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+package bignum;
+use 5.006;
+
+$VERSION = '0.23';
+use Exporter;
+@ISA = qw( bigint );
+@EXPORT_OK = qw( PI e bexp bpi );
+@EXPORT = qw( inf NaN );
+
+use strict;
+use overload;
+require bigint; # no "use" to avoid import being called
+
+##############################################################################
+
+BEGIN
+ {
+ *inf = \&bigint::inf;
+ *NaN = \&bigint::NaN;
+ }
+
+# These are all alike, and thus faked by AUTOLOAD
+
+my @faked = qw/round_mode accuracy precision div_scale/;
+use vars qw/$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 $name)
+ {
+ *{"bignum::$name"} = sub
+ {
+ my $self = shift;
+ no strict 'refs';
+ if (defined $_[0])
+ {
+ Math::BigInt->$name($_[0]);
+ return Math::BigFloat->$name($_[0]);
+ }
+ return Math::BigInt->$name();
+ };
+ return &$name;
+ }
+ }
+
+ # delayed load of Carp and avoid recursion
+ require Carp;
+ Carp::croak ("Can't call bignum\-\>$name, not a valid method");
+ }
+
+sub unimport
+ {
+ $^H{bignum} = undef; # no longer in effect
+ overload::remove_constant('binary','','float','','integer');
+ }
+
+sub in_effect
+ {
+ my $level = shift || 0;
+ my $hinthash = (caller($level))[10];
+ $hinthash->{bignum};
+ }
+
+#############################################################################
+# the following two routines are for Perl 5.9.4 or later and are lexical
+
+sub _hex
+ {
+ return CORE::hex($_[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;
+
+ $^H{bignum} = 1; # we are in effect
+
+ my ($hex,$oct);
+
+ # for newer Perls override hex() and oct() with a lexical version:
+ if ($] > 5.009003)
+ {
+ $hex = \&_hex;
+ $oct = \&_oct;
+ }
+
+ # some defaults
+ my $lib = ''; my $lib_kind = 'try';
+ my $upgrade = 'Math::BigFloat';
+ my $downgrade = 'Math::BigInt';
+
+ my @import = ( ':constant' ); # drive it w/ constant
+ my @a = @_; my $l = scalar @_; my $j = 0;
+ my ($ver,$trace); # version? trace?
+ my ($a,$p); # accuracy, precision
+ 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; $i++;
+ }
+ elsif ($_[$i] eq 'downgrade')
+ {
+ # this causes downgrading
+ $downgrade = $_[$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; $i++;
+ }
+ elsif ($_[$i] =~ /^(l|lib|try|only)$/)
+ {
+ # 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|bexp|bpi)\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 => $upgrade);
+
+ if ($trace)
+ {
+ require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
+ $downgrade = 'Math::BigInt::Trace';
+ }
+ else
+ {
+ require Math::BigFloat; $class = 'Math::BigFloat';
+ }
+ $class->import(':constant','downgrade',$downgrade);
+
+ bignum->accuracy($a) if defined $a;
+ bignum->precision($p) if defined $p;
+ if ($ver)
+ {
+ print "bignum\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$Math::BigFloat::VERSION\n";
+ exit;
+ }
+
+ # Take care of octal/hexadecimal constants
+ overload::constant binary => sub { bigint::_binary_constant(shift) };
+
+ # if another big* was already loaded:
+ my ($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 $hex;
+ }
+ }
+
+sub PI () { Math::BigFloat->new('3.141592653589793238462643383279502884197'); }
+sub e () { Math::BigFloat->new('2.718281828459045235360287471352662497757'); }
+sub bpi ($) { Math::BigFloat::bpi(@_); }
+sub bexp ($$) { my $x = Math::BigFloat->new($_[0]); $x->bexp($_[1]); }
+
+1;
+
+__END__
+
+=head1 NAME
+
+bignum - Transparent BigNumber support for Perl
+
+=head1 SYNOPSIS
+
+ use bignum;
+
+ $x = 2 + 4.5,"\n"; # BigFloat 6.5
+ print 2 ** 512 * 0.1,"\n"; # really is what you think it is
+ print inf * inf,"\n"; # prints inf
+ print NaN * 3,"\n"; # prints NaN
+
+ {
+ no bignum;
+ print 2 ** 256,"\n"; # a normal Perl scalar now
+ }
+
+ # for older Perls, note that this will be global:
+ use bignum 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.
+
+If you do
+
+ use bignum;
+
+at the top of your script, Math::BigFloat and Math::BigInt will be loaded
+and any constant number will be converted to an object (Math::BigFloat for
+floats like 3.1415 and Math::BigInt for integers like 1234).
+
+So, the following line:
+
+ $x = 1234;
+
+creates actually a Math::BigInt and stores a reference to in $x.
+This happens transparently and behind your back, so to speak.
+
+You can see this with the following:
+
+ perl -Mbignum -le 'print ref(1234)'
+
+Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
+if it is installed since it is faster for some operations. It will be
+automatically upgraded to BigInt whenever necessary:
+
+ perl -Mbignum -le 'print ref(2**255)'
+
+This also means it is a bad idea to check for some specific package, since
+the actual contents of $x might be something unexpected. Due to the
+transparent way of bignum C<ref()> should not be necessary, anyway.
+
+Since Math::BigInt and BigFloat also overload the normal math operations,
+the following line will still work:
+
+ perl -Mbignum -le 'print ref(1234+1234)'
+
+Since numbers are actually objects, you can call all the usual methods from
+BigInt/BigFloat on them. This even works to some extent on expressions:
+
+ perl -Mbignum -le '$x = 1234; print $x->bdec()'
+ perl -Mbignum -le 'print 1234->copy()->binc();'
+ perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
+ perl -Mbignum -le 'print +(1234)->copy()->binc()'
+
+(Note that print doesn't do what you expect if the expression starts with
+'(' hence the C<+>)
+
+You can even chain the operations together as usual:
+
+ perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
+ 1241
+
+Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
+appropriately. This means that:
+
+ perl -Mbignum -le 'print 1234+4.5'
+ 1238.5
+
+will work correctly. These mixed cases don't do always work when using
+Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
+scalars work.
+
+If you do want to work with large integers like under C<use integer;>, try
+C<use bigint;>:
+
+ perl -Mbigint -le 'print 1234.5+4.5'
+ 1238
+
+There is also C<use bigrat;> which gives you big rationals:
+
+ perl -Mbigrat -le 'print 1234+4.1'
+ 12381/10
+
+The entire upgrading/downgrading is still experimental and might not work
+as you expect or may even have bugs. You might get errors like this:
+
+ Can't use an undefined value as an ARRAY reference at
+ /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
+
+This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
+vice versa) and the upgrade/downgrad path was missing. This is a bug, please
+report it so that we can fix it.
+
+You might consider using just Math::BigInt or Math::BigFloat, since they
+allow you finer control over what get's done in which module/space. For
+instance, simple loop counters will be Math::BigInts under C<use bignum;> and
+this is slower than keeping them as Perl scalars:
+
+ perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
+
+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):
+
+ perl -Mbignum -le 'for (1..2) { print ref($_); }'
+
+=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 -Mbignum=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 -Mbignum=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<MATH LIBRARY>.
+
+ perl -Mbignum=l,GMP -e 'print 2 ** 512'
+
+Currently there is no way to specify more than one library on the command
+line. This means the following does not work:
+
+ perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
+
+This will be hopefully fixed soon ;)
+
+=item hex
+
+Override the built-in hex() method with a version that can handle big
+integers. Note that under Perl older than v5.9.4, this will be global
+and cannot be disabled with "no bigint;".
+
+=item oct
+
+Override the built-in oct() method with a version that can handle big
+integers. Note that under Perl older than v5.9.4, this will be global
+and cannot be disabled with "no bigint;".
+
+=item v or version
+
+This prints out the name and version of all modules used and then exits.
+
+ perl -Mbignum=v
+
+=back
+
+=head2 Methods
+
+Beside import() and AUTOLOAD() there are only a few other methods.
+
+Since all numbers are now 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 it possible that the underlying object
+might morph into a different class than BigFloat.
+
+=head2 Caveats
+
+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<both> 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 test the contents works:
+
+ $x = 9; $y = $x;
+ $z = 9 if $x->is_zero(); # works fine
+
+See the documentation about the copy constructor and C<=> in overload, as
+well as the documentation in BigInt for further details.
+
+=over 2
+
+=item inf()
+
+A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
+handle bareword C<inf> properly.
+
+=item NaN()
+
+A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
+handle bareword C<NaN> properly.
+
+=item e
+
+ # perl -Mbignum=e -wle 'print e'
+
+Returns Euler's number C<e>, aka exp(1).
+
+=item PI()
+
+ # perl -Mbignum=PI -wle 'print PI'
+
+Returns PI.
+
+=item bexp()
+
+ bexp($power,$accuracy);
+
+Returns Euler's number C<e> raised to the appropriate power, to
+the wanted accuracy.
+
+Example:
+
+ # perl -Mbignum=bexp -wle 'print bexp(1,80)'
+
+=item bpi()
+
+ bpi($accuracy);
+
+Returns PI to the wanted accuracy.
+
+Example:
+
+ # perl -Mbignum=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 bignum;
+
+ print "in effect\n" if bignum::in_effect; # true
+ {
+ no bignum;
+ print "in effect\n" if bignum::in_effect; # false
+ }
+
+Returns true or false if C<bignum> 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
+Math::BigInt::Calc. This is equivalent to saying:
+
+ use bignum 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 bignum lib => 'Foo,Math::BigInt::Bar';
+
+Please see respective module documentation for further details.
+
+Using C<lib> warns if none of the specified libraries can be found and
+L<Math::BigInt> did fall back to one of the default libraries.
+To supress this warning, use C<try> instead:
+
+ use bignum try => 'GMP';
+
+If you want the code to die instead of falling back, use C<only> instead:
+
+ use bignum only => 'GMP';
+
+=head2 INTERNAL FORMAT
+
+The numbers are stored as objects, and their internals might change at anytime,
+especially between math operations. The objects also might belong to different
+classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
+with normal scalars is not extraordinary, but normal and expected.
+
+You should not depend on the internal format, all accesses must go through
+accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
+is no guaranty that the object in question has such a hashkey, nor is a hash
+underneath at all.
+
+=head2 SIGN
+
+The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
+You can access it with the sign() method.
+
+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.
+
+=head1 CAVAETS
+
+=over 2
+
+=item in_effect()
+
+This method only works on Perl v5.9.4 or later.
+
+=item hex()/oct()
+
+C<bigint> 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 "no bigint":
+
+ use bigint qw/hex oct/;
+
+ print hex("0x1234567890123456");
+ {
+ no bigint;
+ print hex("0x1234567890123456");
+ }
+
+The second call to hex() will warn about a non-portable constant.
+
+Compare this to:
+
+ use bigint;
+
+ # will warn only under older than v5.9.4
+ print hex("0x1234567890123456");
+
+=back
+
+=head1 MODULES USED
+
+C<bignum> 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
+
+=head1 EXAMPLES
+
+Some cool command line examples to impress the Python crowd ;)
+
+ perl -Mbignum -le 'print sqrt(33)'
+ perl -Mbignum -le 'print 2*255'
+ perl -Mbignum -le 'print 4.5+2*255'
+ perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
+ perl -Mbignum -le 'print 123->is_odd()'
+ perl -Mbignum -le 'print log(2)'
+ perl -Mbignum -le 'print exp(1)'
+ perl -Mbignum -le 'print 2 ** 0.5'
+ perl -Mbignum=a,65 -le 'print 2 ** 0.2'
+ perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777'
+
+=head1 LICENSE
+
+This program is free software; you may redistribute it and/or modify it under
+the same terms as Perl itself.
+
+=head1 SEE ALSO
+
+Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
+
+L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
+as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
+
+=head1 AUTHORS
+
+(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.
+
+=cut
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