bignum/lib/bigint.pm

package bigint;

use 5.010;
use strict;
use warnings;

our $VERSION = '0.51';

use Exporter;
our @ISA            = qw( Exporter );
our @EXPORT_OK      = qw( PI e bpi bexp hex oct );
our @EXPORT         = qw( inf NaN );

use overload;

##############################################################################

# These are all alike, and thus faked by AUTOLOAD

my @faked = qw/round_mode accuracy precision div_scale/;
our ($AUTOLOAD, $_lite);        # _lite for testsuite

sub AUTOLOAD {
    my $name = $AUTOLOAD;

    $name =~ s/.*:://;          # split package
    no strict 'refs';
    foreach my $n (@faked) {
        if ($n eq $name) {
            *{"bigint::$name"} =
              sub {
                  my $self = shift;
                  no strict 'refs';
                  if (defined $_[0]) {
                      return Math::BigInt->$name($_[0]);
                  }
                  return Math::BigInt->$name();
              };
            return &$name;
        }
    }

    # delayed load of Carp and avoid recursion
    require Carp;
    Carp::croak ("Can't call bigint\-\>$name, not a valid method");
}

sub upgrade {
    $Math::BigInt::upgrade;
}

sub _binary_constant {
    # this takes a binary/hexadecimal/octal constant string and returns it
    # as string suitable for new. Basically it converts octal to decimal, and
    # passes every thing else unmodified back.
    my $string = shift;

    return Math::BigInt->new($string) if $string =~ /^0[bx]/;

    # so it must be an octal constant
    Math::BigInt->from_oct($string);
}

sub _float_constant {
    # this takes a floating point constant string and returns it truncated to
    # integer. For instance, '4.5' => '4', '1.234e2' => '123' etc
    my $float = shift;

    # some simple cases first
    return $float if ($float =~ /^[+-]?[0-9]+$/);       # '+123','-1','0' etc
    return $float
      if ($float =~ /^[+-]?[0-9]+\.?[eE]\+?[0-9]+$/);   # 123e2, 123.e+2
    return '0' if ($float =~ /^[+-]?[0]*\.[0-9]+$/);    # .2, 0.2, -.1
    if ($float =~ /^[+-]?[0-9]+\.[0-9]*$/) {            # 1., 1.23, -1.2 etc
        $float =~ s/\..*//;
        return $float;
    }
    my ($mis, $miv, $mfv, $es, $ev) = Math::BigInt::_split($float);
    return $float if !defined $mis;       # doesn't look like a number to me
    my $ec = int($$ev);
    my $sign = $$mis;
    $sign = '' if $sign eq '+';
    if ($$es eq '-') {
        # ignore fraction part entirely
        if ($ec >= length($$miv)) {                     # 123.23E-4
            return '0';
        }
        return $sign . substr($$miv, 0, length($$miv) - $ec); # 1234.45E-2 = 12
    }
    # xE+y
    if ($ec >= length($$mfv)) {
        $ec -= length($$mfv);
        return $sign.$$miv.$$mfv if $ec == 0;           # 123.45E+2 => 12345
        return $sign.$$miv.$$mfv.'E'.$ec;               # 123.45e+3 => 12345e1
    }
    $mfv = substr($$mfv, 0, $ec);
    $sign.$$miv.$mfv;                                   # 123.45e+1 => 1234
}

sub unimport {
    $^H{bigint} = undef;                                # no longer in effect
    overload::remove_constant('binary', '', 'float', '', 'integer');
}

sub in_effect {
    my $level = shift || 0;
    my $hinthash = (caller($level))[10];
    $hinthash->{bigint};
}

#############################################################################
# the following two routines are for "use bigint qw/hex oct/;":

use constant LEXICAL => $] > 5.009004;

# Internal function with the same semantics as CORE::hex(). This function is
# not used directly, but rather by other front-end functions.

sub _hex_core {
    my $str = shift;

    # Strip off, clean, and parse as much as we can from the beginning.

    my $x;
    if ($str =~ s/ ^ (0?[xX])? ( [0-9a-fA-F]* ( _ [0-9a-fA-F]+ )* ) //x) {
        my $chrs = $2;
        $chrs =~ tr/_//d;
        $chrs = '0' unless CORE::length $chrs;
        $x = Math::BigInt -> from_hex($chrs);
    } else {
        $x = Math::BigInt -> bzero();
    }

    # Warn about trailing garbage.

    if (CORE::length($str)) {
        require Carp;
        Carp::carp(sprintf("Illegal hexadecimal digit '%s' ignored",
                           substr($str, 0, 1)));
    }

    return $x;
}

# Internal function with the same semantics as CORE::oct(). This function is
# not used directly, but rather by other front-end functions.

sub _oct_core {
    my $str = shift;

    $str =~ s/^\s*//;

    # Hexadecimal input.

    return _hex_core($str) if $str =~ /^0?[xX]/;

    my $x;

    # Binary input.

    if ($str =~ /^0?[bB]/) {

        # Strip off, clean, and parse as much as we can from the beginning.

        if ($str =~ s/ ^ (0?[bB])? ( [01]* ( _ [01]+ )* ) //x) {
            my $chrs = $2;
            $chrs =~ tr/_//d;
            $chrs = '0' unless CORE::length $chrs;
            $x = Math::BigInt -> from_bin($chrs);
        }

        # Warn about trailing garbage.

        if (CORE::length($str)) {
            require Carp;
            Carp::carp(sprintf("Illegal binary digit '%s' ignored",
                               substr($str, 0, 1)));
        }

        return $x;
    }

    # Octal input. Strip off, clean, and parse as much as we can from the
    # beginning.

    if ($str =~ s/ ^ ( [0-7]* ( _ [0-7]+ )* ) //x) {
        my $chrs = $1;
        $chrs =~ tr/_//d;
        $chrs = '0' unless CORE::length $chrs;
        $x = Math::BigInt -> from_oct($chrs);
    }

    # Warn about trailing garbage. CORE::oct() only warns about 8 and 9.

    if (CORE::length($str)) {
        my $chr = substr($str, 0, 1);
        if ($chr eq '8' || $chr eq '9') {
            require Carp;
            Carp::carp(sprintf("Illegal octal digit '%s' ignored", $chr));
        }
    }

    return $x;
}

{
    my $proto = LEXICAL ? '_' : ';$';
    eval '
sub hex(' . $proto . ') {' . <<'.';
    my $str = @_ ? $_[0] : $_;
    _hex_core($str);
}
.

    eval '
sub oct(' . $proto . ') {' . <<'.';
    my $str = @_ ? $_[0] : $_;
    _oct_core($str);
}
.
}

#############################################################################
# the following two routines are for Perl 5.9.4 or later and are lexical

my ($prev_oct, $prev_hex, $overridden);

if (LEXICAL) { eval <<'.' }
sub _hex(_) {
    my $hh = (caller 0)[10];
    return $prev_hex ? &$prev_hex($_[0]) : CORE::hex($_[0])
      unless $$hh{bigint}||$$hh{bignum}||$$hh{bigrat};
    _hex_core($_[0]);
}

sub _oct(_) {
    my $hh = (caller 0)[10];
    return $prev_oct ? &$prev_oct($_[0]) : CORE::oct($_[0])
      unless $$hh{bigint}||$$hh{bignum}||$$hh{bigrat};
    _oct_core($_[0]);
}
.

sub _override {
    return if $overridden;
    $prev_oct = *CORE::GLOBAL::oct{CODE};
    $prev_hex = *CORE::GLOBAL::hex{CODE};
    no warnings 'redefine';
    *CORE::GLOBAL::oct = \&_oct;
    *CORE::GLOBAL::hex = \&_hex;
    $overridden++;
}

sub import {
    my $self = shift;

    $^H{bigint} = 1;                            # we are in effect

    # for newer Perls always override hex() and oct() with a lexical version:
    if (LEXICAL) {
        _override();
    }
    # some defaults
    my $lib = '';
    my $lib_kind = 'try';

    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++, $j++) {
        if ($_[$i] =~ /^(l|lib|try|only)$/) {
            # 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-existent..."
            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-existent..."
            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-existent..."
            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] !~ /^(PI|e|bpi|bexp|hex|oct)\z/) {
            die ("unknown option $_[$i]");
        }
    }
    my $class;
    $_lite = 0;                                 # using M::BI::L ?
    if ($trace) {
        require Math::BigInt::Trace;
        $class = 'Math::BigInt::Trace';
    } else {
        # see if we can find Math::BigInt::Lite
        if (!defined $a && !defined $p) {       # rounding won't work to well
            local @INC = @INC;
            pop @INC if $INC[-1] eq '.';
            if (eval { require Math::BigInt::Lite; 1 }) {
                @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);

    bigint->accuracy($a)  if defined $a;
    bigint->precision($p) if defined $p;
    if ($ver) {
        print "bigint\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";
        exit;
    }
    # we take care of floating point constants, since BigFloat isn't available
    # and BigInt doesn't like them:
    overload::constant float =>
        sub {
            Math::BigInt->new(_float_constant(shift));
        };
    # Take care of octal/hexadecimal constants
    overload::constant binary =>
        sub {
            _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, e and PI
    }
}

sub inf () { Math::BigInt->binf(); }
sub NaN () { Math::BigInt->bnan(); }

sub PI () { Math::BigInt->new(3); }
sub e () { Math::BigInt->new(2); }
sub bpi ($) { Math::BigInt->new(3); }
sub bexp ($$) {
    my $x = Math::BigInt->new($_[0]);
    $x->bexp($_[1]);
}

1;

__END__

=pod

=head1 NAME

bigint - Transparent BigInteger support for Perl

=head1 SYNOPSIS

  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";

=head1 DESCRIPTION

All operators (including basic math operations) except the range operator C<..>
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 L<integer>, this pragma creates integer constants that are only
limited in their size by the available memory and CPU time.

=head2 use integer vs. use bigint

There is one small difference between C<use integer> and C<use bigint>: the
former will not affect assignments to variables and the return value of
some functions. C<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 B<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"

=head2 Options

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:

=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 -Mbigint=a,2 -le 'print 12345+1'

Note that setting precision and accuracy 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, 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.

=item t or trace

This enables a trace mode and is primarily for debugging bigint or
Math::BigInt.

=item hex

Override the built-in 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.

=item oct

Override the built-in 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.

=item l, lib, try or only

Load a different math lib, see L<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 ;)

=item v or version

This prints out the name and version of all modules used and then exits.

        perl -Mbigint=v

=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 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 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 suppress 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';

Please see respective module documentation for further details.

=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::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.

=head2 Sign

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.

=head2 Method calls

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
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 that 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.

=head2 Methods

=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 -Mbigint=e -wle 'print e'

Returns Euler's number C<e>, aka exp(1). Note that under bigint, this is
truncated to an integer, and hence simple '2'.

=item PI

        # perl -Mbigint=PI -wle 'print PI'

Returns PI. Note that under bigint, this is truncated to an integer, and hence
simple '3'.

=item bexp()

        bexp($power,$accuracy);

Returns Euler's number C<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)'

=item 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)'

=item upgrade()

Return the class that numbers are upgraded to, is in fact returning
C<$Math::BigInt::upgrade>.

=item 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 C<bigint> is in effect in the current scope.

This method only works on Perl v5.9.4 or later.

=back

=head1 CAVEATS

=over 2

=item Operator vs literal overloading

C<bigint> works by overloading handling of integer and floating point
literals, converting them to L<Math::BigInt> objects.

This means that arithmetic involving only string values or string
literals will be performed using Perl's built-in operators.

For example:

    use bignum;
    my $x = "900000000000000009";
    my $y = "900000000000000007";
    print $x - $y;

will output C<0> on default 32-bit builds, since C<bigint> never sees
the string literals.  To ensure the expression is all treated as
C<Math::BigInt> objects, use a literal number in the expression:

    print +(0+$x) - $y;

=item 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 floating-point number,
                           # not a big integer
          }
        }

=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 Perl older than v5.9.4
        print hex("0x1234567890123456");

=back

=head1 MODULES USED

C<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

=head1 EXAMPLES

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'

=head1 BUGS

For information about bugs and how to report them, see the BUGS section in the
documentation available with the perldoc command.

    perldoc bignum

=head1 SUPPORT

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

=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

L<bignum> and L<bigrat>.

L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as
L<Math::BigInt::FastCalc>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.

=head1 AUTHORS

=over 4

=item *

(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.

=item *

Maintained by Peter John Acklam E<lt>pjacklam@gmail.com<gt>, 2014-.

=back

=cut