# bigrat - phpMan

## NAME
    bigrat - Transparent BigNumber/BigRational support for Perl

## SYNOPSIS
      use bigrat;

      print 2 + 4.5,"\n";                   # BigFloat 6.5
      print 1/3 + 1/4,"\n";                 # produces 7/12

      {
        no bigrat;
        print 1/3,"\n";                     # 0.33333...
      }

      # Import into current package:
      use bigrat qw/hex oct/;
      print hex("0x1234567890123490"),"\n";
      print oct("01234567890123490"),"\n";

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

    Other than bignum, this module upgrades to [Math::BigRat], meaning that
    instead 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::BigInt] family. Think of it as the head of the family, 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]
            [Math::BigRat]

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

            use bigrat lib => 'Calc';

    You can change this by using:

            use bignum lib => 'GMP';

    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 bigrat lib => 'Foo,[Math::BigInt::Bar]';

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

            use bignum try => 'GMP';

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

            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
    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.

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

    inf()
      A shortcut to return [Math::BigInt]->binf(). Useful because Perl does
      not always handle bareword "inf" properly.

    NaN()
      A shortcut to return [Math::BigInt]->bnan(). Useful because Perl does
      not always handle bareword "NaN" properly.

    e
              # perl -Mbigrat=e -wle 'print e'

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

    PI
              # perl -Mbigrat=PI -wle 'print PI'

      Returns PI.

    bexp()
              bexp($power,$accuracy);

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

      Example:

              # perl -Mbigrat=bexp -wle 'print bexp(1,80)'

    bpi()
              bpi($accuracy);

      Returns PI to the wanted accuracy.

      Example:

              # 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()
              use bigrat;

              print "in effect\n" if [bigrat::in_effect];       # true
              {
                no bigrat;
                print "in effect\n" if [bigrat::in_effect];     # false
              }

      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.

            $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 in
    both the original and the copy being destroyed:

            $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

    See the documentation about the copy constructor and "=" in overload, as
    well 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
      greater than or equal to zero. See [Math::BigInt]'s bround() function
      for details.

              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
      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]'s bfround() function for
      details.

              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 or
      [Math::BigInt]/[Math::BigFloat].

    l or lib
      Load a different math lib, see "MATH LIBRARY".

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

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

              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 big
      numbers. This overrides it by exporting it to the current package.
      Under Perl v5.10.0 and higher, this is not so necessary, as hex() is
      lexically overridden in the current scope whenever the bigrat pragma
      is active.

    oct
      Override the built-in oct() method with a version that can handle big
      numbers. This overrides it by exporting it to the current package.
      Under Perl v5.10.0 and higher, this is not so necessary, as oct() is
      lexically overridden in the current scope whenever the bigrat pragma
      is active.

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

              perl -Mbigrat=v

## CAVEATS
    Operator vs literal overloading
      "bigrat" works by overloading handling of integer and floating point
      literals, converting them to [Math::BigInt] or [Math::BigRat] objects.

      This means that arithmetic involving only string values or string
      literals will be performed using Perl's built-in operators.

      For example:

          use bigrat;
          my $x = "900000000000000009";
          my $y = "900000000000000007";
          print $x - $y;

      will output 0 on default 32-bit builds, since "bigrat" never sees the
      string literals. To ensure the expression is all treated as
      "[Math::BigInt]" or "[Math::BigRat]" objects, use a literal number in the
      expression:

          print +(0+$x) - $y;

    in_effect()
      This method only works on Perl v5.9.4 or later.

    hex()/oct()
      "bigint" overrides these routines with versions that can also handle
      big integer values. Under Perl prior to version v5.9.4, however, this
      will not happen unless you specifically ask for it with the two import
      tags "hex" and "oct" - and then it will be global and cannot be
      disabled inside a scope with "no bigint":

              use bigint qw/hex oct/;

              print hex("0x1234567890123456");
              {
                      no bigint;
                      print hex("0x1234567890123456");
              }

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

      Compare this to:

              use bigint;

              # will warn only under Perl older than v5.9.4
              print hex("0x1234567890123456");

## EXAMPLES
            perl -Mbigrat -le 'print [sqrt(33)]'
            perl -Mbigrat -le 'print 2*255'
            perl -Mbigrat -le 'print 4.5+2*255'
            perl -Mbigrat -le 'print 3/7 + 5/7 + 8/3'
            perl -Mbigrat -le 'print 12->is_odd()';
            perl -Mbignum=l,GMP -le 'print 7 ** 7777'

## BUGS
    For information about bugs and how to report them, see the BUGS section
    in the documentation available with the perldoc command.

        perldoc bignum

## SUPPORT
    You can find documentation for this module with the perldoc command.

        perldoc bigrat

    For more information, see the SUPPORT section in the documentation
    available with the perldoc command.

        perldoc bignum

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

## SEE ALSO
    bignum and bigint.

    [Math::BigInt], [Math::BigFloat], [Math::BigRat] and [Math::Big] as well as
    [Math::BigInt::FastCalc], [Math::BigInt::Pari] and [Math::BigInt::GMP].

## AUTHORS
    *   (C) by Tels <<http://bloodgate.com/>> in early 2002 - 2007.

    *   Peter John Acklam <<pjacklam@gmail.com><gt>, 2014-.