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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 | $VERSION = '0.21_02'; |
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5 | use Exporter; |
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6 | @EXPORT_OK = qw( ); |
7 | @EXPORT = qw( inf NaN ); |
8 | @ISA = qw( Exporter ); |
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9 | |
10 | use strict; |
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11 | use overload; |
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12 | |
13 | ############################################################################## |
14 | |
15 | # These are all alike, and thus faked by AUTOLOAD |
16 | |
17 | my @faked = qw/round_mode accuracy precision div_scale/; |
18 | use vars qw/$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($_[0]); |
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38 | } |
39 | return Math::BigInt->$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 | { |
52 | my $self = shift; |
53 | no strict 'refs'; |
54 | # if (defined $_[0]) |
55 | # { |
56 | # $Math::BigInt::upgrade = $_[0]; |
57 | # $Math::BigFloat::upgrade = $_[0]; |
58 | # } |
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59 | $Math::BigInt::upgrade; |
60 | } |
61 | |
62 | sub _binary_constant |
63 | { |
64 | # this takes a binary/hexadecimal/octal constant string and returns it |
65 | # as string suitable for new. Basically it converts octal to decimal, and |
66 | # passes every thing else unmodified back. |
67 | my $string = shift; |
68 | |
69 | return Math::BigInt->new($string) if $string =~ /^0[bx]/; |
70 | |
71 | # so it must be an octal constant |
72 | Math::BigInt->from_oct($string); |
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73 | } |
74 | |
75 | sub import |
76 | { |
77 | my $self = shift; |
78 | |
79 | # some defaults |
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80 | my $lib = ''; my $lib_kind = 'try'; |
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81 | my $upgrade = 'Math::BigFloat'; |
82 | my $downgrade = 'Math::BigInt'; |
83 | |
84 | my @import = ( ':constant' ); # drive it w/ constant |
85 | my @a = @_; my $l = scalar @_; my $j = 0; |
86 | my ($ver,$trace); # version? trace? |
87 | my ($a,$p); # accuracy, precision |
88 | for ( my $i = 0; $i < $l ; $i++,$j++ ) |
89 | { |
90 | if ($_[$i] eq 'upgrade') |
91 | { |
92 | # this causes upgrading |
93 | $upgrade = $_[$i+1]; # or undef to disable |
94 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
95 | splice @a, $j, $s; $j -= $s; $i++; |
96 | } |
97 | elsif ($_[$i] eq 'downgrade') |
98 | { |
99 | # this causes downgrading |
100 | $downgrade = $_[$i+1]; # or undef to disable |
101 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
102 | splice @a, $j, $s; $j -= $s; $i++; |
103 | } |
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104 | elsif ($_[$i] =~ /^(l|lib|try|only)$/) |
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105 | { |
106 | # this causes a different low lib to take care... |
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107 | $lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l'; |
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108 | $lib = $_[$i+1] || ''; |
109 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
110 | splice @a, $j, $s; $j -= $s; $i++; |
111 | } |
112 | elsif ($_[$i] =~ /^(a|accuracy)$/) |
113 | { |
114 | $a = $_[$i+1]; |
115 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
116 | splice @a, $j, $s; $j -= $s; $i++; |
117 | } |
118 | elsif ($_[$i] =~ /^(p|precision)$/) |
119 | { |
120 | $p = $_[$i+1]; |
121 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." |
122 | splice @a, $j, $s; $j -= $s; $i++; |
123 | } |
124 | elsif ($_[$i] =~ /^(v|version)$/) |
125 | { |
126 | $ver = 1; |
127 | splice @a, $j, 1; $j --; |
128 | } |
129 | elsif ($_[$i] =~ /^(t|trace)$/) |
130 | { |
131 | $trace = 1; |
132 | splice @a, $j, 1; $j --; |
133 | } |
134 | else { die "unknown option $_[$i]"; } |
135 | } |
136 | my $class; |
137 | $_lite = 0; # using M::BI::L ? |
138 | if ($trace) |
139 | { |
140 | require Math::BigInt::Trace; $class = 'Math::BigInt::Trace'; |
141 | $upgrade = 'Math::BigFloat::Trace'; |
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142 | } |
143 | else |
144 | { |
145 | # see if we can find Math::BigInt::Lite |
146 | if (!defined $a && !defined $p) # rounding won't work to well |
147 | { |
148 | eval 'require Math::BigInt::Lite;'; |
149 | if ($@ eq '') |
150 | { |
151 | @import = ( ); # :constant in Lite, not MBI |
152 | Math::BigInt::Lite->import( ':constant' ); |
153 | $_lite= 1; # signal okay |
154 | } |
155 | } |
156 | require Math::BigInt if $_lite == 0; # not already loaded? |
157 | $class = 'Math::BigInt'; # regardless of MBIL or not |
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158 | } |
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159 | push @import, $lib_kind => $lib if $lib ne ''; |
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160 | # Math::BigInt::Trace or plain Math::BigInt |
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161 | $class->import(@import, upgrade => $upgrade); |
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162 | |
163 | if ($trace) |
164 | { |
165 | require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace'; |
166 | $downgrade = 'Math::BigInt::Trace'; |
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167 | } |
168 | else |
169 | { |
170 | require Math::BigFloat; $class = 'Math::BigFloat'; |
171 | } |
172 | $class->import(':constant','downgrade',$downgrade); |
173 | |
174 | bignum->accuracy($a) if defined $a; |
175 | bignum->precision($p) if defined $p; |
176 | if ($ver) |
177 | { |
178 | print "bignum\t\t\t v$VERSION\n"; |
179 | print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite; |
180 | print "Math::BigInt\t\t v$Math::BigInt::VERSION"; |
181 | my $config = Math::BigInt->config(); |
182 | print " lib => $config->{lib} v$config->{lib_version}\n"; |
183 | print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n"; |
184 | exit; |
185 | } |
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186 | |
187 | # Take care of octal/hexadecimal constants |
188 | overload::constant 'binary' => sub { _binary_constant(shift) }; |
189 | |
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190 | $self->export_to_level(1,$self,@a); # export inf and NaN |
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191 | } |
192 | |
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193 | sub inf () { Math::BigInt->binf(); } |
194 | sub NaN () { Math::BigInt->bnan(); } |
195 | |
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196 | 1; |
197 | |
198 | __END__ |
199 | |
200 | =head1 NAME |
201 | |
202 | bignum - Transparent BigNumber support for Perl |
203 | |
204 | =head1 SYNOPSIS |
205 | |
206 | use bignum; |
207 | |
208 | $x = 2 + 4.5,"\n"; # BigFloat 6.5 |
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209 | print 2 ** 512 * 0.1,"\n"; # really is what you think it is |
210 | print inf * inf,"\n"; # prints inf |
211 | print NaN * 3,"\n"; # prints NaN |
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212 | |
213 | =head1 DESCRIPTION |
214 | |
215 | All operators (including basic math operations) are overloaded. Integer and |
216 | floating-point constants are created as proper BigInts or BigFloats, |
217 | respectively. |
218 | |
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219 | If you do |
220 | |
221 | use bignum; |
222 | |
223 | at the top of your script, Math::BigFloat and Math::BigInt will be loaded |
224 | and any constant number will be converted to an object (Math::BigFloat for |
225 | floats like 3.1415 and Math::BigInt for integers like 1234). |
226 | |
227 | So, the following line: |
228 | |
229 | $x = 1234; |
230 | |
231 | creates actually a Math::BigInt and stores a reference to in $x. |
232 | This happens transparently and behind your back, so to speak. |
233 | |
234 | You can see this with the following: |
235 | |
236 | perl -Mbignum -le 'print ref(1234)' |
237 | |
238 | Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite |
239 | if it is installed since it is faster for some operations. It will be |
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240 | automatically upgraded to BigInt whenever necessary: |
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241 | |
242 | perl -Mbignum -le 'print ref(2**255)' |
243 | |
244 | This also means it is a bad idea to check for some specific package, since |
245 | the actual contents of $x might be something unexpected. Due to the |
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246 | transparent way of bignum C<ref()> should not be necessary, anyway. |
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247 | |
248 | Since Math::BigInt and BigFloat also overload the normal math operations, |
249 | the following line will still work: |
250 | |
251 | perl -Mbignum -le 'print ref(1234+1234)' |
252 | |
253 | Since numbers are actually objects, you can call all the usual methods from |
254 | BigInt/BigFloat on them. This even works to some extent on expressions: |
255 | |
256 | perl -Mbignum -le '$x = 1234; print $x->bdec()' |
257 | perl -Mbignum -le 'print 1234->binc();' |
258 | perl -Mbignum -le 'print 1234->binc->badd(6);' |
259 | perl -Mbignum -le 'print +(1234)->binc()' |
260 | |
261 | (Note that print doesn't do what you expect if the expression starts with |
262 | '(' hence the C<+>) |
263 | |
264 | You can even chain the operations together as usual: |
265 | |
266 | perl -Mbignum -le 'print 1234->binc->badd(6);' |
267 | 1241 |
268 | |
269 | Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers |
270 | appropriately. This means that: |
271 | |
272 | perl -Mbignum -le 'print 1234+4.5' |
273 | 1238.5 |
274 | |
275 | will work correctly. These mixed cases don't do always work when using |
276 | Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl |
277 | scalars work. |
278 | |
279 | If you do want to work with large integers like under C<use integer;>, try |
280 | C<use bigint;>: |
281 | |
282 | perl -Mbigint -le 'print 1234.5+4.5' |
283 | 1238 |
284 | |
285 | There is also C<use bigrat;> which gives you big rationals: |
286 | |
287 | perl -Mbigrat -le 'print 1234+4.1' |
288 | 12381/10 |
289 | |
290 | The entire upgrading/downgrading is still experimental and might not work |
291 | as you expect or may even have bugs. |
292 | |
293 | You might get errors like this: |
294 | |
295 | Can't use an undefined value as an ARRAY reference at |
296 | /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864 |
297 | |
298 | This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or |
299 | vice versa) and the upgrade/downgrad path was missing. This is a bug, please |
300 | report it so that we can fix it. |
301 | |
302 | You might consider using just Math::BigInt or Math::BigFloat, since they |
303 | allow you finer control over what get's done in which module/space. For |
304 | instance, simple loop counters will be Math::BigInts under C<use bignum;> and |
305 | this is slower than keeping them as Perl scalars: |
306 | |
307 | perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }' |
308 | |
309 | Please note the following does not work as expected (prints nothing), since |
310 | overloading of '..' is not yet possible in Perl (as of v5.8.0): |
311 | |
312 | perl -Mbignum -le 'for (1..2) { print ref($_); }' |
313 | |
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314 | =head2 Options |
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315 | |
316 | bignum recognizes some options that can be passed while loading it via use. |
317 | The options can (currently) be either a single letter form, or the long form. |
318 | The following options exist: |
319 | |
320 | =over 2 |
321 | |
322 | =item a or accuracy |
323 | |
324 | This sets the accuracy for all math operations. The argument must be greater |
325 | than or equal to zero. See Math::BigInt's bround() function for details. |
326 | |
327 | perl -Mbignum=a,50 -le 'print sqrt(20)' |
328 | |
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329 | Note that setting precision and accurary at the same time is not possible. |
330 | |
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331 | =item p or precision |
332 | |
333 | This sets the precision for all math operations. The argument can be any |
334 | integer. Negative values mean a fixed number of digits after the dot, while |
335 | a positive value rounds to this digit left from the dot. 0 or 1 mean round to |
336 | integer. See Math::BigInt's bfround() function for details. |
337 | |
338 | perl -Mbignum=p,-50 -le 'print sqrt(20)' |
339 | |
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340 | Note that setting precision and accurary at the same time is not possible. |
341 | |
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342 | =item t or trace |
343 | |
344 | This enables a trace mode and is primarily for debugging bignum or |
345 | Math::BigInt/Math::BigFloat. |
346 | |
347 | =item l or lib |
348 | |
349 | Load a different math lib, see L<MATH LIBRARY>. |
350 | |
351 | perl -Mbignum=l,GMP -e 'print 2 ** 512' |
352 | |
353 | Currently there is no way to specify more than one library on the command |
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354 | line. This means the following does not work: |
355 | |
356 | perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512' |
357 | |
358 | This will be hopefully fixed soon ;) |
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359 | |
360 | =item v or version |
361 | |
362 | This prints out the name and version of all modules used and then exits. |
363 | |
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364 | perl -Mbignum=v |
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365 | |
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366 | =back |
367 | |
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368 | =head2 Methods |
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369 | |
370 | Beside import() and AUTOLOAD() there are only a few other methods. |
371 | |
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372 | Since all numbers are now objects, you can use all functions that are part of |
373 | the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not |
374 | the fxxx() notation, though. This makes it possible that the underlying object |
375 | might morph into a different class than BigFloat. |
376 | |
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377 | =head2 Caveat |
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378 | |
379 | But a warning is in order. When using the following to make a copy of a number, |
380 | only a shallow copy will be made. |
381 | |
382 | $x = 9; $y = $x; |
383 | $x = $y = 7; |
384 | |
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385 | If you want to make a real copy, use the following: |
386 | |
387 | $y = $x->copy(); |
388 | |
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389 | Using the copy or the original with overloaded math is okay, e.g. the |
390 | following work: |
391 | |
392 | $x = 9; $y = $x; |
393 | print $x + 1, " ", $y,"\n"; # prints 10 9 |
394 | |
395 | but calling any method that modifies the number directly will result in |
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396 | B<both> the original and the copy being destroyed: |
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397 | |
398 | $x = 9; $y = $x; |
399 | print $x->badd(1), " ", $y,"\n"; # prints 10 10 |
400 | |
401 | $x = 9; $y = $x; |
402 | print $x->binc(1), " ", $y,"\n"; # prints 10 10 |
403 | |
404 | $x = 9; $y = $x; |
405 | print $x->bmul(2), " ", $y,"\n"; # prints 18 18 |
406 | |
407 | Using methods that do not modify, but testthe contents works: |
408 | |
409 | $x = 9; $y = $x; |
410 | $z = 9 if $x->is_zero(); # works fine |
411 | |
412 | See the documentation about the copy constructor and C<=> in overload, as |
413 | well as the documentation in BigInt for further details. |
414 | |
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415 | =over 2 |
416 | |
417 | =item inf() |
418 | |
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419 | A shortcut to return Math::BigInt->binf(). Useful because Perl does not always |
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420 | handle bareword C<inf> properly. |
421 | |
422 | =item NaN() |
423 | |
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424 | A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always |
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425 | handle bareword C<NaN> properly. |
426 | |
427 | =item upgrade() |
428 | |
429 | Return the class that numbers are upgraded to, is in fact returning |
430 | C<$Math::BigInt::upgrade>. |
431 | |
432 | =back |
433 | |
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434 | =head2 Math Library |
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435 | |
436 | Math with the numbers is done (by default) by a module called |
437 | Math::BigInt::Calc. This is equivalent to saying: |
438 | |
439 | use bignum lib => 'Calc'; |
440 | |
441 | You can change this by using: |
442 | |
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443 | use bignum lib => 'GMP'; |
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444 | |
445 | The following would first try to find Math::BigInt::Foo, then |
446 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: |
447 | |
448 | use bignum lib => 'Foo,Math::BigInt::Bar'; |
449 | |
450 | Please see respective module documentation for further details. |
451 | |
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452 | Using C<lib> warns if none of the specified libraries can be found and |
453 | L<Math::BigInt> did fall back to one of the default libraries. |
454 | To supress this warning, use C<try> instead: |
455 | |
456 | use bignum try => 'GMP'; |
457 | |
458 | If you want the code to die instead of falling back, use C<only> instead: |
459 | |
460 | use bignum only => 'GMP'; |
461 | |
126f3c5f |
462 | =head2 INTERNAL FORMAT |
463 | |
464 | The numbers are stored as objects, and their internals might change at anytime, |
465 | especially between math operations. The objects also might belong to different |
466 | classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even |
467 | with normal scalars is not extraordinary, but normal and expected. |
468 | |
469 | You should not depend on the internal format, all accesses must go through |
470 | accessor methods. E.g. looking at $x->{sign} is not a bright idea since there |
471 | is no guaranty that the object in question has such a hashkey, nor is a hash |
472 | underneath at all. |
473 | |
474 | =head2 SIGN |
475 | |
476 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. |
477 | You can access it with the sign() method. |
478 | |
479 | A sign of 'NaN' is used to represent the result when input arguments are not |
480 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively |
481 | minus infinity. You will get '+inf' when dividing a positive number by 0, and |
482 | '-inf' when dividing any negative number by 0. |
483 | |
126f3c5f |
484 | =head1 MODULES USED |
485 | |
486 | C<bignum> is just a thin wrapper around various modules of the Math::BigInt |
487 | family. Think of it as the head of the family, who runs the shop, and orders |
488 | the others to do the work. |
489 | |
490 | The following modules are currently used by bignum: |
491 | |
492 | Math::BigInt::Lite (for speed, and only if it is loadable) |
493 | Math::BigInt |
494 | Math::BigFloat |
495 | |
496 | =head1 EXAMPLES |
497 | |
498 | Some cool command line examples to impress the Python crowd ;) |
499 | |
500 | perl -Mbignum -le 'print sqrt(33)' |
501 | perl -Mbignum -le 'print 2*255' |
502 | perl -Mbignum -le 'print 4.5+2*255' |
503 | perl -Mbignum -le 'print 3/7 + 5/7 + 8/3' |
504 | perl -Mbignum -le 'print 123->is_odd()' |
505 | perl -Mbignum -le 'print log(2)' |
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506 | perl -Mbignum -le 'print exp(1)' |
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507 | perl -Mbignum -le 'print 2 ** 0.5' |
508 | perl -Mbignum=a,65 -le 'print 2 ** 0.2' |
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509 | perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777' |
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510 | |
511 | =head1 LICENSE |
512 | |
513 | This program is free software; you may redistribute it and/or modify it under |
514 | the same terms as Perl itself. |
515 | |
516 | =head1 SEE ALSO |
517 | |
518 | Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>. |
519 | |
520 | L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well |
521 | as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. |
522 | |
523 | =head1 AUTHORS |
524 | |
95a2d02c |
525 | (C) by Tels L<http://bloodgate.com/> in early 2002 - 2007. |
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526 | |
527 | =cut |