8 @EXPORT = qw( inf NaN );
12 require bigint; # no "use" to avoid import being called
14 ##############################################################################
22 # These are all alike, and thus faked by AUTOLOAD
24 my @faked = qw/round_mode accuracy precision div_scale/;
25 use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite
31 $name =~ s/.*:://; # split package
33 foreach my $n (@faked)
37 *{"bignum::$name"} = sub
43 Math::BigInt->$name($_[0]);
44 return Math::BigFloat->$name($_[0]);
46 return Math::BigInt->$name();
52 # delayed load of Carp and avoid recursion
54 Carp::croak ("Can't call bignum\-\>$name, not a valid method");
59 $^H{bignum} = undef; # no longer in effect
60 overload::remove_constant('binary','','float','','integer');
65 my $level = shift || 0;
66 my $hinthash = (caller($level))[10];
70 #############################################################################
71 # the following two routines are for Perl 5.9.4 or later and are lexical
75 return CORE::hex($_[0]) unless in_effect(1);
77 $i = '0x'.$i unless $i =~ /^0x/;
78 Math::BigInt->new($i);
83 return CORE::oct($_[0]) unless in_effect(1);
85 return Math::BigInt->from_oct($i) if $i =~ /^0[0-7]/;
86 Math::BigInt->new($i);
93 $^H{bignum} = 1; # we are in effect
97 # for newer Perls override hex() and oct() with a lexical version:
105 my $lib = ''; my $lib_kind = 'try';
106 my $upgrade = 'Math::BigFloat';
107 my $downgrade = 'Math::BigInt';
109 my @import = ( ':constant' ); # drive it w/ constant
110 my @a = @_; my $l = scalar @_; my $j = 0;
111 my ($ver,$trace); # version? trace?
112 my ($a,$p); # accuracy, precision
113 for ( my $i = 0; $i < $l ; $i++,$j++ )
115 if ($_[$i] eq 'upgrade')
117 # this causes upgrading
118 $upgrade = $_[$i+1]; # or undef to disable
119 my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
120 splice @a, $j, $s; $j -= $s; $i++;
122 elsif ($_[$i] eq 'downgrade')
124 # this causes downgrading
125 $downgrade = $_[$i+1]; # or undef to disable
126 my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
127 splice @a, $j, $s; $j -= $s; $i++;
129 elsif ($_[$i] =~ /^(l|lib|try|only)$/)
131 # this causes a different low lib to take care...
132 $lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l';
133 $lib = $_[$i+1] || '';
134 my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
135 splice @a, $j, $s; $j -= $s; $i++;
137 elsif ($_[$i] =~ /^(a|accuracy)$/)
140 my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
141 splice @a, $j, $s; $j -= $s; $i++;
143 elsif ($_[$i] =~ /^(p|precision)$/)
146 my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
147 splice @a, $j, $s; $j -= $s; $i++;
149 elsif ($_[$i] =~ /^(v|version)$/)
152 splice @a, $j, 1; $j --;
154 elsif ($_[$i] =~ /^(t|trace)$/)
157 splice @a, $j, 1; $j --;
159 elsif ($_[$i] eq 'hex')
161 splice @a, $j, 1; $j --;
162 $hex = \&bigint::_hex_global;
164 elsif ($_[$i] eq 'oct')
166 splice @a, $j, 1; $j --;
167 $oct = \&bigint::_oct_global;
169 else { die "unknown option $_[$i]"; }
172 $_lite = 0; # using M::BI::L ?
175 require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
176 $upgrade = 'Math::BigFloat::Trace';
180 # see if we can find Math::BigInt::Lite
181 if (!defined $a && !defined $p) # rounding won't work to well
183 eval 'require Math::BigInt::Lite;';
186 @import = ( ); # :constant in Lite, not MBI
187 Math::BigInt::Lite->import( ':constant' );
188 $_lite= 1; # signal okay
191 require Math::BigInt if $_lite == 0; # not already loaded?
192 $class = 'Math::BigInt'; # regardless of MBIL or not
194 push @import, $lib_kind => $lib if $lib ne '';
195 # Math::BigInt::Trace or plain Math::BigInt
196 $class->import(@import, upgrade => $upgrade);
200 require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
201 $downgrade = 'Math::BigInt::Trace';
205 require Math::BigFloat; $class = 'Math::BigFloat';
207 $class->import(':constant','downgrade',$downgrade);
209 bignum->accuracy($a) if defined $a;
210 bignum->precision($p) if defined $p;
213 print "bignum\t\t\t v$VERSION\n";
214 print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
215 print "Math::BigInt\t\t v$Math::BigInt::VERSION";
216 my $config = Math::BigInt->config();
217 print " lib => $config->{lib} v$config->{lib_version}\n";
218 print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
222 # Take care of octal/hexadecimal constants
223 overload::constant binary => sub { bigint::_binary_constant(shift) };
225 # if another big* was already loaded:
226 my ($package) = caller();
229 if (!defined *{"${package}::inf"})
231 $self->export_to_level(1,$self,@a); # export inf and NaN
234 no warnings 'redefine';
235 *CORE::GLOBAL::oct = $oct if $oct;
236 *CORE::GLOBAL::hex = $hex if $hex;
246 bignum - Transparent BigNumber support for Perl
252 $x = 2 + 4.5,"\n"; # BigFloat 6.5
253 print 2 ** 512 * 0.1,"\n"; # really is what you think it is
254 print inf * inf,"\n"; # prints inf
255 print NaN * 3,"\n"; # prints NaN
259 print 2 ** 256,"\n"; # a normal Perl scalar now
262 # for older Perls, note that this will be global:
263 use bignum qw/hex oct/;
264 print hex("0x1234567890123490"),"\n";
265 print oct("01234567890123490"),"\n";
269 All operators (including basic math operations) are overloaded. Integer and
270 floating-point constants are created as proper BigInts or BigFloats,
277 at the top of your script, Math::BigFloat and Math::BigInt will be loaded
278 and any constant number will be converted to an object (Math::BigFloat for
279 floats like 3.1415 and Math::BigInt for integers like 1234).
281 So, the following line:
285 creates actually a Math::BigInt and stores a reference to in $x.
286 This happens transparently and behind your back, so to speak.
288 You can see this with the following:
290 perl -Mbignum -le 'print ref(1234)'
292 Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
293 if it is installed since it is faster for some operations. It will be
294 automatically upgraded to BigInt whenever necessary:
296 perl -Mbignum -le 'print ref(2**255)'
298 This also means it is a bad idea to check for some specific package, since
299 the actual contents of $x might be something unexpected. Due to the
300 transparent way of bignum C<ref()> should not be necessary, anyway.
302 Since Math::BigInt and BigFloat also overload the normal math operations,
303 the following line will still work:
305 perl -Mbignum -le 'print ref(1234+1234)'
307 Since numbers are actually objects, you can call all the usual methods from
308 BigInt/BigFloat on them. This even works to some extent on expressions:
310 perl -Mbignum -le '$x = 1234; print $x->bdec()'
311 perl -Mbignum -le 'print 1234->copy()->binc();'
312 perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
313 perl -Mbignum -le 'print +(1234)->copy()->binc()'
315 (Note that print doesn't do what you expect if the expression starts with
318 You can even chain the operations together as usual:
320 perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
323 Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
324 appropriately. This means that:
326 perl -Mbignum -le 'print 1234+4.5'
329 will work correctly. These mixed cases don't do always work when using
330 Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
333 If you do want to work with large integers like under C<use integer;>, try
336 perl -Mbigint -le 'print 1234.5+4.5'
339 There is also C<use bigrat;> which gives you big rationals:
341 perl -Mbigrat -le 'print 1234+4.1'
344 The entire upgrading/downgrading is still experimental and might not work
345 as you expect or may even have bugs. You might get errors like this:
347 Can't use an undefined value as an ARRAY reference at
348 /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
350 This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
351 vice versa) and the upgrade/downgrad path was missing. This is a bug, please
352 report it so that we can fix it.
354 You might consider using just Math::BigInt or Math::BigFloat, since they
355 allow you finer control over what get's done in which module/space. For
356 instance, simple loop counters will be Math::BigInts under C<use bignum;> and
357 this is slower than keeping them as Perl scalars:
359 perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
361 Please note the following does not work as expected (prints nothing), since
362 overloading of '..' is not yet possible in Perl (as of v5.8.0):
364 perl -Mbignum -le 'for (1..2) { print ref($_); }'
368 bignum recognizes some options that can be passed while loading it via use.
369 The options can (currently) be either a single letter form, or the long form.
370 The following options exist:
376 This sets the accuracy for all math operations. The argument must be greater
377 than or equal to zero. See Math::BigInt's bround() function for details.
379 perl -Mbignum=a,50 -le 'print sqrt(20)'
381 Note that setting precision and accurary at the same time is not possible.
385 This sets the precision for all math operations. The argument can be any
386 integer. Negative values mean a fixed number of digits after the dot, while
387 a positive value rounds to this digit left from the dot. 0 or 1 mean round to
388 integer. See Math::BigInt's bfround() function for details.
390 perl -Mbignum=p,-50 -le 'print sqrt(20)'
392 Note that setting precision and accurary at the same time is not possible.
396 This enables a trace mode and is primarily for debugging bignum or
397 Math::BigInt/Math::BigFloat.
401 Load a different math lib, see L<MATH LIBRARY>.
403 perl -Mbignum=l,GMP -e 'print 2 ** 512'
405 Currently there is no way to specify more than one library on the command
406 line. This means the following does not work:
408 perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
410 This will be hopefully fixed soon ;)
414 Override the build-in hex() method with a version that can handle big
415 integers. Note that under Perl older than v5.9.4, this will be global
416 and cannot be disabled with "no bigint;".
420 Override the build-in oct() method with a version that can handle big
421 integers. Note that under Perl older than v5.9.4, this will be global
422 and cannot be disabled with "no bigint;".
426 This prints out the name and version of all modules used and then exits.
434 Beside import() and AUTOLOAD() there are only a few other methods.
436 Since all numbers are now objects, you can use all functions that are part of
437 the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
438 the fxxx() notation, though. This makes it possible that the underlying object
439 might morph into a different class than BigFloat.
443 But a warning is in order. When using the following to make a copy of a number,
444 only a shallow copy will be made.
449 If you want to make a real copy, use the following:
453 Using the copy or the original with overloaded math is okay, e.g. the
457 print $x + 1, " ", $y,"\n"; # prints 10 9
459 but calling any method that modifies the number directly will result in
460 B<both> the original and the copy being destroyed:
463 print $x->badd(1), " ", $y,"\n"; # prints 10 10
466 print $x->binc(1), " ", $y,"\n"; # prints 10 10
469 print $x->bmul(2), " ", $y,"\n"; # prints 18 18
471 Using methods that do not modify, but test the contents works:
474 $z = 9 if $x->is_zero(); # works fine
476 See the documentation about the copy constructor and C<=> in overload, as
477 well as the documentation in BigInt for further details.
483 A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
484 handle bareword C<inf> properly.
488 A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
489 handle bareword C<NaN> properly.
493 Return the class that numbers are upgraded to, is in fact returning
494 C<$Math::BigInt::upgrade>.
500 print "in effect\n" if bignum::in_effect; # true
503 print "in effect\n" if bignum::in_effect; # false
506 Returns true or false if C<bignum> is in effect in the current scope.
508 This method only works on Perl v5.9.4 or later.
514 Math with the numbers is done (by default) by a module called
515 Math::BigInt::Calc. This is equivalent to saying:
517 use bignum lib => 'Calc';
519 You can change this by using:
521 use bignum lib => 'GMP';
523 The following would first try to find Math::BigInt::Foo, then
524 Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
526 use bignum lib => 'Foo,Math::BigInt::Bar';
528 Please see respective module documentation for further details.
530 Using C<lib> warns if none of the specified libraries can be found and
531 L<Math::BigInt> did fall back to one of the default libraries.
532 To supress this warning, use C<try> instead:
534 use bignum try => 'GMP';
536 If you want the code to die instead of falling back, use C<only> instead:
538 use bignum only => 'GMP';
540 =head2 INTERNAL FORMAT
542 The numbers are stored as objects, and their internals might change at anytime,
543 especially between math operations. The objects also might belong to different
544 classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
545 with normal scalars is not extraordinary, but normal and expected.
547 You should not depend on the internal format, all accesses must go through
548 accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
549 is no guaranty that the object in question has such a hashkey, nor is a hash
554 The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
555 You can access it with the sign() method.
557 A sign of 'NaN' is used to represent the result when input arguments are not
558 numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
559 minus infinity. You will get '+inf' when dividing a positive number by 0, and
560 '-inf' when dividing any negative number by 0.
568 This method only works on Perl v5.9.4 or later.
572 C<bigint> overrides these routines with versions that can also handle
573 big integer values. Under Perl prior to version v5.9.4, however, this
574 will not happen unless you specifically ask for it with the two
575 import tags "hex" and "oct" - and then it will be global and cannot be
576 disabled inside a scope with "no bigint":
578 use bigint qw/hex oct/;
580 print hex("0x1234567890123456");
583 print hex("0x1234567890123456");
586 The second call to hex() will warn about a non-portable constant.
592 # will warn only under older than v5.9.4
593 print hex("0x1234567890123456");
599 C<bignum> is just a thin wrapper around various modules of the Math::BigInt
600 family. Think of it as the head of the family, who runs the shop, and orders
601 the others to do the work.
603 The following modules are currently used by bignum:
605 Math::BigInt::Lite (for speed, and only if it is loadable)
611 Some cool command line examples to impress the Python crowd ;)
613 perl -Mbignum -le 'print sqrt(33)'
614 perl -Mbignum -le 'print 2*255'
615 perl -Mbignum -le 'print 4.5+2*255'
616 perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
617 perl -Mbignum -le 'print 123->is_odd()'
618 perl -Mbignum -le 'print log(2)'
619 perl -Mbignum -le 'print exp(1)'
620 perl -Mbignum -le 'print 2 ** 0.5'
621 perl -Mbignum=a,65 -le 'print 2 ** 0.2'
622 perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777'
626 This program is free software; you may redistribute it and/or modify it under
627 the same terms as Perl itself.
631 Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
633 L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
634 as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
638 (C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.