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.\" ========================================================================
.\"
.IX Title "bigrat 3perl"
.TH bigrat 3perl 2024-05-30 "perl v5.38.2" "Perl Programmers Reference Guide"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
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.nh
.SH NAME
bigrat \- transparent big rational number support for Perl
.SH SYNOPSIS
.IX Header "SYNOPSIS"
.Vb 1
\&    use bigrat;
\&
\&    print 2 + 4.5;                      # Math::BigRat 13/2
\&    print 1/3 + 1/4;                    # Math::BigRat 7/12
\&    print inf + 42;                     # Math::BigRat inf
\&    print NaN * 7;                      # Math::BigRat NaN
\&    print hex("0x1234567890123490");    # Perl v5.10.0 or later
\&
\&    {
\&        no bigrat;
\&        print 1/3;                      # 0.33333...
\&    }
\&
\&    # for older Perls, import into current package:
\&    use bigrat qw/hex oct/;
\&    print hex("0x1234567890123490");
\&    print oct("01234567890123490");
.Ve
.SH DESCRIPTION
.IX Header "DESCRIPTION"
All numeric literal in the given scope are converted to Math::BigRat objects.
.PP
All operators (including basic math operations) except the range operator \f(CW\*(C`..\*(C'\fR
are overloaded.
.PP
So, the following:
.PP
.Vb 2
\&    use bigrat;
\&    $x = 1234;
.Ve
.PP
creates a Math::BigRat and stores a reference to in \f(CW$x\fR. This happens
transparently and behind your back, so to speak.
.PP
You can see this with the following:
.PP
.Vb 1
\&    perl \-Mbigrat \-le \*(Aqprint ref(1234)\*(Aq
.Ve
.PP
Since numbers are actually objects, you can call all the usual methods from
Math::BigRat on them. This even works to some extent on expressions:
.PP
.Vb 4
\&    perl \-Mbigrat \-le \*(Aq$x = 1234; print $x\->bdec()\*(Aq
\&    perl \-Mbigrat \-le \*(Aqprint 1234\->copy()\->binc();\*(Aq
\&    perl \-Mbigrat \-le \*(Aqprint 1234\->copy()\->binc\->badd(6);\*(Aq
\&    perl \-Mbigrat \-le \*(Aqprint +(1234)\->copy()\->binc()\*(Aq
.Ve
.PP
(Note that print doesn't do what you expect if the expression starts with
\&'(' hence the \f(CW\*(C`+\*(C'\fR)
.PP
You can even chain the operations together as usual:
.PP
.Vb 2
\&    perl \-Mbigrat \-le \*(Aqprint 1234\->copy()\->binc\->badd(6);\*(Aq
\&    1241
.Ve
.PP
Please note the following does not work as expected (prints nothing), since
overloading of '..' is not yet possible in Perl (as of v5.8.0):
.PP
.Vb 1
\&    perl \-Mbigrat \-le \*(Aqfor (1..2) { print ref($_); }\*(Aq
.Ve
.SS Options
.IX Subsection "Options"
\&\f(CW\*(C`bigrat\*(C'\fR recognizes some options that can be passed while loading it via
\&\f(CW\*(C`use\*(C'\fR. The following options exist:
.IP "a or accuracy" 4
.IX Item "a or accuracy"
This sets the accuracy for all math operations. The argument must be greater
than or equal to zero. See Math::BigInt's \fBbround()\fR method for details.
.Sp
.Vb 1
\&    perl \-Mbigrat=a,50 \-le \*(Aqprint sqrt(20)\*(Aq
.Ve
.Sp
Note that setting precision and accuracy at the same time is not possible.
.IP "p or precision" 4
.IX Item "p or precision"
This sets the precision for all math operations. The argument can be any
integer. Negative values mean a fixed number of digits after the dot, while a
positive value rounds to this digit left from the dot. 0 means round to integer.
See Math::BigInt's \fBbfround()\fR method for details.
.Sp
.Vb 1
\&    perl \-Mbigrat=p,\-50 \-le \*(Aqprint sqrt(20)\*(Aq
.Ve
.Sp
Note that setting precision and accuracy at the same time is not possible.
.IP "t or trace" 4
.IX Item "t or trace"
This enables a trace mode and is primarily for debugging.
.IP "l, lib, try, or only" 4
.IX Item "l, lib, try, or only"
Load a different math lib, see "Math Library".
.Sp
.Vb 4
\&    perl \-Mbigrat=l,GMP \-e \*(Aqprint 2 ** 512\*(Aq
\&    perl \-Mbigrat=lib,GMP \-e \*(Aqprint 2 ** 512\*(Aq
\&    perl \-Mbigrat=try,GMP \-e \*(Aqprint 2 ** 512\*(Aq
\&    perl \-Mbigrat=only,GMP \-e \*(Aqprint 2 ** 512\*(Aq
.Ve
.IP hex 4
.IX Item "hex"
Override the built-in \fBhex()\fR method with a version that can handle big numbers.
This overrides it by exporting it to the current package. Under Perl v5.10.0 and
higher, this is not so necessary, as \fBhex()\fR is lexically overridden in the
current scope whenever the \f(CW\*(C`bigrat\*(C'\fR pragma is active.
.IP oct 4
.IX Item "oct"
Override the built-in \fBoct()\fR method with a version that can handle big numbers.
This overrides it by exporting it to the current package. Under Perl v5.10.0 and
higher, this is not so necessary, as \fBoct()\fR is lexically overridden in the
current scope whenever the \f(CW\*(C`bigrat\*(C'\fR pragma is active.
.IP "v or version" 4
.IX Item "v or version"
this prints out the name and version of the modules and then exits.
.Sp
.Vb 1
\&    perl \-Mbigrat=v
.Ve
.SS "Math Library"
.IX Subsection "Math Library"
Math with the numbers is done (by default) by a backend library module called
Math::BigInt::Calc. The default is equivalent to saying:
.PP
.Vb 1
\&    use bigrat lib => \*(AqCalc\*(Aq;
.Ve
.PP
you can change this by using:
.PP
.Vb 1
\&    use bigrat lib => \*(AqGMP\*(Aq;
.Ve
.PP
The following would first try to find Math::BigInt::Foo, then Math::BigInt::Bar,
and if this also fails, revert to Math::BigInt::Calc:
.PP
.Vb 1
\&    use bigrat lib => \*(AqFoo,Math::BigInt::Bar\*(Aq;
.Ve
.PP
Using c<lib> warns if none of the specified libraries can be found and
Math::BigInt fell back to one of the default libraries. To suppress this
warning, use c<try> instead:
.PP
.Vb 1
\&    use bigrat try => \*(AqGMP\*(Aq;
.Ve
.PP
If you want the code to die instead of falling back, use \f(CW\*(C`only\*(C'\fR instead:
.PP
.Vb 1
\&    use bigrat only => \*(AqGMP\*(Aq;
.Ve
.PP
Please see the respective module documentation for further details.
.SS "Method calls"
.IX Subsection "Method calls"
Since all numbers are now objects, you can use all methods that are part of the
Math::BigRat API.
.PP
But a warning is in order. When using the following to make a copy of a number,
only a shallow copy will be made.
.PP
.Vb 2
\&    $x = 9; $y = $x;
\&    $x = $y = 7;
.Ve
.PP
Using the copy or the original with overloaded math is okay, e.g., the following
work:
.PP
.Vb 2
\&    $x = 9; $y = $x;
\&    print $x + 1, " ", $y,"\en";     # prints 10 9
.Ve
.PP
but calling any method that modifies the number directly will result in \fBboth\fR
the original and the copy being destroyed:
.PP
.Vb 2
\&    $x = 9; $y = $x;
\&    print $x\->badd(1), " ", $y,"\en";        # prints 10 10
\&
\&    $x = 9; $y = $x;
\&    print $x\->binc(1), " ", $y,"\en";        # prints 10 10
\&
\&    $x = 9; $y = $x;
\&    print $x\->bmul(2), " ", $y,"\en";        # prints 18 18
.Ve
.PP
Using methods that do not modify, but test that the contents works:
.PP
.Vb 2
\&    $x = 9; $y = $x;
\&    $z = 9 if $x\->is_zero();                # works fine
.Ve
.PP
See the documentation about the copy constructor and \f(CW\*(C`=\*(C'\fR in overload, as well
as the documentation in Math::BigFloat for further details.
.SS Methods
.IX Subsection "Methods"
.IP \fBinf()\fR 4
.IX Item "inf()"
A shortcut to return Math::BigRat\->\fBbinf()\fR. Useful because Perl does not always
handle bareword \f(CW\*(C`inf\*(C'\fR properly.
.IP \fBNaN()\fR 4
.IX Item "NaN()"
A shortcut to return Math::BigRat\->\fBbnan()\fR. Useful because Perl does not always
handle bareword \f(CW\*(C`NaN\*(C'\fR properly.
.IP e 4
.IX Item "e"
.Vb 1
\&    # perl \-Mbigrat=e \-wle \*(Aqprint e\*(Aq
.Ve
.Sp
Returns Euler's number \f(CW\*(C`e\*(C'\fR, aka \fBexp\fR\|(1).
.IP PI 4
.IX Item "PI"
.Vb 1
\&    # perl \-Mbigrat=PI \-wle \*(Aqprint PI\*(Aq
.Ve
.Sp
Returns PI.
.IP \fBbexp()\fR 4
.IX Item "bexp()"
.Vb 1
\&    bexp($power, $accuracy);
.Ve
.Sp
Returns Euler's number \f(CW\*(C`e\*(C'\fR raised to the appropriate power, to the wanted
accuracy.
.Sp
Example:
.Sp
.Vb 1
\&    # perl \-Mbigrat=bexp \-wle \*(Aqprint bexp(1,80)\*(Aq
.Ve
.IP \fBbpi()\fR 4
.IX Item "bpi()"
.Vb 1
\&    bpi($accuracy);
.Ve
.Sp
Returns PI to the wanted accuracy.
.Sp
Example:
.Sp
.Vb 1
\&    # perl \-Mbigrat=bpi \-wle \*(Aqprint bpi(80)\*(Aq
.Ve
.IP \fBaccuracy()\fR 4
.IX Item "accuracy()"
Set or get the accuracy.
.IP \fBprecision()\fR 4
.IX Item "precision()"
Set or get the precision.
.IP \fBround_mode()\fR 4
.IX Item "round_mode()"
Set or get the rounding mode.
.IP \fBdiv_scale()\fR 4
.IX Item "div_scale()"
Set or get the division scale.
.IP \fBin_effect()\fR 4
.IX Item "in_effect()"
.Vb 1
\&    use bigrat;
\&
\&    print "in effect\en" if bigrat::in_effect;       # true
\&    {
\&        no bigrat;
\&        print "in effect\en" if bigrat::in_effect;   # false
\&    }
.Ve
.Sp
Returns true or false if \f(CW\*(C`bigrat\*(C'\fR is in effect in the current scope.
.Sp
This method only works on Perl v5.9.4 or later.
.SH CAVEATS
.IX Header "CAVEATS"
.IP "Hexadecimal, octal, and binary floating point literals" 4
.IX Item "Hexadecimal, octal, and binary floating point literals"
Perl (and this module) accepts hexadecimal, octal, and binary floating point
literals, but use them with care with Perl versions before v5.32.0, because some
versions of Perl silently give the wrong result.
.IP "Operator vs literal overloading" 4
.IX Item "Operator vs literal overloading"
\&\f(CW\*(C`bigrat\*(C'\fR works by overloading handling of integer and floating point literals,
converting them to Math::BigRat objects.
.Sp
This means that arithmetic involving only string values or string literals are
performed using Perl's built-in operators.
.Sp
For example:
.Sp
.Vb 4
\&    use bigrat;
\&    my $x = "900000000000000009";
\&    my $y = "900000000000000007";
\&    print $x \- $y;
.Ve
.Sp
outputs \f(CW0\fR on default 32\-bit builds, since \f(CW\*(C`bigrat\*(C'\fR never sees the string
literals. To ensure the expression is all treated as \f(CW\*(C`Math::BigRat\*(C'\fR objects,
use a literal number in the expression:
.Sp
.Vb 1
\&    print +(0+$x) \- $y;
.Ve
.IP Ranges 4
.IX Item "Ranges"
Perl does not allow overloading of ranges, so you can neither safely use ranges
with \f(CW\*(C`bigrat\*(C'\fR endpoints, nor is the iterator variable a \f(CW\*(C`Math::BigRat\*(C'\fR.
.Sp
.Vb 7
\&    use 5.010;
\&    for my $i (12..13) {
\&      for my $j (20..21) {
\&        say $i ** $j;  # produces a floating\-point number,
\&                       # not an object
\&      }
\&    }
.Ve
.IP \fBin_effect()\fR 4
.IX Item "in_effect()"
This method only works on Perl v5.9.4 or later.
.IP \fBhex()\fR/\fBoct()\fR 4
.IX Item "hex()/oct()"
\&\f(CW\*(C`bigrat\*(C'\fR overrides these routines with versions that can also handle big
integer values. Under Perl prior to version v5.9.4, however, this will not
happen unless you specifically ask for it with the two import tags "hex" and
"oct" \- and then it will be global and cannot be disabled inside a scope with
\&\f(CW\*(C`no bigrat\*(C'\fR:
.Sp
.Vb 1
\&    use bigrat qw/hex oct/;
\&
\&    print hex("0x1234567890123456");
\&    {
\&        no bigrat;
\&        print hex("0x1234567890123456");
\&    }
.Ve
.Sp
The second call to \fBhex()\fR will warn about a non-portable constant.
.Sp
Compare this to:
.Sp
.Vb 1
\&    use bigrat;
\&
\&    # will warn only under Perl older than v5.9.4
\&    print hex("0x1234567890123456");
.Ve
.SH EXAMPLES
.IX Header "EXAMPLES"
.Vb 6
\&    perl \-Mbigrat \-le \*(Aqprint sqrt(33)\*(Aq
\&    perl \-Mbigrat \-le \*(Aqprint 2**255\*(Aq
\&    perl \-Mbigrat \-le \*(Aqprint 4.5+2**255\*(Aq
\&    perl \-Mbigrat \-le \*(Aqprint 3/7 + 5/7 + 8/3\*(Aq
\&    perl \-Mbigrat \-le \*(Aqprint 12\->is_odd()\*(Aq;
\&    perl \-Mbigrat=l,GMP \-le \*(Aqprint 7 ** 7777\*(Aq
.Ve
.SH BUGS
.IX Header "BUGS"
Please report any bugs or feature requests to
\&\f(CW\*(C`bug\-bignum at rt.cpan.org\*(C'\fR, or through the web interface at
<https://rt.cpan.org/Ticket/Create.html?Queue=bignum> (requires login).
We will be notified, and then you'll automatically be notified of
progress on your bug as I make changes.
.SH SUPPORT
.IX Header "SUPPORT"
You can find documentation for this module with the perldoc command.
.PP
.Vb 1
\&    perldoc bigrat
.Ve
.PP
You can also look for information at:
.IP \(bu 4
GitHub
.Sp
<https://github.com/pjacklam/p5\-bignum>
.IP \(bu 4
RT: CPAN's request tracker
.Sp
<https://rt.cpan.org/Dist/Display.html?Name=bignum>
.IP \(bu 4
MetaCPAN
.Sp
<https://metacpan.org/release/bignum>
.IP \(bu 4
CPAN Testers Matrix
.Sp
<http://matrix.cpantesters.org/?dist=bignum>
.IP \(bu 4
CPAN Ratings
.Sp
<https://cpanratings.perl.org/dist/bignum>
.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"
bignum and bigint.
.PP
Math::BigInt, Math::BigFloat, Math::BigRat and Math::Big as well as
Math::BigInt::FastCalc, Math::BigInt::Pari and Math::BigInt::GMP.
.SH AUTHORS
.IX Header "AUTHORS"
.IP \(bu 4
(C) by Tels <http://bloodgate.com/> in early 2002 \- 2007.
.IP \(bu 4
Maintained by Peter John Acklam <pjacklam@gmail.com>, 2014\-.