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Transparent BigNumber/BigRational support for Perl

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NAME

bigrat - Transparent BigNumber/BigRational support for Perl

SYNOPSIS

  1. use bigrat;
  2. print 2 + 4.5,"\n";# BigFloat 6.5
  3. print 1/3 + 1/4,"\n";# produces 7/12
  4. {
  5. no bigrat;
  6. print 1/3,"\n";# 0.33333...
  7. }
  8. # Note that this will make hex() and oct() be globally overridden:
  9. use bigrat qw/hex oct/;
  10. print hex("0x1234567890123490"),"\n";
  11. print oct("01234567890123490"),"\n";

DESCRIPTION

All operators (including basic math operations) are overloaded. Integer andfloating-point constants are created as proper BigInts or BigFloats,respectively.

Other than bignum, this module upgrades to Math::BigRat, meaning thatinstead of 2.5 you will get 2+1/2 as output.

Modules Used

bigrat is just a thin wrapper around various modules of the Math::BigIntfamily. Think of it as the head of the family, who runs the shop, and ordersthe others to do the work.

The following modules are currently used by bignum:

  1. Math::BigInt::Lite (for speed, and only if it is loadable)
  2. Math::BigInt
  3. Math::BigFloat
  4. Math::BigRat

Math Library

Math with the numbers is done (by default) by a module calledMath::BigInt::Calc. This is equivalent to saying:

  1. use bigrat lib => 'Calc';

You can change this by using:

  1. use bignum lib => 'GMP';

The following would first try to find Math::BigInt::Foo, thenMath::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:

  1. use bigrat lib => 'Foo,Math::BigInt::Bar';

Using lib warns if none of the specified libraries can be found andMath::BigInt did fall back to one of the default libraries.To suppress this warning, use try instead:

  1. use bignum try => 'GMP';

If you want the code to die instead of falling back, use only instead:

  1. use bignum only => 'GMP';

Please see respective module documentation for further details.

Sign

The sign is either '+', '-', 'NaN', '+inf' or '-inf'.

A sign of 'NaN' is used to represent the result when input arguments are notnumbers or as a result of 0/0. '+inf' and '-inf' represent plus respectivelyminus infinity. You will get '+inf' when dividing a positive number by 0, and'-inf' when dividing any negative number by 0.

Methods

Since all numbers are not objects, you can use all functions that are part ofthe BigInt or BigFloat API. It is wise to use only the bxxx() notation, and notthe fxxx() notation, though. This makes you independent on the fact that theunderlying object might morph into a different class than BigFloat.

  • inf()

    A shortcut to return Math::BigInt->binf(). Useful because Perl does not alwayshandle bareword inf properly.

  • NaN()

    A shortcut to return Math::BigInt->bnan(). Useful because Perl does not alwayshandle bareword NaN properly.

  • e
    1. # perl -Mbigrat=e -wle 'print e'

    Returns Euler's number e, aka exp(1).

  • PI
    1. # perl -Mbigrat=PI -wle 'print PI'

    Returns PI.

  • bexp()
    1. bexp($power,$accuracy);

    Returns Euler's number e raised to the appropriate power, tothe wanted accuracy.

    Example:

    1. # perl -Mbigrat=bexp -wle 'print bexp(1,80)'
  • bpi()
    1. bpi($accuracy);

    Returns PI to the wanted accuracy.

    Example:

    1. # perl -Mbigrat=bpi -wle 'print bpi(80)'
  • upgrade()

    Return the class that numbers are upgraded to, is in fact returning$Math::BigInt::upgrade.

  • in_effect()
    1. use bigrat;
    2. print "in effect\n" if bigrat::in_effect;# true
    3. {
    4. no bigrat;
    5. print "in effect\n" if bigrat::in_effect;# false
    6. }

    Returns true or false if bigrat is in effect in the current scope.

    This method only works on Perl v5.9.4 or later.

MATH LIBRARY

Math with the numbers is done (by default) by a module called

Caveat

But a warning is in order. When using the following to make a copy of a number,only a shallow copy will be made.

  1. $x = 9; $y = $x;
  2. $x = $y = 7;

If you want to make a real copy, use the following:

  1. $y = $x->copy();

Using the copy or the original with overloaded math is okay, e.g. thefollowing work:

  1. $x = 9; $y = $x;
  2. print $x + 1, " ", $y,"\n"; # prints 10 9

but calling any method that modifies the number directly will result inboth the original and the copy being destroyed:

  1. $x = 9; $y = $x;
  2. print $x->badd(1), " ", $y,"\n"; # prints 10 10
  3. $x = 9; $y = $x;
  4. print $x->binc(1), " ", $y,"\n"; # prints 10 10
  5. $x = 9; $y = $x;
  6. print $x->bmul(2), " ", $y,"\n"; # prints 18 18

Using methods that do not modify, but testthe contents works:

  1. $x = 9; $y = $x;
  2. $z = 9 if $x->is_zero(); # works fine

See the documentation about the copy constructor and = in overload, aswell as the documentation in BigInt for further details.

Options

bignum 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 argument must be greaterthan or equal to zero. See Math::BigInt's bround() function for details.

    1. perl -Mbigrat=a,50 -le 'print sqrt(20)'

    Note that setting precision and accuracy at the same time is not possible.

  • p or precision

    This sets the precision for all math operations. The argument can be anyinteger. Negative values mean a fixed number of digits after the dot, whilea positive value rounds to this digit left from the dot. 0 or 1 mean round tointeger. See Math::BigInt's bfround() function for details.

    1. perl -Mbigrat=p,-50 -le 'print sqrt(20)'

    Note that setting precision and accuracy at the same time is not possible.

  • t or trace

    This enables a trace mode and is primarily for debugging bignum orMath::BigInt/Math::BigFloat.

  • l or lib

    Load a different math lib, see MATH LIBRARY.

    1. perl -Mbigrat=l,GMP -e 'print 2 ** 512'

    Currently there is no way to specify more than one library on the commandline. This means the following does not work:

    1. perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'

    This will be hopefully fixed soon ;)

  • hex

    Override the built-in hex() method with a version that can handle bigintegers. Note that under Perl v5.9.4 or ealier, this will be globaland cannot be disabled with "no bigint;".

  • oct

    Override the built-in oct() method with a version that can handle bigintegers. Note that under Perl v5.9.4 or earlier, this will be globaland cannot be disabled with "no bigint;".

  • v or version

    This prints out the name and version of all modules used and then exits.

    1. perl -Mbigrat=v

CAVEATS

  • in_effect()

    This method only works on Perl v5.9.4 or later.

  • hex()/oct()

    bigint overrides these routines with versions that can also handlebig integer values. Under Perl prior to version v5.9.4, however, thiswill not happen unless you specifically ask for it with the twoimport tags "hex" and "oct" - and then it will be global and cannot bedisabled inside a scope with "no bigint":

    1. use bigint qw/hex oct/;
    2. print hex("0x1234567890123456");
    3. {
    4. no bigint;
    5. print hex("0x1234567890123456");
    6. }

    The second call to hex() will warn about a non-portable constant.

    Compare this to:

    1. use bigint;
    2. # will warn only under Perl older than v5.9.4
    3. print hex("0x1234567890123456");

EXAMPLES

  1. perl -Mbigrat -le 'print sqrt(33)'
  2. perl -Mbigrat -le 'print 2*255'
  3. perl -Mbigrat -le 'print 4.5+2*255'
  4. perl -Mbigrat -le 'print 3/7 + 5/7 + 8/3'
  5. perl -Mbigrat -le 'print 12->is_odd()';
  6. perl -Mbignum=l,GMP -le 'print 7 ** 7777'

LICENSE

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

SEE ALSO

Especially bignum.

Math::BigFloat, Math::BigInt, Math::BigRat and Math::Big as wellas Math::BigInt::BitVect, Math::BigInt::Pari and Math::BigInt::GMP.

AUTHORS

(C) by Tels http://bloodgate.com/ in early 2002 - 2007.

 
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