#!/usr/bin/perl -w
-# mark.biggar@TrustedSysLabs.com
-# eay@mincom.com is dead (math::BigInteger)
-# see: http://www.cypherspace.org/~adam/rsa/pureperl.html (contacted c. adam
-# on 2000/11/13 - but email is dead
-
-# todo:
-# - fully remove funky $# stuff (maybe)
-# - use integer; vs 1e7 as base
-# - speed issues (XS? Bit::Vector?)
-# - split out actual math code to Math::BigNumber
-
# 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)
# The following hash values are used:
-# value: the internal array, base 100000
+# value: unsigned int with actual value (as a Math::BigInt::Calc or similiar)
# sign : +,-,NaN,+inf,-inf
# _a : accuracy
# _p : precision
-# _cow : copy on write: number of objects that share the data (NRY)
-# Internally the numbers are stored in an array with at least 1 element, no
-# leading zero parts (except the first) and in base 100000
+# _f : flags, used by MBF to flag parts of a float as untouchable
-# USE_MUL: due to problems on certain os (os390, posix-bc) "* 1e-5" is used
-# instead of "/ 1e5" at some places, (marked with USE_MUL). But instead of
-# using the reverse only on problematic machines, I used it everytime to avoid
-# the costly comparisations. This _should_ work everywhere. Thanx Peter Prymmer
+# Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
+# underlying lib might change the reference!
package Math::BigInt;
my $class = "Math::BigInt";
+require 5.005;
-$VERSION = 1.35;
+$VERSION = '1.47';
use Exporter;
@ISA = qw( Exporter );
@EXPORT_OK = qw( bneg babs bcmp badd bmul bdiv bmod bnorm bsub
- bgcd blcm
- bround
+ bgcd blcm bround
blsft brsft band bior bxor bnot bpow bnan bzero
- bacmp bstr bsstr binc bdec bint binf bfloor bceil
+ bacmp bstr bsstr binc bdec binf bfloor bceil
is_odd is_even is_zero is_one is_nan is_inf sign
- length as_number
- trace objectify _swap
+ is_positive is_negative
+ length as_number objectify _swap
);
-
#@EXPORT = qw( );
-use vars qw/$rnd_mode $accuracy $precision $div_scale/;
+use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/;
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]); },
+'..' => \&_pointpoint,
+
'<=>' => sub { $_[2] ?
- $class->bcmp($_[1],$_[0]) :
- $class->bcmp($_[0],$_[1])},
-'cmp' => sub {
+ ref($_[0])->bcmp($_[1],$_[0]) :
+ ref($_[0])->bcmp($_[0],$_[1])},
+'cmp' => sub {
$_[2] ?
$_[1] cmp $_[0]->bstr() :
$_[0]->bstr() cmp $_[1] },
'^' => sub { my @a = ref($_[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() },
return $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(); }
;
##############################################################################
# global constants, flags and accessory
-# are NaNs ok?
-my $NaNOK=1;
-# set to 1 for tracing
-my $trace = 0;
-# constants for easier life
-my $nan = 'NaN';
-my $BASE_LEN = 5;
-my $BASE = int("1e".$BASE_LEN); # var for trying to change it to 1e7
-my $RBASE = 1e-5; # see USE_MUL
-
-# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
-$rnd_mode = 'even';
-$accuracy = undef;
-$precision = undef;
-$div_scale = 40;
+use constant MB_NEVER_ROUND => 0x0001;
+
+my $NaNOK=1; # are NaNs ok?
+my $nan = 'NaN'; # constants for easier life
+
+my $CALC = 'Math::BigInt::Calc'; # module to do low level math
+sub _core_lib () { return $CALC; } # for test suite
+
+$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
+$accuracy = undef;
+$precision = undef;
+$div_scale = 40;
+
+##############################################################################
+# the old code had $rnd_mode, so we need to support it, too
+
+$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;
+ ${"${class}::round_mode"} = $m; return $m;
+ }
+ return ${"${class}::round_mode"};
+ }
+
+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;
+ }
+ return $a; # shortcut
+ }
+
+ if (ref($x))
+ {
+ # $object->accuracy() or fallback to global
+ return $x->{_a} || ${"${class}::accuracy"};
}
- return $x->{_a};
+ return ${"${class}::accuracy"};
}
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 P
+ }
+ else
+ {
+ # set global
+ ${"${class}::precision"} = $p;
+ }
+ return $p; # shortcut
+ }
+
+ if (ref($x))
+ {
+ # $object->precision() or fallback to global
+ return $x->{_p} || ${"${class}::precision"};
}
- return $x->{_p};
+ return ${"${class}::precision"};
}
sub _scale_a
my $self = {}; bless $self,$c;
foreach my $k (keys %$x)
{
- if (ref($x->{$k}) eq 'ARRAY')
+ if ($k eq 'value')
+ {
+ $self->{value} = $CALC->_copy($x->{value});
+ }
+ elsif (ref($x->{$k}) eq 'SCALAR')
+ {
+ $self->{$k} = \${$x->{$k}};
+ }
+ elsif (ref($x->{$k}) eq 'ARRAY')
{
$self->{$k} = [ @{$x->{$k}} ];
}
sub new
{
- # create a new BigInts object from a string or another bigint object.
- # value => internal array representation
- # sign => sign (+/-), or "NaN"
+ # 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.
- trace (@_);
my $class = shift;
my $wanted = shift; # avoid numify call by not using || here
my $self = {}; bless $self, $class;
# handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]inf$/)
+ if ($wanted =~ /^[+-]?inf$/)
{
- $self->{value} = [ 0 ];
- $self->{sign} = $wanted;
+ $self->{value} = $CALC->_zero();
+ $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
- $self->{value} = $mis->{value};
- $self->{sign} = $mis->{sign};
- return $self;
- }
if (!ref $mis)
{
die "$wanted is not a number initialized to $class" if !$NaNOK;
#print "NaN 1\n";
- $self->{value} = [ 0 ];
+ $self->{value} = $CALC->_zero();
$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} = $$mis; # store sign
- $self->{value} = [ 0 ]; # for all the NaN cases
+ $self->{value} = $CALC->_zero(); # for all the NaN cases
my $e = int("$$es$$ev"); # exponent (avoid recursion)
if ($e > 0)
{
}
}
$self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0
- $self->_internal($miv) if $self->{sign} ne $nan; # as internal array
- #print "$wanted => $self->{sign} $self->{value}->[0]\n";
- # if any of the globals is set, round to them and thus store them insid $self
- $self->round($accuracy,$precision,$rnd_mode)
+ $self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/;
+ # if any of the globals is set, use them to round and store them inside $self
+ $self->round($accuracy,$precision,$round_mode)
if defined $accuracy || defined $precision;
return $self;
}
-# some shortcuts for easier life
-sub bint
- {
- # exportable version of new
- trace(@_);
- return $class->new(@_);
- }
-
sub bnan
{
# create a bigint 'NaN', if given a BigInt, set it to 'NaN'
my $c = $self; $self = {}; bless $self, $c;
}
return if $self->modify('bnan');
- $self->{value} = [ 0 ];
+ $self->{value} = $CALC->_zero();
$self->{sign} = $nan;
- trace('NaN');
return $self;
}
my $c = $self; $self = {}; bless $self, $c;
}
return if $self->modify('binf');
- $self->{value} = [ 0 ];
+ $self->{value} = $CALC->_zero();
$self->{sign} = $sign.'inf';
- trace('inf');
return $self;
}
# create a bigint '+0', if given a BigInt, set it to 0
my $self = shift;
$self = $class if !defined $self;
+
if (!ref($self))
{
my $c = $self; $self = {}; bless $self, $c;
}
return if $self->modify('bzero');
- $self->{value} = [ 0 ];
+ $self->{value} = $CALC->_zero();
$self->{sign} = '+';
- trace('0');
+ return $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;
+ }
+ return if $self->modify('bone');
+ $self->{value} = $CALC->_one();
+ $self->{sign} = $sign;
return $self;
}
# (ref to BFLOAT or num_str ) return num_str
# Convert number from internal format to scientific string format.
# internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
- trace(@_);
- my ($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
+ # e can only be positive
my $sign = 'e+';
# MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s;
return $m->bstr().$sign.$e->bstr();
sub bstr
{
- # (ref to BINT or num_str ) return num_str
- # Convert number from internal base 100000 format to string format.
- # internal format is always normalized (no leading zeros, "-0" => "+0")
- trace(@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- # my ($self,$x) = objectify(1,@_);
-
- return $x->{sign} if $x->{sign} !~ /^[+-]$/;
- my $ar = $x->{value} || return $nan; # should not happen
- my $es = "";
- $es = $x->{sign} if $x->{sign} eq '-'; # get sign, but not '+'
- my $l = scalar @$ar; # number of parts
- return $nan if $l < 1; # should not happen
- # handle first one different to strip leading zeros from it (there are no
- # leading zero parts in internal representation)
- $l --; $es .= $ar->[$l]; $l--;
- # Interestingly, the pre-padd method uses more time
- # the old grep variant takes longer (14 to 10 sec)
- while ($l >= 0)
+ # make a string from bigint object
+ my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
+ # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ if ($x->{sign} !~ /^[+-]$/)
{
- $es .= substr('0000'.$ar->[$l],-5); # fastest way I could think of
- $l--;
+ return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
+ return 'inf'; # +inf
}
- return $es;
+ my $es = ''; $es = $x->{sign} if $x->{sign} eq '-';
+ return $es.${$CALC->_str($x->{value})};
}
sub numify
{
# Make a number from a BigInt object
- # old: simple return string and let Perl's atoi() handle the rest
- # new: calc because it is faster than bstr()+atoi()
- #trace (@_);
- #my ($self,$x) = objectify(1,@_);
- #return $x->bstr(); # ref($x);
my $x = shift; $x = $class->new($x) unless ref $x;
-
- return $nan if $x->{sign} eq $nan;
- my $fac = 1; $fac = -1 if $x->{sign} eq '-';
- return $fac*$x->{value}->[0] if @{$x->{value}} == 1; # below $BASE
- my $num = 0;
- foreach (@{$x->{value}})
- {
- $num += $fac*$_; $fac *= $BASE;
- }
+ return $x->{sign} if $x->{sign} !~ /^[+-]$/;
+ my $num = $CALC->_num($x->{value});
+ return -$num if $x->{sign} eq '-';
return $num;
}
sub sign
{
# return the sign of the number: +/-/NaN
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
return $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.
my $r = shift; # round_mode, if given by caller
my @args = @_; # all 'other' arguments (0 for unary, 1 for binary ops)
- unshift @args,$self; # add 'first' argument
-
- $self = new($self) unless ref($self); # if not object, make one
+ $self = new($self) unless ref($self); # if not object, make one
+ my $c = ref($self); # find out class of argument(s)
+ unshift @args,$self; # add 'first' argument
+
+ # leave bigfloat parts alone
+ return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
- # find out class of argument to round
- my $c = ref($args[0]);
+ no strict 'refs';
# now pick $a or $p, but only if we have got "arguments"
if ((!defined $a) && (!defined $p) && (@args > 0))
{
foreach (@args)
{
- # take the defined one, or if both defined, the one that is smaller
- $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} < $p);
+ # 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 none defined, use globals (#2)
if (!defined $p)
{
- no strict 'refs';
- my $z = "$c\::accuracy"; $a = $$z;
+ my $z = "$c\::accuracy"; my $a = $$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)
+ my @params = ($self);
+ if (defined $a || defined $p)
+ {
+ $r = $r || ${"$c\::round_mode"};
+ die "Unknown round mode '$r'"
+ if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
+ push @params, ($a,$p,$r);
+ }
+ return @params;
+ }
+
+sub round
+ {
+ # round $self according to given parameters, or given second argument's
+ # parameters or global defaults
+ my $self = shift;
+
+ my @params = $self->_find_round_parameters(@_);
+ return $self->bnorm() if @params == 1; # no-op
+
# now round, by calling fround or ffround:
- if (defined $a)
+ if (defined $params[1])
{
- $self->{_a} = $a; $self->bround($a,$r);
+ $self->bround($params[1],$params[3]);
}
- elsif (defined $p)
+ else
{
- $self->{_p} = $p; $self->bfround($p,$r);
+ $self->bfround($params[2],$params[3]);
}
- return $self->bnorm();
+ return $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,@_);
+ return $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;
}
# 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,@_);
- return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0;
+
+ 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 +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';
+ }
+ # 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
+
+ # shortcut
+ my $xz = $x->is_zero();
+ my $yz = $y->is_zero();
+ return 0 if $xz && $yz; # 0 <=> 0
+ return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y
+ return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0
+
+ # post-normalized compare for internal use (honors signs)
+ if ($x->{sign} eq '+')
+ {
+ return 1 if $y->{sign} eq '-'; # 0 check handled above
+ return $CALC->_acmp($x->{value},$y->{value});
+ }
+
+ # $x->{sign} eq '-'
+ return -1 if $y->{sign} eq '+';
+ return $CALC->_acmp($y->{value},$x->{value}); # swaped
+
+ # &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0;
}
sub bacmp
# 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;
+
+ 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}) <=> 0;
}
sub badd
{
# add second arg (BINT or string) to first (BINT) (modifies first)
# return result as BINT
- trace(@_);
my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('badd');
- return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- # for round calls, make array
- my @bn = ($a,$p,$r,$y);
+ # inf and NaN handling
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
+ {
+ # NaN first
+ return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+ # inf handline
+ if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ # + and + => +, - and - => -, + and - => 0, - and + => 0
+ return $x->bzero() if $x->{sign} ne $y->{sign};
+ return $x;
+ }
+ # +-inf + something => +inf
+ # something +-inf => +-inf
+ $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
+ return $x;
+ }
+
+ my @bn = ($a,$p,$r,$y); # make array for round calls
# speed: no add for 0+y or x+0
- return $x->bnorm(@bn) if $y->is_zero(); # x+0
+ return $x->round(@bn) if $y->is_zero(); # x+0
if ($x->is_zero()) # 0+y
{
# make copy, clobbering up x
- $x->{value} = [ @{$y->{value}} ];
+ $x->{value} = $CALC->_copy($y->{value});
$x->{sign} = $y->{sign} || $nan;
return $x->round(@bn);
}
- # shortcuts
- my $xv = $x->{value};
- my $yv = $y->{value};
my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
if ($sx eq $sy)
{
- 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 = acmp ($yv,$xv); # absolute compare
+ my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare
if ($a > 0)
{
#print "swapped sub (a=$a)\n";
- &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)
{
# speedup, if equal, set result to 0
- $x->{value} = [ 0 ];
+ #print "equal sub, result = 0\n";
+ $x->{value} = $CALC->_zero();
$x->{sign} = '+';
}
else # a < 0
{
#print "unswapped sub (a=$a)\n";
- &sub($xv, $yv); # absolute sub
+ $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
$x->{sign} = $sx;
}
}
# subtract second arg from first, modify first
my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
- trace(@_);
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);
+
+ if (!$y->is_zero()) # don't need to do anything if $y is 0
+ {
+ $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
+ $x->badd($y,$a,$p,$r); # badd does not leave internal zeros
+ $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
+ }
+ $x; # already rounded by badd()
}
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);
- trace(@_);
+ 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});
+ return $x->round($a,$p,$r);
+ }
+ elsif ($x->{sign} eq '-')
+ {
+ $x->{value} = $CALC->_dec($x->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+ return $x->round($a,$p,$r);
+ }
+ # inf, nan handling etc
+ $x->badd($self->__one(),$a,$p,$r); # does round
}
sub bdec
{
# decrement arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
- trace(@_);
+ 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
+ return $x->round($a,$p,$r);
+ }
+ # > 0
+ elsif ($x->{sign} eq '+')
+ {
+ $x->{value} = $CALC->_dec($x->{value});
+ return $x->round($a,$p,$r);
+ }
+ # inf, nan handling etc
+ $x->badd($self->__one('-'),$a,$p,$r); # does round
}
sub blcm
# (BINT or num_str, BINT or num_str) return BINT
# does not modify arguments, but returns new object
# Lowest Common Multiplicator
- trace(@_);
- my ($self,@arg) = objectify(0,@_);
- my $x = $self->new(shift @arg);
- while (@arg) { $x = _lcm($x,shift @arg); }
+ my $y = shift; my ($x);
+ if (ref($y))
+ {
+ $x = $y->copy();
+ }
+ else
+ {
+ $x = $class->new($y);
+ }
+ while (@_) { $x = __lcm($x,shift); }
$x;
}
# (BINT or num_str, BINT or num_str) return BINT
# does not modify arguments, but returns new object
# GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff)
- trace(@_);
-
- my ($self,@arg) = objectify(0,@_);
- my $x = $self->new(shift @arg);
- while (@arg)
- {
- #$x = _gcd($x,shift @arg); last if $x->is_one(); # new fast, but is slower
- $x = _gcd_old($x,shift @arg); last if $x->is_one(); # old, slow, but faster
- }
- $x;
- }
-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];
+ 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 = $self->new($y) if !ref($y);
+ next if $y->is_zero();
+ return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
+ $x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one();
+ }
+ }
+ else
+ {
+ while (@_)
+ {
+ $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 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(); $x->bdec(); # was: bsub(-1,$x);, time it someday
+ return $x->round($a,$p,$r);
}
sub is_zero
{
# return true if arg (BINT or num_str) is zero (array '+', '0')
- #my ($self,$x) = objectify(1,@_);
- #trace(@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- return (@{$x->{value}} == 1) && ($x->{sign} eq '+')
- && ($x->{value}->[0] == 0);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
+ $CALC->_is_zero($x->{value});
}
sub is_nan
{
# return true if arg (BINT or num_str) is NaN
- #my ($self,$x) = objectify(1,@_);
- #trace(@_);
- 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;
+ return 0;
}
sub is_inf
{
# return true if arg (BINT or num_str) is +-inf
- #my ($self,$x) = objectify(1,@_);
- #trace(@_);
- 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 0 if $sign !~ /^([+-]|)$/;
+
+ if ($sign eq '')
+ {
+ return 1 if ($x->{sign} =~ /^[+-]inf$/);
+ return 0;
+ }
+ $sign = quotemeta($sign.'inf');
+ return 1 if ($x->{sign} =~ /^$sign$/);
+ return 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 || '+'; #$_[2] || '+';
- return (@{$x->{value}} == 1) && ($x->{sign} eq $sign)
- && ($x->{value}->[0] == 1);
+ # 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 '-';
+
+ return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
+ return $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,@_);
- return (($x->{sign} ne $nan) && ($x->{value}->[0] & 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} !~ /^[+-]$/; # NaN & +-inf aren't
+ return $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,@_);
- return (($x->{sign} ne $nan) && (!($x->{value}->[0] & 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} !~ /^[+-]$/; # NaN & +-inf aren't
+ return $CALC->_is_even($x->{value});
}
+sub is_positive
+ {
+ # return true when arg (BINT or num_str) is positive (>= 0)
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return 1 if $x->{sign} =~ /^\+/;
+ return 0;
+ }
+
+sub is_negative
+ {
+ # return true when arg (BINT or num_str) is negative (< 0)
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return 1 if ($x->{sign} =~ /^-/);
+ return 0;
+ }
+
+###############################################################################
+
sub bmul
{
# 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,@_);
- #print "$self bmul $x ",ref($x)," $y ",ref($y),"\n";
- trace(@_);
+
return $x if $x->modify('bmul');
return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+ # handle result = 0
+ return $x if $x->is_zero();
+ return $x->bzero() if $y->is_zero();
+ # inf handling
+ if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+ {
+ # 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('-');
+ }
- mul($x,$y); # do actual math
+ $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
+
+ $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
return $x->round($a,$p,$r,$y);
}
+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 == -inf / -inf == 1, remainder is 0 (A / A = 1, remainder 0)
+ if (($x->{sign} eq $y->{sign}) &&
+ ($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return wantarray ? ($x->bone(),$self->bzero()) : $x->bone();
+ }
+ # +inf / -inf == -inf / +inf == -1, remainder 0
+ if (($x->{sign} ne $y->{sign}) &&
+ ($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return wantarray ? ($x->bone('-'),$self->bzero()) : $x->bone('-');
+ }
+ # x / +-inf => 0, remainder x (works even if x == 0)
+ if ($y->{sign} =~ /^[+-]inf$/)
+ {
+ my $t = $x->copy(); # binf 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)
- trace(@_);
my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('bdiv');
- # NaN?
- return wantarray ? ($x->bnan(),bnan()) : $x->bnan()
- if ($x->{sign} eq $nan || $y->{sign} eq $nan || $y->is_zero());
+ return $self->_div_inf($x,$y)
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
# 0 / something
return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero();
# Is $x in the interval [0, $y) ?
- my $cmp = acmp($x->{value},$y->{value});
+ my $cmp = $CALC->_acmp($x->{value},$y->{value});
if (($cmp < 0) and ($x->{sign} eq $y->{sign}))
{
return $x->bzero() unless wantarray;
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());
}
# 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->{value}} == 1) && ($y->{value}->[0] == 1))
+ if (($y == 1) || ($y == -1)) # slow!
{
return wantarray ? ($x,$self->bzero()) : $x;
}
# call div here
my $rem = $self->bzero();
- $rem->{sign} = $y->{sign};
- ($x->{value},$rem->{value}) = div($x->{value},$y->{value});
- # do not leave rest "-0";
- $rem->{sign} = '+' if (@{$rem->{value}} == 1) && ($rem->{value}->[0] == 0);
- if (($x->{sign} eq '-') and (!$rem->is_zero()))
- {
- $x->bdec();
- }
+ ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
+ # do not leave result "-0";
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value});
$x->round($a,$p,$r,$y);
+
if (wantarray)
{
- $rem->round($a,$p,$r,$x,$y);
- return ($x,$y-$rem) if $x->{sign} eq '-'; # was $x,$rem
+ 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
+ }
+ $rem->round($a,$p,$r,$x,$y);
return ($x,$rem);
}
return $x;
}
+sub bmod
+ {
+ # modulus (or remainder)
+ # (BINT or num_str, BINT or num_str) return BINT
+ my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ return $x if $x->modify('bmod');
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
+ {
+ my ($d,$r) = $self->_div_inf($x,$y);
+ return $r;
+ }
+
+ if ($CALC->can('_mod'))
+ {
+ # calc new sign and in case $y == +/- 1, return $x
+ $x->{value} = $CALC->_mod($x->{value},$y->{value});
+ my $xsign = $x->{sign};
+ if (!$CALC->_is_zero($x->{value}))
+ {
+ $x->{sign} = $y->{sign};
+ $x = $y-$x if $xsign ne $y->{sign}; # one of them '-'
+ }
+ else
+ {
+ $x->{sign} = '+'; # dont leave -0
+ }
+ }
+ else
+ {
+ $x = (&bdiv($self,$x,$y))[1]; # slow way
+ }
+ $x->bround($a,$p,$r);
+ }
+
sub bpow
{
# (BINT or num_str, BINT or num_str) return BINT
# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
# modifies first argument
- #trace(@_);
my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('bpow');
+ 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->__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)
+ #if ($x->{sign} eq '-' && @{$x->{value}} == 1 && $x->{value}->[0] == 1)
+ if ($x->{sign} eq '-' && $CALC->_is_one($x->{value}))
{
# if $x == -1 and odd/even y => +1/-1
- return $y->is_odd() ? $x : $x->_set(1); # $x->babs() would work to
- # my Casio FX-5500L has here a bug, -1 ** 2 is -1, but -1 * -1 is 1 LOL
+ return $y->is_odd() ? $x : $x->babs();
+ # my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1;
}
- # shortcut for $x ** 2
- if ($y->{sign} eq '+' && @{$y->{value}} == 1 && $y->{value}->[0] == 2)
- {
- return $x->bmul($x)->bround($a,$p,$r);
- }
- # 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)
- # tels: 10**x is special (actually 100**x etc is special, too) but not here
- #if ((@{$x->{value}} == 1) && ($x->{value}->[0] == 10))
- # {
- # # 10**2
- # my $yi = int($y); my $yi5 = int($yi/5);
- # $x->{value} = [];
- # my $v = $x->{value};
- # if ($yi5 > 0)
- # {
- # # $x->{value}->[$yi5-1] = 0; # pre-padd array (no use)
- # for (my $i = 0; $i < $yi5; $i++)
- # {
- # $v->[$i] = 0;
- # }
- # }
- # push @{$v}, int( '1'.'0' x ($yi % 5));
- # if ($x->{sign} eq '-')
- # {
- # $x->{sign} = $y->is_odd() ? '-' : '+'; # -10**2 = 100, -10**3 = -1000
- # }
- # return $x;
- # }
-
- # based on the assumption that shifting in base 10 is fast, and that bpow()
- # 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), stripping them
- # out of the multiplication, and add $count * $y zeros afterwards:
- # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6
- 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;
- }
-
- my $pow2 = $self->_one();
+ if ($CALC->can('_pow'))
+ {
+ $x->{value} = $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);
+ my $two = $self->new(2);
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); }
+ $pow2->bmul($x) if $y1->is_odd();
+ $y1->bdiv($two);
+ $x->bmul($x);
}
- #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";
+ $x->bmul($pow2) unless $pow2->is_one();
return $x->round($a,$p,$r);
}
return $x if $x->modify('blsft');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- $n = 2 if !defined $n; return $x if $n == 0;
- return $x->bnan() if $n < 0 || $y->{sign} eq '-';
- if ($n != 10)
+ $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
+
+ my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft');
+ if (defined $t)
{
- $x->bmul( $self->bpow($n, $y) );
+ $x->{value} = $t; return $x;
}
- 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;
+ # fallback
+ return $x->bmul( $self->bpow($n, $y) );
}
sub brsft
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- if ($n != 10)
+
+ my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft');
+ if (defined $t)
{
- 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));
+ $x->{value} = $t; return $x;
}
- return $x;
+ # fallback
+ return scalar bdiv($x, $self->bpow($n, $y));
}
sub band
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x & y
- trace(@_);
- my ($self,$x,$y) = objectify(2,@_);
+ my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('band');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
return $x->bzero() if $y->is_zero();
- my $r = $self->bzero(); my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x10000);
- my $y1 = copy(ref($x),$y); # make copy
- while (!$x->is_zero() && !$y1->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 '-';
+
+ if ($CALC->can('_and') && $sx == 1 && $sy == 1)
{
- ($x, $xr) = bdiv($x, $x10000);
+ $x->{value} = $CALC->_and($x->{value},$y->{value});
+ return $x->round($a,$p,$r);
+ }
+
+ my $m = new Math::BigInt 1; my ($xr,$yr);
+ my $x10000 = new Math::BigInt (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);
- $r->badd( bmul( new Math::BigInt ( $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);
}
- $x = $r;
+ $x->bneg() if $sign;
+ return $x->round($a,$p,$r);
}
sub bior
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x | y
- trace(@_);
- my ($self,$x,$y) = objectify(2,@_);
+ my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('bior');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
return $x if $y->is_zero();
- my $r = $self->bzero(); my $m = new Math::BigInt 1; my ($xr,$yr);
+
+ 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)
+ {
+ $x->{value} = $CALC->_or($x->{value},$y->{value});
+ return $x->round($a,$p,$r);
+ }
+
+ my $m = new Math::BigInt 1; my ($xr,$yr);
my $x10000 = new Math::BigInt (0x10000);
- my $y1 = copy(ref($x),$y); # make copy
- while (!$x->is_zero() || !$y1->is_zero())
+ 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())
{
- ($x, $xr) = bdiv($x,$x10000);
+ ($x1, $xr) = bdiv($x1,$x10000);
($y1, $yr) = bdiv($y1,$x10000);
- $r->badd( bmul( new Math::BigInt ( $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);
}
- $x = $r;
+ $x->bneg() if $sign;
+ return $x->round($a,$p,$r);
}
sub bxor
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x ^ y
- my ($self,$x,$y) = objectify(2,@_);
+ my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('bxor');
- return $x->bnan() if ($x->{sign} eq $nan || $y->{sign} eq $nan);
+ return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
return $x if $y->is_zero();
return $x->bzero() if $x == $y; # shortcut
- my $r = $self->bzero(); my $m = new Math::BigInt 1; my ($xr,$yr);
+
+ 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)
+ {
+ $x->{value} = $CALC->_xor($x->{value},$y->{value});
+ return $x->round($a,$p,$r);
+ }
+
+ my $m = new Math::BigInt 1; my ($xr,$yr);
my $x10000 = new Math::BigInt (0x10000);
my $y1 = copy(ref($x),$y); # make copy
- while (!$x->is_zero() || !$y1->is_zero())
+ $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())
{
- ($x, $xr) = bdiv($x, $x10000);
+ ($x1, $xr) = bdiv($x1, $x10000);
($y1, $yr) = bdiv($y1, $x10000);
- $r->badd( bmul( new Math::BigInt ( $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);
}
- $x = $r;
+ $x->bneg() if $sign;
+ return $x->round($a,$p,$r);
}
sub length
{
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return (_digits($x->{value}), 0) if wantarray;
- _digits($x->{value});
+ my $e = $CALC->_len($x->{value});
+ return wantarray ? ($e,0) : $e;
}
sub digit
{
- # return the nth digit, negative values count backward
+ # return the nth decimal digit, negative values count backward, 0 is right
my $x = shift;
my $n = shift || 0;
- my $len = $x->length();
-
- $n = $len+$n if $n < 0; # -1 last, -2 second-to-last
- $n = abs($n); # if negatives are to big
- $len--; $n = $len if $n > $len; # n to big?
-
- my $elem = int($n / 5); # which array element
- my $digit = $n % 5; # which digit in this element
- $elem = '0000'.$x->{value}->[$elem]; # get element padded with 0's
- return substr($elem,-$digit-1,1);
+ return $CALC->_digit($x->{value},$n);
}
sub _trailing_zeros
my $x = shift;
$x = $class->new($x) unless ref $x;
- return 0 if $x->is_zero() || $x->is_nan();
- # check each array elem in _m for having 0 at end as long as elem == 0
- # Upon finding a elem != 0, stop
- my $zeros = 0; my $elem;
- foreach my $e (@{$x->{value}})
- {
- if ($e != 0)
- {
- $elem = "$e"; # preserve x
- $elem =~ s/.*?(0*$)/$1/; # strip anything not zero
- $zeros *= 5; # elems * 5
- $zeros += CORE::length($elem); # count trailing zeros
- last; # early out
- }
- $zeros ++; # real else branch: 50% slower!
- }
- return $zeros;
+ 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 representation:
+ my $es = "$x"; $es =~ /([0]*)$/;
+
+ return 0 if !defined $1; # no zeros
+ return CORE::length("$1"); # as string, not as +0!
}
sub bsqrt
{
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
return $x->bnan() if $x->{sign} =~ /\-|$nan/; # -x or NaN => NaN
return $x->bzero() if $x->is_zero(); # 0 => 0
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();
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} !~ /^[+-]$/)
+ {
+ my $s = $x->{sign}; $s =~ s/^[+]//;
+ return $self->new($s); # +inf => inf
+ }
my $m = $x->copy();
# that's inefficient
my $zeros = $m->_trailing_zeros();
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
# no-op for BigInts if $n <= 0
- return $x if $scale <= 0;
+ if ($scale <= 0)
+ {
+ $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
{
my $x = shift;
my $pad = shift;
+ my $xs = shift;
my $len = $x->length();
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";
- # old, slow way checking string for non-zero characters
+
+ # 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;
-
- # faster way checking array contents; it is actually not faster (even in a
- # rounding-only-shoutout, so I leave the simpler code in)
- #my $rem = $follow % 5; my $div = $follow / 5; my $v = $x->{value};
- # pad with zeros and extract
- #print "last part : ",'00000'.$v->[$div]," $rem = '";
- #print substr('00000'.$v->[$div],-$rem,5),"'\n";
- #my $r1 = substr ('00000'.$v->[$div],-$rem,5);
- #print "$r1\n";
- #return 1 if $r1 =~ /[^0]/;
- #
- #for (my $j = $div-1; $j >= 0; $j --)
- # {
- # #print "part $v->[$j]\n";
- # return 1 if $v->[$j] != 0;
- # }
- #return 0;
}
sub fround
# 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,$rnd_mode,@_);
+ my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_);
return $x if !defined $scale; # no-op
# 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;
+ return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero() || $scale == 0;
# we have fewer digits than we want to scale to
my $len = $x->length();
- # print "$len $scale\n";
- return $x if $len < abs($scale);
+ # print "$scale $len\n";
+ # scale < 0, but > -len (not >=!)
+ if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
+ {
+ $x->{_a} = $scale if !defined $x->{_a}; # if not yet defined overwrite
+ 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;
- $digit_round = '0'; $digit_round = $x->digit($pad) if $pad < $len;
- $digit_after = '0'; $digit_after = $x->digit($pad-1) if $pad > 0;
- # print "r $x: pos:$pad l:$len s:$scale r:$digit_round a:$digit_after m: $mode\n";
+ $pad = abs($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;
+
+ # print "pad $pad pl $pl scale $scale len $len\n";
+ # 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 $pad > 0;
+
+ # print "$pad $pl $$xs dr $digit_round da $digit_after\n";
# in case of 01234 we round down, for 6789 up, and only in case 5 we look
# closer at the remaining digits of the original $x, remember decision
($digit_after =~ /[01234]/) || # round down anyway,
# 6789 => round up
($digit_after eq '5') && # not 5000...0000
- ($x->_scan_for_nonzero($pad) == 0) &&
+ ($x->_scan_for_nonzero($pad,$xs) == 0) &&
(
($mode eq 'even') && ($digit_round =~ /[24680]/) ||
($mode eq 'odd') && ($digit_round =~ /[13579]/) ||
# this is triggering warnings, and buggy for $scale < 0
#if (-$scale != $len)
{
- # split mantissa at $scale and then pad with zeros
- my $s5 = int($pad / 5);
- my $i = 0;
- while ($i < $s5)
+ # old code, depend on internal representation
+ # split mantissa at $pad and then pad with zeros
+ #my $s5 = int($pad / 5);
+ #my $i = 0;
+ #while ($i < $s5)
+ # {
+ # $x->{value}->[$i++] = 0; # replace with 5 x 0
+ # }
+ #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0
+ #my $rem = $pad % 5; # so much left over
+ #if ($rem > 0)
+ # {
+ # #print "remainder $rem\n";
+ ## #print "elem $x->{value}->[$s5]\n";
+ # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0'
+ # }
+ #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5'
+ #print ${$CALC->_str($pad->{value})}," $len\n";
+ if (($pad > 0) && ($pad <= $len))
{
- $x->{value}->[$i++] = 0; # replace with 5 x 0
+ substr($$xs,-$pad,$pad) = '0' x $pad;
+ $x->{value} = $CALC->_new($xs); # put back in
}
- $x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0
- my $rem = $pad % 5; # so much left over
- if ($rem > 0)
+ elsif ($pad > $len)
{
- #print "remainder $rem\n";
- #print "elem $x->{value}->[$s5]\n";
- substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0'
+ $x->bzero(); # round to '0'
}
- $x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5'
+ # print "res $pad $len $x $$xs\n";
}
+ # 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?
{
+ #print " $pad => ";
$pad = $len if $scale < 0; # tlr: whack 0.51=>1.0
# modify $x in place, undef, undef to avoid rounding
- $x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad),
- undef,undef );
# str creation much faster than 10 ** something
+ #print " $pad, $x => ";
+ $x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad) );
+ #print "$x\n";
+ # increment string in place, to avoid dec=>hex for the '1000...000'
+ # $xs ...blah foo
+ }
+ # to here:
+ #$x->{value} = $CALC->_new($xs); # put back in
+
+ $x->{_a} = $scale if $scale >= 0;
+ if ($scale < 0)
+ {
+ $x->{_a} = $len+$scale;
+ $x->{_a} = 0 if $scale < -$len;
}
$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,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
# not needed: return $x if $x->modify('bfloor');
-
return $x->round($a,$p,$r);
}
{
# return integer greater or equal then number, since it is already integer,
# always returns $self
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
# not needed: return $x if $x->modify('bceil');
-
return $x->round($a,$p,$r);
}
##############################################################################
# private stuff (internal use only)
-sub trace
- {
- # print out a number without using bstr (avoid deep recurse) for trace/debug
- return unless $trace;
-
- my ($package,$file,$line,$sub) = caller(1);
- print "'$sub' called from '$package' line $line:\n ";
-
- foreach my $x (@_)
- {
- if (!defined $x)
- {
- print "undef, "; next;
- }
- if (!ref($x))
- {
- print "'$x' "; next;
- }
- next if (ref($x) ne "HASH");
- print "$x->{sign} ";
- foreach (@{$x->{value}})
- {
- print "$_ ";
- }
- print ", ";
- }
- print "\n";
- }
-
-sub _set
- {
- # internal set routine to set X fast to an integer value < [+-]100000
- my $self = shift;
- my $wanted = shift || 0;
-
- $self->{sign} = $nan, return if $wanted !~ /^[+-]?[0-9]+$/;
- $self->{sign} = '-'; $self->{sign} = '+' if $wanted >= 0;
- $self->{value} = [ abs($wanted) ];
- return $self;
- }
-
-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->bone(); # $x->{value} = $CALC->_one();
+ $x->{sign} = shift || '+';
+ return $x;
}
sub _swap
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.
-
- trace(@_);
+
+ # some shortcut for the common cases
+
+ # $x->unary_op();
+ return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
+ # $x->binary_op($y);
+ #return (ref($_[1]),$_[1],$_[2]) if (@_ == 3) && ($_[0]||0 == 2)
+ # && ref($_[1]) && ref($_[2]);
+
+# print "obj '",join ("' '", @_),"'\n";
+
my $count = abs(shift || 0);
- #print caller(),"\n";
+# print "MBI ",caller(),"\n";
my @a; # resulting array
if (ref $_[0])
#print "$count\n";
$count--;
$k = shift;
+# print "$k (",ref($k),") => \n";
if (!ref($k))
{
$k = $a[0]->new($k);
# foreign object, try to convert to integer
$k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
}
+ # print "$k (",ref($k),")\n";
push @a,$k;
}
push @a,@_; # return other params, too
{
my $self = shift;
#print "import $self @_\n";
- for ( my $i = 0; $i < @_ ; $i++ )
+ my @a = @_; my $l = scalar @_; my $j = 0;
+ for ( my $i = 0; $i < $l ; $i++,$j++ )
{
- if ( $_[$i] eq ':constant' )
+ if ($_[$i] eq ':constant')
{
- # this rest causes overlord er load to step in
+ # this causes overlord er load to step in
overload::constant integer => sub { $self->new(shift) };
- splice @_, $i, 1; last;
+ splice @a, $j, 1; $j --;
+ }
+ 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;
}
}
# any non :constant stuff is handled by our parent, Exporter
# even if @_ is empty, to give it a chance
- #$self->SUPER::import(@_); # does not work
- $self->export_to_level(1,$self,@_); # need this instead
+ $self->SUPER::import(@a); # need it for subclasses
+ $self->export_to_level(1,$self,@a); # need it for MBF
+
+ # try to load core math lib
+ my @c = split /\s*,\s*/,$CALC;
+ push @c,'Calc'; # if all fail, try this
+ foreach my $lib (@c)
+ {
+ $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
+ $lib =~ s/\.pm$//;
+ if ($] < 5.6)
+ {
+ # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is
+ # used in the same script, or eval inside import().
+ (my $mod = $lib . '.pm') =~ s!::!/!g;
+ # require does not automatically :: => /, so portability problems arise
+ eval { require $mod; $lib->import( @c ); }
+ }
+ else
+ {
+ eval "use $lib @c;";
+ }
+ $CALC = $lib, last if $@ eq ''; # no error in loading lib?
+ }
}
-sub _internal
- {
- # (ref to self, ref to string) return ref to num_array
- # Convert a number from string format to internal base 100000 format.
- # Assumes normalized value as input.
- my ($s,$d) = @_;
- my $il = CORE::length($$d)-1;
- # these leaves '00000' instead of int 0 and will be corrected after any op
- $s->{value} = [ reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $$d)) ];
- $s;
- }
-
-sub _strip_zeros
- {
- # internal normalization function that strips leading zeros from the array
- # args: ref to array
- #trace(@_);
- my $s = shift;
-
- my $cnt = scalar @$s; # get count of parts
- my $i = $cnt-1;
- #print "strip: cnt $cnt i $i\n";
- # '0', '3', '4', '0', '0',
- # 0 1 2 3 4
- # cnt = 5, i = 4
- # i = 4
- # i = 3
- # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos)
- # >= 1: skip first part (this can be zero)
- while ($i > 0) { last if $s->[$i] != 0; $i--; }
- $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0
- return $s;
- }
-
-sub _from_hex
+sub __from_hex
{
# convert a (ref to) big hex string to BigInt, return undef for error
my $hs = shift;
my $x = Math::BigInt->bzero();
return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/;
- my $mul = Math::BigInt->bzero(); $mul++;
- my $x65536 = Math::BigInt->new(65536);
+ my $sign = '+'; $sign = '-' if ($$hs =~ /^-/);
- my $len = CORE::length($$hs)-2; my $sign = '+';
- if ($$hs =~ /^\-/)
+ $$hs =~ s/^[+-]//; # strip sign
+ if ($CALC->can('_from_hex'))
{
- $sign = '-'; $len--;
+ $x->{value} = $CALC->_from_hex($hs);
}
- $len = int($len/4); # 4-digit parts, w/o '0x'
- my $val; my $i = -4;
- while ($len >= 0)
+ else
{
- $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
+ # 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($$hs,$i,4),"\n";
+ $i -= 4; $len --;
+ $x += $mul * $val if $val != 0;
+ $mul *= $x65536 if $len >= 0; # skip last mul
+ }
}
- $x->{sign} = $sign if !$x->is_zero();
+ $x->{sign} = $sign if !$x->is_zero(); # no '-0'
return $x;
}
-sub _from_bin
+sub __from_bin
{
# convert a (ref to) big binary string to BigInt, return undef for error
my $bs = shift;
my $x = Math::BigInt->bzero();
- return $x->bnan() if $$bs !~ /^[\-\+]?0b[01]+$/;
+ return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/;
my $mul = Math::BigInt->bzero(); $mul++;
my $x256 = Math::BigInt->new(256);
- my $len = CORE::length($$bs)-2; my $sign = '+';
- if ($$bs =~ /^\-/)
+ my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/);
+ $$bs =~ s/^[+-]//; # strip sign
+ if ($CALC->can('_from_bin'))
{
- $sign = '-'; $len--;
+ $x->{value} = $CALC->_from_bin($bs);
}
- $len = int($len/8); # 8-digit parts, w/o '0b'
- my $val; my $i = -8;
- while ($len >= 0)
+ else
{
- $val = substr($$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($$bs,$i,16),"\n";
- $i -= 8; $len --;
- $x += $mul * $val if $val != 0;
- $mul *= $x256 if $len >= 0; # skip last mul
+ my $len = CORE::length($$bs)-2;
+ $len = int($len/8); # 8-digit parts, w/o '0b'
+ my $val; my $i = -8;
+ while ($len >= 0)
+ {
+ $val = substr($$bs,$i,8);
+ $val =~ s/^[+-]?0b// if $len == 0; # for last part only
+ #$val = oct('0b'.$val); # does not work on Perl prior to 5.6.0
+ $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8;
+ $val = ord(pack('B8',$val));
+ # print "$val ",substr($$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;
{
# (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;
- # pre-parse input
- $$x =~ s/^\s+//g; # strip white space at front
+ # strip white space at front, also extranous leading zeros
+ $$x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2'
+ $$x =~ s/^\s+//; # but this will
$$x =~ s/\s+$//g; # strip white space at end
- #$$x =~ s/\s+//g; # strip white space (no longer)
- return if $$x eq "";
- return _from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string
- return _from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string
+ # shortcut, if nothing to split, return early
+ if ($$x =~ /^[+-]?\d+$/)
+ {
+ $$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
+ return (\$sign, $x, \'', \'', \0);
+ }
- return if $$x !~ /^[\-\+]?\.?[0-9]/;
+ # invalid starting char?
+ return if $$x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
$$x =~ s/(\d)_(\d)/$1$2/g; # strip underscores between digits
$$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3
+ return __from_hex($x) if $$x =~ /^[\-\+]?0x/; # hex string
+ return __from_bin($x) if $$x =~ /^[\-\+]?0b/; # binary string
+
# 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
- #print "input: '$$x' ";
+ return if $$x =~ /[Ee].*[Ee]/; # more than one E => error
+
my ($m,$e) = split /[Ee]/,$$x;
$e = '0' if !defined $e || $e eq "";
# print "m '$m' e '$e'\n";
if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
{
$mis = $1||'+'; $miv = $2;
- #print "$mis $miv";
+ # print "$mis $miv";
# valid, existing fraction part of mantissa?
return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros
$mfv = $1;
return; # NaN, not a number
}
-sub _digits
- {
- # computer number of digits in bigint, minus the sign
- # int() because add/sub leaves sometimes strings (like '00005') instead of
- # int ('5') in this place, causing length to fail
- my $cx = shift;
-
- #print "len: ",(@$cx-1)*5+CORE::length(int($cx->[-1])),"\n";
- return (@$cx-1)*5+CORE::length(int($cx->[-1]));
- }
-
sub as_number
{
# an object might be asked to return itself as bigint on certain overloaded
# it or override with their own integer conversion routine
my $self = shift;
- return $self->copy();
+ $self->copy();
}
-##############################################################################
-# internal calculation routines
-
-sub acmp
- {
- # internal absolute post-normalized compare (ignore signs)
- # ref to array, ref to array, return <0, 0, >0
- # arrays must have at least on entry, this is not checked for
-
- my ($cx, $cy) = @_;
-
- #print "$cx $cy\n";
- my ($i,$a,$x,$y,$k);
- # calculate length based on digits, not parts
- $x = _digits($cx); $y = _digits($cy);
- # print "length: ",($x-$y),"\n";
- return $x-$y if ($x - $y); # if different in length
- #print "full compare\n";
- $i = 0; $a = 0;
- # first way takes 5.49 sec instead of 4.87, but has the early out advantage
- # so grep is slightly faster, but more unflexible. hm. $_ instead if $k
- # yields 5.6 instead of 5.5 sec huh?
- # manual way (abort if unequal, good for early ne)
- my $j = scalar @$cx - 1;
- while ($j >= 0)
- {
- # print "$cx->[$j] $cy->[$j] $a",$cx->[$j]-$cy->[$j],"\n";
- last if ($a = $cx->[$j] - $cy->[$j]); $j--;
- }
- return $a;
- # while it early aborts, it is even slower than the manual variant
- #grep { return $a if ($a = $_ - $cy->[$i++]); } @$cx;
- # grep way, go trough all (bad for early ne)
- #grep { $a = $_ - $cy->[$i++]; } @$cx;
- #return $a;
- }
-
-sub cmp
+sub as_hex
{
- # post-normalized compare for internal use (honors signs)
- # ref to array, ref to array, return < 0, 0, >0
- my ($cx,$cy,$sx,$sy) = @_;
+ # return as hex string, with prefixed 0x
+ my $x = shift; $x = $class->new($x) if !ref($x);
- #return 0 if (is0($cx,$sx) && is0($cy,$sy));
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ return '0x0' if $x->is_zero();
- if ($sx eq '+')
+ my $es = ''; my $s = '';
+ $s = $x->{sign} if $x->{sign} eq '-';
+ if ($CALC->can('_as_hex'))
{
- return 1 if $sy eq '-'; # 0 check handled above
- return acmp($cx,$cy);
+ $es = ${$CALC->_as_hex($x->{value})};
}
else
{
- # $sx eq '-'
- return -1 if ($sy eq '+');
- return acmp($cy,$cx);
- }
- return 0; # equal
- }
-
-sub add
- {
- # (ref to int_num_array, ref to int_num_array)
- # routine to add two base 1e5 numbers
- # stolen from Knuth Vol 2 Algorithm A pg 231
- # there are separate routines to add and sub as per Kunth pg 233
- # This routine clobbers up array x, but not y.
-
- my ($x,$y) = @_;
-
- # for each in Y, add Y to X and carry. If after that, something is left in
- # X, foreach in X add carry to X and then return X, carry
- # Trades one "$j++" for having to shift arrays, $j could be made integer
- # but this would impose a limit to number-length to 2**32.
- my $i; my $car = 0; my $j = 0;
- for $i (@$y)
- {
- $x->[$j] -= $BASE
- if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0;
- $j++;
- }
- while ($car != 0)
- {
- $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++;
- }
- }
-
-sub sub
- {
- # (ref to int_num_array, ref to int_num_array)
- # subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
- # subtract Y from X (X is always greater/equal!) by modifiyng x in place
- my ($sx,$sy,$s) = @_;
-
- my $car = 0; my $i; my $j = 0;
- if (!$s)
- {
- #print "case 2\n";
- for $i (@$sx)
- {
- last unless defined $sy->[$j] || $car;
- #print "x: $i y: $sy->[$j] c: $car\n";
- $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++;
- #print "x: $i y: $sy->[$j-1] c: $car\n";
- }
- # might leave leading zeros, so fix that
- _strip_zeros($sx);
- return $sx;
- }
- else
- {
- #print "case 1 (swap)\n";
- for $i (@$sx)
- {
- last unless defined $sy->[$j] || $car;
- #print "$sy->[$j] $i $car => $sx->[$j]\n";
- $sy->[$j] += $BASE
- if $car = (($sy->[$j] = $i-($sy->[$j]||0) - $car) < 0);
- #print "$sy->[$j] $i $car => $sy->[$j]\n";
- $j++;
- }
- # might leave leading zeros, so fix that
- _strip_zeros($sy);
- return $sy;
- }
- }
-
-sub mul
- {
- # (BINT, BINT) return nothing
- # multiply two numbers in internal representation
- # modifies first arg, second needs not be different from first
- my ($x,$y) = @_;
-
- $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+';
- my @prod = (); my ($prod,$car,$cty,$xi,$yi);
- my $xv = $x->{value};
- my $yv = $y->{value};
- # since multiplying $x with $x fails, make copy in this case
- $yv = [@$xv] if "$xv" eq "$yv";
- for $xi (@$xv)
- {
- $car = 0; $cty = 0;
- for $yi (@$yv)
+ my $x1 = $x->copy()->babs(); my $xr;
+ my $x100 = Math::BigInt->new (0x100);
+ while (!$x1->is_zero())
{
- $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
- $prod[$cty++] =
- $prod - ($car = int($prod * 1e-5)) * $BASE; # see USE_MUL
+ ($x1, $xr) = bdiv($x1,$x100);
+ $es .= unpack('h2',pack('C',$xr->numify()));
}
- $prod[$cty] += $car if $car; # need really to check for 0?
- $xi = shift @prod;
+ $es = reverse $es;
+ $es =~ s/^[0]+//; # strip leading zeros
+ $s .= '0x';
}
- push @$xv, @prod;
- _strip_zeros($x->{value});
- # normalize (handled last to save check for $y->is_zero()
- $x->{sign} = '+' if @$xv == 1 && $xv->[0] == 0; # not is_zero due to '-'
+ $s . $es;
}
-sub div
+sub as_bin
{
- # ref to array, ref to array, modify first array and return reminder if
- # in list context
- # does no longer handle sign
- my ($x,$yorg) = @_;
- my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1);
+ # return as binary string, with prefixed 0b
+ my $x = shift; $x = $class->new($x) if !ref($x);
- my (@d,$tmp,$q,$u2,$u1,$u0);
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ return '0b0' if $x->is_zero();
- $car = $bar = $prd = 0;
-
- my $y = [ @$yorg ];
- if (($dd = int($BASE/($y->[-1]+1))) != 1)
- {
- for $xi (@$x)
- {
- $xi = $xi * $dd + $car;
- $xi -= ($car = int($xi * $RBASE)) * $BASE; # see USE_MUL
- }
- push(@$x, $car); $car = 0;
- for $yi (@$y)
- {
- $yi = $yi * $dd + $car;
- $yi -= ($car = int($yi * $RBASE)) * $BASE; # see USE_MUL
- }
- }
- else
- {
- push(@$x, 0);
- }
- @q = (); ($v2,$v1) = @$y[-2,-1];
- $v2 = 0 unless $v2;
- while ($#$x > $#$y)
+ my $es = ''; my $s = '';
+ $s = $x->{sign} if $x->{sign} eq '-';
+ if ($CALC->can('_as_bin'))
{
- ($u2,$u1,$u0) = @$x[-3..-1];
- $u2 = 0 unless $u2;
- print "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n"
- if $v1 == 0;
- $q = (($u0 == $v1) ? 99999 : int(($u0*$BASE+$u1)/$v1));
- --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*$BASE+$u2);
- if ($q)
- {
- ($car, $bar) = (0,0);
- for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi)
- {
- $prd = $q * $y->[$yi] + $car;
- $prd -= ($car = int($prd * $RBASE)) * $BASE; # see USE_MUL
- $x->[$xi] += 1e5 if ($bar = (($x->[$xi] -= $prd + $bar) < 0));
- }
- if ($x->[-1] < $car + $bar)
- {
- $car = 0; --$q;
- for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi)
- {
- $x->[$xi] -= 1e5
- if ($car = (($x->[$xi] += $y->[$yi] + $car) > $BASE));
- }
- }
- }
- pop(@$x); unshift(@q, $q);
+ $es = ${$CALC->_as_bin($x->{value})};
}
- if (wantarray)
+ else
{
- @d = ();
- if ($dd != 1)
- {
- $car = 0;
- for $xi (reverse @$x)
- {
- $prd = $car * $BASE + $xi;
- $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL
- unshift(@d, $tmp);
- }
- }
- else
+ my $x1 = $x->copy()->babs(); my $xr;
+ my $x100 = Math::BigInt->new (0x100);
+ while (!$x1->is_zero())
{
- @d = @$x;
+ ($x1, $xr) = bdiv($x1,$x100);
+ $es .= unpack('b8',pack('C',$xr->numify()));
}
- @$x = @q;
- _strip_zeros($x);
- _strip_zeros(\@d);
- return ($x,\@d);
+ $es = reverse $es;
+ $es =~ s/^[0]+//; # strip leading zeros
+ $s .= '0b';
}
- @$x = @q;
- _strip_zeros($x);
- return $x;
+ $s . $es;
}
-sub _lcm
+##############################################################################
+# 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
return $x * $ty / bgcd($x,$ty);
}
-sub _gcd_old
+sub __gcd
{
# (BINT or num_str, BINT or num_str) return BINT
- # does modify first arg
+ # does modify both arguments
# GCD -- Euclids algorithm E, Knuth Vol 2 pg 296
- trace(@_);
-
- my $x = shift; my $ty = $class->new(shift); # preserve y
- return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan);
+ my ($x,$ty) = @_;
+
+ return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/;
while (!$ty->is_zero())
{
$x;
}
-sub _gcd
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does not modify arguments
- # GCD -- Euclids algorithm, variant L (Lehmer), Knuth Vol 3 pg 347 ff
- # unfortunately, it is slower and also seems buggy (the A=0, B=1, C=1, D=0
- # case..)
- trace(@_);
-
- my $u = $class->new(shift); my $v = $class->new(shift); # preserve u,v
- return $u->bnan() if ($u->{sign} eq $nan) || ($v->{sign} eq $nan);
-
- $u->babs(); $v->babs(); # Euclid is valid for |u| and |v|
-
- my ($U,$V,$A,$B,$C,$D,$T,$Q); # single precision variables
- my ($t); # multiprecision variables
-
- while ($v > $BASE)
- {
- #sleep 1;
- ($u,$v) = ($v,$u) if ($u < $v); # make sure that u >= v
- #print "gcd: $u $v\n";
- # step L1, initialize
- $A = 1; $B = 0; $C = 0; $D = 1;
- $U = $u->{value}->[-1]; # leading digits of u
- $V = $v->{value}->[-1]; # leading digits of v
-
- # step L2, test quotient
- if (($V + $C != 0) && ($V + $D != 0)) # div by zero => go to L4
- {
- $Q = int(($U + $A)/($V + $C)); # quotient
- #print "L1 A=$A B=$B C=$C D=$D U=$U V=$V Q=$Q\n";
- # do L3? (div by zero => go to L4)
- while ($Q == int(($U + $B)/($V + $D)))
- {
- # step L3, emulate Euclid
- #print "L3a A=$A B=$B C=$C D=$D U=$U V=$V Q=$Q\n";
- $T = $A - $Q*$C; $A = $C; $C = $T;
- $T = $B - $Q*$D; $B = $D; $D = $T;
- $T = $U - $Q*$V; $U = $V; $V = $T;
- last if ($V + $D == 0) || ($V + $C == 0); # div by zero => L4
- $Q = int(($U + $A)/($V + $C)); # quotient for next test
- #print "L3b A=$A B=$B C=$C D=$D U=$U V=$V Q=$Q\n";
- }
- }
- # step L4, multiprecision step
- # was if ($B == 0)
- # in case A = 0, B = 1, C = 0 and D = 1, this case would simple swap u & v
- # and loop endless. Not sure why this happens, Knuth does not make a
- # remark about this special case. bug?
- if (($B == 0) || (($A == 0) && ($C == 1) && ($D == 0)))
- {
- #print "L4b1: u=$u v=$v\n";
- ($u,$v) = ($v,bmod($u,$v));
- #$t = $u % $v; $u = $v->copy(); $v = $t;
- #print "L4b12: u=$u v=$v\n";
- }
- else
- {
- #print "L4b: $u $v $A $B $C $D\n";
- $t = $A*$u + $B*$v; $v *= $D; $v += $C*$u; $u = $t;
- #print "L4b2: $u $v\n";
- }
- } # back to L1
-
- return _gcd_old($u,$v) if $v != 1; # v too small
- return $v; # 1
- }
-
###############################################################################
# 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)
-use constant modify => 0;
-
-#sub modify
-# {
-# my $self = shift;
-# my $method = shift;
-# print "original $self modify by $method\n";
-# return 0; # $self;
-# }
+sub modify () { 0; }
1;
__END__
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"
+ $x = Math::BigInt->new($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
- $x->is_zero(); # return whether arg is zero or not
- $x->is_nan(); # return whether arg is NaN or not
- $x->is_one(); # return true if arg is +1
- $x->is_one('-'); # return true if arg is -1
- $x->is_odd(); # return true if odd, false for even
- $x->is_even(); # return true if even, false for odd
+ $x->is_zero(); # true if arg is +0
+ $x->is_nan(); # true if arg is NaN
+ $x->is_one(); # true if arg is +1
+ $x->is_one('-'); # true if arg is -1
+ $x->is_odd(); # true if odd, false for even
+ $x->is_even(); # true if even, false for odd
+ $x->is_positive(); # true if >= 0
+ $x->is_negative(); # true if < 0
+ $x->is_inf(sign); # true if +inf, or -inf (sign is default '+')
+
$x->bcmp($y); # compare numbers (undef,<0,=0,>0)
$x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
$x->sign(); # return the sign, either +,- or NaN
# set
$x->bzero(); # set $x to 0
$x->bnan(); # set $x to NaN
+ $x->bone(); # set $x to +1
+ $x->bone('-'); # set $x to -1
$x->bneg(); # negation
$x->babs(); # absolute value
# The following do not modify their arguments:
- bgcd(@values); # greatest common divisor
- blcm(@values); # lowest common multiplicator
-
- $x->bstr(); # normalized string
- $x->bsstr(); # normalized string in scientific notation
+ 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) = $x->length(); # length of number and length of fraction part
+ ($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 mantissa 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
+ $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
=head1 DESCRIPTION
=back
-=head2 Rounding
+=head1 ACCURACY and PRECISION
+
+Since version v1.33, Math::BigInt and Math::BigFloat have full support for
+accuracy and precision based rounding, both automatically after every
+operation as well as manually.
+
+This section describes the accuracy/precision handling in Math::Big* as it
+used to be and as it is now, complete with an explanation of all terms and
+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 documentation).
+
+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 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. 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
+dividing numbers.
+
+=head2 Rounding mode R
-Only C<bround()> is defined for BigInts, for further details of rounding see
-L<Math::BigFloat>.
+When rounding a number, different 'styles' or 'kinds'
+of rounding are possible. (Note that random rounding, as in
+Math::Round, is not implemented.)
=over 2
-=item bfround ( +$scale ) rounds to the $scale'th place left from the '.'
+=item 'trunc'
-=item bround ( +$scale ) preserves accuracy to $scale sighnificant digits counted from the left and paddes the number with zeros
+truncation invariably removes all digits following the
+rounding place, replacing them with zeros. Thus, 987.65 rounded
+to tens (P=1) becomes 980, and rounded to the fourth sigdig
+becomes 987.6 (A=4). 123.456 rounded to the second place after the
+decimal point (P=-2) becomes 123.46.
-=item bround ( -$scale ) preserves accuracy to $scale significant digits counted from the right and paddes the number with zeros.
+All other implemented styles of rounding attempt to round to the
+"nearest digit." If the digit D immediately to the right of the
+rounding place (skipping the decimal point) is greater than 5, the
+number is incremented at the rounding place (possibly causing a
+cascade of incrementation): e.g. when rounding to units, 0.9 rounds
+to 1, and -19.9 rounds to -20. If D < 5, the number is similarly
+truncated at the rounding place: e.g. when rounding to units, 0.4
+rounds to 0, and -19.4 rounds to -19.
+
+However the results of other styles of rounding differ if the
+digit immediately to the right of the rounding place (skipping the
+decimal point) is 5 and if there are no digits, or no digits other
+than 0, after that 5. In such cases:
+
+=item 'even'
+
+rounds the digit at the rounding place to 0, 2, 4, 6, or 8
+if it is not already. E.g., when rounding to the first sigdig, 0.45
+becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5.
+
+=item 'odd'
+
+rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if
+it is not already. E.g., when rounding to the first sigdig, 0.45
+becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6.
+
+=item '+inf'
+
+round to plus infinity, i.e. always round up. E.g., when
+rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5,
+and 0.4501 also becomes 0.5.
+
+=item '-inf'
+
+round to minus infinity, i.e. always round down. E.g., when
+rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6,
+but 0.4501 becomes 0.5.
+
+=item 'zero'
+
+round to zero, i.e. positive numbers down, negative ones up.
+E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55
+becomes -0.5, but 0.4501 becomes 0.5.
+
+=back
+
+The handling of A & P in MBI/MBF (the old core code shipped with Perl
+versions <= 5.7.2) is like this:
+
+=over 2
+
+=item Precision
+
+ * ffround($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 $a significant digits
+ * only fdiv() and fsqrt() take A as (optional) paramater
+ + other operations simply create the same number (fneg etc), or more (fmul)
+ of digits
+ + rounding/truncating is only done when explicitly calling one of fround
+ or ffround, and never for BigInt (not implemented)
+ * fsqrt() simply hands its accuracy argument over to fdiv.
+ * the documentation and the comment in the code indicate two different ways
+ on how fdiv() determines the maximum number of digits it should calculate,
+ and the actual code does yet another thing
+ POD:
+ max($Math::BigFloat::div_scale,length(dividend)+length(divisor))
+ Comment:
+ result has at most max(scale, length(dividend), length(divisor)) digits
+ Actual code:
+ scale = max(scale, length(dividend)-1,length(divisor)-1);
+ scale += length(divisior) - length(dividend);
+ So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3).
+ Actually, the 'difference' added to the scale is calculated from the
+ number of "significant digits" in dividend and divisor, which is derived
+ by looking at the length of the mantissa. Which is wrong, since it includes
+ the + sign (oups) and actually gets 2 for '+100' and 4 for '+101'. Oups
+ 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 remainder and $y to determine
+ wether it must round up or down.
+ ? 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
+
+This is how it works now:
+
+=over 2
+
+=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.
+ * 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 be valid, A must be > 0, P can have any value.
+ * If P is negative, this means round to the P'th place to the right of the
+ decimal point; positive values mean to the left of the decimal point.
+ P of 0 means round to integer.
+ * to find out the current global A, take $Math::SomeClass::accuracy
+ * 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
+
+=item Creating numbers
+
+ !* When you create a number, there should be a way to define its 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 immediately and also
+ stored locally with the number. 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)
+
+=item Usage
+
+ * If A or P are enabled/defined, they are used to round the result of each
+ operation according to the rules below
+ * Negative P is ignored in Math::BigInt, since BigInts never have digits
+ after the decimal point
+ * Math::BigFloat uses Math::BigInts internally, but setting A or P inside
+ Math::BigInt as globals should not tamper with the parts of a BigFloat.
+ Thus a flag is used to mark all Math::BigFloat numbers as 'never round'
+
+=item Precedence
+
+ * It only makes sense that a number has only one of A or P at a time.
+ Since you can set/get both A and P, there is a rule that will practically
+ enforce only A or P to be in effect at a time, even if both are set.
+ This is called precedence.
+ !* If two objects are involved 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.
+ * A takes precendence over P (Hint: A comes before P). If A is defined, it
+ is used, otherwise P is used. If neither of them is defined, nothing is
+ used, i.e. the result will have as many digits as it can (with an
+ exception for fdiv/fsqrt) and will not be rounded.
+ * 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 1 more digit than required (determined by
+ A, P or F), and, if F is not used, round the result
+ (this will still fail in the case of a result like 0.12345000000001 with A
+ or P of 5, but this can not be helped - or can it?)
+ * Thus you can have the math done by on Math::Big* class in three modes:
+ + never round (this is the default):
+ This is done by setting A and P to undef. No math operation
+ will round the result, with fdiv() and fsqrt() as exceptions to guard
+ against overflows. You must explicitely call bround(), bfround() or
+ 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:
+
+ $x = Math::BigFloat->new(12.34);
+ $y = Math::BigFloat->new(98.76);
+ $z = $x * $y; # 1218.6984
+ print $x->copy()->fround(3); # 12.3 (but A is now 3!)
+ $z = $x * $y; # still 1218.6984, without
+ # 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 is rounded appropriately. By
+ setting proper values for A and P, you can have all-the-same-A or
+ 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 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 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: 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)
+ + global A
+ + global P
+ + global F
+ * 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 immediately rounds $x to the new value.
+
+=item Rounding
+
+ * 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::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 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 modifies the local settings of the number:
+
+ $x = Math::BigFloat->new(123.456);
+ $x->accuracy(5);
+ $x->bround(4);
+
+ Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy()
+ will be 4 from now on.
+
+=item Default values
+
+ * R: 'even'
+ * F: 40
+ * A: undef
+ * P: undef
+
+=item Remarks
+
+ * The defaults are set up so that the new code gives the same results as
+ the old code (except in a few cases on fdiv):
+ + Both A and P are undefined and thus will not be used for rounding
+ after each operation.
+ + round() is thus a no-op, unless given extra parameters A and P
=back
-C<bfround()> does nothing in case of negative C<$scale>. Both C<bround()> and
-C<bfround()> are a no-ops for a scale of 0.
+=head1 INTERNALS
+
+The actual numbers are stored as unsigned big integers (with seperate sign).
+You should neither care about nor depend on the internal representation; it
+might change without notice. Use only method calls like C<< $x->sign(); >>
+instead relying on the internal hash keys like in C<< $x->{sign}; >>.
-All rounding functions take as a second parameter a rounding mode from one of
-the following: 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
+=head2 MATH LIBRARY
-The default is 'even'. By using C<< Math::BigInt->round_mode($rnd_mode); >>
-you can get and set the default round mode for subsequent rounding.
+Math with the numbers is done (by default) by a module called
+Math::BigInt::Calc. This is equivalent to saying:
-The second parameter to the round functions than overrides the default
-temporarily.
+ use Math::BigInt lib => 'Calc';
-=head2 Internals
+You can change this by using:
-Actual math is done in an internal format consisting of an array of
-elements of base 100000 digits with the least significant digit first.
-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.
+ use Math::BigInt lib => 'BitVect';
-You sould neither care nor depend on the internal represantation, 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}; >>.
+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, but this might change to 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.
+
+=head2 SIGN
+
+The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
+
+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
-numerical sense, e.g. $m might get minized.
-
+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);
+ use Math::BigInt qw(bstr);
+
+ sub bint { Math::BigInt->new(shift); }
+
$x = bstr("1234") # string "1234"
$x = "$x"; # same as bstr()
$x = bneg("1234") # Bigint "-1234"
$x = Math::BigInt::badd(4,5) # BigInt "9"
print $x->bsstr(); # 9e+0
+Examples for rounding:
+
+ use Math::BigFloat;
+ use Test;
+
+ $x = Math::BigFloat->new(123.4567);
+ $y = Math::BigFloat->new(123.456789);
+ $Math::BigFloat::accuracy = 4; # no more A than 4
+
+ ok ($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->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
+
+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.
-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
-constants the expression 2**100 will be calculated as floating point
-number.
+constants the expression 2**100 will be calculated as perl scalar.
Please note that strings and floating point constants are not affected,
so that
$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.
=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
+With a technique called copy-on-write, the cost of copying with overload could
be minimized or even completely avoided. This is currently not implemented.
The new version of this module is slower on new(), bstr() and numify(). Some
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.
+If you find the Calc module to slow, try to install any of the replacement
+modules and see if they help you.
+
+=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 implementation
+that consists mainly of the standard routine present in earlier versions of
+Math::BigInt.
+
+There are also Math::BigInt::Scalar (primarily for testing) and
+Math::BigInt::BitVect; as well as Math::BigInt::Pari and likely others.
+All these can be found via L<http://search.cpan.org/>:
+
+ use Math::BigInt lib => 'BitVect';
+
+ my $x = Math::BigInt->new(2);
+ print $x ** (1024*1024);
+
For more benchmark results see http://bloodgate.com/perl/benchmarks.html
=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
+There is not yet a way to get a number automatically represented in 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 L<overload> 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 $x, the last one won't:
since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant
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).
+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...
$float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong!
-Beware of the order of more complicated expressions like:
+Beware also of the order of more complicated expressions like:
$integer = ($mbi2 + $mbi) / $mbf; # int / float => int
$integer = $mbi2 / Math::BigFloat->new($mbi); # ditto
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
+=head1 SEE ALSO
+
+L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>,
+L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
+
+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
Original code by Mark Biggar, overloaded interface by Ilya Zakharevich.
projects / p5sagit/p5-mst-13.2.git / blobdiff