Math::BigRat - Arbitrary big rational numbers

- NAME
- SYNOPSIS
- DESCRIPTION

- MATH LIBRARY

- METHODS

- `new()`
- `numerator()`
- `denominator()`
- `parts()`
- `numify()`
- as_int()/as_number()
- `as_hex()`
- `as_bin()`
- `as_oct()`
- from_hex()/from_bin()/from_oct()
- `length()`
- `digit()`
- `bnorm()`
- `bfac()`
- bround()/round()/bfround()
- `bmod()`
- `bneg()`
- `is_one()`
- `is_zero()`
- is_pos()/is_positive()
- is_neg()/is_negative()
- `is_int()`
- `is_odd()`
- `is_even()`
- `bceil()`
- `bfloor()`
- `bsqrt()`
- `broot()`
- badd()/bmul()/bsub()/bdiv()/bdec()/binc()
- `copy()`
- bstr()/bsstr()
- bacmp()/bcmp()
- blsft()/brsft()
- `bpow()`
- `bexp()`
- `bnok()`
- `config()`

- BUGS
- 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()` instead.

This routine is automatically used whenever a scalar is required:

            my $x = Math::BigRat->new('3/1');
            @array = (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_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()/from_bin()/from_oct()

            my $h = Math::BigRat->from_hex('0x10');
            my $b = Math::BigRat->from_bin('0b10000000');
            my $o = Math::BigRat->from_oct('020');

Create a BigRat from an hexadecimal, binary or octal number in string form.

## `length()`

            $len = $x->length();

Return the length of $x in digitis 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()`

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

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

## `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.

## `bsqrt()`

            $x->bsqrt();

Calculate the square root of $x.

## `broot()`

            $x->broot($n);

Calculate the N'th root of $x.

## badd()/bmul()/bsub()/bdiv()/bdec()/binc()

Please see the documentation in the Math::BigInt manpage.

## `copy()`

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

Makes a deep copy of the object.

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

## bstr()/bsstr()

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

Return a string representating this object.

## bacmp()/bcmp()

Used to compare numbers.

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

## blsft()/brsft()

Used to shift numbers left/right.

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

## `bpow()`

            $x->bpow($y);

Compute $x ** $y.

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

## `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

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)

# LICENSE

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

# SEE ALSO

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

See http://search.cpan.org/search for a way to use Math::BigRat.

The package at http://search.cpan.org/search may contain more documentation and examples as well as testcases.

# AUTHORS

(C) by Tels http://bloodgate.com/ 2001 - 2007.

Math::BigRat - Arbitrary big rational numbers