-#!/usr/bin/perl -w
+package Math::BigInt;
-# Qs: what exactly happens on numify of HUGE numbers? overflow?
-# $a = -$a is much slower (making copy of $a) than $a->bneg(), hm!?
-# (copy_on_write will help there, but that is not yet implemented)
+#
+# "Mike had an infinite amount to do and a negative amount of time in which
+# to do it." - Before and After
+#
# The following hash values are used:
# value: unsigned int with actual value (as a Math::BigInt::Calc or similiar)
# _a : accuracy
# _p : precision
# _f : flags, used by MBF to flag parts of a float as untouchable
-# _cow : copy on write: number of objects that share the data (NRY)
# 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 = '1.40';
+$VERSION = '1.53';
use Exporter;
@ISA = qw( Exporter );
-@EXPORT_OK = qw( bneg babs bcmp badd bmul bdiv bmod bnorm bsub
- bgcd blcm
- bround
- blsft brsft band bior bxor bnot bpow bnan bzero
- bacmp bstr bsstr binc bdec binf bfloor bceil
- is_odd is_even is_zero is_one is_nan is_inf sign
- is_positive is_negative
- length as_number
- objectify _swap
- );
-
-#@EXPORT = qw( );
-use vars qw/$rnd_mode $accuracy $precision $div_scale/;
+@EXPORT_OK = qw( objectify _swap bgcd blcm);
+use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/;
+use vars qw/$upgrade $downgrade/;
use strict;
# Inside overload, the first arg is always an object. If the original code had
'-=' => sub { $_[0]->bsub($_[1]); },
'*=' => sub { $_[0]->bmul($_[1]); },
'/=' => sub { scalar $_[0]->bdiv($_[1]); },
+'%=' => sub { $_[0]->bmod($_[1]); },
+'^=' => sub { $_[0]->bxor($_[1]); },
+'&=' => sub { $_[0]->band($_[1]); },
+'|=' => sub { $_[0]->bior($_[1]); },
'**=' => sub { $_[0]->bpow($_[1]); },
+# not supported by Perl yet
+'..' => \&_pointpoint,
+
'<=>' => sub { $_[2] ?
- $class->bcmp($_[1],$_[0]) :
- $class->bcmp($_[0],$_[1])},
-'cmp' => sub {
+ ref($_[0])->bcmp($_[1],$_[0]) :
+ ref($_[0])->bcmp($_[0],$_[1])},
+'cmp' => sub {
$_[2] ?
- $_[1] cmp $_[0]->bstr() :
- $_[0]->bstr() cmp $_[1] },
+ "$_[1]" cmp $_[0]->bstr() :
+ $_[0]->bstr() cmp "$_[1]" },
+'log' => sub { $_[0]->copy()->blog(); },
'int' => sub { $_[0]->copy(); },
'neg' => sub { $_[0]->copy()->bneg(); },
'abs' => sub { $_[0]->copy()->babs(); },
+'sqrt' => sub { $_[0]->copy()->bsqrt(); },
'~' => sub { $_[0]->copy()->bnot(); },
'*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); },
# v5.6.1 dumps on that: return !$_[0]->is_zero() || undef; :-(
my $t = !$_[0]->is_zero();
undef $t if $t == 0;
- return $t;
+ $t;
},
-qw(
-"" bstr
-0+ numify), # Order of arguments unsignificant
+# the original qw() does not work with the TIESCALAR below, why?
+# Order of arguments unsignificant
+'""' => sub { $_[0]->bstr(); },
+'0+' => sub { $_[0]->numify(); }
;
##############################################################################
my $nan = 'NaN'; # constants for easier life
my $CALC = 'Math::BigInt::Calc'; # module to do low level math
-sub _core_lib () { return $CALC; } # for test suite
+my $IMPORT = 0; # did import() yet?
+
+$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
+$accuracy = undef;
+$precision = undef;
+$div_scale = 40;
+
+$upgrade = undef; # default is no upgrade
+$downgrade = undef; # default is no downgrade
+
+##############################################################################
+# the old code had $rnd_mode, so we need to support it, too
-# Rounding modes, one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
-$rnd_mode = 'even';
-$accuracy = undef;
-$precision = undef;
-$div_scale = 40;
+$rnd_mode = 'even';
+sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; }
+sub FETCH { return $round_mode; }
+sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
+
+BEGIN { tie $rnd_mode, 'Math::BigInt'; }
+
+##############################################################################
sub round_mode
{
+ no strict 'refs';
# make Class->round_mode() work
- my $self = shift || $class;
- # shift @_ if defined $_[0] && $_[0] eq $class;
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
if (defined $_[0])
{
my $m = shift;
die "Unknown round mode $m"
if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
- $rnd_mode = $m; return;
+ return ${"${class}::round_mode"} = $m;
+ }
+ return ${"${class}::round_mode"};
+ }
+
+sub upgrade
+ {
+ no strict 'refs';
+ # make Class->upgrade() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ if (defined $_[0])
+ {
+ my $u = shift;
+ return ${"${class}::upgrade"} = $u;
+ }
+ return ${"${class}::upgrade"};
+ }
+
+sub downgrade
+ {
+ no strict 'refs';
+ # make Class->downgrade() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ if (defined $_[0])
+ {
+ my $u = shift;
+ return ${"${class}::downgrade"} = $u;
}
- return $rnd_mode;
+ return ${"${class}::downgrade"};
+ }
+
+sub div_scale
+ {
+ no strict 'refs';
+ # make Class->round_mode() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ if (defined $_[0])
+ {
+ die ('div_scale must be greater than zero') if $_[0] < 0;
+ ${"${class}::div_scale"} = shift;
+ }
+ return ${"${class}::div_scale"};
}
sub accuracy
{
- # $x->accuracy($a); ref($x) a
- # $x->accuracy(); ref($x);
- # Class::accuracy(); # not supported
- #print "MBI @_ ($class)\n";
- my $x = shift;
+ # $x->accuracy($a); ref($x) $a
+ # $x->accuracy(); ref($x)
+ # Class->accuracy(); class
+ # Class->accuracy($a); class $a
- die ("accuracy() needs reference to object as first parameter.")
- if !ref $x;
+ my $x = shift;
+ my $class = ref($x) || $x || __PACKAGE__;
+ no strict 'refs';
+ # need to set new value?
if (@_ > 0)
{
- $x->{_a} = shift;
- $x->round() if defined $x->{_a};
+ my $a = shift;
+ die ('accuracy must not be zero') if defined $a && $a == 0;
+ if (ref($x))
+ {
+ # $object->accuracy() or fallback to global
+ $x->bround($a) if defined $a;
+ $x->{_a} = $a; # set/overwrite, even if not rounded
+ $x->{_p} = undef; # clear P
+ }
+ else
+ {
+ # set global
+ ${"${class}::accuracy"} = $a;
+ ${"${class}::precision"} = undef; # clear P
+ }
+ return $a; # shortcut
+ }
+
+ if (ref($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 A
+ }
+ else
+ {
+ # set global
+ ${"${class}::precision"} = $p;
+ ${"${class}::accuracy"} = undef; # clear A
+ }
+ return $p; # shortcut
+ }
+
+ if (ref($x))
+ {
+ # $object->precision() or fallback to global
+ return $x->{_p} || ${"${class}::precision"};
}
- return $x->{_p};
+ return ${"${class}::precision"};
}
+sub config
+ {
+ # return (later set?) configuration data as hash ref
+ my $class = shift || 'Math::BigInt';
+
+ no strict 'refs';
+ my $lib = $CALC;
+ my $cfg = {
+ lib => $lib,
+ lib_version => ${"${lib}::VERSION"},
+ class => $class,
+ };
+ foreach (
+ qw/upgrade downgrade precision accuracy round_mode VERSION div_scale/)
+ {
+ $cfg->{lc($_)} = ${"${class}::$_"};
+ };
+ $cfg;
+ }
+
sub _scale_a
{
# select accuracy parameter based on precedence,
return unless ref($x); # only for objects
my $self = {}; bless $self,$c;
+ my $r;
foreach my $k (keys %$x)
{
if ($k eq 'value')
{
- $self->{$k} = $CALC->_copy($x->{$k});
+ $self->{value} = $CALC->_copy($x->{value}); next;
}
- elsif (ref($x->{$k}) eq 'SCALAR')
+ if (!($r = ref($x->{$k})))
+ {
+ $self->{$k} = $x->{$k}; next;
+ }
+ if ($r eq 'SCALAR')
{
$self->{$k} = \${$x->{$k}};
}
- elsif (ref($x->{$k}) eq 'ARRAY')
+ elsif ($r eq 'ARRAY')
{
$self->{$k} = [ @{$x->{$k}} ];
}
- elsif (ref($x->{$k}) eq 'HASH')
+ elsif ($r eq 'HASH')
{
# only one level deep!
foreach my $h (keys %{$x->{$k}})
$self->{$k}->{$h} = $x->{$k}->{$h};
}
}
- elsif (ref($x->{$k}))
+ else # normal ref
{
- my $c = ref($x->{$k});
- $self->{$k} = $c->new($x->{$k}); # no copy() due to deep rec
- }
- else
- {
- $self->{$k} = $x->{$k};
+ my $xk = $x->{$k};
+ if ($xk->can('copy'))
+ {
+ $self->{$k} = $xk->copy();
+ }
+ else
+ {
+ $self->{$k} = $xk->new($xk);
+ }
}
}
$self;
# cause costly overloaded code to be called. The only allowed ops are
# ref() and defined.
- my $class = shift;
+ my ($class,$wanted,$a,$p,$r) = @_;
- my $wanted = shift; # avoid numify call by not using || here
- return $class->bzero() if !defined $wanted; # default to 0
- return $class->copy($wanted) if ref($wanted);
+ # avoid numify-calls by not using || on $wanted!
+ return $class->bzero($a,$p) if !defined $wanted; # default to 0
+ return $class->copy($wanted,$a,$p,$r) if ref($wanted);
+ $class->import() if $IMPORT == 0; # make require work
+
my $self = {}; bless $self, $class;
# handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]inf$/)
+ if ($wanted =~ /^[+-]?inf$/)
{
$self->{value} = $CALC->_zero();
- $self->{sign} = $wanted;
+ $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf';
return $self;
}
# split str in m mantissa, e exponent, i integer, f fraction, v value, s sign
if ($diff < 0) # Not integer
{
#print "NOI 1\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
else # diff >= 0
{
# fraction and negative/zero E => NOI
#print "NOI 2 \$\$mfv '$$mfv'\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
elsif ($e < 0)
if ($$miv !~ s/0{$e}$//) # can strip so many zero's?
{
#print "NOI 3\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
}
}
$self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0
$self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/;
- #print "$wanted => $self->{sign}\n";
# if any of the globals is set, use them to round and store them inside $self
- $self->round($accuracy,$precision,$rnd_mode)
- if defined $accuracy || defined $precision;
+ # do not round for new($x,undef,undef) since that is used by MBF to signal
+ # no rounding
+ $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p;
+ # print "mbi new $self\n";
return $self;
}
{
my $c = $self; $self = {}; bless $self, $c;
}
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('bnan');
+ my $c = ref($self);
+ if ($self->can('_bnan'))
+ {
+ # use subclass to initialize
+ $self->_bnan();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
$self->{value} = $CALC->_zero();
$self->{sign} = $nan;
+ delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly
return $self;
}
{
my $c = $self; $self = {}; bless $self, $c;
}
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('binf');
- $self->{value} = $CALC->_zero();
+ my $c = ref($self);
+ if ($self->can('_binf'))
+ {
+ # use subclass to initialize
+ $self->_binf();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
$self->{sign} = $sign.'inf';
+ ($self->{_a},$self->{_p}) = @_; # take over requested rounding
return $self;
}
{
my $c = $self; $self = {}; bless $self, $c;
}
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('bzero');
- $self->{value} = $CALC->_zero();
+
+ if ($self->can('_bzero'))
+ {
+ # use subclass to initialize
+ $self->_bzero();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
$self->{sign} = '+';
- #print "result: $self\n";
+ if (@_ > 0)
+ {
+ $self->{_a} = $_[0]
+ if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a});
+ $self->{_p} = $_[1]
+ if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p});
+ }
return $self;
}
my $self = shift;
my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
$self = $class if !defined $self;
- #print "bone $self\n";
-
+
if (!ref($self))
{
my $c = $self; $self = {}; bless $self, $c;
}
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('bone');
- $self->{value} = $CALC->_one();
+
+ if ($self->can('_bone'))
+ {
+ # use subclass to initialize
+ $self->_bone();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_one();
+ }
$self->{sign} = $sign;
- #print "result: $self\n";
+ if (@_ > 0)
+ {
+ $self->{_a} = $_[0]
+ if (defined $self->{_a} && defined $_[0] && $_[0] > $self->{_a});
+ $self->{_p} = $_[1]
+ if (defined $self->{_p} && defined $_[1] && $_[1] < $self->{_p});
+ }
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")
- 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,@_);
if ($x->{sign} !~ /^[+-]$/)
{
sub bstr
{
# make a string from bigint object
- my $x = shift; $x = $class->new($x) unless ref $x;
+ my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
+ # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
if ($x->{sign} !~ /^[+-]$/)
{
return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
sub numify
{
- # Make a number from a BigInt object
+ # Make a "normal" scalar from a BigInt object
my $x = shift; $x = $class->new($x) unless ref $x;
return $x->{sign} if $x->{sign} !~ /^[+-]$/;
my $num = $CALC->_num($x->{value});
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.
- # The result's A or P are set by the rounding, but not inspected beforehand
- # (aka only the arguments enter into it). This works because the given
- # 'first' argument is both the result and true first argument with unchanged
- # A and P settings.
- # This does not yet handle $x with A, and $y with P (which should be an
- # error).
- my $self = shift;
- my $a = shift; # accuracy, if given by caller
- my $p = shift; # precision, if given by caller
- my $r = shift; # round_mode, if given by caller
- my @args = @_; # all 'other' arguments (0 for unary, 1 for binary ops)
-
- $self = new($self) unless ref($self); # if not object, make one
- my $c = ref($args[0]); # find out class of argument
- unshift @args,$self; # add 'first' argument
-
+
+ # This procedure finds the round parameters, but it is for speed reasons
+ # duplicated in round. Otherwise, it is tested by the testsuite and used
+ # by fdiv().
+
+ my ($self,$a,$p,$r,@args) = @_;
+ # $a accuracy, if given by caller
+ # $p precision, if given by caller
+ # $r round_mode, if given by caller
+ # @args all 'other' arguments (0 for unary, 1 for binary ops)
+
+ # leave bigfloat parts alone
+ return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
+
+ my $c = ref($self); # find out class of argument(s)
no strict 'refs';
- my $z = "$c\::accuracy"; my $aa = $$z; my $ap = undef;
- if (!defined $aa)
+
+ # now pick $a or $p, but only if we have got "arguments"
+ if (!defined $a)
{
- $z = "$c\::precision"; $ap = $$z;
+ foreach ($self,@args)
+ {
+ # take the defined one, or if both defined, the one that is smaller
+ $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
+ }
}
+ if (!defined $p)
+ {
+ # even if $a is defined, take $p, to signal error for both defined
+ foreach ($self,@args)
+ {
+ # take the defined one, or if both defined, the one that is bigger
+ # -2 > -3, and 3 > 2
+ $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
+ }
+ }
+ # if still none defined, use globals (#2)
+ $a = ${"$c\::accuracy"} unless defined $a;
+ $p = ${"$c\::precision"} unless defined $p;
+
+ # no rounding today?
+ return ($self) unless defined $a || defined $p; # early out
+
+ # set A and set P is an fatal error
+ return ($self->bnan()) if defined $a && defined $p;
+
+ $r = ${"$c\::round_mode"} unless defined $r;
+ die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
+
+ return ($self,$a,$p,$r);
+ }
+
+sub round
+ {
+ # Round $self according to given parameters, or given second argument's
+ # parameters or global defaults
+
+ # for speed reasons, _find_round_parameters is embeded here:
+
+ my ($self,$a,$p,$r,@args) = @_;
+ # $a accuracy, if given by caller
+ # $p precision, if given by caller
+ # $r round_mode, if given by caller
+ # @args all 'other' arguments (0 for unary, 1 for binary ops)
# leave bigfloat parts alone
- return $self if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
+ return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
+
+ my $c = ref($self); # find out class of argument(s)
+ no strict 'refs';
# now pick $a or $p, but only if we have got "arguments"
- if ((!defined $a) && (!defined $p) && (@args > 0))
+ if (!defined $a)
{
- foreach (@args)
+ foreach ($self,@args)
{
# take the defined one, or if both defined, the one that is smaller
$a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
}
- if (!defined $a) # if it still is not defined, take p
+ }
+ if (!defined $p)
+ {
+ # even if $a is defined, take $p, to signal error for both defined
+ foreach ($self,@args)
{
- foreach (@args)
- {
- # take the defined one, or if both defined, the one that is smaller
- $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} < $p);
- }
- # if none defined, use globals (#2)
- if (!defined $p)
- {
- $a = $aa; $p = $ap; # save the check: if !defined $a;
- }
- } # endif !$a
- } # endif !$a || !$P && args > 0
- # for clearity, this is not merged at place (#2)
- # now round, by calling fround or ffround:
+ # take the defined one, or if both defined, the one that is bigger
+ # -2 > -3, and 3 > 2
+ $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
+ }
+ }
+ # if still none defined, use globals (#2)
+ $a = ${"$c\::accuracy"} unless defined $a;
+ $p = ${"$c\::precision"} unless defined $p;
+
+ # no rounding today?
+ return $self unless defined $a || defined $p; # early out
+
+ # set A and set P is an fatal error
+ return $self->bnan() if defined $a && defined $p;
+
+ $r = ${"$c\::round_mode"} unless defined $r;
+ die "Unknown round mode '$r'" if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
+
+ # now round, by calling either fround or ffround:
if (defined $a)
{
- $self->{_a} = $a; $self->bround($a,$r);
+ $self->bround($a,$r) if !defined $self->{_a} || $self->{_a} >= $a;
}
- elsif (defined $p)
+ else # both can't be undefined due to early out
{
- $self->{_p} = $p; $self->bfround($p,$r);
+ $self->bfround($p,$r) if !defined $self->{_p} || $self->{_p} <= $p;
}
- return $self->bnorm();
+ $self->bnorm(); # after round, normalize
}
-sub bnorm
+sub bnorm
{
- # (num_str or BINT) return BINT
+ # (numstr or BINT) return BINT
# Normalize number -- no-op here
- return $_[0];
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ $x;
}
sub babs
{
# (BINT or num_str) return BINT
# make number absolute, or return absolute BINT from string
- my $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 $x = shift; $x = $class->new($x) unless ref $x;
+ 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->{sign} =~ tr/+-/-+/ if !$x->is_zero(); # does nothing for NaN
$x;
}
return +1 if $x->{sign} eq '+inf';
return -1 if $x->{sign} eq '-inf';
return -1 if $y->{sign} eq '+inf';
- return +1 if $y->{sign} eq '-inf';
+ return +1;
}
# check sign for speed first
return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
return 0 if $xz && $yz; # 0 <=> 0
return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y
return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0
- # normal compare now
- &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 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 '+';
+ $CALC->_acmp($y->{value},$x->{value}); # swaped (lib does only 0,1,-1)
}
sub bacmp
return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
return +1; # inf is always bigger
}
- $CALC->_acmp($x->{value},$y->{value}) <=> 0;
+ $CALC->_acmp($x->{value},$y->{value}); # lib does only 0,1,-1
}
sub badd
{
# add second arg (BINT or string) to first (BINT) (modifies first)
# return result as BINT
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ my ($self,$x,$y,@r) = objectify(2,@_);
return $x if $x->modify('badd');
-
+# print "mbi badd ",join(' ',caller()),"\n";
+# print "upgrade => ",$upgrade||'undef',
+# " \$x (",ref($x),") \$y (",ref($y),")\n";
+# return $upgrade->badd($x,$y,@r) if defined $upgrade &&
+# ((ref($x) eq $upgrade) || (ref($y) eq $upgrade));
+# print "still badd\n";
+
+ $r[3] = $y; # no push!
# 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$/))
+ # inf handling
+ 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++inf or -inf+-inf => same, rest is NaN
+ return $x if $x->{sign} eq $y->{sign};
+ return $x->bnan();
}
# +-inf + something => +inf
# something +-inf => +-inf
return $x;
}
- my @bn = ($a,$p,$r,$y); # make array for round calls
- # speed: no add for 0+y or x+0
- return $x->round(@bn) if $y->is_zero(); # x+0
- if ($x->is_zero()) # 0+y
- {
- # make copy, clobbering up x
- $x->{value} = $CALC->_copy($y->{value});
- $x->{sign} = $y->{sign} || $nan;
- return $x->round(@bn);
- }
-
my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
if ($sx eq $sy)
$x->{sign} = $sx;
}
}
- return $x->round(@bn);
+ $x->round(@r);
}
sub bsub
{
# (BINT or num_str, BINT or num_str) return num_str
# subtract second arg from first, modify first
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ my ($self,$x,$y,@r) = objectify(2,@_);
return $x if $x->modify('bsub');
- $x->badd($y->bneg()); # badd does not leave internal zeros
- $y->bneg(); # refix y, assumes no one reads $y in between
- return $x->round($a,$p,$r,$y);
+# return $upgrade->badd($x,$y,@r) if defined $upgrade &&
+# ((ref($x) eq $upgrade) || (ref($y) eq $upgrade));
+
+ if ($y->is_zero())
+ {
+ return $x->round(@r);
+ }
+
+ $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
+ $x->badd($y,@r); # badd does not leave internal zeros
+ $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
+ $x; # already rounded by badd() or no round necc.
}
sub binc
{
# increment arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
- # my $x = shift; $x = $class->new($x) unless ref $x; my $self = ref($x);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('binc');
- $x->badd($self->__one())->round($a,$p,$r);
+
+ if ($x->{sign} eq '+')
+ {
+ $x->{value} = $CALC->_inc($x->{value});
+ 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); # badd does round
}
sub bdec
{
# decrement arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('bdec');
- $x->badd($self->__one('-'))->round($a,$p,$r);
+
+ my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+';
+ # <= 0
+ if (($x->{sign} eq '-') || $zero)
+ {
+ $x->{value} = $CALC->_inc($x->{value});
+ $x->{sign} = '-' if $zero; # 0 => 1 => -1
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+ 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); # badd does round
}
+sub blog
+ {
+ # not implemented yet
+ my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ return $upgrade->blog($x,$base,$a,$p,$r) if defined $upgrade;
+
+ return $x->bnan();
+ }
+
sub blcm
{
# (BINT or num_str, BINT or num_str) return BINT
{
$x = $class->new($y);
}
- while (@_) { $x = _lcm($x,shift); }
+ while (@_) { $x = __lcm($x,shift); }
$x;
}
# does not modify arguments, but returns new object
# GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff)
- my $y = shift; my ($x);
- if (ref($y))
- {
- $x = $y->copy();
- }
- else
- {
- $x = $class->new($y);
- }
-
+ my $y = shift;
+ $y = __PACKAGE__->new($y) if !ref($y);
+ my $self = ref($y);
+ my $x = $y->copy(); # keep arguments
if ($CALC->can('_gcd'))
{
while (@_)
{
- $y = shift; $y = $class->new($y) if !ref($y);
+ $y = shift; $y = $self->new($y) if !ref($y);
next if $y->is_zero();
return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
$x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one();
{
while (@_)
{
- $x = __gcd($x,shift); last if $x->is_one(); # _gcd handles NaN
+ $y = shift; $y = $self->new($y) if !ref($y);
+ $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN
}
}
$x->babs();
}
-sub bmod
- {
- # modulus
- # (BINT or num_str, BINT or num_str) return BINT
- my ($self,$x,$y) = objectify(2,@_);
-
- return $x if $x->modify('bmod');
- (&bdiv($self,$x,$y))[1];
- }
-
sub bnot
{
# (num_str or BINT) return BINT
# represent ~x as twos-complement number
- my ($self,$x) = objectify(1,@_);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
return $x if $x->modify('bnot');
- $x->bneg(); $x->bdec(); # was: bsub(-1,$x);, time it someday
- $x;
+ $x->bneg()->bdec(); # bdec already does round
}
+# is_foo test routines
+
sub is_zero
{
# return true if arg (BINT or num_str) is zero (array '+', '0')
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
- return $CALC->_is_zero($x->{value});
+ $CALC->_is_zero($x->{value});
}
sub is_nan
{
# return true if arg (BINT or num_str) is NaN
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} eq $nan);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ return 1 if $x->{sign} eq $nan;
+ 0;
}
sub is_inf
{
# return true if arg (BINT or num_str) is +-inf
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- my $sign = shift || '';
+ my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x->{sign} =~ /^[+-]inf$/ if $sign eq '';
- return $x->{sign} =~ /^[$sign]inf$/;
+ $sign = '' if !defined $sign;
+ return 0 if $sign !~ /^([+-]|)$/;
+
+ if ($sign eq '')
+ {
+ return 1 if ($x->{sign} =~ /^[+-]inf$/);
+ return 0;
+ }
+ $sign = quotemeta($sign.'inf');
+ return 1 if ($x->{sign} =~ /^$sign$/);
+ 0;
}
sub is_one
{
# return true if arg (BINT or num_str) is +1
# or -1 if sign is given
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- my $sign = shift || ''; $sign = '+' if $sign ne '-';
+ # 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;
- return $CALC->_is_one($x->{value});
+ return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
+ $CALC->_is_one($x->{value});
}
sub is_odd
{
# return true when arg (BINT or num_str) is odd, false for even
- my $x = shift; $x = $class->new($x) unless ref $x;
- #my ($self,$x) = objectify(1,@_);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
- return $CALC->_is_odd($x->{value});
+ $CALC->_is_odd($x->{value});
}
sub is_even
{
# return true when arg (BINT or num_str) is even, false for odd
- my $x = shift; $x = $class->new($x) unless ref $x;
- #my ($self,$x) = objectify(1,@_);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
- return $CALC->_is_even($x->{value});
+ $CALC->_is_even($x->{value});
}
sub is_positive
{
# return true when arg (BINT or num_str) is positive (>= 0)
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} =~ /^\+/);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return 1 if $x->{sign} =~ /^\+/;
+ 0;
}
sub is_negative
{
# return true when arg (BINT or num_str) is negative (< 0)
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} =~ /^-/);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return 1 if ($x->{sign} =~ /^-/);
+ 0;
+ }
+
+sub is_int
+ {
+ # return true when arg (BINT or num_str) is an integer
+ # always true for BigInt, but different for Floats
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't
}
###############################################################################
{
# multiply two numbers -- stolen from Knuth Vol 2 pg 233
# (BINT or num_str, BINT or num_str) return BINT
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ my ($self,$x,$y,@r) = objectify(2,@_);
return $x if $x->modify('bmul');
+
+ $r[3] = $y; # no push here
+
return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- # 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$/))
{
+ return $x->bnan() if $x->is_zero() || $y->is_zero();
# result will always be +-inf:
# +inf * +/+inf => +inf, -inf * -/-inf => +inf
# +inf * -/-inf => -inf, -inf * +/+inf => -inf
}
$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);
+
+ $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
+ $x->round(@r);
+ }
+
+sub _div_inf
+ {
+ # helper function that handles +-inf cases for bdiv()/bmod() to reuse code
+ my ($self,$x,$y) = @_;
+
+ # NaN if x == NaN or y == NaN or x==y==0
+ return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
+ if (($x->is_nan() || $y->is_nan()) ||
+ ($x->is_zero() && $y->is_zero()));
+
+ # +-inf / +-inf == NaN, reminder also NaN
+ if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan();
+ }
+ # x / +-inf => 0, remainder x (works even if x == 0)
+ if ($y->{sign} =~ /^[+-]inf$/)
+ {
+ my $t = $x->copy(); # 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)
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ my ($self,$x,$y,@r) = objectify(2,@_);
return $x if $x->modify('bdiv');
- # x / +-inf => 0, reminder x
- return wantarray ? ($x->bzero(),$x->copy()) : $x->bzero()
- if $y->{sign} =~ /^[+-]inf$/;
-
- # NaN if x == NaN or y == NaN or x==y==0
- return wantarray ? ($x->bnan(),bnan()) : $x->bnan()
- if (($x->is_nan() || $y->is_nan()) ||
- ($x->is_zero() && $y->is_zero()));
-
- # 5 / 0 => +inf, -6 / 0 => -inf
- return wantarray
- ? ($x->binf($x->{sign}),$self->bnan()) : $x->binf($x->{sign})
- if ($x->{sign} =~ /^[+-]$/ && $y->is_zero());
-
- # old code: always NaN if /0
- #return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
- # if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || $y->is_zero());
+ return $self->_div_inf($x,$y)
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
+
+ $r[3] = $y; # no push!
# 0 / something
- return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero();
+ return
+ wantarray ? ($x->round(@r),$self->bzero(@r)):$x->round(@r) if $x->is_zero();
- # Is $x in the interval [0, $y) ?
+ # Is $x in the interval [0, $y) (aka $x <= $y) ?
my $cmp = $CALC->_acmp($x->{value},$y->{value});
- if (($cmp < 0) and ($x->{sign} eq $y->{sign}))
+ if (($cmp < 0) and (($x->{sign} eq $y->{sign}) or !wantarray))
{
- return $x->bzero() unless wantarray;
+ return $upgrade->bdiv($x,$y,@r) if defined $upgrade;
+
+ return $x->bzero()->round(@r) unless wantarray;
my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x
- return ($x->bzero(),$t);
+ return ($x->bzero()->round(@r),$t);
}
elsif ($cmp == 0)
{
# shortcut, both are the same, so set to +/- 1
$x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') );
return $x unless wantarray;
- return ($x,$self->bzero());
+ return ($x->round(@r),$self->bzero(@r));
}
# calc new sign and in case $y == +/- 1, return $x
+ my $xsign = $x->{sign}; # keep
$x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+');
# check for / +-1 (cant use $y->is_one due to '-'
- if (($y == 1) || ($y == -1)) # slow!
- #if ((@{$y->{value}} == 1) && ($y->{value}->[0] == 1))
+ if ($CALC->_is_one($y->{value}))
{
- return wantarray ? ($x,$self->bzero()) : $x;
+ return wantarray ? ($x->round(@r),$self->bzero(@r)) : $x->round(@r);
}
- # call div here
- my $rem = $self->bzero();
- $rem->{sign} = $y->{sign};
- #($x->{value},$rem->{value}) = div($x->{value},$y->{value});
- ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
- # do not leave rest "-0";
- # $rem->{sign} = '+' if (@{$rem->{value}} == 1) && ($rem->{value}->[0] == 0);
- $rem->{sign} = '+' if $CALC->_is_zero($rem->{value});
- if (($x->{sign} eq '-') and (!$rem->is_zero()))
- {
- $x->bdec();
- }
- $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
+ my $rem = $self->bzero();
+ ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value});
+ $x->round(@r);
+ 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(@r);
return ($x,$rem);
}
- return $x;
+
+ $x->{value} = $CALC->_div($x->{value},$y->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value});
+ $x->round(@r);
}
+sub bmod
+ {
+ # modulus (or remainder)
+ # (BINT or num_str, BINT or num_str) return BINT
+ my ($self,$x,$y,@r) = objectify(2,@_);
+
+ return $x if $x->modify('bmod');
+ $r[3] = $y; # no push!
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
+ {
+ my ($d,$r) = $self->_div_inf($x,$y);
+ return $r->round(@r);
+ }
+
+ if ($CALC->can('_mod'))
+ {
+ # calc new sign and in case $y == +/- 1, return $x
+ $x->{value} = $CALC->_mod($x->{value},$y->{value});
+ if (!$CALC->_is_zero($x->{value}))
+ {
+ my $xsign = $x->{sign};
+ $x->{sign} = $y->{sign};
+ $x = $y-$x if $xsign ne $y->{sign}; # one of them '-'
+ }
+ else
+ {
+ $x->{sign} = '+'; # dont leave -0
+ }
+ return $x->round(@r);
+ }
+ my ($t,$rem) = $self->bdiv($x->copy(),$y,@r); # slow way (also rounds)
+ # modify in place
+ foreach (qw/value sign _a _p/)
+ {
+ $x->{$_} = $rem->{$_};
+ }
+ $x;
+ }
+
+sub bfac
+ {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # compute factorial numbers
+ # modifies first argument
+ my ($self,$x,@r) = objectify(1,@_);
+
+ return $x if $x->modify('bfac');
+
+ return $x->bnan() if $x->{sign} ne '+'; # inf, NnN, <0 etc => NaN
+ return $x->bone(@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1
+
+ if ($CALC->can('_fac'))
+ {
+ $x->{value} = $CALC->_fac($x->{value});
+ return $x->round(@r);
+ }
+
+ my $n = $x->copy();
+ $x->bone();
+ my $f = $self->new(2);
+ while ($f->bacmp($n) < 0)
+ {
+ $x->bmul($f); $f->binc();
+ }
+ $x->bmul($f); # last step
+ $x->round(@r); # round
+ }
+
sub bpow
{
# (BINT or num_str, BINT or num_str) return BINT
# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
# modifies first argument
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ my ($self,$x,$y,@r) = objectify(2,@_);
return $x if $x->modify('bpow');
+ $r[3] = $y; # no push!
return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x
return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
- return $x->__one() if $y->is_zero();
- return $x if $x->is_one() || $y->is_one();
- #if ($x->{sign} eq '-' && @{$x->{value}} == 1 && $x->{value}->[0] == 1)
+ return $x->bone(@r) if $y->is_zero();
+ return $x->round(@r) if $x->is_one() || $y->is_one();
if ($x->{sign} eq '-' && $CALC->_is_one($x->{value}))
{
# if $x == -1 and odd/even y => +1/-1
- return $y->is_odd() ? $x : $x->babs();
+ return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r);
# my Casio FX-5500L has a bug here: -1 ** 2 is -1, but -1 * -1 is 1;
}
# 1 ** -y => 1 / (1 ** |y|)
# so do test for negative $y after above's clause
return $x->bnan() if $y->{sign} eq '-';
- return $x if $x->is_zero(); # 0**y => 0 (if not y <= 0)
+ return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0)
if ($CALC->can('_pow'))
{
$x->{value} = $CALC->_pow($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ return $x->round(@r);
}
- # based on the assumption that shifting in base 10 is fast, and that mul
- # works faster if numbers are small: we count trailing zeros (this step is
- # O(1)..O(N), but in case of O(N) we save much more time due to this),
- # stripping them out of the multiplication, and add $count * $y zeros
- # afterwards like this:
- # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6
- # creates deep recursion?
+
+# 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)
# {
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); }
- #print "$x $y\n";
+ $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";
- return $x->round($a,$p,$r);
+ $x->bmul($pow2) unless $pow2->is_one();
+ return $x->round(@r);
}
sub blsft
{
# (BINT or num_str, BINT or num_str) return BINT
# compute x << y, base n, y >= 0
- my ($self,$x,$y,$n) = objectify(2,@_);
+ my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('blsft');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+ return $x->round($a,$p,$r) if $y->is_zero();
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- my $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft');
+ my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft');
if (defined $t)
{
- $x->{value} = $t; return $x;
+ $x->{value} = $t; return $x->round($a,$p,$r);
}
# fallback
- return $x->bmul( $self->bpow($n, $y) );
+ return $x->bmul( $self->bpow($n, $y, $a, $p, $r), $a, $p, $r );
}
sub brsft
{
# (BINT or num_str, BINT or num_str) return BINT
# compute x >> y, base n, y >= 0
- my ($self,$x,$y,$n) = objectify(2,@_);
+ my ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('brsft');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+ return $x->round($a,$p,$r) if $y->is_zero();
+ return $x->bzero($a,$p,$r) if $x->is_zero(); # 0 => 0
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- my $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft');
+ # this only works for negative numbers when shifting in base 2
+ if (($x->{sign} eq '-') && ($n == 2))
+ {
+ return $x->round($a,$p,$r) if $x->is_one('-'); # -1 => -1
+ if (!$y->is_one())
+ {
+ # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al
+ # but perhaps there is a better emulation for two's complement shift...
+ # if $y != 1, we must simulate it by doing:
+ # convert to bin, flip all bits, shift, and be done
+ $x->binc(); # -3 => -2
+ my $bin = $x->as_bin();
+ $bin =~ s/^-0b//; # strip '-0b' prefix
+ $bin =~ tr/10/01/; # flip bits
+ # now shift
+ if (length($bin) <= $y)
+ {
+ $bin = '0'; # shifting to far right creates -1
+ # 0, because later increment makes
+ # that 1, attached '-' makes it '-1'
+ # because -1 >> x == -1 !
+ }
+ else
+ {
+ $bin =~ s/.{$y}$//; # cut off at the right side
+ $bin = '1' . $bin; # extend left side by one dummy '1'
+ $bin =~ tr/10/01/; # flip bits back
+ }
+ my $res = $self->new('0b'.$bin); # add prefix and convert back
+ $res->binc(); # remember to increment
+ $x->{value} = $res->{value}; # take over value
+ return $x->round($a,$p,$r); # we are done now, magic, isn't?
+ }
+ $x->bdec(); # n == 2, but $y == 1: this fixes it
+ }
+
+ my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft');
if (defined $t)
{
- $x->{value} = $t; return $x;
+ $x->{value} = $t;
+ return $x->round($a,$p,$r);
}
# fallback
- return scalar bdiv($x, $self->bpow($n, $y));
+ $x->bdiv($self->bpow($n,$y, $a,$p,$r), $a,$p,$r);
+ $x;
}
sub band
return $x if $x->modify('band');
+ local $Math::BigInt::upgrade = undef;
+
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x->bzero() if $y->is_zero();
+ return $x->bzero() if $y->is_zero() || $x->is_zero();
my $sign = 0; # sign of result
$sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-');
return $x->round($a,$p,$r);
}
- my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x1000);
+ my $m = $self->bone(); my ($xr,$yr);
+ my $x10000 = $self->new (0x1000);
my $y1 = copy(ref($x),$y); # make copy
$y1->babs(); # and positive
my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place!
return $x if $x->modify('bior');
+ local $Math::BigInt::upgrade = undef;
+
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
return $x if $y->is_zero();
return $x->round($a,$p,$r);
}
- my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x10000);
+ my $m = $self->bone(); my ($xr,$yr);
+ my $x10000 = $self->new(0x10000);
my $y1 = copy(ref($x),$y); # make copy
$y1->babs(); # and positive
my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place!
$x->badd( bmul( $class->new(
abs($sx*int($xr->numify()) | $sy*int($yr->numify()))),
$m));
-# $x->badd( bmul( $class->new(int($xr->numify()) | int($yr->numify())), $m));
$m->bmul($x10000);
}
$x->bneg() if $sign;
return $x if $x->modify('bxor');
+ local $Math::BigInt::upgrade = undef;
+
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
return $x if $y->is_zero();
- return $x->bzero() if $x == $y; # shortcut
my $sign = 0; # sign of result
$sign = 1 if $x->{sign} ne $y->{sign};
return $x->round($a,$p,$r);
}
- my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x10000);
+ my $m = $self->bone(); my ($xr,$yr);
+ my $x10000 = $self->new(0x10000);
my $y1 = copy(ref($x),$y); # make copy
$y1->babs(); # and positive
my $x1 = $x->copy()->babs(); $x->bzero(); # modify x in place!
$x->badd( bmul( $class->new(
abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))),
$m));
-# $x->badd( bmul( $class->new(int($xr->numify()) ^ int($yr->numify())), $m));
$m->bmul($x10000);
}
$x->bneg() if $sign;
sub length
{
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
my $e = $CALC->_len($x->{value});
- # # fallback, since we do not know the underlying representation
- #my $es = "$x"; my $c = 0; $c = 1 if $es =~ /^[+-]/; # if lib returns '+123'
- #my $e = CORE::length($es)-$c;
return wantarray ? ($e,0) : $e;
}
my $x = shift;
$x = $class->new($x) unless ref $x;
- return 0 if $x->is_zero() || $x->{sign} !~ /^[+-]$/;
+ 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,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ return $x if $x->modify('bsqrt');
+
+ return $x->bnan() if $x->{sign} ne '+'; # -x or inf or NaN => NaN
+ return $x->bzero($a,$p) if $x->is_zero(); # 0 => 0
+ return $x->round($a,$p,$r) if $x->is_one(); # 1 => 1
+
+ return $upgrade->bsqrt($x,$a,$p,$r) if defined $upgrade;
- return $x->bnan() if $x->{sign} =~ /\-|$nan/; # -x or NaN => NaN
- return $x->bzero() if $x->is_zero(); # 0 => 0
- return $x if $x == 1; # 1 => 1
+ if ($CALC->can('_sqrt'))
+ {
+ $x->{value} = $CALC->_sqrt($x->{value});
+ return $x->round($a,$p,$r);
+ }
- my $y = $x->copy(); # give us one more digit accur.
+ return $x->bone($a,$p) if $x < 4; # 2,3 => 1
+ my $y = $x->copy();
my $l = int($x->length()/2);
- $x->bzero();
- $x->binc(); # keep ref($x), but modify it
- $x *= 10 ** $l;
-
- # print "x: $y guess $x\n";
+ $x->bone(); # keep ref($x), but modify it
+ $x->blsft($l,10);
my $last = $self->bzero();
- while ($last != $x)
+ my $two = $self->new(2);
+ my $lastlast = $x+$two;
+ while ($last != $x && $lastlast != $x)
{
- $last = $x;
+ $lastlast = $last; $last = $x;
$x += $y / $x;
- $x /= 2;
+ $x /= $two;
}
- return $x;
+ $x-- if $x * $x > $y; # overshot?
+ $x->round($a,$p,$r);
}
sub exponent
{
# return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return bnan() if $x->is_nan();
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ my $s = $x->{sign}; $s =~ s/^[+-]//;
+ return $self->new($s); # -inf,+inf => inf
+ }
my $e = $class->bzero();
return $e->binc() if $x->is_zero();
$e += $x->_trailing_zeros();
sub mantissa
{
- # return a copy of the mantissa (here always $self)
- my ($self,$x) = objectify(1,@_);
+ # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return bnan() if $x->is_nan();
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ return $self->new($x->{sign}); # keep + or - sign
+ }
my $m = $x->copy();
# that's inefficient
my $zeros = $m->_trailing_zeros();
sub parts
{
- # return a copy of both the exponent and the mantissa (here 0 and self)
- my $self = shift;
- $self = $class->new($self) unless ref $self;
+ # return a copy of both the exponent and the mantissa
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return ($self->mantissa(),$self->exponent());
+ return ($x->mantissa(),$x->exponent());
}
##############################################################################
sub bfround
{
# precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
- # $n == 0 => round to integer
+ # $n == 0 || $n == 1 => round to integer
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_p($precision,$rnd_mode,@_);
+ my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_);
return $x if !defined $scale; # no-op
+ return $x if $x->modify('bfround');
# no-op for BigInts if $n <= 0
- return $x if $scale <= 0;
+ if ($scale <= 0)
+ {
+ $x->{_a} = undef; # clear an eventual set A
+ $x->{_p} = $scale; return $x;
+ }
$x->bround( $x->length()-$scale, $mode);
+ $x->{_a} = undef; # bround sets {_a}
+ $x->{_p} = $scale; # so correct it
+ $x;
}
sub _scan_for_nonzero
return 0 if $len == 1; # '5' is trailed by invisible zeros
my $follow = $pad - 1;
return 0 if $follow > $len || $follow < 1;
- #print "checking $x $r\n";
# since we do not know underlying represention of $x, use decimal string
#my $r = substr ($$xs,-$follow);
# no-op for $n == 0
# and overwrite the rest with 0's, return normalized number
# do not return $x->bnorm(), but $x
+
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_a($accuracy,$rnd_mode,@_);
- return $x if !defined $scale; # no-op
+ my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_);
+ return $x if !defined $scale; # no-op
+ return $x if $x->modify('bround');
- # print "MBI round: $x to $scale $mode\n";
- # -scale means what? tom? hullo? -$scale needed by MBF round, but what for?
- return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero() || $scale == 0;
+ if ($x->is_zero() || $scale == 0)
+ {
+ $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+ return $x;
+ }
+ return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN
# we have fewer digits than we want to scale to
my $len = $x->length();
- # print "$len $scale\n";
- return $x if $len < abs($scale);
+ # scale < 0, but > -len (not >=!)
+ if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
+ {
+ $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+ return $x;
+ }
# count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
my ($pad,$digit_round,$digit_after);
$pad = $len - $scale;
- $pad = abs($scale)+1 if $scale < 0;
+ $pad = abs($scale-1) if $scale < 0;
+
# do not use digit(), it is costly for binary => decimal
- #$digit_round = '0'; $digit_round = $x->digit($pad) if $pad < $len;
- #$digit_after = '0'; $digit_after = $x->digit($pad-1) if $pad > 0;
+
my $xs = $CALC->_str($x->{value});
my $pl = -$pad-1;
+
# pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
# pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
$digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len;
$pl++; $pl ++ if $pad >= $len;
- $digit_after = '0'; $digit_after = substr($$xs,$pl,1)
- if $pad > 0;
-
- #my $d_round = '0'; $d_round = $x->digit($pad) if $pad < $len;
- #my $d_after = '0'; $d_after = $x->digit($pad-1) if $pad > 0;
- # print "$pad $pl $$xs $digit_round:$d_round $digit_after:$d_after\n";
+ $digit_after = '0'; $digit_after = substr($$xs,$pl,1) if $pad > 0;
+
+ # print "$pad $pl $$xs dr $digit_round da $digit_after\n";
# in case of 01234 we round down, for 6789 up, and only in case 5 we look
# closer at the remaining digits of the original $x, remember decision
($mode eq '-inf') && ($x->{sign} eq '+') ||
($mode eq 'zero') # round down if zero, sign adjusted below
);
- # allow rounding one place left of mantissa
- #print "$pad $len $scale\n";
- # this is triggering warnings, and buggy for $scale < 0
- #if (-$scale != $len)
- {
- # old code, depend on internal representation
- # split mantissa at $pad and then pad with zeros
- #my $s5 = int($pad / 5);
- #my $i = 0;
- #while ($i < $s5)
- # {
- # $x->{value}->[$i++] = 0; # replace with 5 x 0
- # }
- #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0
- #my $rem = $pad % 5; # so much left over
- #if ($rem > 0)
- # {
- # #print "remainder $rem\n";
- ## #print "elem $x->{value}->[$s5]\n";
- # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0'
- # }
- #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5'
- #print ${$CALC->_str($pad->{value})}," $len\n";
- if (($pad > 0) && ($pad <= $len))
- {
- substr($$xs,-$pad,$pad) = '0' x $pad;
- $x->{value} = $CALC->_new($xs); # put back in
- }
- elsif ($pad > $len)
+ my $put_back = 0; # not yet modified
+
+ # old code, depend on internal representation
+ # split mantissa at $pad and then pad with zeros
+ #my $s5 = int($pad / 5);
+ #my $i = 0;
+ #while ($i < $s5)
+ # {
+ # $x->{value}->[$i++] = 0; # replace with 5 x 0
+ # }
+ #$x->{value}->[$s5] = '00000'.$x->{value}->[$s5]; # pad with 0
+ #my $rem = $pad % 5; # so much left over
+ #if ($rem > 0)
+ # {
+ # #print "remainder $rem\n";
+ ## #print "elem $x->{value}->[$s5]\n";
+ # substr($x->{value}->[$s5],-$rem,$rem) = '0' x $rem; # stamp w/ '0'
+ # }
+ #$x->{value}->[$s5] = int ($x->{value}->[$s5]); # str '05' => int '5'
+ #print ${$CALC->_str($pad->{value})}," $len\n";
+
+ if (($pad > 0) && ($pad <= $len))
+ {
+ substr($$xs,-$pad,$pad) = '0' x $pad;
+ $put_back = 1;
+ }
+ elsif ($pad > $len)
+ {
+ $x->bzero(); # round to '0'
+ }
+
+ if ($round_up) # what gave test above?
+ {
+ $put_back = 1;
+ $pad = $len, $$xs = '0'x$pad if $scale < 0; # tlr: whack 0.51=>1.0
+
+ # we modify directly the string variant instead of creating a number and
+ # adding it
+ my $c = 0; $pad ++; # for $pad == $len case
+ while ($pad <= $len)
{
- $x->bzero(); # round to '0'
+ $c = substr($$xs,-$pad,1) + 1; $c = '0' if $c eq '10';
+ substr($$xs,-$pad,1) = $c; $pad++;
+ last if $c != 0; # no overflow => early out
}
- # print "res $pad $len $x $$xs\n";
+ $$xs = '1'.$$xs if $c == 0;
+
+ # $x->badd( Math::BigInt->new($x->{sign}.'1'. '0' x $pad) );
}
- # move this later on after the inc of the string
- #$x->{value} = $CALC->_new($xs); # put back in
- if ($round_up) # what gave test above?
+ $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back in
+
+ $x->{_a} = $scale if $scale >= 0;
+ if ($scale < 0)
{
- $pad = $len if $scale < 0; # tlr: whack 0.51=>1.0
- # modify $x in place, undef, undef to avoid rounding
- # str creation much faster than 10 ** something
- $x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad) );
- # increment string in place, to avoid dec=>hex for the '1000...000'
- # $xs ...blah foo
+ $x->{_a} = $len+$scale;
+ $x->{_a} = 0 if $scale < -$len;
}
- # to here:
- #$x->{value} = $CALC->_new($xs); # put back in
$x;
}
{
# return integer less or equal then number, since it is already integer,
# always returns $self
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,$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);
}
{
# internal speedup, set argument to 1, or create a +/- 1
my $self = shift;
- my $x = $self->bzero(); $x->{value} = $CALC->_one();
+ my $x = $self->bone(); # $x->{value} = $CALC->_one();
$x->{sign} = shift || '+';
return $x;
}
# args, hence the copy().
# You can override this method in a subclass, the overload section will call
# $object->_swap() to make sure it arrives at the proper subclass, with some
- # exceptions like '+' and '-'.
+ # exceptions like '+' and '-'. To make '+' and '-' work, you also need to
+ # specify your own overload for them.
# object, (object|scalar) => preserve first and make copy
# scalar, object => swapped, re-swap and create new from first
# (using class of second object, not $class!!)
my $self = shift; # for override in subclass
- #print "swap $self 0:$_[0] 1:$_[1] 2:$_[2]\n";
if ($_[2])
{
my $c = ref ($_[0]) || $class; # fallback $class should not happen
return ( $c->new($_[1]), $_[0] );
}
- else
- {
- return ( $_[0]->copy(), $_[1] );
- }
+ return ( $_[0]->copy(), $_[1] );
}
sub objectify
# $class,1,2. (We can not take '1' as class ;o)
# badd($class,1) is not supported (it should, eventually, try to add undef)
# currently it tries 'Math::BigInt' + 1, which will not work.
-
+
+ # some shortcut for the common cases
+
+ # $x->unary_op();
+ return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
+ # $x->binary_op($y);
+ #return (ref($_[1]),$_[1],$_[2]) if (@_ == 3) && ($_[0]||0 == 2)
+ # && ref($_[1]) && ref($_[2]);
+
my $count = abs(shift || 0);
- #print caller(),"\n";
-
my @a; # resulting array
if (ref $_[0])
{
{
# nope, got 1,2 (Class->xxx(1) => Class,1 and not supported)
$a[0] = $class;
- #print "@_\n"; sleep(1);
$a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first?
}
- #print caller(),"\n";
# print "Now in objectify, my class is today $a[0]\n";
my $k;
if ($count == 0)
{
while ($count > 0)
{
- #print "$count\n";
$count--;
$k = shift;
if (!ref($k))
}
push @a,@_; # return other params, too
}
- #my $i = 0;
- #foreach (@a)
- # {
- # print "o $i $a[0]\n" if $i == 0;
- # print "o $i ",ref($_),"\n" if $i != 0; $i++;
- # }
- #print "objectify done: would return ",scalar @a," values\n";
- #print caller(1),"\n" unless wantarray;
die "$class objectify needs list context" unless wantarray;
@a;
}
sub import
{
my $self = shift;
- #print "import $self @_\n";
+
+ $IMPORT++;
my @a = @_; my $l = scalar @_; my $j = 0;
for ( my $i = 0; $i < $l ; $i++,$j++ )
{
overload::constant integer => sub { $self->new(shift) };
splice @a, $j, 1; $j --;
}
+ elsif ($_[$i] eq 'upgrade')
+ {
+ # this causes upgrading
+ $upgrade = $_[$i+1]; # or undef to disable
+ my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
+ splice @a, $j, $s; $j -= $s;
+ }
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..."
+ $CALC = $_[$i+1] || '';
+ 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(@a); # does not work
- $self->export_to_level(1,$self,@a); # 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
+ $CALC = ''; # signal error
foreach my $lib (@c)
{
$lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
$lib =~ s/\.pm$//;
- if ($] < 5.6)
+ if ($] < 5.006)
{
# Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is
# used in the same script, or eval inside import().
(my $mod = $lib . '.pm') =~ s!::!/!g;
# require does not automatically :: => /, so portability problems arise
- eval { require $mod; $lib->import(); }
+ eval { require $mod; $lib->import( @c ); }
}
else
{
- eval "use $lib;";
+ eval "use $lib qw/@c/;";
}
- $CALC = $lib, last if $@ eq '';
+ $CALC = $lib, last if $@ eq ''; # no error in loading lib?
}
+ die "Couldn't load any math lib, not even the default" if $CALC eq '';
}
sub __from_hex
my $hs = shift;
my $x = Math::BigInt->bzero();
+
+ # strip underscores
+ $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
+ $$hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;
+
return $x->bnan() if $$hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/;
my $sign = '+'; $sign = '-' if ($$hs =~ /^-/);
$val = substr($$hs,$i,4);
$val =~ s/^[+-]?0x// if $len == 0; # for last part only because
$val = hex($val); # hex does not like wrong chars
- # print "$val ",substr($$hs,$i,4),"\n";
$i -= 4; $len --;
$x += $mul * $val if $val != 0;
$mul *= $x65536 if $len >= 0; # skip last mul
}
}
- $x->{sign} = $sign if !$x->is_zero(); # no '-0'
- return $x;
+ $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0'
+ $x;
}
sub __from_bin
my $bs = shift;
my $x = Math::BigInt->bzero();
+ # strip underscores
+ $$bs =~ s/([01])_([01])/$1$2/g;
+ $$bs =~ s/([01])_([01])/$1$2/g;
return $x->bnan() if $$bs !~ /^[+-]?0b[01]+$/;
- my $mul = Math::BigInt->bzero(); $mul++;
- my $x256 = Math::BigInt->new(256);
-
my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/);
$$bs =~ s/^[+-]//; # strip sign
if ($CALC->can('_from_bin'))
}
else
{
+ my $mul = Math::BigInt->bzero(); $mul++;
+ my $x256 = Math::BigInt->new(256);
my $len = CORE::length($$bs)-2;
$len = int($len/8); # 8-digit parts, w/o '0b'
my $val; my $i = -8;
$val = substr($$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($$bs,$i,16),"\n";
+ # slower:
+ # $val = ('0' x (8-CORE::length($val))).$val if CORE::length($val) < 8;
+ $val = ord(pack('B8',substr('00000000'.$val,-8,8)));
$i -= 8; $len --;
$x += $mul * $val if $val != 0;
$mul *= $x256 if $len >= 0; # skip last mul
}
}
- $x->{sign} = $sign if !$x->is_zero();
- return $x;
+ $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); # no '-0'
+ $x;
}
sub _split
{
# (ref to num_str) return num_str
# internal, take apart a string and return the pieces
- # strip leading/trailing whitespace, leading zeros, underscore, reject
+ # strip leading/trailing whitespace, leading zeros, underscore and reject
# invalid input
my $x = shift;
# invalid starting char?
return if $$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
+
+ # strip underscores between digits
+ $$x =~ s/(\d)_(\d)/$1$2/g;
+ $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3
# some possible inputs:
# 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
# .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2
- #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 '$e'\n";
# sign,value for exponent,mantint,mantfrac
my ($es,$ev,$mis,$miv,$mfv);
# valid exponent?
if ($e =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
{
$es = $1; $ev = $2;
- #print "'$m' '$e' e: $es $ev ";
# valid mantissa?
return if $m eq '.' || $m eq '';
my ($mi,$mf) = split /\./,$m;
if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
{
$mis = $1||'+'; $miv = $2;
- # print "$mis $miv";
- # valid, existing fraction part of mantissa?
return unless ($mf =~ /^(\d*?)0*$/); # strip trailing zeros
$mfv = $1;
- #print " split: $mis $miv . $mfv E $es $ev\n";
return (\$mis,\$miv,\$mfv,\$es,\$ev);
}
}
- return; # NaN, not a number
+ return; # NaN, not a number
+ }
+
+sub as_number
+ {
+ # an object might be asked to return itself as bigint on certain overloaded
+ # operations, this does exactly this, so that sub classes can simple inherit
+ # it or override with their own integer conversion routine
+ my $self = shift;
+
+ $self->copy();
+ }
+
+sub as_hex
+ {
+ # return as hex string, with prefixed 0x
+ my $x = shift; $x = $class->new($x) if !ref($x);
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ return '0x0' if $x->is_zero();
+
+ my $es = ''; my $s = '';
+ $s = $x->{sign} if $x->{sign} eq '-';
+ if ($CALC->can('_as_hex'))
+ {
+ $es = ${$CALC->_as_hex($x->{value})};
+ }
+ else
+ {
+ my $x1 = $x->copy()->babs(); my $xr;
+ my $x10000 = Math::BigInt->new (0x10000);
+ while (!$x1->is_zero())
+ {
+ ($x1, $xr) = bdiv($x1,$x10000);
+ $es .= unpack('h4',pack('v',$xr->numify()));
+ }
+ $es = reverse $es;
+ $es =~ s/^[0]+//; # strip leading zeros
+ $s .= '0x';
+ }
+ $s . $es;
}
-sub as_number
+sub as_bin
{
- # an object might be asked to return itself as bigint on certain overloaded
- # operations, this does exactly this, so that sub classes can simple inherit
- # it or override with their own integer conversion routine
- my $self = shift;
-
- return $self->copy();
- }
-
-##############################################################################
-# internal calculation routines (others are in Math::BigInt::Calc etc)
+ # return as binary string, with prefixed 0b
+ my $x = shift; $x = $class->new($x) if !ref($x);
-sub cmp
- {
- # post-normalized compare for internal use (honors signs)
- # input: ref to value, ref to value, sign, sign
- # output: <0, 0, >0
- my ($cx,$cy,$sx,$sy) = @_;
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ return '0b0' if $x->is_zero();
- if ($sx eq '+')
+ my $es = ''; my $s = '';
+ $s = $x->{sign} if $x->{sign} eq '-';
+ if ($CALC->can('_as_bin'))
{
- return 1 if $sy eq '-'; # 0 check handled above
- #return acmp($cx,$cy);
- return $CALC->_acmp($cx,$cy);
+ $es = ${$CALC->_as_bin($x->{value})};
}
else
{
- # $sx eq '-'
- return -1 if $sy eq '+';
- #return acmp($cy,$cx);
- return $CALC->_acmp($cy,$cx);
+ my $x1 = $x->copy()->babs(); my $xr;
+ my $x10000 = Math::BigInt->new (0x10000);
+ while (!$x1->is_zero())
+ {
+ ($x1, $xr) = bdiv($x1,$x10000);
+ $es .= unpack('b16',pack('v',$xr->numify()));
+ }
+ $es = reverse $es;
+ $es =~ s/^[0]+//; # strip leading zeros
+ $s .= '0b';
}
- return 0; # equal
+ $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
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
-
- my $x = shift; my $ty = $class->new(shift); # preserve y, but make class
+ my ($x,$ty) = @_;
+
return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/;
while (!$ty->is_zero())
$x->is_positive(); # true if >= 0
$x->is_negative(); # true if < 0
$x->is_inf(sign); # true if +inf, or -inf (sign is default '+')
+ $x->is_int(); # true if $x is an integer (not a float)
$x->bcmp($y); # compare numbers (undef,<0,=0,>0)
$x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
$x->bnan(); # set $x to NaN
$x->bone(); # set $x to +1
$x->bone('-'); # set $x to -1
+ $x->binf(); # set $x to inf
+ $x->binf('-'); # set $x to -inf
$x->bneg(); # negation
$x->babs(); # absolute value
$x->bnot(); # bitwise not (two's complement)
$x->bsqrt(); # calculate square-root
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
$x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r
$x->bround($N); # accuracy: preserve $N digits
# 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
+ $x->as_bin(); # as signed binary string with prefixed 0b
=head1 DESCRIPTION
=back
+=head1 METHODS
+
+Each of the methods below accepts three additional parameters. These arguments
+$A, $P and $R are accuracy, precision and round_mode. Please see more in the
+section about ACCURACY and ROUNDIND.
+
+=head2 accuracy
+
+ $x->accuracy(5); # local for $x
+ $class->accuracy(5); # global for all members of $class
+
+Set or get the global or local accuracy, aka how many significant digits the
+results have. Please see the section about L<ACCURACY AND PRECISION> for
+further details.
+
+Value must be greater than zero. Pass an undef value to disable it:
+
+ $x->accuracy(undef);
+ Math::BigInt->accuracy(undef);
+
+Returns the current accuracy. For C<$x->accuracy()> it will return either the
+local accuracy, or if not defined, the global. This means the return value
+represents the accuracy that will be in effect for $x:
+
+ $y = Math::BigInt->new(1234567); # unrounded
+ print Math::BigInt->accuracy(4),"\n"; # set 4, print 4
+ $x = Math::BigInt->new(123456); # will be automatically rounded
+ print "$x $y\n"; # '123500 1234567'
+ print $x->accuracy(),"\n"; # will be 4
+ print $y->accuracy(),"\n"; # also 4, since global is 4
+ print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5
+ print $x->accuracy(),"\n"; # still 4
+ print $y->accuracy(),"\n"; # 5, since global is 5
+
+=head2 brsft
+
+ $x->brsft($y,$n);
+
+Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and
+2, but others work, too.
+
+Right shifting usually amounts to dividing $x by $n ** $y and truncating the
+result:
+
+
+ $x = Math::BigInt->new(10);
+ $x->brsft(1); # same as $x >> 1: 5
+ $x = Math::BigInt->new(1234);
+ $x->brsft(2,10); # result 12
+
+There is one exception, and that is base 2 with negative $x:
+
+
+ $x = Math::BigInt->new(-5);
+ print $x->brsft(1);
+
+This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the
+result).
+
+=head2 new
+
+ $x = Math::BigInt->new($str,$A,$P,$R);
+
+Creates a new BigInt object from a string or another BigInt object. The
+input is accepted as decimal, hex (with leading '0x') or binary (with leading
+'0b').
+
+=head2 bnan
+
+ $x = Math::BigInt->bnan();
+
+Creates a new BigInt object representing NaN (Not A Number).
+If used on an object, it will set it to NaN:
+
+ $x->bnan();
+
+=head2 bzero
+
+ $x = Math::BigInt->bzero();
+
+Creates a new BigInt object representing zero.
+If used on an object, it will set it to zero:
+
+ $x->bzero();
+
+=head2 binf
+
+ $x = Math::BigInt->binf($sign);
+
+Creates a new BigInt object representing infinity. The optional argument is
+either '-' or '+', indicating whether you want infinity or minus infinity.
+If used on an object, it will set it to infinity:
+
+ $x->binf();
+ $x->binf('-');
+
+=head2 bone
+
+ $x = Math::BigInt->binf($sign);
+
+Creates a new BigInt object representing one. The optional argument is
+either '-' or '+', indicating whether you want one or minus one.
+If used on an object, it will set it to one:
+
+ $x->bone(); # +1
+ $x->bone('-'); # -1
+
+=head2 is_one() / is_zero() / is_nan() / is_positive() / is_negative() /
+is_inf() / is_odd() / is_even() / is_int()
+
+ $x->is_zero(); # true if arg is +0
+ $x->is_nan(); # true if arg is NaN
+ $x->is_one(); # true if arg is +1
+ $x->is_one('-'); # true if arg is -1
+ $x->is_odd(); # true if odd, false for even
+ $x->is_even(); # true if even, false for odd
+ $x->is_positive(); # true if >= 0
+ $x->is_negative(); # true if < 0
+ $x->is_inf(); # true if +inf
+ $x->is_inf('-'); # true if -inf (sign is default '+')
+ $x->is_int(); # true if $x is an integer
+
+These methods all test the BigInt for one condition and return true or false
+depending on the input.
+
+=head2 bcmp
+
+ $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
+
+=head2 bacmp
+
+ $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
+
+=head2 sign
+
+ $x->sign(); # return the sign, either +,- or NaN
+
+=head2 bcmp
+
+ $x->digit($n); # return the nth digit, counting from right
+
+=head2 bneg
+
+ $x->bneg();
+
+Negate the number, e.g. change the sign between '+' and '-', or between '+inf'
+and '-inf', respectively. Does nothing for NaN or zero.
+
+=head2 babs
+
+ $x->babs();
+
+Set the number to it's absolute value, e.g. change the sign from '-' to '+'
+and from '-inf' to '+inf', respectively. Does nothing for NaN or positive
+numbers.
+
+=head2 bnorm
+
+ $x->bnorm(); # normalize (no-op)
+
+=head2 bnot
+
+ $x->bnot(); # two's complement (bit wise not)
+
+=head2 binc
+
+ $x->binc(); # increment x by 1
+
+=head2 bdec
+
+ $x->bdec(); # decrement x by 1
+
+=head2 badd
+
+ $x->badd($y); # addition (add $y to $x)
+
+=head2 bsub
+
+ $x->bsub($y); # subtraction (subtract $y from $x)
+
+=head2 bmul
+
+ $x->bmul($y); # multiplication (multiply $x by $y)
+
+=head2 bdiv
+
+ $x->bdiv($y); # divide, set $x to quotient
+ # return (quo,rem) or quo if scalar
+
+=head2 bmod
+
+ $x->bmod($y); # modulus (x % y)
+
+=head2 bpow
+
+ $x->bpow($y); # power of arguments (x ** y)
+
+=head2 blsft
+
+ $x->blsft($y); # left shift
+ $x->blsft($y,$n); # left shift, by base $n (like 10)
+
+=head2 brsft
+
+ $x->brsft($y); # right shift
+ $x->brsft($y,$n); # right shift, by base $n (like 10)
+
+=head2 band
+
+ $x->band($y); # bitwise and
+
+=head2 bior
+
+ $x->bior($y); # bitwise inclusive or
+
+=head2 bxor
+
+ $x->bxor($y); # bitwise exclusive or
+
+=head2 bnot
+
+ $x->bnot(); # bitwise not (two's complement)
+
+=head2 bsqrt
+
+ $x->bsqrt(); # calculate square-root
+
+=head2 bfac
+
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
+
+=head2 round
+
+ $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r
+
+=head2 bround
+
+ $x->bround($N); # accuracy: preserve $N digits
+
+=head2 bfround
+
+ $x->bfround($N); # round to $Nth digit, no-op for BigInts
+
+=head2 bfloor
+
+ $x->bfloor();
+
+Set $x to the integer less or equal than $x. This is a no-op in BigInt, but
+does change $x in BigFloat.
+
+=head2 bceil
+
+ $x->bceil();
+
+Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but
+does change $x in BigFloat.
+
+=head2 bgcd
+
+ bgcd(@values); # greatest common divisor (no OO style)
+
+=head2 blcm
+
+ blcm(@values); # lowest common multiplicator (no OO style)
+
+head2 length
+
+ $x->length();
+ ($xl,$fl) = $x->length();
+
+Returns the number of digits in the decimal representation of the number.
+In list context, returns the length of the integer and fraction part. For
+BigInt's, the length of the fraction part will always be 0.
+
+=head2 exponent
+
+ $x->exponent();
+
+Return the exponent of $x as BigInt.
+
+=head2 mantissa
+
+ $x->mantissa();
+
+Return the signed mantissa of $x as BigInt.
+
+=head2 parts
+
+ $x->parts(); # return (mantissa,exponent) as BigInt
+
+=head2 copy
+
+ $x->copy(); # make a true copy of $x (unlike $y = $x;)
+
+=head2 as_number
+
+ $x->as_number(); # return as BigInt (in BigInt: same as copy())
+
+=head2 bsrt
+
+ $x->bstr(); # normalized string
+
+=head2 bsstr
+
+ $x->bsstr(); # normalized string in scientific notation
+
+=head2 as_hex
+
+ $x->as_hex(); # as signed hexadecimal string with prefixed 0x
+
+=head2 as_bin
+
+ $x->as_bin(); # as signed binary string with prefixed 0b
+
=head1 ACCURACY and PRECISION
Since version v1.33, Math::BigInt and Math::BigFloat have full support for
again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange
assumption that 124 has 3 significant digits, while 120/7 will get you
'17', not '17.1' since 120 is thought to have 2 significant digits.
- The rounding after the division then uses the reminder and $y to determine
+ The rounding after the division then uses the remainder and $y to determine
wether it must round up or down.
? I have no idea which is the right way. That's why I used a slightly more
? simple scheme and tweaked the few failing testcases to match it.
=item Setting/Accessing
- * You can set the A global via $Math::BigInt::accuracy or
- $Math::BigFloat::accuracy or whatever class you are using.
- * You can also set P globally by using $Math::SomeClass::precision likewise.
+ * You can set the A global via Math::BigInt->accuracy() or
+ Math::BigFloat->accuracy() or whatever class you are using.
+ * You can also set P globally by using Math::SomeClass->precision() likewise.
* Globals are classwide, and not inherited by subclasses.
- * to undefine A, use $Math::SomeCLass::accuracy = undef
- * to undefine P, use $Math::SomeClass::precision = undef
+ * to undefine A, use Math::SomeCLass->accuracy(undef);
+ * to undefine P, use Math::SomeClass->precision(undef);
+ * Setting Math::SomeClass->accuracy() clears automatically
+ Math::SomeClass->precision(), and vice versa.
* To be valid, A must be > 0, P can have any value.
* If P is negative, this means round to the P'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
+ * to find out the current global A, take Math::SomeClass->accuracy()
+ * to find out the current global P, take Math::SomeClass->precision()
+ * use $x->accuracy() respective $x->precision() for the local setting of $x.
+ * Please note that $x->accuracy() respecive $x->precision() fall back to the
+ defined globals, when $x's A or P is not set.
=item Creating numbers
- !* When you create a number, there should be a way to define 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
+ * When you create a number, you can give it's desired A or P via:
+ $x = Math::BigInt->new($number,$A,$P);
+ * Only one of A or P can be defined, otherwise the result is NaN
+ * If no A or P is give ($x = Math::BigInt->new($number) form), then the
+ globals (if set) will be used. Thus changing the global defaults later on
will not change the A or P of previously created numbers (i.e., A and P of
- $x will be what was in effect when $x was created)
+ $x will be what was in effect when $x was created)
+ * If given undef for A and P, B<no> rounding will occur, and the globals will
+ B<not> be used. This is used by subclasses to create numbers without
+ suffering rounding in the parent. Thus a subclass is able to have it's own
+ globals enforced upon creation of a number by using
+ $x = Math::BigInt->new($number,undef,undef):
+
+ use Math::Bigint::SomeSubclass;
+ use Math::BigInt;
+
+ Math::BigInt->accuracy(2);
+ Math::BigInt::SomeSubClass->accuracy(3);
+ $x = Math::BigInt::SomeSubClass->new(1234);
+
+ $x is now 1230, and not 1200. A subclass might choose to implement
+ this otherwise, e.g. falling back to the parent's A and P.
=item Usage
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.
+ * If two objects are involved in an operation, and one of them has A in
+ effect, and the other P, this results in an error (NaN).
* A takes precendence over P (Hint: A comes before P). If A is defined, it
is used, otherwise P is used. If neither of them is defined, nothing is
used, i.e. the result will have as many digits as it can (with an
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
+ * fdiv will calculate (at least) 4 more digits than required (determined by
A, P or F), and, if F is not used, round the result
(this will still fail in the case of a result like 0.12345000000001 with A
or P of 5, but this can not be helped - or can it?)
* 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
+ R (shift right by one for binary operations like badd). P is used only if
the first parameter (A) is undefined. These three parameters override the
globals in the order detailed as follows, i.e. the first defined value
wins:
+ parameter A
+ parameter P
+ local A (if defined on both of the operands: smaller one is taken)
- + local P (if defined on both of the operands: smaller one is taken)
+ + local P (if defined on both of the operands: bigger one is taken)
+ global A
+ global P
+ global F
* 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.
+ * $x->accuracy() clears $x->precision(), and vice versa.
=item Rounding
following rounding modes (R):
'even', 'odd', '+inf', '-inf', 'zero', 'trunc'
* you can set and get the global R by using Math::SomeClass->round_mode()
- or by setting $Math::SomeClass::rnd_mode
+ or by setting $Math::SomeClass::round_mode
* after each operation, $result->round() is called, and the result may
eventually be rounded (that is, if A or P were set either locally,
globally or as parameter to the operation)
- * to manually round a number, call $x->round($A,$P,$rnd_mode);
+ * 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:
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.
+(usually 1e5 or 1e7) with the least significant digit first, while BitVect.pm
+uses a bit vector of base 2, most significant bit first. Other modules might
+use even different means of representing the numbers. See the respective
+module documentation for further details.
=head2 SIGN
=head1 EXAMPLES
- use Math::BigInt qw(bstr);
+ use Math::BigInt;
sub bint { Math::BigInt->new(shift); }
- $x = bstr("1234") # string "1234"
+ $x = Math::BigInt->bstr("1234") # string "1234"
$x = "$x"; # same as bstr()
- $x = bneg("1234") # Bigint "-1234"
$x = Math::BigInt->bneg("1234"); # Bigint "-1234"
$x = Math::BigInt->babs("-12345"); # Bigint "12345"
$x = Math::BigInt->bnorm("-0 00"); # BigInt "0"
$x = $x + 5 / 2; # BigInt "3"
$x = $x ** 3; # BigInt "27"
$x *= 2; # BigInt "54"
- $x = new Math::BigInt; # BigInt "0"
+ $x = Math::BigInt->new(0); # BigInt "0"
$x--; # BigInt "-1"
$x = Math::BigInt->badd(4,5) # BigInt "9"
- $x = Math::BigInt::badd(4,5) # BigInt "9"
print $x->bsstr(); # 9e+0
Examples for rounding:
$x = Math::BigFloat->new(123.4567);
$y = Math::BigFloat->new(123.456789);
- $Math::BigFloat::accuracy = 4; # no more A than 4
+ Math::BigFloat->accuracy(4); # no more A than 4
ok ($x->copy()->fround(),123.4); # even rounding
print $x->copy()->fround(),"\n"; # 123.4
Math::BigFloat->round_mode('odd'); # round to odd
print $x->copy()->fround(),"\n"; # 123.5
- $Math::BigFloat::accuracy = 5; # no more A than 5
+ Math::BigFloat->accuracy(5); # no more A than 5
Math::BigFloat->round_mode('odd'); # round to odd
print $x->copy()->fround(),"\n"; # 123.46
$y = $x->copy()->fround(4),"\n"; # A = 4: 123.4
print "$y, ",$y->accuracy(),"\n"; # 123.4, 4
- $Math::BigFloat::accuracy = undef; # A not important
- $Math::BigFloat::precision = 2; # P important
- print $x->copy()->bnorm(),"\n"; # 123.46
- print $x->copy()->fround(),"\n"; # 123.46
+ Math::BigFloat->accuracy(undef); # A not important now
+ Math::BigFloat->precision(2); # P important
+ print $x->copy()->bnorm(),"\n"; # 123.46
+ print $x->copy()->fround(),"\n"; # 123.46
+
+Examples for converting:
+
+ my $x = Math::BigInt->new('0b1'.'01' x 123);
+ print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n";
=head1 Autocreating constants
+ '123456789123456789';
do not work. You need an explicit Math::BigInt->new() around one of the
-operands.
+operands. You should also quote large constants to protect loss of precision:
+
+ use Math::Bigint;
+
+ $x = Math::BigInt->new('1234567889123456789123456789123456789');
+
+Without the quotes Perl would convert the large number to a floating point
+constant at compile time and then hand the result to BigInt, which results in
+an truncated result or a NaN.
=head1 PERFORMANCE
more time then the actual addition.
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.
+be minimized or even completely avoided. A test implementation of COW did show
+performance gains for overloaded math, but introduced a performance loss due
+to a constant overhead for all other operatons.
+
+The rewritten version of this module is slower on certain operations, like
+new(), bstr() and numify(). The reason are that it does now more work and
+handles more cases. The time spent in these operations is usually gained in
+the other operations so that programs on the average should get faster. If
+they don't, please contect the author.
-The new version of this module is slower on new(), bstr() and numify(). Some
-operations may be slower for small numbers, but are significantly faster for
-big numbers. Other operations are now constant (O(1), like bneg(), babs()
-etc), instead of O(N) and thus nearly always take much less time.
+Some operations may be slower for small numbers, but are significantly faster
+for big numbers. Other operations are now constant (O(1), like bneg(), babs()
+etc), instead of O(N) and thus nearly always take much less time. These
+optimizations were done on purpose.
If you find the Calc module to slow, try to install any of the replacement
modules and see if they help you.
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.
+See L<MATH LIBRARY> for more information.
-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/>:
+For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>.
- use Math::BigInt lib => 'BitVect';
+=head2 SUBCLASSING
+
+=head1 Subclassing Math::BigInt
+
+The basic design of Math::BigInt allows simple subclasses with very little
+work, as long as a few simple rules are followed:
+
+=over 2
+
+=item *
+
+The public API must remain consistent, i.e. if a sub-class is overloading
+addition, the sub-class must use the same name, in this case badd(). The
+reason for this is that Math::BigInt is optimized to call the object methods
+directly.
+
+=item *
+
+The private object hash keys like C<$x->{sign}> may not be changed, but
+additional keys can be added, like C<$x->{_custom}>.
+
+=item *
+
+Accessor functions are available for all existing object hash keys and should
+be used instead of directly accessing the internal hash keys. The reason for
+this is that Math::BigInt itself has a pluggable interface which permits it
+to support different storage methods.
+
+=back
+
+More complex sub-classes may have to replicate more of the logic internal of
+Math::BigInt if they need to change more basic behaviors. A subclass that
+needs to merely change the output only needs to overload C<bstr()>.
+
+All other object methods and overloaded functions can be directly inherited
+from the parent class.
+
+At the very minimum, any subclass will need to provide it's own C<new()> and can
+store additional hash keys in the object. There are also some package globals
+that must be defined, e.g.:
+
+ # Globals
+ $accuracy = undef;
+ $precision = -2; # round to 2 decimal places
+ $round_mode = 'even';
+ $div_scale = 40;
+
+Additionally, you might want to provide the following two globals to allow
+auto-upgrading and auto-downgrading to work correctly:
+
+ $upgrade = undef;
+ $downgrade = undef;
+
+This allows Math::BigInt to correctly retrieve package globals from the
+subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or
+t/Math/BigFloat/SubClass.pm completely functional subclass examples.
+
+Don't forget to
+
+ use overload;
+
+in your subclass to automatically inherit the overloading from the parent. If
+you like, you can change part of the overloading, look at Math::String for an
+example.
+
+=head1 UPGRADING
- my $x = Math::BigInt->new(2);
- print $x ** (1024*1024);
+When used like this:
-For more benchmark results see http://bloodgate.com/perl/benchmarks.html
+ use Math::BigInt upgrade => 'Foo::Bar';
+
+certain operations will 'upgrade' their calculation and thus the result to
+the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat:
+
+ use Math::BigInt upgrade => 'Math::BigFloat';
+
+As a shortcut, you can use the module C<bignum>:
+
+ use bignum;
+
+Also good for oneliners:
+
+ perl -Mbignum -le 'print 2 ** 255'
+
+This makes it possible to mix arguments of different classes (as in 2.5 + 2)
+as well es preserve accuracy (as in sqrt(3)).
+
+Beware: This feature is not fully implemented yet.
+
+=head2 Auto-upgrade
+
+The following methods upgrade themselves unconditionally; that is if upgrade
+is in effect, they will always hand up their work:
+
+=over 2
+
+=item bsqrt()
+
+=item div()
+
+=item blog()
+
+=back
+
+Beware: This list is not complete.
+
+All other methods upgrade themselves only when one (or all) of their
+arguments are of the class mentioned in $upgrade (This might change in later
+versions to a more sophisticated scheme):
=head1 BUGS
$y = Math::BigInt->new($y);
ok ($x,$y); # okay
-There is not yet a way to get a number automatically represented in exactly
-the way Perl represents it.
+Alternatively, simple use <=> for comparisations, that will get it always
+right. There is not yet a way to get a number automatically represented as
+a string that matches exactly the way Perl represents it.
=item int()
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();
+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
needs to preserve $x since it does not know that it later will get overwritten.
This makes a copy of $x and takes O(N), but $x->bneg() is O(1).
-With Copy-On-Write, this issue will be gone. Stay tuned...
+With Copy-On-Write, this issue would be gone, but C-o-W is not implemented
+since it is slower for all other things.
=item Mixing different object types
$integer = $mbi2 / $mbf; # $mbi2->bdiv()
This is because math with overloaded operators follows the first (dominating)
-operand, this one's operation is called and returns thus the result. So,
+operand, and the operation of that is called and returns thus the result. So,
Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether
the result should be a Math::BigFloat or the second operant is one.
This section also applies to other overloaded math packages, like Math::String.
+One solution to you problem might be L<autoupgrading|upgrading>.
+
=item bsqrt()
-C<bsqrt()> works only good if the result is an big integer, e.g. the square
+C<bsqrt()> works only good if the result is a big integer, e.g. the square
root of 144 is 12, but from 12 the square root is 3, regardless of rounding
mode.
If you want a better approximation of the square root, then use:
$x = Math::BigFloat->new(12);
- $Math::BigFloat::precision = 0;
+ Math::BigFloat->precision(0);
Math::BigFloat->round_mode('even');
print $x->copy->bsqrt(),"\n"; # 4
- $Math::BigFloat::precision = 2;
+ Math::BigFloat->precision(2);
print $x->bsqrt(),"\n"; # 3.46
print $x->bsqrt(3),"\n"; # 3.464
+=item brsft()
+
+For negative numbers in base see also L<brsft|brsft>.
+
=back
=head1 LICENSE
=head1 SEE ALSO
-L<Math::BigFloat> and L<Math::Big>.
+L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>,
+L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
-L<Math::BigInt::BitVect> and L<Math::BigInt::Pari>.
+The package at
+L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
+more documentation including a full version history, testcases, empty
+subclass files and benchmarks.
=head1 AUTHORS
projects / p5sagit/p5-mst-13.2.git / blobdiff