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126f3c5f JH |
1 | package bignum; |
2 | require 5.005; | |
3 | ||
233f7bc0 | 4 | $VERSION = '0.17'; |
126f3c5f | 5 | use Exporter; |
b4bc5691 T |
6 | @EXPORT_OK = qw( ); |
7 | @EXPORT = qw( inf NaN ); | |
8 | @ISA = qw( Exporter ); | |
126f3c5f JH |
9 | |
10 | use strict; | |
11 | ||
12 | ############################################################################## | |
13 | ||
14 | # These are all alike, and thus faked by AUTOLOAD | |
15 | ||
16 | my @faked = qw/round_mode accuracy precision div_scale/; | |
17 | use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite | |
18 | ||
19 | sub AUTOLOAD | |
20 | { | |
21 | my $name = $AUTOLOAD; | |
22 | ||
23 | $name =~ s/.*:://; # split package | |
24 | no strict 'refs'; | |
25 | foreach my $n (@faked) | |
26 | { | |
27 | if ($n eq $name) | |
28 | { | |
29 | *{"bignum::$name"} = sub | |
30 | { | |
31 | my $self = shift; | |
32 | no strict 'refs'; | |
33 | if (defined $_[0]) | |
34 | { | |
35 | Math::BigInt->$name($_[0]); | |
990fb837 | 36 | return Math::BigFloat->$name($_[0]); |
126f3c5f JH |
37 | } |
38 | return Math::BigInt->$name(); | |
39 | }; | |
40 | return &$name; | |
41 | } | |
42 | } | |
43 | ||
44 | # delayed load of Carp and avoid recursion | |
45 | require Carp; | |
46 | Carp::croak ("Can't call bignum\-\>$name, not a valid method"); | |
47 | } | |
48 | ||
49 | sub upgrade | |
50 | { | |
51 | my $self = shift; | |
52 | no strict 'refs'; | |
53 | # if (defined $_[0]) | |
54 | # { | |
55 | # $Math::BigInt::upgrade = $_[0]; | |
56 | # $Math::BigFloat::upgrade = $_[0]; | |
57 | # } | |
58 | return $Math::BigInt::upgrade; | |
59 | } | |
60 | ||
61 | sub import | |
62 | { | |
63 | my $self = shift; | |
64 | ||
65 | # some defaults | |
233f7bc0 | 66 | my $lib = ''; |
126f3c5f JH |
67 | my $upgrade = 'Math::BigFloat'; |
68 | my $downgrade = 'Math::BigInt'; | |
69 | ||
70 | my @import = ( ':constant' ); # drive it w/ constant | |
71 | my @a = @_; my $l = scalar @_; my $j = 0; | |
72 | my ($ver,$trace); # version? trace? | |
73 | my ($a,$p); # accuracy, precision | |
74 | for ( my $i = 0; $i < $l ; $i++,$j++ ) | |
75 | { | |
76 | if ($_[$i] eq 'upgrade') | |
77 | { | |
78 | # this causes upgrading | |
79 | $upgrade = $_[$i+1]; # or undef to disable | |
80 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." | |
81 | splice @a, $j, $s; $j -= $s; $i++; | |
82 | } | |
83 | elsif ($_[$i] eq 'downgrade') | |
84 | { | |
85 | # this causes downgrading | |
86 | $downgrade = $_[$i+1]; # or undef to disable | |
87 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." | |
88 | splice @a, $j, $s; $j -= $s; $i++; | |
89 | } | |
90 | elsif ($_[$i] =~ /^(l|lib)$/) | |
91 | { | |
92 | # this causes a different low lib to take care... | |
93 | $lib = $_[$i+1] || ''; | |
94 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." | |
95 | splice @a, $j, $s; $j -= $s; $i++; | |
96 | } | |
97 | elsif ($_[$i] =~ /^(a|accuracy)$/) | |
98 | { | |
99 | $a = $_[$i+1]; | |
100 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." | |
101 | splice @a, $j, $s; $j -= $s; $i++; | |
102 | } | |
103 | elsif ($_[$i] =~ /^(p|precision)$/) | |
104 | { | |
105 | $p = $_[$i+1]; | |
106 | my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." | |
107 | splice @a, $j, $s; $j -= $s; $i++; | |
108 | } | |
109 | elsif ($_[$i] =~ /^(v|version)$/) | |
110 | { | |
111 | $ver = 1; | |
112 | splice @a, $j, 1; $j --; | |
113 | } | |
114 | elsif ($_[$i] =~ /^(t|trace)$/) | |
115 | { | |
116 | $trace = 1; | |
117 | splice @a, $j, 1; $j --; | |
118 | } | |
119 | else { die "unknown option $_[$i]"; } | |
120 | } | |
121 | my $class; | |
122 | $_lite = 0; # using M::BI::L ? | |
123 | if ($trace) | |
124 | { | |
125 | require Math::BigInt::Trace; $class = 'Math::BigInt::Trace'; | |
126 | $upgrade = 'Math::BigFloat::Trace'; | |
126f3c5f JH |
127 | } |
128 | else | |
129 | { | |
130 | # see if we can find Math::BigInt::Lite | |
131 | if (!defined $a && !defined $p) # rounding won't work to well | |
132 | { | |
133 | eval 'require Math::BigInt::Lite;'; | |
134 | if ($@ eq '') | |
135 | { | |
136 | @import = ( ); # :constant in Lite, not MBI | |
137 | Math::BigInt::Lite->import( ':constant' ); | |
138 | $_lite= 1; # signal okay | |
139 | } | |
140 | } | |
141 | require Math::BigInt if $_lite == 0; # not already loaded? | |
142 | $class = 'Math::BigInt'; # regardless of MBIL or not | |
233f7bc0 T |
143 | } |
144 | push @import, 'lib' => $lib if $lib ne ''; | |
126f3c5f | 145 | # Math::BigInt::Trace or plain Math::BigInt |
233f7bc0 | 146 | $class->import(@import, upgrade => $upgrade); |
126f3c5f JH |
147 | |
148 | if ($trace) | |
149 | { | |
150 | require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace'; | |
151 | $downgrade = 'Math::BigInt::Trace'; | |
126f3c5f JH |
152 | } |
153 | else | |
154 | { | |
155 | require Math::BigFloat; $class = 'Math::BigFloat'; | |
156 | } | |
157 | $class->import(':constant','downgrade',$downgrade); | |
158 | ||
159 | bignum->accuracy($a) if defined $a; | |
160 | bignum->precision($p) if defined $p; | |
161 | if ($ver) | |
162 | { | |
163 | print "bignum\t\t\t v$VERSION\n"; | |
164 | print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite; | |
165 | print "Math::BigInt\t\t v$Math::BigInt::VERSION"; | |
166 | my $config = Math::BigInt->config(); | |
167 | print " lib => $config->{lib} v$config->{lib_version}\n"; | |
168 | print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n"; | |
169 | exit; | |
170 | } | |
b4bc5691 | 171 | $self->export_to_level(1,$self,@a); # export inf and NaN |
126f3c5f JH |
172 | } |
173 | ||
b4bc5691 T |
174 | sub inf () { Math::BigInt->binf(); } |
175 | sub NaN () { Math::BigInt->bnan(); } | |
176 | ||
126f3c5f JH |
177 | 1; |
178 | ||
179 | __END__ | |
180 | ||
181 | =head1 NAME | |
182 | ||
183 | bignum - Transparent BigNumber support for Perl | |
184 | ||
185 | =head1 SYNOPSIS | |
186 | ||
187 | use bignum; | |
188 | ||
189 | $x = 2 + 4.5,"\n"; # BigFloat 6.5 | |
b4bc5691 T |
190 | print 2 ** 512 * 0.1,"\n"; # really is what you think it is |
191 | print inf * inf,"\n"; # prints inf | |
192 | print NaN * 3,"\n"; # prints NaN | |
126f3c5f JH |
193 | |
194 | =head1 DESCRIPTION | |
195 | ||
196 | All operators (including basic math operations) are overloaded. Integer and | |
197 | floating-point constants are created as proper BigInts or BigFloats, | |
198 | respectively. | |
199 | ||
24716a00 HS |
200 | If you do |
201 | ||
202 | use bignum; | |
203 | ||
204 | at the top of your script, Math::BigFloat and Math::BigInt will be loaded | |
205 | and any constant number will be converted to an object (Math::BigFloat for | |
206 | floats like 3.1415 and Math::BigInt for integers like 1234). | |
207 | ||
208 | So, the following line: | |
209 | ||
210 | $x = 1234; | |
211 | ||
212 | creates actually a Math::BigInt and stores a reference to in $x. | |
213 | This happens transparently and behind your back, so to speak. | |
214 | ||
215 | You can see this with the following: | |
216 | ||
217 | perl -Mbignum -le 'print ref(1234)' | |
218 | ||
219 | Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite | |
220 | if it is installed since it is faster for some operations. It will be | |
3c4b39be | 221 | automatically upgraded to BigInt whenever necessary: |
24716a00 HS |
222 | |
223 | perl -Mbignum -le 'print ref(2**255)' | |
224 | ||
225 | This also means it is a bad idea to check for some specific package, since | |
226 | the actual contents of $x might be something unexpected. Due to the | |
3c4b39be | 227 | transparent way of bignum C<ref()> should not be necessary, anyway. |
24716a00 HS |
228 | |
229 | Since Math::BigInt and BigFloat also overload the normal math operations, | |
230 | the following line will still work: | |
231 | ||
232 | perl -Mbignum -le 'print ref(1234+1234)' | |
233 | ||
234 | Since numbers are actually objects, you can call all the usual methods from | |
235 | BigInt/BigFloat on them. This even works to some extent on expressions: | |
236 | ||
237 | perl -Mbignum -le '$x = 1234; print $x->bdec()' | |
238 | perl -Mbignum -le 'print 1234->binc();' | |
239 | perl -Mbignum -le 'print 1234->binc->badd(6);' | |
240 | perl -Mbignum -le 'print +(1234)->binc()' | |
241 | ||
242 | (Note that print doesn't do what you expect if the expression starts with | |
243 | '(' hence the C<+>) | |
244 | ||
245 | You can even chain the operations together as usual: | |
246 | ||
247 | perl -Mbignum -le 'print 1234->binc->badd(6);' | |
248 | 1241 | |
249 | ||
250 | Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers | |
251 | appropriately. This means that: | |
252 | ||
253 | perl -Mbignum -le 'print 1234+4.5' | |
254 | 1238.5 | |
255 | ||
256 | will work correctly. These mixed cases don't do always work when using | |
257 | Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl | |
258 | scalars work. | |
259 | ||
260 | If you do want to work with large integers like under C<use integer;>, try | |
261 | C<use bigint;>: | |
262 | ||
263 | perl -Mbigint -le 'print 1234.5+4.5' | |
264 | 1238 | |
265 | ||
266 | There is also C<use bigrat;> which gives you big rationals: | |
267 | ||
268 | perl -Mbigrat -le 'print 1234+4.1' | |
269 | 12381/10 | |
270 | ||
271 | The entire upgrading/downgrading is still experimental and might not work | |
272 | as you expect or may even have bugs. | |
273 | ||
274 | You might get errors like this: | |
275 | ||
276 | Can't use an undefined value as an ARRAY reference at | |
277 | /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864 | |
278 | ||
279 | This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or | |
280 | vice versa) and the upgrade/downgrad path was missing. This is a bug, please | |
281 | report it so that we can fix it. | |
282 | ||
283 | You might consider using just Math::BigInt or Math::BigFloat, since they | |
284 | allow you finer control over what get's done in which module/space. For | |
285 | instance, simple loop counters will be Math::BigInts under C<use bignum;> and | |
286 | this is slower than keeping them as Perl scalars: | |
287 | ||
288 | perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }' | |
289 | ||
290 | Please note the following does not work as expected (prints nothing), since | |
291 | overloading of '..' is not yet possible in Perl (as of v5.8.0): | |
292 | ||
293 | perl -Mbignum -le 'for (1..2) { print ref($_); }' | |
294 | ||
b68b7ab1 | 295 | =head2 Options |
126f3c5f JH |
296 | |
297 | bignum recognizes some options that can be passed while loading it via use. | |
298 | The options can (currently) be either a single letter form, or the long form. | |
299 | The following options exist: | |
300 | ||
301 | =over 2 | |
302 | ||
303 | =item a or accuracy | |
304 | ||
305 | This sets the accuracy for all math operations. The argument must be greater | |
306 | than or equal to zero. See Math::BigInt's bround() function for details. | |
307 | ||
308 | perl -Mbignum=a,50 -le 'print sqrt(20)' | |
309 | ||
310 | =item p or precision | |
311 | ||
312 | This sets the precision for all math operations. The argument can be any | |
313 | integer. Negative values mean a fixed number of digits after the dot, while | |
314 | a positive value rounds to this digit left from the dot. 0 or 1 mean round to | |
315 | integer. See Math::BigInt's bfround() function for details. | |
316 | ||
317 | perl -Mbignum=p,-50 -le 'print sqrt(20)' | |
318 | ||
319 | =item t or trace | |
320 | ||
321 | This enables a trace mode and is primarily for debugging bignum or | |
322 | Math::BigInt/Math::BigFloat. | |
323 | ||
324 | =item l or lib | |
325 | ||
326 | Load a different math lib, see L<MATH LIBRARY>. | |
327 | ||
328 | perl -Mbignum=l,GMP -e 'print 2 ** 512' | |
329 | ||
330 | Currently there is no way to specify more than one library on the command | |
331 | line. This will be hopefully fixed soon ;) | |
332 | ||
333 | =item v or version | |
334 | ||
335 | This prints out the name and version of all modules used and then exits. | |
336 | ||
b68b7ab1 | 337 | perl -Mbignum=v |
126f3c5f | 338 | |
b68b7ab1 | 339 | =head2 Methods |
b4bc5691 T |
340 | |
341 | Beside import() and AUTOLOAD() there are only a few other methods. | |
342 | ||
24716a00 HS |
343 | Since all numbers are now objects, you can use all functions that are part of |
344 | the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not | |
345 | the fxxx() notation, though. This makes it possible that the underlying object | |
346 | might morph into a different class than BigFloat. | |
347 | ||
b68b7ab1 | 348 | =head2 Caveat |
990fb837 RGS |
349 | |
350 | But a warning is in order. When using the following to make a copy of a number, | |
351 | only a shallow copy will be made. | |
352 | ||
353 | $x = 9; $y = $x; | |
354 | $x = $y = 7; | |
355 | ||
b68b7ab1 T |
356 | If you want to make a real copy, use the following: |
357 | ||
358 | $y = $x->copy(); | |
359 | ||
990fb837 RGS |
360 | Using the copy or the original with overloaded math is okay, e.g. the |
361 | following work: | |
362 | ||
363 | $x = 9; $y = $x; | |
364 | print $x + 1, " ", $y,"\n"; # prints 10 9 | |
365 | ||
366 | but calling any method that modifies the number directly will result in | |
3c4b39be | 367 | B<both> the original and the copy being destroyed: |
990fb837 RGS |
368 | |
369 | $x = 9; $y = $x; | |
370 | print $x->badd(1), " ", $y,"\n"; # prints 10 10 | |
371 | ||
372 | $x = 9; $y = $x; | |
373 | print $x->binc(1), " ", $y,"\n"; # prints 10 10 | |
374 | ||
375 | $x = 9; $y = $x; | |
376 | print $x->bmul(2), " ", $y,"\n"; # prints 18 18 | |
377 | ||
378 | Using methods that do not modify, but testthe contents works: | |
379 | ||
380 | $x = 9; $y = $x; | |
381 | $z = 9 if $x->is_zero(); # works fine | |
382 | ||
383 | See the documentation about the copy constructor and C<=> in overload, as | |
384 | well as the documentation in BigInt for further details. | |
385 | ||
b4bc5691 T |
386 | =over 2 |
387 | ||
388 | =item inf() | |
389 | ||
3c4b39be | 390 | A shortcut to return Math::BigInt->binf(). Useful because Perl does not always |
b4bc5691 T |
391 | handle bareword C<inf> properly. |
392 | ||
393 | =item NaN() | |
394 | ||
3c4b39be | 395 | A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always |
b4bc5691 T |
396 | handle bareword C<NaN> properly. |
397 | ||
398 | =item upgrade() | |
399 | ||
400 | Return the class that numbers are upgraded to, is in fact returning | |
401 | C<$Math::BigInt::upgrade>. | |
402 | ||
403 | =back | |
404 | ||
126f3c5f JH |
405 | =head2 MATH LIBRARY |
406 | ||
407 | Math with the numbers is done (by default) by a module called | |
408 | Math::BigInt::Calc. This is equivalent to saying: | |
409 | ||
410 | use bignum lib => 'Calc'; | |
411 | ||
412 | You can change this by using: | |
413 | ||
414 | use bignum lib => 'BitVect'; | |
415 | ||
416 | The following would first try to find Math::BigInt::Foo, then | |
417 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
418 | ||
419 | use bignum lib => 'Foo,Math::BigInt::Bar'; | |
420 | ||
421 | Please see respective module documentation for further details. | |
422 | ||
423 | =head2 INTERNAL FORMAT | |
424 | ||
425 | The numbers are stored as objects, and their internals might change at anytime, | |
426 | especially between math operations. The objects also might belong to different | |
427 | classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even | |
428 | with normal scalars is not extraordinary, but normal and expected. | |
429 | ||
430 | You should not depend on the internal format, all accesses must go through | |
431 | accessor methods. E.g. looking at $x->{sign} is not a bright idea since there | |
432 | is no guaranty that the object in question has such a hashkey, nor is a hash | |
433 | underneath at all. | |
434 | ||
435 | =head2 SIGN | |
436 | ||
437 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. | |
438 | You can access it with the sign() method. | |
439 | ||
440 | A sign of 'NaN' is used to represent the result when input arguments are not | |
441 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively | |
442 | minus infinity. You will get '+inf' when dividing a positive number by 0, and | |
443 | '-inf' when dividing any negative number by 0. | |
444 | ||
126f3c5f JH |
445 | =head1 MODULES USED |
446 | ||
447 | C<bignum> is just a thin wrapper around various modules of the Math::BigInt | |
448 | family. Think of it as the head of the family, who runs the shop, and orders | |
449 | the others to do the work. | |
450 | ||
451 | The following modules are currently used by bignum: | |
452 | ||
453 | Math::BigInt::Lite (for speed, and only if it is loadable) | |
454 | Math::BigInt | |
455 | Math::BigFloat | |
456 | ||
457 | =head1 EXAMPLES | |
458 | ||
459 | Some cool command line examples to impress the Python crowd ;) | |
460 | ||
461 | perl -Mbignum -le 'print sqrt(33)' | |
462 | perl -Mbignum -le 'print 2*255' | |
463 | perl -Mbignum -le 'print 4.5+2*255' | |
464 | perl -Mbignum -le 'print 3/7 + 5/7 + 8/3' | |
465 | perl -Mbignum -le 'print 123->is_odd()' | |
466 | perl -Mbignum -le 'print log(2)' | |
467 | perl -Mbignum -le 'print 2 ** 0.5' | |
468 | perl -Mbignum=a,65 -le 'print 2 ** 0.2' | |
469 | ||
470 | =head1 LICENSE | |
471 | ||
472 | This program is free software; you may redistribute it and/or modify it under | |
473 | the same terms as Perl itself. | |
474 | ||
475 | =head1 SEE ALSO | |
476 | ||
477 | Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>. | |
478 | ||
479 | L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well | |
480 | as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
481 | ||
482 | =head1 AUTHORS | |
483 | ||
27e7b8bb | 484 | (C) by Tels L<http://bloodgate.com/> in early 2002, 2003. |
126f3c5f JH |
485 | |
486 | =cut |