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126f3c5f JH |
1 | package bignum; |
2 | require 5.005; | |
3 | ||
27e7b8bb | 4 | $VERSION = '0.15'; |
126f3c5f | 5 | use Exporter; |
b4bc5691 T |
6 | @EXPORT_OK = qw( ); |
7 | @EXPORT = qw( inf NaN ); | |
8 | @ISA = qw( Exporter ); | |
126f3c5f JH |
9 | |
10 | use strict; | |
11 | ||
12 | ############################################################################## | |
13 | ||
14 | # These are all alike, and thus faked by AUTOLOAD | |
15 | ||
16 | my @faked = qw/round_mode accuracy precision div_scale/; | |
17 | use vars qw/$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 | |
66 | my $lib = 'Calc'; | |
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 | |
143 | } | |
144 | # Math::BigInt::Trace or plain Math::BigInt | |
145 | $class->import(@import, upgrade => $upgrade, lib => $lib); | |
146 | ||
147 | if ($trace) | |
148 | { | |
149 | require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace'; | |
150 | $downgrade = 'Math::BigInt::Trace'; | |
126f3c5f JH |
151 | } |
152 | else | |
153 | { | |
154 | require Math::BigFloat; $class = 'Math::BigFloat'; | |
155 | } | |
156 | $class->import(':constant','downgrade',$downgrade); | |
157 | ||
158 | bignum->accuracy($a) if defined $a; | |
159 | bignum->precision($p) if defined $p; | |
160 | if ($ver) | |
161 | { | |
162 | print "bignum\t\t\t v$VERSION\n"; | |
163 | print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite; | |
164 | print "Math::BigInt\t\t v$Math::BigInt::VERSION"; | |
165 | my $config = Math::BigInt->config(); | |
166 | print " lib => $config->{lib} v$config->{lib_version}\n"; | |
167 | print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n"; | |
168 | exit; | |
169 | } | |
b4bc5691 | 170 | $self->export_to_level(1,$self,@a); # export inf and NaN |
126f3c5f JH |
171 | } |
172 | ||
b4bc5691 T |
173 | sub inf () { Math::BigInt->binf(); } |
174 | sub NaN () { Math::BigInt->bnan(); } | |
175 | ||
126f3c5f JH |
176 | 1; |
177 | ||
178 | __END__ | |
179 | ||
180 | =head1 NAME | |
181 | ||
182 | bignum - Transparent BigNumber support for Perl | |
183 | ||
184 | =head1 SYNOPSIS | |
185 | ||
186 | use bignum; | |
187 | ||
188 | $x = 2 + 4.5,"\n"; # BigFloat 6.5 | |
b4bc5691 T |
189 | print 2 ** 512 * 0.1,"\n"; # really is what you think it is |
190 | print inf * inf,"\n"; # prints inf | |
191 | print NaN * 3,"\n"; # prints NaN | |
126f3c5f JH |
192 | |
193 | =head1 DESCRIPTION | |
194 | ||
195 | All operators (including basic math operations) are overloaded. Integer and | |
196 | floating-point constants are created as proper BigInts or BigFloats, | |
197 | respectively. | |
198 | ||
24716a00 HS |
199 | If you do |
200 | ||
201 | use bignum; | |
202 | ||
203 | at the top of your script, Math::BigFloat and Math::BigInt will be loaded | |
204 | and any constant number will be converted to an object (Math::BigFloat for | |
205 | floats like 3.1415 and Math::BigInt for integers like 1234). | |
206 | ||
207 | So, the following line: | |
208 | ||
209 | $x = 1234; | |
210 | ||
211 | creates actually a Math::BigInt and stores a reference to in $x. | |
212 | This happens transparently and behind your back, so to speak. | |
213 | ||
214 | You can see this with the following: | |
215 | ||
216 | perl -Mbignum -le 'print ref(1234)' | |
217 | ||
218 | Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite | |
219 | if it is installed since it is faster for some operations. It will be | |
220 | automatically upgraded to BigInt whenever neccessary: | |
221 | ||
222 | perl -Mbignum -le 'print ref(2**255)' | |
223 | ||
224 | This also means it is a bad idea to check for some specific package, since | |
225 | the actual contents of $x might be something unexpected. Due to the | |
226 | transparent way of bignum C<ref()> should not be neccessary, anyway. | |
227 | ||
228 | Since Math::BigInt and BigFloat also overload the normal math operations, | |
229 | the following line will still work: | |
230 | ||
231 | perl -Mbignum -le 'print ref(1234+1234)' | |
232 | ||
233 | Since numbers are actually objects, you can call all the usual methods from | |
234 | BigInt/BigFloat on them. This even works to some extent on expressions: | |
235 | ||
236 | perl -Mbignum -le '$x = 1234; print $x->bdec()' | |
237 | perl -Mbignum -le 'print 1234->binc();' | |
238 | perl -Mbignum -le 'print 1234->binc->badd(6);' | |
239 | perl -Mbignum -le 'print +(1234)->binc()' | |
240 | ||
241 | (Note that print doesn't do what you expect if the expression starts with | |
242 | '(' hence the C<+>) | |
243 | ||
244 | You can even chain the operations together as usual: | |
245 | ||
246 | perl -Mbignum -le 'print 1234->binc->badd(6);' | |
247 | 1241 | |
248 | ||
249 | Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers | |
250 | appropriately. This means that: | |
251 | ||
252 | perl -Mbignum -le 'print 1234+4.5' | |
253 | 1238.5 | |
254 | ||
255 | will work correctly. These mixed cases don't do always work when using | |
256 | Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl | |
257 | scalars work. | |
258 | ||
259 | If you do want to work with large integers like under C<use integer;>, try | |
260 | C<use bigint;>: | |
261 | ||
262 | perl -Mbigint -le 'print 1234.5+4.5' | |
263 | 1238 | |
264 | ||
265 | There is also C<use bigrat;> which gives you big rationals: | |
266 | ||
267 | perl -Mbigrat -le 'print 1234+4.1' | |
268 | 12381/10 | |
269 | ||
270 | The entire upgrading/downgrading is still experimental and might not work | |
271 | as you expect or may even have bugs. | |
272 | ||
273 | You might get errors like this: | |
274 | ||
275 | Can't use an undefined value as an ARRAY reference at | |
276 | /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864 | |
277 | ||
278 | This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or | |
279 | vice versa) and the upgrade/downgrad path was missing. This is a bug, please | |
280 | report it so that we can fix it. | |
281 | ||
282 | You might consider using just Math::BigInt or Math::BigFloat, since they | |
283 | allow you finer control over what get's done in which module/space. For | |
284 | instance, simple loop counters will be Math::BigInts under C<use bignum;> and | |
285 | this is slower than keeping them as Perl scalars: | |
286 | ||
287 | perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }' | |
288 | ||
289 | Please note the following does not work as expected (prints nothing), since | |
290 | overloading of '..' is not yet possible in Perl (as of v5.8.0): | |
291 | ||
292 | perl -Mbignum -le 'for (1..2) { print ref($_); }' | |
293 | ||
126f3c5f JH |
294 | =head2 OPTIONS |
295 | ||
296 | bignum recognizes some options that can be passed while loading it via use. | |
297 | The options can (currently) be either a single letter form, or the long form. | |
298 | The following options exist: | |
299 | ||
300 | =over 2 | |
301 | ||
302 | =item a or accuracy | |
303 | ||
304 | This sets the accuracy for all math operations. The argument must be greater | |
305 | than or equal to zero. See Math::BigInt's bround() function for details. | |
306 | ||
307 | perl -Mbignum=a,50 -le 'print sqrt(20)' | |
308 | ||
309 | =item p or precision | |
310 | ||
311 | This sets the precision for all math operations. The argument can be any | |
312 | integer. Negative values mean a fixed number of digits after the dot, while | |
313 | a positive value rounds to this digit left from the dot. 0 or 1 mean round to | |
314 | integer. See Math::BigInt's bfround() function for details. | |
315 | ||
316 | perl -Mbignum=p,-50 -le 'print sqrt(20)' | |
317 | ||
318 | =item t or trace | |
319 | ||
320 | This enables a trace mode and is primarily for debugging bignum or | |
321 | Math::BigInt/Math::BigFloat. | |
322 | ||
323 | =item l or lib | |
324 | ||
325 | Load a different math lib, see L<MATH LIBRARY>. | |
326 | ||
327 | perl -Mbignum=l,GMP -e 'print 2 ** 512' | |
328 | ||
329 | Currently there is no way to specify more than one library on the command | |
330 | line. This will be hopefully fixed soon ;) | |
331 | ||
332 | =item v or version | |
333 | ||
334 | This prints out the name and version of all modules used and then exits. | |
335 | ||
336 | perl -Mbignum=v -e '' | |
337 | ||
b4bc5691 T |
338 | =head2 METHODS |
339 | ||
340 | Beside import() and AUTOLOAD() there are only a few other methods. | |
341 | ||
24716a00 HS |
342 | Since all numbers are now objects, you can use all functions that are part of |
343 | the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not | |
344 | the fxxx() notation, though. This makes it possible that the underlying object | |
345 | might morph into a different class than BigFloat. | |
346 | ||
990fb837 RGS |
347 | =head2 CAVEAT |
348 | ||
349 | But a warning is in order. When using the following to make a copy of a number, | |
350 | only a shallow copy will be made. | |
351 | ||
352 | $x = 9; $y = $x; | |
353 | $x = $y = 7; | |
354 | ||
355 | Using the copy or the original with overloaded math is okay, e.g. the | |
356 | following work: | |
357 | ||
358 | $x = 9; $y = $x; | |
359 | print $x + 1, " ", $y,"\n"; # prints 10 9 | |
360 | ||
361 | but calling any method that modifies the number directly will result in | |
362 | B<both> the original and the copy beeing destroyed: | |
363 | ||
364 | $x = 9; $y = $x; | |
365 | print $x->badd(1), " ", $y,"\n"; # prints 10 10 | |
366 | ||
367 | $x = 9; $y = $x; | |
368 | print $x->binc(1), " ", $y,"\n"; # prints 10 10 | |
369 | ||
370 | $x = 9; $y = $x; | |
371 | print $x->bmul(2), " ", $y,"\n"; # prints 18 18 | |
372 | ||
373 | Using methods that do not modify, but testthe contents works: | |
374 | ||
375 | $x = 9; $y = $x; | |
376 | $z = 9 if $x->is_zero(); # works fine | |
377 | ||
378 | See the documentation about the copy constructor and C<=> in overload, as | |
379 | well as the documentation in BigInt for further details. | |
380 | ||
b4bc5691 T |
381 | =over 2 |
382 | ||
383 | =item inf() | |
384 | ||
385 | A shortcut to return Math::BigInt->binf(). Usefull because Perl does not always | |
386 | handle bareword C<inf> properly. | |
387 | ||
388 | =item NaN() | |
389 | ||
390 | A shortcut to return Math::BigInt->bnan(). Usefull because Perl does not always | |
391 | handle bareword C<NaN> properly. | |
392 | ||
393 | =item upgrade() | |
394 | ||
395 | Return the class that numbers are upgraded to, is in fact returning | |
396 | C<$Math::BigInt::upgrade>. | |
397 | ||
398 | =back | |
399 | ||
126f3c5f JH |
400 | =head2 MATH LIBRARY |
401 | ||
402 | Math with the numbers is done (by default) by a module called | |
403 | Math::BigInt::Calc. This is equivalent to saying: | |
404 | ||
405 | use bignum lib => 'Calc'; | |
406 | ||
407 | You can change this by using: | |
408 | ||
409 | use bignum lib => 'BitVect'; | |
410 | ||
411 | The following would first try to find Math::BigInt::Foo, then | |
412 | Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: | |
413 | ||
414 | use bignum lib => 'Foo,Math::BigInt::Bar'; | |
415 | ||
416 | Please see respective module documentation for further details. | |
417 | ||
418 | =head2 INTERNAL FORMAT | |
419 | ||
420 | The numbers are stored as objects, and their internals might change at anytime, | |
421 | especially between math operations. The objects also might belong to different | |
422 | classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even | |
423 | with normal scalars is not extraordinary, but normal and expected. | |
424 | ||
425 | You should not depend on the internal format, all accesses must go through | |
426 | accessor methods. E.g. looking at $x->{sign} is not a bright idea since there | |
427 | is no guaranty that the object in question has such a hashkey, nor is a hash | |
428 | underneath at all. | |
429 | ||
430 | =head2 SIGN | |
431 | ||
432 | The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. | |
433 | You can access it with the sign() method. | |
434 | ||
435 | A sign of 'NaN' is used to represent the result when input arguments are not | |
436 | numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively | |
437 | minus infinity. You will get '+inf' when dividing a positive number by 0, and | |
438 | '-inf' when dividing any negative number by 0. | |
439 | ||
126f3c5f JH |
440 | =head1 MODULES USED |
441 | ||
442 | C<bignum> is just a thin wrapper around various modules of the Math::BigInt | |
443 | family. Think of it as the head of the family, who runs the shop, and orders | |
444 | the others to do the work. | |
445 | ||
446 | The following modules are currently used by bignum: | |
447 | ||
448 | Math::BigInt::Lite (for speed, and only if it is loadable) | |
449 | Math::BigInt | |
450 | Math::BigFloat | |
451 | ||
452 | =head1 EXAMPLES | |
453 | ||
454 | Some cool command line examples to impress the Python crowd ;) | |
455 | ||
456 | perl -Mbignum -le 'print sqrt(33)' | |
457 | perl -Mbignum -le 'print 2*255' | |
458 | perl -Mbignum -le 'print 4.5+2*255' | |
459 | perl -Mbignum -le 'print 3/7 + 5/7 + 8/3' | |
460 | perl -Mbignum -le 'print 123->is_odd()' | |
461 | perl -Mbignum -le 'print log(2)' | |
462 | perl -Mbignum -le 'print 2 ** 0.5' | |
463 | perl -Mbignum=a,65 -le 'print 2 ** 0.2' | |
464 | ||
465 | =head1 LICENSE | |
466 | ||
467 | This program is free software; you may redistribute it and/or modify it under | |
468 | the same terms as Perl itself. | |
469 | ||
470 | =head1 SEE ALSO | |
471 | ||
472 | Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>. | |
473 | ||
474 | L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well | |
475 | as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>. | |
476 | ||
477 | =head1 AUTHORS | |
478 | ||
27e7b8bb | 479 | (C) by Tels L<http://bloodgate.com/> in early 2002, 2003. |
126f3c5f JH |
480 | |
481 | =cut |