bigint  Transparent BigInteger support for Perl
use bigint;
$x = 2 + 4.5,"\n"; # BigInt 6
print 2 ** 512,"\n"; # really is what you think it is
print inf + 42,"\n"; # inf
print NaN * 7,"\n"; # NaN
print hex("0x1234567890123490"),"\n"; # Perl v5.10.0 or later
{
no bigint;
print 2 ** 256,"\n"; # a normal Perl scalar now
}
# Import into current package:
use bigint qw/hex oct/;
print hex("0x1234567890123490"),"\n";
print oct("01234567890123490"),"\n";
All operators (including basic math operations) except the range operator
".." are overloaded. Integer constants are created as proper
BigInts.
Floating point constants are truncated to integer. All parts and results of
expressions are also truncated.
Unlike integer, this pragma creates integer constants that are only limited in
their size by the available memory and CPU time.
There is one small difference between "use integer" and "use
bigint": the former will not affect assignments to variables and the
return value of some functions. "bigint" truncates these results to
integer too:
# perl Minteger wle 'print 3.2'
3.2
# perl Minteger wle 'print 3.2 + 0'
3
# perl Mbigint wle 'print 3.2'
3
# perl Mbigint wle 'print 3.2 + 0'
3
# perl Mbigint wle 'print exp(1) + 0'
2
# perl Mbigint wle 'print exp(1)'
2
# perl Minteger wle 'print exp(1)'
2.71828182845905
# perl Minteger wle 'print exp(1) + 0'
2
In practice this makes seldom a difference as
parts and results of
expressions will be truncated anyway, but this can, for instance, affect the
return value of subroutines:
sub three_integer { use integer; return 3.2; }
sub three_bigint { use bigint; return 3.2; }
print three_integer(), " ", three_bigint(),"\n"; # prints "3.2 3"
bigint 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:
 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 Mbigint=a,2 le 'print 12345+1'
Note that setting precision and accuracy at the same time is not
possible.
 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, and
are <B>ignored</B> since all operations happen in integer
space. A positive value rounds to this digit left from the dot. 0 or 1
mean round to integer and are ignore like negative values.
See Math::BigInt's bfround() function for details.
perl Mbignum=p,5 le 'print 123456789+123'
Note that setting precision and accuracy at the same time is not
possible.
 t or trace
 This enables a trace mode and is primarily for debugging bigint or
Math::BigInt.
 hex
 Override the builtin hex() method with a version that can handle
big integers. This overrides it by exporting it to the current package.
Under Perl v5.10.0 and higher, this is not so necessary, as hex()
is lexically overridden in the current scope whenever the bigint pragma is
active.
 oct
 Override the builtin oct() method with a version that can handle
big integers. This overrides it by exporting it to the current package.
Under Perl v5.10.0 and higher, this is not so necessary, as oct()
is lexically overridden in the current scope whenever the bigint pragma is
active.
 l, lib, try or only
 Load a different math lib, see "Math Library".
perl Mbigint=lib,GMP e 'print 2 ** 512'
perl Mbigint=try,GMP e 'print 2 ** 512'
perl Mbigint=only,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 ;)
 v or version
 This prints out the name and version of all modules used and then exits.
perl Mbigint=v
Math with the numbers is done (by default) by a module called
Math::BigInt::Calc. This is equivalent to saying:
use bigint 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 bigint lib => 'Foo,Math::BigInt::Bar';
Using "lib" 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 "try" instead:
use bignum try => 'GMP';
If you want the code to die instead of falling back, use "only"
instead:
use bignum only => 'GMP';
Please see respective module documentation for further details.
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::BigInt::Lite. 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 good idea since there
is no guaranty that the object in question has such a hash key, nor is a hash
underneath at all.
The sign is either '+', '', 'NaN', '+inf' or 'inf'. 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.
Since all numbers are now objects, you can use all functions that are part of
the BigInt API. You can only use the
bxxx() notation, and not the
fxxx() notation, though.
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;
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
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 that the contents works:
$x = 9; $y = $x;
$z = 9 if $x>is_zero(); # works fine
See the documentation about the copy constructor and "=" in overload,
as well as the documentation in BigInt for further details.
 inf()
 A shortcut to return Math::BigInt>binf(). Useful because Perl
does not always handle bareword "inf" properly.
 NaN()
 A shortcut to return Math::BigInt>bnan(). Useful because Perl
does not always handle bareword "NaN" properly.
 e

# perl Mbigint=e wle 'print e'
Returns Euler's number "e", aka exp(1). Note that under
bigint, this is truncated to an integer, and hence simple '2'.
 PI

# perl Mbigint=PI wle 'print PI'
Returns PI. Note that under bigint, this is truncated to an integer, and
hence simple '3'.
 bexp()

bexp($power,$accuracy);
Returns Euler's number "e" raised to the appropriate power, to the
wanted accuracy.
Note that under bigint, the result is truncated to an integer.
Example:
# perl Mbigint=bexp wle 'print bexp(1,80)'
 bpi()

bpi($accuracy);
Returns PI to the wanted accuracy. Note that under bigint, this is truncated
to an integer, and hence simple '3'.
Example:
# perl Mbigint=bpi wle 'print bpi(80)'
 upgrade()
 Return the class that numbers are upgraded to, is in fact returning
$Math::BigInt::upgrade.
 in_effect()

use bigint;
print "in effect\n" if bigint::in_effect; # true
{
no bigint;
print "in effect\n" if bigint::in_effect; # false
}
Returns true or false if "bigint" is in effect in the current
scope.
This method only works on Perl v5.9.4 or later.
 Operator vs literal overloading
 "bigint" works by overloading handling of integer and floating
point literals, converting them to Math::BigInt objects.
This means that arithmetic involving only string values or string literals
will be performed using Perl's builtin operators.
For example:
use bignum;
my $x = "900000000000000009";
my $y = "900000000000000007";
print $x  $y;
will output 0 on default 32bit builds, since "bigint" never sees
the string literals. To ensure the expression is all treated as
"Math::BigInt" objects, use a literal number in the expression:
print +(0+$x)  $y;
 ranges
 Perl does not allow overloading of ranges, so you can neither safely use
ranges with bigint endpoints, nor is the iterator variable a bigint.
use 5.010;
for my $i (12..13) {
for my $j (20..21) {
say $i ** $j; # produces a floatingpoint number,
# not a big integer
}
}
 in_effect()
 This method only works on Perl v5.9.4 or later.
 hex()/oct()
 "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 nonportable constant.
Compare this to:
use bigint;
# will warn only under Perl older than v5.9.4
print hex("0x1234567890123456");
"bigint" 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 bigint:
Math::BigInt::Lite (for speed, and only if it is loadable)
Math::BigInt
Some cool command line examples to impress the Python crowd ;) You might want to
compare them to the results under Mbignum or Mbigrat:
perl Mbigint le 'print sqrt(33)'
perl Mbigint le 'print 2*255'
perl Mbigint le 'print 4.5+2*255'
perl Mbigint le 'print 3/7 + 5/7 + 8/3'
perl Mbigint le 'print 123>is_odd()'
perl Mbigint le 'print log(2)'
perl Mbigint le 'print 2 ** 0.5'
perl Mbigint=a,65 le 'print 2 ** 0.2'
perl Mbignum=a,65,l,GMP le 'print 7 ** 7777'
For information about bugs and how to report them, see the BUGS section in the
documentation available with the perldoc command.
perldoc bignum
You can find documentation for this module with the perldoc command.
perldoc bigint
For more information, see the SUPPORT section in the documentation available
with the perldoc command.
perldoc bignum
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
bignum and bigrat.
Math::BigInt, Math::BigFloat, Math::BigRat and Math::Big as well as
Math::BigInt::FastCalc, Math::BigInt::Pari and Math::BigInt::GMP.
 •
 (C) by Tels <http://bloodgate.com/> in early 2002  2007.
 •
 Maintained by Peter John Acklam <pjacklam@gmail.com<gt>,
2014.