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.\" ========================================================================
.\"
.IX Title "Math::BigRat 3"
.TH Math::BigRat 3 "2009-09-09" "perl v5.8.8" "User Contributed Perl Documentation"
.SH "NAME"
Math::BigRat \- Arbitrary big rational numbers
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&        use Math::BigRat;
.Ve
.PP
.Vb 1
\&        my $x = Math::BigRat->new('3/7'); $x += '5/9';
.Ve
.PP
.Vb 2
\&        print $x->bstr(),"\en";
\&        print $x ** 2,"\en";
.Ve
.PP
.Vb 2
\&        my $y = Math::BigRat->new('inf');
\&        print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\en";
.Ve
.PP
.Vb 1
\&        my $z = Math::BigRat->new(144); $z->bsqrt();
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
Math::BigRat complements Math::BigInt and Math::BigFloat by providing support
for arbitrary big rational numbers.
.Sh "\s-1MATH\s0 \s-1LIBRARY\s0"
.IX Subsection "MATH LIBRARY"
You can change the underlying module that does the low-level
math operations by using:
.PP
.Vb 1
\&        use Math::BigRat try => 'GMP';
.Ve
.PP
Note: This needs Math::BigInt::GMP installed.
.PP
The following would first try to find Math::BigInt::Foo, then
Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
.PP
.Vb 1
\&        use Math::BigRat try => 'Foo,Math::BigInt::Bar';
.Ve
.PP
If you want to get warned when the fallback occurs, replace \*(L"try\*(R" with
\&\*(L"lib\*(R":
.PP
.Vb 1
\&        use Math::BigRat lib => 'Foo,Math::BigInt::Bar';
.Ve
.PP
If you want the code to die instead, replace \*(L"try\*(R" with
\&\*(L"only\*(R":
.PP
.Vb 1
\&        use Math::BigRat only => 'Foo,Math::BigInt::Bar';
.Ve
.SH "METHODS"
.IX Header "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.
.Sh "\fInew()\fP"
.IX Subsection "new()"
.Vb 1
\&        $x = Math::BigRat->new('1/3');
.Ve
.PP
Create a new Math::BigRat object. Input can come in various forms:
.PP
.Vb 9
\&        $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
.Ve
.PP
.Vb 5
\&        # You can also give D and N as different objects:
\&        $x = Math::BigRat->new(
\&                Math::BigInt->new(-123),
\&                Math::BigInt->new(7),
\&                );                      # => -123/7
.Ve
.Sh "\fInumerator()\fP"
.IX Subsection "numerator()"
.Vb 1
\&        $n = $x->numerator();
.Ve
.PP
Returns a copy of the numerator (the part above the line) as signed BigInt.
.Sh "\fIdenominator()\fP"
.IX Subsection "denominator()"
.Vb 1
\&        $d = $x->denominator();
.Ve
.PP
Returns a copy of the denominator (the part under the line) as positive BigInt.
.Sh "\fIparts()\fP"
.IX Subsection "parts()"
.Vb 1
\&        ($n,$d) = $x->parts();
.Ve
.PP
Return a list consisting of (signed) numerator and (unsigned) denominator as
BigInts.
.Sh "\fInumify()\fP"
.IX Subsection "numify()"
.Vb 1
\&        my $y = $x->numify();
.Ve
.PP
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 \fIas_int()\fR or \fIas_float()\fR instead.
.PP
This routine is automatically used whenever a scalar is required:
.PP
.Vb 3
\&        my $x = Math::BigRat->new('3/1');
\&        @array = (0,1,2,3);
\&        $y = $array[$x];                # set $y to 3
.Ve
.Sh "\fIas_int()\fP/\fIas_number()\fP"
.IX Subsection "as_int()/as_number()"
.Vb 2
\&        $x = Math::BigRat->new('13/7');
\&        print $x->as_int(),"\en";                # '1'
.Ve
.PP
Returns a copy of the object as BigInt, truncated to an integer.
.PP
\&\f(CW\*(C`as_number()\*(C'\fR is an alias for \f(CW\*(C`as_int()\*(C'\fR.
.Sh "\fIas_float()\fP"
.IX Subsection "as_float()"
.Vb 2
\&        $x = Math::BigRat->new('13/7');
\&        print $x->as_float(),"\en";              # '1'
.Ve
.PP
.Vb 2
\&        $x = Math::BigRat->new('2/3');
\&        print $x->as_float(5),"\en";             # '0.66667'
.Ve
.PP
Returns a copy of the object as BigFloat, preserving the
accuracy as wanted, or the default of 40 digits.
.PP
This method was added in v0.22 of Math::BigRat (April 2008).
.Sh "\fIas_hex()\fP"
.IX Subsection "as_hex()"
.Vb 2
\&        $x = Math::BigRat->new('13');
\&        print $x->as_hex(),"\en";                # '0xd'
.Ve
.PP
Returns the BigRat as hexadecimal string. Works only for integers. 
.Sh "\fIas_bin()\fP"
.IX Subsection "as_bin()"
.Vb 2
\&        $x = Math::BigRat->new('13');
\&        print $x->as_bin(),"\en";                # '0x1101'
.Ve
.PP
Returns the BigRat as binary string. Works only for integers. 
.Sh "\fIas_oct()\fP"
.IX Subsection "as_oct()"
.Vb 2
\&        $x = Math::BigRat->new('13');
\&        print $x->as_oct(),"\en";                # '015'
.Ve
.PP
Returns the BigRat as octal string. Works only for integers. 
.Sh "\fIfrom_hex()\fP/\fIfrom_bin()\fP/\fIfrom_oct()\fP"
.IX Subsection "from_hex()/from_bin()/from_oct()"
.Vb 3
\&        my $h = Math::BigRat->from_hex('0x10');
\&        my $b = Math::BigRat->from_bin('0b10000000');
\&        my $o = Math::BigRat->from_oct('020');
.Ve
.PP
Create a BigRat from an hexadecimal, binary or octal number
in string form.
.Sh "\fIlength()\fP"
.IX Subsection "length()"
.Vb 1
\&        $len = $x->length();
.Ve
.PP
Return the length of \f(CW$x\fR in digitis for integer values.
.Sh "\fIdigit()\fP"
.IX Subsection "digit()"
.Vb 2
\&        print Math::BigRat->new('123/1')->digit(1);     # 1
\&        print Math::BigRat->new('123/1')->digit(-1);    # 3
.Ve
.PP
Return the N'ths digit from X when X is an integer value.
.Sh "\fIbnorm()\fP"
.IX Subsection "bnorm()"
.Vb 1
\&        $x->bnorm();
.Ve
.PP
Reduce the number to the shortest form. This routine is called
automatically whenever it is needed.
.Sh "\fIbfac()\fP"
.IX Subsection "bfac()"
.Vb 1
\&        $x->bfac();
.Ve
.PP
Calculates the factorial of \f(CW$x\fR. For instance:
.PP
.Vb 2
\&        print Math::BigRat->new('3/1')->bfac(),"\en";    # 1*2*3
\&        print Math::BigRat->new('5/1')->bfac(),"\en";    # 1*2*3*4*5
.Ve
.PP
Works currently only for integers.
.Sh "\fIbround()\fP/\fIround()\fP/\fIbfround()\fP"
.IX Subsection "bround()/round()/bfround()"
Are not yet implemented.
.Sh "\fIbmod()\fP"
.IX Subsection "bmod()"
.Vb 4
\&        use Math::BigRat;
\&        my $x = Math::BigRat->new('7/4');
\&        my $y = Math::BigRat->new('4/3');
\&        print $x->bmod($y);
.Ve
.PP
Set \f(CW$x\fR to the remainder of the division of \f(CW$x\fR by \f(CW$y\fR.
.Sh "\fIbneg()\fP"
.IX Subsection "bneg()"
.Vb 1
\&        $x->bneg();
.Ve
.PP
Used to negate the object in\-place.
.Sh "\fIis_one()\fP"
.IX Subsection "is_one()"
.Vb 1
\&        print "$x is 1\en" if $x->is_one();
.Ve
.PP
Return true if \f(CW$x\fR is exactly one, otherwise false.
.Sh "\fIis_zero()\fP"
.IX Subsection "is_zero()"
.Vb 1
\&        print "$x is 0\en" if $x->is_zero();
.Ve
.PP
Return true if \f(CW$x\fR is exactly zero, otherwise false.
.Sh "\fIis_pos()\fP/\fIis_positive()\fP"
.IX Subsection "is_pos()/is_positive()"
.Vb 1
\&        print "$x is >= 0\en" if $x->is_positive();
.Ve
.PP
Return true if \f(CW$x\fR is positive (greater than or equal to zero), otherwise
false. Please note that '+inf' is also positive, while 'NaN' and '\-inf' aren't.
.PP
\&\f(CW\*(C`is_positive()\*(C'\fR is an alias for \f(CW\*(C`is_pos()\*(C'\fR.
.Sh "\fIis_neg()\fP/\fIis_negative()\fP"
.IX Subsection "is_neg()/is_negative()"
.Vb 1
\&        print "$x is < 0\en" if $x->is_negative();
.Ve
.PP
Return true if \f(CW$x\fR is negative (smaller than zero), otherwise false. Please
note that '\-inf' is also negative, while 'NaN' and '+inf' aren't.
.PP
\&\f(CW\*(C`is_negative()\*(C'\fR is an alias for \f(CW\*(C`is_neg()\*(C'\fR.
.Sh "\fIis_int()\fP"
.IX Subsection "is_int()"
.Vb 1
\&        print "$x is an integer\en" if $x->is_int();
.Ve
.PP
Return true if \f(CW$x\fR has a denominator of 1 (e.g. no fraction parts), otherwise
false. Please note that '\-inf', 'inf' and 'NaN' aren't integer.
.Sh "\fIis_odd()\fP"
.IX Subsection "is_odd()"
.Vb 1
\&        print "$x is odd\en" if $x->is_odd();
.Ve
.PP
Return true if \f(CW$x\fR is odd, otherwise false.
.Sh "\fIis_even()\fP"
.IX Subsection "is_even()"
.Vb 1
\&        print "$x is even\en" if $x->is_even();
.Ve
.PP
Return true if \f(CW$x\fR is even, otherwise false.
.Sh "\fIbceil()\fP"
.IX Subsection "bceil()"
.Vb 1
\&        $x->bceil();
.Ve
.PP
Set \f(CW$x\fR to the next bigger integer value (e.g. truncate the number to integer
and then increment it by one).
.Sh "\fIbfloor()\fP"
.IX Subsection "bfloor()"
.Vb 1
\&        $x->bfloor();
.Ve
.PP
Truncate \f(CW$x\fR to an integer value.
.Sh "\fIbsqrt()\fP"
.IX Subsection "bsqrt()"
.Vb 1
\&        $x->bsqrt();
.Ve
.PP
Calculate the square root of \f(CW$x\fR.
.Sh "\fIbroot()\fP"
.IX Subsection "broot()"
.Vb 1
\&        $x->broot($n);
.Ve
.PP
Calculate the N'th root of \f(CW$x\fR.
.Sh "\fIbadd()\fP/\fIbmul()\fP/\fIbsub()\fP/\fIbdiv()\fP/\fIbdec()\fP/\fIbinc()\fP"
.IX Subsection "badd()/bmul()/bsub()/bdiv()/bdec()/binc()"
Please see the documentation in Math::BigInt.
.Sh "\fIcopy()\fP"
.IX Subsection "copy()"
.Vb 1
\&        my $z = $x->copy();
.Ve
.PP
Makes a deep copy of the object.
.PP
Please see the documentation in Math::BigInt for further details.
.Sh "\fIbstr()\fP/\fIbsstr()\fP"
.IX Subsection "bstr()/bsstr()"
.Vb 3
\&        my $x = Math::BigInt->new('8/4');
\&        print $x->bstr(),"\en";                  # prints 1/2
\&        print $x->bsstr(),"\en";                 # prints 1/2
.Ve
.PP
Return a string representating this object.
.Sh "\fIbacmp()\fP/\fIbcmp()\fP"
.IX Subsection "bacmp()/bcmp()"
Used to compare numbers.
.PP
Please see the documentation in Math::BigInt for further details.
.Sh "\fIblsft()\fP/\fIbrsft()\fP"
.IX Subsection "blsft()/brsft()"
Used to shift numbers left/right.
.PP
Please see the documentation in Math::BigInt for further details.
.Sh "\fIbpow()\fP"
.IX Subsection "bpow()"
.Vb 1
\&        $x->bpow($y);
.Ve
.PP
Compute \f(CW$x\fR ** \f(CW$y\fR.
.PP
Please see the documentation in Math::BigInt for further details.
.Sh "\fIbexp()\fP"
.IX Subsection "bexp()"
.Vb 1
\&        $x->bexp($accuracy);            # calculate e ** X
.Ve
.PP
Calculates two integers A and B so that A/B is equal to \f(CW\*(C`e ** $x\*(C'\fR, where \f(CW\*(C`e\*(C'\fR is
Euler's number.
.PP
This method was added in v0.20 of Math::BigRat (May 2007).
.PP
See also \fIblog()\fR.
.Sh "\fIbnok()\fP"
.IX Subsection "bnok()"
.Vb 1
\&        $x->bnok($y);              # x over y (binomial coefficient n over k)
.Ve
.PP
Calculates the binomial coefficient n over k, also called the \*(L"choose\*(R"
function. The result is equivalent to:
.PP
.Vb 3
\&        ( n )      n!
\&        | - |  = -------
\&        ( k )    k!(n-k)!
.Ve
.PP
This method was added in v0.20 of Math::BigRat (May 2007).
.Sh "\fIconfig()\fP"
.IX Subsection "config()"
.Vb 1
\&        use Data::Dumper;
.Ve
.PP
.Vb 2
\&        print Dumper ( Math::BigRat->config() );
\&        print Math::BigRat->config()->{lib},"\en";
.Ve
.PP
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.
.PP
.Vb 27
\&        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
.Ve
.PP
By passing a reference to a hash you may set the configuration values. This
works only for values that a marked with a \f(CW\*(C`RW\*(C'\fR above, anything else is
read\-only.
.Sh "\fIobjectify()\fP"
.IX Subsection "objectify()"
This is an internal routine that turns scalars into objects.
.SH "BUGS"
.IX Header "BUGS"
Some things are not yet implemented, or only implemented half\-way:
.IP "inf handling (partial)" 2
.IX Item "inf handling (partial)"
.PD 0
.IP "NaN handling (partial)" 2
.IX Item "NaN handling (partial)"
.IP "rounding (not implemented except for bceil/bfloor)" 2
.IX Item "rounding (not implemented except for bceil/bfloor)"
.ie n .IP "$x ** $y\fR where \f(CW$y is not an integer" 2
.el .IP "$x ** \f(CW$y\fR where \f(CW$y\fR is not an integer" 2
.IX Item "$x ** $y where $y is not an integer"
.IP "\fIbmod()\fR, \fIblog()\fR, \fIbmodinv()\fR and \fIbmodpow()\fR (partial)" 2
.IX Item "bmod(), blog(), bmodinv() and bmodpow() (partial)"
.PD
.SH "LICENSE"
.IX Header "LICENSE"
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Math::BigFloat and Math::Big as well as Math::BigInt::BitVect,
Math::BigInt::Pari and  Math::BigInt::GMP.
.PP
See <http://search.cpan.org/search?dist=bignum> for a way to use
Math::BigRat.
.PP
The package at <http://search.cpan.org/search?dist=Math%3A%3ABigRat>
may contain more documentation and examples as well as testcases.
.SH "AUTHORS"
.IX Header "AUTHORS"
(C) by Tels <http://bloodgate.com/> 2001 \- 2009.
.PP
Currently maintained by Jonathan \*(L"Duke\*(R" Leto <jonathan@leto.net> <http://leto.net>