Math::BigRat - Arbitrary big rational numbers

- NAME
- SYNOPSIS
- DESCRIPTION
  - MATH LIBRARY
- METHODS
- BUGS
- SUPPORT
- LICENSE
- SEE ALSO
- AUTHORS

# NAME

Math::BigRat - Arbitrary big rational numbers

# SYNOPSIS

        use Math::BigRat;

        my $x = Math::BigRat->new('3/7'); $x += '5/9';

        print $x->bstr(), "\n";
        print $x ** 2, "\n";

        my $y = Math::BigRat->new('inf');
        print "$y ", ($y->is_inf ? 'is' : 'is not'), " infinity\n";

        my $z = Math::BigRat->new(144); $z->bsqrt();

# DESCRIPTION

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

## MATH LIBRARY

You can change the underlying module that does the low-level math operations by using:

        use Math::BigRat try => 'GMP';

Note: This needs Math::BigInt::GMP installed.

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 Math::BigRat try => 'Foo,Math::BigInt::Bar';

If you want to get warned when the fallback occurs, replace "try" with "lib":

        use Math::BigRat lib => 'Foo,Math::BigInt::Bar';

If you want the code to die instead, replace "try" with "only":

        use Math::BigRat only => 'Foo,Math::BigInt::Bar';

# METHODS

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

new()

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

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

          $x = Math::BigRat->new(123);                            # scalars
          $x = Math::BigRat->new('inf');                          # infinity
          $x = Math::BigRat->new('123.3');                        # float
          $x = Math::BigRat->new('1/3');                          # simple string
          $x = Math::BigRat->new('1 / 3');                        # spaced
          $x = Math::BigRat->new('1 / 0.1');                      # w/ floats
          $x = Math::BigRat->new(Math::BigInt->new(3));           # BigInt
          $x = Math::BigRat->new(Math::BigFloat->new('3.1'));     # BigFloat
          $x = Math::BigRat->new(Math::BigInt::Lite->new('2'));   # BigLite

          # You can also give D and N as different objects:
          $x = Math::BigRat->new(
                  Math::BigInt->new(-123),
                  Math::BigInt->new(7),
               );                      # => -123/7

numerator()

          $n = $x->numerator();

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

denominator()

          $d = $x->denominator();

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

parts()

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

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

numify()

          my $y = $x->numify();

  Returns the object as a scalar. This will lose some data if the object cannot be represented by a normal Perl scalar (integer or float), so use as_int() or "as_float()" instead.

  This routine is automatically used whenever a scalar is required:

          my $x = Math::BigRat->new('3/1');
          @array = (0, 1, 2, 3);
          $y = $array[$x];                # set $y to 3

as_int()/as_number()

          $x = Math::BigRat->new('13/7');
          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()`.

as_float()

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

          $x = Math::BigRat->new('2/3');
          print $x->as_float(5), "\n";            # '0.66667'

  Returns a copy of the object as BigFloat, preserving the accuracy as wanted, or the default of 40 digits.

  This method was added in v0.22 of Math::BigRat (April 2008).

as_hex()

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

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

as_bin()

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

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

as_oct()

          $x = Math::BigRat->new('13');
          print $x->as_oct(), "\n";               # '015'

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

from_hex()

          my $h = Math::BigRat->from_hex('0x10');

  Create a BigRat from a hexadecimal number in string form.

from_oct()

          my $o = Math::BigRat->from_oct('020');

  Create a BigRat from an octal number in string form.

from_bin()

          my $b = Math::BigRat->from_bin('0b10000000');

  Create a BigRat from an binary number in string form.

bnan()

          $x = Math::BigRat->bnan();

  Creates a new BigRat object representing NaN (Not A Number). If used on an object, it will set it to NaN:

          $x->bnan();

bzero()

          $x = Math::BigRat->bzero();

  Creates a new BigRat object representing zero. If used on an object, it will set it to zero:

          $x->bzero();

binf()

          $x = Math::BigRat->binf($sign);

  Creates a new BigRat object representing infinity. The optional argument is either '-' or '+', indicating whether you want infinity or minus infinity. If used on an object, it will set it to infinity:

          $x->binf();
          $x->binf('-');

bone()

          $x = Math::BigRat->bone($sign);

  Creates a new BigRat object representing one. The optional argument is either '-' or '+', indicating whether you want one or minus one. If used on an object, it will set it to one:

          $x->bone();                 # +1
          $x->bone('-');              # -1

length()

          $len = $x->length();

  Return the length of $x in digits for integer values.

digit()

          print Math::BigRat->new('123/1')->digit(1);     # 1
          print Math::BigRat->new('123/1')->digit(-1);    # 3

  Return the N'ths digit from X when X is an integer value.

bnorm()

          $x->bnorm();

  Reduce the number to the shortest form. This routine is called automatically whenever it is needed.

bfac()

          $x->bfac();

  Calculates the factorial of $x. For instance:

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

  Works currently only for integers.

bround()/round()/bfround()

  Are not yet implemented.

bmod()

          $x->bmod($y);

  Returns $x modulo $y. When $x is finite, and $y is finite and non-zero, the result is identical to the remainder after floored division (F-division). If, in addition, both $x and $y are integers, the result is identical to the result from Perl's % operator.

bmodinv()

          $x->bmodinv($mod);          # modular multiplicative inverse

  Returns the multiplicative inverse of `$x` modulo `$mod`. If

          $y = $x -> copy() -> bmodinv($mod)

  then `$y` is the number closest to zero, and with the same sign as `$mod`, satisfying

          ($x * $y) % $mod = 1 % $mod

  If `$x` and `$y` are non-zero, they must be relative primes, i.e., `bgcd($y, $mod)==1`. '`NaN`' is returned when no modular multiplicative inverse exists.

bmodpow()

          $num->bmodpow($exp,$mod);           # modular exponentiation
                                              # ($num**$exp % $mod)

  Returns the value of `$num` taken to the power `$exp` in the modulus `$mod` using binary exponentiation. `bmodpow` is far superior to writing

          $num ** $exp % $mod

  because it is much faster - it reduces internal variables into the modulus whenever possible, so it operates on smaller numbers.

  `bmodpow` also supports negative exponents.

          bmodpow($num, -1, $mod)

  is exactly equivalent to

          bmodinv($num, $mod)

bneg()

          $x->bneg();

  Used to negate the object in-place.

is_one()

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

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

is_zero()

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

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

is_pos()/is_positive()

          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()`.

is_neg()/is_negative()

          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()`.

is_int()

          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.

is_odd()

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

  Return true if $x is odd, otherwise false.

is_even()

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

  Return true if $x is even, otherwise false.

bceil()

          $x->bceil();

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

bfloor()

          $x->bfloor();

  Truncate $x to an integer value.

bint()

          $x->bint();

  Round $x towards zero.

bsqrt()

          $x->bsqrt();

  Calculate the square root of $x.

broot()

          $x->broot($n);

  Calculate the N'th root of $x.

badd()

          $x->badd($y);

  Adds $y to $x and returns the result.

bmul()

          $x->bmul($y);

  Multiplies $y to $x and returns the result.

bsub()

          $x->bsub($y);

  Subtracts $y from $x and returns the result.

bdiv()

          $q = $x->bdiv($y);
          ($q, $r) = $x->bdiv($y);

  In scalar context, divides $x by $y and returns the result. In list context, does floored division (F-division), returning an integer $q and a remainder $r so that $x = $q * $y + $r. The remainer (modulo) is equal to what is returned by `$x-`bmod($y)>.

bdec()

          $x->bdec();

  Decrements $x by 1 and returns the result.

binc()

          $x->binc();

  Increments $x by 1 and returns the result.

copy()

          my $z = $x->copy();

  Makes a deep copy of the object.

  Please see the documentation in Math::BigInt for further details.

bstr()/bsstr()

          my $x = Math::BigRat->new('8/4');
          print $x->bstr(), "\n";             # prints 1/2
          print $x->bsstr(), "\n";            # prints 1/2

  Return a string representing this object.

bcmp()

          $x->bcmp($y);

  Compares $x with $y and takes the sign into account. Returns -1, 0, 1 or undef.

bacmp()

          $x->bacmp($y);

  Compares $x with $y while ignoring their sign. Returns -1, 0, 1 or undef.

beq()

          $x -> beq($y);

  Returns true if and only if $x is equal to $y, and false otherwise.

bne()

          $x -> bne($y);

  Returns true if and only if $x is not equal to $y, and false otherwise.

blt()

          $x -> blt($y);

  Returns true if and only if $x is equal to $y, and false otherwise.

ble()

          $x -> ble($y);

  Returns true if and only if $x is less than or equal to $y, and false otherwise.

bgt()

          $x -> bgt($y);

  Returns true if and only if $x is greater than $y, and false otherwise.

bge()

          $x -> bge($y);

  Returns true if and only if $x is greater than or equal to $y, and false otherwise.

blsft()/brsft()

  Used to shift numbers left/right.

  Please see the documentation in Math::BigInt for further details.

band()

          $x->band($y);               # bitwise and

bior()

          $x->bior($y);               # bitwise inclusive or

bxor()

          $x->bxor($y);               # bitwise exclusive or

bnot()

          $x->bnot();                 # bitwise not (two's complement)

bpow()

          $x->bpow($y);

  Compute $x ** $y.

  Please see the documentation in Math::BigInt for further details.

blog()

          $x->blog($base, $accuracy);         # logarithm of x to the base $base

  If `$base` is not defined, Euler's number (e) is used:

          print $x->blog(undef, 100);         # log(x) to 100 digits

bexp()

          $x->bexp($accuracy);        # calculate e ** X

  Calculates two integers A and B so that A/B is equal to `e ** $x`, where `e` is Euler's number.

  This method was added in v0.20 of Math::BigRat (May 2007).

  See also `blog()`.

bnok()

          $x->bnok($y);               # x over y (binomial coefficient n over k)

  Calculates the binomial coefficient n over k, also called the "choose" function. The result is equivalent to:

          ( n )      n!
          | - |  = -------
          ( k )    k!(n-k)!

  This method was added in v0.20 of Math::BigRat (May 2007).

config()

          use Data::Dumper;

          print Dumper ( Math::BigRat->config() );
          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.

          key             RO/RW   Description
                                  Example
          ============================================================
          lib             RO      Name of the Math library
                                  Math::BigInt::Calc
          lib_version     RO      Version of 'lib'
                                  0.30
          class           RO      The class of config you just called
                                  Math::BigRat
          version         RO      version number of the class you used
                                  0.10
          upgrade         RW      To which class numbers are upgraded
                                  undef
          downgrade       RW      To which class numbers are downgraded
                                  undef
          precision       RW      Global precision
                                  undef
          accuracy        RW      Global accuracy
                                  undef
          round_mode      RW      Global round mode
                                  even
          div_scale       RW      Fallback accuracy for div
                                  40
          trap_nan        RW      Trap creation of NaN (undef = no)
                                  undef
          trap_inf        RW      Trap creation of +inf/-inf (undef = no)
                                  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.

# BUGS

Please report any bugs or feature requests to `bug-math-bigrat at rt.cpan.org`, or through the web interface at https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigRat (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

# SUPPORT

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

        perldoc Math::BigRat

You can also look for information at:

- RT: CPAN's request tracker

  https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigRat

- AnnoCPAN: Annotated CPAN documentation

  http://annocpan.org/dist/Math-BigRat

- CPAN Ratings

  http://cpanratings.perl.org/dist/Math-BigRat

- Search CPAN

  http://search.cpan.org/dist/Math-BigRat/

- CPAN Testers Matrix

  http://matrix.cpantesters.org/?dist=Math-BigRat

- The Bignum mailing list

  - Post to mailing list

    `bignum at lists.scsys.co.uk`

  - View mailing list

    http://lists.scsys.co.uk/pipermail/bignum/

  - Subscribe/Unsubscribe

    http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum

# LICENSE

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

# SEE ALSO

bigrat, Math::BigFloat and Math::BigInt as well as the backends Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari.

# AUTHORS

- Tels http://bloodgate.com/ 2001-2009.

- Maintained by Peter John Acklam <pjacklam@online.no> 2011-

Math::BigRat - Arbitrary big rational numbers