# underlying lib might change the reference!
my $class = "Math::BigInt";
-require 5.005;
+use 5.006002;
-$VERSION = '1.77';
+$VERSION = '1.87';
@ISA = qw(Exporter);
@EXPORT_OK = qw(objectify bgcd blcm);
# not supported by Perl yet
'..' => \&_pointpoint,
-# we might need '==' and '!=' to get things like "NaN == NaN" right
-'<=>' => sub { $_[2] ?
+'<=>' => sub { my $rc = $_[2] ?
ref($_[0])->bcmp($_[1],$_[0]) :
- $_[0]->bcmp($_[1]); },
+ $_[0]->bcmp($_[1]);
+ $rc = 1 unless defined $rc;
+ $rc <=> 0;
+ },
+# we need '>=' to get things like "1 >= NaN" right:
+'>=' => sub { my $rc = $_[2] ?
+ ref($_[0])->bcmp($_[1],$_[0]) :
+ $_[0]->bcmp($_[1]);
+ # if there was a NaN involved, return false
+ return '' unless defined $rc;
+ $rc >= 0;
+ },
'cmp' => sub {
$_[2] ?
"$_[1]" cmp $_[0]->bstr() :
$_[0]->bstr() cmp "$_[1]" },
-# make cos()/sin()/exp() "work" with BigInt's or subclasses
+# make cos()/sin()/atan2() "work" with BigInt's or subclasses
'cos' => sub { cos($_[0]->numify()) },
'sin' => sub { sin($_[0]->numify()) },
-'exp' => sub { exp($_[0]->numify()) },
'atan2' => sub { $_[2] ?
atan2($_[1],$_[0]->numify()) :
atan2($_[0]->numify(),$_[1]) },
#'hex' => sub { print "hex"; $_[0]; },
#'oct' => sub { print "oct"; $_[0]; },
-'log' => sub { $_[0]->copy()->blog($_[1]); },
+# log(N) is log(N, e), where e is Euler's number
+'log' => sub { $_[0]->copy()->blog($_[1], undef); },
+'exp' => sub { $_[0]->copy()->bexp($_[1]); },
'int' => sub { $_[0]->copy(); },
'neg' => sub { $_[0]->copy()->bneg(); },
'abs' => sub { $_[0]->copy()->babs(); },
# These vars are public, but their direct usage is not recommended, use the
# accessor methods instead
-$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
+$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
$accuracy = undef;
$precision = undef;
$div_scale = 40;
if (defined $_[0])
{
my $m = shift;
- if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
+ if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
{
require Carp; Carp::croak ("Unknown round mode '$m'");
}
my $class = shift || 'Math::BigInt';
no strict 'refs';
- if (@_ > 0)
+ if (@_ > 1 || (@_ == 1 && (ref($_[0]) eq 'HASH')))
{
# try to set given options as arguments from hash
{
$cfg->{$key} = ${"${class}::$key"};
};
+ if (@_ == 1 && (ref($_[0]) ne 'HASH'))
+ {
+ # calls of the style config('lib') return just this value
+ return $cfg->{$_[0]};
+ }
$cfg;
}
my $c = ref($self); # find out class of argument(s)
no strict 'refs';
+ # convert to normal scalar for speed and correctness in inner parts
+ $a = $a->numify() if defined $a && ref($a);
+ $p = $p->numify() if defined $a && ref($p);
+
# now pick $a or $p, but only if we have got "arguments"
if (!defined $a)
{
return ($self->bnan()) if defined $a && defined $p; # error
$r = ${"$c\::round_mode"} unless defined $r;
- if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
+ if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
{
require Carp; Carp::croak ("Unknown round mode '$r'");
}
return $self->bnan() if defined $a && defined $p;
$r = ${"$c\::round_mode"} unless defined $r;
- if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
+ if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
{
require Carp; Carp::croak ("Unknown round mode '$r'");
}
{
$self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p;
}
- # bround() or bfround() already callled bnorm() if necc.
+ # bround() or bfround() already callled bnorm() if nec.
$self;
}
# set up parameters
my ($self,$x,$y,@r) = (ref($_[0]),@_);
+
# objectify is costly, so avoid it
if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
{
}
$x->badd($y,@r); # badd does not leave internal zeros
$y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
- $x; # already rounded by badd() or no round necc.
+ $x; # already rounded by badd() or no round nec.
}
sub binc
{
($self,$x,$base,@r) = objectify(1,ref($x),@_);
}
-
+
return $x if $x->modify('blog');
+ $base = $self->new($base) if defined $base && !ref $base;
+
# inf, -inf, NaN, <0 => NaN
return $x->bnan()
if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+');
return $upgrade->blog($upgrade->new($x),$base,@r) if
defined $upgrade;
+ # fix for bug #24969:
+ # the default base is e (Euler's number) which is not an integer
+ if (!defined $base)
+ {
+ require Math::BigFloat;
+ my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int();
+ # modify $x in place
+ $x->{value} = $u->{value};
+ $x->{sign} = $u->{sign};
+ return $x;
+ }
+
my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value});
return $x->bnan() unless defined $rc; # not possible to take log?
$x->{value} = $rc;
$x->round(@r);
}
+sub bnok
+ {
+ # Calculate n over k (binomial coefficient or "choose" function) as integer.
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
+
+ return $x if $x->modify('bnok');
+ return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN';
+ return $x->binf() if $x->{sign} eq '+inf';
+
+ # k > n or k < 0 => 0
+ my $cmp = $x->bacmp($y);
+ return $x->bzero() if $cmp < 0 || $y->{sign} =~ /^-/;
+ # k == n => 1
+ return $x->bone(@r) if $cmp == 0;
+
+ if ($CALC->can('_nok'))
+ {
+ $x->{value} = $CALC->_nok($x->{value},$y->{value});
+ }
+ else
+ {
+ # ( 7 ) 7! 7*6*5 * 4*3*2*1 7 * 6 * 5
+ # ( - ) = --------- = --------------- = ---------
+ # ( 3 ) 3! (7-3)! 3*2*1 * 4*3*2*1 3 * 2 * 1
+
+ # compute n - k + 2 (so we start with 5 in the example above)
+ my $z = $x - $y;
+ if (!$z->is_one())
+ {
+ $z->binc();
+ my $r = $z->copy(); $z->binc();
+ my $d = $self->new(2);
+ while ($z->bacmp($x) <= 0) # f < x ?
+ {
+ $r->bmul($z); $r->bdiv($d);
+ $z->binc(); $d->binc();
+ }
+ $x->{value} = $r->{value}; $x->{sign} = '+';
+ }
+ else { $x->bone(); }
+ }
+ $x->round(@r);
+ }
+
+sub bexp
+ {
+ # Calculate e ** $x (Euler's number to the power of X), truncated to
+ # an integer value.
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+ return $x if $x->modify('bexp');
+
+ # inf, -inf, NaN, <0 => NaN
+ return $x->bnan() if $x->{sign} eq 'NaN';
+ return $x->bone() if $x->is_zero();
+ return $x if $x->{sign} eq '+inf';
+ return $x->bzero() if $x->{sign} eq '-inf';
+
+ my $u;
+ {
+ # run through Math::BigFloat unless told otherwise
+ require Math::BigFloat unless defined $upgrade;
+ local $upgrade = 'Math::BigFloat' unless defined $upgrade;
+ # calculate result, truncate it to integer
+ $u = $upgrade->bexp($upgrade->new($x),@r);
+ }
+
+ if (!defined $upgrade)
+ {
+ $u = $u->as_int();
+ # modify $x in place
+ $x->{value} = $u->{value};
+ $x->round(@r);
+ }
+ else { $x = $u; }
+ }
+
sub blcm
{
# (BINT or num_str, BINT or num_str) return BINT
{
($self,$x,$y,@r) = objectify(2,@_);
}
-
+
return $x if $x->modify('bmul');
return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
}
return $upgrade->bpow($upgrade->new($x),$y,@r)
- if defined $upgrade && !$y->isa($self);
+ if defined $upgrade && (!$y->isa($self) || $y->{sign} eq '-');
$r[3] = $y; # no push!
$bin =~ s/^-0b//; # strip '-0b' prefix
$bin =~ tr/10/01/; # flip bits
# now shift
- if (CORE::length($bin) <= $y)
+ if ($y >= CORE::length($bin))
{
$bin = '0'; # shifting to far right creates -1
# 0, because later increment makes
}
return $self->bone() if $x->is_zero();
- $self->new($x->_trailing_zeros());
+ # 12300 => 2 trailing zeros => exponent is 2
+ $self->new( $CALC->_zeros($x->{value}) );
}
sub mantissa
return $self->new($x->{sign});
}
my $m = $x->copy(); delete $m->{_p}; delete $m->{_a};
+
# that's a bit inefficient:
- my $zeros = $m->_trailing_zeros();
+ my $zeros = $CALC->_zeros($m->{value});
$m->brsft($zeros,10) if $zeros != 0;
$m;
}
sub as_number
{
# An object might be asked to return itself as bigint on certain overloaded
- # operations, this does exactly this, so that sub classes can simple inherit
+ # operations. This does exactly this, so that sub classes can simple inherit
# it or override with their own integer conversion routine.
$_[0]->copy();
}
return $s . $CALC->_as_bin($x->{value});
}
+sub as_oct
+ {
+ # return as octal string, with prefixed 0
+ my $x = shift; $x = $class->new($x) if !ref($x);
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+
+ my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
+ return $s . $CALC->_as_oct($x->{value});
+ }
+
##############################################################################
# private stuff (internal use only)
}
my $up = ${"$a[0]::upgrade"};
- #print "Now in objectify, my class is today $a[0], count = $count\n";
+ # print STDERR "# Now in objectify, my class is today $a[0], count = $count\n";
if ($count == 0)
{
while (@_)
while ($count > 0)
{
$count--;
- $k = shift;
+ $k = shift;
if (!ref($k))
{
$k = $a[0]->new($k);
elsif (!defined $up && ref($k) ne $a[0])
{
# foreign object, try to convert to integer
- $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
+ $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
}
push @a,$k;
}
$IMPORT++; # remember we did import()
my @a; my $l = scalar @_;
+ my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die
for ( my $i = 0; $i < $l ; $i++ )
{
if ($_[$i] eq ':constant')
$upgrade = $_[$i+1]; # or undef to disable
$i++;
}
- elsif ($_[$i] =~ /^lib$/i)
+ elsif ($_[$i] =~ /^(lib|try|only)\z/)
{
# this causes a different low lib to take care...
$CALC = $_[$i+1] || '';
+ # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback)
+ $warn_or_die = 1 if $_[$i] eq 'lib';
+ $warn_or_die = 2 if $_[$i] eq 'only';
$i++;
}
else
{
$_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters
}
- push @c, 'FastCalc', 'Calc'; # if all fail, try these
+ push @c, \'FastCalc', \'Calc' # if all fail, try these
+ if $warn_or_die < 2; # but not for "only"
$CALC = ''; # signal error
- foreach my $lib (@c)
+ foreach my $l (@c)
{
+ # fallback libraries are "marked" as \'string', extract string if nec.
+ my $lib = $l; $lib = $$l if ref($l);
+
next if ($lib || '') eq '';
$lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
$lib =~ s/\.pm$//;
add mul div sub dec inc
acmp len digit is_one is_zero is_even is_odd
is_two is_ten
- new copy check from_hex from_bin as_hex as_bin zeros
+ zeros new copy check
+ from_hex from_oct from_bin as_hex as_bin as_oct
rsft lsft xor and or
mod sqrt root fac pow modinv modpow log_int gcd
/)
if ($ok == 0)
{
$CALC = $lib;
+ if ($warn_or_die > 0 && ref($l))
+ {
+ require Carp;
+ my $msg = "Math::BigInt: couldn't load specified math lib(s), fallback to $lib";
+ Carp::carp ($msg) if $warn_or_die == 1;
+ Carp::croak ($msg) if $warn_or_die == 2;
+ }
last; # found a usable one, break
}
else
if ($CALC eq '')
{
require Carp;
- Carp::croak ("Couldn't load any math lib, not even 'Calc.pm'");
+ if ($warn_or_die == 2)
+ {
+ Carp::croak ("Couldn't load specified math lib(s) and fallback disallowed");
+ }
+ else
+ {
+ Carp::croak ("Couldn't load any math lib(s), not even fallback to Calc.pm");
+ }
}
# notify callbacks
# import done
}
+sub from_hex
+ {
+ # create a bigint from a hexadecimal string
+ my ($self, $hs) = @_;
+
+ my $rc = $self->__from_hex($hs);
+
+ return $self->bnan() unless defined $rc;
+
+ $rc;
+ }
+
+sub from_bin
+ {
+ # create a bigint from a hexadecimal string
+ my ($self, $bs) = @_;
+
+ my $rc = $self->__from_bin($bs);
+
+ return $self->bnan() unless defined $rc;
+
+ $rc;
+ }
+
+sub from_oct
+ {
+ # create a bigint from a hexadecimal string
+ my ($self, $os) = @_;
+
+ my $x = $self->bzero();
+
+ # strip underscores
+ $os =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
+ $os =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
+
+ return $x->bnan() if $os !~ /^[\-\+]?0[0-9]+$/;
+
+ my $sign = '+'; $sign = '-' if $os =~ /^-/;
+
+ $os =~ s/^[+-]//; # strip sign
+ $x->{value} = $CALC->_from_oct($os);
+ $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0'
+ $x;
+ }
+
sub __from_hex
{
# internal
my $bs = shift;
my $x = Math::BigInt->bzero();
+
# strip underscores
$bs =~ s/([01])_([01])/$1$2/g;
$bs =~ s/([01])_([01])/$1$2/g;
my $x = shift;
# strip white space at front, also extranous leading zeros
- $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2'
- $x =~ s/^\s+//; # but this will
- $x =~ s/\s+$//g; # strip white space at end
+ $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2'
+ $x =~ s/^\s+//; # but this will
+ $x =~ s/\s+$//g; # strip white space at end
# shortcut, if nothing to split, return early
- if ($x =~ /^[+-]?\d+\z/)
+ if ($x =~ /^[+-]?[0-9]+\z/)
{
$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
return (\$sign, \$x, \'', \'', \0);
# invalid starting char?
return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
- return __from_hex($x) if $x =~ /^[\-\+]?0x/; # hex string
- return __from_bin($x) if $x =~ /^[\-\+]?0b/; # binary string
+ return __from_hex($x) if $x =~ /^[\-\+]?0x/; # hex string
+ return __from_bin($x) if $x =~ /^[\-\+]?0b/; # binary string
# strip underscores between digits
- $x =~ s/(\d)_(\d)/$1$2/g;
- $x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3
+ $x =~ s/([0-9])_([0-9])/$1$2/g;
+ $x =~ s/([0-9])_([0-9])/$1$2/g; # do twice for 1_2_3
# some possible inputs:
# 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
# sign,value for exponent,mantint,mantfrac
my ($es,$ev,$mis,$miv,$mfv);
# valid exponent?
- if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
+ if ($e =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
{
$es = $1; $ev = $2;
# valid mantissa?
$mi = '0' if !defined $mi;
$mi .= '0' if $mi =~ /^[\-\+]?$/;
$mf = '0' if !defined $mf || $mf eq '';
- if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
+ if ($mi =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
{
$mis = $1||'+'; $miv = $2;
- return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros
+ return unless ($mf =~ /^([0-9]*?)0*$/); # strip trailing zeros
$mfv = $1;
# handle the 0e999 case here
$ev = 0 if $miv eq '0' && $mfv eq '';
# and always use (it will fall back to pure Perl if the
# GMP library is not installed):
+ # will warn if Math::BigInt::GMP cannot be found
use Math::BigInt lib => 'GMP';
+ # to supress the warning use this:
+ # use Math::BigInt try => 'GMP';
+
my $str = '1234567890';
my @values = (64,74,18);
my $n = 1; my $sign = '-';
$one = Math::BigInt->bone(); # create a +1
$one = Math::BigInt->bone('-'); # create a -1
+ $h = Math::BigInt->new('0x123'); # from hexadecimal
+ $b = Math::BigInt->new('0b101'); # from binary
+ $o = Math::BigInt->from_oct('0101'); # from octal
+
# Testing (don't modify their arguments)
# (return true if the condition is met, otherwise false)
$x->bmodinv($mod); # the inverse of $x in the given modulus $mod
$x->bpow($y); # power of arguments (x ** y)
- $x->blsft($y); # left shift
- $x->brsft($y); # right shift
- $x->blsft($y,$n); # left shift, by base $n (like 10)
- $x->brsft($y,$n); # right shift, by base $n (like 10)
+ $x->blsft($y); # left shift in base 2
+ $x->brsft($y); # right shift in base 2
+ # returns (quo,rem) or quo if in scalar context
+ $x->blsft($y,$n); # left shift by $y places in base $n
+ $x->brsft($y,$n); # right shift by $y places in base $n
+ # returns (quo,rem) or quo if in scalar context
$x->band($y); # bitwise and
$x->bior($y); # bitwise inclusive or
$x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root)
$x->bfac(); # factorial of $x (1*2*3*4*..$x)
+ $x->bnok($y); # x over y (binomial coefficient n over k)
+
+ $x->blog(); # logarithm of $x to base e (Euler's number)
+ $x->blog($base); # logarithm of $x to base $base (f.i. 2)
+ $x->bexp(); # calculate e ** $x where e is Euler's number
+
$x->round($A,$P,$mode); # round to accuracy or precision using mode $mode
$x->bround($n); # accuracy: preserve $n digits
$x->bfround($n); # round to $nth digit, no-op for BigInts
$x->bsstr(); # norm. string in scientific notation (e.g. '3E0')
$x->as_hex(); # as signed hexadecimal string with prefixed 0x
$x->as_bin(); # as signed binary string with prefixed 0b
+ $x->as_oct(); # as signed octal string with prefixed 0
# precision and accuracy (see section about rounding for more)
Math::BigInt->precision(); # get/set global P for all BigInt objects
Math::BigInt->accuracy(); # get/set global A for all BigInt objects
Math::BigInt->round_mode(); # get/set global round mode, one of
- # 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
+ # 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
Math::BigInt->config(); # return hash containing configuration
=head1 DESCRIPTION
This means integer values like 1.01E2 or even 1000E-2 are also accepted.
Non-integer values result in NaN.
+Hexadecimal (prefixed with "0x") and binary numbers (prefixed with "0b")
+are accepted, too. Please note that octal numbers are not recognized
+by new(), so the following will print "123":
+
+ perl -MMath::BigInt -le 'print Math::BigInt->new("0123")'
+
+To convert an octal number, use from_oct();
+
+ perl -MMath::BigInt -le 'print Math::BigInt->from_oct("0123")'
+
Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('')
results in 'NaN'. This might change in the future, so use always the following
explicit forms to get a zero or NaN:
are C<accuracy>, C<precision> and C<round_mode>. Please see the section about
L<ACCURACY and PRECISION> for more information.
-=head2 config
+=head2 config()
use Data::Dumper;
$new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } );
-=head2 accuracy
+=head2 accuracy()
$x->accuracy(5); # local for $x
CLASS->accuracy(5); # global for all members of CLASS
Math::BigInt and make the globals of the subclass aliases to the ones from
Math::BigInt.
-=head2 precision
+=head2 precision()
$x->precision(-2); # local for $x, round at the second digit right of the dot
$x->precision(2); # ditto, round at the second digit left of the dot
Math::BigInt and make the globals of the subclass aliases to the ones from
Math::BigInt.
-=head2 brsft
+=head2 brsft()
$x->brsft($y,$n);
This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the
result).
-=head2 new
+=head2 new()
$x = Math::BigInt->new($str,$A,$P,$R);
See L<Input> for more info on accepted input formats.
-=head2 bnan
+=head2 from_oct()
+
+ $x = Math::BigIn->from_oct("0775"); # input is octal
+
+=head2 from_hex()
+
+ $x = Math::BigIn->from_hex("0xcafe"); # input is hexadecimal
+
+=head2 from_bin()
+
+ $x = Math::BigIn->from_oct("0x10011"); # input is binary
+
+=head2 bnan()
$x = Math::BigInt->bnan();
$x->bnan();
-=head2 bzero
+=head2 bzero()
$x = Math::BigInt->bzero();
$x->bzero();
-=head2 binf
+=head2 binf()
$x = Math::BigInt->binf($sign);
$x->binf();
$x->binf('-');
-=head2 bone
+=head2 bone()
$x = Math::BigInt->binf($sign);
if ($x == 0)
-=head2 is_pos()/is_neg()
+=head2 is_pos()/is_neg()/is_positive()/is_negative()
$x->is_pos(); # true if > 0
$x->is_neg(); # true if < 0
In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers.
-=head2 bcmp
+=head2 bcmp()
$x->bcmp($y);
Compares $x with $y and takes the sign into account.
Returns -1, 0, 1 or undef.
-=head2 bacmp
+=head2 bacmp()
$x->bacmp($y);
Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef.
-=head2 sign
+=head2 sign()
$x->sign();
$x->binf(); # '+inf'
$x->binf('-'); # '-inf'
-=head2 digit
+=head2 digit()
$x->digit($n); # return the nth digit, counting from right
If C<$n> is negative, returns the digit counting from left.
-=head2 bneg
+=head2 bneg()
$x->bneg();
Negate the number, e.g. change the sign between '+' and '-', or between '+inf'
and '-inf', respectively. Does nothing for NaN or zero.
-=head2 babs
+=head2 babs()
$x->babs();
-Set the number to it's absolute value, e.g. change the sign from '-' to '+'
+Set the number to its absolute value, e.g. change the sign from '-' to '+'
and from '-inf' to '+inf', respectively. Does nothing for NaN or positive
numbers.
-=head2 bnorm
+=head2 bnorm()
$x->bnorm(); # normalize (no-op)
-=head2 bnot
+=head2 bnot()
$x->bnot();
-Two's complement (bit wise not). This is equivalent to
+Two's complement (bitwise not). This is equivalent to
$x->binc()->bneg();
but faster.
-=head2 binc
+=head2 binc()
$x->binc(); # increment x by 1
-=head2 bdec
+=head2 bdec()
$x->bdec(); # decrement x by 1
-=head2 badd
+=head2 badd()
$x->badd($y); # addition (add $y to $x)
-=head2 bsub
+=head2 bsub()
$x->bsub($y); # subtraction (subtract $y from $x)
-=head2 bmul
+=head2 bmul()
$x->bmul($y); # multiplication (multiply $x by $y)
-=head2 bdiv
+=head2 bdiv()
$x->bdiv($y); # divide, set $x to quotient
# return (quo,rem) or quo if scalar
-=head2 bmod
+=head2 bmod()
$x->bmod($y); # modulus (x % y)
-=head2 bmodinv
+=head2 bmodinv()
num->bmodinv($mod); # modular inverse
returned unless C<$num> is relatively prime to C<$mod>, i.e. unless
C<bgcd($num, $mod)==1>.
-=head2 bmodpow
+=head2 bmodpow()
$num->bmodpow($exp,$mod); # modular exponentation
# ($num**$exp % $mod)
bmodinv($num, $mod)
-=head2 bpow
+=head2 bpow()
$x->bpow($y); # power of arguments (x ** y)
-=head2 blsft
+=head2 blog()
- $x->blsft($y); # left shift
+ $x->blog($base, $accuracy); # logarithm of x to the base $base
+
+If C<$base> is not defined, Euler's number (e) is used:
+
+ print $x->blog(undef, 100); # log(x) to 100 digits
+
+=head2 bexp()
+
+ $x->bexp($accuracy); # calculate e ** X
+
+Calculates the expression C<e ** $x> where C<e> is Euler's number.
+
+This method was added in v1.82 of Math::BigInt (April 2007).
+
+See also L<blog()>.
+
+=head2 bnok()
+
+ $x->bnok($y); # x over y (binomial coefficient n over k)
+
+Calculates the binomial coefficient n over k, also called the "choose"
+function. The result is equivalent to:
+
+ ( n ) n!
+ | - | = -------
+ ( k ) k!(n-k)!
+
+This method was added in v1.84 of Math::BigInt (April 2007).
+
+=head2 blsft()
+
+ $x->blsft($y); # left shift in base 2
$x->blsft($y,$n); # left shift, in base $n (like 10)
-=head2 brsft
+=head2 brsft()
- $x->brsft($y); # right shift
+ $x->brsft($y); # right shift in base 2
$x->brsft($y,$n); # right shift, in base $n (like 10)
-=head2 band
+=head2 band()
$x->band($y); # bitwise and
-=head2 bior
+=head2 bior()
$x->bior($y); # bitwise inclusive or
-=head2 bxor
+=head2 bxor()
$x->bxor($y); # bitwise exclusive or
-=head2 bnot
+=head2 bnot()
$x->bnot(); # bitwise not (two's complement)
-=head2 bsqrt
+=head2 bsqrt()
$x->bsqrt(); # calculate square-root
-=head2 bfac
+=head2 bfac()
$x->bfac(); # factorial of $x (1*2*3*4*..$x)
-=head2 round
+=head2 round()
$x->round($A,$P,$round_mode);
Round $x to accuracy C<$A> or precision C<$P> using the round mode
C<$round_mode>.
-=head2 bround
+=head2 bround()
$x->bround($N); # accuracy: preserve $N digits
-=head2 bfround
+=head2 bfround()
$x->bfround($N); # round to $Nth digit, no-op for BigInts
-=head2 bfloor
+=head2 bfloor()
$x->bfloor();
Set $x to the integer less or equal than $x. This is a no-op in BigInt, but
does change $x in BigFloat.
-=head2 bceil
+=head2 bceil()
$x->bceil();
Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but
does change $x in BigFloat.
-=head2 bgcd
+=head2 bgcd()
bgcd(@values); # greatest common divisor (no OO style)
-=head2 blcm
+=head2 blcm()
blcm(@values); # lowest common multiplicator (no OO style)
-head2 length
+head2 length()
$x->length();
($xl,$fl) = $x->length();
In list context, returns the length of the integer and fraction part. For
BigInt's, the length of the fraction part will always be 0.
-=head2 exponent
+=head2 exponent()
$x->exponent();
Return the exponent of $x as BigInt.
-=head2 mantissa
+=head2 mantissa()
$x->mantissa();
Return the signed mantissa of $x as BigInt.
-=head2 parts
+=head2 parts()
$x->parts(); # return (mantissa,exponent) as BigInt
-=head2 copy
+=head2 copy()
$x->copy(); # make a true copy of $x (unlike $y = $x;)
-=head2 as_int
+=head2 as_int()/as_number()
$x->as_int();
C<as_number()> is an alias to this method. C<as_number> was introduced in
v1.22, while C<as_int()> was only introduced in v1.68.
-=head2 bstr
+=head2 bstr()
$x->bstr();
Returns a normalized string representation of C<$x>.
-=head2 bsstr
+=head2 bsstr()
$x->bsstr(); # normalized string in scientific notation
-=head2 as_hex
+=head2 as_hex()
$x->as_hex(); # as signed hexadecimal string with prefixed 0x
-=head2 as_bin
+=head2 as_bin()
$x->as_bin(); # as signed binary string with prefixed 0b
+=head2 as_oct()
+
+ $x->as_oct(); # as signed octal string with prefixed 0
+
+=head2 numify()
+
+ print $x->numify();
+
+This returns a normal Perl scalar from $x. It is used automatically
+whenever a scalar is needed, for instance in array index operations.
+
+This loses precision, to avoid this use L<as_int()> instead.
+
+=head2 modify()
+
+ $x->modify('bpowd');
+
+This method returns 0 if the object can be modified with the given
+peration, or 1 if not.
+
+This is used for instance by L<Math::BigInt::Constant>.
+
+=head2 upgrade()/downgrade()
+
+Set/get the class for downgrade/upgrade operations. Thuis is used
+for instance by L<bignum>. The defaults are '', thus the following
+operation will create a BigInt, not a BigFloat:
+
+ my $i = Math::BigInt->new(123);
+ my $f = Math::BigFloat->new('123.1');
+
+ print $i + $f,"\n"; # print 246
+
+=head2 div_scale()
+
+Set/get the number of digits for the default precision in divide
+operations.
+
+=head2 round_mode()
+
+Set/get the current round mode.
+
=head1 ACCURACY and PRECISION
Since version v1.33, Math::BigInt and Math::BigFloat have full support for
E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55
becomes -0.5, but 0.4501 becomes 0.5.
+=item 'common'
+
+round up if the digit immediately to the right of the rounding place
+is 5 or greater, otherwise round down. E.g., 0.15 becomes 0.2 and
+0.149 becomes 0.1.
+
=back
The handling of A & P in MBI/MBF (the old core code shipped with Perl
=item Creating numbers
- * When you create a number, you can give it's desired A or P via:
+ * When you create a number, you can give the desired A or P via:
$x = Math::BigInt->new($number,$A,$P);
* Only one of A or P can be defined, otherwise the result is NaN
* If no A or P is give ($x = Math::BigInt->new($number) form), then the
$x will be what was in effect when $x was created)
* If given undef for A and P, B<no> rounding will occur, and the globals will
B<not> be used. This is used by subclasses to create numbers without
- suffering rounding in the parent. Thus a subclass is able to have it's own
+ suffering rounding in the parent. Thus a subclass is able to have its own
globals enforced upon creation of a number by using
C<< $x = Math::BigInt->new($number,undef,undef) >>:
is for precision
* the two rounding functions take as the second parameter one of the
following rounding modes (R):
- 'even', 'odd', '+inf', '-inf', 'zero', 'trunc'
+ 'even', 'odd', '+inf', '-inf', 'zero', 'trunc', 'common'
* you can set/get the global R by using C<< Math::SomeClass->round_mode() >>
or by setting C<< $Math::SomeClass::round_mode >>
* after each operation, C<< $result->round() >> is called, and the result may
C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them
in one go. Both the returned mantissa and exponent have a sign.
-Currently, for BigInts C<$e> is always 0, except for NaN, +inf and -inf,
-where it is C<NaN>; and for C<$x == 0>, where it is C<1> (to be compatible
-with Math::BigFloat's internal representation of a zero as C<0E1>).
+Currently, for BigInts C<$e> is always 0, except +inf and -inf, where it is
+C<+inf>; and for NaN, where it is C<NaN>; and for C<$x == 0>, where it is C<1>
+(to be compatible with Math::BigFloat's internal representation of a zero as
+C<0E1>).
C<$m> is currently just a copy of the original number. The relation between
C<$e> and C<$m> will stay always the same, though their real values might
$x = "$x"; # same as bstr()
$x = Math::BigInt->bneg("1234"); # BigInt "-1234"
$x = Math::BigInt->babs("-12345"); # BigInt "12345"
- $x = Math::BigInt->bnorm("-0 00"); # BigInt "0"
+ $x = Math::BigInt->bnorm("-0.00"); # BigInt "0"
$x = bint(1) + bint(2); # BigInt "3"
$x = bint(1) + "2"; # ditto (auto-BigIntify of "2")
$x = bint(1); # BigInt "1"
All other object methods and overloaded functions can be directly inherited
from the parent class.
-At the very minimum, any subclass will need to provide it's own C<new()> and can
+At the very minimum, any subclass will need to provide its own C<new()> and can
store additional hash keys in the object. There are also some package globals
that must be defined, e.g.:
=item blog()
+=item bexp()
+
=back
Beware: This list is not complete.
drop the leading '+'. The old code would return '+3', the new returns '3'.
This is to be consistent with Perl and to make C<cmp> (especially with
overloading) to work as you expect. It also solves problems with C<Test.pm>,
-because it's C<ok()> uses 'eq' internally.
+because its C<ok()> uses 'eq' internally.
Mark Biggar said, when asked about to drop the '+' altogether, or make only
C<cmp> work:
This also works for other subclasses, like Math::String.
-It is yet unclear whether overloaded int() should return a scalar or a BigInt.
-
If you want a real Perl scalar, use C<numify()>:
$y = $x->numify(); # 123 as scalar
=head1 AUTHORS
Original code by Mark Biggar, overloaded interface by Ilya Zakharevich.
-Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2004
-and still at it in 2005.
+Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2006
+and still at it in 2007.
Many people contributed in one or more ways to the final beast, see the file
CREDITS for an (incomplete) list. If you miss your name, please drop me a
projects / p5sagit/p5-mst-13.2.git / blobdiff