 0 ) |
613 | ( 1.0,0):( 1.57079632679490, 0 ) |
614 | ( 2.0,0):( 1.57079632679490, -1.31695789692482) |
615 | |
616 | &asin |
0c721ce2 |
617 | ( 2, 3):( 0.57065278432110, 1.98338702991654) |
618 | (-2, 3):( -0.57065278432110, 1.98338702991654) |
619 | (-2,-3):( -0.57065278432110, -1.98338702991654) |
620 | ( 2,-3):( 0.57065278432110, -1.98338702991654) |
621 | |
622 | &acos |
8c03c583 |
623 | (-2.0,0):( 3.14159265358979, -1.31695789692482) |
624 | (-1.0,0):( 3.14159265358979, 0 ) |
625 | (-0.5,0):( 2.09439510239320, 0 ) |
626 | ( 0.0,0):( 1.57079632679490, 0 ) |
627 | ( 0.5,0):( 1.04719755119660, 0 ) |
628 | ( 1.0,0):( 0 , 0 ) |
629 | ( 2.0,0):( 0 , 1.31695789692482) |
630 | |
631 | &acos |
0c721ce2 |
632 | ( 2, 3):( 1.00014354247380, -1.98338702991654) |
633 | (-2, 3):( 2.14144911111600, -1.98338702991654) |
634 | (-2,-3):( 2.14144911111600, 1.98338702991654) |
635 | ( 2,-3):( 1.00014354247380, 1.98338702991654) |
636 | |
637 | &atan |
8c03c583 |
638 | (-2.0,0):( -1.10714871779409, 0 ) |
639 | (-1.0,0):( -0.78539816339745, 0 ) |
640 | (-0.5,0):( -0.46364760900081, 0 ) |
641 | ( 0.0,0):( 0 , 0 ) |
642 | ( 0.5,0):( 0.46364760900081, 0 ) |
643 | ( 1.0,0):( 0.78539816339745, 0 ) |
644 | ( 2.0,0):( 1.10714871779409, 0 ) |
645 | |
646 | &atan |
0c721ce2 |
647 | ( 2, 3):( 1.40992104959658, 0.22907268296854) |
648 | (-2, 3):( -1.40992104959658, 0.22907268296854) |
649 | (-2,-3):( -1.40992104959658, -0.22907268296854) |
650 | ( 2,-3):( 1.40992104959658, -0.22907268296854) |
651 | |
652 | &asec |
8c03c583 |
653 | (-2.0,0):( 2.09439510239320, 0 ) |
654 | (-1.0,0):( 3.14159265358979, 0 ) |
655 | (-0.5,0):( 3.14159265358979, -1.31695789692482) |
656 | ( 0.5,0):( 0 , 1.31695789692482) |
657 | ( 1.0,0):( 0 , 0 ) |
658 | ( 2.0,0):( 1.04719755119660, 0 ) |
659 | |
660 | &asec |
0c721ce2 |
661 | ( 2, 3):( 1.42041072246703, 0.23133469857397) |
662 | (-2, 3):( 1.72118193112276, 0.23133469857397) |
663 | (-2,-3):( 1.72118193112276, -0.23133469857397) |
664 | ( 2,-3):( 1.42041072246703, -0.23133469857397) |
665 | |
666 | &acsc |
8c03c583 |
667 | (-2.0,0):( -0.52359877559830, 0 ) |
668 | (-1.0,0):( -1.57079632679490, 0 ) |
669 | (-0.5,0):( -1.57079632679490, 1.31695789692482) |
670 | ( 0.5,0):( 1.57079632679490, -1.31695789692482) |
671 | ( 1.0,0):( 1.57079632679490, 0 ) |
672 | ( 2.0,0):( 0.52359877559830, 0 ) |
673 | |
674 | &acsc |
0c721ce2 |
675 | ( 2, 3):( 0.15038560432786, -0.23133469857397) |
676 | (-2, 3):( -0.15038560432786, -0.23133469857397) |
677 | (-2,-3):( -0.15038560432786, 0.23133469857397) |
678 | ( 2,-3):( 0.15038560432786, 0.23133469857397) |
679 | |
680 | &acot |
8c03c583 |
681 | (-2.0,0):( -0.46364760900081, 0 ) |
682 | (-1.0,0):( -0.78539816339745, 0 ) |
683 | (-0.5,0):( -1.10714871779409, 0 ) |
684 | ( 0.5,0):( 1.10714871779409, 0 ) |
685 | ( 1.0,0):( 0.78539816339745, 0 ) |
686 | ( 2.0,0):( 0.46364760900081, 0 ) |
687 | |
688 | &acot |
0c721ce2 |
689 | ( 2, 3):( 0.16087527719832, -0.22907268296854) |
690 | (-2, 3):( -0.16087527719832, -0.22907268296854) |
691 | (-2,-3):( -0.16087527719832, 0.22907268296854) |
692 | ( 2,-3):( 0.16087527719832, 0.22907268296854) |
693 | |
694 | &sinh |
8c03c583 |
695 | (-2.0,0):( -3.62686040784702, 0 ) |
696 | (-1.0,0):( -1.17520119364380, 0 ) |
697 | (-0.5,0):( -0.52109530549375, 0 ) |
698 | ( 0.0,0):( 0 , 0 ) |
699 | ( 0.5,0):( 0.52109530549375, 0 ) |
700 | ( 1.0,0):( 1.17520119364380, 0 ) |
701 | ( 2.0,0):( 3.62686040784702, 0 ) |
702 | |
703 | &sinh |
0c721ce2 |
704 | ( 2, 3):( -3.59056458998578, 0.53092108624852) |
705 | (-2, 3):( 3.59056458998578, 0.53092108624852) |
706 | (-2,-3):( 3.59056458998578, -0.53092108624852) |
707 | ( 2,-3):( -3.59056458998578, -0.53092108624852) |
708 | |
709 | &cosh |
8c03c583 |
710 | (-2.0,0):( 3.76219569108363, 0 ) |
711 | (-1.0,0):( 1.54308063481524, 0 ) |
712 | (-0.5,0):( 1.12762596520638, 0 ) |
713 | ( 0.0,0):( 1 , 0 ) |
714 | ( 0.5,0):( 1.12762596520638, 0 ) |
715 | ( 1.0,0):( 1.54308063481524, 0 ) |
716 | ( 2.0,0):( 3.76219569108363, 0 ) |
717 | |
718 | &cosh |
0c721ce2 |
719 | ( 2, 3):( -3.72454550491532, 0.51182256998738) |
720 | (-2, 3):( -3.72454550491532, -0.51182256998738) |
721 | (-2,-3):( -3.72454550491532, 0.51182256998738) |
722 | ( 2,-3):( -3.72454550491532, -0.51182256998738) |
723 | |
724 | &tanh |
8c03c583 |
725 | (-2.0,0):( -0.96402758007582, 0 ) |
726 | (-1.0,0):( -0.76159415595576, 0 ) |
727 | (-0.5,0):( -0.46211715726001, 0 ) |
728 | ( 0.0,0):( 0 , 0 ) |
729 | ( 0.5,0):( 0.46211715726001, 0 ) |
730 | ( 1.0,0):( 0.76159415595576, 0 ) |
731 | ( 2.0,0):( 0.96402758007582, 0 ) |
732 | |
733 | &tanh |
0c721ce2 |
734 | ( 2, 3):( 0.96538587902213, -0.00988437503832) |
735 | (-2, 3):( -0.96538587902213, -0.00988437503832) |
736 | (-2,-3):( -0.96538587902213, 0.00988437503832) |
737 | ( 2,-3):( 0.96538587902213, 0.00988437503832) |
738 | |
739 | &sech |
8c03c583 |
740 | (-2.0,0):( 0.26580222883408, 0 ) |
741 | (-1.0,0):( 0.64805427366389, 0 ) |
742 | (-0.5,0):( 0.88681888397007, 0 ) |
743 | ( 0.0,0):( 1 , 0 ) |
744 | ( 0.5,0):( 0.88681888397007, 0 ) |
745 | ( 1.0,0):( 0.64805427366389, 0 ) |
746 | ( 2.0,0):( 0.26580222883408, 0 ) |
747 | |
748 | &sech |
0c721ce2 |
749 | ( 2, 3):( -0.26351297515839, -0.03621163655877) |
750 | (-2, 3):( -0.26351297515839, 0.03621163655877) |
751 | (-2,-3):( -0.26351297515839, -0.03621163655877) |
752 | ( 2,-3):( -0.26351297515839, 0.03621163655877) |
753 | |
754 | &csch |
8c03c583 |
755 | (-2.0,0):( -0.27572056477178, 0 ) |
756 | (-1.0,0):( -0.85091812823932, 0 ) |
757 | (-0.5,0):( -1.91903475133494, 0 ) |
758 | ( 0.5,0):( 1.91903475133494, 0 ) |
759 | ( 1.0,0):( 0.85091812823932, 0 ) |
760 | ( 2.0,0):( 0.27572056477178, 0 ) |
761 | |
762 | &csch |
0c721ce2 |
763 | ( 2, 3):( -0.27254866146294, -0.04030057885689) |
764 | (-2, 3):( 0.27254866146294, -0.04030057885689) |
765 | (-2,-3):( 0.27254866146294, 0.04030057885689) |
766 | ( 2,-3):( -0.27254866146294, 0.04030057885689) |
767 | |
768 | &coth |
8c03c583 |
769 | (-2.0,0):( -1.03731472072755, 0 ) |
770 | (-1.0,0):( -1.31303528549933, 0 ) |
771 | (-0.5,0):( -2.16395341373865, 0 ) |
772 | ( 0.5,0):( 2.16395341373865, 0 ) |
773 | ( 1.0,0):( 1.31303528549933, 0 ) |
774 | ( 2.0,0):( 1.03731472072755, 0 ) |
775 | |
776 | &coth |
0c721ce2 |
777 | ( 2, 3):( 1.03574663776500, 0.01060478347034) |
778 | (-2, 3):( -1.03574663776500, 0.01060478347034) |
779 | (-2,-3):( -1.03574663776500, -0.01060478347034) |
780 | ( 2,-3):( 1.03574663776500, -0.01060478347034) |
781 | |
782 | &asinh |
8c03c583 |
783 | (-2.0,0):( -1.44363547517881, 0 ) |
784 | (-1.0,0):( -0.88137358701954, 0 ) |
785 | (-0.5,0):( -0.48121182505960, 0 ) |
786 | ( 0.0,0):( 0 , 0 ) |
787 | ( 0.5,0):( 0.48121182505960, 0 ) |
788 | ( 1.0,0):( 0.88137358701954, 0 ) |
789 | ( 2.0,0):( 1.44363547517881, 0 ) |
790 | |
791 | &asinh |
0c721ce2 |
792 | ( 2, 3):( 1.96863792579310, 0.96465850440760) |
793 | (-2, 3):( -1.96863792579310, 0.96465850440761) |
794 | (-2,-3):( -1.96863792579310, -0.96465850440761) |
795 | ( 2,-3):( 1.96863792579310, -0.96465850440760) |
796 | |
797 | &acosh |
8c03c583 |
798 | (-2.0,0):( -1.31695789692482, 3.14159265358979) |
799 | (-1.0,0):( 0, 3.14159265358979) |
800 | (-0.5,0):( 0, 2.09439510239320) |
801 | ( 0.0,0):( 0, 1.57079632679490) |
802 | ( 0.5,0):( 0, 1.04719755119660) |
803 | ( 1.0,0):( 0 , 0 ) |
804 | ( 2.0,0):( 1.31695789692482, 0 ) |
805 | |
806 | &acosh |
0c721ce2 |
807 | ( 2, 3):( 1.98338702991654, 1.00014354247380) |
808 | (-2, 3):( -1.98338702991653, -2.14144911111600) |
809 | (-2,-3):( -1.98338702991653, 2.14144911111600) |
810 | ( 2,-3):( 1.98338702991654, -1.00014354247380) |
811 | |
812 | &atanh |
8c03c583 |
813 | (-2.0,0):( -0.54930614433405, 1.57079632679490) |
814 | (-0.5,0):( -0.54930614433405, 0 ) |
815 | ( 0.0,0):( 0 , 0 ) |
816 | ( 0.5,0):( 0.54930614433405, 0 ) |
817 | ( 2.0,0):( 0.54930614433405, 1.57079632679490) |
818 | |
819 | &atanh |
0c721ce2 |
820 | ( 2, 3):( 0.14694666622553, 1.33897252229449) |
821 | (-2, 3):( -0.14694666622553, 1.33897252229449) |
822 | (-2,-3):( -0.14694666622553, -1.33897252229449) |
823 | ( 2,-3):( 0.14694666622553, -1.33897252229449) |
824 | |
825 | &asech |
8c03c583 |
826 | (-2.0,0):( 0 , 2.09439510239320) |
827 | (-1.0,0):( 0 , 3.14159265358979) |
828 | (-0.5,0):( -1.31695789692482, 3.14159265358979) |
829 | ( 0.5,0):( 1.31695789692482, 0 ) |
830 | ( 1.0,0):( 0 , 0 ) |
831 | ( 2.0,0):( 0 , 1.04719755119660) |
832 | |
833 | &asech |
0c721ce2 |
834 | ( 2, 3):( 0.23133469857397, -1.42041072246703) |
835 | (-2, 3):( -0.23133469857397, 1.72118193112276) |
836 | (-2,-3):( -0.23133469857397, -1.72118193112276) |
837 | ( 2,-3):( 0.23133469857397, 1.42041072246703) |
838 | |
839 | &acsch |
8c03c583 |
840 | (-2.0,0):( -0.48121182505960, 0 ) |
841 | (-1.0,0):( -0.88137358701954, 0 ) |
842 | (-0.5,0):( -1.44363547517881, 0 ) |
843 | ( 0.5,0):( 1.44363547517881, 0 ) |
844 | ( 1.0,0):( 0.88137358701954, 0 ) |
845 | ( 2.0,0):( 0.48121182505960, 0 ) |
846 | |
847 | &acsch |
0c721ce2 |
848 | ( 2, 3):( 0.15735549884499, -0.22996290237721) |
849 | (-2, 3):( -0.15735549884499, -0.22996290237721) |
850 | (-2,-3):( -0.15735549884499, 0.22996290237721) |
851 | ( 2,-3):( 0.15735549884499, 0.22996290237721) |
852 | |
853 | &acoth |
8c03c583 |
854 | (-2.0,0):( -0.54930614433405, 0 ) |
855 | (-0.5,0):( -0.54930614433405, 1.57079632679490) |
856 | ( 0.5,0):( 0.54930614433405, 1.57079632679490) |
857 | ( 2.0,0):( 0.54930614433405, 0 ) |
858 | |
859 | &acoth |
0c721ce2 |
860 | ( 2, 3):( 0.14694666622553, -0.23182380450040) |
861 | (-2, 3):( -0.14694666622553, -0.23182380450040) |
862 | (-2,-3):( -0.14694666622553, 0.23182380450040) |
863 | ( 2,-3):( 0.14694666622553, 0.23182380450040) |
864 | |
865 | # eof |