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.\" ========================================================================
.\"
.IX Title "Math::BigRat 3"
.TH Math::BigRat 3 "2013-03-04" "perl v5.16.3" "Perl Programmers Reference Guide"
.\" For nroff, turn off justification. Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
Math::BigRat \- Arbitrary big rational numbers
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& use Math::BigRat;
\&
\& my $x = Math::BigRat\->new(\*(Aq3/7\*(Aq); $x += \*(Aq5/9\*(Aq;
\&
\& print $x\->bstr(),"\en";
\& print $x ** 2,"\en";
\&
\& my $y = Math::BigRat\->new(\*(Aqinf\*(Aq);
\& print "$y ", ($y\->is_inf ? \*(Aqis\*(Aq : \*(Aqis not\*(Aq) , " infinity\en";
\&
\& 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.
.SS "\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 => \*(AqGMP\*(Aq;
.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 => \*(AqFoo,Math::BigInt::Bar\*(Aq;
.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 => \*(AqFoo,Math::BigInt::Bar\*(Aq;
.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 => \*(AqFoo,Math::BigInt::Bar\*(Aq;
.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.
.SS "\fInew()\fP"
.IX Subsection "new()"
.Vb 1
\& $x = Math::BigRat\->new(\*(Aq1/3\*(Aq);
.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(\*(Aqinf\*(Aq); # infinity
\& $x = Math::BigRat\->new(\*(Aq123.3\*(Aq); # float
\& $x = Math::BigRat\->new(\*(Aq1/3\*(Aq); # simple string
\& $x = Math::BigRat\->new(\*(Aq1 / 3\*(Aq); # spaced
\& $x = Math::BigRat\->new(\*(Aq1 / 0.1\*(Aq); # w/ floats
\& $x = Math::BigRat\->new(Math::BigInt\->new(3)); # BigInt
\& $x = Math::BigRat\->new(Math::BigFloat\->new(\*(Aq3.1\*(Aq)); # BigFloat
\& $x = Math::BigRat\->new(Math::BigInt::Lite\->new(\*(Aq2\*(Aq)); # 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
.Ve
.SS "\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.
.SS "\fIdenominator()\fP"
.IX Subsection "denominator()"
.Vb 1
\& $d = $x\->denominator();
.Ve
.PP
Returns a copy of the denominator (the part under the line) as positive BigInt.
.SS "\fIparts()\fP"
.IX Subsection "parts()"
.Vb 1
\& ($n,$d) = $x\->parts();
.Ve
.PP
Return a list consisting of (signed) numerator and (unsigned) denominator as
BigInts.
.SS "\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(\*(Aq3/1\*(Aq);
\& @array = (0,1,2,3);
\& $y = $array[$x]; # set $y to 3
.Ve
.SS "\fIas_int()\fP/\fIas_number()\fP"
.IX Subsection "as_int()/as_number()"
.Vb 2
\& $x = Math::BigRat\->new(\*(Aq13/7\*(Aq);
\& print $x\->as_int(),"\en"; # \*(Aq1\*(Aq
.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.
.SS "\fIas_float()\fP"
.IX Subsection "as_float()"
.Vb 2
\& $x = Math::BigRat\->new(\*(Aq13/7\*(Aq);
\& print $x\->as_float(),"\en"; # \*(Aq1\*(Aq
\&
\& $x = Math::BigRat\->new(\*(Aq2/3\*(Aq);
\& print $x\->as_float(5),"\en"; # \*(Aq0.66667\*(Aq
.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).
.SS "\fIas_hex()\fP"
.IX Subsection "as_hex()"
.Vb 2
\& $x = Math::BigRat\->new(\*(Aq13\*(Aq);
\& print $x\->as_hex(),"\en"; # \*(Aq0xd\*(Aq
.Ve
.PP
Returns the BigRat as hexadecimal string. Works only for integers.
.SS "\fIas_bin()\fP"
.IX Subsection "as_bin()"
.Vb 2
\& $x = Math::BigRat\->new(\*(Aq13\*(Aq);
\& print $x\->as_bin(),"\en"; # \*(Aq0x1101\*(Aq
.Ve
.PP
Returns the BigRat as binary string. Works only for integers.
.SS "\fIas_oct()\fP"
.IX Subsection "as_oct()"
.Vb 2
\& $x = Math::BigRat\->new(\*(Aq13\*(Aq);
\& print $x\->as_oct(),"\en"; # \*(Aq015\*(Aq
.Ve
.PP
Returns the BigRat as octal string. Works only for integers.
.SS "\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(\*(Aq0x10\*(Aq);
\& my $b = Math::BigRat\->from_bin(\*(Aq0b10000000\*(Aq);
\& my $o = Math::BigRat\->from_oct(\*(Aq020\*(Aq);
.Ve
.PP
Create a BigRat from an hexadecimal, binary or octal number
in string form.
.SS "\fIlength()\fP"
.IX Subsection "length()"
.Vb 1
\& $len = $x\->length();
.Ve
.PP
Return the length of \f(CW$x\fR in digits for integer values.
.SS "\fIdigit()\fP"
.IX Subsection "digit()"
.Vb 2
\& print Math::BigRat\->new(\*(Aq123/1\*(Aq)\->digit(1); # 1
\& print Math::BigRat\->new(\*(Aq123/1\*(Aq)\->digit(\-1); # 3
.Ve
.PP
Return the N'ths digit from X when X is an integer value.
.SS "\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.
.SS "\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(\*(Aq3/1\*(Aq)\->bfac(),"\en"; # 1*2*3
\& print Math::BigRat\->new(\*(Aq5/1\*(Aq)\->bfac(),"\en"; # 1*2*3*4*5
.Ve
.PP
Works currently only for integers.
.SS "\fIbround()\fP/\fIround()\fP/\fIbfround()\fP"
.IX Subsection "bround()/round()/bfround()"
Are not yet implemented.
.SS "\fIbmod()\fP"
.IX Subsection "bmod()"
.Vb 4
\& use Math::BigRat;
\& my $x = Math::BigRat\->new(\*(Aq7/4\*(Aq);
\& my $y = Math::BigRat\->new(\*(Aq4/3\*(Aq);
\& 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.
.SS "\fIbneg()\fP"
.IX Subsection "bneg()"
.Vb 1
\& $x\->bneg();
.Ve
.PP
Used to negate the object in-place.
.SS "\fIis_one()\fP"
.IX Subsection "is_one()"
.Vb 1
\& print "$x is 1\en" if $x\->is_one();
.Ve
.PP
Return true if \f(CW$x\fR is exactly one, otherwise false.
.SS "\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.
.SS "\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.
.SS "\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.
.SS "\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.
.SS "\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.
.SS "\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.
.SS "\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).
.SS "\fIbfloor()\fP"
.IX Subsection "bfloor()"
.Vb 1
\& $x\->bfloor();
.Ve
.PP
Truncate \f(CW$x\fR to an integer value.
.SS "\fIbsqrt()\fP"
.IX Subsection "bsqrt()"
.Vb 1
\& $x\->bsqrt();
.Ve
.PP
Calculate the square root of \f(CW$x\fR.
.SS "\fIbroot()\fP"
.IX Subsection "broot()"
.Vb 1
\& $x\->broot($n);
.Ve
.PP
Calculate the N'th root of \f(CW$x\fR.
.SS "\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.
.SS "\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.
.SS "\fIbstr()\fP/\fIbsstr()\fP"
.IX Subsection "bstr()/bsstr()"
.Vb 3
\& my $x = Math::BigInt\->new(\*(Aq8/4\*(Aq);
\& print $x\->bstr(),"\en"; # prints 1/2
\& print $x\->bsstr(),"\en"; # prints 1/2
.Ve
.PP
Return a string representing this object.
.SS "\fIbacmp()\fP/\fIbcmp()\fP"
.IX Subsection "bacmp()/bcmp()"
Used to compare numbers.
.PP
Please see the documentation in Math::BigInt for further details.
.SS "\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.
.SS "\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.
.SS "\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.
.SS "\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).
.SS "\fIconfig()\fP"
.IX Subsection "config()"
.Vb 1
\& use Data::Dumper;
\&
\& 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 10
\& key RO/RW Description
\& Example
\& ============================================================
\& lib RO Name of the Math library
\& Math::BigInt::Calc
\& lib_version RO Version of \*(Aqlib\*(Aq
\& 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.
.SS "\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 where $y is not an integer" 2
.el .IP "\f(CW$x\fR ** \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>
y~or5J ={Eeu磝Qk ᯘG{?+]ן?wM3X^歌>{7پK>on\jy R g/=fOroNVv~Y+ NGuÝHWyw[eQʨSb> >}Gmx[o[<{Ϯ_qF vM IENDB`
