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Math::BigRat - Arbitrary big rational numbers


  1. use Math::BigRat;
  2. my $x = Math::BigRat->new('3/7'); $x += '5/9';
  3. print $x->bstr(),"\n";
  4. print $x ** 2,"\n";
  5. my $y = Math::BigRat->new('inf');
  6. print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n";
  7. my $z = Math::BigRat->new(144); $z->bsqrt();


Math::BigRat complements Math::BigInt and Math::BigFloat by providing support for arbitrary big rational numbers.


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

  1. use Math::BigRat lib => 'Calc';

You can change this by using:

  1. use Math::BigRat 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:

  1. use Math::BigRat lib => 'Foo,Math::BigInt::Bar'; uses as internal format an array of elements of some decimal base (usually 1e7, but this might be different for some systems) with the least significant digit first, while uses a bit vector of base 2, most significant bit first. Other modules might use even different means of representing the numbers. See the respective module documentation for further details.

Currently the following replacement libraries exist, search for them at CPAN:

  1. Math::BigInt::BitVect
  2. Math::BigInt::GMP
  3. Math::BigInt::Pari
  4. Math::BigInt::FastCalc


Any methods not listed here are dervied from Math::BigFloat (or Math::BigInt), so make sure you check these two modules for further information.


  1. $x = Math::BigRat->new('1/3');

Create a new Math::BigRat object. Input can come in various forms:

  1. $x = Math::BigRat->new(123); # scalars
  2. $x = Math::BigRat->new('inf'); # infinity
  3. $x = Math::BigRat->new('123.3'); # float
  4. $x = Math::BigRat->new('1/3'); # simple string
  5. $x = Math::BigRat->new('1 / 3'); # spaced
  6. $x = Math::BigRat->new('1 / 0.1'); # w/ floats
  7. $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt
  8. $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat
  9. $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite
  10. # You can also give D and N as different objects:
  11. $x = Math::BigRat->new(
  12. Math::BigInt->new(-123),
  13. Math::BigInt->new(7),
  14. ); # => -123/7


  1. $n = $x->numerator();

Returns a copy of the numerator (the part above the line) as signed BigInt.


  1. $d = $x->denominator();

Returns a copy of the denominator (the part under the line) as positive BigInt.


  1. ($n,$d) = $x->parts();

Return a list consisting of (signed) numerator and (unsigned) denominator as BigInts.


  1. $x = Math::BigRat->new('13/7');
  2. print $x->as_int(),"\n"; # '1'

Returns a copy of the object as BigInt, truncated to an integer.

as_number() is an alias for as_int() .


  1. $x = Math::BigRat->new('13');
  2. print $x->as_hex(),"\n"; # '0xd'

Returns the BigRat as hexadecimal string. Works only for integers.


  1. $x = Math::BigRat->new('13');
  2. print $x->as_bin(),"\n"; # '0x1101'

Returns the BigRat as binary string. Works only for integers.


  1. $x->bfac();

Calculates the factorial of $x. For instance:

  1. print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3
  2. print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5

Works currently only for integers.


Is not yet implemented.


Are not yet implemented.


  1. use Math::BigRat;
  2. my $x = Math::BigRat->new('7/4');
  3. my $y = Math::BigRat->new('4/3');
  4. print $x->bmod($y);

Set $x to the remainder of the division of $x by $y.


  1. print "$x is 1\n" if $x->is_one();

Return true if $x is exactly one, otherwise false.


  1. print "$x is 0\n" if $x->is_zero();

Return true if $x is exactly zero, otherwise false.


  1. print "$x is >= 0\n" if $x->is_positive();

Return true if $x is positive (greater than or equal to zero), otherwise false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't.

is_positive() is an alias for is_pos() .


  1. print "$x is < 0\n" if $x->is_negative();

Return true if $x is negative (smaller than zero), otherwise false. Please note that '-inf' is also negative, while 'NaN' and '+inf' aren't.

is_negative() is an alias for is_neg() .


  1. print "$x is an integer\n" if $x->is_int();

Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise false. Please note that '-inf', 'inf' and 'NaN' aren't integer.


  1. print "$x is odd\n" if $x->is_odd();

Return true if $x is odd, otherwise false.


  1. print "$x is even\n" if $x->is_even();

Return true if $x is even, otherwise false.


  1. $x->bceil();

Set $x to the next bigger integer value (e.g. truncate the number to integer and then increment it by one).


  1. $x->bfloor();

Truncate $x to an integer value.


  1. $x->bsqrt();

Calculate the square root of $x.


  1. use Data::Dumper;
  2. print Dumper ( Math::BigRat->config() );
  3. print Math::BigRat->config()->{lib},"\n";

Returns a hash containing the configuration, e.g. the version number, lib loaded etc. The following hash keys are currently filled in with the appropriate information.

  1. key RO/RW Description
  2. Example
  3. ============================================================
  4. lib RO Name of the Math library
  5. Math::BigInt::Calc
  6. lib_version RO Version of 'lib'
  7. 0.30
  8. class RO The class of config you just called
  9. Math::BigRat
  10. version RO version number of the class you used
  11. 0.10
  12. upgrade RW To which class numbers are upgraded
  13. undef
  14. downgrade RW To which class numbers are downgraded
  15. undef
  16. precision RW Global precision
  17. undef
  18. accuracy RW Global accuracy
  19. undef
  20. round_mode RW Global round mode
  21. even
  22. div_scale RW Fallback acccuracy for div
  23. 40
  24. trap_nan RW Trap creation of NaN (undef = no)
  25. undef
  26. trap_inf RW Trap creation of +inf/-inf (undef = no)
  27. undef

By passing a reference to a hash you may set the configuration values. This works only for values that a marked with a RW above, anything else is read-only.


Some things are not yet implemented, or only implemented half-way:

  • inf handling (partial)
  • NaN handling (partial)
  • rounding (not implemented except for bceil/bfloor)
  • $x ** $y where $y is not an integer
  • bmod(), blog(), bmodinv() and bmodpow() (partial)


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


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

See for a way to use Math::BigRat.

The package at may contain more documentation and examples as well as testcases.


(C) by Tels 2001 - 2005.