+package Math::BigInt;
+
+#
+# "Mike had an infinite amount to do and a negative amount of time in which
+# to do it." - Before and After
+#
+
# The following hash values are used:
# value: unsigned int with actual value (as a Math::BigInt::Calc or similiar)
# sign : +,-,NaN,+inf,-inf
# Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
# underlying lib might change the reference!
-package Math::BigInt;
my $class = "Math::BigInt";
require 5.005;
-$VERSION = '1.51';
-use Exporter;
-@ISA = qw( Exporter );
-@EXPORT_OK = qw( objectify _swap bgcd blcm);
-use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/;
-use vars qw/$upgrade $downgrade/;
+$VERSION = '1.77';
+
+@ISA = qw(Exporter);
+@EXPORT_OK = qw(objectify bgcd blcm);
+
+# _trap_inf and _trap_nan are internal and should never be accessed from the
+# outside
+use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode
+ $upgrade $downgrade $_trap_nan $_trap_inf/;
use strict;
# Inside overload, the first arg is always an object. If the original code had
-# it reversed (like $x = 2 * $y), then the third paramater indicates this
-# swapping. To make it work, we use a helper routine which not only reswaps the
-# params, but also makes a new object in this case. See _swap() for details,
-# especially the cases of operators with different classes.
+# it reversed (like $x = 2 * $y), then the third paramater is true.
+# In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes
+# no difference, but in some cases it does.
# For overloaded ops with only one argument we simple use $_[0]->copy() to
# preserve the argument.
use overload
'=' => sub { $_[0]->copy(); },
-# '+' and '-' do not use _swap, since it is a triffle slower. If you want to
-# override _swap (if ever), then override overload of '+' and '-', too!
-# for sub it is a bit tricky to keep b: b-a => -a+b
-'-' => sub { my $c = $_[0]->copy; $_[2] ?
- $c->bneg()->badd($_[1]) :
- $c->bsub( $_[1]) },
-'+' => sub { $_[0]->copy()->badd($_[1]); },
-
# some shortcuts for speed (assumes that reversed order of arguments is routed
# to normal '+' and we thus can always modify first arg. If this is changed,
# this breaks and must be adjusted.)
'^=' => sub { $_[0]->bxor($_[1]); },
'&=' => sub { $_[0]->band($_[1]); },
'|=' => sub { $_[0]->bior($_[1]); },
+
'**=' => sub { $_[0]->bpow($_[1]); },
+'<<=' => sub { $_[0]->blsft($_[1]); },
+'>>=' => sub { $_[0]->brsft($_[1]); },
# not supported by Perl yet
'..' => \&_pointpoint,
+# we might need '==' and '!=' to get things like "NaN == NaN" right
'<=>' => sub { $_[2] ?
ref($_[0])->bcmp($_[1],$_[0]) :
- ref($_[0])->bcmp($_[0],$_[1])},
+ $_[0]->bcmp($_[1]); },
'cmp' => sub {
$_[2] ?
"$_[1]" cmp $_[0]->bstr() :
$_[0]->bstr() cmp "$_[1]" },
-'log' => sub { $_[0]->copy()->blog(); },
+# make cos()/sin()/exp() "work" with BigInt's or subclasses
+'cos' => sub { cos($_[0]->numify()) },
+'sin' => sub { sin($_[0]->numify()) },
+'exp' => sub { exp($_[0]->numify()) },
+'atan2' => sub { $_[2] ?
+ atan2($_[1],$_[0]->numify()) :
+ atan2($_[0]->numify(),$_[1]) },
+
+# are not yet overloadable
+#'hex' => sub { print "hex"; $_[0]; },
+#'oct' => sub { print "oct"; $_[0]; },
+
+'log' => sub { $_[0]->copy()->blog($_[1]); },
'int' => sub { $_[0]->copy(); },
'neg' => sub { $_[0]->copy()->bneg(); },
'abs' => sub { $_[0]->copy()->babs(); },
'sqrt' => sub { $_[0]->copy()->bsqrt(); },
'~' => sub { $_[0]->copy()->bnot(); },
-'*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); },
-'/' => sub { my @a = ref($_[0])->_swap(@_);scalar $a[0]->bdiv($a[1]);},
-'%' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmod($a[1]); },
-'**' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bpow($a[1]); },
-'<<' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->blsft($a[1]); },
-'>>' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->brsft($a[1]); },
-
-'&' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->band($a[1]); },
-'|' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bior($a[1]); },
-'^' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bxor($a[1]); },
-
-# can modify arg of ++ and --, so avoid a new-copy for speed, but don't
-# use $_[0]->__one(), it modifies $_[0] to be 1!
+# for subtract it's a bit tricky to not modify b: b-a => -a+b
+'-' => sub { my $c = $_[0]->copy; $_[2] ?
+ $c->bneg()->badd( $_[1]) :
+ $c->bsub( $_[1]) },
+'+' => sub { $_[0]->copy()->badd($_[1]); },
+'*' => sub { $_[0]->copy()->bmul($_[1]); },
+
+'/' => sub {
+ $_[2] ? ref($_[0])->new($_[1])->bdiv($_[0]) : $_[0]->copy->bdiv($_[1]);
+ },
+'%' => sub {
+ $_[2] ? ref($_[0])->new($_[1])->bmod($_[0]) : $_[0]->copy->bmod($_[1]);
+ },
+'**' => sub {
+ $_[2] ? ref($_[0])->new($_[1])->bpow($_[0]) : $_[0]->copy->bpow($_[1]);
+ },
+'<<' => sub {
+ $_[2] ? ref($_[0])->new($_[1])->blsft($_[0]) : $_[0]->copy->blsft($_[1]);
+ },
+'>>' => sub {
+ $_[2] ? ref($_[0])->new($_[1])->brsft($_[0]) : $_[0]->copy->brsft($_[1]);
+ },
+'&' => sub {
+ $_[2] ? ref($_[0])->new($_[1])->band($_[0]) : $_[0]->copy->band($_[1]);
+ },
+'|' => sub {
+ $_[2] ? ref($_[0])->new($_[1])->bior($_[0]) : $_[0]->copy->bior($_[1]);
+ },
+'^' => sub {
+ $_[2] ? ref($_[0])->new($_[1])->bxor($_[0]) : $_[0]->copy->bxor($_[1]);
+ },
+
+# can modify arg of ++ and --, so avoid a copy() for speed, but don't
+# use $_[0]->bone(), it would modify $_[0] to be 1!
'++' => sub { $_[0]->binc() },
'--' => sub { $_[0]->bdec() },
# if overloaded, O(1) instead of O(N) and twice as fast for small numbers
'bool' => sub {
# this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/
- # v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-(
- my $t = !$_[0]->is_zero();
- undef $t if $t == 0;
+ # v5.6.1 dumps on this: return !$_[0]->is_zero() || undef; :-(
+ my $t = undef;
+ $t = 1 if !$_[0]->is_zero();
$t;
},
##############################################################################
# global constants, flags and accessory
-use constant MB_NEVER_ROUND => 0x0001;
-
-my $NaNOK=1; # are NaNs ok?
-my $nan = 'NaN'; # constants for easier life
-
-my $CALC = 'Math::BigInt::Calc'; # module to do low level math
-my $IMPORT = 0; # did import() yet?
+# 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'
$accuracy = undef;
$upgrade = undef; # default is no upgrade
$downgrade = undef; # default is no downgrade
+# These are internally, and not to be used from the outside at all
+
+$_trap_nan = 0; # are NaNs ok? set w/ config()
+$_trap_inf = 0; # are infs ok? set w/ config()
+my $nan = 'NaN'; # constants for easier life
+
+my $CALC = 'Math::BigInt::FastCalc'; # module to do the low level math
+ # default is FastCalc.pm
+my $IMPORT = 0; # was import() called yet?
+ # used to make require work
+my %WARN; # warn only once for low-level libs
+my %CAN; # cache for $CALC->can(...)
+my %CALLBACKS; # callbacks to notify on lib loads
+my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math
+
##############################################################################
# the old code had $rnd_mode, so we need to support it, too
sub FETCH { return $round_mode; }
sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
-BEGIN { tie $rnd_mode, 'Math::BigInt'; }
+BEGIN
+ {
+ # tie to enable $rnd_mode to work transparently
+ tie $rnd_mode, 'Math::BigInt';
+
+ # set up some handy alias names
+ *as_int = \&as_number;
+ *is_pos = \&is_positive;
+ *is_neg = \&is_negative;
+ }
##############################################################################
if (defined $_[0])
{
my $m = shift;
- die "Unknown round mode $m"
- if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
+ if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
+ {
+ require Carp; Carp::croak ("Unknown round mode '$m'");
+ }
return ${"${class}::round_mode"} = $m;
}
- return ${"${class}::round_mode"};
+ ${"${class}::round_mode"};
}
sub upgrade
{
no strict 'refs';
- # make Class->round_mode() work
+ # make Class->upgrade() work
my $self = shift;
my $class = ref($self) || $self || __PACKAGE__;
- if (defined $_[0])
+ # need to set new value?
+ if (@_ > 0)
{
- my $u = shift;
- return ${"${class}::upgrade"} = $u;
+ return ${"${class}::upgrade"} = $_[0];
}
- return ${"${class}::upgrade"};
+ ${"${class}::upgrade"};
+ }
+
+sub downgrade
+ {
+ no strict 'refs';
+ # make Class->downgrade() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ # need to set new value?
+ if (@_ > 0)
+ {
+ return ${"${class}::downgrade"} = $_[0];
+ }
+ ${"${class}::downgrade"};
}
sub div_scale
{
no strict 'refs';
- # make Class->round_mode() work
+ # make Class->div_scale() work
my $self = shift;
my $class = ref($self) || $self || __PACKAGE__;
if (defined $_[0])
{
- die ('div_scale must be greater than zero') if $_[0] < 0;
- ${"${class}::div_scale"} = shift;
+ if ($_[0] < 0)
+ {
+ require Carp; Carp::croak ('div_scale must be greater than zero');
+ }
+ ${"${class}::div_scale"} = $_[0];
}
- return ${"${class}::div_scale"};
+ ${"${class}::div_scale"};
}
sub accuracy
if (@_ > 0)
{
my $a = shift;
- die ('accuracy must not be zero') if defined $a && $a == 0;
+ # convert objects to scalars to avoid deep recursion. If object doesn't
+ # have numify(), then hopefully it will have overloading for int() and
+ # boolean test without wandering into a deep recursion path...
+ $a = $a->numify() if ref($a) && $a->can('numify');
+
+ if (defined $a)
+ {
+ # also croak on non-numerical
+ if (!$a || $a <= 0)
+ {
+ require Carp;
+ Carp::croak ('Argument to accuracy must be greater than zero');
+ }
+ if (int($a) != $a)
+ {
+ require Carp; Carp::croak ('Argument to accuracy must be an integer');
+ }
+ }
if (ref($x))
{
# $object->accuracy() or fallback to global
- $x->bround($a) if defined $a;
+ $x->bround($a) if $a; # not for undef, 0
$x->{_a} = $a; # set/overwrite, even if not rounded
- $x->{_p} = undef; # clear P
+ delete $x->{_p}; # clear P
+ $a = ${"${class}::accuracy"} unless defined $a; # proper return value
}
else
{
- # set global
- ${"${class}::accuracy"} = $a;
- ${"${class}::precision"} = undef; # clear P
+ ${"${class}::accuracy"} = $a; # set global A
+ ${"${class}::precision"} = undef; # clear global P
}
return $a; # shortcut
}
- if (ref($x))
- {
- # $object->accuracy() or fallback to global
- return $x->{_a} || ${"${class}::accuracy"};
- }
- return ${"${class}::accuracy"};
- }
+ my $a;
+ # $object->accuracy() or fallback to global
+ $a = $x->{_a} if ref($x);
+ # but don't return global undef, when $x's accuracy is 0!
+ $a = ${"${class}::accuracy"} if !defined $a;
+ $a;
+ }
sub precision
{
my $class = ref($x) || $x || __PACKAGE__;
no strict 'refs';
- # need to set new value?
if (@_ > 0)
{
my $p = shift;
+ # convert objects to scalars to avoid deep recursion. If object doesn't
+ # have numify(), then hopefully it will have overloading for int() and
+ # boolean test without wandering into a deep recursion path...
+ $p = $p->numify() if ref($p) && $p->can('numify');
+ if ((defined $p) && (int($p) != $p))
+ {
+ require Carp; Carp::croak ('Argument to precision must be an integer');
+ }
if (ref($x))
{
# $object->precision() or fallback to global
- $x->bfround($p) if defined $p;
+ $x->bfround($p) if $p; # not for undef, 0
$x->{_p} = $p; # set/overwrite, even if not rounded
- $x->{_a} = undef; # clear A
+ delete $x->{_a}; # clear A
+ $p = ${"${class}::precision"} unless defined $p; # proper return value
}
else
{
- # set global
- ${"${class}::precision"} = $p;
- ${"${class}::accuracy"} = undef; # clear A
+ ${"${class}::precision"} = $p; # set global P
+ ${"${class}::accuracy"} = undef; # clear global A
}
return $p; # shortcut
}
- if (ref($x))
- {
- # $object->precision() or fallback to global
- return $x->{_p} || ${"${class}::precision"};
- }
- return ${"${class}::precision"};
- }
+ my $p;
+ # $object->precision() or fallback to global
+ $p = $x->{_p} if ref($x);
+ # but don't return global undef, when $x's precision is 0!
+ $p = ${"${class}::precision"} if !defined $p;
+ $p;
+ }
sub config
{
- # return (later set?) configuration data as hash ref
+ # return (or set) configuration data as hash ref
my $class = shift || 'Math::BigInt';
no strict 'refs';
- my $lib = $CALC;
+ if (@_ > 0)
+ {
+ # try to set given options as arguments from hash
+
+ my $args = $_[0];
+ if (ref($args) ne 'HASH')
+ {
+ $args = { @_ };
+ }
+ # these values can be "set"
+ my $set_args = {};
+ foreach my $key (
+ qw/trap_inf trap_nan
+ upgrade downgrade precision accuracy round_mode div_scale/
+ )
+ {
+ $set_args->{$key} = $args->{$key} if exists $args->{$key};
+ delete $args->{$key};
+ }
+ if (keys %$args > 0)
+ {
+ require Carp;
+ Carp::croak ("Illegal key(s) '",
+ join("','",keys %$args),"' passed to $class\->config()");
+ }
+ foreach my $key (keys %$set_args)
+ {
+ if ($key =~ /^trap_(inf|nan)\z/)
+ {
+ ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0);
+ next;
+ }
+ # use a call instead of just setting the $variable to check argument
+ $class->$key($set_args->{$key});
+ }
+ }
+
+ # now return actual configuration
+
my $cfg = {
- lib => $lib,
- lib_version => ${"${lib}::VERSION"},
+ lib => $CALC,
+ lib_version => ${"${CALC}::VERSION"},
class => $class,
+ trap_nan => ${"${class}::_trap_nan"},
+ trap_inf => ${"${class}::_trap_inf"},
+ version => ${"${class}::VERSION"},
};
- foreach (
- qw/upgrade downgrade precisison accuracy round_mode VERSION div_scale/)
+ foreach my $key (qw/
+ upgrade downgrade precision accuracy round_mode div_scale
+ /)
{
- $cfg->{lc($_)} = ${"${class}::$_"};
+ $cfg->{$key} = ${"${class}::$key"};
};
$cfg;
}
{
# select accuracy parameter based on precedence,
# used by bround() and bfround(), may return undef for scale (means no op)
- my ($x,$s,$m,$scale,$mode) = @_;
- $scale = $x->{_a} if !defined $scale;
- $scale = $s if (!defined $scale);
- $mode = $m if !defined $mode;
- return ($scale,$mode);
+ my ($x,$scale,$mode) = @_;
+
+ $scale = $x->{_a} unless defined $scale;
+
+ no strict 'refs';
+ my $class = ref($x);
+
+ $scale = ${ $class . '::accuracy' } unless defined $scale;
+ $mode = ${ $class . '::round_mode' } unless defined $mode;
+
+ ($scale,$mode);
}
sub _scale_p
{
# select precision parameter based on precedence,
# used by bround() and bfround(), may return undef for scale (means no op)
- my ($x,$s,$m,$scale,$mode) = @_;
- $scale = $x->{_p} if !defined $scale;
- $scale = $s if (!defined $scale);
- $mode = $m if !defined $mode;
- return ($scale,$mode);
+ my ($x,$scale,$mode) = @_;
+
+ $scale = $x->{_p} unless defined $scale;
+
+ no strict 'refs';
+ my $class = ref($x);
+
+ $scale = ${ $class . '::precision' } unless defined $scale;
+ $mode = ${ $class . '::round_mode' } unless defined $mode;
+
+ ($scale,$mode);
}
##############################################################################
}
return unless ref($x); # only for objects
- my $self = {}; bless $self,$c;
- my $r;
- foreach my $k (keys %$x)
- {
- if ($k eq 'value')
- {
- $self->{value} = $CALC->_copy($x->{value}); next;
- }
- if (!($r = ref($x->{$k})))
- {
- $self->{$k} = $x->{$k}; next;
- }
- if ($r eq 'SCALAR')
- {
- $self->{$k} = \${$x->{$k}};
- }
- elsif ($r eq 'ARRAY')
- {
- $self->{$k} = [ @{$x->{$k}} ];
- }
- elsif ($r eq 'HASH')
- {
- # only one level deep!
- foreach my $h (keys %{$x->{$k}})
- {
- $self->{$k}->{$h} = $x->{$k}->{$h};
- }
- }
- else # normal ref
- {
- my $xk = $x->{$k};
- if ($xk->can('copy'))
- {
- $self->{$k} = $xk->copy();
- }
- else
- {
- $self->{$k} = $xk->new($xk);
- }
- }
- }
+ my $self = bless {}, $c;
+
+ $self->{sign} = $x->{sign};
+ $self->{value} = $CALC->_copy($x->{value});
+ $self->{_a} = $x->{_a} if defined $x->{_a};
+ $self->{_p} = $x->{_p} if defined $x->{_p};
$self;
}
# avoid numify-calls by not using || on $wanted!
return $class->bzero($a,$p) if !defined $wanted; # default to 0
- return $class->copy($wanted,$a,$p,$r) if ref($wanted);
+ return $class->copy($wanted,$a,$p,$r)
+ if ref($wanted) && $wanted->isa($class); # MBI or subclass
$class->import() if $IMPORT == 0; # make require work
- my $self = {}; bless $self, $class;
- # handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]?inf$/)
+ my $self = bless {}, $class;
+
+ # shortcut for "normal" numbers
+ if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/))
{
- $self->{value} = $CALC->_zero();
- $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf';
+ $self->{sign} = $1 || '+';
+
+ if ($wanted =~ /^[+-]/)
+ {
+ # remove sign without touching wanted to make it work with constants
+ my $t = $wanted; $t =~ s/^[+-]//;
+ $self->{value} = $CALC->_new($t);
+ }
+ else
+ {
+ $self->{value} = $CALC->_new($wanted);
+ }
+ no strict 'refs';
+ if ( (defined $a) || (defined $p)
+ || (defined ${"${class}::precision"})
+ || (defined ${"${class}::accuracy"})
+ )
+ {
+ $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p);
+ }
return $self;
}
+
+ # handle '+inf', '-inf' first
+ if ($wanted =~ /^[+-]?inf\z/)
+ {
+ $self->{sign} = $wanted; # set a default sign for bstr()
+ return $self->binf($wanted);
+ }
# split str in m mantissa, e exponent, i integer, f fraction, v value, s sign
- my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted);
+ my ($mis,$miv,$mfv,$es,$ev) = _split($wanted);
if (!ref $mis)
{
- die "$wanted is not a number initialized to $class" if !$NaNOK;
- #print "NaN 1\n";
+ if ($_trap_nan)
+ {
+ require Carp; Carp::croak("$wanted is not a number in $class");
+ }
$self->{value} = $CALC->_zero();
$self->{sign} = $nan;
return $self;
my $diff = $e - CORE::length($$mfv);
if ($diff < 0) # Not integer
{
+ if ($_trap_nan)
+ {
+ require Carp; Carp::croak("$wanted not an integer in $class");
+ }
#print "NOI 1\n";
return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
else # diff >= 0
{
# adjust fraction and add it to value
- # print "diff > 0 $$miv\n";
+ #print "diff > 0 $$miv\n";
$$miv = $$miv . ($$mfv . '0' x $diff);
}
}
if ($$mfv ne '') # e <= 0
{
# fraction and negative/zero E => NOI
+ if ($_trap_nan)
+ {
+ require Carp; Carp::croak("$wanted not an integer in $class");
+ }
#print "NOI 2 \$\$mfv '$$mfv'\n";
return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
$e = abs($e);
if ($$miv !~ s/0{$e}$//) # can strip so many zero's?
{
+ if ($_trap_nan)
+ {
+ require Carp; Carp::croak("$wanted not an integer in $class");
+ }
#print "NOI 3\n";
return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
}
$self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0
- $self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/;
+ $self->{value} = $CALC->_new($$miv) if $self->{sign} =~ /^[+-]$/;
# if any of the globals is set, use them to round and store them inside $self
# do not round for new($x,undef,undef) since that is used by MBF to signal
# no rounding
$self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p;
- # print "mbi new $self\n";
- return $self;
+ $self;
}
sub bnan
{
my $c = $self; $self = {}; bless $self, $c;
}
+ no strict 'refs';
+ if (${"${class}::_trap_nan"})
+ {
+ require Carp;
+ Carp::croak ("Tried to set $self to NaN in $class\::bnan()");
+ }
$self->import() if $IMPORT == 0; # make require work
return if $self->modify('bnan');
- $self->{value} = $CALC->_zero();
+ if ($self->can('_bnan'))
+ {
+ # use subclass to initialize
+ $self->_bnan();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
$self->{sign} = $nan;
delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly
- return $self;
+ $self;
}
sub binf
# create a bigint '+-inf', if given a BigInt, set it to '+-inf'
# the sign is either '+', or if given, used from there
my $self = shift;
- my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
+ my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/;
$self = $class if !defined $self;
if (!ref($self))
{
my $c = $self; $self = {}; bless $self, $c;
}
+ no strict 'refs';
+ if (${"${class}::_trap_inf"})
+ {
+ require Carp;
+ Carp::croak ("Tried to set $self to +-inf in $class\::binf()");
+ }
$self->import() if $IMPORT == 0; # make require work
return if $self->modify('binf');
- $self->{value} = $CALC->_zero();
- $self->{sign} = $sign.'inf';
+ if ($self->can('_binf'))
+ {
+ # use subclass to initialize
+ $self->_binf();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
+ $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf
+ $self->{sign} = $sign;
($self->{_a},$self->{_p}) = @_; # take over requested rounding
- return $self;
+ $self;
}
sub bzero
{
# create a bigint '+0', if given a BigInt, set it to 0
my $self = shift;
- $self = $class if !defined $self;
+ $self = __PACKAGE__ if !defined $self;
if (!ref($self))
{
}
$self->import() if $IMPORT == 0; # make require work
return if $self->modify('bzero');
- $self->{value} = $CALC->_zero();
+
+ if ($self->can('_bzero'))
+ {
+ # use subclass to initialize
+ $self->_bzero();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
$self->{sign} = '+';
if (@_ > 0)
{
- $self->{_a} = $_[0]
- if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a});
- $self->{_p} = $_[1]
- if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p});
+ if (@_ > 3)
+ {
+ # call like: $x->bzero($a,$p,$r,$y);
+ ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
+ }
+ else
+ {
+ $self->{_a} = $_[0]
+ if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
+ $self->{_p} = $_[1]
+ if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
+ }
}
- return $self;
+ $self;
}
sub bone
{
# create a bigint '+1' (or -1 if given sign '-'),
- # if given a BigInt, set it to +1 or -1, respecively
+ # if given a BigInt, set it to +1 or -1, respectively
my $self = shift;
my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
$self = $class if !defined $self;
-
+
if (!ref($self))
{
my $c = $self; $self = {}; bless $self, $c;
}
$self->import() if $IMPORT == 0; # make require work
return if $self->modify('bone');
- $self->{value} = $CALC->_one();
+
+ if ($self->can('_bone'))
+ {
+ # use subclass to initialize
+ $self->_bone();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_one();
+ }
$self->{sign} = $sign;
if (@_ > 0)
{
- $self->{_a} = $_[0]
- if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a});
- $self->{_p} = $_[1]
- if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p});
+ if (@_ > 3)
+ {
+ # call like: $x->bone($sign,$a,$p,$r,$y);
+ ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
+ }
+ else
+ {
+ # call like: $x->bone($sign,$a,$p,$r);
+ $self->{_a} = $_[0]
+ if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
+ $self->{_p} = $_[1]
+ if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
+ }
}
- return $self;
+ $self;
}
##############################################################################
# (ref to BFLOAT or num_str ) return num_str
# Convert number from internal format to scientific string format.
# internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
- my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
- # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
if ($x->{sign} !~ /^[+-]$/)
{
return 'inf'; # +inf
}
my ($m,$e) = $x->parts();
- # e can only be positive
- my $sign = 'e+';
- # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s;
- return $m->bstr().$sign.$e->bstr();
+ #$m->bstr() . 'e+' . $e->bstr(); # e can only be positive in BigInt
+ # 'e+' because E can only be positive in BigInt
+ $m->bstr() . 'e+' . $CALC->_str($e->{value});
}
sub bstr
{
# make a string from bigint object
- my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
- # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
-
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
if ($x->{sign} !~ /^[+-]$/)
{
return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
return 'inf'; # +inf
}
my $es = ''; $es = $x->{sign} if $x->{sign} eq '-';
- return $es.${$CALC->_str($x->{value})};
+ $es.$CALC->_str($x->{value});
}
sub numify
{
# Make a "normal" scalar from a BigInt object
my $x = shift; $x = $class->new($x) unless ref $x;
- return $x->{sign} if $x->{sign} !~ /^[+-]$/;
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/;
my $num = $CALC->_num($x->{value});
return -$num if $x->{sign} eq '-';
- return $num;
+ $num;
}
##############################################################################
sub sign
{
- # return the sign of the number: +/-/NaN
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ # return the sign of the number: +/-/-inf/+inf/NaN
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- return $x->{sign};
+ $x->{sign};
}
sub _find_round_parameters
# After any operation or when calling round(), the result is rounded by
# regarding the A & P from arguments, local parameters, or globals.
+ # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!!
+
# This procedure finds the round parameters, but it is for speed reasons
# duplicated in round. Otherwise, it is tested by the testsuite and used
# by fdiv().
+
+ # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P
+ # were requested/defined (locally or globally or both)
my ($self,$a,$p,$r,@args) = @_;
# $a accuracy, if given by caller
# $r round_mode, if given by caller
# @args all 'other' arguments (0 for unary, 1 for binary ops)
- # leave bigfloat parts alone
- return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
-
my $c = ref($self); # find out class of argument(s)
no strict 'refs';
# if still none defined, use globals (#2)
$a = ${"$c\::accuracy"} unless defined $a;
$p = ${"$c\::precision"} unless defined $p;
+
+ # A == 0 is useless, so undef it to signal no rounding
+ $a = undef if defined $a && $a == 0;
# no rounding today?
return ($self) unless defined $a || defined $p; # early out
# set A and set P is an fatal error
- return ($self->bnan()) if defined $a && defined $p;
+ return ($self->bnan()) if defined $a && defined $p; # error
$r = ${"$c\::round_mode"} unless defined $r;
- die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
-
- return ($self,$a,$p,$r);
+ if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
+ {
+ require Carp; Carp::croak ("Unknown round mode '$r'");
+ }
+
+ ($self,$a,$p,$r);
}
sub round
# $r round_mode, if given by caller
# @args all 'other' arguments (0 for unary, 1 for binary ops)
- # leave bigfloat parts alone
- return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
-
my $c = ref($self); # find out class of argument(s)
no strict 'refs';
$a = ${"$c\::accuracy"} unless defined $a;
$p = ${"$c\::precision"} unless defined $p;
+ # A == 0 is useless, so undef it to signal no rounding
+ $a = undef if defined $a && $a == 0;
+
# no rounding today?
return $self unless defined $a || defined $p; # early out
return $self->bnan() if defined $a && defined $p;
$r = ${"$c\::round_mode"} unless defined $r;
- die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
+ if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
+ {
+ require Carp; Carp::croak ("Unknown round mode '$r'");
+ }
# now round, by calling either fround or ffround:
if (defined $a)
{
$self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p;
}
- $self->bnorm(); # after round, normalize
+ # bround() or bfround() already callled bnorm() if necc.
+ $self;
}
sub bnorm
{
# (numstr or BINT) return BINT
# Normalize number -- no-op here
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
$x;
}
{
# (BINT or num_str) return BINT
# make number absolute, or return absolute BINT from string
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return $x if $x->modify('babs');
# post-normalized abs for internal use (does nothing for NaN)
{
# (BINT or num_str) return BINT
# negate number or make a negated number from string
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return $x if $x->modify('bneg');
- # for +0 dont negate (to have always normalized)
- $x->{sign} =~ tr/+-/-+/ if !$x->is_zero(); # does nothing for NaN
+ # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN'
+ $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value}));
$x;
}
{
# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT or num_str, BINT or num_str) return cond_code
- my ($self,$x,$y) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y) = (ref($_[0]),@_);
+
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y) = objectify(2,@_);
+ }
+
+ return $upgrade->bcmp($x,$y) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
- # shortcut
- my $xz = $x->is_zero();
- my $yz = $y->is_zero();
- return 0 if $xz && $yz; # 0 <=> 0
- return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y
- return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0
-
+ # have same sign, so compare absolute values. Don't make tests for zero here
+ # because it's actually slower than testin in Calc (especially w/ Pari et al)
+
# post-normalized compare for internal use (honors signs)
if ($x->{sign} eq '+')
{
- return 1 if $y->{sign} eq '-'; # 0 check handled above
+ # $x and $y both > 0
return $CALC->_acmp($x->{value},$y->{value});
}
- # $x->{sign} eq '-'
- return -1 if $y->{sign} eq '+';
- $CALC->_acmp($y->{value},$x->{value}); # swaped (lib does only 0,1,-1)
+ # $x && $y both < 0
+ $CALC->_acmp($y->{value},$x->{value}); # swaped acmp (lib returns 0,1,-1)
}
sub bacmp
# Compares 2 values, ignoring their signs.
# Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT, BINT) return cond_code
- my ($self,$x,$y) = objectify(2,@_);
+ # set up parameters
+ my ($self,$x,$y) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y) = objectify(2,@_);
+ }
+
+ return $upgrade->bacmp($x,$y) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
+
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
# handle +-inf and NaN
return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
- return +1; # inf is always bigger
+ return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
+ return -1;
}
$CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1
}
{
# add second arg (BINT or string) to first (BINT) (modifies first)
# return result as BINT
- my ($self,$x,$y,@r) = objectify(2,@_);
+
+ # 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('badd');
-# print "mbi badd ",join(' ',caller()),"\n";
-# print "upgrade => ",$upgrade||'undef',
-# " \$x (",ref($x),") \$y (",ref($y),")\n";
-# return $upgrade->badd($x,$y,@r) if defined $upgrade &&
-# ((ref($x) eq $upgrade) || (ref($y) eq $upgrade));
-# print "still badd\n";
+ return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
$r[3] = $y; # no push!
# inf and NaN handling
{
# NaN first
return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- # inf handline
- if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ # inf handling
+ if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
{
# +inf++inf or -inf+-inf => same, rest is NaN
return $x if $x->{sign} eq $y->{sign};
return $x;
}
- my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
+ my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
if ($sx eq $sy)
{
$x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add
- $x->{sign} = $sx;
}
else
{
my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare
if ($a > 0)
{
- #print "swapped sub (a=$a)\n";
$x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap
$x->{sign} = $sy;
}
elsif ($a == 0)
{
# speedup, if equal, set result to 0
- #print "equal sub, result = 0\n";
$x->{value} = $CALC->_zero();
$x->{sign} = '+';
}
else # a < 0
{
- #print "unswapped sub (a=$a)\n";
$x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
- $x->{sign} = $sx;
}
}
$x->round(@r);
sub bsub
{
- # (BINT or num_str, BINT or num_str) return num_str
+ # (BINT or num_str, BINT or num_str) return BINT
# subtract second arg from first, modify first
- my ($self,$x,$y,@r) = objectify(2,@_);
+
+ # 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('bsub');
-# return $upgrade->badd($x,$y,@r) if defined $upgrade &&
-# ((ref($x) eq $upgrade) || (ref($y) eq $upgrade));
- if ($y->is_zero())
- {
- return $x->round(@r);
- }
+ return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
+
+ return $x->round(@r) if $y->is_zero();
+ # To correctly handle the lone special case $x->bsub($x), we note the sign
+ # of $x, then flip the sign from $y, and if the sign of $x did change, too,
+ # then we caught the special case:
+ my $xsign = $x->{sign};
$y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
+ if ($xsign ne $x->{sign})
+ {
+ # special case of $x->bsub($x) results in 0
+ return $x->bzero(@r) if $xsign =~ /^[+-]$/;
+ return $x->bnan(); # NaN, -inf, +inf
+ }
$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.
return $x->round($a,$p,$r);
}
# inf, nan handling etc
- $x->badd($self->__one(),$a,$p,$r); # badd does round
+ $x->badd($self->bone(),$a,$p,$r); # badd does round
}
sub bdec
{
# decrement arg by one
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('bdec');
- my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+';
- # <= 0
- if (($x->{sign} eq '-') || $zero)
+ if ($x->{sign} eq '-')
{
+ # x already < 0
$x->{value} = $CALC->_inc($x->{value});
- $x->{sign} = '-' if $zero; # 0 => 1 => -1
- $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
- return $x->round($a,$p,$r);
- }
- # > 0
- elsif ($x->{sign} eq '+')
+ }
+ else
{
- $x->{value} = $CALC->_dec($x->{value});
- return $x->round($a,$p,$r);
+ return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf or NaN
+ # >= 0
+ if ($CALC->_is_zero($x->{value}))
+ {
+ # == 0
+ $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1
+ }
+ else
+ {
+ # > 0
+ $x->{value} = $CALC->_dec($x->{value});
+ }
}
- # inf, nan handling etc
- $x->badd($self->__one('-'),$a,$p,$r); # badd does round
- }
+ $x->round(@r);
+ }
sub blog
{
- # not implemented yet
- my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
-
- return $upgrade->blog($x,$base,$a,$p,$r) if defined $upgrade;
+ # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base
+ # $base of $x)
+
+ # set up parameters
+ my ($self,$x,$base,@r) = (undef,@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$base,@r) = objectify(1,ref($x),@_);
+ }
+
+ return $x if $x->modify('blog');
- return $x->bnan();
+ # 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;
+
+ 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 blcm
{
# (BINT or num_str, BINT or num_str) return BINT
{
$x = $class->new($y);
}
- while (@_) { $x = __lcm($x,shift); }
+ my $self = ref($x);
+ while (@_)
+ {
+ my $y = shift; $y = $self->new($y) if !ref ($y);
+ $x = __lcm($x,$y);
+ }
$x;
}
# GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff)
my $y = shift;
- $y = __PACKAGE__->new($y) if !ref($y);
+ $y = $class->new($y) if !ref($y);
my $self = ref($y);
- my $x = $y->copy(); # keep arguments
- if ($CALC->can('_gcd'))
- {
- while (@_)
- {
- $y = shift; $y = $self->new($y) if !ref($y);
- next if $y->is_zero();
- return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
- $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one();
- }
- }
- else
+ my $x = $y->copy()->babs(); # keep arguments
+ return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
+
+ while (@_)
{
- while (@_)
- {
- $y = shift; $y = $self->new($y) if !ref($y);
- $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN
- }
+ $y = shift; $y = $self->new($y) if !ref($y);
+ return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
+ $x->{value} = $CALC->_gcd($x->{value},$y->{value});
+ last if $CALC->_is_one($x->{value});
}
- $x->babs();
+ $x;
}
sub bnot
my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
return $x if $x->modify('bnot');
- $x->bneg()->bdec(); # bdec already does round
+ $x->binc()->bneg(); # binc already does round
}
+##############################################################################
# is_foo test routines
+# we don't need $self, so undef instead of ref($_[0]) make it slightly faster
sub is_zero
{
# return true if arg (BINT or num_str) is zero (array '+', '0')
- # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
sub is_nan
{
# return true if arg (BINT or num_str) is NaN
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- return 1 if $x->{sign} eq $nan;
- return 0;
+ $x->{sign} eq $nan ? 1 : 0;
}
sub is_inf
{
# return true if arg (BINT or num_str) is +-inf
- my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
-
- $sign = '' if !defined $sign;
- return 0 if $sign !~ /^([+-]|)$/;
+ my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
- if ($sign eq '')
+ if (defined $sign)
{
- return 1 if ($x->{sign} =~ /^[+-]inf$/);
- return 0;
+ $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf
+ $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-'
+ return $x->{sign} =~ /^$sign$/ ? 1 : 0;
}
- $sign = quotemeta($sign.'inf');
- return 1 if ($x->{sign} =~ /^$sign$/);
- return 0;
+ $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity
}
sub is_one
{
- # return true if arg (BINT or num_str) is +1
- # or -1 if sign is given
- # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ # return true if arg (BINT or num_str) is +1, or -1 if sign is given
my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
- $sign = '' if !defined $sign; $sign = '+' if $sign ne '-';
+ $sign = '+' if !defined $sign || $sign ne '-';
return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
$CALC->_is_one($x->{value});
sub is_odd
{
# return true when arg (BINT or num_str) is odd, false for even
- # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
sub is_even
{
# return true when arg (BINT or num_str) is even, false for odd
- # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
sub is_positive
{
# return true when arg (BINT or num_str) is positive (>= 0)
- # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- return 1 if $x->{sign} =~ /^\+/;
- 0;
+
+ return 1 if $x->{sign} eq '+inf'; # +inf is positive
+
+ # 0+ is neither positive nor negative
+ ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0;
}
sub is_negative
{
# return true when arg (BINT or num_str) is negative (< 0)
- # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- return 1 if ($x->{sign} =~ /^-/);
- 0;
+ $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not
}
sub is_int
{
# return true when arg (BINT or num_str) is an integer
- # always true for BigInt, but different for Floats
- # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ # always true for BigInt, but different for BigFloats
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
$x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't
{
# multiply two numbers -- stolen from Knuth Vol 2 pg 233
# (BINT or num_str, BINT or num_str) return BINT
- my ($self,$x,$y,@r) = objectify(2,@_);
+
+ # 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('bmul');
- $r[3] = $y; # no push here
-
return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
# inf handling
return $x->binf('-');
}
+ return $upgrade->bmul($x,$upgrade->new($y),@r)
+ if defined $upgrade && !$y->isa($self);
+
+ $r[3] = $y; # no push here
+
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
$x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
$x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
+
$x->round(@r);
}
# x / +-inf => 0, remainder x (works even if x == 0)
if ($y->{sign} =~ /^[+-]inf$/)
{
- my $t = $x->copy(); # binf clobbers up $x
+ my $t = $x->copy(); # bzero clobbers up $x
return wantarray ? ($x->bzero(),$t) : $x->bzero()
}
{
# (dividend: BINT or num_str, divisor: BINT or num_str) return
# (BINT,BINT) (quo,rem) or BINT (only rem)
- my ($self,$x,$y,@r) = objectify(2,@_);
+
+ # 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('bdiv');
return $self->_div_inf($x,$y)
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
+ return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r)
+ if defined $upgrade;
+
$r[3] = $y; # no push!
- # 0 / something
- return
- wantarray ? ($x->round(@r),$self->bzero(@r)):$x->round(@r) if $x->is_zero();
-
- # Is $x in the interval [0, $y) (aka $x <= $y) ?
- my $cmp = $CALC->_acmp($x->{value},$y->{value});
- if (($cmp < 0) and (($x->{sign} eq $y->{sign}) or !wantarray))
- {
- return $upgrade->bdiv($x,$y,@r) if defined $upgrade;
-
- return $x->bzero()->round(@r) unless wantarray;
- my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x
- return ($x->bzero()->round(@r),$t);
- }
- elsif ($cmp == 0)
- {
- # shortcut, both are the same, so set to +/- 1
- $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') );
- return $x unless wantarray;
- return ($x->round(@r),$self->bzero(@r));
- }
-
# calc new sign and in case $y == +/- 1, return $x
my $xsign = $x->{sign}; # keep
$x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+');
- # check for / +-1 (cant use $y->is_one due to '-'
- if ($CALC->_is_one($y->{value}))
- {
- return wantarray ? ($x->round(@r),$self->bzero(@r)) : $x->round(@r);
- }
- my $rem;
if (wantarray)
{
my $rem = $self->bzero();
($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
$x->{sign} = '+' if $CALC->_is_zero($x->{value});
- $x->round(@r);
+ $rem->{_a} = $x->{_a};
+ $rem->{_p} = $x->{_p};
+ $x->round(@r);
if (! $CALC->_is_zero($rem->{value}))
{
$rem->{sign} = $y->{sign};
- $rem = $y-$rem if $xsign ne $y->{sign}; # one of them '-'
+ $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-'
}
else
{
$x->{value} = $CALC->_div($x->{value},$y->{value});
$x->{sign} = '+' if $CALC->_is_zero($x->{value});
- $x->round(@r);
- $x;
+
+ $x->round(@r);
}
+###############################################################################
+# modulus functions
+
sub bmod
{
# modulus (or remainder)
# (BINT or num_str, BINT or num_str) return BINT
- my ($self,$x,$y,@r) = objectify(2,@_);
-
+
+ # 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('bmod');
$r[3] = $y; # no push!
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
{
my ($d,$r) = $self->_div_inf($x,$y);
- return $r->round(@r);
+ $x->{sign} = $r->{sign};
+ $x->{value} = $r->{value};
+ return $x->round(@r);
}
- if ($CALC->can('_mod'))
+ # calc new sign and in case $y == +/- 1, return $x
+ $x->{value} = $CALC->_mod($x->{value},$y->{value});
+ if (!$CALC->_is_zero($x->{value}))
{
- # calc new sign and in case $y == +/- 1, return $x
- $x->{value} = $CALC->_mod($x->{value},$y->{value});
- if (!$CALC->_is_zero($x->{value}))
- {
- my $xsign = $x->{sign};
- $x->{sign} = $y->{sign};
- $x = $y-$x if $xsign ne $y->{sign}; # one of them '-'
- }
- else
- {
- $x->{sign} = '+'; # dont leave -0
- }
- return $x->round(@r);
+ $x->{value} = $CALC->_sub($y->{value},$x->{value},1) # $y-$x
+ if ($x->{sign} ne $y->{sign});
+ $x->{sign} = $y->{sign};
+ }
+ else
+ {
+ $x->{sign} = '+'; # dont leave -0
}
- my ($t,$rem) = $self->bdiv($x->copy(),$y,@r); # slow way (also rounds)
- # modify in place
- foreach (qw/value sign _a _p/)
+ $x->round(@r);
+ }
+
+sub bmodinv
+ {
+ # Modular inverse. given a number which is (hopefully) relatively
+ # prime to the modulus, calculate its inverse using Euclid's
+ # alogrithm. If the number is not relatively prime to the modulus
+ # (i.e. their gcd is not one) then NaN is returned.
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (undef,@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
{
- $x->{$_} = $rem->{$_};
+ ($self,$x,$y,@r) = objectify(2,@_);
}
+
+ return $x if $x->modify('bmodinv');
+
+ return $x->bnan()
+ if ($y->{sign} ne '+' # -, NaN, +inf, -inf
+ || $x->is_zero() # or num == 0
+ || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf
+ );
+
+ # put least residue into $x if $x was negative, and thus make it positive
+ $x->bmod($y) if $x->{sign} eq '-';
+
+ my $sign;
+ ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value});
+ return $x->bnan() if !defined $x->{value}; # in case no GCD found
+ return $x if !defined $sign; # already real result
+ $x->{sign} = $sign; # flip/flop see below
+ $x->bmod($y); # calc real result
$x;
}
-sub bfac
+sub bmodpow
{
- # (BINT or num_str, BINT or num_str) return BINT
- # compute factorial numbers
- # modifies first argument
- my ($self,$x,@r) = objectify(1,@_);
+ # takes a very large number to a very large exponent in a given very
+ # large modulus, quickly, thanks to binary exponentation. supports
+ # negative exponents.
+ my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
- return $x if $x->modify('bfac');
-
- return $x->bnan() if $x->{sign} ne '+'; # inf, NnN, <0 etc => NaN
- return $x->bone(@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1
+ return $num if $num->modify('bmodpow');
- if ($CALC->can('_fac'))
- {
- $x->{value} = $CALC->_fac($x->{value});
- return $x->round(@r);
- }
+ # check modulus for valid values
+ return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf
+ || $mod->is_zero());
- my $n = $x->copy();
- $x->bone();
- my $f = $self->new(2);
- while ($f->bacmp($n) < 0)
+ # check exponent for valid values
+ if ($exp->{sign} =~ /\w/)
{
- $x->bmul($f); $f->binc();
+ # i.e., if it's NaN, +inf, or -inf...
+ return $num->bnan();
}
- $x->bmul($f); # last step
- $x->round(@r); # round
+
+ $num->bmodinv ($mod) if ($exp->{sign} eq '-');
+
+ # check num for valid values (also NaN if there was no inverse but $exp < 0)
+ return $num->bnan() if $num->{sign} !~ /^[+-]$/;
+
+ # $mod is positive, sign on $exp is ignored, result also positive
+ $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value});
+ $num;
+ }
+
+###############################################################################
+
+sub bfac
+ {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # compute factorial number from $x, modify $x in place
+ my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+ return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf
+ return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN
+
+ $x->{value} = $CALC->_fac($x->{value});
+ $x->round(@r);
}
sub bpow
# (BINT or num_str, BINT or num_str) return BINT
# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
# modifies first argument
- my ($self,$x,$y,@r) = objectify(2,@_);
+
+ # 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('bpow');
-
- $r[3] = $y; # no push!
- return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x
+
return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
- return $x->bone(@r) if $y->is_zero();
- return $x->round(@r) if $x->is_one() || $y->is_one();
- if ($x->{sign} eq '-' && $CALC->_is_one($x->{value}))
+
+ # inf handling
+ if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
{
- # if $x == -1 and odd/even y => +1/-1
- return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r);
- # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1;
+ if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ # +-inf ** +-inf
+ return $x->bnan();
+ }
+ # +-inf ** Y
+ if ($x->{sign} =~ /^[+-]inf/)
+ {
+ # +inf ** 0 => NaN
+ return $x->bnan() if $y->is_zero();
+ # -inf ** -1 => 1/inf => 0
+ return $x->bzero() if $y->is_one('-') && $x->is_negative();
+
+ # +inf ** Y => inf
+ return $x if $x->{sign} eq '+inf';
+
+ # -inf ** Y => -inf if Y is odd
+ return $x if $y->is_odd();
+ return $x->babs();
+ }
+ # X ** +-inf
+
+ # 1 ** +inf => 1
+ return $x if $x->is_one();
+
+ # 0 ** inf => 0
+ return $x if $x->is_zero() && $y->{sign} =~ /^[+]/;
+
+ # 0 ** -inf => inf
+ return $x->binf() if $x->is_zero();
+
+ # -1 ** -inf => NaN
+ return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/;
+
+ # -X ** -inf => 0
+ return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/;
+
+ # -1 ** inf => NaN
+ return $x->bnan() if $x->{sign} eq '-';
+
+ # X ** inf => inf
+ return $x->binf() if $y->{sign} =~ /^[+]/;
+ # X ** -inf => 0
+ return $x->bzero();
}
+
+ return $upgrade->bpow($upgrade->new($x),$y,@r)
+ if defined $upgrade && !$y->isa($self);
+
+ $r[3] = $y; # no push!
+
+ # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu
+
+ my $new_sign = '+';
+ $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+');
+
+ # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf
+ return $x->binf()
+ if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value});
# 1 ** -y => 1 / (1 ** |y|)
# so do test for negative $y after above's clause
- return $x->bnan() if $y->{sign} eq '-';
- return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0)
+ return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value});
- if ($CALC->can('_pow'))
- {
- $x->{value} = $CALC->_pow($x->{value},$y->{value});
- return $x->round(@r);
- }
-
-# based on the assumption that shifting in base 10 is fast, and that mul
-# works faster if numbers are small: we count trailing zeros (this step is
-# O(1)..O(N), but in case of O(N) we save much more time due to this),
-# stripping them out of the multiplication, and add $count * $y zeros
-# afterwards like this:
-# 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6
-# creates deep recursion?
-# my $zeros = $x->_trailing_zeros();
-# if ($zeros > 0)
-# {
-# $x->brsft($zeros,10); # remove zeros
-# $x->bpow($y); # recursion (will not branch into here again)
-# $zeros = $y * $zeros; # real number of zeros to add
-# $x->blsft($zeros,10);
-# return $x->round($a,$p,$r);
-# }
-
- my $pow2 = $self->__one();
- my $y1 = $class->new($y);
- my $two = $self->new(2);
- while (!$y1->is_one())
- {
- $pow2->bmul($x) if $y1->is_odd();
- $y1->bdiv($two);
- $x->bmul($x);
- }
- $x->bmul($pow2) unless $pow2->is_one();
- return $x->round(@r);
+ $x->{value} = $CALC->_pow($x->{value},$y->{value});
+ $x->{sign} = $new_sign;
+ $x->{sign} = '+' if $CALC->_is_zero($y->{value});
+ $x->round(@r);
}
sub blsft
{
# (BINT or num_str, BINT or num_str) return BINT
# compute x << y, base n, y >= 0
- my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_);
-
+
+ # set up parameters
+ my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,$n,@r) = objectify(2,@_);
+ }
+
return $x if $x->modify('blsft');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x->round($a,$p,$r) if $y->is_zero();
+ return $x->round(@r) if $y->is_zero();
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft');
- if (defined $t)
- {
- $x->{value} = $t; return $x->round($a,$p,$r);
- }
- # fallback
- return $x->bmul( $self->bpow($n, $y, $a, $p, $r), $a, $p, $r );
+ $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n);
+ $x->round(@r);
}
sub brsft
{
# (BINT or num_str, BINT or num_str) return BINT
# compute x >> y, base n, y >= 0
- my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,$n,@r) = objectify(2,@_);
+ }
return $x if $x->modify('brsft');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x->round($a,$p,$r) if $y->is_zero();
- return $x->bzero($a,$p,$r) if $x->is_zero(); # 0 => 0
+ return $x->round(@r) if $y->is_zero();
+ return $x->bzero(@r) if $x->is_zero(); # 0 => 0
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
# this only works for negative numbers when shifting in base 2
if (($x->{sign} eq '-') && ($n == 2))
{
- return $x->round($a,$p,$r) if $x->is_one('-'); # -1 => -1
+ return $x->round(@r) if $x->is_one('-'); # -1 => -1
if (!$y->is_one())
{
# although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al
$bin =~ s/^-0b//; # strip '-0b' prefix
$bin =~ tr/10/01/; # flip bits
# now shift
- if (length($bin) <= $y)
+ if (CORE::length($bin) <= $y)
{
$bin = '0'; # shifting to far right creates -1
# 0, because later increment makes
my $res = $self->new('0b'.$bin); # add prefix and convert back
$res->binc(); # remember to increment
$x->{value} = $res->{value}; # take over value
- return $x->round($a,$p,$r); # we are done now, magic, isn't?
+ return $x->round(@r); # we are done now, magic, isn't?
}
+ # x < 0, n == 2, y == 1
$x->bdec(); # n == 2, but $y == 1: this fixes it
}
- my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft');
- if (defined $t)
- {
- $x->{value} = $t;
- return $x->round($a,$p,$r);
- }
- # fallback
- $x->bdiv($self->bpow($n,$y, $a,$p,$r), $a,$p,$r);
- $x;
+ $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n);
+ $x->round(@r);
}
sub band
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x & y
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # 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('band');
- local $Math::BigInt::upgrade = undef;
+ $r[3] = $y; # no push!
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x->bzero() if $y->is_zero() || $x->is_zero();
- my $sign = 0; # sign of result
- $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-');
- my $sx = 1; $sx = -1 if $x->{sign} eq '-';
- my $sy = 1; $sy = -1 if $y->{sign} eq '-';
+ my $sx = $x->{sign} eq '+' ? 1 : -1;
+ my $sy = $y->{sign} eq '+' ? 1 : -1;
- if ($CALC->can('_and') && $sx == 1 && $sy == 1)
+ if ($sx == 1 && $sy == 1)
{
$x->{value} = $CALC->_and($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ return $x->round(@r);
}
-
- my $m = $self->bone(); my ($xr,$yr);
- my $x10000 = $self->new (0x1000);
- my $y1 = copy(ref($x),$y); # make copy
- $y1->babs(); # and positive
- my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place!
- use integer; # need this for negative bools
- while (!$x1->is_zero() && !$y1->is_zero())
+
+ if ($CAN{signed_and})
{
- ($x1, $xr) = bdiv($x1, $x10000);
- ($y1, $yr) = bdiv($y1, $x10000);
- # make both op's numbers!
- $x->badd( bmul( $class->new(
- abs($sx*int($xr->numify()) & $sy*int($yr->numify()))),
- $m));
- $m->bmul($x10000);
+ $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy);
+ return $x->round(@r);
}
- $x->bneg() if $sign;
- return $x->round($a,$p,$r);
+
+ require $EMU_LIB;
+ __emu_band($self,$x,$y,$sx,$sy,@r);
}
sub bior
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x | y
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # 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('bior');
-
- local $Math::BigInt::upgrade = undef;
+ $r[3] = $y; # no push!
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x if $y->is_zero();
- my $sign = 0; # sign of result
- $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-');
- my $sx = 1; $sx = -1 if $x->{sign} eq '-';
- my $sy = 1; $sy = -1 if $y->{sign} eq '-';
+ my $sx = $x->{sign} eq '+' ? 1 : -1;
+ my $sy = $y->{sign} eq '+' ? 1 : -1;
+ # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior()
+
# don't use lib for negative values
- if ($CALC->can('_or') && $sx == 1 && $sy == 1)
+ if ($sx == 1 && $sy == 1)
{
$x->{value} = $CALC->_or($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ return $x->round(@r);
}
- my $m = $self->bone(); my ($xr,$yr);
- my $x10000 = $self->new(0x10000);
- my $y1 = copy(ref($x),$y); # make copy
- $y1->babs(); # and positive
- my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place!
- use integer; # need this for negative bools
- while (!$x1->is_zero() || !$y1->is_zero())
+ # if lib can do negative values, let it handle this
+ if ($CAN{signed_or})
{
- ($x1, $xr) = bdiv($x1,$x10000);
- ($y1, $yr) = bdiv($y1,$x10000);
- # make both op's numbers!
- $x->badd( bmul( $class->new(
- abs($sx*int($xr->numify()) | $sy*int($yr->numify()))),
- $m));
- $m->bmul($x10000);
+ $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy);
+ return $x->round(@r);
}
- $x->bneg() if $sign;
- return $x->round($a,$p,$r);
+
+ require $EMU_LIB;
+ __emu_bior($self,$x,$y,$sx,$sy,@r);
}
sub bxor
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x ^ y
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # 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('bxor');
-
- local $Math::BigInt::upgrade = undef;
+ $r[3] = $y; # no push!
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x if $y->is_zero();
- my $sign = 0; # sign of result
- $sign = 1 if $x->{sign} ne $y->{sign};
- my $sx = 1; $sx = -1 if $x->{sign} eq '-';
- my $sy = 1; $sy = -1 if $y->{sign} eq '-';
+ my $sx = $x->{sign} eq '+' ? 1 : -1;
+ my $sy = $y->{sign} eq '+' ? 1 : -1;
# don't use lib for negative values
- if ($CALC->can('_xor') && $sx == 1 && $sy == 1)
+ if ($sx == 1 && $sy == 1)
{
$x->{value} = $CALC->_xor($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ return $x->round(@r);
}
-
- my $m = $self->bone(); my ($xr,$yr);
- my $x10000 = $self->new(0x10000);
- my $y1 = copy(ref($x),$y); # make copy
- $y1->babs(); # and positive
- my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place!
- use integer; # need this for negative bools
- while (!$x1->is_zero() || !$y1->is_zero())
+
+ # if lib can do negative values, let it handle this
+ if ($CAN{signed_xor})
{
- ($x1, $xr) = bdiv($x1, $x10000);
- ($y1, $yr) = bdiv($y1, $x10000);
- # make both op's numbers!
- $x->badd( bmul( $class->new(
- abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))),
- $m));
- $m->bmul($x10000);
+ $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy);
+ return $x->round(@r);
}
- $x->bneg() if $sign;
- return $x->round($a,$p,$r);
+
+ require $EMU_LIB;
+ __emu_bxor($self,$x,$y,$sx,$sy,@r);
}
sub length
{
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
my $e = $CALC->_len($x->{value});
- return wantarray ? ($e,0) : $e;
+ wantarray ? ($e,0) : $e;
}
sub digit
{
# return the nth decimal digit, negative values count backward, 0 is right
- my $x = shift;
- my $n = shift || 0;
+ my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
- return $CALC->_digit($x->{value},$n);
+ $n = $n->numify() if ref($n);
+ $CALC->_digit($x->{value},$n||0);
}
sub _trailing_zeros
{
- # return the amount of trailing zeros in $x
+ # return the amount of trailing zeros in $x (as scalar)
my $x = shift;
$x = $class->new($x) unless ref $x;
- return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/;
+ return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc
- return $CALC->_zeros($x->{value}) if $CALC->can('_zeros');
-
- # if not: since we do not know underlying internal representation:
- my $es = "$x"; $es =~ /([0]*)$/;
- return 0 if !defined $1; # no zeros
- return CORE::length("$1"); # as string, not as +0!
+ $CALC->_zeros($x->{value}); # must handle odd values, 0 etc
}
sub bsqrt
{
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ # calculate square root of $x
+ my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
return $x if $x->modify('bsqrt');
- return $x->bnan() if $x->{sign} ne '+'; # -x or inf or NaN => NaN
- return $x->bzero($a,$p) if $x->is_zero(); # 0 => 0
- return $x->round($a,$p,$r) if $x->is_one(); # 1 => 1
+ return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN
+ return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf
- return $upgrade->bsqrt($x,$a,$p,$r) if defined $upgrade;
+ return $upgrade->bsqrt($x,@r) if defined $upgrade;
- if ($CALC->can('_sqrt'))
- {
- $x->{value} = $CALC->_sqrt($x->{value});
- return $x->round($a,$p,$r);
- }
+ $x->{value} = $CALC->_sqrt($x->{value});
+ $x->round(@r);
+ }
- return $x->bone($a,$p) if $x < 4; # 2,3 => 1
- my $y = $x->copy();
- my $l = int($x->length()/2);
-
- $x->bone(); # keep ref($x), but modify it
- $x->blsft($l,10);
+sub broot
+ {
+ # calculate $y'th root of $x
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
- my $last = $self->bzero();
- my $two = $self->new(2);
- my $lastlast = $x+$two;
- while ($last != $x && $lastlast != $x)
+ $y = $self->new(2) unless defined $y;
+
+ # objectify is costly, so avoid it
+ if ((!ref($x)) || (ref($x) ne ref($y)))
{
- $lastlast = $last; $last = $x;
- $x += $y / $x;
- $x /= $two;
+ ($self,$x,$y,@r) = objectify(2,$self || $class,@_);
}
- $x-- if $x * $x > $y; # overshot?
- $x->round($a,$p,$r);
+
+ return $x if $x->modify('broot');
+
+ # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
+ return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
+ $y->{sign} !~ /^\+$/;
+
+ return $x->round(@r)
+ if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
+
+ return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade;
+
+ $x->{value} = $CALC->_root($x->{value},$y->{value});
+ $x->round(@r);
}
sub exponent
if ($x->{sign} !~ /^[+-]$/)
{
- my $s = $x->{sign}; $s =~ s/^[+-]//;
- return $self->new($s); # -inf,+inf => inf
+ my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf
+ return $self->new($s);
}
- my $e = $class->bzero();
- return $e->binc() if $x->is_zero();
- $e += $x->_trailing_zeros();
- return $e;
+ return $self->bone() if $x->is_zero();
+
+ $self->new($x->_trailing_zeros());
}
sub mantissa
if ($x->{sign} !~ /^[+-]$/)
{
- my $s = $x->{sign}; $s =~ s/^[+]//;
- return $self->new($s); # +inf => inf
+ # for NaN, +inf, -inf: keep the sign
+ return $self->new($x->{sign});
}
- my $m = $x->copy();
- # that's inefficient
+ my $m = $x->copy(); delete $m->{_p}; delete $m->{_a};
+ # that's a bit inefficient:
my $zeros = $m->_trailing_zeros();
- $m /= 10 ** $zeros if $zeros != 0;
- return $m;
+ $m->brsft($zeros,10) if $zeros != 0;
+ $m;
}
sub parts
{
# return a copy of both the exponent and the mantissa
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- return ($x->mantissa(),$x->exponent());
+ ($x->mantissa(),$x->exponent());
}
##############################################################################
{
# precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
# $n == 0 || $n == 1 => round to integer
- my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_);
- return $x if !defined $scale; # no-op
- return $x if $x->modify('bfround');
+ my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x;
+
+ my ($scale,$mode) = $x->_scale_p(@_);
+
+ return $x if !defined $scale || $x->modify('bfround'); # no-op
# no-op for BigInts if $n <= 0
- if ($scale <= 0)
- {
- $x->{_a} = undef; # clear an eventual set A
- $x->{_p} = $scale; return $x;
- }
+ $x->bround( $x->length()-$scale, $mode) if $scale > 0;
- $x->bround( $x->length()-$scale, $mode);
- $x->{_a} = undef; # bround sets {_a}
- $x->{_p} = $scale; # so correct it
+ delete $x->{_a}; # delete to save memory
+ $x->{_p} = $scale; # store new _p
$x;
}
sub _scan_for_nonzero
{
- my $x = shift;
- my $pad = shift;
- my $xs = shift;
+ # internal, used by bround() to scan for non-zeros after a '5'
+ my ($x,$pad,$xs,$len) = @_;
- my $len = $x->length();
- return 0 if $len == 1; # '5' is trailed by invisible zeros
+ return 0 if $len == 1; # "5" is trailed by invisible zeros
my $follow = $pad - 1;
return 0 if $follow > $len || $follow < 1;
- # since we do not know underlying represention of $x, use decimal string
- #my $r = substr ($$xs,-$follow);
- my $r = substr ("$x",-$follow);
- return 1 if $r =~ /[^0]/; return 0;
+ # use the string form to check whether only '0's follow or not
+ substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0;
}
sub fround
{
- # to make life easier for switch between MBF and MBI (autoload fxxx()
- # like MBF does for bxxx()?)
- my $x = shift;
- return $x->bround(@_);
+ # Exists to make life easier for switch between MBF and MBI (should we
+ # autoload fxxx() like MBF does for bxxx()?)
+ my $x = shift; $x = $class->new($x) unless ref $x;
+ $x->bround(@_);
}
sub bround
# do not return $x->bnorm(), but $x
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_);
- return $x if !defined $scale; # no-op
- return $x if $x->modify('bround');
+ my ($scale,$mode) = $x->_scale_a(@_);
+ return $x if !defined $scale || $x->modify('bround'); # no-op
if ($x->is_zero() || $scale == 0)
{
# we have fewer digits than we want to scale to
my $len = $x->length();
+ # convert $scale to a scalar in case it is an object (put's a limit on the
+ # number length, but this would already limited by memory constraints), makes
+ # it faster
+ $scale = $scale->numify() if ref ($scale);
+
# scale < 0, but > -len (not >=!)
if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
{
$pad = $len - $scale;
$pad = abs($scale-1) if $scale < 0;
- # do not use digit(), it is costly for binary => decimal
-
+ # do not use digit(), it is very costly for binary => decimal
+ # getting the entire string is also costly, but we need to do it only once
my $xs = $CALC->_str($x->{value});
my $pl = -$pad-1;
-
+
# pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
# pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
- $digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len;
+ $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len;
$pl++; $pl ++ if $pad >= $len;
- $digit_after = '0'; $digit_after = substr($$xs,$pl,1) if $pad > 0;
-
- # print "$pad $pl $$xs dr $digit_round da $digit_after\n";
+ $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0;
# in case of 01234 we round down, for 6789 up, and only in case 5 we look
# closer at the remaining digits of the original $x, remember decision
($digit_after =~ /[01234]/) || # round down anyway,
# 6789 => round up
($digit_after eq '5') && # not 5000...0000
- ($x->_scan_for_nonzero($pad,$xs) == 0) &&
+ ($x->_scan_for_nonzero($pad,$xs,$len) == 0) &&
(
($mode eq 'even') && ($digit_round =~ /[24680]/) ||
($mode eq 'odd') && ($digit_round =~ /[13579]/) ||
);
my $put_back = 0; # not yet modified
- # old code, depend on internal representation
- # split mantissa at $pad and then pad with zeros
- #my $s5 = int($pad / 5);
- #my $i = 0;
- #while ($i < $s5)
- # {
- # $x->{value}->[$i++] = 0; # replace with 5 x 0
- # }
- #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0
- #my $rem = $pad % 5; # so much left over
- #if ($rem > 0)
- # {
- # #print "remainder $rem\n";
- ## #print "elem $x->{value}->[$s5]\n";
- # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0'
- # }
- #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5'
- #print ${$CALC->_str($pad->{value})}," $len\n";
-
if (($pad > 0) && ($pad <= $len))
{
- substr($$xs,-$pad,$pad) = '0' x $pad;
- $put_back = 1;
+ substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...'
+ $put_back = 1; # need to put back
}
elsif ($pad > $len)
{
if ($round_up) # what gave test above?
{
- $put_back = 1;
- $pad = $len, $$xs = '0'x$pad if $scale < 0; # tlr: whack 0.51=>1.0
+ $put_back = 1; # need to put back
+ $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
# we modify directly the string variant instead of creating a number and
- # adding it
+ # adding it, since that is faster (we already have the string)
my $c = 0; $pad ++; # for $pad == $len case
while ($pad <= $len)
{
- $c = substr($$xs,-$pad,1) + 1; $c = '0' if $c eq '10';
- substr($$xs,-$pad,1) = $c; $pad++;
+ $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10';
+ substr($xs,-$pad,1) = $c; $pad++;
last if $c != 0; # no overflow => early out
}
- $$xs = '1'.$$xs if $c == 0;
+ $xs = '1'.$xs if $c == 0;
- # $x->badd( Math::BigInt->new($x->{sign}.'1'. '0' x $pad) );
}
- $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back in
+ $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed
$x->{_a} = $scale if $scale >= 0;
if ($scale < 0)
sub bfloor
{
- # return integer less or equal then number, since it is already integer,
- # always returns $self
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+ # return integer less or equal then number; no-op since it's already integer
+ my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
- # not needed: return $x if $x->modify('bfloor');
- return $x->round($a,$p,$r);
+ $x->round(@r);
}
sub bceil
{
- # return integer greater or equal then number, since it is already integer,
- # always returns $self
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+ # return integer greater or equal then number; no-op since it's already int
+ my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
- # not needed: return $x if $x->modify('bceil');
- return $x->round($a,$p,$r);
+ $x->round(@r);
}
-##############################################################################
-# private stuff (internal use only)
+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
+ # it or override with their own integer conversion routine.
+ $_[0]->copy();
+ }
-sub __one
+sub as_hex
{
- # internal speedup, set argument to 1, or create a +/- 1
- my $self = shift;
- my $x = $self->bone(); # $x->{value} = $CALC->_one();
- $x->{sign} = shift || '+';
- return $x;
+ # return as hex string, with prefixed 0x
+ 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 '-';
+ $s . $CALC->_as_hex($x->{value});
}
-sub _swap
+sub as_bin
{
- # Overload will swap params if first one is no object ref so that the first
- # one is always an object ref. In this case, third param is true.
- # This routine is to overcome the effect of scalar,$object creating an object
- # of the class of this package, instead of the second param $object. This
- # happens inside overload, when the overload section of this package is
- # inherited by sub classes.
- # For overload cases (and this is used only there), we need to preserve the
- # args, hence the copy().
- # You can override this method in a subclass, the overload section will call
- # $object->_swap() to make sure it arrives at the proper subclass, with some
- # exceptions like '+' and '-'. To make '+' and '-' work, you also need to
- # specify your own overload for them.
+ # return as binary string, with prefixed 0b
+ my $x = shift; $x = $class->new($x) if !ref($x);
- # object, (object|scalar) => preserve first and make copy
- # scalar, object => swapped, re-swap and create new from first
- # (using class of second object, not $class!!)
- my $self = shift; # for override in subclass
- if ($_[2])
- {
- my $c = ref ($_[0]) || $class; # fallback $class should not happen
- return ( $c->new($_[1]), $_[0] );
- }
- return ( $_[0]->copy(), $_[1] );
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+
+ my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
+ return $s . $CALC->_as_bin($x->{value});
}
+##############################################################################
+# private stuff (internal use only)
+
sub objectify
{
# check for strings, if yes, return objects instead
# the first argument is number of args objectify() should look at it will
# return $count+1 elements, the first will be a classname. This is because
# overloaded '""' calls bstr($object,undef,undef) and this would result in
- # useless objects beeing created and thrown away. So we cannot simple loop
+ # useless objects being created and thrown away. So we cannot simple loop
# over @_. If the given count is 0, all arguments will be used.
# If the second arg is a ref, use it as class.
# currently it tries 'Math::BigInt' + 1, which will not work.
# some shortcut for the common cases
-
# $x->unary_op();
return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
- # $x->binary_op($y);
- #return (ref($_[1]),$_[1],$_[2]) if (@_ == 3) && ($_[0]||0 == 2)
- # && ref($_[1]) && ref($_[2]);
my $count = abs(shift || 0);
- my @a; # resulting array
+ my (@a,$k,$d); # resulting array, temp, and downgrade
if (ref $_[0])
{
# okay, got object as first
$a[0] = $class;
$a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first?
}
- # print "Now in objectify, my class is today $a[0]\n";
- my $k;
+
+ no strict 'refs';
+ # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats
+ if (defined ${"$a[0]::downgrade"})
+ {
+ $d = ${"$a[0]::downgrade"};
+ ${"$a[0]::downgrade"} = undef;
+ }
+
+ my $up = ${"$a[0]::upgrade"};
+ #print "Now in objectify, my class is today $a[0], count = $count\n";
if ($count == 0)
{
while (@_)
{
$k = $a[0]->new($k);
}
- elsif (ref($k) ne $a[0])
+ 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 = $a[0]->new($k);
}
- elsif (ref($k) ne $a[0])
+ 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);
}
push @a,@_; # return other params, too
}
- die "$class objectify needs list context" unless wantarray;
+ if (! wantarray)
+ {
+ require Carp; Carp::croak ("$class objectify needs list context");
+ }
+ ${"$a[0]::downgrade"} = $d;
@a;
}
+sub _register_callback
+ {
+ my ($class,$callback) = @_;
+
+ if (ref($callback) ne 'CODE')
+ {
+ require Carp;
+ Carp::croak ("$callback is not a coderef");
+ }
+ $CALLBACKS{$class} = $callback;
+ }
+
sub import
{
my $self = shift;
- $IMPORT++;
- my @a = @_; my $l = scalar @_; my $j = 0;
- for ( my $i = 0; $i < $l ; $i++,$j++ )
+ $IMPORT++; # remember we did import()
+ my @a; my $l = scalar @_;
+ for ( my $i = 0; $i < $l ; $i++ )
{
if ($_[$i] eq ':constant')
{
# this causes overlord er load to step in
- overload::constant integer => sub { $self->new(shift) };
- splice @a, $j, 1; $j --;
+ overload::constant
+ integer => sub { $self->new(shift) },
+ binary => sub { $self->new(shift) };
}
elsif ($_[$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] =~ /^lib$/i)
{
# this causes a different low lib to take care...
$CALC = $_[$i+1] || '';
- my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
- splice @a, $j, $s; $j -= $s;
+ $i++;
+ }
+ else
+ {
+ push @a, $_[$i];
}
}
# any non :constant stuff is handled by our parent, Exporter
- # even if @_ is empty, to give it a chance
- $self->SUPER::import(@a); # need it for subclasses
- $self->export_to_level(1,$self,@a); # need it for MBF
+ if (@a > 0)
+ {
+ require Exporter;
+
+ $self->SUPER::import(@a); # need it for subclasses
+ $self->export_to_level(1,$self,@a); # need it for MBF
+ }
# try to load core math lib
my @c = split /\s*,\s*/,$CALC;
- push @c,'Calc'; # if all fail, try this
+ foreach (@c)
+ {
+ $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters
+ }
+ push @c, 'FastCalc', 'Calc'; # if all fail, try these
$CALC = ''; # signal error
foreach my $lib (@c)
{
+ next if ($lib || '') eq '';
$lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
$lib =~ s/\.pm$//;
if ($] < 5.006)
{
- # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is
- # used in the same script, or eval inside import().
- (my $mod = $lib . '.pm') =~ s!::!/!g;
- # require does not automatically :: => /, so portability problems arise
- eval { require $mod; $lib->import( @c ); }
+ # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is
+ # used in the same script, or eval("") inside import().
+ my @parts = split /::/, $lib; # Math::BigInt => Math BigInt
+ my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
+ require File::Spec;
+ $file = File::Spec->catfile (@parts, $file);
+ eval { require "$file"; $lib->import( @c ); }
}
else
{
eval "use $lib qw/@c/;";
}
- $CALC = $lib, last if $@ eq ''; # no error in loading lib?
+ if ($@ eq '')
+ {
+ my $ok = 1;
+ # loaded it ok, see if the api_version() is high enough
+ if ($lib->can('api_version') && $lib->api_version() >= 1.0)
+ {
+ $ok = 0;
+ # api_version matches, check if it really provides anything we need
+ for my $method (qw/
+ one two ten
+ str num
+ 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
+ rsft lsft xor and or
+ mod sqrt root fac pow modinv modpow log_int gcd
+ /)
+ {
+ if (!$lib->can("_$method"))
+ {
+ if (($WARN{$lib}||0) < 2)
+ {
+ require Carp;
+ Carp::carp ("$lib is missing method '_$method'");
+ $WARN{$lib} = 1; # still warn about the lib
+ }
+ $ok++; last;
+ }
+ }
+ }
+ if ($ok == 0)
+ {
+ $CALC = $lib;
+ last; # found a usable one, break
+ }
+ else
+ {
+ if (($WARN{$lib}||0) < 2)
+ {
+ my $ver = eval "\$$lib\::VERSION" || 'unknown';
+ require Carp;
+ Carp::carp ("Cannot load outdated $lib v$ver, please upgrade");
+ $WARN{$lib} = 2; # never warn again
+ }
+ }
+ }
+ }
+ if ($CALC eq '')
+ {
+ require Carp;
+ Carp::croak ("Couldn't load any math lib, not even 'Calc.pm'");
+ }
+
+ # notify callbacks
+ foreach my $class (keys %CALLBACKS)
+ {
+ &{$CALLBACKS{$class}}($CALC);
+ }
+
+ # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib
+ # functions
+
+ %CAN = ();
+ for my $method (qw/ signed_and signed_or signed_xor /)
+ {
+ $CAN{$method} = $CALC->can("_$method") ? 1 : 0;
}
- die "Couldn't load any math lib, not even the default" if $CALC eq '';
+
+ # import done
}
sub __from_hex
{
+ # internal
# convert a (ref to) big hex string to BigInt, return undef for error
my $hs = shift;
my $x = Math::BigInt->bzero();
# strip underscores
- $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
- $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
+ $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
+ $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
- return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/;
+ return $x->bnan() if $hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/;
- my $sign = '+'; $sign = '-' if ($$hs =~ /^-/);
+ my $sign = '+'; $sign = '-' if $hs =~ /^-/;
- $$hs =~ s/^[+-]//; # strip sign
- if ($CALC->can('_from_hex'))
- {
- $x->{value} = $CALC->_from_hex($hs);
- }
- else
- {
- # fallback to pure perl
- my $mul = Math::BigInt->bzero(); $mul++;
- my $x65536 = Math::BigInt->new(65536);
- my $len = CORE::length($$hs)-2;
- $len = int($len/4); # 4-digit parts, w/o '0x'
- my $val; my $i = -4;
- while ($len >= 0)
- {
- $val = substr($$hs,$i,4);
- $val =~ s/^[+-]?0x// if $len == 0; # for last part only because
- $val = hex($val); # hex does not like wrong chars
- $i -= 4; $len --;
- $x += $mul * $val if $val != 0;
- $mul *= $x65536 if $len >= 0; # skip last mul
- }
- }
- $x->{sign} = $sign if !$x->is_zero(); # no '-0'
- return $x;
+ $hs =~ s/^[+-]//; # strip sign
+ $x->{value} = $CALC->_from_hex($hs);
+ $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0'
+ $x;
}
sub __from_bin
{
+ # internal
# convert a (ref to) big binary string to BigInt, return undef for error
my $bs = shift;
my $x = Math::BigInt->bzero();
# strip underscores
- $$bs =~ s/([01])_([01])/$1$2/g;
- $$bs =~ s/([01])_([01])/$1$2/g;
- return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/;
+ $bs =~ s/([01])_([01])/$1$2/g;
+ $bs =~ s/([01])_([01])/$1$2/g;
+ return $x->bnan() if $bs !~ /^[+-]?0b[01]+$/;
- my $mul = Math::BigInt->bzero(); $mul++;
- my $x256 = Math::BigInt->new(256);
+ my $sign = '+'; $sign = '-' if $bs =~ /^\-/;
+ $bs =~ s/^[+-]//; # strip sign
- my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/);
- $$bs =~ s/^[+-]//; # strip sign
- if ($CALC->can('_from_bin'))
- {
- $x->{value} = $CALC->_from_bin($bs);
- }
- else
- {
- my $len = CORE::length($$bs)-2;
- $len = int($len/8); # 8-digit parts, w/o '0b'
- my $val; my $i = -8;
- while ($len >= 0)
- {
- $val = substr($$bs,$i,8);
- $val =~ s/^[+-]?0b// if $len == 0; # for last part only
- #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0
- # slower:
- # $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8;
- $val = ord(pack('B8',substr('00000000'.$val,-8,8)));
- $i -= 8; $len --;
- $x += $mul * $val if $val != 0;
- $mul *= $x256 if $len >= 0; # skip last mul
- }
- }
- $x->{sign} = $sign if !$x->is_zero();
- return $x;
+ $x->{value} = $CALC->_from_bin($bs);
+ $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0'
+ $x;
}
sub _split
{
- # (ref to num_str) return num_str
- # internal, take apart a string and return the pieces
- # strip leading/trailing whitespace, leading zeros, underscore and reject
- # invalid input
+ # input: num_str; output: undef for invalid or
+ # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,\$exp_sign,\$exp_value)
+ # Internal, take apart a string and return the pieces.
+ # Strip leading/trailing whitespace, leading zeros, underscore and reject
+ # invalid input.
my $x = shift;
# strip white space at front, also extranous leading zeros
- $$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 ($$x =~ /^[+-]?\d+$/)
+ if ($x =~ /^[+-]?\d+\z/)
{
- $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
- return (\$sign, $x, \'', \'', \0);
+ $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
+ return (\$sign, \$x, \'', \'', \0);
}
# invalid starting char?
- return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
+ return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
- return __from_hex($x) if $$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;
- $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3
+ $x =~ s/(\d)_(\d)/$1$2/g;
+ $x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3
# some possible inputs:
# 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
- # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2
-
- return if $$x =~ /[Ee].*[Ee]/; # more than one E => error
+ # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999
- my ($m,$e) = split /[Ee]/,$$x;
+ my ($m,$e,$last) = split /[Ee]/,$x;
+ return if defined $last; # last defined => 1e2E3 or others
$e = '0' if !defined $e || $e eq "";
+
# sign,value for exponent,mantint,mantfrac
my ($es,$ev,$mis,$miv,$mfv);
# valid exponent?
$es = $1; $ev = $2;
# valid mantissa?
return if $m eq '.' || $m eq '';
- my ($mi,$mf) = split /\./,$m;
+ my ($mi,$mf,$lastf) = split /\./,$m;
+ return if defined $lastf; # lastf defined => 1.2.3 or others
$mi = '0' if !defined $mi;
$mi .= '0' if $mi =~ /^[\-\+]?$/;
$mf = '0' if !defined $mf || $mf eq '';
$mis = $1||'+'; $miv = $2;
return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros
$mfv = $1;
+ # handle the 0e999 case here
+ $ev = 0 if $miv eq '0' && $mfv eq '';
return (\$mis,\$miv,\$mfv,\$es,\$ev);
}
}
return; # NaN, not a number
}
-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
- # it or override with their own integer conversion routine
- my $self = shift;
-
- $self->copy();
- }
-
-sub as_hex
- {
- # return as hex string, with prefixed 0x
- my $x = shift; $x = $class->new($x) if !ref($x);
-
- return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
- return '0x0' if $x->is_zero();
-
- my $es = ''; my $s = '';
- $s = $x->{sign} if $x->{sign} eq '-';
- if ($CALC->can('_as_hex'))
- {
- $es = ${$CALC->_as_hex($x->{value})};
- }
- else
- {
- my $x1 = $x->copy()->babs(); my $xr;
- my $x10000 = Math::BigInt->new (0x10000);
- while (!$x1->is_zero())
- {
- ($x1, $xr) = bdiv($x1,$x10000);
- $es .= unpack('h4',pack('v',$xr->numify()));
- }
- $es = reverse $es;
- $es =~ s/^[0]+//; # strip leading zeros
- $s .= '0x';
- }
- $s . $es;
- }
-
-sub as_bin
- {
- # return as binary string, with prefixed 0b
- my $x = shift; $x = $class->new($x) if !ref($x);
-
- return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
- return '0b0' if $x->is_zero();
-
- my $es = ''; my $s = '';
- $s = $x->{sign} if $x->{sign} eq '-';
- if ($CALC->can('_as_bin'))
- {
- $es = ${$CALC->_as_bin($x->{value})};
- }
- else
- {
- my $x1 = $x->copy()->babs(); my $xr;
- my $x10000 = Math::BigInt->new (0x10000);
- while (!$x1->is_zero())
- {
- ($x1, $xr) = bdiv($x1,$x10000);
- $es .= unpack('b16',pack('v',$xr->numify()));
- }
- $es = reverse $es;
- $es =~ s/^[0]+//; # strip leading zeros
- $s .= '0b';
- }
- $s . $es;
- }
-
##############################################################################
# internal calculation routines (others are in Math::BigInt::Calc etc)
# does modify first argument
# LCM
- my $x = shift; my $ty = shift;
- return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan);
- return $x * $ty / bgcd($x,$ty);
- }
-
-sub __gcd
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does modify both arguments
- # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296
my ($x,$ty) = @_;
-
- return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/;
-
- while (!$ty->is_zero())
- {
- ($x, $ty) = ($ty,bmod($x,$ty));
- }
- $x;
+ return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan);
+ my $method = ref($x) . '::bgcd';
+ no strict 'refs';
+ $x * $ty / &$method($x,$ty);
}
###############################################################################
-# this method return 0 if the object can be modified, or 1 for not
-# We use a fast use constant statement here, to avoid costly calls. Subclasses
+# this method returns 0 if the object can be modified, or 1 if not.
+# We use a fast constant sub() here, to avoid costly calls. Subclasses
# may override it with special code (f.i. Math::BigInt::Constant does so)
sub modify () { 0; }
1;
__END__
+=pod
+
=head1 NAME
-Math::BigInt - Arbitrary size integer math package
+Math::BigInt - Arbitrary size integer/float math package
=head1 SYNOPSIS
use Math::BigInt;
+ # or make it faster: install (optional) Math::BigInt::GMP
+ # and always use (it will fall back to pure Perl if the
+ # GMP library is not installed):
+
+ use Math::BigInt lib => 'GMP';
+
+ my $str = '1234567890';
+ my @values = (64,74,18);
+ my $n = 1; my $sign = '-';
+
# Number creation
$x = Math::BigInt->new($str); # defaults to 0
+ $y = $x->copy(); # make a true copy
$nan = Math::BigInt->bnan(); # create a NotANumber
$zero = Math::BigInt->bzero(); # create a +0
$inf = Math::BigInt->binf(); # create a +inf
$one = Math::BigInt->bone(); # create a +1
$one = Math::BigInt->bone('-'); # create a -1
- # Testing
- $x->is_zero(); # true if arg is +0
- $x->is_nan(); # true if arg is NaN
- $x->is_one(); # true if arg is +1
- $x->is_one('-'); # true if arg is -1
- $x->is_odd(); # true if odd, false for even
- $x->is_even(); # true if even, false for odd
- $x->is_positive(); # true if >= 0
- $x->is_negative(); # true if < 0
- $x->is_inf(sign); # true if +inf, or -inf (sign is default '+')
- $x->is_int(); # true if $x is an integer (not a float)
-
- $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
- $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
- $x->sign(); # return the sign, either +,- or NaN
- $x->digit($n); # return the nth digit, counting from right
- $x->digit(-$n); # return the nth digit, counting from left
-
- # The following all modify their first argument:
-
- # set
- $x->bzero(); # set $x to 0
- $x->bnan(); # set $x to NaN
- $x->bone(); # set $x to +1
- $x->bone('-'); # set $x to -1
- $x->binf(); # set $x to inf
- $x->binf('-'); # set $x to -inf
-
- $x->bneg(); # negation
- $x->babs(); # absolute value
- $x->bnorm(); # normalize (no-op)
- $x->bnot(); # two's complement (bit wise not)
- $x->binc(); # increment x by 1
- $x->bdec(); # decrement x by 1
+ # Testing (don't modify their arguments)
+ # (return true if the condition is met, otherwise false)
+
+ $x->is_zero(); # if $x is +0
+ $x->is_nan(); # if $x is NaN
+ $x->is_one(); # if $x is +1
+ $x->is_one('-'); # if $x is -1
+ $x->is_odd(); # if $x is odd
+ $x->is_even(); # if $x is even
+ $x->is_pos(); # if $x >= 0
+ $x->is_neg(); # if $x < 0
+ $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+')
+ $x->is_int(); # if $x is an integer (not a float)
+
+ # comparing and digit/sign extraction
+ $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
+ $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
+ $x->sign(); # return the sign, either +,- or NaN
+ $x->digit($n); # return the nth digit, counting from right
+ $x->digit(-$n); # return the nth digit, counting from left
+
+ # The following all modify their first argument. If you want to preserve
+ # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is
+ # necessary when mixing $a = $b assignments with non-overloaded math.
+
+ $x->bzero(); # set $x to 0
+ $x->bnan(); # set $x to NaN
+ $x->bone(); # set $x to +1
+ $x->bone('-'); # set $x to -1
+ $x->binf(); # set $x to inf
+ $x->binf('-'); # set $x to -inf
+
+ $x->bneg(); # negation
+ $x->babs(); # absolute value
+ $x->bnorm(); # normalize (no-op in BigInt)
+ $x->bnot(); # two's complement (bit wise not)
+ $x->binc(); # increment $x by 1
+ $x->bdec(); # decrement $x by 1
- $x->badd($y); # addition (add $y to $x)
- $x->bsub($y); # subtraction (subtract $y from $x)
- $x->bmul($y); # multiplication (multiply $x by $y)
- $x->bdiv($y); # divide, set $x to quotient
- # return (quo,rem) or quo if scalar
-
- $x->bmod($y); # modulus (x % y)
- $x->bpow($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)
+ $x->badd($y); # addition (add $y to $x)
+ $x->bsub($y); # subtraction (subtract $y from $x)
+ $x->bmul($y); # multiplication (multiply $x by $y)
+ $x->bdiv($y); # divide, set $x to quotient
+ # return (quo,rem) or quo if scalar
+
+ $x->bmod($y); # modulus (x % y)
+ $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod))
+ $x->bmodinv($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)
- $x->band($y); # bitwise and
- $x->bior($y); # bitwise inclusive or
- $x->bxor($y); # bitwise exclusive or
- $x->bnot(); # bitwise not (two's complement)
+ $x->band($y); # bitwise and
+ $x->bior($y); # bitwise inclusive or
+ $x->bxor($y); # bitwise exclusive or
+ $x->bnot(); # bitwise not (two's complement)
- $x->bsqrt(); # calculate square-root
- $x->bfac(); # factorial of $x (1*2*3*4*..$x)
+ $x->bsqrt(); # calculate square-root
+ $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root)
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
- $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r
- $x->bround($N); # accuracy: preserve $N digits
- $x->bfround($N); # round to $Nth digit, no-op for BigInts
+ $x->round($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
- # The following do not modify their arguments in BigInt, but do in BigFloat:
- $x->bfloor(); # return integer less or equal than $x
- $x->bceil(); # return integer greater or equal than $x
+ # The following do not modify their arguments in BigInt (are no-ops),
+ # but do so in BigFloat:
+
+ $x->bfloor(); # return integer less or equal than $x
+ $x->bceil(); # return integer greater or equal than $x
# The following do not modify their arguments:
- bgcd(@values); # greatest common divisor (no OO style)
- blcm(@values); # lowest common multiplicator (no OO style)
+ # greatest common divisor (no OO style)
+ my $gcd = Math::BigInt::bgcd(@values);
+ # lowest common multiplicator (no OO style)
+ my $lcm = Math::BigInt::blcm(@values);
- $x->length(); # return number of digits in number
- ($x,$f) = $x->length(); # length of number and length of fraction part,
- # latter is always 0 digits long for BigInt's
-
- $x->exponent(); # return exponent as BigInt
- $x->mantissa(); # return (signed) mantissa as BigInt
- $x->parts(); # return (mantissa,exponent) as BigInt
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
- $x->as_number(); # return as BigInt (in BigInt: same as copy())
+ $x->length(); # return number of digits in number
+ ($xl,$f) = $x->length(); # length of number and length of fraction part,
+ # latter is always 0 digits long for BigInts
+
+ $x->exponent(); # return exponent as BigInt
+ $x->mantissa(); # return (signed) mantissa as BigInt
+ $x->parts(); # return (mantissa,exponent) as BigInt
+ $x->copy(); # make a true copy of $x (unlike $y = $x;)
+ $x->as_int(); # return as BigInt (in BigInt: same as copy())
+ $x->numify(); # return as scalar (might overflow!)
- # conversation to string
- $x->bstr(); # normalized string
- $x->bsstr(); # normalized string in scientific notation
- $x->as_hex(); # as signed hexadecimal string with prefixed 0x
- $x->as_bin(); # as signed binary string with prefixed 0b
+ # conversation to string (do not modify their argument)
+ $x->bstr(); # normalized string (e.g. '3')
+ $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
+
+
+ # precision and accuracy (see section about rounding for more)
+ $x->precision(); # return P of $x (or global, if P of $x undef)
+ $x->precision($n); # set P of $x to $n
+ $x->accuracy(); # return A of $x (or global, if A of $x undef)
+ $x->accuracy($n); # set A $x to $n
+
+ # Global methods
+ 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'
+ Math::BigInt->config(); # return hash containing configuration
=head1 DESCRIPTION
-All operators (inlcuding basic math operations) are overloaded if you
+All operators (including basic math operations) are overloaded if you
declare your big integers as
$i = new Math::BigInt '123_456_789_123_456_789';
=over 2
-=item Canonical notation
-
-Big integer values are strings of the form C</^[+-]\d+$/> with leading
-zeros suppressed.
+=item Input
- '-0' canonical value '-0', normalized '0'
- ' -123_123_123' canonical value '-123123123'
- '1_23_456_7890' canonical value '1234567890'
+Input values to these routines may be any string, that looks like a number
+and results in an integer, including hexadecimal and binary numbers.
-=item Input
+Scalars holding numbers may also be passed, but note that non-integer numbers
+may already have lost precision due to the conversation to float. Quote
+your input if you want BigInt to see all the digits:
-Input values to these routines may be either Math::BigInt objects or
-strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>.
+ $x = Math::BigInt->new(12345678890123456789); # bad
+ $x = Math::BigInt->new('12345678901234567890'); # good
You can include one underscore between any two digits.
This means integer values like 1.01E2 or even 1000E-2 are also accepted.
-Non integer values result in NaN.
+Non-integer values result in NaN.
-Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results
-in 'NaN'.
+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:
-bnorm() on a BigInt object is now effectively a no-op, since the numbers
-are always stored in normalized form. On a string, it creates a BigInt
-object.
+ $zero = Math::BigInt->bzero();
+ $nan = Math::BigInt->bnan();
+
+C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers
+are always stored in normalized form. If passed a string, creates a BigInt
+object from the input.
=item Output
-Output values are BigInt objects (normalized), except for bstr(), which
-returns a string in normalized form.
+Output values are BigInt objects (normalized), except for the methods which
+return a string (see L<SYNOPSIS>).
+
Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>,
-C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>)
-return either undef, <0, 0 or >0 and are suited for sort.
+C<is_nan()>, etc.) return true or false, while others (C<bcmp()>, C<bacmp()>)
+return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort.
=back
=head1 METHODS
-Each of the methods below accepts three additional parameters. These arguments
-$A, $P and $R are accuracy, precision and round_mode. Please see more in the
-section about ACCURACY and ROUNDIND.
+Each of the methods below (except config(), accuracy() and precision())
+accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R>
+are C<accuracy>, C<precision> and C<round_mode>. Please see the section about
+L<ACCURACY and PRECISION> for more information.
+
+=head2 config
+
+ use Data::Dumper;
+
+ print Dumper ( Math::BigInt->config() );
+ print Math::BigInt->config()->{lib},"\n";
+
+Returns a hash containing the configuration, e.g. the version number, lib
+loaded etc. The following hash keys are currently filled in with the
+appropriate information.
+
+ key Description
+ Example
+ ============================================================
+ lib Name of the low-level math library
+ Math::BigInt::Calc
+ lib_version Version of low-level math library (see 'lib')
+ 0.30
+ class The class name of config() you just called
+ Math::BigInt
+ upgrade To which class math operations might be upgraded
+ Math::BigFloat
+ downgrade To which class math operations might be downgraded
+ undef
+ precision Global precision
+ undef
+ accuracy Global accuracy
+ undef
+ round_mode Global round mode
+ even
+ version version number of the class you used
+ 1.61
+ div_scale Fallback accuracy for div
+ 40
+ trap_nan If true, traps creation of NaN via croak()
+ 1
+ trap_inf If true, traps creation of +inf/-inf via croak()
+ 1
+
+The following values can be set by passing C<config()> a reference to a hash:
+
+ trap_inf trap_nan
+ upgrade downgrade precision accuracy round_mode div_scale
+
+Example:
+
+ $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } );
+
+=head2 accuracy
+
+ $x->accuracy(5); # local for $x
+ CLASS->accuracy(5); # global for all members of CLASS
+ # Note: This also applies to new()!
+
+ $A = $x->accuracy(); # read out accuracy that affects $x
+ $A = CLASS->accuracy(); # read out global accuracy
+
+Set or get the global or local accuracy, aka how many significant digits the
+results have. If you set a global accuracy, then this also applies to new()!
+
+Warning! The accuracy I<sticks>, e.g. once you created a number under the
+influence of C<< CLASS->accuracy($A) >>, all results from math operations with
+that number will also be rounded.
+
+In most cases, you should probably round the results explicitly using one of
+L<round()>, L<bround()> or L<bfround()> or by passing the desired accuracy
+to the math operation as additional parameter:
+
+ my $x = Math::BigInt->new(30000);
+ my $y = Math::BigInt->new(7);
+ print scalar $x->copy()->bdiv($y, 2); # print 4300
+ print scalar $x->copy()->bdiv($y)->bround(2); # print 4300
+
+Please see the section about L<ACCURACY AND PRECISION> for further details.
+
+Value must be greater than zero. Pass an undef value to disable it:
+
+ $x->accuracy(undef);
+ Math::BigInt->accuracy(undef);
+
+Returns the current accuracy. For C<$x->accuracy()> it will return either the
+local accuracy, or if not defined, the global. This means the return value
+represents the accuracy that will be in effect for $x:
+
+ $y = Math::BigInt->new(1234567); # unrounded
+ print Math::BigInt->accuracy(4),"\n"; # set 4, print 4
+ $x = Math::BigInt->new(123456); # $x will be automatically rounded!
+ print "$x $y\n"; # '123500 1234567'
+ print $x->accuracy(),"\n"; # will be 4
+ print $y->accuracy(),"\n"; # also 4, since global is 4
+ print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5
+ print $x->accuracy(),"\n"; # still 4
+ print $y->accuracy(),"\n"; # 5, since global is 5
+
+Note: Works also for subclasses like Math::BigFloat. Each class has it's own
+globals separated from Math::BigInt, but it is possible to subclass
+Math::BigInt and make the globals of the subclass aliases to the ones from
+Math::BigInt.
+
+=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
+
+ CLASS->precision(5); # Global for all members of CLASS
+ # This also applies to new()!
+ CLASS->precision(-5); # ditto
+
+ $P = CLASS->precision(); # read out global precision
+ $P = $x->precision(); # read out precision that affects $x
+
+Note: You probably want to use L<accuracy()> instead. With L<accuracy> you
+set the number of digits each result should have, with L<precision> you
+set the place where to round!
+
+C<precision()> sets or gets the global or local precision, aka at which digit
+before or after the dot to round all results. A set global precision also
+applies to all newly created numbers!
+
+In Math::BigInt, passing a negative number precision has no effect since no
+numbers have digits after the dot. In L<Math::BigFloat>, it will round all
+results to P digits after the dot.
+
+Please see the section about L<ACCURACY AND PRECISION> for further details.
+
+Pass an undef value to disable it:
+
+ $x->precision(undef);
+ Math::BigInt->precision(undef);
+
+Returns the current precision. For C<$x->precision()> it will return either the
+local precision of $x, or if not defined, the global. This means the return
+value represents the prevision that will be in effect for $x:
+
+ $y = Math::BigInt->new(1234567); # unrounded
+ print Math::BigInt->precision(4),"\n"; # set 4, print 4
+ $x = Math::BigInt->new(123456); # will be automatically rounded
+ print $x; # print "120000"!
+
+Note: Works also for subclasses like L<Math::BigFloat>. Each class has its
+own globals separated from Math::BigInt, but it is possible to subclass
+Math::BigInt and make the globals of the subclass aliases to the ones from
+Math::BigInt.
=head2 brsft
$x = Math::BigInt->new($str,$A,$P,$R);
-Creates a new BigInt object from a string or another BigInt object. The
+Creates a new BigInt object from a scalar or another BigInt object. The
input is accepted as decimal, hex (with leading '0x') or binary (with leading
'0b').
+See L<Input> for more info on accepted input formats.
+
=head2 bnan
$x = Math::BigInt->bnan();
$x->bone(); # +1
$x->bone('-'); # -1
-=head2 is_one()/is_zero()/is_nan()/is_positive()/is_negative()/is_inf()/is_odd()/is_even()/is_int()
+=head2 is_one()/is_zero()/is_nan()/is_inf()
+
$x->is_zero(); # true if arg is +0
$x->is_nan(); # true if arg is NaN
$x->is_one(); # true if arg is +1
$x->is_one('-'); # true if arg is -1
- $x->is_odd(); # true if odd, false for even
- $x->is_even(); # true if even, false for odd
- $x->is_positive(); # true if >= 0
- $x->is_negative(); # true if < 0
$x->is_inf(); # true if +inf
$x->is_inf('-'); # true if -inf (sign is default '+')
+
+These methods all test the BigInt for being one specific value and return
+true or false depending on the input. These are faster than doing something
+like:
+
+ if ($x == 0)
+
+=head2 is_pos()/is_neg()
+
+ $x->is_pos(); # true if > 0
+ $x->is_neg(); # true if < 0
+
+The methods return true if the argument is positive or negative, respectively.
+C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and
+C<-inf> is negative. A C<zero> is neither positive nor negative.
+
+These methods are only testing the sign, and not the value.
+
+C<is_positive()> and C<is_negative()> are aliases to C<is_pos()> and
+C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were
+introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced
+in v1.68.
+
+=head2 is_odd()/is_even()/is_int()
+
+ $x->is_odd(); # true if odd, false for even
+ $x->is_even(); # true if even, false for odd
$x->is_int(); # true if $x is an integer
-These methods all test the BigInt for one condition and return true or false
-depending on the input.
+The return true when the argument satisfies the condition. C<NaN>, C<+inf>,
+C<-inf> are not integers and are neither odd nor even.
+
+In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers.
=head2 bcmp
- $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
+ $x->bcmp($y);
+
+Compares $x with $y and takes the sign into account.
+Returns -1, 0, 1 or undef.
=head2 bacmp
- $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
+ $x->bacmp($y);
+
+Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef.
=head2 sign
- $x->sign(); # return the sign, either +,- or NaN
+ $x->sign();
-=head2 bcmp
+Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
+
+If you want $x to have a certain sign, use one of the following methods:
+
+ $x->babs(); # '+'
+ $x->babs()->bneg(); # '-'
+ $x->bnan(); # 'NaN'
+ $x->binf(); # '+inf'
+ $x->binf('-'); # '-inf'
- $x->digit($n); # return the nth digit, counting from right
+=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 bnorm
- $x->bnorm(); # normalize (no-op)
+ $x->bnorm(); # normalize (no-op)
=head2 bnot
- $x->bnot(); # two's complement (bit wise not)
+ $x->bnot();
+
+Two's complement (bit wise not). This is equivalent to
+
+ $x->binc()->bneg();
+
+but faster.
=head2 binc
- $x->binc(); # increment x by 1
+ $x->binc(); # increment x by 1
=head2 bdec
- $x->bdec(); # decrement x by 1
+ $x->bdec(); # decrement x by 1
=head2 badd
- $x->badd($y); # addition (add $y to $x)
+ $x->badd($y); # addition (add $y to $x)
=head2 bsub
- $x->bsub($y); # subtraction (subtract $y from $x)
+ $x->bsub($y); # subtraction (subtract $y from $x)
=head2 bmul
- $x->bmul($y); # multiplication (multiply $x by $y)
+ $x->bmul($y); # multiplication (multiply $x by $y)
=head2 bdiv
- $x->bdiv($y); # divide, set $x to quotient
- # return (quo,rem) or quo if scalar
+ $x->bdiv($y); # divide, set $x to quotient
+ # return (quo,rem) or quo if scalar
=head2 bmod
- $x->bmod($y); # modulus (x % y)
+ $x->bmod($y); # modulus (x % y)
+
+=head2 bmodinv
+
+ num->bmodinv($mod); # modular inverse
+
+Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is
+returned unless C<$num> is relatively prime to C<$mod>, i.e. unless
+C<bgcd($num, $mod)==1>.
+
+=head2 bmodpow
+
+ $num->bmodpow($exp,$mod); # modular exponentation
+ # ($num**$exp % $mod)
+
+Returns the value of C<$num> taken to the power C<$exp> in the modulus
+C<$mod> using binary exponentation. C<bmodpow> is far superior to
+writing
+
+ $num ** $exp % $mod
+
+because it is much faster - it reduces internal variables into
+the modulus whenever possible, so it operates on smaller numbers.
+
+C<bmodpow> also supports negative exponents.
+
+ bmodpow($num, -1, $mod)
+
+is exactly equivalent to
+
+ bmodinv($num, $mod)
=head2 bpow
- $x->bpow($y); # power of arguments (x ** y)
+ $x->bpow($y); # power of arguments (x ** y)
=head2 blsft
- $x->blsft($y); # left shift
- $x->blsft($y,$n); # left shift, by base $n (like 10)
+ $x->blsft($y); # left shift
+ $x->blsft($y,$n); # left shift, in base $n (like 10)
=head2 brsft
- $x->brsft($y); # right shift
- $x->brsft($y,$n); # right shift, by base $n (like 10)
+ $x->brsft($y); # right shift
+ $x->brsft($y,$n); # right shift, in base $n (like 10)
=head2 band
- $x->band($y); # bitwise and
+ $x->band($y); # bitwise and
=head2 bior
- $x->bior($y); # bitwise inclusive or
+ $x->bior($y); # bitwise inclusive or
=head2 bxor
- $x->bxor($y); # bitwise exclusive or
+ $x->bxor($y); # bitwise exclusive or
=head2 bnot
- $x->bnot(); # bitwise not (two's complement)
+ $x->bnot(); # bitwise not (two's complement)
=head2 bsqrt
- $x->bsqrt(); # calculate square-root
+ $x->bsqrt(); # calculate square-root
=head2 bfac
- $x->bfac(); # factorial of $x (1*2*3*4*..$x)
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
=head2 round
- $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r
+ $x->round($A,$P,$round_mode);
+
+Round $x to accuracy C<$A> or precision C<$P> using the round mode
+C<$round_mode>.
=head2 bround
- $x->bround($N); # accuracy: preserve $N digits
+ $x->bround($N); # accuracy: preserve $N digits
=head2 bfround
- $x->bfround($N); # round to $Nth digit, no-op for BigInts
+ $x->bfround($N); # round to $Nth digit, no-op for BigInts
=head2 bfloor
=head2 bgcd
- bgcd(@values); # greatest common divisor (no OO style)
+ bgcd(@values); # greatest common divisor (no OO style)
=head2 blcm
- blcm(@values); # lowest common multiplicator (no OO style)
+ blcm(@values); # lowest common multiplicator (no OO style)
head2 length
=head2 parts
- $x->parts(); # return (mantissa,exponent) as BigInt
+ $x->parts(); # return (mantissa,exponent) as BigInt
=head2 copy
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
+ $x->copy(); # make a true copy of $x (unlike $y = $x;)
+
+=head2 as_int
+
+ $x->as_int();
-=head2 as_number
+Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as
+C<copy()>.
- $x->as_number(); # return as BigInt (in BigInt: same as copy())
+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 bsrt
+=head2 bstr
- $x->bstr(); # normalized string
+ $x->bstr();
+
+Returns a normalized string representation of C<$x>.
=head2 bsstr
- $x->bsstr(); # normalized string in scientific notation
+ $x->bsstr(); # normalized string in scientific notation
=head2 as_hex
- $x->as_hex(); # as signed hexadecimal string with prefixed 0x
+ $x->as_hex(); # as signed hexadecimal string with prefixed 0x
=head2 as_bin
- $x->as_bin(); # as signed binary string with prefixed 0b
+ $x->as_bin(); # as signed binary string with prefixed 0b
=head1 ACCURACY and PRECISION
Since version v1.33, Math::BigInt and Math::BigFloat have full support for
accuracy and precision based rounding, both automatically after every
-operation as well as manually.
+operation, as well as manually.
This section describes the accuracy/precision handling in Math::Big* as it
used to be and as it is now, complete with an explanation of all terms and
result has at most max(scale, length(dividend), length(divisor)) digits
Actual code:
scale = max(scale, length(dividend)-1,length(divisor)-1);
- scale += length(divisior) - length(dividend);
+ scale += length(divisor) - length(dividend);
So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3).
Actually, the 'difference' added to the scale is calculated from the
number of "significant digits" in dividend and divisor, which is derived
by looking at the length of the mantissa. Which is wrong, since it includes
- the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups
+ the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops
again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange
assumption that 124 has 3 significant digits, while 120/7 will get you
'17', not '17.1' since 120 is thought to have 2 significant digits.
=item Setting/Accessing
- * You can set the A global via Math::BigInt->accuracy() or
- Math::BigFloat->accuracy() or whatever class you are using.
- * You can also set P globally by using Math::SomeClass->precision() likewise.
+ * You can set the A global via C<< Math::BigInt->accuracy() >> or
+ C<< Math::BigFloat->accuracy() >> or whatever class you are using.
+ * You can also set P globally by using C<< Math::SomeClass->precision() >>
+ likewise.
* Globals are classwide, and not inherited by subclasses.
- * to undefine A, use Math::SomeCLass->accuracy(undef);
- * to undefine P, use Math::SomeClass->precision(undef);
- * Setting Math::SomeClass->accuracy() clears automatically
- Math::SomeClass->precision(), and vice versa.
+ * to undefine A, use C<< Math::SomeCLass->accuracy(undef); >>
+ * to undefine P, use C<< Math::SomeClass->precision(undef); >>
+ * Setting C<< Math::SomeClass->accuracy() >> clears automatically
+ C<< Math::SomeClass->precision() >>, and vice versa.
* To be valid, A must be > 0, P can have any value.
* If P is negative, this means round to the P'th place to the right of the
decimal point; positive values mean to the left of the decimal point.
P of 0 means round to integer.
- * to find out the current global A, take Math::SomeClass->accuracy()
- * to find out the current global P, take Math::SomeClass->precision()
- * use $x->accuracy() respective $x->precision() for the local setting of $x.
- * Please note that $x->accuracy() respecive $x->precision() fall back to the
- defined globals, when $x's A or P is not set.
+ * to find out the current global A, use C<< Math::SomeClass->accuracy() >>
+ * to find out the current global P, use C<< Math::SomeClass->precision() >>
+ * use C<< $x->accuracy() >> respective C<< $x->precision() >> for the local
+ setting of C<< $x >>.
+ * Please note that C<< $x->accuracy() >> respective C<< $x->precision() >>
+ return eventually defined global A or P, when C<< $x >>'s A or P is not
+ set.
=item Creating numbers
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
globals enforced upon creation of a number by using
- $x = Math::BigInt->new($number,undef,undef):
+ C<< $x = Math::BigInt->new($number,undef,undef) >>:
- use Math::Bigint::SomeSubclass;
+ use Math::BigInt::SomeSubclass;
use Math::BigInt;
Math::BigInt->accuracy(2);
operation according to the rules below
* Negative P is ignored in Math::BigInt, since BigInts never have digits
after the decimal point
- * Math::BigFloat uses Math::BigInts internally, but setting A or P inside
- Math::BigInt as globals should not tamper with the parts of a BigFloat.
- Thus a flag is used to mark all Math::BigFloat numbers as 'never round'
+ * Math::BigFloat uses Math::BigInt internally, but setting A or P inside
+ Math::BigInt as globals does not tamper with the parts of a BigFloat.
+ A flag is used to mark all Math::BigFloat numbers as 'never round'.
=item Precedence
* It only makes sense that a number has only one of A or P at a time.
- Since you can set/get both A and P, there is a rule that will practically
- enforce only A or P to be in effect at a time, even if both are set.
- This is called precedence.
+ If you set either A or P on one object, or globally, the other one will
+ be automatically cleared.
* If two objects are involved in an operation, and one of them has A in
effect, and the other P, this results in an error (NaN).
- * A takes precendence over P (Hint: A comes before P). If A is defined, it
- is used, otherwise P is used. If neither of them is defined, nothing is
- used, i.e. the result will have as many digits as it can (with an
- exception for fdiv/fsqrt) and will not be rounded.
+ * A takes precedence over P (Hint: A comes before P).
+ If neither of them is defined, nothing is used, i.e. the result will have
+ as many digits as it can (with an exception for fdiv/fsqrt) and will not
+ be rounded.
* There is another setting for fdiv() (and thus for fsqrt()). If neither of
A or P is defined, fdiv() will use a fallback (F) of $div_scale digits.
If either the dividend's or the divisor's mantissa has more digits than
A, P or F), and, if F is not used, round the result
(this will still fail in the case of a result like 0.12345000000001 with A
or P of 5, but this can not be helped - or can it?)
- * Thus you can have the math done by on Math::Big* class in three modes:
+ * Thus you can have the math done by on Math::Big* class in two modi:
+ never round (this is the default):
This is done by setting A and P to undef. No math operation
will round the result, with fdiv() and fsqrt() as exceptions to guard
- against overflows. You must explicitely call bround(), bfround() or
+ against overflows. You must explicitly call bround(), bfround() or
round() (the latter with parameters).
Note: Once you have rounded a number, the settings will 'stick' on it
and 'infect' all other numbers engaged in math operations with it, since
=item Local settings
- * You can set A and P locally by using $x->accuracy() and $x->precision()
+ * You can set A or P locally by using C<< $x->accuracy() >> or
+ C<< $x->precision() >>
and thus force different A and P for different objects/numbers.
* Setting A or P this way immediately rounds $x to the new value.
- * $x->accuracy() clears $x->precision(), and vice versa.
+ * C<< $x->accuracy() >> clears C<< $x->precision() >>, and vice versa.
=item Rounding
* the two rounding functions take as the second parameter one of the
following rounding modes (R):
'even', 'odd', '+inf', '-inf', 'zero', 'trunc'
- * you can set and get the global R by using Math::SomeClass->round_mode()
- or by setting $Math::SomeClass::round_mode
- * after each operation, $result->round() is called, and the result may
+ * 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
eventually be rounded (that is, if A or P were set either locally,
globally or as parameter to the operation)
- * to manually round a number, call $x->round($A,$P,$round_mode);
+ * to manually round a number, call C<< $x->round($A,$P,$round_mode); >>
this will round the number by using the appropriate rounding function
and then normalize it.
* rounding modifies the local settings of the number:
=back
+=head1 Infinity and Not a Number
+
+While BigInt has extensive handling of inf and NaN, certain quirks remain.
+
+=over 2
+
+=item oct()/hex()
+
+These perl routines currently (as of Perl v.5.8.6) cannot handle passed
+inf.
+
+ te@linux:~> perl -wle 'print 2 ** 3333'
+ inf
+ te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333'
+ 1
+ te@linux:~> perl -wle 'print oct(2 ** 3333)'
+ 0
+ te@linux:~> perl -wle 'print hex(2 ** 3333)'
+ Illegal hexadecimal digit 'i' ignored at -e line 1.
+ 0
+
+The same problems occur if you pass them Math::BigInt->binf() objects. Since
+overloading these routines is not possible, this cannot be fixed from BigInt.
+
+=item ==, !=, <, >, <=, >= with NaNs
+
+BigInt's bcmp() routine currently returns undef to signal that a NaN was
+involved in a comparison. However, the overload code turns that into
+either 1 or '' and thus operations like C<< NaN != NaN >> might return
+wrong values.
+
+=item log(-inf)
+
+C<< log(-inf) >> is highly weird. Since log(-x)=pi*i+log(x), then
+log(-inf)=pi*i+inf. However, since the imaginary part is finite, the real
+infinity "overshadows" it, so the number might as well just be infinity.
+However, the result is a complex number, and since BigInt/BigFloat can only
+have real numbers as results, the result is NaN.
+
+=item exp(), cos(), sin(), atan2()
+
+These all might have problems handling infinity right.
+
+=back
+
=head1 INTERNALS
The actual numbers are stored as unsigned big integers (with seperate sign).
+
You should neither care about nor depend on the internal representation; it
-might change without notice. Use only method calls like C<< $x->sign(); >>
-instead relying on the internal hash keys like in C<< $x->{sign}; >>.
+might change without notice. Use B<ONLY> method calls like C<< $x->sign(); >>
+instead relying on the internal representation.
=head2 MATH LIBRARY
Math with the numbers is done (by default) by a module called
-Math::BigInt::Calc. This is equivalent to saying:
+C<Math::BigInt::Calc>. This is equivalent to saying:
use Math::BigInt lib => 'Calc';
use Math::BigInt lib => 'Foo,Math::BigInt::Bar';
-Calc.pm uses as internal format an array of elements of some decimal base
-(usually 1e5 or 1e7) with the least significant digit first, while BitVect.pm
-uses a bit vector of base 2, most significant bit first. Other modules might
-use even different means of representing the numbers. See the respective
-module documentation for further details.
+Since Math::BigInt::GMP is in almost all cases faster than Calc (especially in
+math involving really big numbers, where it is B<much> faster), and there is
+no penalty if Math::BigInt::GMP is not installed, it is a good idea to always
+use the following:
+
+ use Math::BigInt lib => 'GMP';
+
+Different low-level libraries use different formats to store the
+numbers. You should B<NOT> depend on the number having a specific format
+internally.
+
+See the respective math library module documentation for further details.
=head2 SIGN
-The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
+The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
A sign of 'NaN' is used to represent the result when input arguments are not
numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
C<< ($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> will be always 0, except for NaN, +inf and -inf,
-where it will be NaN; and for $x == 0, where it will be 1
-(to be compatible with Math::BigFloat's internal representation of a zero as
-C<0E1>).
+Currently, for BigInts C<$e> is always 0, except for NaN, +inf and -inf,
+where it is C<NaN>; and for C<$x == 0>, where it is C<1> (to be compatible
+with Math::BigFloat's internal representation of a zero as C<0E1>).
-C<$m> will always be a copy of the original number. The relation between $e
-and $m might change in the future, but will always be equivalent in a
-numerical sense, e.g. $m might get minimized.
+C<$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
+change.
=head1 EXAMPLES
$x = Math::BigInt->bstr("1234") # string "1234"
$x = "$x"; # same as bstr()
- $x = Math::BigInt->bneg("1234"); # Bigint "-1234"
- $x = Math::BigInt->babs("-12345"); # Bigint "12345"
+ $x = Math::BigInt->bneg("1234"); # BigInt "-1234"
+ $x = Math::BigInt->babs("-12345"); # BigInt "12345"
$x = Math::BigInt->bnorm("-0 00"); # BigInt "0"
$x = bint(1) + bint(2); # BigInt "3"
$x = bint(1) + "2"; # ditto (auto-BigIntify of "2")
=head1 Autocreating constants
-After C<use Math::BigInt ':constant'> all the B<integer> decimal constants
-in the given scope are converted to C<Math::BigInt>. This conversion
-happens at compile time.
+After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal
+and binary constants in the given scope are converted to C<Math::BigInt>.
+This conversion happens at compile time.
In particular,
perl -MMath::BigInt=:constant -e 'print 2**100,"\n"'
-prints the integer value of C<2**100>. Note that without conversion of
+prints the integer value of C<2**100>. Note that without conversion of
constants the expression 2**100 will be calculated as perl scalar.
Please note that strings and floating point constants are not affected,
do not work. You need an explicit Math::BigInt->new() around one of the
operands. You should also quote large constants to protect loss of precision:
- use Math::Bigint;
+ use Math::BigInt;
$x = Math::BigInt->new('1234567889123456789123456789123456789');
constant at compile time and then hand the result to BigInt, which results in
an truncated result or a NaN.
+This also applies to integers that look like floating point constants:
+
+ use Math::BigInt ':constant';
+
+ print ref(123e2),"\n";
+ print ref(123.2e2),"\n";
+
+will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat>
+to get this to work.
+
=head1 PERFORMANCE
Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x
With a technique called copy-on-write, the cost of copying with overload could
be minimized or even completely avoided. A test implementation of COW did show
performance gains for overloaded math, but introduced a performance loss due
-to a constant overhead for all other operatons.
+to a constant overhead for all other operations. So Math::BigInt does currently
+not COW.
-The rewritten version of this module is slower on certain operations, like
-new(), bstr() and numify(). The reason are that it does now more work and
-handles more cases. The time spent in these operations is usually gained in
-the other operations so that programs on the average should get faster. If
-they don't, please contect the author.
+The rewritten version of this module (vs. v0.01) is slower on certain
+operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it
+does now more work and handles much more cases. The time spent in these
+operations is usually gained in the other math operations so that code on
+the average should get (much) faster. If they don't, please contact the author.
Some operations may be slower for small numbers, but are significantly faster
-for big numbers. Other operations are now constant (O(1), like bneg(), babs()
-etc), instead of O(N) and thus nearly always take much less time. These
-optimizations were done on purpose.
+for big numbers. Other operations are now constant (O(1), like C<bneg()>,
+C<babs()> etc), instead of O(N) and thus nearly always take much less time.
+These optimizations were done on purpose.
If you find the Calc module to slow, try to install any of the replacement
modules and see if they help you.
=over 2
+=item broot() does not work
+
+The broot() function in BigInt may only work for small values. This will be
+fixed in a later version.
+
=item Out of Memory!
Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and
=over 1
-=item stringify, bstr(), bsstr() and 'cmp'
+=item bstr(), bsstr() and 'cmp'
-Both stringify and bstr() now drop the leading '+'. The old code would return
-'+3', the new returns '3'. This is to be consistent with Perl and to make
-cmp (especially with overloading) to work as you expect. It also solves
-problems with Test.pm, it's ok() uses 'eq' internally.
+Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now
+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.
-Mark said, when asked about to drop the '+' altogether, or make only cmp work:
+Mark Biggar said, when asked about to drop the '+' altogether, or make only
+C<cmp> work:
I agree (with the first alternative), don't add the '+' on positive
numbers. It's not as important anymore with the new internal
There is now a C<bsstr()> method to get the string in scientific notation aka
C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr()
-for comparisation, but Perl will represent some numbers as 100 and others
-as 1e+308. If in doubt, convert both arguments to Math::BigInt before doing eq:
+for comparison, but Perl will represent some numbers as 100 and others
+as 1e+308. If in doubt, convert both arguments to Math::BigInt before
+comparing them as strings:
use Test;
BEGIN { plan tests => 3 }
$y = Math::BigInt->new($y);
ok ($x,$y); # okay
-Alternatively, simple use <=> for comparisations, that will get it always
-right. There is not yet a way to get a number automatically represented as
-a string that matches exactly the way Perl represents it.
+Alternatively, simple use C<< <=> >> for comparisons, this will get it
+always right. There is not yet a way to get a number automatically represented
+as a string that matches exactly the way Perl represents it.
+
+See also the section about L<Infinity and Not a Number> for problems in
+comparing NaNs.
=item int()
$x = Math::BigFloat->new(123.45);
$y = int($x); # BigInt 123
-In all Perl versions you can use C<as_number()> for the same effect:
+In all Perl versions you can use C<as_number()> or C<as_int> for the same
+effect:
$x = Math::BigFloat->new(123.45);
$y = $x->as_number(); # BigInt 123
+ $y = $x->as_int(); # ditto
This also works for other subclasses, like Math::String.
-It is yet unlcear whether overloaded int() should return a scalar or a BigInt.
+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
+
+This is seldom necessary, though, because this is done automatically, like
+when you access an array:
+
+ $z = $array[$x]; # does work automatically
=item length
print $c->bdiv(10000),"\n";
It prints both quotient and remainder since print calls C<bdiv()> in list
-context. Also, C<bdiv()> will modify $c, so be carefull. You probably want
+context. Also, C<bdiv()> will modify $c, so be careful. You probably want
to use
print $c / 10000,"\n";
holds true for any $x and $y, which justifies calling the two return
values of bdiv() the quotient and remainder. The only exception to this rule
are when $y == 0 and $x is negative, then the remainder will also be
-negative. See below under "infinity handling" for the reasoning behing this.
+negative. See below under "infinity handling" for the reasoning behind this.
Perl's 'use integer;' changes the behaviour of % and / for scalars, but will
not change BigInt's way to do things. This is because under 'use integer' Perl
needs to preserve $x since it does not know that it later will get overwritten.
This makes a copy of $x and takes O(N), but $x->bneg() is O(1).
-With Copy-On-Write, this issue would be gone, but C-o-W is not implemented
-since it is slower for all other things.
-
=item Mixing different object types
In Perl you will get a floating point value if you do one of the following:
This section also applies to other overloaded math packages, like Math::String.
-One solution to you problem might be L<autoupgrading|upgrading>.
+One solution to you problem might be autoupgrading|upgrading. See the
+pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this.
=item bsqrt()
C<bsqrt()> works only good if the result is a big integer, e.g. the square
root of 144 is 12, but from 12 the square root is 3, regardless of rounding
-mode.
+mode. The reason is that the result is always truncated to an integer.
If you want a better approximation of the square root, then use:
=head1 SEE ALSO
-L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>,
-L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
+L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as
+L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
+
+The pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest
+because they solve the autoupgrading/downgrading issue, at least partly.
The package at
L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
=head1 AUTHORS
Original code by Mark Biggar, overloaded interface by Ilya Zakharevich.
-Completely rewritten by Tels http://bloodgate.com in late 2000, 2001.
+Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2004
+and still at it in 2005.
+
+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
+mail. Thank you!
=cut
https://perl5.git.perl.org / perl5.git / blobdiff