bignum(3p) Perl Programmers Reference Guide bignum(3p)

bignum - Transparent BigNumber support for Perl

use bignum; $x = 2 + 4.5,"\n"; # BigFloat 6.5 print 2 ** 512 * 0.1,"\n"; # really is what you think it is print inf * inf,"\n"; # prints inf print NaN * 3,"\n"; # prints NaN

All operators (including basic math operations) are over- loaded. Integer and floating-point constants are created as proper BigInts or BigFloats, respectively. If you do use bignum; at the top of your script, Math::BigFloat and Math::BigInt will be loaded and any constant number will be converted to an object (Math::BigFloat for floats like 3.1415 and Math::BigInt for integers like 1234). So, the following line: $x = 1234; creates actually a Math::BigInt and stores a reference to in $x. This happens transparently and behind your back, so to speak. You can see this with the following: perl -Mbignum -le 'print ref(1234)' Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite if it is installed since it is faster for some operations. It will be automatically upgraded to BigInt whenever neccessary: perl -Mbignum -le 'print ref(2**255)' This also means it is a bad idea to check for some specific package, since the actual contents of $x might be something unexpected. Due to the transparent way of bignum "ref()" should not be neccessary, anyway. Since Math::BigInt and BigFloat also overload the normal math operations, the following line will still work: perl v5.8.8 2005-02-05 1 bignum(3p) Perl Programmers Reference Guide bignum(3p) perl -Mbignum -le 'print ref(1234+1234)' Since numbers are actually objects, you can call all the usual methods from BigInt/BigFloat on them. This even works to some extent on expressions: perl -Mbignum -le '$x = 1234; print $x->bdec()' perl -Mbignum -le 'print 1234->binc();' perl -Mbignum -le 'print 1234->binc->badd(6);' perl -Mbignum -le 'print +(1234)->binc()' (Note that print doesn't do what you expect if the expres- sion starts with '(' hence the "+") You can even chain the operations together as usual: perl -Mbignum -le 'print 1234->binc->badd(6);' 1241 Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers appropriately. This means that: perl -Mbignum -le 'print 1234+4.5' 1238.5 will work correctly. These mixed cases don't do always work when using Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl scalars work. If you do want to work with large integers like under "use integer;", try "use bigint;": perl -Mbigint -le 'print 1234.5+4.5' 1238 There is also "use bigrat;" which gives you big rationals: perl -Mbigrat -le 'print 1234+4.1' 12381/10 The entire upgrading/downgrading is still experimental and might not work as you expect or may even have bugs. You might get errors like this: Can't use an undefined value as an ARRAY reference at /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864 This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or vice versa) and the upgrade/downgrad path was missing. This is a bug, please report it so that we can fix it. perl v5.8.8 2005-02-05 2 bignum(3p) Perl Programmers Reference Guide bignum(3p) You might consider using just Math::BigInt or Math::BigFloat, since they allow you finer control over what get's done in which module/space. For instance, simple loop counters will be Math::BigInts under "use bignum;" and this is slower than keeping them as Perl scalars: perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }' Please note the following does not work as expected (prints nothing), since overloading of '..' is not yet possible in Perl (as of v5.8.0): perl -Mbignum -le 'for (1..2) { print ref($_); }'Optionsbignum recognizes some options that can be passed while loading it via use. The options can (currently) be either a single letter form, or the long form. The following options exist: a or accuracy This sets the accuracy for all math operations. The argu- ment must be greater than or equal to zero. See Math::BigInt'sbround() function for details. perl -Mbignum=a,50 -le 'print sqrt(20)' p or precision This sets the precision for all math operations. The argu- ment can be any integer. Negative values mean a fixed number of digits after the dot, while a positive value rounds to this digit left from the dot. 0 or 1 mean round to integer. See Math::BigInt'sbfround() function for details. perl -Mbignum=p,-50 -le 'print sqrt(20)' t or trace This enables a trace mode and is primarily for debugging bignum or Math::BigInt/Math::BigFloat. l or lib Load a different math lib, see "MATH LIBRARY". perl -Mbignum=l,GMP -e 'print 2 ** 512' Currently there is no way to specify more than one library on the command line. This will be hopefully fixed soon ;) v or version This prints out the name and version of all modules used perl v5.8.8 2005-02-05 3 bignum(3p) Perl Programmers Reference Guide bignum(3p) and then exits. perl -Mbignum=vMethodsBesideimport() andAUTOLOAD() there are only a few other methods. Since all numbers are now objects, you can use all functions that are part of the BigInt or BigFloat API. It is wise to use only thebxxx() notation, and not thefxxx() notation, though. This makes it possible that the underlying object might morph into a different class than BigFloat.CaveatBut a warning is in order. When using the following to make a copy of a number, only a shallow copy will be made. $x = 9; $y = $x; $x = $y = 7; If you want to make a real copy, use the following: $y = $x->copy(); Using the copy or the original with overloaded math is okay, e.g. the following work: $x = 9; $y = $x; print $x + 1, " ", $y,"\n"; # prints 10 9 but calling any method that modifies the number directly will result inboththe original and the copy beeing des- troyed: $x = 9; $y = $x; print $x->badd(1), " ", $y,"\n"; # prints 10 10 $x = 9; $y = $x; print $x->binc(1), " ", $y,"\n"; # prints 10 10 $x = 9; $y = $x; print $x->bmul(2), " ", $y,"\n"; # prints 18 18 Using methods that do not modify, but testthe contents works: $x = 9; $y = $x; $z = 9 if $x->is_zero(); # works fine perl v5.8.8 2005-02-05 4 bignum(3p) Perl Programmers Reference Guide bignum(3p) See the documentation about the copy constructor and "=" in overload, as well as the documentation in BigInt for further details.inf() A shortcut to return Math::BigInt->binf(). Usefull because Perl does not always handle bareword "inf" prop- erly.NaN() A shortcut to return Math::BigInt->bnan(). Usefull because Perl does not always handle bareword "NaN" prop- erly.upgrade() Return the class that numbers are upgraded to, is in fact returning $Math::BigInt::upgrade.MATH LIBRARYMath with the numbers is done (by default) by a module called Math::BigInt::Calc. This is equivalent to saying: use bignum lib => 'Calc'; You can change this by using: use bignum lib => 'BitVect'; The following would first try to find Math::BigInt::Foo, then Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: use bignum lib => 'Foo,Math::BigInt::Bar'; Please see respective module documentation for further details.INTERNAL FORMATThe numbers are stored as objects, and their internals might change at anytime, especially between math opera- tions. The objects also might belong to different classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even with normal scalars is not extraordinary, but normal and expected. You should not depend on the internal format, all accesses must go through accessor methods. E.g. looking at $x->{sign} is not a bright idea since there is no guaranty that the object in question has such a hashkey, nor is a hash underneath at all. perl v5.8.8 2005-02-05 5 bignum(3p) Perl Programmers Reference Guide bignum(3p)SIGNThe sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. You can access it with thesign() method. A sign of 'NaN' is used to represent the result when input arguments are not numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively minus infinity. You will get '+inf' when dividing a positive number by 0, and '-inf' when dividing any negative number by 0.

"bignum" is just a thin wrapper around various modules of the Math::BigInt family. Think of it as the head of the fam- ily, who runs the shop, and orders the others to do the work. The following modules are currently used by bignum: Math::BigInt::Lite (for speed, and only if it is loadable) Math::BigInt Math::BigFloat

Some cool command line examples to impress the Python crowd ;) perl -Mbignum -le 'print sqrt(33)' perl -Mbignum -le 'print 2*255' perl -Mbignum -le 'print 4.5+2*255' perl -Mbignum -le 'print 3/7 + 5/7 + 8/3' perl -Mbignum -le 'print 123->is_odd()' perl -Mbignum -le 'print log(2)' perl -Mbignum -le 'print 2 ** 0.5' perl -Mbignum=a,65 -le 'print 2 ** 0.2'

This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.

Especially bigrat as in "perl -Mbigrat -le 'print 1/3+1/4'". Math::BigFloat, Math::BigInt, Math::BigRat and Math::Big as well as Math::BigInt::BitVect, Math::BigInt::Pari and Math::BigInt::GMP.

(C) by Tels <http://bloodgate.com/> in early 2002, 2003. perl v5.8.8 2005-02-05 6

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