# 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()/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.

Please see the documentation in Math::BigInt.

## 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::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 Math::BigInt for further details.

## blsft()/brsft()

Used to shift numbers left/right.

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

## bpow()

``        \$x->bpow(\$y);``

Compute \$x ** \$y.

Please see the documentation in Math::BigInt 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).

## 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
undef
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.

## objectify()

This is an internal routine that turns scalars into objects.

# 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)

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