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1 | package bignum; |
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2 | use 5.006002; |
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3 | |
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4 | $VERSION = '0.22'; |
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5 | use Exporter; |
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6 | @EXPORT_OK = qw( ); |
7 | @EXPORT = qw( inf NaN ); |
8 | @ISA = qw( Exporter ); |
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9 | |
10 | use strict; |
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11 | use overload; |
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12 | |
13 | ############################################################################## |
14 | |
15 | # These are all alike, and thus faked by AUTOLOAD |
16 | |
17 | my @faked = qw/round_mode accuracy precision div_scale/; |
18 | use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite |
19 | |
20 | sub AUTOLOAD |
21 | { |
22 | my $name = $AUTOLOAD; |
23 | |
24 | $name =~ s/.*:://; # split package |
25 | no strict 'refs'; |
26 | foreach my $n (@faked) |
27 | { |
28 | if ($n eq $name) |
29 | { |
30 | *{"bignum::$name"} = sub |
31 | { |
32 | my $self = shift; |
33 | no strict 'refs'; |
34 | if (defined $_[0]) |
35 | { |
36 | Math::BigInt->$name($_[0]); |
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37 | return Math::BigFloat->$name($_[0]); |
126f3c5f |
38 | } |
39 | return Math::BigInt->$name(); |
40 | }; |
41 | return &$name; |
42 | } |
43 | } |
44 | |
45 | # delayed load of Carp and avoid recursion |
46 | require Carp; |
47 | Carp::croak ("Can't call bignum\-\>$name, not a valid method"); |
48 | } |
49 | |
50 | sub upgrade |
51 | { |
95a2d02c |
52 | $Math::BigInt::upgrade; |
53 | } |
54 | |
55 | sub _binary_constant |
56 | { |
57 | # this takes a binary/hexadecimal/octal constant string and returns it |
58 | # as string suitable for new. Basically it converts octal to decimal, and |
59 | # passes every thing else unmodified back. |
60 | my $string = shift; |
61 | |
62 | return Math::BigInt->new($string) if $string =~ /^0[bx]/; |
63 | |
64 | # so it must be an octal constant |
65 | Math::BigInt->from_oct($string); |
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66 | } |
67 | |
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68 | sub unimport |
69 | { |
70 | $^H{bignum} = undef; # no longer in effect |
71 | overload::remove_constant('binary','','float','','integer'); |
72 | } |
73 | |
74 | sub in_effect |
75 | { |
76 | my $level = shift || 0; |
77 | my $hinthash = (caller($level))[10]; |
78 | $hinthash->{bignum}; |
79 | } |
80 | |
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81 | sub import |
82 | { |
83 | my $self = shift; |
84 | |
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85 | $^H{bignum} = 1; # we are in effect |
86 | |
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87 | # some defaults |
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88 | my $lib = ''; my $lib_kind = 'try'; |
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89 | my $upgrade = 'Math::BigFloat'; |
90 | my $downgrade = 'Math::BigInt'; |
91 | |
92 | my @import = ( ':constant' ); # drive it w/ constant |
93 | my @a = @_; my $l = scalar @_; my $j = 0; |
94 | my ($ver,$trace); # version? trace? |
95 | my ($a,$p); # accuracy, precision |
96 | for ( my $i = 0; $i < $l ; $i++,$j++ ) |
97 | { |
98 | if ($_[$i] eq 'upgrade') |
99 | { |
100 | # this causes upgrading |
101 | $upgrade = $_[$i+1]; # or undef to disable |
102 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
103 | splice @a, $j, $s; $j -= $s; $i++; |
104 | } |
105 | elsif ($_[$i] eq 'downgrade') |
106 | { |
107 | # this causes downgrading |
108 | $downgrade = $_[$i+1]; # or undef to disable |
109 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
110 | splice @a, $j, $s; $j -= $s; $i++; |
111 | } |
bd49aa09 |
112 | elsif ($_[$i] =~ /^(l|lib|try|only)$/) |
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113 | { |
114 | # this causes a different low lib to take care... |
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115 | $lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l'; |
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116 | $lib = $_[$i+1] || ''; |
117 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
118 | splice @a, $j, $s; $j -= $s; $i++; |
119 | } |
120 | elsif ($_[$i] =~ /^(a|accuracy)$/) |
121 | { |
122 | $a = $_[$i+1]; |
123 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
124 | splice @a, $j, $s; $j -= $s; $i++; |
125 | } |
126 | elsif ($_[$i] =~ /^(p|precision)$/) |
127 | { |
128 | $p = $_[$i+1]; |
129 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
130 | splice @a, $j, $s; $j -= $s; $i++; |
131 | } |
132 | elsif ($_[$i] =~ /^(v|version)$/) |
133 | { |
134 | $ver = 1; |
135 | splice @a, $j, 1; $j --; |
136 | } |
137 | elsif ($_[$i] =~ /^(t|trace)$/) |
138 | { |
139 | $trace = 1; |
140 | splice @a, $j, 1; $j --; |
141 | } |
142 | else { die "unknown option $_[$i]"; } |
143 | } |
144 | my $class; |
145 | $_lite = 0; # using M::BI::L ? |
146 | if ($trace) |
147 | { |
148 | require Math::BigInt::Trace; $class = 'Math::BigInt::Trace'; |
149 | $upgrade = 'Math::BigFloat::Trace'; |
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150 | } |
151 | else |
152 | { |
153 | # see if we can find Math::BigInt::Lite |
154 | if (!defined $a && !defined $p) # rounding won't work to well |
155 | { |
156 | eval 'require Math::BigInt::Lite;'; |
157 | if ($@ eq '') |
158 | { |
159 | @import = ( ); # :constant in Lite, not MBI |
160 | Math::BigInt::Lite->import( ':constant' ); |
161 | $_lite= 1; # signal okay |
162 | } |
163 | } |
164 | require Math::BigInt if $_lite == 0; # not already loaded? |
165 | $class = 'Math::BigInt'; # regardless of MBIL or not |
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166 | } |
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167 | push @import, $lib_kind => $lib if $lib ne ''; |
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168 | # Math::BigInt::Trace or plain Math::BigInt |
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169 | $class->import(@import, upgrade => $upgrade); |
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170 | |
171 | if ($trace) |
172 | { |
173 | require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace'; |
174 | $downgrade = 'Math::BigInt::Trace'; |
126f3c5f |
175 | } |
176 | else |
177 | { |
178 | require Math::BigFloat; $class = 'Math::BigFloat'; |
179 | } |
180 | $class->import(':constant','downgrade',$downgrade); |
181 | |
182 | bignum->accuracy($a) if defined $a; |
183 | bignum->precision($p) if defined $p; |
184 | if ($ver) |
185 | { |
186 | print "bignum\t\t\t v$VERSION\n"; |
187 | print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite; |
188 | print "Math::BigInt\t\t v$Math::BigInt::VERSION"; |
189 | my $config = Math::BigInt->config(); |
190 | print " lib => $config->{lib} v$config->{lib_version}\n"; |
191 | print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n"; |
192 | exit; |
193 | } |
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194 | |
195 | # Take care of octal/hexadecimal constants |
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196 | overload::constant binary => sub { _binary_constant(shift) }; |
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197 | |
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198 | # if another big* was already loaded: |
199 | my ($package) = caller(); |
200 | |
201 | no strict 'refs'; |
202 | if (!defined *{"${package}::inf"}) |
203 | { |
204 | $self->export_to_level(1,$self,@a); # export inf and NaN |
205 | } |
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206 | } |
207 | |
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208 | sub inf () { Math::BigInt->binf(); } |
209 | sub NaN () { Math::BigInt->bnan(); } |
210 | |
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211 | 1; |
212 | |
213 | __END__ |
214 | |
215 | =head1 NAME |
216 | |
217 | bignum - Transparent BigNumber support for Perl |
218 | |
219 | =head1 SYNOPSIS |
220 | |
221 | use bignum; |
222 | |
223 | $x = 2 + 4.5,"\n"; # BigFloat 6.5 |
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224 | print 2 ** 512 * 0.1,"\n"; # really is what you think it is |
225 | print inf * inf,"\n"; # prints inf |
226 | print NaN * 3,"\n"; # prints NaN |
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227 | |
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228 | { |
229 | no bignum; |
230 | print 2 ** 256,"\n"; # a normal Perl scalar now |
231 | } |
232 | |
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233 | =head1 DESCRIPTION |
234 | |
235 | All operators (including basic math operations) are overloaded. Integer and |
236 | floating-point constants are created as proper BigInts or BigFloats, |
237 | respectively. |
238 | |
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239 | If you do |
240 | |
241 | use bignum; |
242 | |
243 | at the top of your script, Math::BigFloat and Math::BigInt will be loaded |
244 | and any constant number will be converted to an object (Math::BigFloat for |
245 | floats like 3.1415 and Math::BigInt for integers like 1234). |
246 | |
247 | So, the following line: |
248 | |
249 | $x = 1234; |
250 | |
251 | creates actually a Math::BigInt and stores a reference to in $x. |
252 | This happens transparently and behind your back, so to speak. |
253 | |
254 | You can see this with the following: |
255 | |
256 | perl -Mbignum -le 'print ref(1234)' |
257 | |
258 | Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite |
259 | if it is installed since it is faster for some operations. It will be |
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260 | automatically upgraded to BigInt whenever necessary: |
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261 | |
262 | perl -Mbignum -le 'print ref(2**255)' |
263 | |
264 | This also means it is a bad idea to check for some specific package, since |
265 | the actual contents of $x might be something unexpected. Due to the |
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266 | transparent way of bignum C<ref()> should not be necessary, anyway. |
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267 | |
268 | Since Math::BigInt and BigFloat also overload the normal math operations, |
269 | the following line will still work: |
270 | |
271 | perl -Mbignum -le 'print ref(1234+1234)' |
272 | |
273 | Since numbers are actually objects, you can call all the usual methods from |
274 | BigInt/BigFloat on them. This even works to some extent on expressions: |
275 | |
276 | perl -Mbignum -le '$x = 1234; print $x->bdec()' |
277 | perl -Mbignum -le 'print 1234->binc();' |
278 | perl -Mbignum -le 'print 1234->binc->badd(6);' |
279 | perl -Mbignum -le 'print +(1234)->binc()' |
280 | |
281 | (Note that print doesn't do what you expect if the expression starts with |
282 | '(' hence the C<+>) |
283 | |
284 | You can even chain the operations together as usual: |
285 | |
286 | perl -Mbignum -le 'print 1234->binc->badd(6);' |
287 | 1241 |
288 | |
289 | Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers |
290 | appropriately. This means that: |
291 | |
292 | perl -Mbignum -le 'print 1234+4.5' |
293 | 1238.5 |
294 | |
295 | will work correctly. These mixed cases don't do always work when using |
296 | Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl |
297 | scalars work. |
298 | |
299 | If you do want to work with large integers like under C<use integer;>, try |
300 | C<use bigint;>: |
301 | |
302 | perl -Mbigint -le 'print 1234.5+4.5' |
303 | 1238 |
304 | |
305 | There is also C<use bigrat;> which gives you big rationals: |
306 | |
307 | perl -Mbigrat -le 'print 1234+4.1' |
308 | 12381/10 |
309 | |
310 | The entire upgrading/downgrading is still experimental and might not work |
311 | as you expect or may even have bugs. |
312 | |
313 | You might get errors like this: |
314 | |
315 | Can't use an undefined value as an ARRAY reference at |
316 | /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864 |
317 | |
318 | This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or |
319 | vice versa) and the upgrade/downgrad path was missing. This is a bug, please |
320 | report it so that we can fix it. |
321 | |
322 | You might consider using just Math::BigInt or Math::BigFloat, since they |
323 | allow you finer control over what get's done in which module/space. For |
324 | instance, simple loop counters will be Math::BigInts under C<use bignum;> and |
325 | this is slower than keeping them as Perl scalars: |
326 | |
327 | perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }' |
328 | |
329 | Please note the following does not work as expected (prints nothing), since |
330 | overloading of '..' is not yet possible in Perl (as of v5.8.0): |
331 | |
332 | perl -Mbignum -le 'for (1..2) { print ref($_); }' |
333 | |
b68b7ab1 |
334 | =head2 Options |
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335 | |
336 | bignum recognizes some options that can be passed while loading it via use. |
337 | The options can (currently) be either a single letter form, or the long form. |
338 | The following options exist: |
339 | |
340 | =over 2 |
341 | |
342 | =item a or accuracy |
343 | |
344 | This sets the accuracy for all math operations. The argument must be greater |
345 | than or equal to zero. See Math::BigInt's bround() function for details. |
346 | |
347 | perl -Mbignum=a,50 -le 'print sqrt(20)' |
348 | |
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349 | Note that setting precision and accurary at the same time is not possible. |
350 | |
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351 | =item p or precision |
352 | |
353 | This sets the precision for all math operations. The argument can be any |
354 | integer. Negative values mean a fixed number of digits after the dot, while |
355 | a positive value rounds to this digit left from the dot. 0 or 1 mean round to |
356 | integer. See Math::BigInt's bfround() function for details. |
357 | |
358 | perl -Mbignum=p,-50 -le 'print sqrt(20)' |
359 | |
95a2d02c |
360 | Note that setting precision and accurary at the same time is not possible. |
361 | |
126f3c5f |
362 | =item t or trace |
363 | |
364 | This enables a trace mode and is primarily for debugging bignum or |
365 | Math::BigInt/Math::BigFloat. |
366 | |
367 | =item l or lib |
368 | |
369 | Load a different math lib, see L<MATH LIBRARY>. |
370 | |
371 | perl -Mbignum=l,GMP -e 'print 2 ** 512' |
372 | |
373 | Currently there is no way to specify more than one library on the command |
95a2d02c |
374 | line. This means the following does not work: |
375 | |
376 | perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512' |
377 | |
378 | This will be hopefully fixed soon ;) |
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379 | |
380 | =item v or version |
381 | |
382 | This prints out the name and version of all modules used and then exits. |
383 | |
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384 | perl -Mbignum=v |
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385 | |
95a2d02c |
386 | =back |
387 | |
b68b7ab1 |
388 | =head2 Methods |
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389 | |
390 | Beside import() and AUTOLOAD() there are only a few other methods. |
391 | |
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392 | Since all numbers are now objects, you can use all functions that are part of |
393 | the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not |
394 | the fxxx() notation, though. This makes it possible that the underlying object |
395 | might morph into a different class than BigFloat. |
396 | |
4440d13a |
397 | =head2 Caveats |
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398 | |
399 | But a warning is in order. When using the following to make a copy of a number, |
400 | only a shallow copy will be made. |
401 | |
402 | $x = 9; $y = $x; |
403 | $x = $y = 7; |
404 | |
b68b7ab1 |
405 | If you want to make a real copy, use the following: |
406 | |
407 | $y = $x->copy(); |
408 | |
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409 | Using the copy or the original with overloaded math is okay, e.g. the |
410 | following work: |
411 | |
412 | $x = 9; $y = $x; |
413 | print $x + 1, " ", $y,"\n"; # prints 10 9 |
414 | |
415 | but calling any method that modifies the number directly will result in |
3c4b39be |
416 | B<both> the original and the copy being destroyed: |
990fb837 |
417 | |
418 | $x = 9; $y = $x; |
419 | print $x->badd(1), " ", $y,"\n"; # prints 10 10 |
420 | |
421 | $x = 9; $y = $x; |
422 | print $x->binc(1), " ", $y,"\n"; # prints 10 10 |
423 | |
424 | $x = 9; $y = $x; |
425 | print $x->bmul(2), " ", $y,"\n"; # prints 18 18 |
426 | |
427 | Using methods that do not modify, but testthe contents works: |
428 | |
429 | $x = 9; $y = $x; |
430 | $z = 9 if $x->is_zero(); # works fine |
431 | |
432 | See the documentation about the copy constructor and C<=> in overload, as |
433 | well as the documentation in BigInt for further details. |
434 | |
b4bc5691 |
435 | =over 2 |
436 | |
437 | =item inf() |
438 | |
3c4b39be |
439 | A shortcut to return Math::BigInt->binf(). Useful because Perl does not always |
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440 | handle bareword C<inf> properly. |
441 | |
442 | =item NaN() |
443 | |
3c4b39be |
444 | A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always |
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445 | handle bareword C<NaN> properly. |
446 | |
447 | =item upgrade() |
448 | |
449 | Return the class that numbers are upgraded to, is in fact returning |
450 | C<$Math::BigInt::upgrade>. |
451 | |
4440d13a |
452 | =item in_effect() |
453 | |
454 | use bignum; |
455 | |
456 | print "in effect\n" if bignum::in_effect; # true |
457 | { |
458 | no bignum; |
459 | print "in effect\n" if bignum::in_effect; # false |
460 | } |
461 | |
462 | Returns true or false if C<bignum> is in effect in the current scope. |
463 | |
464 | This method only works on Perl v5.9.4 or later. |
465 | |
b4bc5691 |
466 | =back |
467 | |
bd49aa09 |
468 | =head2 Math Library |
126f3c5f |
469 | |
470 | Math with the numbers is done (by default) by a module called |
471 | Math::BigInt::Calc. This is equivalent to saying: |
472 | |
473 | use bignum lib => 'Calc'; |
474 | |
475 | You can change this by using: |
476 | |
bd49aa09 |
477 | use bignum lib => 'GMP'; |
126f3c5f |
478 | |
479 | The following would first try to find Math::BigInt::Foo, then |
480 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
481 | |
482 | use bignum lib => 'Foo,Math::BigInt::Bar'; |
483 | |
484 | Please see respective module documentation for further details. |
485 | |
bd49aa09 |
486 | Using C<lib> warns if none of the specified libraries can be found and |
487 | L<Math::BigInt> did fall back to one of the default libraries. |
488 | To supress this warning, use C<try> instead: |
489 | |
490 | use bignum try => 'GMP'; |
491 | |
492 | If you want the code to die instead of falling back, use C<only> instead: |
493 | |
494 | use bignum only => 'GMP'; |
495 | |
126f3c5f |
496 | =head2 INTERNAL FORMAT |
497 | |
498 | The numbers are stored as objects, and their internals might change at anytime, |
499 | especially between math operations. The objects also might belong to different |
500 | classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even |
501 | with normal scalars is not extraordinary, but normal and expected. |
502 | |
503 | You should not depend on the internal format, all accesses must go through |
504 | accessor methods. E.g. looking at $x->{sign} is not a bright idea since there |
505 | is no guaranty that the object in question has such a hashkey, nor is a hash |
506 | underneath at all. |
507 | |
508 | =head2 SIGN |
509 | |
510 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. |
511 | You can access it with the sign() method. |
512 | |
513 | A sign of 'NaN' is used to represent the result when input arguments are not |
514 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively |
515 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
516 | '-inf' when dividing any negative number by 0. |
517 | |
126f3c5f |
518 | =head1 MODULES USED |
519 | |
520 | C<bignum> is just a thin wrapper around various modules of the Math::BigInt |
521 | family. Think of it as the head of the family, who runs the shop, and orders |
522 | the others to do the work. |
523 | |
524 | The following modules are currently used by bignum: |
525 | |
526 | Math::BigInt::Lite (for speed, and only if it is loadable) |
527 | Math::BigInt |
528 | Math::BigFloat |
529 | |
530 | =head1 EXAMPLES |
531 | |
532 | Some cool command line examples to impress the Python crowd ;) |
533 | |
534 | perl -Mbignum -le 'print sqrt(33)' |
535 | perl -Mbignum -le 'print 2*255' |
536 | perl -Mbignum -le 'print 4.5+2*255' |
537 | perl -Mbignum -le 'print 3/7 + 5/7 + 8/3' |
538 | perl -Mbignum -le 'print 123->is_odd()' |
539 | perl -Mbignum -le 'print log(2)' |
bce28014 |
540 | perl -Mbignum -le 'print exp(1)' |
126f3c5f |
541 | perl -Mbignum -le 'print 2 ** 0.5' |
542 | perl -Mbignum=a,65 -le 'print 2 ** 0.2' |
95a2d02c |
543 | perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777' |
126f3c5f |
544 | |
545 | =head1 LICENSE |
546 | |
547 | This program is free software; you may redistribute it and/or modify it under |
548 | the same terms as Perl itself. |
549 | |
550 | =head1 SEE ALSO |
551 | |
552 | Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>. |
553 | |
554 | L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well |
555 | as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
556 | |
557 | =head1 AUTHORS |
558 | |
95a2d02c |
559 | (C) by Tels L<http://bloodgate.com/> in early 2002 - 2007. |
126f3c5f |
560 | |
561 | =cut |