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.\" ========================================================================
.\"
.IX Title "bigrat 3"
.TH bigrat 3 "2019-10-24" "perl v5.30.2" "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"
bigrat \- Transparent BigNumber/BigRational support for Perl
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& use bigrat;
\&
\& print 2 + 4.5,"\en"; # BigFloat 6.5
\& print 1/3 + 1/4,"\en"; # produces 7/12
\&
\& {
\& no bigrat;
\& print 1/3,"\en"; # 0.33333...
\& }
\&
\& # Import into current package:
\& use bigrat qw/hex oct/;
\& print hex("0x1234567890123490"),"\en";
\& print oct("01234567890123490"),"\en";
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
All operators (including basic math operations) are overloaded. Integer and
floating-point constants are created as proper BigInts or BigFloats,
respectively.
.PP
Other than bignum, this module upgrades to Math::BigRat, meaning that
instead of 2.5 you will get 2+1/2 as output.
.SS "Modules Used"
.IX Subsection "Modules Used"
\&\f(CW\*(C`bigrat\*(C'\fR is just a thin wrapper around various modules of the Math::BigInt
family. Think of it as the head of the family, who runs the shop, and orders
the others to do the work.
.PP
The following modules are currently used by bignum:
.PP
.Vb 4
\& Math::BigInt::Lite (for speed, and only if it is loadable)
\& Math::BigInt
\& Math::BigFloat
\& Math::BigRat
.Ve
.SS "Math Library"
.IX Subsection "Math Library"
Math with the numbers is done (by default) by a module called
Math::BigInt::Calc. This is equivalent to saying:
.PP
.Vb 1
\& use bigrat lib => \*(AqCalc\*(Aq;
.Ve
.PP
You can change this by using:
.PP
.Vb 1
\& use bignum lib => \*(AqGMP\*(Aq;
.Ve
.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 bigrat lib => \*(AqFoo,Math::BigInt::Bar\*(Aq;
.Ve
.PP
Using \f(CW\*(C`lib\*(C'\fR warns if none of the specified libraries can be found and
Math::BigInt did fall back to one of the default libraries.
To suppress this warning, use \f(CW\*(C`try\*(C'\fR instead:
.PP
.Vb 1
\& use bignum 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 bignum only => \*(AqGMP\*(Aq;
.Ve
.PP
Please see respective module documentation for further details.
.SS "Sign"
.IX Subsection "Sign"
The sign is either '+', '\-', 'NaN', '+inf' or '\-inf'.
.PP
A sign of 'NaN' is used to represent the result when input arguments are not
numbers or as a result of 0/0. '+inf' and '\-inf' represent plus respectively
minus infinity. You will get '+inf' when dividing a positive number by 0, and
\&'\-inf' when dividing any negative number by 0.
.SS "Methods"
.IX Subsection "Methods"
Since all numbers are not objects, you can use all functions that are part of
the BigInt or BigFloat \s-1API.\s0 It is wise to use only the \fBbxxx()\fR notation, and not
the \fBfxxx()\fR notation, though. This makes you independent on the fact that the
underlying object might morph into a different class than BigFloat.
.IP "\fBinf()\fR" 2
.IX Item "inf()"
A shortcut to return Math::BigInt\->\fBbinf()\fR. Useful because Perl does not always
handle bareword \f(CW\*(C`inf\*(C'\fR properly.
.IP "\fBNaN()\fR" 2
.IX Item "NaN()"
A shortcut to return Math::BigInt\->\fBbnan()\fR. Useful because Perl does not always
handle bareword \f(CW\*(C`NaN\*(C'\fR properly.
.IP "e" 2
.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 "\s-1PI\s0" 2
.IX Item "PI"
.Vb 1
\& # perl \-Mbigrat=PI \-wle \*(Aqprint PI\*(Aq
.Ve
.Sp
Returns \s-1PI.\s0
.IP "\fBbexp()\fR" 2
.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" 2
.IX Item "bpi()"
.Vb 1
\& bpi($accuracy);
.Ve
.Sp
Returns \s-1PI\s0 to the wanted accuracy.
.Sp
Example:
.Sp
.Vb 1
\& # perl \-Mbigrat=bpi \-wle \*(Aqprint bpi(80)\*(Aq
.Ve
.IP "\fBupgrade()\fR" 2
.IX Item "upgrade()"
Return the class that numbers are upgraded to, is in fact returning
\&\f(CW$Math::BigInt::upgrade\fR.
.IP "\fBin_effect()\fR" 2
.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.
.SS "\s-1MATH LIBRARY\s0"
.IX Subsection "MATH LIBRARY"
Math with the numbers is done (by default) by a module called
.SS "Caveat"
.IX Subsection "Caveat"
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
If you want to make a real copy, use the following:
.PP
.Vb 1
\& $y = $x\->copy();
.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 testthe 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 BigInt for further details.
.SS "Options"
.IX Subsection "Options"
bignum recognizes some options that can be passed while loading it via use.
The options can (currently) be either a single letter form, or the long form.
The following options exist:
.IP "a or accuracy" 2
.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 function 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" 2
.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 or 1 mean round to
integer. See Math::BigInt's \fBbfround()\fR function 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" 2
.IX Item "t or trace"
This enables a trace mode and is primarily for debugging bignum or
Math::BigInt/Math::BigFloat.
.IP "l or lib" 2
.IX Item "l or lib"
Load a different math lib, see \*(L"\s-1MATH LIBRARY\*(R"\s0.
.Sp
.Vb 1
\& perl \-Mbigrat=l,GMP \-e \*(Aqprint 2 ** 512\*(Aq
.Ve
.Sp
Currently there is no way to specify more than one library on the command
line. This means the following does not work:
.Sp
.Vb 1
\& perl \-Mbignum=l,GMP,Pari \-e \*(Aqprint 2 ** 512\*(Aq
.Ve
.Sp
This will be hopefully fixed soon ;)
.IP "hex" 2
.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 bigrat pragma is active.
.IP "oct" 2
.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 bigrat pragma is active.
.IP "v or version" 2
.IX Item "v or version"
This prints out the name and version of all modules used and then exits.
.Sp
.Vb 1
\& perl \-Mbigrat=v
.Ve
.SH "CAVEATS"
.IX Header "CAVEATS"
.IP "Operator vs literal overloading" 2
.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::BigInt or Math::BigRat
objects.
.Sp
This means that arithmetic involving only string values or string
literals will be performed using Perl's built-in operators.
.Sp
For example:
.Sp
.Vb 4
\& use bigrat;
\& my $x = "900000000000000009";
\& my $y = "900000000000000007";
\& print $x \- $y;
.Ve
.Sp
will output \f(CW0\fR on default 32\-bit builds, since \f(CW\*(C`bigrat\*(C'\fR never sees
the string literals. To ensure the expression is all treated as
\&\f(CW\*(C`Math::BigInt\*(C'\fR or \f(CW\*(C`Math::BigRat\*(C'\fR objects, use a literal number in
the expression:
.Sp
.Vb 1
\& print +(0+$x) \- $y;
.Ve
.IP "\fBin_effect()\fR" 2
.IX Item "in_effect()"
This method only works on Perl v5.9.4 or later.
.IP "\fBhex()\fR/\fBoct()\fR" 2
.IX Item "hex()/oct()"
\&\f(CW\*(C`bigint\*(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 \*(L"hex\*(R" and \*(L"oct\*(R" \- and then it will be global and cannot be
disabled inside a scope with \*(L"no bigint\*(R":
.Sp
.Vb 1
\& use bigint qw/hex oct/;
\&
\& print hex("0x1234567890123456");
\& {
\& no bigint;
\& 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 bigint;
\&
\& # 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 \-Mbignum=l,GMP \-le \*(Aqprint 7 ** 7777\*(Aq
.Ve
.SH "BUGS"
.IX Header "BUGS"
For information about bugs and how to report them, see the \s-1BUGS\s0 section in the
documentation available with the perldoc command.
.PP
.Vb 1
\& perldoc bignum
.Ve
.SH "SUPPORT"
.IX Header "SUPPORT"
You can find documentation for this module with the perldoc command.
.PP
.Vb 1
\& perldoc bigrat
.Ve
.PP
For more information, see the \s-1SUPPORT\s0 section in the documentation available
with the perldoc command.
.PP
.Vb 1
\& perldoc bignum
.Ve
.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
Peter John Acklam <pjacklam@gmail.com<gt>, 2014\-.