-#!/usr/bin/perl -w
+package Math::BigInt;
-# Qs: what exactly happens on numify of HUGE numbers? overflow?
-# $a = -$a is much slower (making copy of $a) than $a->bneg(), hm!?
-# (copy_on_write will help there, but that is not yet implemented)
+#
+# "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)
# _a : accuracy
# _p : precision
# _f : flags, used by MBF to flag parts of a float as untouchable
-# _cow : copy on write: number of objects that share the data (NRY)
-package Math::BigInt;
+# Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
+# underlying lib might change the reference!
+
my $class = "Math::BigInt";
require 5.005;
-$VERSION = 1.36;
+$VERSION = '1.64_01';
use Exporter;
@ISA = qw( Exporter );
-@EXPORT_OK = qw( bneg babs bcmp badd bmul bdiv bmod bnorm bsub
- bgcd blcm
- bround
- blsft brsft band bior bxor bnot bpow bnan bzero
- bacmp bstr bsstr binc bdec bint binf bfloor bceil
- is_odd is_even is_zero is_one is_nan is_inf sign
- is_positive is_negative
- length as_number
- objectify _swap
- );
-
-#@EXPORT = qw( );
-use vars qw/$rnd_mode $accuracy $precision $div_scale/;
+@EXPORT_OK = qw( objectify _swap bgcd blcm);
+use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/;
+use vars qw/$upgrade $downgrade/;
use strict;
# Inside overload, the first arg is always an object. If the original code had
'-=' => sub { $_[0]->bsub($_[1]); },
'*=' => sub { $_[0]->bmul($_[1]); },
'/=' => sub { scalar $_[0]->bdiv($_[1]); },
+'%=' => sub { $_[0]->bmod($_[1]); },
+'^=' => sub { $_[0]->bxor($_[1]); },
+'&=' => sub { $_[0]->band($_[1]); },
+'|=' => sub { $_[0]->bior($_[1]); },
'**=' => sub { $_[0]->bpow($_[1]); },
+# not supported by Perl yet
+'..' => \&_pointpoint,
+
'<=>' => sub { $_[2] ?
- $class->bcmp($_[1],$_[0]) :
- $class->bcmp($_[0],$_[1])},
-'cmp' => sub {
+ ref($_[0])->bcmp($_[1],$_[0]) :
+ $_[0]->bcmp($_[1])},
+'cmp' => sub {
$_[2] ?
- $_[1] cmp $_[0]->bstr() :
- $_[0]->bstr() cmp $_[1] },
+ "$_[1]" cmp $_[0]->bstr() :
+ $_[0]->bstr() cmp "$_[1]" },
+'log' => sub { $_[0]->copy()->blog(); },
'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(@_); $a[0]->bxor($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!
+# use $_[0]->__one(), it modifies $_[0] to be 1!
'++' => sub { $_[0]->binc() },
'--' => sub { $_[0]->bdec() },
# v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-(
my $t = !$_[0]->is_zero();
undef $t if $t == 0;
- return $t;
+ $t;
},
-qw(
-"" bstr
-0+ numify), # Order of arguments unsignificant
+# the original qw() does not work with the TIESCALAR below, why?
+# Order of arguments unsignificant
+'""' => sub { $_[0]->bstr(); },
+'0+' => sub { $_[0]->numify(); }
;
##############################################################################
my $nan = 'NaN'; # constants for easier life
my $CALC = 'Math::BigInt::Calc'; # module to do low level math
-sub _core_lib () { return $CALC; } # for test suite
+my $IMPORT = 0; # did import() yet?
+
+$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
+$accuracy = undef;
+$precision = undef;
+$div_scale = 40;
+
+$upgrade = undef; # default is no upgrade
+$downgrade = undef; # default is no downgrade
+
+##############################################################################
+# the old code had $rnd_mode, so we need to support it, too
-# Rounding modes, one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
-$rnd_mode = 'even';
-$accuracy = undef;
-$precision = undef;
-$div_scale = 40;
+$rnd_mode = 'even';
+sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; }
+sub FETCH { return $round_mode; }
+sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
+
+BEGIN { tie $rnd_mode, 'Math::BigInt'; }
+
+##############################################################################
sub round_mode
{
+ no strict 'refs';
# make Class->round_mode() work
- my $self = shift || $class;
- # shift @_ if defined $_[0] && $_[0] eq $class;
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
if (defined $_[0])
{
my $m = shift;
die "Unknown round mode $m"
if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
- $rnd_mode = $m; return;
+ return ${"${class}::round_mode"} = $m;
+ }
+ return ${"${class}::round_mode"};
+ }
+
+sub upgrade
+ {
+ no strict 'refs';
+ # make Class->upgrade() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ # need to set new value?
+ if (@_ > 0)
+ {
+ my $u = shift;
+ return ${"${class}::upgrade"} = $u;
+ }
+ return ${"${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)
+ {
+ my $u = shift;
+ return ${"${class}::downgrade"} = $u;
+ }
+ return ${"${class}::downgrade"};
+ }
+
+sub div_scale
+ {
+ no strict 'refs';
+ # make Class->round_mode() 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;
}
- return $rnd_mode;
+ return ${"${class}::div_scale"};
}
sub accuracy
{
- # $x->accuracy($a); ref($x) a
- # $x->accuracy(); ref($x);
- # Class::accuracy(); # not supported
- #print "MBI @_ ($class)\n";
- my $x = shift;
+ # $x->accuracy($a); ref($x) $a
+ # $x->accuracy(); ref($x)
+ # Class->accuracy(); class
+ # Class->accuracy($a); class $a
- die ("accuracy() needs reference to object as first parameter.")
- if !ref $x;
+ my $x = shift;
+ my $class = ref($x) || $x || __PACKAGE__;
+ no strict 'refs';
+ # need to set new value?
if (@_ > 0)
{
- $x->{_a} = shift;
- $x->round() if defined $x->{_a};
+ my $a = shift;
+ die ('accuracy must not be zero') if defined $a && $a == 0;
+ if (ref($x))
+ {
+ # $object->accuracy() or fallback to global
+ $x->bround($a) if defined $a;
+ $x->{_a} = $a; # set/overwrite, even if not rounded
+ $x->{_p} = undef; # clear P
+ }
+ else
+ {
+ # set global
+ ${"${class}::accuracy"} = $a;
+ ${"${class}::precision"} = undef; # clear P
+ }
+ return $a; # shortcut
}
- return $x->{_a};
+
+ my $r;
+ # $object->accuracy() or fallback to global
+ $r = $x->{_a} if ref($x);
+ # but don't return global undef, when $x's accuracy is 0!
+ $r = ${"${class}::accuracy"} if !defined $r;
+ $r;
}
sub precision
{
- my $x = shift;
+ # $x->precision($p); ref($x) $p
+ # $x->precision(); ref($x)
+ # Class->precision(); class
+ # Class->precision($p); class $p
- die ("precision() needs reference to object as first parameter.")
- unless ref $x;
+ my $x = shift;
+ my $class = ref($x) || $x || __PACKAGE__;
+ no strict 'refs';
+ # need to set new value?
if (@_ > 0)
{
- $x->{_p} = shift;
- $x->round() if defined $x->{_p};
+ my $p = shift;
+ if (ref($x))
+ {
+ # $object->precision() or fallback to global
+ $x->bfround($p) if defined $p;
+ $x->{_p} = $p; # set/overwrite, even if not rounded
+ $x->{_a} = undef; # clear A
+ }
+ else
+ {
+ # set global
+ ${"${class}::precision"} = $p;
+ ${"${class}::accuracy"} = undef; # clear A
+ }
+ return $p; # shortcut
}
- return $x->{_p};
+
+ my $r;
+ # $object->precision() or fallback to global
+ $r = $x->{_p} if ref($x);
+ # but don't return global undef, when $x's precision is 0!
+ $r = ${"${class}::precision"} if !defined $r;
+ $r;
}
+sub config
+ {
+ # return (later set?) configuration data as hash ref
+ my $class = shift || 'Math::BigInt';
+
+ no strict 'refs';
+ my $lib = $CALC;
+ my $cfg = {
+ lib => $lib,
+ lib_version => ${"${lib}::VERSION"},
+ class => $class,
+ };
+ foreach (
+ qw/upgrade downgrade precision accuracy round_mode VERSION div_scale/)
+ {
+ $cfg->{lc($_)} = ${"${class}::$_"};
+ };
+ $cfg;
+ }
+
sub _scale_a
{
# select accuracy parameter based on precedence,
return unless ref($x); # only for objects
my $self = {}; bless $self,$c;
+ my $r;
foreach my $k (keys %$x)
{
if ($k eq 'value')
{
- $self->{$k} = $CALC->_copy($x->{$k});
+ $self->{value} = $CALC->_copy($x->{value}); next;
+ }
+ if (!($r = ref($x->{$k})))
+ {
+ $self->{$k} = $x->{$k}; next;
}
- elsif (ref($x->{$k}) eq 'SCALAR')
+ if ($r eq 'SCALAR')
{
$self->{$k} = \${$x->{$k}};
}
- elsif (ref($x->{$k}) eq 'ARRAY')
+ elsif ($r eq 'ARRAY')
{
$self->{$k} = [ @{$x->{$k}} ];
}
- elsif (ref($x->{$k}) eq 'HASH')
+ elsif ($r eq 'HASH')
{
# only one level deep!
foreach my $h (keys %{$x->{$k}})
$self->{$k}->{$h} = $x->{$k}->{$h};
}
}
- elsif (ref($x->{$k}))
- {
- my $c = ref($x->{$k});
- $self->{$k} = $c->new($x->{$k}); # no copy() due to deep rec
- }
- else
+ else # normal ref
{
- $self->{$k} = $x->{$k};
+ my $xk = $x->{$k};
+ if ($xk->can('copy'))
+ {
+ $self->{$k} = $xk->copy();
+ }
+ else
+ {
+ $self->{$k} = $xk->new($xk);
+ }
}
}
$self;
sub new
{
- # create a new BigInt object from a string or another BigIint object.
+ # create a new BigInt object from a string or another BigInt object.
# see hash keys documented at top
# the argument could be an object, so avoid ||, && etc on it, this would
- # cause costly overloaded code to be called. The only allowed op are ref()
- # and definend.
+ # cause costly overloaded code to be called. The only allowed ops are
+ # ref() and defined.
- my $class = shift;
+ my ($class,$wanted,$a,$p,$r) = @_;
- my $wanted = shift; # avoid numify call by not using || here
- return $class->bzero() if !defined $wanted; # default to 0
- return $class->copy($wanted) if ref($wanted);
+ # 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) && $wanted->isa($class); # MBI or subclass
+
+ $class->import() if $IMPORT == 0; # make require work
+
+ my $self = bless {}, $class;
+
+ # shortcut for "normal" numbers
+ if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/))
+ {
+ $self->{sign} = $1 || '+';
+ my $ref = \$wanted;
+ if ($wanted =~ /^[+-]/)
+ {
+ # remove sign without touching wanted to make it work with constants
+ my $t = $wanted; $t =~ s/^[+-]//; $ref = \$t;
+ }
+ $self->{value} = $CALC->_new($ref);
+ 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;
+ }
- my $self = {}; bless $self, $class;
# handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]inf$/)
+ if ($wanted =~ /^[+-]?inf$/)
{
$self->{value} = $CALC->_zero();
- $self->{sign} = $wanted;
+ $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf';
return $self;
}
# split str in m mantissa, e exponent, i integer, f fraction, v value, s sign
my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted);
- if (ref $mis && !ref $miv)
- {
- # _from_hex or _from_bin
- $self->{value} = $mis->{value};
- $self->{sign} = $mis->{sign};
- return $self; # throw away $mis
- }
if (!ref $mis)
{
die "$wanted is not a number initialized to $class" if !$NaNOK;
$self->{sign} = $nan;
return $self;
}
+ if (!ref $miv)
+ {
+ # _from_hex or _from_bin
+ $self->{value} = $mis->{value};
+ $self->{sign} = $mis->{sign};
+ return $self; # throw away $mis
+ }
# make integer from mantissa by adjusting exp, then convert to bigint
$self->{sign} = $$mis; # store sign
$self->{value} = $CALC->_zero(); # for all the NaN cases
if ($diff < 0) # Not integer
{
#print "NOI 1\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
else # diff >= 0
{
# fraction and negative/zero E => NOI
#print "NOI 2 \$\$mfv '$$mfv'\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
elsif ($e < 0)
if ($$miv !~ s/0{$e}$//) # can strip so many zero's?
{
#print "NOI 3\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
}
}
$self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0
$self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/;
- #print "$wanted => $self->{sign}\n";
# if any of the globals is set, use them to round and store them inside $self
- $self->round($accuracy,$precision,$rnd_mode)
- if defined $accuracy || defined $precision;
- return $self;
- }
-
-# some shortcuts for easier life
-sub bint
- {
- # exportable version of new
- return $class->new(@_);
+ # do not round for new($x,undef,undef) since that is used by MBF to signal
+ # no rounding
+ $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p;
+ $self;
}
sub bnan
{
my $c = $self; $self = {}; bless $self, $c;
}
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('bnan');
- $self->{value} = $CALC->_zero();
+ my $c = ref($self);
+ 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;
}
# 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;
}
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('binf');
- $self->{value} = $CALC->_zero();
- $self->{sign} = $sign.'inf';
+ my $c = ref($self);
+ 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;
}
# create a bigint '+0', if given a BigInt, set it to 0
my $self = shift;
$self = $class if !defined $self;
- #print "bzero $self\n";
if (!ref($self))
{
my $c = $self; $self = {}; bless $self, $c;
}
+ $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} = '+';
- #print "result: $self\n";
- return $self;
+ if (@_ > 0)
+ {
+ 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}));
+ }
+ }
+ $self;
+ }
+
+sub bone
+ {
+ # create a bigint '+1' (or -1 if given sign '-'),
+ # if given a BigInt, set it to +1 or -1, respecively
+ 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 $self->modify('bone');
+
+ if ($self->can('_bone'))
+ {
+ # use subclass to initialize
+ $self->_bone();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_one();
+ }
+ $self->{sign} = $sign;
+ if (@_ > 0)
+ {
+ if (@_ > 3)
+ {
+ # call like: $x->bone($sign,$a,$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}));
+ }
+ }
+ $self;
}
##############################################################################
# (ref to BFLOAT or num_str ) return num_str
# Convert number from internal format to scientific string format.
# internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
- my ($self,$x) = objectify(1,@_);
+ my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
+ # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return $x->{sign} if $x->{sign} !~ /^[+-]$/;
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
+ return 'inf'; # +inf
+ }
my ($m,$e) = $x->parts();
- # can be only '+', so
- my $sign = 'e+';
- # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s;
+ my $sign = 'e+'; # e can only be positive
return $m->bstr().$sign.$e->bstr();
}
sub bstr
{
# make a string from bigint object
- my $x = shift; $x = $class->new($x) unless ref $x;
- return $x->{sign} if $x->{sign} !~ /^[+-]$/;
+ my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
+ # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ if ($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})};
}
sub numify
{
- # Make a number from a BigInt object
+ # 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) = objectify(1,@_);
- return $x->{sign};
+ # return the sign of the number: +/-/-inf/+inf/NaN
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ $x->{sign};
}
-sub round
+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.
- # The result's A or P are set by the rounding, but not inspected beforehand
- # (aka only the arguments enter into it). This works because the given
- # 'first' argument is both the result and true first argument with unchanged
- # A and P settings.
- # This does not yet handle $x with A, and $y with P (which should be an
- # error).
- my $self = shift;
- my $a = shift; # accuracy, if given by caller
- my $p = shift; # precision, if given by caller
- my $r = shift; # round_mode, if given by caller
- my @args = @_; # all 'other' arguments (0 for unary, 1 for binary ops)
+
+ # This procedure finds the round parameters, but it is for speed reasons
+ # duplicated in round. Otherwise, it is tested by the testsuite and used
+ # by fdiv().
+
+ my ($self,$a,$p,$r,@args) = @_;
+ # $a accuracy, if given by caller
+ # $p precision, 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} && $self->{_f} & MB_NEVER_ROUND != 0;
+ return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
+
+ my $c = ref($self); # find out class of argument(s)
+ no strict 'refs';
+
+ # now pick $a or $p, but only if we have got "arguments"
+ if (!defined $a)
+ {
+ foreach ($self,@args)
+ {
+ # take the defined one, or if both defined, the one that is smaller
+ $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
+ }
+ }
+ if (!defined $p)
+ {
+ # even if $a is defined, take $p, to signal error for both defined
+ foreach ($self,@args)
+ {
+ # take the defined one, or if both defined, the one that is bigger
+ # -2 > -3, and 3 > 2
+ $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
+ }
+ }
+ # if still none defined, use globals (#2)
+ $a = ${"$c\::accuracy"} unless defined $a;
+ $p = ${"$c\::precision"} unless defined $p;
+
+ # no rounding today?
+ return ($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;
+
+ $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);
+ }
+
+sub round
+ {
+ # Round $self according to given parameters, or given second argument's
+ # parameters or global defaults
+
+ # for speed reasons, _find_round_parameters is embeded here:
- unshift @args,$self; # add 'first' argument
+ my ($self,$a,$p,$r,@args) = @_;
+ # $a accuracy, if given by caller
+ # $p precision, if given by caller
+ # $r round_mode, if given by caller
+ # @args all 'other' arguments (0 for unary, 1 for binary ops)
- $self = new($self) unless ref($self); # if not object, make one
+ # leave bigfloat parts alone
+ return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
- # find out class of argument to round
- my $c = ref($args[0]);
+ my $c = ref($self); # find out class of argument(s)
+ no strict 'refs';
# now pick $a or $p, but only if we have got "arguments"
- if ((!defined $a) && (!defined $p) && (@args > 0))
+ if (!defined $a)
{
- foreach (@args)
+ foreach ($self,@args)
{
# take the defined one, or if both defined, the one that is smaller
$a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
}
- if (!defined $a) # if it still is not defined, take p
+ }
+ if (!defined $p)
+ {
+ # even if $a is defined, take $p, to signal error for both defined
+ foreach ($self,@args)
{
- foreach (@args)
- {
- # take the defined one, or if both defined, the one that is smaller
- $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} < $p);
- }
- # if none defined, use globals (#2)
- if (!defined $p)
- {
- no strict 'refs';
- my $z = "$c\::accuracy"; $a = $$z;
- if (!defined $a)
- {
- $z = "$c\::precision"; $p = $$z;
- }
- }
- } # endif !$a
- } # endif !$a || !$P && args > 0
- # for clearity, this is not merged at place (#2)
- # now round, by calling fround or ffround:
+ # take the defined one, or if both defined, the one that is bigger
+ # -2 > -3, and 3 > 2
+ $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
+ }
+ }
+ # if still none defined, use globals (#2)
+ $a = ${"$c\::accuracy"} unless defined $a;
+ $p = ${"$c\::precision"} unless defined $p;
+
+ # 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;
+
+ $r = ${"$c\::round_mode"} unless defined $r;
+ die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
+
+ # now round, by calling either fround or ffround:
if (defined $a)
{
- $self->{_a} = $a; $self->bround($a,$r);
+ $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a;
}
- elsif (defined $p)
+ else # both can't be undefined due to early out
{
- $self->{_p} = $p; $self->bfround($p,$r);
+ $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p;
}
- return $self->bnorm();
+ $self->bnorm(); # after round, normalize
}
-sub bnorm
+sub bnorm
{
- # (num_str or BINT) return BINT
+ # (numstr or BINT) return BINT
# Normalize number -- no-op here
- my $self = shift;
-
- return $self;
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ $x;
}
sub babs
{
# (BINT or num_str) return BINT
# make number absolute, or return absolute BINT from string
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
return $x if $x->modify('babs');
# post-normalized abs for internal use (does nothing for NaN)
$x->{sign} =~ s/^-/+/;
{
# (BINT or num_str) return BINT
# negate number or make a negated number from string
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
return $x if $x->modify('bneg');
+
# for +0 dont negate (to have always normalized)
- return $x if $x->is_zero();
- $x->{sign} =~ tr/+\-/-+/; # does nothing for NaN
- # $x->round($a,$p,$r); # changing this makes $x - $y modify $y!!
+ $x->{sign} =~ tr/+-/-+/ if !$x->is_zero(); # does nothing for NaN
$x;
}
{
# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT or num_str, BINT or num_str) return cond_code
- my ($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} !~ /^[+-]$/))
{
# handle +-inf and NaN
return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/);
+ return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
return +1 if $x->{sign} eq '+inf';
return -1 if $x->{sign} eq '-inf';
return -1 if $y->{sign} eq '+inf';
- return +1 if $y->{sign} eq '-inf';
+ return +1;
+ }
+ # check sign for speed first
+ return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
+ return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
+
+ # have same sign, so compare absolute values. Don't make tests for zero here
+ # because it's actually slower than testin in Calc (especially w/ Pari et al)
+
+ # post-normalized compare for internal use (honors signs)
+ if ($x->{sign} eq '+')
+ {
+ # $x and $y both > 0
+ return $CALC->_acmp($x->{value},$y->{value});
}
- # normal compare now
- &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0;
+
+ # $x && $y both < 0
+ $CALC->_acmp($y->{value},$x->{value}); # swaped (lib returns 0,1,-1)
}
sub bacmp
# Compares 2 values, ignoring their signs.
# Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT, BINT) return cond_code
- my ($self,$x,$y) = objectify(2,@_);
- return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- #acmp($x->{value},$y->{value}) <=> 0;
- $CALC->_acmp($x->{value},$y->{value}) <=> 0;
+
+ # set up parameters
+ my ($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
+ }
+ $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1
}
sub badd
{
# add second arg (BINT or string) to first (BINT) (modifies first)
# return result as BINT
- my ($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('badd');
- return $x->bnan() if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/));
+ return $upgrade->badd($x,$y,@r) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
- my @bn = ($a,$p,$r,$y); # make array for round calls
- # speed: no add for 0+y or x+0
- return $x->round(@bn) if $y->is_zero(); # x+0
- if ($x->is_zero()) # 0+y
+ $r[3] = $y; # no push!
+ # inf and NaN handling
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
- # make copy, clobbering up x
- $x->{value} = $CALC->_copy($y->{value});
- #$x->{value} = [ @{$y->{value}} ];
- $x->{sign} = $y->{sign} || $nan;
- return $x->round(@bn);
+ # NaN first
+ return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+ # inf handling
+ if (($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->bnan();
+ }
+ # +-inf + something => +inf
+ # something +-inf => +-inf
+ $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
+ return $x;
}
-
- # shortcuts
- my $xv = $x->{value};
- my $yv = $y->{value};
+
my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
if ($sx eq $sy)
{
- $CALC->_add($xv,$yv); # if same sign, absolute add
+ $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add
$x->{sign} = $sx;
}
else
{
- my $a = $CALC->_acmp ($yv,$xv); # absolute compare
+ my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare
if ($a > 0)
{
#print "swapped sub (a=$a)\n";
- $CALC->_sub($yv,$xv,1); # absolute sub w/ swapped params
+ $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap
$x->{sign} = $sy;
}
elsif ($a == 0)
else # a < 0
{
#print "unswapped sub (a=$a)\n";
- $CALC->_sub($xv, $yv); # absolute sub
+ $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
$x->{sign} = $sx;
}
}
- return $x->round(@bn);
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ $x;
}
sub bsub
{
# (BINT or num_str, BINT or num_str) return num_str
# subtract second arg from first, modify first
- my ($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('bsub');
- $x->badd($y->bneg()); # badd does not leave internal zeros
- $y->bneg(); # refix y, assumes no one reads $y in between
- return $x->round($a,$p,$r,$y);
+
+# upgrade done by badd():
+# return $upgrade->badd($x,$y,@r) if defined $upgrade &&
+# ((!$x->isa($self)) || (!$y->isa($self)));
+
+ if ($y->is_zero())
+ {
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+
+ $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
+ $x->badd($y,@r); # badd does not leave internal zeros
+ $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
+ $x; # already rounded by badd() or no round necc.
}
sub binc
{
# increment arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
- # my $x = shift; $x = $class->new($x) unless ref $x; my $self = ref($x);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('binc');
- $x->badd($self->_one())->round($a,$p,$r);
+
+ if ($x->{sign} eq '+')
+ {
+ $x->{value} = $CALC->_inc($x->{value});
+ $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ elsif ($x->{sign} eq '-')
+ {
+ $x->{value} = $CALC->_dec($x->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+ $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ # inf, nan handling etc
+ $x->badd($self->__one(),$a,$p,$r); # badd does round
}
sub bdec
{
# decrement arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('bdec');
- $x->badd($self->_one('-'))->round($a,$p,$r);
+
+ my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+';
+ # <= 0
+ if (($x->{sign} eq '-') || $zero)
+ {
+ $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
+ $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ # > 0
+ elsif ($x->{sign} eq '+')
+ {
+ $x->{value} = $CALC->_dec($x->{value});
+ $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ # inf, nan handling etc
+ $x->badd($self->__one('-'),$a,$p,$r); # badd does round
}
+sub blog
+ {
+ # not implemented yet
+ my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ return $upgrade->blog($x,$base,$a,$p,$r) if defined $upgrade;
+
+ return $x->bnan();
+ }
+
sub blcm
{
# (BINT or num_str, BINT or num_str) return BINT
{
$x = $class->new($y);
}
- while (@_) { $x = _lcm($x,shift); }
+ while (@_) { $x = __lcm($x,shift); }
$x;
}
# does not modify arguments, but returns new object
# GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff)
- my $y = shift; my ($x);
- if (ref($y))
- {
- $x = $y->copy();
- }
- else
- {
- $x = $class->new($y);
- }
-
- if ($CALC->can('_gcd'))
+ my $y = shift;
+ $y = __PACKAGE__->new($y) if !ref($y);
+ my $self = ref($y);
+ my $x = $y->copy(); # keep arguments
+ if ($CALC->can('_gcd'))
{
while (@_)
{
- $y = shift; $y = $class->new($y) if !ref($y);
+ $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();
{
while (@_)
{
- $x = _gcd($x,shift); last if $x->is_one(); # _gcd handles NaN
+ $y = shift; $y = $self->new($y) if !ref($y);
+ $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN
}
}
$x->babs();
}
-sub bmod
- {
- # modulus
- # (BINT or num_str, BINT or num_str) return BINT
- my ($self,$x,$y) = objectify(2,@_);
-
- return $x if $x->modify('bmod');
- (&bdiv($self,$x,$y))[1];
- }
-
sub bnot
{
# (num_str or BINT) return BINT
# represent ~x as twos-complement number
- my ($self,$x) = objectify(1,@_);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
return $x if $x->modify('bnot');
- $x->bneg(); $x->bdec(); # was: bsub(-1,$x);, time it someday
- $x;
+ $x->bneg()->bdec(); # bdec already does round
}
+# is_foo test routines
+
sub is_zero
{
# return true if arg (BINT or num_str) is zero (array '+', '0')
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
+ # 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 $x->{sign} !~ /^[+-]$/;
- return $CALC->_is_zero($x->{value});
- #return (@{$x->{value}} == 1) && ($x->{sign} eq '+')
- # && ($x->{value}->[0] == 0);
+ return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
+ $CALC->_is_zero($x->{value});
}
sub is_nan
{
# return true if arg (BINT or num_str) is NaN
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} eq $nan);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ return 1 if $x->{sign} eq $nan;
+ 0;
}
sub is_inf
{
# return true if arg (BINT or num_str) is +-inf
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- my $sign = shift || '';
+ my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x->{sign} =~ /^[+-]inf$/ if $sign eq '';
- return $x->{sign} =~ /^[$sign]inf$/;
+ $sign = '' if !defined $sign;
+ return 1 if $sign eq $x->{sign}; # match ("+inf" eq "+inf")
+ return 0 if $sign !~ /^([+-]|)$/;
+
+ if ($sign eq '')
+ {
+ return 1 if ($x->{sign} =~ /^[+-]inf$/);
+ return 0;
+ }
+ $sign = quotemeta($sign.'inf');
+ return 1 if ($x->{sign} =~ /^$sign$/);
+ 0;
}
sub is_one
{
- # return true if arg (BINT or num_str) is +1 (array '+', '1')
- # or -1 if signis given
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- my $sign = shift || '+';
+ # 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
+ my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+ $sign = '' if !defined $sign; $sign = '+' if $sign ne '-';
- # catch also NaN, +inf, -inf
- return 0 if $x->{sign} ne $sign || $x->{sign} !~ /^[+-]$/;
- return $CALC->_is_one($x->{value});
- #return (@{$x->{value}} == 1) && ($x->{sign} eq $sign)
- # && ($x->{value}->[0] == 1);
+ 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
- my $x = shift; $x = $class->new($x) unless ref $x;
- #my ($self,$x) = objectify(1,@_);
+ # 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 ($x->{sign} !~ /^[+-]$/);
- return $CALC->_is_odd($x->{value});
- #return (($x->{sign} ne $nan) && ($x->{value}->[0] & 1));
+ return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
+ $CALC->_is_odd($x->{value});
}
sub is_even
{
# return true when arg (BINT or num_str) is even, false for odd
- my $x = shift; $x = $class->new($x) unless ref $x;
- #my ($self,$x) = objectify(1,@_);
+ # 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 ($x->{sign} !~ /^[+-]$/);
- return $CALC->_is_even($x->{value});
- #return (($x->{sign} ne $nan) && (!($x->{value}->[0] & 1)));
- #return (($x->{sign} !~ /^[+-]$/) && ($CALC->_is_even($x->{value})));
+ return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
+ $CALC->_is_even($x->{value});
}
sub is_positive
{
# return true when arg (BINT or num_str) is positive (>= 0)
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} =~ /^[\+]/);
+ # 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;
}
sub is_negative
{
# return true when arg (BINT or num_str) is negative (< 0)
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} =~ /^[\-]/);
+ # 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;
+ }
+
+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
+ 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,$y,$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('bmul');
- return $x->bnan() if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/));
- return $x->bzero() if $x->is_zero() || $y->is_zero(); # handle result = 0
+ return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+
+ # inf handling
+ if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return $x->bnan() if $x->is_zero() || $y->is_zero();
+ # result will always be +-inf:
+ # +inf * +/+inf => +inf, -inf * -/-inf => +inf
+ # +inf * -/-inf => -inf, -inf * +/+inf => -inf
+ return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
+ return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
+ return $x->binf('-');
+ }
+
+ return $upgrade->bmul($x,$y,@r)
+ if defined $upgrade && $y->isa($upgrade);
+
+ $r[3] = $y; # no push here
+
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
- $CALC->_mul($x->{value},$y->{value}); # do actual math
- return $x->round($a,$p,$r,$y);
+
+ $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
+
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ $x;
+ }
+
+sub _div_inf
+ {
+ # helper function that handles +-inf cases for bdiv()/bmod() to reuse code
+ my ($self,$x,$y) = @_;
+
+ # NaN if x == NaN or y == NaN or x==y==0
+ return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
+ if (($x->is_nan() || $y->is_nan()) ||
+ ($x->is_zero() && $y->is_zero()));
+
+ # +-inf / +-inf == NaN, reminder also NaN
+ if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan();
+ }
+ # x / +-inf => 0, remainder x (works even if x == 0)
+ if ($y->{sign} =~ /^[+-]inf$/)
+ {
+ my $t = $x->copy(); # bzero clobbers up $x
+ return wantarray ? ($x->bzero(),$t) : $x->bzero()
+ }
+
+ # 5 / 0 => +inf, -6 / 0 => -inf
+ # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf
+ # exception: -8 / 0 has remainder -8, not 8
+ # exception: -inf / 0 has remainder -inf, not inf
+ if ($y->is_zero())
+ {
+ # +-inf / 0 => special case for -inf
+ return wantarray ? ($x,$x->copy()) : $x if $x->is_inf();
+ if (!$x->is_zero() && !$x->is_inf())
+ {
+ my $t = $x->copy(); # binf clobbers up $x
+ return wantarray ?
+ ($x->binf($x->{sign}),$t) : $x->binf($x->{sign})
+ }
+ }
+
+ # last case: +-inf / ordinary number
+ my $sign = '+inf';
+ $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign};
+ $x->{sign} = $sign;
+ return wantarray ? ($x,$self->bzero()) : $x;
}
sub bdiv
{
# (dividend: BINT or num_str, divisor: BINT or num_str) return
# (BINT,BINT) (quo,rem) or BINT (only rem)
- my ($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 $x->modify('bdiv');
- # 5 / 0 => +inf, -6 / 0 => -inf (0 /0 => 1 or +inf?)
- #return wantarray
- # ? ($x->binf($x->{sign}),binf($x->{sign})) : $x->binf($x->{sign})
- # if ($x->{sign} =~ /^[+-]$/ && $y->is_zero());
-
- # NaN?
- return wantarray ? ($x->bnan(),bnan()) : $x->bnan()
- if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || $y->is_zero());
+ return $self->_div_inf($x,$y)
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
+
+ return $upgrade->bdiv($upgrade->new($x),$y,@r)
+ if defined $upgrade && !$y->isa($self);
+
+ $r[3] = $y; # no push!
# 0 / something
- return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero();
+ return
+ wantarray ? ($x->round(@r),$self->bzero(@r)):$x->round(@r) if $x->is_zero();
- # Is $x in the interval [0, $y) ?
+ # 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 $y->{sign}))
+ if (($cmp < 0) and (($x->{sign} eq $y->{sign}) or !wantarray))
{
- return $x->bzero() unless wantarray;
+ return $upgrade->bdiv($upgrade->new($x),$upgrade->new($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(),$t);
+ return ($x->bzero()->round(@r),$t);
}
elsif ($cmp == 0)
{
# shortcut, both are the same, so set to +/- 1
- $x->_one( ($x->{sign} ne $y->{sign} ? '-' : '+') );
+ $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') );
return $x unless wantarray;
- return ($x,$self->bzero());
+ return ($x->round(@r),$self->bzero(@r));
}
+ return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r)
+ if defined $upgrade;
# 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 $y->is_one due to '-'
- if (($y == 1) || ($y == -1)) # slow!
- #if ((@{$y->{value}} == 1) && ($y->{value}->[0] == 1))
+ if ($CALC->_is_one($y->{value}))
{
- return wantarray ? ($x,$self->bzero()) : $x;
+ return wantarray ? ($x->round(@r),$self->bzero(@r)) : $x->round(@r);
}
- # call div here
- my $rem = $self->bzero();
- $rem->{sign} = $y->{sign};
- #($x->{value},$rem->{value}) = div($x->{value},$y->{value});
- ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
- # do not leave rest "-0";
- # $rem->{sign} = '+' if (@{$rem->{value}} == 1) && ($rem->{value}->[0] == 0);
- $rem->{sign} = '+' if $CALC->_is_zero($rem->{value});
- if (($x->{sign} eq '-') and (!$rem->is_zero()))
+ if (wantarray)
{
- $x->bdec();
+ my $rem = $self->bzero();
+ ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value});
+ $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 '-'
+ }
+ else
+ {
+ $rem->{sign} = '+'; # dont leave -0
+ }
+ return ($x,$rem->round(@r));
}
- $x->round($a,$p,$r,$y);
- if (wantarray)
+
+ $x->{value} = $CALC->_div($x->{value},$y->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value});
+
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ $x;
+ }
+
+###############################################################################
+# modulus functions
+
+sub bmod
+ {
+ # modulus (or remainder)
+ # (BINT or num_str, BINT or num_str) return BINT
+
+ # set up parameters
+ my ($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);
+ $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}))
+ {
+ my $xsign = $x->{sign};
+ $x->{sign} = $y->{sign};
+ if ($xsign ne $y->{sign})
+ {
+ my $t = $CALC->_copy($x->{value}); # copy $x
+ $x->{value} = $CALC->_copy($y->{value}); # copy $y to $x
+ $x->{value} = $CALC->_sub($y->{value},$t,1); # $y-$x
+ }
+ }
+ else
+ {
+ $x->{sign} = '+'; # dont leave -0
+ }
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ my ($t,$rem) = $self->bdiv($x->copy(),$y,@r); # slow way (also rounds)
+ # modify in place
+ foreach (qw/value sign _a _p/)
+ {
+ $x->{$_} = $rem->{$_};
+ }
+ $x;
+ }
+
+sub bmodinv
+ {
+ # Modular inverse. given a number which is (hopefully) relatively
+ # prime to the modulus, calculate its inverse using Euclid's
+ # alogrithm. If the number is not relatively prime to the modulus
+ # (i.e. their gcd is not one) then NaN is returned.
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (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('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 $x->{sign} eq '-';
+
+ if ($CALC->can('_modinv'))
+ {
+ my $sign;
+ ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value});
+ $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
+ return $x;
+ }
+ my ($u, $u1) = ($self->bzero(), $self->bone());
+ my ($a, $b) = ($y->copy(), $x->copy());
+
+ # first step need always be done since $num (and thus $b) is never 0
+ # Note that the loop is aligned so that the check occurs between #2 and #1
+ # thus saving us one step #2 at the loop end. Typical loop count is 1. Even
+ # a case with 28 loops still gains about 3% with this layout.
+ my $q;
+ ($a, $q, $b) = ($b, $a->bdiv($b)); # step #1
+ # Euclid's Algorithm (calculate GCD of ($a,$b) in $a and also calculate
+ # two values in $u and $u1, we use only $u1 afterwards)
+ my $sign = 1; # flip-flop
+ while (!$b->is_zero()) # found GCD if $b == 0
+ {
+ # the original algorithm had:
+ # ($u, $u1) = ($u1, $u->bsub($u1->copy()->bmul($q))); # step #2
+ # The following creates exact the same sequence of numbers in $u1,
+ # except for the sign ($u1 is now always positive). Since formerly
+ # the sign of $u1 was alternating between '-' and '+', the $sign
+ # flip-flop will take care of that, so that at the end of the loop
+ # we have the real sign of $u1. Keeping numbers positive gains us
+ # speed since badd() is faster than bsub() and makes it possible
+ # to have the algorithmn in Calc for even more speed.
+
+ ($u, $u1) = ($u1, $u->badd($u1->copy()->bmul($q))); # step #2
+ $sign = - $sign; # flip sign
+
+ ($a, $q, $b) = ($b, $a->bdiv($b)); # step #1 again
+ }
+
+ # If the gcd is not 1, then return NaN! It would be pointless to
+ # have called bgcd to check this first, because we would then be
+ # performing the same Euclidean Algorithm *twice*.
+ return $x->bnan() unless $a->is_one();
+
+ $u1->bneg() if $sign != 1; # need to flip?
+
+ $u1->bmod($y); # calc result
+ $x->{value} = $u1->{value}; # and copy over to $x
+ $x->{sign} = $u1->{sign}; # to modify in place
+ $x;
+ }
+
+sub bmodpow
+ {
+ # takes a very large number to a very large exponent in a given very
+ # large modulus, quickly, thanks to binary exponentation. supports
+ # negative exponents.
+ my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
+
+ return $num if $num->modify('bmodpow');
+
+ # check modulus for valid values
+ return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf
+ || $mod->is_zero());
+
+ # check exponent for valid values
+ if ($exp->{sign} =~ /\w/)
+ {
+ # i.e., if it's NaN, +inf, or -inf...
+ return $num->bnan();
+ }
+
+ $num->bmodinv ($mod) if ($exp->{sign} eq '-');
+
+ # check num for valid values (also NaN if there was no inverse but $exp < 0)
+ return $num->bnan() if $num->{sign} !~ /^[+-]$/;
+
+ if ($CALC->can('_modpow'))
+ {
+ # $mod is positive, sign on $exp is ignored, result also positive
+ $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value});
+ return $num;
+ }
+
+ # in the trivial case,
+ return $num->bzero(@r) if $mod->is_one();
+ return $num->bone('+',@r) if $num->is_zero() or $num->is_one();
+
+ # $num->bmod($mod); # if $x is large, make it smaller first
+ my $acc = $num->copy(); # but this is not really faster...
+
+ $num->bone(); # keep ref to $num
+
+ my $expbin = $exp->as_bin(); $expbin =~ s/^[-]?0b//; # ignore sign and prefix
+ my $len = length($expbin);
+ while (--$len >= 0)
{
- $rem->round($a,$p,$r,$x,$y);
- return ($x,$y-$rem) if $x->{sign} eq '-'; # was $x,$rem
- return ($x,$rem);
+ if( substr($expbin,$len,1) eq '1')
+ {
+ $num->bmul($acc)->bmod($mod);
+ }
+ $acc->bmul($acc)->bmod($mod);
}
- return $x;
+
+ $num;
}
+###############################################################################
+
+sub bfac
+ {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # compute factorial numbers
+ # modifies first argument
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ 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() || $x->is_one(); # 0 or 1 => 1
+
+ if ($CALC->can('_fac'))
+ {
+ $x->{value} = $CALC->_fac($x->{value});
+ return $x->round(@r);
+ }
+
+ my $n = $x->copy();
+ $x->bone();
+ # seems we need not to temp. clear A/P of $x since the result is the same
+ my $f = $self->new(2);
+ while ($f->bacmp($n) < 0)
+ {
+ $x->bmul($f); $f->binc();
+ }
+ $x->bmul($f,@r); # last step and also round
+ }
+
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,$y,$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('bpow');
-
+
+ return $upgrade->bpow($upgrade->new($x),$y,@r)
+ if defined $upgrade && !$y->isa($self);
+
+ $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->_one() if $y->is_zero();
- return $x if $x->is_one() || $y->is_one();
- #if ($x->{sign} eq '-' && @{$x->{value}} == 1 && $x->{value}->[0] == 1)
+ 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}))
{
# if $x == -1 and odd/even y => +1/-1
- return $y->is_odd() ? $x : $x->babs();
- # my Casio FX-5500L has here a bug, -1 ** 2 is -1, but -1 * -1 is 1; LOL
+ 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;
}
- # 1 ** -y => 1 / (1**y), so do test for negative $y after above's clause
+ # 1 ** -y => 1 / (1 ** |y|)
+ # so do test for negative $y after above's clause
return $x->bnan() if $y->{sign} eq '-';
- return $x if $x->is_zero(); # 0**y => 0 (if not y <= 0)
+ return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0)
if ($CALC->can('_pow'))
{
- $CALC->_pow($x->{value},$y->{value});
- return $x->round($a,$p,$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 ($res);
- while (!$y1->is_one())
- {
- #print "bpow: p2: $pow2 x: $x y: $y1 r: $res\n";
- #print "len ",$x->length(),"\n";
- ($y1,$res)=&bdiv($y1,2);
- if (!$res->is_zero()) { &bmul($pow2,$x); }
- if (!$y1->is_zero()) { &bmul($x,$x); }
- #print "$x $y\n";
- }
- #print "bpow: e p2: $pow2 x: $x y: $y1 r: $res\n";
- &bmul($x,$pow2) if (!$pow2->is_one());
- #print "bpow: e p2: $pow2 x: $x y: $y1 r: $res\n";
- return $x->round($a,$p,$r);
+ $x->{value} = $CALC->_pow($x->{value},$y->{value});
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+
+# 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 since brsft/blsft use bpow sometimes.
+# 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(@r);
+# }
+
+ my $pow2 = $self->__one();
+ my $y_bin = $y->as_bin(); $y_bin =~ s/^0b//;
+ my $len = length($y_bin);
+ while (--$len > 0)
+ {
+ $pow2->bmul($x) if substr($y_bin,$len,1) eq '1'; # is odd?
+ $x->bmul($x);
+ }
+ $x->bmul($pow2);
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ $x;
}
sub blsft
{
# (BINT or num_str, BINT or num_str) return BINT
# compute x << y, base n, y >= 0
- my ($self,$x,$y,$n) = objectify(2,@_);
-
+
+ # set up parameters
+ my ($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(@r) if $y->is_zero();
+
+ $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- $n = 2 if !defined $n; return $x if $n == 0;
- return $x->bnan() if $n < 0 || $y->{sign} eq '-';
- #if ($n != 10)
- # {
- $x->bmul( $self->bpow($n, $y) );
- # }
- #else
- # {
- # # shortcut (faster) for shifting by 10) since we are in base 10eX
- # # multiples of 5:
- # my $src = scalar @{$x->{value}}; # source
- # my $len = $y->numify(); # shift-len as normal int
- # my $rem = $len % 5; # reminder to shift
- # my $dst = $src + int($len/5); # destination
- #
- # my $v = $x->{value}; # speed-up
- # my $vd; # further speedup
- # #print "src $src:",$v->[$src]||0," dst $dst:",$v->[$dst]||0," rem $rem\n";
- # $v->[$src] = 0; # avoid first ||0 for speed
- # while ($src >= 0)
- # {
- # $vd = $v->[$src]; $vd = '00000'.$vd;
- # #print "s $src d $dst '$vd' ";
- # $vd = substr($vd,-5+$rem,5-$rem);
- # #print "'$vd' ";
- # $vd .= $src > 0 ? substr('00000'.$v->[$src-1],-5,$rem) : '0' x $rem;
- # #print "'$vd' ";
- # $vd = substr($vd,-5,5) if length($vd) > 5;
- # #print "'$vd'\n";
- # $v->[$dst] = int($vd);
- # $dst--; $src--;
- # }
- # # set lowest parts to 0
- # while ($dst >= 0) { $v->[$dst--] = 0; }
- # # fix spurios last zero element
- # splice @$v,-1 if $v->[-1] == 0;
- # #print "elems: "; my $i = 0;
- # #foreach (reverse @$v) { print "$i $_ "; $i++; } print "\n";
- # # old way: $x->bmul( $self->bpow($n, $y) );
- # }
- return $x;
+ my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft');
+ if (defined $t)
+ {
+ $x->{value} = $t; return $x->round(@r);
+ }
+ # fallback
+ return $x->bmul( $self->bpow($n, $y, @r), @r );
}
sub brsft
{
# (BINT or num_str, BINT or num_str) return BINT
# compute x >> y, base n, y >= 0
- my ($self,$x,$y,$n) = objectify(2,@_);
+
+ # set up parameters
+ my ($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(@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 || $y->{sign} eq '-';
- #if ($n != 10)
- # {
- scalar bdiv($x, $self->bpow($n, $y));
- # }
- #else
- # {
- # # shortcut (faster) for shifting by 10)
- # # multiples of 5:
- # my $dst = 0; # destination
- # my $src = $y->numify(); # as normal int
- # my $rem = $src % 5; # reminder to shift
- # $src = int($src / 5); # source
- # my $len = scalar @{$x->{value}} - $src; # elems to go
- # my $v = $x->{value}; # speed-up
- # if ($rem == 0)
- # {
- # splice (@$v,0,$src); # even faster, 38.4 => 39.3
- # }
- # else
- # {
- # my $vd;
- # $v->[scalar @$v] = 0; # avoid || 0 test inside loop
- # while ($dst < $len)
- # {
- # $vd = '00000'.$v->[$src];
- # #print "$dst $src '$vd' ";
- # $vd = substr($vd,-5,5-$rem);
- # #print "'$vd' ";
- # $src++;
- # $vd = substr('00000'.$v->[$src],-$rem,$rem) . $vd;
- # #print "'$vd1' ";
- # #print "'$vd'\n";
- # $vd = substr($vd,-5,5) if length($vd) > 5;
- # $v->[$dst] = int($vd);
- # $dst++;
- # }
- # splice (@$v,$dst) if $dst > 0; # kill left-over array elems
- # pop @$v if $v->[-1] == 0; # kill last element
- # } # else rem == 0
- # # old way: scalar bdiv($x, $self->bpow($n, $y));
- # }
- return $x;
+
+ # this only works for negative numbers when shifting in base 2
+ if (($x->{sign} eq '-') && ($n == 2))
+ {
+ 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
+ # but perhaps there is a better emulation for two's complement shift...
+ # if $y != 1, we must simulate it by doing:
+ # convert to bin, flip all bits, shift, and be done
+ $x->binc(); # -3 => -2
+ my $bin = $x->as_bin();
+ $bin =~ s/^-0b//; # strip '-0b' prefix
+ $bin =~ tr/10/01/; # flip bits
+ # now shift
+ if (CORE::length($bin) <= $y)
+ {
+ $bin = '0'; # shifting to far right creates -1
+ # 0, because later increment makes
+ # that 1, attached '-' makes it '-1'
+ # because -1 >> x == -1 !
+ }
+ else
+ {
+ $bin =~ s/.{$y}$//; # cut off at the right side
+ $bin = '1' . $bin; # extend left side by one dummy '1'
+ $bin =~ tr/10/01/; # flip bits back
+ }
+ 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(@r); # we are done now, magic, isn't?
+ }
+ $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(@r);
+ }
+ # fallback
+ $x->bdiv($self->bpow($n,$y, @r), @r);
+ $x;
}
sub band
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x & y
- my ($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');
+ $r[3] = $y; # no push!
+ local $Math::BigInt::upgrade = undef;
+
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x->bzero() if $y->is_zero();
+ return $x->bzero(@r) if $y->is_zero() || $x->is_zero();
- if ($CALC->can('_and'))
+ 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 $y->{sign} eq '-';
+
+ if ($CALC->can('_and') && $sx == 1 && $sy == 1)
{
- $CALC->_and($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ $x->{value} = $CALC->_and($x->{value},$y->{value});
+ return $x->round(@r);
}
-
- my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x10000);
- my $y1 = copy(ref($x),$y); # make copy
- my $x1 = $x->copy(); $x->bzero(); # modify x in place!
+
+ 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() && !$y1->is_zero())
{
($x1, $xr) = bdiv($x1, $x10000);
($y1, $yr) = bdiv($y1, $x10000);
- #print ref($xr), " $xr ", $xr->numify(),"\n";
- #print ref($yr), " $yr ", $yr->numify(),"\n";
- #print "res: ",$yr->numify() & $xr->numify(),"\n";
- my $u = bmul( $class->new( $xr->numify() & $yr->numify() ), $m);
- #print "res: $u\n";
- $x->badd( bmul( $class->new( $xr->numify() & $yr->numify() ), $m));
+ # make both op's numbers!
+ $x->badd( bmul( $class->new(
+ abs($sx*int($xr->numify()) & $sy*int($yr->numify()))),
+ $m));
$m->bmul($x10000);
}
- return $x->round($a,$p,$r);
+ $x->bneg() if $sign;
+ $x->round(@r);
}
sub bior
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x | y
- my ($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');
+ $r[3] = $y; # no push!
+
+ local $Math::BigInt::upgrade = undef;
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x if $y->is_zero();
- if ($CALC->can('_or'))
+ return $x->round(@r) 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 $y->{sign} eq '-';
+
+ # don't use lib for negative values
+ if ($CALC->can('_or') && $sx == 1 && $sy == 1)
{
- $CALC->_or($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ $x->{value} = $CALC->_or($x->{value},$y->{value});
+ return $x->round(@r);
}
- my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x10000);
- my $y1 = copy(ref($x),$y); # make copy
- my $x1 = $x->copy(); $x->bzero(); # modify x in place!
+ 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() || !$y1->is_zero())
{
($x1, $xr) = bdiv($x1,$x10000);
($y1, $yr) = bdiv($y1,$x10000);
- $x->badd( bmul( $class->new( $xr->numify() | $yr->numify() ), $m));
+ # make both op's numbers!
+ $x->badd( bmul( $class->new(
+ abs($sx*int($xr->numify()) | $sy*int($yr->numify()))),
+ $m));
$m->bmul($x10000);
}
- return $x->round($a,$p,$r);
+ $x->bneg() if $sign;
+ $x->round(@r);
}
sub bxor
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x ^ y
- my ($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');
+ $r[3] = $y; # no push!
+
+ local $Math::BigInt::upgrade = undef;
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x if $y->is_zero();
- return $x->bzero() if $x == $y; # shortcut
+ return $x->round(@r) if $y->is_zero();
- if ($CALC->can('_xor'))
+ 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 $y->{sign} eq '-';
+
+ # don't use lib for negative values
+ if ($CALC->can('_xor') && $sx == 1 && $sy == 1)
{
- $CALC->_xor($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ $x->{value} = $CALC->_xor($x->{value},$y->{value});
+ return $x->round(@r);
}
- my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x10000);
+ my $m = $self->bone(); my ($xr,$yr);
+ my $x10000 = $self->new(0x10000);
my $y1 = copy(ref($x),$y); # make copy
- my $x1 = $x->copy(); $x->bzero(); # modify x in place!
+ $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() || !$y1->is_zero())
{
($x1, $xr) = bdiv($x1, $x10000);
($y1, $yr) = bdiv($y1, $x10000);
- $x->badd( bmul( $class->new( $xr->numify() ^ $yr->numify() ), $m));
+ # make both op's numbers!
+ $x->badd( bmul( $class->new(
+ abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))),
+ $m));
$m->bmul($x10000);
}
- return $x->round($a,$p,$r);
+ $x->bneg() if $sign;
+ $x->round(@r);
}
sub length
{
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
my $e = $CALC->_len($x->{value});
- # # fallback, since we do not know the underlying representation
- #my $es = "$x"; my $c = 0; $c = 1 if $es =~ /^[+-]/; # if lib returns '+123'
- #my $e = CORE::length($es)-$c;
return wantarray ? ($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($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $CALC->_digit($x->{value},$n);
+ $CALC->_digit($x->{value},$n||0);
}
sub _trailing_zeros
my $x = shift;
$x = $class->new($x) unless ref $x;
- return 0 if $x->is_zero() || $x->is_nan() || $x->is_inf();
+ return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/;
return $CALC->_zeros($x->{value}) if $CALC->can('_zeros');
- # if not: since we do not know underlying internal represantation:
+ # 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!
+ CORE::length("$1"); # as string, not as +0!
}
sub bsqrt
{
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ return $x if $x->modify('bsqrt');
- return $x->bnan() if $x->{sign} =~ /\-|$nan/; # -x or NaN => NaN
- return $x->bzero() if $x->is_zero(); # 0 => 0
- return $x if $x == 1; # 1 => 1
+ return $x->bnan() if $x->{sign} ne '+'; # -x or inf or NaN => NaN
+ return $x->bzero(@r) if $x->is_zero(); # 0 => 0
+ return $x->round(@r) if $x->is_one(); # 1 => 1
- my $y = $x->copy(); # give us one more digit accur.
+ return $upgrade->bsqrt($x,@r) if defined $upgrade;
+
+ if ($CALC->can('_sqrt'))
+ {
+ $x->{value} = $CALC->_sqrt($x->{value});
+ return $x->round(@r);
+ }
+
+ return $x->bone('+',@r) if $x < 4; # 2,3 => 1
+ my $y = $x->copy();
my $l = int($x->length()/2);
- $x->bzero();
- $x->binc(); # keep ref($x), but modify it
- $x *= 10 ** $l;
-
- # print "x: $y guess $x\n";
+ $x->bone(); # keep ref($x), but modify it
+ $x->blsft($l,10);
my $last = $self->bzero();
- while ($last != $x)
+ my $two = $self->new(2);
+ my $lastlast = $x+$two;
+ while ($last != $x && $lastlast != $x)
{
- $last = $x;
- $x += $y / $x;
- $x /= 2;
+ $lastlast = $last; $last = $x->copy();
+ $x->badd($y / $x);
+ $x->bdiv($two);
}
- return $x;
+ $x->bdec() if $x * $x > $y; # overshot?
+ $x->round(@r);
}
sub exponent
{
# return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return bnan() if $x->is_nan();
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ my $s = $x->{sign}; $s =~ s/^[+-]//;
+ return $self->new($s); # -inf,+inf => inf
+ }
my $e = $class->bzero();
return $e->binc() if $x->is_zero();
$e += $x->_trailing_zeros();
- return $e;
+ $e;
}
sub mantissa
{
- # return a copy of the mantissa (here always $self)
- my ($self,$x) = objectify(1,@_);
+ # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return bnan() if $x->is_nan();
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ return $self->new($x->{sign}); # keep + or - sign
+ }
my $m = $x->copy();
# that's 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 (here 0 and self)
- my $self = shift;
- $self = $class->new($self) unless ref $self;
+ # return a copy of both the exponent and the mantissa
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return ($self->mantissa(),$self->exponent());
+ return ($x->mantissa(),$x->exponent());
}
##############################################################################
sub bfround
{
# precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
- # $n == 0 => round to integer
+ # $n == 0 || $n == 1 => round to integer
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_p($precision,$rnd_mode,@_);
+ my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_);
return $x if !defined $scale; # no-op
+ return $x if $x->modify('bfround');
# no-op for BigInts if $n <= 0
- return $x if $scale <= 0;
+ if ($scale <= 0)
+ {
+ $x->{_a} = undef; # clear an eventual set A
+ $x->{_p} = $scale; return $x;
+ }
$x->bround( $x->length()-$scale, $mode);
+ $x->{_a} = undef; # bround sets {_a}
+ $x->{_p} = $scale; # so correct it
+ $x;
}
sub _scan_for_nonzero
return 0 if $len == 1; # '5' is trailed by invisible zeros
my $follow = $pad - 1;
return 0 if $follow > $len || $follow < 1;
- #print "checking $x $r\n";
- # since we do not know underlying represantion of $x, use decimal string
+ # 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;
+ return 1 if $r =~ /[^0]/;
+ 0;
}
sub fround
# no-op for $n == 0
# and overwrite the rest with 0's, return normalized number
# do not return $x->bnorm(), but $x
+
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_a($accuracy,$rnd_mode,@_);
- return $x if !defined $scale; # no-op
+ my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_);
+ return $x if !defined $scale; # no-op
+ return $x if $x->modify('bround');
- # print "MBI round: $x to $scale $mode\n";
- # -scale means what? tom? hullo? -$scale needed by MBF round, but what for?
- return $x if $x->is_nan() || $x->is_zero() || $scale == 0;
+ if ($x->is_zero() || $scale == 0)
+ {
+ $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+ return $x;
+ }
+ return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN
# we have fewer digits than we want to scale to
my $len = $x->length();
- # print "$len $scale\n";
- return $x if $len < abs($scale);
+ # 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))
+ {
+ $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+ return $x;
+ }
# count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
my ($pad,$digit_round,$digit_after);
$pad = $len - $scale;
- $pad = abs($scale)+1 if $scale < 0;
+ $pad = abs($scale-1) if $scale < 0;
+
# do not use digit(), it is costly for binary => decimal
- #$digit_round = '0'; $digit_round = $x->digit($pad) if $pad < $len;
- #$digit_after = '0'; $digit_after = $x->digit($pad-1) if $pad > 0;
+
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;
$pl++; $pl ++ if $pad >= $len;
- $digit_after = '0'; $digit_after = substr($$xs,$pl,1)
- if $pad > 0;
-
- #my $d_round = '0'; $d_round = $x->digit($pad) if $pad < $len;
- #my $d_after = '0'; $d_after = $x->digit($pad-1) if $pad > 0;
- # print "$pad $pl $$xs $digit_round:$d_round $digit_after:$d_after\n";
+ $digit_after = '0'; $digit_after = substr($$xs,$pl,1) if $pad > 0;
# in case of 01234 we round down, for 6789 up, and only in case 5 we look
# closer at the remaining digits of the original $x, remember decision
($mode eq '-inf') && ($x->{sign} eq '+') ||
($mode eq 'zero') # round down if zero, sign adjusted below
);
- # allow rounding one place left of mantissa
- #print "$pad $len $scale\n";
- # this is triggering warnings, and buggy for $scale < 0
- #if (-$scale != $len)
- {
- # old code, depend on internal represantation
- # split mantissa at $pad and then pad with zeros
- #my $s5 = int($pad / 5);
- #my $i = 0;
- #while ($i < $s5)
- # {
- # $x->{value}->[$i++] = 0; # replace with 5 x 0
- # }
- #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0
- #my $rem = $pad % 5; # so much left over
- #if ($rem > 0)
- # {
- # #print "remainder $rem\n";
- ## #print "elem $x->{value}->[$s5]\n";
- # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0'
- # }
- #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5'
- #print ${$CALC->_str($pad->{value})}," $len\n";
- if (($pad > 0) && ($pad <= $len))
- {
- substr($$xs,-$pad,$pad) = '0' x $pad;
- $x->{value} = $CALC->_new($xs); # put back in
- }
- elsif ($pad > $len)
+ my $put_back = 0; # not yet modified
+
+ if (($pad > 0) && ($pad <= $len))
+ {
+ substr($$xs,-$pad,$pad) = '0' x $pad;
+ $put_back = 1;
+ }
+ elsif ($pad > $len)
+ {
+ $x->bzero(); # round to '0'
+ }
+
+ if ($round_up) # what gave test above?
+ {
+ $put_back = 1;
+ $pad = $len, $$xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
+
+ # we modify directly the string variant instead of creating a number and
+ # adding it, since that is faster (we already have the string)
+ my $c = 0; $pad ++; # for $pad == $len case
+ while ($pad <= $len)
{
- $x->{value} = $CALC->_zero(); # round to '0'
+ $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
}
- #print "res $$xs\n";
+ $$xs = '1'.$$xs if $c == 0;
+
}
- # move this later on after the inc of the string
- #$x->{value} = $CALC->_new($xs); # put back in
- if ($round_up) # what gave test above?
+ $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back in if needed
+
+ $x->{_a} = $scale if $scale >= 0;
+ if ($scale < 0)
{
- $pad = $len if $scale < 0; # tlr: whack 0.51=>1.0
- # modify $x in place, undef, undef to avoid rounding
- # str creation much faster than 10 ** something
- $x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad) );
- # increment string in place, to avoid dec=>hex for the '1000...000'
- # $xs ...blah foo
+ $x->{_a} = $len+$scale;
+ $x->{_a} = 0 if $scale < -$len;
}
- # to here:
- #$x->{value} = $CALC->_new($xs); # put back in
$x;
}
{
# return integer less or equal then number, since it is already integer,
# always returns $self
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : 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) = objectify(1,@_);
-
- # not needed: return $x if $x->modify('bceil');
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x->round($a,$p,$r);
+ $x->round(@r);
}
##############################################################################
# private stuff (internal use only)
-sub _one
+sub __one
{
# internal speedup, set argument to 1, or create a +/- 1
my $self = shift;
- #my $x = $self->bzero(); $x->{value} = [ 1 ]; $x->{sign} = shift || '+'; $x;
- my $x = $self->bzero(); $x->{value} = $CALC->_one();
+ my $x = $self->bone(); # $x->{value} = $CALC->_one();
$x->{sign} = shift || '+';
- return $x;
+ $x;
}
sub _swap
# 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 '-'.
+ # exceptions like '+' and '-'. To make '+' and '-' work, you also need to
+ # specify your own overload for them.
# 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
- #print "swap $self 0:$_[0] 1:$_[1] 2:$_[2]\n";
if ($_[2])
{
my $c = ref ($_[0]) || $class; # fallback $class should not happen
return ( $c->new($_[1]), $_[0] );
}
- else
- {
- return ( $_[0]->copy(), $_[1] );
- }
+ return ( $_[0]->copy(), $_[1] );
}
sub objectify
# $class,1,2. (We can not take '1' as class ;o)
# badd($class,1) is not supported (it should, eventually, try to add undef)
# 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]);
+
my $count = abs(shift || 0);
- #print caller(),"\n";
-
- my @a; # resulting array
+ my (@a,$k,$d); # resulting array, temp, and downgrade
if (ref $_[0])
{
# okay, got object as first
{
# nope, got 1,2 (Class->xxx(1) => Class,1 and not supported)
$a[0] = $class;
- #print "@_\n"; sleep(1);
$a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first?
}
- #print caller(),"\n";
+
+ 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]\n";
- my $k;
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);
{
while ($count > 0)
{
- #print "$count\n";
$count--;
$k = shift;
if (!ref($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
}
- #my $i = 0;
- #foreach (@a)
- # {
- # print "o $i $a[0]\n" if $i == 0;
- # print "o $i ",ref($_),"\n" if $i != 0; $i++;
- # }
- #print "objectify done: would return ",scalar @a," values\n";
- #print caller(1),"\n" unless wantarray;
die "$class objectify needs list context" unless wantarray;
+ ${"$a[0]::downgrade"} = $d;
@a;
}
sub import
{
my $self = shift;
- #print "import $self @_\n";
- my @a = @_; my $l = scalar @_; my $j = 0;
- for ( my $i = 0; $i < $l ; $i++,$j++ )
+
+ $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 binary => sub { $self->new(shift) };
+ }
+ elsif ($_[$i] eq 'upgrade')
+ {
+ # this causes upgrading
+ $upgrade = $_[$i+1]; # or undef to disable
+ $i++;
}
elsif ($_[$i] =~ /^lib$/i)
{
# this causes a different low lib to take care...
- $CALC = $_[$i+1] || $CALC;
- my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
- splice @a, $j, $s; $j -= $s;
+ $CALC = $_[$i+1] || '';
+ $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); # does not work
- $self->export_to_level(1,$self,@a); # need this instead
-
- # load core math lib
- $CALC = 'Math::BigInt::'.$CALC if $CALC !~ /^Math::BigInt/i;
- my $c = $CALC; $c =~ s/::/\//g; $c .= '.pm' if $c !~ /\.pm$/;
- require $c;
+ $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
+ $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 @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?
+ }
+ die "Couldn't load any math lib, not even the default" if $CALC eq '';
}
-sub _strip_zeros
- {
- # internal normalization function that strips leading zeros from the array
- # args: ref to array
- my $s = shift;
-
- my $cnt = scalar @$s; # get count of parts
- my $i = $cnt-1;
- #print "strip: cnt $cnt i $i\n";
- # '0', '3', '4', '0', '0',
- # 0 1 2 3 4
- # cnt = 5, i = 4
- # i = 4
- # i = 3
- # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos)
- # >= 1: skip first part (this can be zero)
- while ($i > 0) { last if $s->[$i] != 0; $i--; }
- $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0
- return $s;
- }
-
-sub _from_hex
+sub __from_hex
{
# 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;
+ $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
+
return $x->bnan() if $$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($$hs,$i,4);
+ $val =~ s/^[+-]?0x// if $len == 0; # for last part only because
+ $val = hex($val); # hex does not like wrong chars
+ $i -= 4; $len --;
+ $x += $mul * $val if $val != 0;
+ $mul *= $x65536 if $len >= 0; # skip last mul
+ }
+ }
+ $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0'
+ $x;
+ }
+
+sub __from_bin
+ {
+ # convert a (ref to) big binary string to BigInt, return undef for error
+ my $bs = shift;
+
+ my $x = Math::BigInt->bzero();
+ # strip underscores
+ $$bs =~ s/([01])_([01])/$1$2/g;
+ $$bs =~ s/([01])_([01])/$1$2/g;
+ return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/;
+
+ my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/);
+ $$bs =~ s/^[+-]//; # strip sign
+ if ($CALC->can('_from_bin'))
+ {
+ $x->{value} = $CALC->_from_bin($bs);
+ }
+ else
+ {
+ my $mul = Math::BigInt->bzero(); $mul++;
+ my $x256 = Math::BigInt->new(256);
+ 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 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
+ 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
+ $$x =~ s/\s+$//g; # strip white space at end
+
+ # shortcut, if nothing to split, return early
+ if ($$x =~ /^[+-]?\d+\z/)
+ {
+ $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
+ return (\$sign, $x, \'', \'', \0);
+ }
+
+ # invalid starting char?
+ return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
+
+ return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string
+ return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string
+
+ # strip underscores between digits
+ $$x =~ s/(\d)_(\d)/$1$2/g;
+ $$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 $$x =~ /[Ee].*[Ee]/; # more than one E => error
+
+ my ($m,$e,$last) = split /[Ee]/,$$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?
+ if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
+ {
+ $es = $1; $ev = $2;
+ # valid mantissa?
+ return if $m eq '.' || $m eq '';
+ my ($mi,$mf,$lastf) = split /\./,$m;
+ return if defined $lastf; # last defined => 1.2.3 or others
+ $mi = '0' if !defined $mi;
+ $mi .= '0' if $mi =~ /^[\-\+]?$/;
+ $mf = '0' if !defined $mf || $mf eq '';
+ if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
+ {
+ $mis = $1||'+'; $miv = $2;
+ return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros
+ $mfv = $1;
+ 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,$x10000,$h);
+ if ($] >= 5.006)
+ {
+ $x10000 = Math::BigInt->new (0x10000); $h = 'h4';
+ }
+ else
+ {
+ $x10000 = Math::BigInt->new (0x1000); $h = 'h3';
+ }
+ while (!$x1->is_zero())
+ {
+ ($x1, $xr) = bdiv($x1,$x10000);
+ $es .= unpack($h,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,$x10000,$b);
+ if ($] >= 5.006)
+ {
+ $x10000 = Math::BigInt->new (0x10000); $b = 'b16';
+ }
+ else
+ {
+ $x10000 = Math::BigInt->new (0x1000); $b = 'b12';
+ }
+ while (!$x1->is_zero())
+ {
+ ($x1, $xr) = bdiv($x1,$x10000);
+ $es .= unpack($b,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)
+
+sub __lcm
+ {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # 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;
+ }
+
+###############################################################################
+# 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
+# may override it with special code (f.i. Math::BigInt::Constant does so)
+
+sub modify () { 0; }
+
+1;
+__END__
+
+=head1 NAME
+
+Math::BigInt - Arbitrary size integer math package
+
+=head1 SYNOPSIS
+
+ use Math::BigInt;
+
+ # Number creation
+ $x = Math::BigInt->new($str); # defaults to 0
+ $nan = Math::BigInt->bnan(); # create a NotANumber
+ $zero = Math::BigInt->bzero(); # create a +0
+ $inf = Math::BigInt->binf(); # create a +inf
+ $inf = Math::BigInt->binf('-'); # create a -inf
+ $one = Math::BigInt->bone(); # create a +1
+ $one = Math::BigInt->bone('-'); # create a -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_positive(); # if $x >= 0
+ $x->is_negative(); # 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 extration
+ $x->bcmp($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:
+
+ $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)
+ $x->bmodpow($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->bsqrt(); # calculate square-root
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
+
+ $x->round($A,$P,$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
+
+ # The following do not modify their arguments in BigInt,
+ # 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)
+
+ $x->length(); # return number of digits in number
+ ($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())
+
+ # conversation to string (do not modify their argument)
+ $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
+
+
+ # 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->config(); # return hash containing configuration
+
+=head1 DESCRIPTION
+
+All operators (inlcuding basic math operations) are overloaded if you
+declare your big integers as
+
+ $i = new Math::BigInt '123_456_789_123_456_789';
+
+Operations with overloaded operators preserve the arguments which is
+exactly what you expect.
+
+=over 2
+
+=item Canonical notation
+
+Big integer values are strings of the form C</^[+-]\d+$/> with leading
+zeros suppressed.
+
+ '-0' canonical value '-0', normalized '0'
+ ' -123_123_123' canonical value '-123123123'
+ '1_23_456_7890' canonical value '1234567890'
+
+=item Input
+
+Input values to these routines may be either Math::BigInt objects or
+strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>.
+
+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.
+
+Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results
+in '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.
+
+=item Output
+
+Output values are BigInt objects (normalized), except for bstr(), which
+returns a string in normalized form.
+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.
+
+=back
+
+=head1 METHODS
+
+Each of the methods below (except config(), accuracy() and precision())
+accepts three additional parameters. These arguments $A, $P and $R are
+accuracy, precision and 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 Math library
+ Math::BigInt::Calc
+ lib_version Version of 'lib'
+ 0.30
+ class The class of config you just called
+ Math::BigInt
+ upgrade To which class numbers are upgraded
+ Math::BigFloat
+ downgrade To which class numbers are 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 acccuracy for div
+ 40
+
+It is currently not supported to set the configuration parameters by passing
+a hash ref to C<config()>.
+
+=head2 accuracy
+
+ $x->accuracy(5); # local for $x
+ CLASS->accuracy(5); # global for all members of CLASS
+ $A = $x->accuracy(); # read out
+ $A = CLASS->accuracy(); # read out
+
+Set or get the global or local accuracy, aka how many significant digits the
+results have.
+
+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
+ $x = Math::BigInt->new(123456); # will be automatically rounded
+ print "$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 right of the dot
+ $x->precision(2); # ditto, but round left of the dot
+ CLASS->accuracy(5); # global for all members of CLASS
+ CLASS->precision(-5); # ditto
+ $P = CLASS->precision(); # read out
+ $P = $x->precision(); # read out
+
+Set or get the global or local precision, aka how many digits the result has
+after the dot (or where to round it when passing a positive number). In
+Math::BigInt, passing a negative number precision has no effect since no
+numbers have digits after the dot.
+
+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:
+
+ $x->precision(undef);
+ Math::BigInt->precision(undef);
+
+Returns the current precision. For C<$x->precision()> it will return either the
+local precision of $x, or if not defined, the global. This means the return
+value represents the accuracy 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
+
+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 brsft
+
+ $x->brsft($y,$n);
+
+Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and
+2, but others work, too.
+
+Right shifting usually amounts to dividing $x by $n ** $y and truncating the
+result:
+
+
+ $x = Math::BigInt->new(10);
+ $x->brsft(1); # same as $x >> 1: 5
+ $x = Math::BigInt->new(1234);
+ $x->brsft(2,10); # result 12
+
+There is one exception, and that is base 2 with negative $x:
+
+
+ $x = Math::BigInt->new(-5);
+ print $x->brsft(1);
+
+This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the
+result).
+
+=head2 new
+
+ $x = Math::BigInt->new($str,$A,$P,$R);
+
+Creates a new BigInt object from a string or another BigInt object. The
+input is accepted as decimal, hex (with leading '0x') or binary (with leading
+'0b').
+
+=head2 bnan
+
+ $x = Math::BigInt->bnan();
+
+Creates a new BigInt object representing NaN (Not A Number).
+If used on an object, it will set it to NaN:
+
+ $x->bnan();
+
+=head2 bzero
+
+ $x = Math::BigInt->bzero();
+
+Creates a new BigInt object representing zero.
+If used on an object, it will set it to zero:
+
+ $x->bzero();
+
+=head2 binf
+
+ $x = Math::BigInt->binf($sign);
+
+Creates a new BigInt object representing infinity. The optional argument is
+either '-' or '+', indicating whether you want infinity or minus infinity.
+If used on an object, it will set it to infinity:
+
+ $x->binf();
+ $x->binf('-');
+
+=head2 bone
+
+ $x = Math::BigInt->binf($sign);
+
+Creates a new BigInt object representing one. The optional argument is
+either '-' or '+', indicating whether you want one or minus one.
+If used on an object, it will set it to one:
+
+ $x->bone(); # +1
+ $x->bone('-'); # -1
+
+=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_inf(); # true if +inf
+ $x->is_inf('-'); # true if -inf (sign is default '+')
+
+These methods all test the BigInt for beeing one specific value and return
+true or false depending on the input. These are faster than doing something
+like:
+
+ if ($x == 0)
+
+=head2 is_positive()/is_negative()
+
+ $x->is_positive(); # true if >= 0
+ $x->is_negative(); # 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 positive.
+
+These methods are only testing the sign, and not the value.
+
+=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
+
+The return true when the argument satisfies the condition. C<NaN>, C<+inf>,
+C<-inf> are not integers and are neither odd nor even.
+
+=head2 bcmp
+
+ $x->bcmp($y);
+
+Compares $x with $y and takes the sign into account.
+Returns -1, 0, 1 or undef.
+
+=head2 bacmp
+
+ $x->bacmp($y);
+
+Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef.
+
+=head2 sign
+
+ $x->sign();
+
+Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
+
+=head2 bcmp
+
+ $x->digit($n); # return the nth digit, counting from right
+
+=head2 bneg
+
+ $x->bneg();
+
+Negate the number, e.g. change the sign between '+' and '-', or between '+inf'
+and '-inf', respectively. Does nothing for NaN or zero.
+
+=head2 babs
+
+ $x->babs();
+
+Set the number to it's absolute value, e.g. change the sign from '-' to '+'
+and from '-inf' to '+inf', respectively. Does nothing for NaN or positive
+numbers.
+
+=head2 bnorm
+
+ $x->bnorm(); # normalize (no-op)
+
+=head2 bnot
+
+ $x->bnot(); # two's complement (bit wise not)
+
+=head2 binc
+
+ $x->binc(); # increment x by 1
+
+=head2 bdec
+
+ $x->bdec(); # decrement x by 1
+
+=head2 badd
+
+ $x->badd($y); # addition (add $y to $x)
+
+=head2 bsub
+
+ $x->bsub($y); # subtraction (subtract $y from $x)
+
+=head2 bmul
+
+ $x->bmul($y); # multiplication (multiply $x by $y)
+
+=head2 bdiv
+
+ $x->bdiv($y); # divide, set $x to quotient
+ # return (quo,rem) or quo if scalar
+
+=head2 bmod
+
+ $x->bmod($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 % $mod
+
+because C<bmodpow> is much faster--it reduces internal variables into
+the modulus whenever possible, so it operates on smaller numbers.
+
+C<bmodpow> also supports negative exponents.
+
+ bmodpow($num, -1, $mod)
+
+is exactly equivalent to
+
+ bmodinv($num, $mod)
+
+=head2 bpow
+
+ $x->bpow($y); # power of arguments (x ** y)
+
+=head2 blsft
- $$hs =~ s/^[+-]?//; # strip sign
- if ($CALC->can('_from_hex'))
- {
- $x->{value} = $CALC->_from_hex($hs);
- }
- else
- {
- # fallback to pure perl
- my $mul = Math::BigInt->bzero(); $mul++;
- my $x65536 = Math::BigInt->new(65536);
- my $len = CORE::length($$hs)-2;
- $len = int($len/4); # 4-digit parts, w/o '0x'
- my $val; my $i = -4;
- while ($len >= 0)
- {
- $val = substr($$hs,$i,4);
- $val =~ s/^[\-\+]?0x// if $len == 0; # for last part only because
- $val = hex($val); # hex does not like wrong chars
- # print "$val ",substr($$hs,$i,4),"\n";
- $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;
- }
+ $x->blsft($y); # left shift
+ $x->blsft($y,$n); # left shift, in base $n (like 10)
-sub _from_bin
- {
- # convert a (ref to) big binary string to BigInt, return undef for error
- my $bs = shift;
+=head2 brsft
- my $x = Math::BigInt->bzero();
- return $x->bnan() if $$bs !~ /^[\-\+]?0b[01]+$/;
+ $x->brsft($y); # right shift
+ $x->brsft($y,$n); # right shift, in base $n (like 10)
- my $mul = Math::BigInt->bzero(); $mul++;
- my $x256 = Math::BigInt->new(256);
+=head2 band
- my $sign = '+'; $sign = '-' if ($$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($$bs,$i,8);
- $val =~ s/^[\-\+]?0b// if $len == 0; # for last part only
- #$val = oct('0b'.$val); # does not work on Perl prior 5.6.0
- $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8;
- $val = ord(pack('B8',$val));
- # print "$val ",substr($$bs,$i,16),"\n";
- $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;
- }
+ $x->band($y); # bitwise and
-sub _split
- {
- # (ref to num_str) return num_str
- # internal, take apart a string and return the pieces
- my $x = shift;
+=head2 bior
- # pre-parse input
- $$x =~ s/^\s+//g; # strip white space at front
- $$x =~ s/\s+$//g; # strip white space at end
- #$$x =~ s/\s+//g; # strip white space (no longer)
- return if $$x eq "";
+ $x->bior($y); # bitwise inclusive or
- return _from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string
- return _from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string
+=head2 bxor
- return if $$x !~ /^[\-\+]?\.?[0-9]/;
+ $x->bxor($y); # bitwise exclusive or
- $$x =~ s/(\d)_(\d)/$1$2/g; # strip underscores between digits
- $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3
-
- # some possible inputs:
- # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
- # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2
+=head2 bnot
- #print "input: '$$x' ";
- my ($m,$e) = split /[Ee]/,$$x;
- $e = '0' if !defined $e || $e eq "";
- # print "m '$m' e '$e'\n";
- # sign,value for exponent,mantint,mantfrac
- my ($es,$ev,$mis,$miv,$mfv);
- # valid exponent?
- if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
- {
- $es = $1; $ev = $2;
- #print "'$m' '$e' e: $es $ev ";
- # valid mantissa?
- return if $m eq '.' || $m eq '';
- my ($mi,$mf) = split /\./,$m;
- $mi = '0' if !defined $mi;
- $mi .= '0' if $mi =~ /^[\-\+]?$/;
- $mf = '0' if !defined $mf || $mf eq '';
- if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
- {
- $mis = $1||'+'; $miv = $2;
- # print "$mis $miv";
- # valid, existing fraction part of mantissa?
- return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros
- $mfv = $1;
- #print " split: $mis $miv . $mfv E $es $ev\n";
- return (\$mis,\$miv,\$mfv,\$es,\$ev);
- }
- }
- return; # NaN, not a number
- }
+ $x->bnot(); # bitwise not (two's complement)
-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;
+=head2 bsqrt
- return $self->copy();
- }
+ $x->bsqrt(); # calculate square-root
-##############################################################################
-# internal calculation routines (others are in Math::BigInt::Calc etc)
+=head2 bfac
-sub cmp
- {
- # post-normalized compare for internal use (honors signs)
- # input: ref to value, ref to value, sign, sign
- # output: <0, 0, >0
- my ($cx,$cy,$sx,$sy) = @_;
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
- if ($sx eq '+')
- {
- return 1 if $sy eq '-'; # 0 check handled above
- #return acmp($cx,$cy);
- return $CALC->_acmp($cx,$cy);
- }
- else
- {
- # $sx eq '-'
- return -1 if $sy eq '+';
- #return acmp($cy,$cx);
- return $CALC->_acmp($cy,$cx);
- }
- return 0; # equal
- }
+=head2 round
-sub _lcm
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # 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);
- }
+ $x->round($A,$P,$round_mode);
+
+Round $x to accuracy C<$A> or precision C<$P> using the round mode
+C<$round_mode>.
-sub _gcd
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does modify first arg
- # GCD -- Euclids algorithm E, Knuth Vol 2 pg 296
-
- my $x = shift; my $ty = $class->new(shift); # preserve y, but make class
- return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/;
+=head2 bround
- while (!$ty->is_zero())
- {
- ($x, $ty) = ($ty,bmod($x,$ty));
- }
- $x;
- }
+ $x->bround($N); # accuracy: preserve $N digits
-###############################################################################
-# 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
-# may override it with special code (f.i. Math::BigInt::Constant does so)
+=head2 bfround
-sub modify () { 0; }
+ $x->bfround($N); # round to $Nth digit, no-op for BigInts
-1;
-__END__
+=head2 bfloor
-=head1 NAME
+ $x->bfloor();
-Math::BigInt - Arbitrary size integer math package
+Set $x to the integer less or equal than $x. This is a no-op in BigInt, but
+does change $x in BigFloat.
-=head1 SYNOPSIS
+=head2 bceil
- use Math::BigInt;
+ $x->bceil();
- # Number creation
- $x = Math::BigInt->new($str); # defaults to 0
- $nan = Math::BigInt->bnan(); # create a NotANumber
- $zero = Math::BigInt->bzero();# create a "+0"
-
- # Testing
- $x->is_zero(); # return whether arg is zero or not
- $x->is_nan(); # return whether arg is NaN or not
- $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 '+')
-
- $x->bcmp($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
+Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but
+does change $x in BigFloat.
- # The following all modify their first argument:
+=head2 bgcd
- # set
- $x->bzero(); # set $x to 0
- $x->bnan(); # set $x to NaN
+ bgcd(@values); # greatest common divisor (no OO style)
- $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
-
- $x->badd($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)
-
- $x->band($y); # bitwise and
- $x->bior($y); # bitwise inclusive or
- $x->bxor($y); # bitwise exclusive or
- $x->bnot(); # bitwise not (two's complement)
+=head2 blcm
- $x->bsqrt(); # calculate square-root
+ blcm(@values); # lowest common multiplicator (no OO style)
+
+head2 length
- $x->round($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
+ $x->length();
+ ($xl,$fl) = $x->length();
- # 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:
+Returns the number of digits in the decimal representation of the number.
+In list context, returns the length of the integer and fraction part. For
+BigInt's, the length of the fraction part will always be 0.
- bgcd(@values); # greatest common divisor
- blcm(@values); # lowest common multiplicator
-
- $x->bstr(); # normalized string
- $x->bsstr(); # normalized string in scientific notation
- $x->length(); # return number of digits in number
- ($x,$f) = $x->length(); # length of number and length of fraction part
+=head2 exponent
- $x->exponent(); # return exponent as BigInt
- $x->mantissa(); # return 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->exponent();
-=head1 DESCRIPTION
+Return the exponent of $x as BigInt.
-All operators (inlcuding basic math operations) are overloaded if you
-declare your big integers as
+=head2 mantissa
- $i = new Math::BigInt '123_456_789_123_456_789';
+ $x->mantissa();
-Operations with overloaded operators preserve the arguments which is
-exactly what you expect.
+Return the signed mantissa of $x as BigInt.
-=over 2
+=head2 parts
-=item Canonical notation
+ $x->parts(); # return (mantissa,exponent) as BigInt
-Big integer values are strings of the form C</^[+-]\d+$/> with leading
-zeros suppressed.
+=head2 copy
- '-0' canonical value '-0', normalized '0'
- ' -123_123_123' canonical value '-123123123'
- '1_23_456_7890' canonical value '1234567890'
+ $x->copy(); # make a true copy of $x (unlike $y = $x;)
-=item Input
+=head2 as_number
-Input values to these routines may be either Math::BigInt objects or
-strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>.
+ $x->as_number(); # return as BigInt (in BigInt: same as copy())
+
+=head2 bsrt
-You can include one underscore between any two digits.
+ $x->bstr(); # return normalized string
-This means integer values like 1.01E2 or even 1000E-2 are also accepted.
-Non integer values result in NaN.
+=head2 bsstr
-Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results
-in 'NaN'.
+ $x->bsstr(); # normalized string in scientific notation
-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.
+=head2 as_hex
-=item Output
+ $x->as_hex(); # as signed hexadecimal string with prefixed 0x
-Output values are BigInt objects (normalized), except for bstr(), which
-returns a string in normalized form.
-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.
+=head2 as_bin
-=back
+ $x->as_bin(); # as signed binary string with prefixed 0b
=head1 ACCURACY and PRECISION
-Since version v1.33 Math::BigInt and Math::BigFloat do have full support for
+Since version v1.33, Math::BigInt and Math::BigFloat have full support for
accuracy and precision based rounding, both automatically after every
-operation as manual.
+operation as well as manually.
This section describes the accuracy/precision handling in Math::Big* as it
-used to be and is now, completed with an explanation of all terms and
+used to be and as it is now, complete with an explanation of all terms and
abbreviations.
Not yet implemented things (but with correct description) are marked with '!',
things that need to be answered are marked with '?'.
In the next paragraph follows a short description of terms used here (because
-these may differ from terms used by others people or documentations).
+these may differ from terms used by others people or documentation).
-During the rest of this document the shortcuts A (for accuracy), P (for
+During the rest of this document, the shortcuts A (for accuracy), P (for
precision), F (fallback) and R (rounding mode) will be used.
=head2 Precision P
A fixed number of digits before (positive) or after (negative)
-the dot. F.i. 123.45 has a precision of -2. 0 means an integer like 123
-(or 120). A precision of 2 means two digits left of the dot are zero, so
-123 with P = 1 becomes 120. Note that numbers with zeros before the dot may
-have different precisions, because 1200 can have p = 0, 1 or 2 (depending
-on what the inital value was). It could also have p < 0, when the digits
-after the dot are zero.
-
- !The string output of such a number should be padded with zeros:
- !
- ! Initial value P Result String
- ! 1234.01 -3 1000 1000
- ! 1234 -2 1200 1200
- ! 1234.5 -1 1230 1230
- ! 1234.001 1 1234 1234.0
- ! 1234.01 0 1234 1234
- ! 1234.01 2 1234.01 1234.01
- ! 1234.01 5 1234.01 1234.01000
+the decimal point. For example, 123.45 has a precision of -2. 0 means an
+integer like 123 (or 120). A precision of 2 means two digits to the left
+of the decimal point are zero, so 123 with P = 1 becomes 120. Note that
+numbers with zeros before the decimal point may have different precisions,
+because 1200 can have p = 0, 1 or 2 (depending on what the inital value
+was). It could also have p < 0, when the digits after the decimal point
+are zero.
+
+The string output (of floating point numbers) will be padded with zeros:
+
+ Initial value P A Result String
+ ------------------------------------------------------------
+ 1234.01 -3 1000 1000
+ 1234 -2 1200 1200
+ 1234.5 -1 1230 1230
+ 1234.001 1 1234 1234.0
+ 1234.01 0 1234 1234
+ 1234.01 2 1234.01 1234.01
+ 1234.01 5 1234.01 1234.01000
+
+For BigInts, no padding occurs.
=head2 Accuracy A
Number of significant digits. Leading zeros are not counted. A
number may have an accuracy greater than the non-zero digits
-when there are zeros in it or trailing zeros. F.i. 123.456 has A of 6,
-10203 has 5, 123.0506 has 7, 123.450000 has 8, and 0.000123 has 3.
+when there are zeros in it or trailing zeros. For example, 123.456 has
+A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3.
+
+The string output (of floating point numbers) will be padded with zeros:
+
+ Initial value P A Result String
+ ------------------------------------------------------------
+ 1234.01 3 1230 1230
+ 1234.01 6 1234.01 1234.01
+ 1234.1 8 1234.1 1234.1000
+
+For BigInts, no padding occurs.
=head2 Fallback F
-When both A and P are undefined, this is used as a fallback accuracy.
+When both A and P are undefined, this is used as a fallback accuracy when
+dividing numbers.
=head2 Rounding mode R
truncation invariably removes all digits following the
rounding place, replacing them with zeros. Thus, 987.65 rounded
-to tenths (P=1) becomes 980, and rounded to the fourth sigdig
+to tens (P=1) becomes 980, and rounded to the fourth sigdig
becomes 987.6 (A=4). 123.456 rounded to the second place after the
-dot (P=-2) becomes 123.46.
+decimal point (P=-2) becomes 123.46.
All other implemented styles of rounding attempt to round to the
"nearest digit." If the digit D immediately to the right of the
round to plus infinity, i.e. always round up. E.g., when
rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5,
-but 0.4501 becomes 0.5.
+and 0.4501 also becomes 0.5.
=item '-inf'
=item Precision
- * ffround($p) is able to round to $p number of digits after the dot
+ * ffround($p) is able to round to $p number of digits after the decimal
+ point
* otherwise P is unused
=item Accuracy (significant digits)
* fround($a) rounds to $a significant digits
* only fdiv() and fsqrt() take A as (optional) paramater
- + other operations simple create the same amount (fneg etc), or more (fmul)
+ + other operations simply create the same number (fneg etc), or more (fmul)
of digits
+ rounding/truncating is only done when explicitly calling one of fround
or ffround, and never for BigInt (not implemented)
- * fsqrt() simple hands it's accuracy argument over to fdiv.
+ * fsqrt() simply hands its accuracy argument over to fdiv.
* the documentation and the comment in the code indicate two different ways
on how fdiv() determines the maximum number of digits it should calculate,
and the actual code does yet another thing
Actual code:
scale = max(scale, length(dividend)-1,length(divisor)-1);
scale += length(divisior) - length(dividend);
- So for lx =3, ly = 9, scale = 10, scale will be actually 16 (10+9-3).
+ 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
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.
- The rounding after the division then uses the reminder and $y to determine
+ The rounding after the division then uses the remainder and $y to determine
wether it must round up or down.
- ? I have no idea which is the right way. Thats why I used scheme a bit more
- ? simple and tweaked the few failing the testcases to match it.
+ ? I have no idea which is the right way. That's why I used a slightly more
+ ? simple scheme and tweaked the few failing testcases to match it.
=back
=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 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.
* Globals are classwide, and not inherited by subclasses.
- * to undefine A, use $Math::SomeCLass::accuracy = undef
- * to undefine P, use $Math::SomeClass::precision = undef
+ * 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 be valid, A must be > 0, P can have any value.
- * If P is negative, this means round to the P's place right of the dot,
- positive values mean left from the dot. P of 0 means round to integer.
- * to find out the current global A, take $Math::SomeClass::accuracy
- * use $x->accuracy() for the local setting of $x.
- * to find out the current global P, take $Math::SomeClass::precision
- * use $x->precision() for the local setting
+ * 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.
=item Creating numbers
- !* When you create a number, there should be a way to define it's A & P
- * When a number without specific A or P is created, but the globals are
- defined, these should be used to round the number immidiately and also
- stored locally at the number. Thus changing the global defaults later on
- will not change the A or P of previously created numbers (aka A and P of
- $x will be what was in effect when $x was created)
+ * When you create a number, you can give it's desired A or P via:
+ $x = Math::BigInt->new($number,$A,$P);
+ * Only one of A or P can be defined, otherwise the result is NaN
+ * If no A or P is give ($x = Math::BigInt->new($number) form), then the
+ globals (if set) will be used. Thus changing the global defaults later on
+ will not change the A or P of previously created numbers (i.e., A and P of
+ $x will be what was in effect when $x was created)
+ * If given undef for A and P, B<no> rounding will occur, and the globals will
+ B<not> be used. This is used by subclasses to create numbers without
+ suffering rounding in the parent. Thus a subclass is able to have it's own
+ globals enforced upon creation of a number by using
+ $x = Math::BigInt->new($number,undef,undef):
+
+ use Math::Bigint::SomeSubclass;
+ use Math::BigInt;
+
+ Math::BigInt->accuracy(2);
+ Math::BigInt::SomeSubClass->accuracy(3);
+ $x = Math::BigInt::SomeSubClass->new(1234);
+
+ $x is now 1230, and not 1200. A subclass might choose to implement
+ this otherwise, e.g. falling back to the parent's A and P.
=item Usage
- * If A or P are enabled/defined, the are used to round the result of each
+ * If A or P are enabled/defined, they are used to round the result of each
operation according to the rules below
- * Negative P are ignored in Math::BigInt, since it never has digits after
- the dot
- !* Since Math::BigFloat uses Math::BigInts internally, setting A or P inside
- ! Math::BigInt as globals should not hamper with the parts of a BigFloat.
- ! Thus a flag is used to mark all Math::BigFloat numbers as 'do never round'
+ * 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'
=item Precedence
- * It makes only sense that a number has only 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 two objects are engaged in an operation, and one of them has A in
- ! effect, and the other P, this should result in a warning or an error,
- ! probably in NaN.
+ * 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 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 none of them is defined, nothing is used,
- e.g. 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 none of A
- or P are defined, fdiv() will use a fallback (F) of $div_scale digits.
- If either the dividend or the divisors mantissa have more digits than the
- F, the higher value will be used instead as F.
- This is to limit the digits (A) of the result (just think if what happens
- with unlimited A and P in case of 1/3 :-)
- * fdiv will calculate 1 more digits than required (determined by
+ 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.
+ * 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
+ the value of F, the higher value will be used instead of F.
+ This is to limit the digits (A) of the result (just consider what would
+ happen with unlimited A and P in the case of 1/3 :-)
+ * fdiv will calculate (at least) 4 more digits than required (determined by
A, P or F), and, if F is not used, round the result
- (this will still fail in case of a result like 0.12345000000001 with A
+ (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 modi:
+ * Thus you can have the math done by on Math::Big* class in three modes:
+ 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 exception to guard
+ will round the result, with fdiv() and fsqrt() as exceptions to guard
against overflows. You must explicitely call bround(), bfround() or
- round() (the latter with with parameters).
- Note: Once you rounded a number, the settings will 'stick' on it and
- 'infect' all other numbers engaged in math operations with it, since
+ 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
local settings have the highest precedence. So, to get SaferRound[tm],
use a copy() before rounding like this:
# copy would have been 1210!
+ round after each op:
- After each single operation (except for testing like is_zero()) the
- method round() is called and the result appropriately rounded. By
+ After each single operation (except for testing like is_zero()), the
+ method round() is called and the result is rounded appropriately. By
setting proper values for A and P, you can have all-the-same-A or
- all-the-same-P modi. F.i. Math::Current might set A to undef, and P
- to -2, globally.
+ all-the-same-P modes. For example, Math::Currency might set A to undef,
+ and P to -2, globally.
- ?Maybe an extra option, that forbids local A & P settings would be in order,
- ?so that intermidiate rounding does not 'poison' further math?
+ ?Maybe an extra option that forbids local A & P settings would be in order,
+ ?so that intermediate rounding does not 'poison' further math?
=item Overriding globals
* you will be able to give A, P and R as an argument to all the calculation
- routines, the second parameter is A, the third one is P, and the fourth is
- R (shift place by one for binary operations like add). P is used only if
- the first one (A) is undefined. These three parameters override the
- globals in the order detailed as follows, aka the first defined value
+ routines; the second parameter is A, the third one is P, and the fourth is
+ R (shift right by one for binary operations like badd). P is used only if
+ the first parameter (A) is undefined. These three parameters override the
+ globals in the order detailed as follows, i.e. the first defined value
wins:
- (local: per object, global: globally default, parameter: argument to sub)
+ (local: per object, global: global default, parameter: argument to sub)
+ parameter A
+ parameter P
+ local A (if defined on both of the operands: smaller one is taken)
- + local P (if defined on both of the operands: smaller one is taken)
+ + local P (if defined on both of the operands: bigger one is taken)
+ global A
+ global P
+ global F
- * fsqrt() will hand it's arguments to fdiv(), as it used to, only now for two
+ * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two
arguments (A and P) instead of one
=item Local settings
* You can set A and P locally by using $x->accuracy() and $x->precision()
and thus force different A and P for different objects/numbers.
- * Setting A or P this way immidiately rounds $x to the new value.
+ * Setting A or P this way immediately rounds $x to the new value.
+ * $x->accuracy() clears $x->precision(), and vice versa.
=item Rounding
- * the rounding routines will use the respective global or local settings
+ * the rounding routines will use the respective global or local settings.
fround()/bround() is for accuracy rounding, while ffround()/bfround()
is for precision
* the two rounding functions take as the second parameter one of the
following rounding modes (R):
'even', 'odd', '+inf', '-inf', 'zero', 'trunc'
* you can set and get the global R by using Math::SomeClass->round_mode()
- or by setting $Math::SomeClass::rnd_mode
+ or by setting $Math::SomeClass::round_mode
* after each operation, $result->round() is called, and the result may
- eventually be rounded (that is, if A or P were set either local, global
- or as parameter to the operation)
- * to manually round a number, call $x->round($A,$P,$rnd_mode);
- This will round the number by using the appropriate rounding function
+ 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);
+ this will round the number by using the appropriate rounding function
and then normalize it.
- * rounding does modify the local settings of the number, so that
+ * rounding modifies the local settings of the number:
$x = Math::BigFloat->new(123.456);
$x->accuracy(5);
=head1 INTERNALS
-The actual numbers are stored as unsigned big integers, and math with them
-done (by default) by a module called Math::BigInt::Calc. This is equivalent to:
+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<< $x->{sign}; >>.
- use Math::BigInt lib => 'calc';
+=head2 MATH LIBRARY
+
+Math with the numbers is done (by default) by a module called
+Math::BigInt::Calc. This is equivalent to saying:
+
+ use Math::BigInt lib => 'Calc';
You can change this by using:
use Math::BigInt lib => 'BitVect';
-('Math::BitInt::BitVect' works, too.)
+The following would first try to find Math::BigInt::Foo, then
+Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
+
+ use Math::BigInt lib => 'Foo,Math::BigInt::Bar';
+
+Calc.pm uses as internal format an array of elements of some decimal base
+(usually 1e5 or 1e7) with the least significant digit first, while BitVect.pm
+uses a bit vector of base 2, most significant bit first. Other modules might
+use even different means of representing the numbers. See the respective
+module documentation for further details.
-Calc.pm uses as internal format an array of elements of base 100000 digits
-with the least significant digit first, BitVect.pm uses a bit vector of base 2,
-most significant bit first.
+=head2 SIGN
-The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to
-represent the result when input arguments are not numbers, as well as
-the result of dividing by zero. '+inf' or '-inf' represent infinity.
+The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
-You sould neither care 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}; >>.
+A sign of 'NaN' is used to represent the result when input arguments are not
+numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
+minus infinity. You will get '+inf' when dividing a positive number by 0, and
+'-inf' when dividing any negative number by 0.
=head2 mantissa(), exponent() and parts()
$y = $m * ( 10 ** $e );
print "ok\n" if $x == $y;
-C<($m,$e) = $x->parts()> is just a shortcut that gives you both of them in one
-go. Both the returned mantissa and exponent do have a sign.
+C<< ($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 where it will be
-NaN and for $x == 0, then it will be 1 (to be compatible with Math::BigFlaot's
-internal representation of a zero as C<0E1>).
+Currently, for BigInts C<$e> will be always 0, except for NaN, +inf and -inf,
+where it will be NaN; and for $x == 0, where it will be 1
+(to be compatible with Math::BigFloat's internal representation of a zero as
+C<0E1>).
C<$m> will always be a copy of the original number. The relation between $e
-and $m might change in the future, but will be always equivalent in a
+and $m might change in the future, but will always be equivalent in a
numerical sense, e.g. $m might get minimized.
=head1 EXAMPLES
- use Math::BigInt qw(bstr bint);
- $x = bstr("1234") # string "1234"
+ use Math::BigInt;
+
+ sub bint { Math::BigInt->new(shift); }
+
+ $x = Math::BigInt->bstr("1234") # string "1234"
$x = "$x"; # same as bstr()
- $x = bneg("1234") # Bigint "-1234"
$x = Math::BigInt->bneg("1234"); # Bigint "-1234"
$x = Math::BigInt->babs("-12345"); # Bigint "12345"
$x = Math::BigInt->bnorm("-0 00"); # BigInt "0"
$x = $x + 5 / 2; # BigInt "3"
$x = $x ** 3; # BigInt "27"
$x *= 2; # BigInt "54"
- $x = new Math::BigInt; # BigInt "0"
+ $x = Math::BigInt->new(0); # BigInt "0"
$x--; # BigInt "-1"
$x = Math::BigInt->badd(4,5) # BigInt "9"
- $x = Math::BigInt::badd(4,5) # BigInt "9"
print $x->bsstr(); # 9e+0
Examples for rounding:
$x = Math::BigFloat->new(123.4567);
$y = Math::BigFloat->new(123.456789);
- $Math::BigFloat::accuracy = 4; # no more A than 4
+ Math::BigFloat->accuracy(4); # no more A than 4
ok ($x->copy()->fround(),123.4); # even rounding
print $x->copy()->fround(),"\n"; # 123.4
Math::BigFloat->round_mode('odd'); # round to odd
print $x->copy()->fround(),"\n"; # 123.5
- $Math::BigFloat::accuracy = 5; # no more A than 5
+ Math::BigFloat->accuracy(5); # no more A than 5
Math::BigFloat->round_mode('odd'); # round to odd
print $x->copy()->fround(),"\n"; # 123.46
$y = $x->copy()->fround(4),"\n"; # A = 4: 123.4
print "$y, ",$y->accuracy(),"\n"; # 123.4, 4
- $Math::BigFloat::accuracy = undef; # A not important
- $Math::BigFloat::precision = 2; # P important
- print $x->copy()->bnorm(),"\n"; # 123.46
- print $x->copy()->fround(),"\n"; # 123.46
+ Math::BigFloat->accuracy(undef); # A not important now
+ Math::BigFloat->precision(2); # P important
+ print $x->copy()->bnorm(),"\n"; # 123.46
+ print $x->copy()->fround(),"\n"; # 123.46
+
+Examples for converting:
+
+ my $x = Math::BigInt->new('0b1'.'01' x 123);
+ print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n";
=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
+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,
$x = 1234567890123456789012345678901234567890
+ 123456789123456789;
- $x = '1234567890123456789012345678901234567890'
+ $y = '1234567890123456789012345678901234567890'
+ '123456789123456789';
-do both not work. You need a explicit Math::BigInt->new() around one of them.
+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;
+
+ $x = Math::BigInt->new('1234567889123456789123456789123456789');
+
+Without the quotes Perl would convert the large number to a floating point
+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
must be made in the second case. For long numbers, the copy can eat up to 20%
-of the work (in case of addition/subtraction, less for
+of the work (in the case of addition/subtraction, less for
multiplication/division). If $y is very small compared to $x, the form
$x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes
more time then the actual addition.
-With a technic called copy-on-write the cost of copying with overload could
-be minimized or even completely avoided. This is currently not implemented.
+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.
+
+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 new version of this module is slower on new(), bstr() and numify(). 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.
+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 more benchmark results see http://bloodgate.com/perl/benchmarks.html
+If you find the Calc module to slow, try to install any of the replacement
+modules and see if they help you.
-=head2 Replacing the math library
+=head2 Alternative math libraries
You can use an alternative library to drive Math::BigInt via:
use Math::BigInt lib => 'Module';
-The default is called Math::BigInt::Calc and is a pure-perl base 100,000
-math package that consist of the standard routine present in earlier versions
-of Math::BigInt.
+See L<MATH LIBRARY> for more information.
-There are also Math::BigInt::Scalar (primarily for testing) and
-Math::BigInt::BitVect, these and others can be found via
-L<http://search.cpan.org/>:
+For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>.
- use Math::BigInt lib => 'BitVect';
+=head2 SUBCLASSING
+
+=head1 Subclassing Math::BigInt
+
+The basic design of Math::BigInt allows simple subclasses with very little
+work, as long as a few simple rules are followed:
+
+=over 2
+
+=item *
+
+The public API must remain consistent, i.e. if a sub-class is overloading
+addition, the sub-class must use the same name, in this case badd(). The
+reason for this is that Math::BigInt is optimized to call the object methods
+directly.
+
+=item *
+
+The private object hash keys like C<$x->{sign}> may not be changed, but
+additional keys can be added, like C<$x->{_custom}>.
+
+=item *
+
+Accessor functions are available for all existing object hash keys and should
+be used instead of directly accessing the internal hash keys. The reason for
+this is that Math::BigInt itself has a pluggable interface which permits it
+to support different storage methods.
+
+=back
+
+More complex sub-classes may have to replicate more of the logic internal of
+Math::BigInt if they need to change more basic behaviors. A subclass that
+needs to merely change the output only needs to overload C<bstr()>.
+
+All other object methods and overloaded functions can be directly inherited
+from the parent class.
+
+At the very minimum, any subclass will need to provide it's own C<new()> and can
+store additional hash keys in the object. There are also some package globals
+that must be defined, e.g.:
+
+ # Globals
+ $accuracy = undef;
+ $precision = -2; # round to 2 decimal places
+ $round_mode = 'even';
+ $div_scale = 40;
+
+Additionally, you might want to provide the following two globals to allow
+auto-upgrading and auto-downgrading to work correctly:
+
+ $upgrade = undef;
+ $downgrade = undef;
+
+This allows Math::BigInt to correctly retrieve package globals from the
+subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or
+t/Math/BigFloat/SubClass.pm completely functional subclass examples.
+
+Don't forget to
+
+ use overload;
+
+in your subclass to automatically inherit the overloading from the parent. If
+you like, you can change part of the overloading, look at Math::String for an
+example.
+
+=head1 UPGRADING
+
+When used like this:
+
+ use Math::BigInt upgrade => 'Foo::Bar';
+
+certain operations will 'upgrade' their calculation and thus the result to
+the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat:
+
+ use Math::BigInt upgrade => 'Math::BigFloat';
+
+As a shortcut, you can use the module C<bignum>:
+
+ use bignum;
- my $x = Math::BigInt->new(2);
- print $x ** (1024*1024);
+Also good for oneliners:
+
+ perl -Mbignum -le 'print 2 ** 255'
+
+This makes it possible to mix arguments of different classes (as in 2.5 + 2)
+as well es preserve accuracy (as in sqrt(3)).
+
+Beware: This feature is not fully implemented yet.
+
+=head2 Auto-upgrade
+
+The following methods upgrade themselves unconditionally; that is if upgrade
+is in effect, they will always hand up their work:
+
+=over 2
+
+=item bsqrt()
+
+=item div()
+
+=item blog()
+
+=back
+
+Beware: This list is not complete.
+
+All other methods upgrade themselves only when one (or all) of their
+arguments are of the class mentioned in $upgrade (This might change in later
+versions to a more sophisticated scheme):
=head1 BUGS
=over 2
-=item :constant and eval()
+=item Out of Memory!
Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and
C<eval()> in your code will crash with "Out of memory". This is probably an
overload/exporter bug. You can workaround by not having C<eval()>
-and ':constant' at the same time or upgrade your Perl.
+and ':constant' at the same time or upgrade your Perl to a newer version.
+
+=item Fails to load Calc on Perl prior 5.6.0
+
+Since eval(' use ...') can not be used in conjunction with ':constant', BigInt
+will fall back to eval { require ... } when loading the math lib on Perls
+prior to 5.6.0. This simple replaces '::' with '/' and thus might fail on
+filesystems using a different seperator.
=back
$y = Math::BigInt->new($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.
+
=item int()
C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a
This also works for other subclasses, like Math::String.
+It is yet unlcear whether overloaded int() should return a scalar or a BigInt.
+
+=item length
+
+The following will probably not do what you expect:
+
+ $c = Math::BigInt->new(123);
+ print $c->length(),"\n"; # prints 30
+
+It prints both the number of digits in the number and in the fraction part
+since print calls C<length()> in list context. Use something like:
+
+ print scalar $c->length(),"\n"; # prints 3
+
=item bdiv
The following will probably not do what you expect:
print $c->bdiv(10000),"\n";
-It prints both quotient and reminder since print calls C<bdiv()> in list
+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
to use
nonzero) always has the same sign as the second operand; so, for
example,
- 1 / 4 => ( 0, 1)
- 1 / -4 => (-1,-3)
- -3 / 4 => (-1, 1)
- -3 / -4 => ( 0,-3)
+ 1 / 4 => ( 0, 1)
+ 1 / -4 => (-1,-3)
+ -3 / 4 => (-1, 1)
+ -3 / -4 => ( 0,-3)
+ -11 / 2 => (-5,1)
+ 11 /-2 => (-5,-1)
As a consequence, the behavior of the operator % agrees with the
behavior of Perl's built-in % operator (as documented in the perlop
$x == ($x / $y) * $y + ($x % $y)
holds true for any $x and $y, which justifies calling the two return
-values of bdiv() the quotient and remainder.
+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.
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
system. If you need BigInt's behaving exactly like Perl's 'use integer', bug
the author to implement it ;)
+=item infinity handling
+
+Here are some examples that explain the reasons why certain results occur while
+handling infinity:
+
+The following table shows the result of the division and the remainder, so that
+the equation above holds true. Some "ordinary" cases are strewn in to show more
+clearly the reasoning:
+
+ A / B = C, R so that C * B + R = A
+ =========================================================
+ 5 / 8 = 0, 5 0 * 8 + 5 = 5
+ 0 / 8 = 0, 0 0 * 8 + 0 = 0
+ 0 / inf = 0, 0 0 * inf + 0 = 0
+ 0 /-inf = 0, 0 0 * -inf + 0 = 0
+ 5 / inf = 0, 5 0 * inf + 5 = 5
+ 5 /-inf = 0, 5 0 * -inf + 5 = 5
+ -5/ inf = 0, -5 0 * inf + -5 = -5
+ -5/-inf = 0, -5 0 * -inf + -5 = -5
+ inf/ 5 = inf, 0 inf * 5 + 0 = inf
+ -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf
+ inf/ -5 = -inf, 0 -inf * -5 + 0 = inf
+ -inf/ -5 = inf, 0 inf * -5 + 0 = -inf
+ 5/ 5 = 1, 0 1 * 5 + 0 = 5
+ -5/ -5 = 1, 0 1 * -5 + 0 = -5
+ inf/ inf = 1, 0 1 * inf + 0 = inf
+ -inf/-inf = 1, 0 1 * -inf + 0 = -inf
+ inf/-inf = -1, 0 -1 * -inf + 0 = inf
+ -inf/ inf = -1, 0 1 * -inf + 0 = -inf
+ 8/ 0 = inf, 8 inf * 0 + 8 = 8
+ inf/ 0 = inf, inf inf * 0 + inf = inf
+ 0/ 0 = NaN
+
+These cases below violate the "remainder has the sign of the second of the two
+arguments", since they wouldn't match up otherwise.
+
+ A / B = C, R so that C * B + R = A
+ ========================================================
+ -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf
+ -8/ 0 = -inf, -8 -inf * 0 + 8 = -8
+
=item Modifying and =
Beware of:
It will not do what you think, e.g. making a copy of $x. Instead it just makes
a second reference to the B<same> object and stores it in $y. Thus anything
-that modifies $x will modify $y, and vice versa.
+that modifies $x (except overloaded operators) will modify $y, and vice versa.
+Or in other words, C<=> is only safe if you modify your BigInts only via
+overloaded math. As soon as you use a method call it breaks:
$x->bmul(2);
print "$x, $y\n"; # prints '10, 10'
$y = $x->copy();
-See also the documentation in for overload.pm regarding C<=>.
+You can also chain the calls like this, this will make first a copy and then
+multiply it by 2:
+
+ $y = $x->copy()->bmul(2);
+
+See also the documentation for overload.pm regarding C<=>.
=item bpow
C<bpow()> (and the rounding functions) now modifies the first argument and
-return it, unlike the old code which left it alone and only returned the
+returns it, unlike the old code which left it alone and only returned the
result. This is to be consistent with C<badd()> etc. The first three will
modify $x, the last one won't:
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 will be gone. Stay tuned...
+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
$integer = $mbi2 / $mbf; # $mbi2->bdiv()
This is because math with overloaded operators follows the first (dominating)
-operand, this one's operation is called and returns thus the result. So,
+operand, and the operation of that is called and returns thus the result. So,
Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether
the result should be a Math::BigFloat or the second operant is one.
This section also applies to other overloaded math packages, like Math::String.
+One solution to you problem might be L<autoupgrading|upgrading>.
+
=item bsqrt()
-C<bsqrt()> works only good if the result is an big integer, e.g. the square
+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.
If you want a better approximation of the square root, then use:
$x = Math::BigFloat->new(12);
- $Math::BigFloat::precision = 0;
+ Math::BigFloat->precision(0);
Math::BigFloat->round_mode('even');
print $x->copy->bsqrt(),"\n"; # 4
- $Math::BigFloat::precision = 2;
+ Math::BigFloat->precision(2);
print $x->bsqrt(),"\n"; # 3.46
print $x->bsqrt(3),"\n"; # 3.464
+=item brsft()
+
+For negative numbers in base see also L<brsft|brsft>.
+
=back
=head1 LICENSE
=head1 SEE ALSO
-L<Math::BigFloat> and L<Math::Big>.
+L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>,
+L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
+
+The package at
+L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
+more documentation including a full version history, testcases, empty
+subclass files and benchmarks.
=head1 AUTHORS
projects / p5sagit/p5-mst-13.2.git / blobdiff