package bigrat; use 5.006; $VERSION = '0.23'; require Exporter; @ISA = qw( bigint ); @EXPORT_OK = qw( PI e bpi bexp ); @EXPORT = qw( inf NaN ); use strict; use overload; require bigint; # no "use" to avoid callind import ############################################################################## BEGIN { *inf = \&bigint::inf; *NaN = \&bigint::NaN; } # These are all alike, and thus faked by AUTOLOAD my @faked = qw/round_mode accuracy precision div_scale/; use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite sub AUTOLOAD { my $name = $AUTOLOAD; $name =~ s/.*:://; # split package no strict 'refs'; foreach my $n (@faked) { if ($n eq $name) { *{"bigrat::$name"} = sub { my $self = shift; no strict 'refs'; if (defined $_[0]) { Math::BigInt->$name($_[0]); Math::BigFloat->$name($_[0]); return Math::BigRat->$name($_[0]); } return Math::BigInt->$name(); }; return &$name; } } # delayed load of Carp and avoid recursion require Carp; Carp::croak ("Can't call bigrat\-\>$name, not a valid method"); } sub unimport { $^H{bigrat} = undef; # no longer in effect overload::remove_constant('binary','','float','','integer'); } sub in_effect { my $level = shift || 0; my $hinthash = (caller($level))[10]; $hinthash->{bigrat}; } ############################################################################# # the following two routines are for Perl 5.9.4 or later and are lexical sub _hex { return CORE::hex($_[0]) unless in_effect(1); my $i = $_[0]; $i = '0x'.$i unless $i =~ /^0x/; Math::BigInt->new($i); } sub _oct { return CORE::oct($_[0]) unless in_effect(1); my $i = $_[0]; return Math::BigInt->from_oct($i) if $i =~ /^0[0-7]/; Math::BigInt->new($i); } sub import { my $self = shift; # see also bignum->import() for additional comments $^H{bigrat} = 1; # we are in effect my ($hex,$oct); # for newer Perls always override hex() and oct() with a lexical version: if ($] > 5.009004) { $oct = \&_oct; $hex = \&_hex; } # some defaults my $lib = ''; my $lib_kind = 'try'; my $upgrade = 'Math::BigFloat'; my @import = ( ':constant' ); # drive it w/ constant my @a = @_; my $l = scalar @_; my $j = 0; my ($a,$p); my ($ver,$trace); # version? trace? for ( my $i = 0; $i < $l ; $i++,$j++ ) { if ($_[$i] eq 'upgrade') { # this causes upgrading $upgrade = $_[$i+1]; # or undef to disable my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." splice @a, $j, $s; $j -= $s; } elsif ($_[$i] =~ /^(l|lib|try|only)$/) { # this causes a different low lib to take care... $lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l'; $lib = $_[$i+1] || ''; my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." splice @a, $j, $s; $j -= $s; $i++; } elsif ($_[$i] =~ /^(a|accuracy)$/) { $a = $_[$i+1]; my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." splice @a, $j, $s; $j -= $s; $i++; } elsif ($_[$i] =~ /^(p|precision)$/) { $p = $_[$i+1]; my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..." splice @a, $j, $s; $j -= $s; $i++; } elsif ($_[$i] =~ /^(v|version)$/) { $ver = 1; splice @a, $j, 1; $j --; } elsif ($_[$i] =~ /^(t|trace)$/) { $trace = 1; splice @a, $j, 1; $j --; } elsif ($_[$i] eq 'hex') { splice @a, $j, 1; $j --; $hex = \&bigint::_hex_global; } elsif ($_[$i] eq 'oct') { splice @a, $j, 1; $j --; $oct = \&bigint::_oct_global; } elsif ($_[$i] !~ /^(PI|e|bpi|bexp)\z/) { die ("unknown option $_[$i]"); } } my $class; $_lite = 0; # using M::BI::L ? if ($trace) { require Math::BigInt::Trace; $class = 'Math::BigInt::Trace'; $upgrade = 'Math::BigFloat::Trace'; } else { # see if we can find Math::BigInt::Lite if (!defined $a && !defined $p) # rounding won't work to well { eval 'require Math::BigInt::Lite;'; if ($@ eq '') { @import = ( ); # :constant in Lite, not MBI Math::BigInt::Lite->import( ':constant' ); $_lite= 1; # signal okay } } require Math::BigInt if $_lite == 0; # not already loaded? $class = 'Math::BigInt'; # regardless of MBIL or not } push @import, $lib_kind => $lib if $lib ne ''; # Math::BigInt::Trace or plain Math::BigInt $class->import(@import, upgrade => $upgrade); require Math::BigFloat; Math::BigFloat->import( upgrade => 'Math::BigRat', ':constant' ); require Math::BigRat; bigrat->accuracy($a) if defined $a; bigrat->precision($p) if defined $p; if ($ver) { print "bigrat\t\t\t v$VERSION\n"; print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite; print "Math::BigInt\t\t v$Math::BigInt::VERSION"; my $config = Math::BigInt->config(); print " lib => $config->{lib} v$config->{lib_version}\n"; print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n"; print "Math::BigRat\t\t v$Math::BigRat::VERSION\n"; exit; } # Take care of octal/hexadecimal constants overload::constant binary => sub { bigint::_binary_constant(shift) }; # if another big* was already loaded: my ($package) = caller(); no strict 'refs'; if (!defined *{"${package}::inf"}) { $self->export_to_level(1,$self,@a); # export inf and NaN } { no warnings 'redefine'; *CORE::GLOBAL::oct = $oct if $oct; *CORE::GLOBAL::hex = $hex if $hex; } } sub PI () { Math::BigFloat->new('3.141592653589793238462643383279502884197'); } sub e () { Math::BigFloat->new('2.718281828459045235360287471352662497757'); } sub bpi ($) { local $Math::BigFloat::upgrade; Math::BigFloat::bpi(@_); } sub bexp ($$) { local $Math::BigFloat::upgrade; my $x = Math::BigFloat->new($_[0]); $x->bexp($_[1]); } 1; __END__ =head1 NAME bigrat - Transparent BigNumber/BigRational support for Perl =head1 SYNOPSIS use bigrat; print 2 + 4.5,"\n"; # BigFloat 6.5 print 1/3 + 1/4,"\n"; # produces 7/12 { no bigrat; print 1/3,"\n"; # 0.33333... } # Note that this will make hex() and oct() be globally overriden: use bigrat qw/hex oct/; print hex("0x1234567890123490"),"\n"; print oct("01234567890123490"),"\n"; =head1 DESCRIPTION All operators (including basic math operations) are overloaded. Integer and floating-point constants are created as proper BigInts or BigFloats, respectively. Other than L, this module upgrades to Math::BigRat, meaning that instead of 2.5 you will get 2+1/2 as output. =head2 Modules Used C 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. The following modules are currently used by bignum: Math::BigInt::Lite (for speed, and only if it is loadable) Math::BigInt Math::BigFloat Math::BigRat =head2 Math Library Math with the numbers is done (by default) by a module called Math::BigInt::Calc. This is equivalent to saying: use bigrat lib => 'Calc'; You can change this by using: use bignum lib => 'GMP'; 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 bigrat lib => 'Foo,Math::BigInt::Bar'; Using C warns if none of the specified libraries can be found and L did fall back to one of the default libraries. To supress this warning, use C instead: use bignum try => 'GMP'; If you want the code to die instead of falling back, use C instead: use bignum only => 'GMP'; Please see respective module documentation for further details. =head2 Sign The sign is either '+', '-', 'NaN', '+inf' or '-inf'. 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. =head2 Methods Since all numbers are not objects, you can use all functions that are part of the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not the fxxx() notation, though. This makes you independed on the fact that the underlying object might morph into a different class than BigFloat. =over 2 =item inf() A shortcut to return Math::BigInt->binf(). Useful because Perl does not always handle bareword C properly. =item NaN() A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always handle bareword C properly. =item e # perl -Mbigrat=e -wle 'print e' Returns Euler's number C, aka exp(1). =item PI # perl -Mbigrat=PI -wle 'print PI' Returns PI. =item bexp() bexp($power,$accuracy); Returns Euler's number C raised to the appropriate power, to the wanted accuracy. Example: # perl -Mbigrat=bexp -wle 'print bexp(1,80)' =item bpi() bpi($accuracy); Returns PI to the wanted accuracy. Example: # perl -Mbigrat=bpi -wle 'print bpi(80)' =item upgrade() Return the class that numbers are upgraded to, is in fact returning C<$Math::BigInt::upgrade>. =item in_effect() use bigrat; print "in effect\n" if bigrat::in_effect; # true { no bigrat; print "in effect\n" if bigrat::in_effect; # false } Returns true or false if C is in effect in the current scope. This method only works on Perl v5.9.4 or later. =back =head2 MATH LIBRARY Math with the numbers is done (by default) by a module called =head2 Cavaet But a warning is in order. When using the following to make a copy of a number, only a shallow copy will be made. $x = 9; $y = $x; $x = $y = 7; If you want to make a real copy, use the following: $y = $x->copy(); Using the copy or the original with overloaded math is okay, e.g. the following work: $x = 9; $y = $x; print $x + 1, " ", $y,"\n"; # prints 10 9 but calling any method that modifies the number directly will result in B the original and the copy being destroyed: $x = 9; $y = $x; print $x->badd(1), " ", $y,"\n"; # prints 10 10 $x = 9; $y = $x; print $x->binc(1), " ", $y,"\n"; # prints 10 10 $x = 9; $y = $x; print $x->bmul(2), " ", $y,"\n"; # prints 18 18 Using methods that do not modify, but testthe contents works: $x = 9; $y = $x; $z = 9 if $x->is_zero(); # works fine See the documentation about the copy constructor and C<=> in overload, as well as the documentation in BigInt for further details. =head2 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: =over 2 =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 bround() function for details. perl -Mbigrat=a,50 -le 'print sqrt(20)' Note that setting precision and accurary at the same time is not possible. =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 bfround() function for details. perl -Mbigrat=p,-50 -le 'print sqrt(20)' Note that setting precision and accurary at the same time is not possible. =item t or trace This enables a trace mode and is primarily for debugging bignum or Math::BigInt/Math::BigFloat. =item l or lib Load a different math lib, see L