7 @EXPORT = qw( inf NaN );
12 ##############################################################################
14 # These are all alike, and thus faked by AUTOLOAD
16 my @faked = qw/round_mode accuracy precision div_scale/;
17 use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite
23 $name =~ s/.*:://; # split package
25 foreach my $n (@faked)
29 *{"bignum::$name"} = sub
35 Math::BigInt->$name($_[0]);
36 return Math::BigFloat->$name($_[0]);
38 return Math::BigInt->$name();
44 # delayed load of Carp and avoid recursion
46 Carp::croak ("Can't call bignum\-\>$name, not a valid method");
55 # $Math::BigInt::upgrade = $_[0];
56 # $Math::BigFloat::upgrade = $_[0];
58 return $Math::BigInt::upgrade;
67 my $upgrade = 'Math::BigFloat';
68 my $downgrade = 'Math::BigInt';
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++ )
76 if ($_[$i] eq 'upgrade')
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; $i++;
83 elsif ($_[$i] eq 'downgrade')
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; $i++;
90 elsif ($_[$i] =~ /^(l|lib)$/)
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; $i++;
97 elsif ($_[$i] =~ /^(a|accuracy)$/)
100 my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
101 splice @a, $j, $s; $j -= $s; $i++;
103 elsif ($_[$i] =~ /^(p|precision)$/)
106 my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
107 splice @a, $j, $s; $j -= $s; $i++;
109 elsif ($_[$i] =~ /^(v|version)$/)
112 splice @a, $j, 1; $j --;
114 elsif ($_[$i] =~ /^(t|trace)$/)
117 splice @a, $j, 1; $j --;
119 else { die "unknown option $_[$i]"; }
122 $_lite = 0; # using M::BI::L ?
125 require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
126 $upgrade = 'Math::BigFloat::Trace';
130 # see if we can find Math::BigInt::Lite
131 if (!defined $a && !defined $p) # rounding won't work to well
133 eval 'require Math::BigInt::Lite;';
136 @import = ( ); # :constant in Lite, not MBI
137 Math::BigInt::Lite->import( ':constant' );
138 $_lite= 1; # signal okay
141 require Math::BigInt if $_lite == 0; # not already loaded?
142 $class = 'Math::BigInt'; # regardless of MBIL or not
144 # Math::BigInt::Trace or plain Math::BigInt
145 $class->import(@import, upgrade => $upgrade, lib => $lib);
149 require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
150 $downgrade = 'Math::BigInt::Trace';
154 require Math::BigFloat; $class = 'Math::BigFloat';
156 $class->import(':constant','downgrade',$downgrade);
158 bignum->accuracy($a) if defined $a;
159 bignum->precision($p) if defined $p;
162 print "bignum\t\t\t v$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";
170 $self->export_to_level(1,$self,@a); # export inf and NaN
173 sub inf () { Math::BigInt->binf(); }
174 sub NaN () { Math::BigInt->bnan(); }
182 bignum - Transparent BigNumber support for Perl
188 $x = 2 + 4.5,"\n"; # BigFloat 6.5
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
195 All operators (including basic math operations) are overloaded. Integer and
196 floating-point constants are created as proper BigInts or BigFloats,
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).
207 So, the following line:
211 creates actually a Math::BigInt and stores a reference to in $x.
212 This happens transparently and behind your back, so to speak.
214 You can see this with the following:
216 perl -Mbignum -le 'print ref(1234)'
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:
222 perl -Mbignum -le 'print ref(2**255)'
224 This also means it is a bad idea to check for some specific package, since
225 the actual contents of $x might be something unexpected. Due to the
226 transparent way of bignum C<ref()> should not be neccessary, anyway.
228 Since Math::BigInt and BigFloat also overload the normal math operations,
229 the following line will still work:
231 perl -Mbignum -le 'print ref(1234+1234)'
233 Since numbers are actually objects, you can call all the usual methods from
234 BigInt/BigFloat on them. This even works to some extent on expressions:
236 perl -Mbignum -le '$x = 1234; print $x->bdec()'
237 perl -Mbignum -le 'print 1234->binc();'
238 perl -Mbignum -le 'print 1234->binc->badd(6);'
239 perl -Mbignum -le 'print +(1234)->binc()'
241 (Note that print doesn't do what you expect if the expression starts with
244 You can even chain the operations together as usual:
246 perl -Mbignum -le 'print 1234->binc->badd(6);'
249 Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
250 appropriately. This means that:
252 perl -Mbignum -le 'print 1234+4.5'
255 will work correctly. These mixed cases don't do always work when using
256 Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
259 If you do want to work with large integers like under C<use integer;>, try
262 perl -Mbigint -le 'print 1234.5+4.5'
265 There is also C<use bigrat;> which gives you big rationals:
267 perl -Mbigrat -le 'print 1234+4.1'
270 The entire upgrading/downgrading is still experimental and might not work
271 as you expect or may even have bugs.
273 You might get errors like this:
275 Can't use an undefined value as an ARRAY reference at
276 /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
278 This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
279 vice versa) and the upgrade/downgrad path was missing. This is a bug, please
280 report it so that we can fix it.
282 You might consider using just Math::BigInt or Math::BigFloat, since they
283 allow you finer control over what get's done in which module/space. For
284 instance, simple loop counters will be Math::BigInts under C<use bignum;> and
285 this is slower than keeping them as Perl scalars:
287 perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
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):
292 perl -Mbignum -le 'for (1..2) { print ref($_); }'
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:
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.
307 perl -Mbignum=a,50 -le 'print sqrt(20)'
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.
316 perl -Mbignum=p,-50 -le 'print sqrt(20)'
320 This enables a trace mode and is primarily for debugging bignum or
321 Math::BigInt/Math::BigFloat.
325 Load a different math lib, see L<MATH LIBRARY>.
327 perl -Mbignum=l,GMP -e 'print 2 ** 512'
329 Currently there is no way to specify more than one library on the command
330 line. This will be hopefully fixed soon ;)
334 This prints out the name and version of all modules used and then exits.
336 perl -Mbignum=v -e ''
340 Beside import() and AUTOLOAD() there are only a few other methods.
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.
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.
355 Using the copy or the original with overloaded math is okay, e.g. the
359 print $x + 1, " ", $y,"\n"; # prints 10 9
361 but calling any method that modifies the number directly will result in
362 B<both> the original and the copy beeing destroyed:
365 print $x->badd(1), " ", $y,"\n"; # prints 10 10
368 print $x->binc(1), " ", $y,"\n"; # prints 10 10
371 print $x->bmul(2), " ", $y,"\n"; # prints 18 18
373 Using methods that do not modify, but testthe contents works:
376 $z = 9 if $x->is_zero(); # works fine
378 See the documentation about the copy constructor and C<=> in overload, as
379 well as the documentation in BigInt for further details.
385 A shortcut to return Math::BigInt->binf(). Usefull because Perl does not always
386 handle bareword C<inf> properly.
390 A shortcut to return Math::BigInt->bnan(). Usefull because Perl does not always
391 handle bareword C<NaN> properly.
395 Return the class that numbers are upgraded to, is in fact returning
396 C<$Math::BigInt::upgrade>.
402 Math with the numbers is done (by default) by a module called
403 Math::BigInt::Calc. This is equivalent to saying:
405 use bignum lib => 'Calc';
407 You can change this by using:
409 use bignum lib => 'BitVect';
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:
414 use bignum lib => 'Foo,Math::BigInt::Bar';
416 Please see respective module documentation for further details.
418 =head2 INTERNAL FORMAT
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.
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
432 The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
433 You can access it with the sign() method.
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.
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.
446 The following modules are currently used by bignum:
448 Math::BigInt::Lite (for speed, and only if it is loadable)
454 Some cool command line examples to impress the Python crowd ;)
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'
467 This program is free software; you may redistribute it and/or modify it under
468 the same terms as Perl itself.
472 Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
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>.
479 (C) by Tels L<http://bloodgate.com/> in early 2002.