-#!/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 = '1.42';
+$VERSION = '1.66';
use Exporter;
@ISA = qw( Exporter );
-@EXPORT_OK = qw( bneg babs bcmp badd bmul bdiv bmod bnorm bsub
- bgcd blcm
- bround
- blsft brsft band bior bxor bnot bpow bnan bzero
- bacmp bstr bsstr binc bdec binf bfloor bceil
- is_odd is_even is_zero is_one is_nan is_inf sign
- is_positive is_negative
- length as_number
- objectify _swap
- );
-#@EXPORT = qw( );
-use vars qw/$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 $downgrade/;
+# the following are internal and should never be accessed from the outside
+use vars qw/$_trap_nan $_trap_inf/;
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 { $_[2] ?
ref($_[0])->bcmp($_[1],$_[0]) :
- ref($_[0])->bcmp($_[0],$_[1])},
-'cmp' => sub {
+ $_[0]->bcmp($_[1])},
+'cmp' => sub {
$_[2] ?
- $_[1] cmp $_[0]->bstr() :
- $_[0]->bstr() cmp $_[1] },
+ "$_[1]" cmp $_[0]->bstr() :
+ $_[0]->bstr() cmp "$_[1]" },
+'log' => sub { $_[0]->copy()->blog(); },
'int' => sub { $_[0]->copy(); },
'neg' => sub { $_[0]->copy()->bneg(); },
'abs' => sub { $_[0]->copy()->babs(); },
+'sqrt' => sub { $_[0]->copy()->bsqrt(); },
'~' => sub { $_[0]->copy()->bnot(); },
'*' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bmul($a[1]); },
# 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 { $_[0]->numify(); }
;
##############################################################################
# global constants, flags and accessory
+# these are public, but their usage is not recommended, use the accessor
+# methods instead
+
+$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
+
+# these are internally, and not to be used from the outside
+
use constant MB_NEVER_ROUND => 0x0001;
-my $NaNOK=1; # are NaNs ok?
+$_trap_nan = 0; # are NaNs ok? set w/ config()
+$_trap_inf = 0; # are infs ok? set w/ config()
my $nan = 'NaN'; # constants for easier life
-my $CALC = 'Math::BigInt::Calc'; # module to do low level math
-sub _core_lib () { return $CALC; } # for test suite
+my $CALC = 'Math::BigInt::Calc'; # module to do the low level math
+my $IMPORT = 0; # was import() called yet?
+ # used to make require work
-# Rounding modes, one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
-$rnd_mode = 'even';
-$accuracy = undef;
-$precision = undef;
-$div_scale = 40;
+##############################################################################
+# the old code had $rnd_mode, so we need to support it, too
+
+$rnd_mode = 'even';
+sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; }
+sub FETCH { return $round_mode; }
+sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
+
+BEGIN { tie $rnd_mode, 'Math::BigInt'; }
+
+##############################################################################
sub round_mode
{
+ no strict 'refs';
# make Class->round_mode() work
- my $self = shift || $class;
- # shift @_ if defined $_[0] && $_[0] eq $class;
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
if (defined $_[0])
{
my $m = shift;
- die "Unknown round mode $m"
- if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
- $rnd_mode = $m; return;
+ if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
+ {
+ require Carp; Carp::croak ("Unknown round mode '$m'");
+ }
+ return ${"${class}::round_mode"} = $m;
+ }
+ ${"${class}::round_mode"};
+ }
+
+sub upgrade
+ {
+ no strict 'refs';
+ # make Class->upgrade() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ # need to set new value?
+ if (@_ > 0)
+ {
+ my $u = shift;
+ return ${"${class}::upgrade"} = $u;
+ }
+ ${"${class}::upgrade"};
+ }
+
+sub downgrade
+ {
+ no strict 'refs';
+ # make Class->downgrade() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ # need to set new value?
+ if (@_ > 0)
+ {
+ my $u = shift;
+ return ${"${class}::downgrade"} = $u;
}
- return $rnd_mode;
+ ${"${class}::downgrade"};
+ }
+
+sub div_scale
+ {
+ no strict 'refs';
+ # make Class->div_scale() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ if (defined $_[0])
+ {
+ if ($_[0] < 0)
+ {
+ require Carp; Carp::croak ('div_scale must be greater than zero');
+ }
+ ${"${class}::div_scale"} = shift;
+ }
+ ${"${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;
+ # convert objects to scalars to avoid deep recursion. If object doesn't
+ # have numify(), then hopefully it will have overloading for int() and
+ # boolean test without wandering into a deep recursion path...
+ $a = $a->numify() if ref($a) && $a->can('numify');
+
+ if (defined $a)
+ {
+ # also croak on non-numerical
+ if (!$a || $a <= 0)
+ {
+ require Carp;
+ Carp::croak ('Argument to accuracy must be greater than zero');
+ }
+ if (int($a) != $a)
+ {
+ require Carp; Carp::croak ('Argument to accuracy must be an integer');
+ }
+ }
+ if (ref($x))
+ {
+ # $object->accuracy() or fallback to global
+ $x->bround($a) if $a; # not for undef, 0
+ $x->{_a} = $a; # set/overwrite, even if not rounded
+ $x->{_p} = undef; # clear P
+ $a = ${"${class}::accuracy"} unless defined $a; # proper return value
+ }
+ else
+ {
+ # set global
+ ${"${class}::accuracy"} = $a;
+ ${"${class}::precision"} = undef; # clear P
+ }
+ return $a; # shortcut
}
- return $x->{_a};
- }
+
+ my $r;
+ # $object->accuracy() or fallback to global
+ $r = $x->{_a} if ref($x);
+ # but don't return global undef, when $x's accuracy is 0!
+ $r = ${"${class}::accuracy"} if !defined $r;
+ $r;
+ }
sub precision
{
+ # $x->precision($p); ref($x) $p
+ # $x->precision(); ref($x)
+ # Class->precision(); class
+ # Class->precision($p); class $p
+
my $x = shift;
+ my $class = ref($x) || $x || __PACKAGE__;
- die ("precision() needs reference to object as first parameter.")
- if !ref $x;
+ no strict 'refs';
+ if (@_ > 0)
+ {
+ my $p = shift;
+ # convert objects to scalars to avoid deep recursion. If object doesn't
+ # have numify(), then hopefully it will have overloading for int() and
+ # boolean test without wandering into a deep recursion path...
+ $p = $p->numify() if ref($p) && $p->can('numify');
+ if ((defined $p) && (int($p) != $p))
+ {
+ require Carp; Carp::croak ('Argument to precision must be an integer');
+ }
+ if (ref($x))
+ {
+ # $object->precision() or fallback to global
+ $x->bfround($p) if $p; # not for undef, 0
+ $x->{_p} = $p; # set/overwrite, even if not rounded
+ $x->{_a} = undef; # clear A
+ $p = ${"${class}::precision"} unless defined $p; # proper return value
+ }
+ else
+ {
+ # set global
+ ${"${class}::precision"} = $p;
+ ${"${class}::accuracy"} = undef; # clear A
+ }
+ return $p; # shortcut
+ }
+
+ my $r;
+ # $object->precision() or fallback to global
+ $r = $x->{_p} if ref($x);
+ # but don't return global undef, when $x's precision is 0!
+ $r = ${"${class}::precision"} if !defined $r;
+ $r;
+ }
+
+sub config
+ {
+ # return (or set) configuration data as hash ref
+ my $class = shift || 'Math::BigInt';
+ no strict 'refs';
if (@_ > 0)
{
- $x->{_p} = shift;
- $x->round() if defined $x->{_p};
+ # try to set given options as arguments from hash
+
+ my $args = $_[0];
+ if (ref($args) ne 'HASH')
+ {
+ $args = { @_ };
+ }
+ # these values can be "set"
+ my $set_args = {};
+ foreach my $key (
+ qw/trap_inf trap_nan
+ upgrade downgrade precision accuracy round_mode div_scale/
+ )
+ {
+ $set_args->{$key} = $args->{$key} if exists $args->{$key};
+ delete $args->{$key};
+ }
+ if (keys %$args > 0)
+ {
+ require Carp;
+ Carp::croak ("Illegal key(s) '",
+ join("','",keys %$args),"' passed to $class\->config()");
+ }
+ foreach my $key (keys %$set_args)
+ {
+ if ($key =~ /^trap_(inf|nan)\z/)
+ {
+ ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0);
+ next;
+ }
+ # use a call instead of just setting the $variable to check argument
+ $class->$key($set_args->{$key});
+ }
}
- return $x->{_p};
- }
+
+ # now return actual configuration
+
+ my $cfg = {
+ lib => $CALC,
+ lib_version => ${"${CALC}::VERSION"},
+ class => $class,
+ trap_nan => ${"${class}::_trap_nan"},
+ trap_inf => ${"${class}::_trap_inf"},
+ version => ${"${class}::VERSION"},
+ };
+ foreach my $key (qw/
+ upgrade downgrade precision accuracy round_mode div_scale
+ /)
+ {
+ $cfg->{$key} = ${"${class}::$key"};
+ };
+ $cfg;
+ }
sub _scale_a
{
return unless ref($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}))
- {
- my $c = ref($x->{$k});
- $self->{$k} = $c->new($x->{$k}); # no copy() due to deep rec
- }
- else
+ else # normal ref
{
- $self->{$k} = $x->{$k};
+ my $xk = $x->{$k};
+ if ($xk->can('copy'))
+ {
+ $self->{$k} = $xk->copy();
+ }
+ else
+ {
+ $self->{$k} = $xk->new($xk);
+ }
}
}
$self;
# cause costly overloaded code to be called. The only allowed ops are
# ref() and defined.
- my $class = shift;
+ my ($class,$wanted,$a,$p,$r) = @_;
- my $wanted = shift; # avoid numify call by not using || here
- return $class->bzero() if !defined $wanted; # default to 0
- return $class->copy($wanted) if ref($wanted);
+ # avoid numify-calls by not using || on $wanted!
+ return $class->bzero($a,$p) if !defined $wanted; # default to 0
+ return $class->copy($wanted,$a,$p,$r)
+ if ref($wanted) && $wanted->isa($class); # MBI or subclass
+
+ $class->import() if $IMPORT == 0; # make require work
+
+ my $self = bless {}, $class;
+
+ # shortcut for "normal" numbers
+ if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/))
+ {
+ $self->{sign} = $1 || '+';
+ my $ref = \$wanted;
+ if ($wanted =~ /^[+-]/)
+ {
+ # remove sign without touching wanted to make it work with constants
+ my $t = $wanted; $t =~ s/^[+-]//; $ref = \$t;
+ }
+ # force to string version (otherwise Pari is unhappy about overflowed
+ # constants, for instance)
+ # not good, BigInt shouldn't need to know about alternative libs:
+ # $ref = \"$$ref" if $CALC eq 'Math::BigInt::Pari';
+ $self->{value} = $CALC->_new($ref);
+ no strict 'refs';
+ if ( (defined $a) || (defined $p)
+ || (defined ${"${class}::precision"})
+ || (defined ${"${class}::accuracy"})
+ )
+ {
+ $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p);
+ }
+ return $self;
+ }
- my $self = {}; bless $self, $class;
# handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]inf$/)
+ if ($wanted =~ /^[+-]?inf$/)
{
$self->{value} = $CALC->_zero();
- $self->{sign} = $wanted;
+ $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf';
return $self;
}
# split str in m mantissa, e exponent, i integer, f fraction, v value, s sign
my ($mis,$miv,$mfv,$es,$ev) = _split(\$wanted);
if (!ref $mis)
{
- die "$wanted is not a number initialized to $class" if !$NaNOK;
- #print "NaN 1\n";
+ if ($_trap_nan)
+ {
+ require Carp; Carp::croak("$wanted is not a number in $class");
+ }
$self->{value} = $CALC->_zero();
$self->{sign} = $nan;
return $self;
my $diff = $e - CORE::length($$mfv);
if ($diff < 0) # Not integer
{
+ if ($_trap_nan)
+ {
+ require Carp; Carp::croak("$wanted not an integer in $class");
+ }
#print "NOI 1\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
else # diff >= 0
{
# adjust fraction and add it to value
- # print "diff > 0 $$miv\n";
+ #print "diff > 0 $$miv\n";
$$miv = $$miv . ($$mfv . '0' x $diff);
}
}
if ($$mfv ne '') # e <= 0
{
# fraction and negative/zero E => NOI
+ if ($_trap_nan)
+ {
+ require Carp; Carp::croak("$wanted not an integer in $class");
+ }
#print "NOI 2 \$\$mfv '$$mfv'\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
elsif ($e < 0)
$e = abs($e);
if ($$miv !~ s/0{$e}$//) # can strip so many zero's?
{
+ if ($_trap_nan)
+ {
+ require Carp; Carp::croak("$wanted not an integer in $class");
+ }
#print "NOI 3\n";
+ return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
$self->{sign} = $nan;
}
}
}
$self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0
$self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/;
- #print "$wanted => $self->{sign}\n";
# if any of the globals is set, use them to round and store them inside $self
- $self->round($accuracy,$precision,$rnd_mode)
- if defined $accuracy || defined $precision;
- return $self;
+ # do not round for new($x,undef,undef) since that is used by MBF to signal
+ # no rounding
+ $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p;
+ $self;
}
sub bnan
{
my $c = $self; $self = {}; bless $self, $c;
}
+ no strict 'refs';
+ if (${"${class}::_trap_nan"})
+ {
+ require Carp;
+ Carp::croak ("Tried to set $self to NaN in $class\::bnan()");
+ }
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('bnan');
- $self->{value} = $CALC->_zero();
+ if ($self->can('_bnan'))
+ {
+ # use subclass to initialize
+ $self->_bnan();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
$self->{sign} = $nan;
+ delete $self->{_a}; delete $self->{_p}; # rounding NaN is silly
return $self;
}
# create a bigint '+-inf', if given a BigInt, set it to '+-inf'
# the sign is either '+', or if given, used from there
my $self = shift;
- my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
+ my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/;
$self = $class if !defined $self;
if (!ref($self))
{
my $c = $self; $self = {}; bless $self, $c;
}
+ no strict 'refs';
+ if (${"${class}::_trap_inf"})
+ {
+ require Carp;
+ Carp::croak ("Tried to set $self to +-inf in $class\::binfn()");
+ }
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('binf');
- $self->{value} = $CALC->_zero();
- $self->{sign} = $sign.'inf';
+ if ($self->can('_binf'))
+ {
+ # use subclass to initialize
+ $self->_binf();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
+ $sign = $sign . 'inf' if $sign !~ /inf$/; # - => -inf
+ $self->{sign} = $sign;
+ ($self->{_a},$self->{_p}) = @_; # take over requested rounding
return $self;
}
{
my $c = $self; $self = {}; bless $self, $c;
}
+ $self->import() if $IMPORT == 0; # make require work
return if $self->modify('bzero');
- $self->{value} = $CALC->_zero();
+
+ if ($self->can('_bzero'))
+ {
+ # use subclass to initialize
+ $self->_bzero();
+ }
+ else
+ {
+ # otherwise do our own thing
+ $self->{value} = $CALC->_zero();
+ }
$self->{sign} = '+';
- #print "result: $self\n";
- return $self;
+ if (@_ > 0)
+ {
+ if (@_ > 3)
+ {
+ # call like: $x->bzero($a,$p,$r,$y);
+ ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
+ }
+ else
+ {
+ $self->{_a} = $_[0]
+ if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
+ $self->{_p} = $_[1]
+ if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
+ }
+ }
+ $self;
}
sub bone
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";
- return $self;
+ if (@_ > 0)
+ {
+ if (@_ > 3)
+ {
+ # call like: $x->bone($sign,$a,$p,$r,$y);
+ ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
+ }
+ else
+ {
+ $self->{_a} = $_[0]
+ if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
+ $self->{_p} = $_[1]
+ if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
+ }
+ }
+ $self;
}
##############################################################################
# (ref to BFLOAT or num_str ) return num_str
# Convert number from internal format to scientific string format.
# internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
- my ($self,$x) = objectify(1,@_);
+ my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
+ # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
if ($x->{sign} !~ /^[+-]$/)
{
return 'inf'; # +inf
}
my ($m,$e) = $x->parts();
- # e can only be positive
- my $sign = 'e+';
- # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s;
+ my $sign = 'e+'; # e can only be positive
return $m->bstr().$sign.$e->bstr();
}
sub bstr
{
# make a string from bigint object
- my $x = shift; $x = $class->new($x) unless ref $x;
+ 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} !~ /^[+-]$/;
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/;
my $num = $CALC->_num($x->{value});
return -$num if $x->{sign} eq '-';
- return $num;
+ $num;
}
##############################################################################
sub sign
{
- # return the sign of the number: +/-/NaN
- my ($self,$x) = objectify(1,@_);
- return $x->{sign};
+ # return the sign of the number: +/-/-inf/+inf/NaN
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ $x->{sign};
}
-sub round
+sub _find_round_parameters
{
# After any operation or when calling round(), the result is rounded by
# regarding the A & P from arguments, local parameters, or globals.
- # The result's A or P are set by the rounding, but not inspected beforehand
- # (aka only the arguments enter into it). This works because the given
- # 'first' argument is both the result and true first argument with unchanged
- # A and P settings.
- # This does not yet handle $x with A, and $y with P (which should be an
- # error).
- my $self = shift;
- my $a = shift; # accuracy, if given by caller
- my $p = shift; # precision, if given by caller
- my $r = shift; # round_mode, if given by caller
- my @args = @_; # all 'other' arguments (0 for unary, 1 for binary ops)
-
- $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
-
+
+ # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!!
+
+ # This procedure finds the round parameters, but it is for speed reasons
+ # duplicated in round. Otherwise, it is tested by the testsuite and used
+ # by fdiv().
+
+ # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P
+ # were requested/defined (locally or globally or both)
+
+ my ($self,$a,$p,$r,@args) = @_;
+ # $a accuracy, if given by caller
+ # $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';
- 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;
+
+ # A == 0 is useless, so undef it to signal no rounding
+ $a = undef if defined $a && $a == 0;
+
+ # no rounding today?
+ return ($self) unless defined $a || defined $p; # early out
+
+ # set A and set P is an fatal error
+ return ($self->bnan()) if defined $a && defined $p; # error
+
+ $r = ${"$c\::round_mode"} unless defined $r;
+ if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
+ {
+ require Carp; Carp::croak ("Unknown round mode '$r'");
}
+ ($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;
+
+ 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;
+
+ # A == 0 is useless, so undef it to signal no rounding
+ $a = undef if defined $a && $a == 0;
+
+ # no rounding today?
+ return $self unless defined $a || defined $p; # early out
+
+ # set A and set P is an fatal error
+ return $self->bnan() if defined $a && defined $p;
+
+ $r = ${"$c\::round_mode"} unless defined $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
{
- # (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;
}
{
# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT or num_str, BINT or num_str) return cond_code
- my ($self,$x,$y) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y) = (ref($_[0]),@_);
+
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y) = objectify(2,@_);
+ }
+
+ return $upgrade->bcmp($x,$y) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
return +1 if $x->{sign} eq '+inf';
return -1 if $x->{sign} eq '-inf';
return -1 if $y->{sign} eq '+inf';
- return +1 if $y->{sign} eq '-inf';
+ return +1;
}
# check sign for speed first
return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
- # shortcut
- my $xz = $x->is_zero();
- my $yz = $y->is_zero();
- return 0 if $xz && $yz; # 0 <=> 0
- return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y
- return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0
- # normal compare now
- &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0;
+ # have same sign, so compare absolute values. Don't make tests for zero here
+ # because it's actually slower than testin in Calc (especially w/ Pari et al)
+
+ # post-normalized compare for internal use (honors signs)
+ if ($x->{sign} eq '+')
+ {
+ # $x and $y both > 0
+ return $CALC->_acmp($x->{value},$y->{value});
+ }
+
+ # $x && $y both < 0
+ $CALC->_acmp($y->{value},$x->{value}); # swaped (lib returns 0,1,-1)
}
sub bacmp
# Compares 2 values, ignoring their signs.
# Returns one of undef, <0, =0, >0. (suitable for sort)
# (BINT, BINT) return cond_code
- my ($self,$x,$y) = objectify(2,@_);
+ # set up parameters
+ my ($self,$x,$y) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y) = objectify(2,@_);
+ }
+
+ return $upgrade->bacmp($x,$y) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
+
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
# handle +-inf and NaN
return 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,@_);
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
return $x if $x->modify('badd');
+ return $upgrade->badd($x,$y,@r) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
+ $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) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ $x;
}
sub bsub
{
# (BINT or num_str, BINT or num_str) return num_str
# subtract second arg from first, modify first
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
return $x if $x->modify('bsub');
- $x->badd($y->bneg()); # badd does not leave internal zeros
- $y->bneg(); # refix y, assumes no one reads $y in between
- return $x->round($a,$p,$r,$y);
+
+# upgrade done by badd():
+# return $upgrade->badd($x,$y,@r) if defined $upgrade &&
+# ((!$x->isa($self)) || (!$y->isa($self)));
+
+ if ($y->is_zero())
+ {
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+
+ $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
+ $x->badd($y,@r); # badd does not leave internal zeros
+ $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
+ $x; # already rounded by badd() or no round necc.
}
sub binc
{
# increment arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
- # my $x = shift; $x = $class->new($x) unless ref $x; my $self = ref($x);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('binc');
- $x->badd($self->__one())->round($a,$p,$r);
+
+ if ($x->{sign} eq '+')
+ {
+ $x->{value} = $CALC->_inc($x->{value});
+ $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ elsif ($x->{sign} eq '-')
+ {
+ $x->{value} = $CALC->_dec($x->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+ $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ # inf, nan handling etc
+ $x->badd($self->__one(),$a,$p,$r); # badd does round
}
sub bdec
{
# decrement arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('bdec');
- $x->badd($self->__one('-'))->round($a,$p,$r);
+
+ my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+';
+ # <= 0
+ if (($x->{sign} eq '-') || $zero)
+ {
+ $x->{value} = $CALC->_inc($x->{value});
+ $x->{sign} = '-' if $zero; # 0 => 1 => -1
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+ $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ # > 0
+ elsif ($x->{sign} eq '+')
+ {
+ $x->{value} = $CALC->_dec($x->{value});
+ $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ # inf, nan handling etc
+ $x->badd($self->__one('-'),$a,$p,$r); # badd does round
}
+sub blog
+ {
+ # not implemented yet
+ my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ return $upgrade->blog($upgrade->new($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
$CALC->_is_zero($x->{value});
- #return $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,@_);
+
+ $sign = '' if !defined $sign;
+ return 1 if $sign eq $x->{sign}; # match ("+inf" eq "+inf")
+ return 0 if $sign !~ /^([+-]|)$/;
- return $x->{sign} =~ /^[+-]inf$/ if $sign eq '';
- return $x->{sign} =~ /^[$sign]inf$/;
+ 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 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)
+ # 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
+ }
+
+###############################################################################
+
+sub bmul
+ {
+ # multiply two numbers -- stolen from Knuth Vol 2 pg 233
+ # (BINT or num_str, BINT or num_str) return BINT
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
+
+ return $x if $x->modify('bmul');
+
+ return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+
+ # inf handling
+ if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return $x->bnan() if $x->is_zero() || $y->is_zero();
+ # result will always be +-inf:
+ # +inf * +/+inf => +inf, -inf * -/-inf => +inf
+ # +inf * -/-inf => -inf, -inf * +/+inf => -inf
+ return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
+ return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
+ return $x->binf('-');
+ }
+
+ return $upgrade->bmul($x,$y,@r)
+ if defined $upgrade && $y->isa($upgrade);
+
+ $r[3] = $y; # no push here
+
+ $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
+
+ $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
+
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ $x;
}
-sub 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} =~ /^-/);
+sub _div_inf
+ {
+ # helper function that handles +-inf cases for bdiv()/bmod() to reuse code
+ my ($self,$x,$y) = @_;
+
+ # NaN if x == NaN or y == NaN or x==y==0
+ return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
+ if (($x->is_nan() || $y->is_nan()) ||
+ ($x->is_zero() && $y->is_zero()));
+
+ # +-inf / +-inf == NaN, reminder also NaN
+ if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan();
+ }
+ # x / +-inf => 0, remainder x (works even if x == 0)
+ if ($y->{sign} =~ /^[+-]inf$/)
+ {
+ my $t = $x->copy(); # bzero clobbers up $x
+ return wantarray ? ($x->bzero(),$t) : $x->bzero()
+ }
+
+ # 5 / 0 => +inf, -6 / 0 => -inf
+ # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf
+ # exception: -8 / 0 has remainder -8, not 8
+ # exception: -inf / 0 has remainder -inf, not inf
+ if ($y->is_zero())
+ {
+ # +-inf / 0 => special case for -inf
+ return wantarray ? ($x,$x->copy()) : $x if $x->is_inf();
+ if (!$x->is_zero() && !$x->is_inf())
+ {
+ my $t = $x->copy(); # binf clobbers up $x
+ return wantarray ?
+ ($x->binf($x->{sign}),$t) : $x->binf($x->{sign})
+ }
+ }
+
+ # last case: +-inf / ordinary number
+ my $sign = '+inf';
+ $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign};
+ $x->{sign} = $sign;
+ return wantarray ? ($x,$self->bzero()) : $x;
+ }
+
+sub bdiv
+ {
+ # (dividend: BINT or num_str, divisor: BINT or num_str) return
+ # (BINT,BINT) (quo,rem) or BINT (only rem)
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
+
+ return $x if $x->modify('bdiv');
+
+ return $self->_div_inf($x,$y)
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
+
+ return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r)
+ if defined $upgrade;
+
+ $r[3] = $y; # no push!
+
+ # calc new sign and in case $y == +/- 1, return $x
+ my $xsign = $x->{sign}; # keep
+ $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+');
+
+ if (wantarray)
+ {
+ my $rem = $self->bzero();
+ ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value});
+ $rem->{_a} = $x->{_a};
+ $rem->{_p} = $x->{_p};
+ $x->round(@r) if !exists $x->{_f} || ($x->{_f} & MB_NEVER_ROUND) == 0;
+ if (! $CALC->_is_zero($rem->{value}))
+ {
+ $rem->{sign} = $y->{sign};
+ $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-'
+ }
+ else
+ {
+ $rem->{sign} = '+'; # dont leave -0
+ }
+ $rem->round(@r) if !exists $rem->{_f} || ($rem->{_f} & MB_NEVER_ROUND) == 0;
+ return ($x,$rem);
+ }
+
+ $x->{value} = $CALC->_div($x->{value},$y->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value});
+
+ $x->round(@r) if !exists $x->{_f} || ($x->{_f} & MB_NEVER_ROUND) == 0;
+ $x;
}
###############################################################################
+# modulus functions
-sub bmul
- {
- # multiply two numbers -- stolen from Knuth Vol 2 pg 233
+sub bmod
+ {
+ # modulus (or remainder)
# (BINT or num_str, BINT or num_str) return BINT
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
- return $x if $x->modify('bmul');
- return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- # handle result = 0
- return $x if $x->is_zero();
- return $x->bzero() if $y->is_zero();
- # inf handling
- if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
{
- # result will always be +-inf:
- # +inf * +/+inf => +inf, -inf * -/-inf => +inf
- # +inf * -/-inf => -inf, -inf * +/+inf => -inf
- return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
- return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
- return $x->binf('-');
+ ($self,$x,$y,@r) = objectify(2,@_);
}
- $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);
+ return $x if $x->modify('bmod');
+ $r[3] = $y; # no push!
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
+ {
+ my ($d,$r) = $self->_div_inf($x,$y);
+ $x->{sign} = $r->{sign};
+ $x->{value} = $r->{value};
+ return $x->round(@r);
+ }
+
+ if ($CALC->can('_mod'))
+ {
+ # calc new sign and in case $y == +/- 1, return $x
+ $x->{value} = $CALC->_mod($x->{value},$y->{value});
+ if (!$CALC->_is_zero($x->{value}))
+ {
+ my $xsign = $x->{sign};
+ $x->{sign} = $y->{sign};
+ if ($xsign ne $y->{sign})
+ {
+ my $t = $CALC->_copy($x->{value}); # copy $x
+ $x->{value} = $CALC->_copy($y->{value}); # copy $y to $x
+ $x->{value} = $CALC->_sub($y->{value},$t,1); # $y-$x
+ }
+ }
+ else
+ {
+ $x->{sign} = '+'; # dont leave -0
+ }
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+ my ($t,$rem) = $self->bdiv($x->copy(),$y,@r); # slow way (also rounds)
+ # modify in place
+ foreach (qw/value sign _a _p/)
+ {
+ $x->{$_} = $rem->{$_};
+ }
+ $x;
}
-sub bdiv
+sub bmodinv
{
- # (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,@_);
+ # Modular inverse. given a number which is (hopefully) relatively
+ # prime to the modulus, calculate its inverse using Euclid's
+ # alogrithm. If the number is not relatively prime to the modulus
+ # (i.e. their gcd is not one) then NaN is returned.
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
- return $x if $x->modify('bdiv');
+ return $x if $x->modify('bmodinv');
- # 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 $x->bnan()
+ if ($y->{sign} ne '+' # -, NaN, +inf, -inf
+ || $x->is_zero() # or num == 0
+ || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf
+ );
- # 0 / something
- return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero();
-
- # Is $x in the interval [0, $y) ?
- my $cmp = $CALC->_acmp($x->{value},$y->{value});
- if (($cmp < 0) and ($x->{sign} eq $y->{sign}))
+ # put least residue into $x if $x was negative, and thus make it positive
+ $x->bmod($y) if $x->{sign} eq '-';
+
+ if ($CALC->can('_modinv'))
{
- return $x->bzero() unless wantarray;
- my $t = $x->copy(); # make copy first, because $x->bzero() clobbers $x
- return ($x->bzero(),$t);
+ my $sign;
+ ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value});
+ $x->bnan() if !defined $x->{value}; # in case no GCD found
+ return $x if !defined $sign; # already real result
+ $x->{sign} = $sign; # flip/flop see below
+ $x->bmod($y); # calc real result
+ return $x;
}
- elsif ($cmp == 0)
+ my ($u, $u1) = ($self->bzero(), $self->bone());
+ my ($a, $b) = ($y->copy(), $x->copy());
+
+ # first step need always be done since $num (and thus $b) is never 0
+ # Note that the loop is aligned so that the check occurs between #2 and #1
+ # thus saving us one step #2 at the loop end. Typical loop count is 1. Even
+ # a case with 28 loops still gains about 3% with this layout.
+ my $q;
+ ($a, $q, $b) = ($b, $a->bdiv($b)); # step #1
+ # Euclid's Algorithm (calculate GCD of ($a,$b) in $a and also calculate
+ # two values in $u and $u1, we use only $u1 afterwards)
+ my $sign = 1; # flip-flop
+ while (!$b->is_zero()) # found GCD if $b == 0
{
- # shortcut, both are the same, so set to +/- 1
- $x->__one( ($x->{sign} ne $y->{sign} ? '-' : '+') );
- return $x unless wantarray;
- return ($x,$self->bzero());
+ # the original algorithm had:
+ # ($u, $u1) = ($u1, $u->bsub($u1->copy()->bmul($q))); # step #2
+ # The following creates exact the same sequence of numbers in $u1,
+ # except for the sign ($u1 is now always positive). Since formerly
+ # the sign of $u1 was alternating between '-' and '+', the $sign
+ # flip-flop will take care of that, so that at the end of the loop
+ # we have the real sign of $u1. Keeping numbers positive gains us
+ # speed since badd() is faster than bsub() and makes it possible
+ # to have the algorithmn in Calc for even more speed.
+
+ ($u, $u1) = ($u1, $u->badd($u1->copy()->bmul($q))); # step #2
+ $sign = - $sign; # flip sign
+
+ ($a, $q, $b) = ($b, $a->bdiv($b)); # step #1 again
}
-
- # calc new sign and in case $y == +/- 1, return $x
- $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 the gcd is not 1, then return NaN! It would be pointless to
+ # have called bgcd to check this first, because we would then be
+ # performing the same Euclidean Algorithm *twice*.
+ return $x->bnan() unless $a->is_one();
+
+ $u1->bneg() if $sign != 1; # need to flip?
+
+ $u1->bmod($y); # calc result
+ $x->{value} = $u1->{value}; # and copy over to $x
+ $x->{sign} = $u1->{sign}; # to modify in place
+ $x;
+ }
+
+sub bmodpow
+ {
+ # takes a very large number to a very large exponent in a given very
+ # large modulus, quickly, thanks to binary exponentation. supports
+ # negative exponents.
+ my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
+
+ return $num if $num->modify('bmodpow');
+
+ # check modulus for valid values
+ return $num->bnan() if ($mod->{sign} ne '+' # NaN, - , -inf, +inf
+ || $mod->is_zero());
+
+ # check exponent for valid values
+ if ($exp->{sign} =~ /\w/)
{
- return wantarray ? ($x,$self->bzero()) : $x;
+ # i.e., if it's NaN, +inf, or -inf...
+ return $num->bnan();
}
- # 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()))
+ $num->bmodinv ($mod) if ($exp->{sign} eq '-');
+
+ # check num for valid values (also NaN if there was no inverse but $exp < 0)
+ return $num->bnan() if $num->{sign} !~ /^[+-]$/;
+
+ if ($CALC->can('_modpow'))
{
- $x->bdec();
+ # $mod is positive, sign on $exp is ignored, result also positive
+ $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value});
+ return $num;
}
- $x->round($a,$p,$r,$y);
- if (wantarray)
+
+ # in the trivial case,
+ return $num->bzero(@r) if $mod->is_one();
+ return $num->bone('+',@r) if $num->is_zero() or $num->is_one();
+
+ # $num->bmod($mod); # if $x is large, make it smaller first
+ my $acc = $num->copy(); # but this is not really faster...
+
+ $num->bone(); # keep ref to $num
+
+ my $expbin = $exp->as_bin(); $expbin =~ s/^[-]?0b//; # ignore sign and prefix
+ my $len = CORE::length($expbin);
+ while (--$len >= 0)
{
- $rem->round($a,$p,$r,$x,$y);
- return ($x,$y-$rem) if $x->{sign} eq '-'; # was $x,$rem
- return ($x,$rem);
+ if( substr($expbin,$len,1) eq '1')
+ {
+ $num->bmul($acc)->bmod($mod);
+ }
+ $acc->bmul($acc)->bmod($mod);
}
- return $x;
+
+ $num;
}
+###############################################################################
+
+sub bfac
+ {
+ # (BINT or num_str, BINT or num_str) return BINT
+ # compute factorial numbers
+ # modifies first argument
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ return $x if $x->modify('bfac');
+
+ return $x->bnan() if $x->{sign} ne '+'; # inf, NnN, <0 etc => NaN
+ return $x->bone('+',@r) if $x->is_zero() || $x->is_one(); # 0 or 1 => 1
+
+ if ($CALC->can('_fac'))
+ {
+ $x->{value} = $CALC->_fac($x->{value});
+ return $x->round(@r);
+ }
+
+ my $n = $x->copy();
+ $x->bone();
+ # seems we need not to temp. clear A/P of $x since the result is the same
+ my $f = $self->new(2);
+ while ($f->bacmp($n) < 0)
+ {
+ $x->bmul($f); $f->binc();
+ }
+ $x->bmul($f,@r); # last step and also round
+ }
+
sub bpow
{
# (BINT or num_str, BINT or num_str) return BINT
# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
# modifies first argument
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
return $x if $x->modify('bpow');
-
+
+ return $upgrade->bpow($upgrade->new($x),$y,@r)
+ if defined $upgrade && !$y->isa($self);
+
+ $r[3] = $y; # no push!
return $x if $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x
return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
- return $x->__one() if $y->is_zero();
- return $x if $x->is_one() || $y->is_one();
- #if ($x->{sign} eq '-' && @{$x->{value}} == 1 && $x->{value}->[0] == 1)
+ return $x->bone('+',@r) if $y->is_zero();
+ return $x->round(@r) if $x->is_one() || $y->is_one();
if ($x->{sign} eq '-' && $CALC->_is_one($x->{value}))
{
# if $x == -1 and odd/even y => +1/-1
- return $y->is_odd() ? $x : $x->babs();
+ 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);
- }
- # 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?
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ return $x;
+ }
+
+# based on the assumption that shifting in base 10 is fast, and that mul
+# works faster if numbers are small: we count trailing zeros (this step is
+# O(1)..O(N), but in case of O(N) we save much more time due to this),
+# stripping them out of the multiplication, and add $count * $y zeros
+# afterwards like this:
+# 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6
+# creates deep recursion since brsft/blsft use bpow sometimes.
# my $zeros = $x->_trailing_zeros();
# if ($zeros > 0)
# {
# $x->bpow($y); # recursion (will not branch into here again)
# $zeros = $y * $zeros; # real number of zeros to add
# $x->blsft($zeros,10);
-# return $x->round($a,$p,$r);
+# return $x->round(@r);
# }
my $pow2 = $self->__one();
- my $y1 = $class->new($y);
- my ($res);
- while (!$y1->is_one())
+ my $y_bin = $y->as_bin(); $y_bin =~ s/^0b//;
+ my $len = CORE::length($y_bin);
+ while (--$len > 0)
{
- #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 substr($y_bin,$len,1) eq '1'; # is odd?
+ $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);
+ $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+ $x;
}
sub blsft
{
# (BINT or num_str, BINT or num_str) return BINT
# compute x << y, base n, y >= 0
- my ($self,$x,$y,$n) = objectify(2,@_);
-
+
+ # set up parameters
+ my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,$n,@r) = objectify(2,@_);
+ }
+
return $x if $x->modify('blsft');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+ return $x->round(@r) if $y->is_zero();
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- 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(@r);
}
# fallback
- return $x->bmul( $self->bpow($n, $y) );
+ return $x->bmul( $self->bpow($n, $y, @r), @r );
}
sub brsft
{
# (BINT or num_str, BINT or num_str) return BINT
# compute x >> y, base n, y >= 0
- my ($self,$x,$y,$n) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,$n,@r) = objectify(2,@_);
+ }
return $x if $x->modify('brsft');
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+ return $x->round(@r) if $y->is_zero();
+ return $x->bzero(@r) if $x->is_zero(); # 0 => 0
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- 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(@r) if $x->is_one('-'); # -1 => -1
+ if (!$y->is_one())
+ {
+ # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al
+ # but perhaps there is a better emulation for two's complement shift...
+ # if $y != 1, we must simulate it by doing:
+ # convert to bin, flip all bits, shift, and be done
+ $x->binc(); # -3 => -2
+ my $bin = $x->as_bin();
+ $bin =~ s/^-0b//; # strip '-0b' prefix
+ $bin =~ tr/10/01/; # flip bits
+ # now shift
+ if (CORE::length($bin) <= $y)
+ {
+ $bin = '0'; # shifting to far right creates -1
+ # 0, because later increment makes
+ # that 1, attached '-' makes it '-1'
+ # because -1 >> x == -1 !
+ }
+ else
+ {
+ $bin =~ s/.{$y}$//; # cut off at the right side
+ $bin = '1' . $bin; # extend left side by one dummy '1'
+ $bin =~ tr/10/01/; # flip bits back
+ }
+ my $res = $self->new('0b'.$bin); # add prefix and convert back
+ $res->binc(); # remember to increment
+ $x->{value} = $res->{value}; # take over value
+ return $x->round(@r); # we are done now, magic, isn't?
+ }
+ $x->bdec(); # n == 2, but $y == 1: this fixes it
+ }
+
+ my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft');
if (defined $t)
{
- $x->{value} = $t; return $x;
+ $x->{value} = $t;
+ return $x->round(@r);
}
# fallback
- return scalar bdiv($x, $self->bpow($n, $y));
+ $x->bdiv($self->bpow($n,$y, @r), @r);
+ $x;
}
sub band
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x & y
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
return $x if $x->modify('band');
+ $r[3] = $y; # no push!
+ local $Math::BigInt::upgrade = undef;
+
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x->bzero() if $y->is_zero();
+ return $x->bzero(@r) if $y->is_zero() || $x->is_zero();
my $sign = 0; # sign of result
$sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-');
if ($CALC->can('_and') && $sx == 1 && $sy == 1)
{
$x->{value} = $CALC->_and($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ return $x->round(@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!
$m->bmul($x10000);
}
$x->bneg() if $sign;
- return $x->round($a,$p,$r);
+ $x->round(@r);
}
sub bior
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x | y
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
return $x if $x->modify('bior');
+ $r[3] = $y; # no push!
+
+ local $Math::BigInt::upgrade = undef;
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x if $y->is_zero();
+ return $x->round(@r) if $y->is_zero();
my $sign = 0; # sign of result
$sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-');
if ($CALC->can('_or') && $sx == 1 && $sy == 1)
{
$x->{value} = $CALC->_or($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ return $x->round(@r);
}
- my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x10000);
+ my $m = $self->bone(); my ($xr,$yr);
+ my $x10000 = $self->new(0x10000);
my $y1 = copy(ref($x),$y); # make copy
$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->round($a,$p,$r);
+ $x->round(@r);
}
sub bxor
{
#(BINT or num_str, BINT or num_str) return BINT
# compute x ^ y
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
return $x if $x->modify('bxor');
+ $r[3] = $y; # no push!
+
+ local $Math::BigInt::upgrade = undef;
return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
- return $x if $y->is_zero();
- return $x->bzero() if $x == $y; # shortcut
+ return $x->round(@r) if $y->is_zero();
my $sign = 0; # sign of result
$sign = 1 if $x->{sign} ne $y->{sign};
if ($CALC->can('_xor') && $sx == 1 && $sy == 1)
{
$x->{value} = $CALC->_xor($x->{value},$y->{value});
- return $x->round($a,$p,$r);
+ return $x->round(@r);
}
- my $m = new Math::BigInt 1; my ($xr,$yr);
- my $x10000 = new Math::BigInt (0x10000);
+ my $m = $self->bone(); my ($xr,$yr);
+ my $x10000 = $self->new(0x10000);
my $y1 = copy(ref($x),$y); # make copy
$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->round($a,$p,$r);
+ $x->round(@r);
}
sub length
{
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
my $e = $CALC->_len($x->{value});
- # # fallback, since we do not know the underlying representation
- #my $es = "$x"; my $c = 0; $c = 1 if $es =~ /^[+-]/; # if lib returns '+123'
- #my $e = CORE::length($es)-$c;
return wantarray ? ($e,0) : $e;
}
sub digit
{
# return the nth decimal digit, negative values count backward, 0 is right
- my $x = shift;
- my $n = shift || 0;
+ my ($self,$x,$n) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $CALC->_digit($x->{value},$n);
+ $CALC->_digit($x->{value},$n||0);
}
sub _trailing_zeros
my $x = shift;
$x = $class->new($x) unless ref $x;
- #return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/;
- 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!
+ CORE::length("$1"); # as string, not as +0!
}
sub bsqrt
{
- my ($self,$x) = objectify(1,@_);
+ # calculate square root of $x
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x->bnan() if $x->{sign} =~ /\-|$nan/; # -x or NaN => NaN
- return $x->bzero() if $x->is_zero(); # 0 => 0
- return $x if $x == 1; # 1 => 1
+ return $x if $x->modify('bsqrt');
+
+ return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN
+ return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf
+ return $x->round(@r) if $x->is_zero() || $x->is_one(); # 0,1 => 0,1
+
+ return $upgrade->bsqrt($x,@r) if defined $upgrade;
+
+ if ($CALC->can('_sqrt'))
+ {
+ $x->{value} = $CALC->_sqrt($x->{value});
+ return $x->round(@r);
+ }
- my $y = $x->copy(); # give us one more digit accur.
+ return $x->bone('+',@r) if $x < 4; # 2,3 => 1
+ my $y = $x->copy();
my $l = int($x->length()/2);
- $x->bzero();
- $x->binc(); # keep ref($x), but modify it
- $x *= 10 ** $l;
+ $x->bone(); # keep ref($x), but modify it
+ $x->blsft($l,10) if $l != 0; # first guess: 1.('0' x (l/2))
+
+ my $last = $self->bzero();
+ my $two = $self->new(2);
+ my $lastlast = $self->bzero();
+ #my $lastlast = $x+$two;
+ while ($last != $x && $lastlast != $x)
+ {
+ $lastlast = $last; $last = $x->copy();
+ $x->badd($y / $x);
+ $x->bdiv($two);
+ }
+ $x->bdec() if $x * $x > $y; # overshot?
+ $x->round(@r);
+ }
+
+sub broot
+ {
+ # calculate $y'th root of $x
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
+
+ return $x if $x->modify('broot');
+
+ # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
+ return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
+ $y->{sign} !~ /^\+$/;
+
+ return $x->round(@r)
+ if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
+
+ return $upgrade->broot($x,@r) if defined $upgrade;
+
+ if ($CALC->can('_root'))
+ {
+ $x->{value} = $CALC->_root($x->{value},$y->{value});
+ return $x->round(@r);
+ }
+
+ return $x->bsqrt() if $y->bacmp(2) == 0; # 2 => square root
+
+ # since we take at least a cubic root, and only 8 ** 1/3 >= 2 (==2):
+ return $x->bone('+',@r) if $x < 8; # $x=2..7 => 1
- # print "x: $y guess $x\n";
+ my $org = $x->copy();
+ my $l = int($x->length()/$y->numify());
+
+ $x->bone(); # keep ref($x), but modify it
+ $x->blsft($l,10) if $l != 0; # first guess: 1.('0' x (l/$y))
my $last = $self->bzero();
- while ($last != $x)
+ my $lastlast = $self->bzero();
+ #my $lastlast = $x+$y;
+ my $divider = $self->new(2);
+ my $up = $y-1;
+ #print "start $org divider $divider up $up\n";
+ while ($last != $x && $lastlast != $x)
+ {
+ #print "at $x ($last $lastlast)\n";
+ $lastlast = $last; $last = $x->copy();
+ #print "at $x ($last ",($org / ($x ** $up)),"\n";
+ $x->badd($org / ($x ** 2));
+ $x->bdiv($divider);
+ }
+ #print $x ** $y," org ",$org,"\n";
+ # correct overshot
+ while ($x ** $y < $org)
{
- $last = $x;
- $x += $y / $x;
- $x /= 2;
+ #print "correcting $x to ";
+ $x->binc();
+ #print "$x ( $x ** $y == ",$x ** $y,")\n";
}
- return $x;
+ $x->round(@r);
}
sub exponent
{
# return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return bnan() if $x->is_nan();
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ my $s = $x->{sign}; $s =~ s/^[+-]//;
+ return $self->new($s); # -inf,+inf => inf
+ }
my $e = $class->bzero();
return $e->binc() if $x->is_zero();
$e += $x->_trailing_zeros();
- return $e;
+ $e;
}
sub mantissa
{
- # return a copy of the mantissa (here always $self)
- my ($self,$x) = objectify(1,@_);
+ # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return bnan() if $x->is_nan();
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ return $self->new($x->{sign}); # keep + or - sign
+ }
my $m = $x->copy();
# that's inefficient
my $zeros = $m->_trailing_zeros();
- $m /= 10 ** $zeros if $zeros != 0;
- return $m;
+ $m->brsft($zeros,10) if $zeros != 0;
+ $m;
}
sub parts
{
- # return a copy of both the exponent and the mantissa (here 0 and self)
- my $self = shift;
- $self = $class->new($self) unless ref $self;
+ # return a copy of both the exponent and the mantissa
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return ($self->mantissa(),$self->exponent());
+ return ($x->mantissa(),$x->exponent());
}
##############################################################################
sub bfround
{
# precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
- # $n == 0 => round to integer
+ # $n == 0 || $n == 1 => round to integer
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_p($precision,$rnd_mode,@_);
+ my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_);
return $x if !defined $scale; # no-op
+ return $x if $x->modify('bfround');
# no-op for BigInts if $n <= 0
- return $x if $scale <= 0;
+ if ($scale <= 0)
+ {
+ $x->{_a} = undef; # clear an eventual set A
+ $x->{_p} = $scale; return $x;
+ }
$x->bround( $x->length()-$scale, $mode);
+ $x->{_a} = undef; # bround sets {_a}
+ $x->{_p} = $scale; # so correct it
+ $x;
}
sub _scan_for_nonzero
return 0 if $len == 1; # '5' is trailed by invisible zeros
my $follow = $pad - 1;
return 0 if $follow > $len || $follow < 1;
- #print "checking $x $r\n";
# since we do not know underlying represention of $x, use decimal string
#my $r = substr ($$xs,-$follow);
my $r = substr ("$x",-$follow);
- return 1 if $r =~ /[^0]/; return 0;
+ return 1 if $r =~ /[^0]/;
+ 0;
}
sub fround
# no-op for $n == 0
# and overwrite the rest with 0's, return normalized number
# do not return $x->bnorm(), but $x
+
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_a($accuracy,$rnd_mode,@_);
- return $x if !defined $scale; # no-op
+ my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_);
+ return $x if !defined $scale; # no-op
+ return $x if $x->modify('bround');
- # print "MBI round: $x to $scale $mode\n";
- # -scale means what? tom? hullo? -$scale needed by MBF round, but what for?
- return $x if $x->{sign} !~ /^[+-]$/ || $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);
+ # convert $scale to a scalar in case it is an object (put's a limit on the
+ # number length, but this would already limited by memory constraints), makes
+ # it faster
+ $scale = $scale->numify() if ref ($scale);
+
+ # scale < 0, but > -len (not >=!)
+ if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
+ {
+ $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+ return $x;
+ }
# count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
my ($pad,$digit_round,$digit_after);
$pad = $len - $scale;
- $pad = abs($scale)+1 if $scale < 0;
+ $pad = abs($scale-1) if $scale < 0;
+
# do not use digit(), it is costly for binary => decimal
- #$digit_round = '0'; $digit_round = $x->digit($pad) if $pad < $len;
- #$digit_after = '0'; $digit_after = $x->digit($pad-1) if $pad > 0;
+
my $xs = $CALC->_str($x->{value});
my $pl = -$pad-1;
+
# pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
# pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
$digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len;
$pl++; $pl ++ if $pad >= $len;
- $digit_after = '0'; $digit_after = substr($$xs,$pl,1)
- if $pad > 0;
-
- #my $d_round = '0'; $d_round = $x->digit($pad) if $pad < $len;
- #my $d_after = '0'; $d_after = $x->digit($pad-1) if $pad > 0;
- # print "$pad $pl $$xs $digit_round:$d_round $digit_after:$d_after\n";
+ $digit_after = '0'; $digit_after = substr($$xs,$pl,1) if $pad > 0;
# in case of 01234 we round down, for 6789 up, and only in case 5 we look
# closer at the remaining digits of the original $x, remember decision
($mode eq '-inf') && ($x->{sign} eq '+') ||
($mode eq 'zero') # round down if zero, sign adjusted below
);
- # allow rounding one place left of mantissa
- #print "$pad $len $scale\n";
- # this is triggering warnings, and buggy for $scale < 0
- #if (-$scale != $len)
- {
- # old code, depend on internal 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($$xs,-$pad,$pad) = '0' x $pad;
- $x->{value} = $CALC->_new($xs); # put back in
- }
- elsif ($pad > $len)
+ my $put_back = 0; # not yet modified
+
+ if (($pad > 0) && ($pad <= $len))
+ {
+ substr($$xs,-$pad,$pad) = '0' x $pad;
+ $put_back = 1;
+ }
+ elsif ($pad > $len)
+ {
+ $x->bzero(); # round to '0'
+ }
+
+ if ($round_up) # what gave test above?
+ {
+ $put_back = 1;
+ $pad = $len, $$xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
+
+ # we modify directly the string variant instead of creating a number and
+ # adding it, since that is faster (we already have the string)
+ my $c = 0; $pad ++; # for $pad == $len case
+ while ($pad <= $len)
{
- $x->bzero(); # round to '0'
+ $c = substr($$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 $c == 0;
+
}
- # move this later on after the inc of the string
- #$x->{value} = $CALC->_new($xs); # put back in
- if ($round_up) # what gave test above?
+ $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back in if needed
+
+ $x->{_a} = $scale if $scale >= 0;
+ if ($scale < 0)
{
- $pad = $len if $scale < 0; # tlr: whack 0.51=>1.0
- # modify $x in place, undef, undef to avoid rounding
- # str creation much faster than 10 ** something
- $x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad) );
- # increment string in place, to avoid dec=>hex for the '1000...000'
- # $xs ...blah foo
+ $x->{_a} = $len+$scale;
+ $x->{_a} = 0 if $scale < -$len;
}
- # to here:
- #$x->{value} = $CALC->_new($xs); # put back in
$x;
}
{
# return integer less or equal then number, since it is already integer,
# always returns $self
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
-
- # not needed: return $x if $x->modify('bfloor');
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x->round($a,$p,$r);
+ $x->round(@r);
}
sub bceil
{
# return integer greater or equal then number, since it is already integer,
# always returns $self
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- # not needed: return $x if $x->modify('bceil');
-
- return $x->round($a,$p,$r);
+ $x->round(@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;
+ $x;
}
sub _swap
# args, hence the copy().
# You can override this method in a subclass, the overload section will call
# $object->_swap() to make sure it arrives at the proper subclass, with some
- # exceptions like '+' and '-'.
+ # exceptions like '+' and '-'. To make '+' and '-' work, you also need to
+ # specify your own overload for them.
# object, (object|scalar) => preserve first and make copy
# scalar, object => swapped, re-swap and create new from first
# (using class of second object, not $class!!)
my $self = shift; # for override in subclass
- #print "swap $self 0:$_[0] 1:$_[1] 2:$_[2]\n";
if ($_[2])
{
my $c = ref ($_[0]) || $class; # fallback $class should not happen
# $class,1,2. (We can not take '1' as class ;o)
# badd($class,1) is not supported (it should, eventually, try to add undef)
# currently it tries 'Math::BigInt' + 1, which will not work.
-
+
+ # some shortcut for the common cases
+ # $x->unary_op();
+ return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
+
my $count = abs(shift || 0);
- #print caller(),"\n";
-
- my @a; # resulting array
+ my (@a,$k,$d); # resulting array, temp, and downgrade
if (ref $_[0])
{
# okay, got object as first
{
# nope, got 1,2 (Class->xxx(1) => Class,1 and not supported)
$a[0] = $class;
- #print "@_\n"; sleep(1);
$a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first?
}
- #print caller(),"\n";
- # print "Now in objectify, my class is today $a[0]\n";
- my $k;
+
+ no strict 'refs';
+ # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats
+ if (defined ${"$a[0]::downgrade"})
+ {
+ $d = ${"$a[0]::downgrade"};
+ ${"$a[0]::downgrade"} = undef;
+ }
+
+ my $up = ${"$a[0]::upgrade"};
+ #print "Now in objectify, my class is today $a[0]\n";
if ($count == 0)
{
while (@_)
{
$k = $a[0]->new($k);
}
- elsif (ref($k) ne $a[0])
+ elsif (!defined $up && ref($k) ne $a[0])
{
# foreign object, try to convert to integer
$k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
{
while ($count > 0)
{
- #print "$count\n";
$count--;
$k = shift;
if (!ref($k))
{
$k = $a[0]->new($k);
}
- elsif (ref($k) ne $a[0])
+ elsif (!defined $up && ref($k) ne $a[0])
{
# foreign object, try to convert to integer
$k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
}
push @a,@_; # return other params, too
}
- #my $i = 0;
- #foreach (@a)
- # {
- # print "o $i $a[0]\n" if $i == 0;
- # print "o $i ",ref($_),"\n" if $i != 0; $i++;
- # }
- #print "objectify done: would return ",scalar @a," values\n";
- #print caller(1),"\n" unless wantarray;
- die "$class objectify needs list context" unless wantarray;
+ if (! wantarray)
+ {
+ require Carp; Carp::croak ("$class objectify needs list context");
+ }
+ ${"$a[0]::downgrade"} = $d;
@a;
}
sub import
{
my $self = shift;
- #print "import $self @_\n";
- my @a = @_; my $l = scalar @_; my $j = 0;
- for ( my $i = 0; $i < $l ; $i++,$j++ )
+
+ $IMPORT++;
+ my @a; my $l = scalar @_;
+ for ( my $i = 0; $i < $l ; $i++ )
{
if ($_[$i] eq ':constant')
{
# this causes overlord er load to step in
overload::constant integer => sub { $self->new(shift) };
- splice @a, $j, 1; $j --;
+ overload::constant binary => sub { $self->new(shift) };
+ }
+ elsif ($_[$i] eq 'upgrade')
+ {
+ # this causes upgrading
+ $upgrade = $_[$i+1]; # or undef to disable
+ $i++;
}
elsif ($_[$i] =~ /^lib$/i)
{
# this causes a different low lib to take care...
- $CALC = $_[$i+1] || $CALC;
- my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
- splice @a, $j, $s; $j -= $s;
+ $CALC = $_[$i+1] || '';
+ $i++;
+ }
+ else
+ {
+ push @a, $_[$i];
}
}
# any non :constant stuff is handled by our parent, Exporter
# even if @_ is empty, to give it a chance
- #$self->SUPER::import(@a); # does not work
- $self->export_to_level(1,$self,@a); # need this instead
+ $self->SUPER::import(@a); # need it for subclasses
+ $self->export_to_level(1,$self,@a); # need it for MBF
# try to load core math lib
my @c = split /\s*,\s*/,$CALC;
push @c,'Calc'; # if all fail, try this
+ $CALC = ''; # signal error
foreach my $lib (@c)
{
+ next if ($lib || '') eq '';
$lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
$lib =~ s/\.pm$//;
- if ($] < 5.6)
+ if ($] < 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( @c ); }
+ my @parts = split /::/, $lib; # Math::BigInt => Math BigInt
+ my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
+ require File::Spec;
+ $file = File::Spec->catfile (@parts, $file);
+ eval { require "$file"; $lib->import( @c ); }
}
else
{
- eval "use $lib @c;";
+ eval "use $lib qw/@c/;";
}
$CALC = $lib, last if $@ eq ''; # no error in loading lib?
}
+ if ($CALC eq '')
+ {
+ require Carp;
+ Carp::croak ("Couldn't load any math lib, not even the default");
+ }
}
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;
$$x =~ s/\s+$//g; # strip white space at end
# shortcut, if nothing to split, return early
- if ($$x =~ /^[+-]?\d+$/)
+ if ($$x =~ /^[+-]?\d+\z/)
{
$$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
return (\$sign, $x, \'', \'', \0);
# 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;
+ $$x =~ s/(\d)_(\d)/$1$2/g; # do twice for 1_2_3
# some possible inputs:
# 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
- # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2
+ # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999
+
+ #return if $$x =~ /[Ee].*[Ee]/; # more than one E => error
- #print "input: '$$x' ";
- my ($m,$e) = split /[Ee]/,$$x;
+ my ($m,$e,$last) = split /[Ee]/,$$x;
+ return if defined $last; # last defined => 1e2E3 or others
$e = '0' if !defined $e || $e eq "";
- # print "m '$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;
+ my ($mi,$mf,$lastf) = split /\./,$m;
+ return if defined $lastf; # last defined => 1.2.3 or others
$mi = '0' if !defined $mi;
$mi .= '0' if $mi =~ /^[\-\+]?$/;
$mf = '0' if !defined $mf || $mf eq '';
if ($mi =~ /^([+-]?)0*(\d+)$/) # strip leading zeros
{
$mis = $1||'+'; $miv = $2;
- # print "$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";
+ # handle the 0e999 case here
+ $ev = 0 if $miv eq '0' && $mfv eq '';
return (\$mis,\$miv,\$mfv,\$es,\$ev);
}
}
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 '-';
- $s .= '0x';
if ($CALC->can('_as_hex'))
{
- $es = $CALC->_as_hex($x->{value});
+ $es = ${$CALC->_as_hex($x->{value})};
}
else
{
- my $x1 = $x->copy()->babs(); my $xr;
- my $x100 = Math::BigInt->new (0x100);
+ return '0x0' if $x->is_zero();
+
+ my $x1 = $x->copy()->babs(); my ($xr,$x10000,$h);
+ if ($] >= 5.006)
+ {
+ $x10000 = Math::BigInt->new (0x10000); $h = 'h4';
+ }
+ else
+ {
+ $x10000 = Math::BigInt->new (0x1000); $h = 'h3';
+ }
while (!$x1->is_zero())
{
- ($x1, $xr) = bdiv($x1,$x100);
- $es .= unpack('h2',pack('C',$xr->numify()));
+ ($x1, $xr) = bdiv($x1,$x10000);
+ $es .= unpack($h,pack('v',$xr->numify()));
}
$es = reverse $es;
$es =~ s/^[0]+//; # strip leading zeros
+ $s .= '0x';
}
$s . $es;
}
my $x = shift; $x = $class->new($x) if !ref($x);
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
- return '0b0' if $x->is_zero();
my $es = ''; my $s = '';
$s = $x->{sign} if $x->{sign} eq '-';
- $s .= '0b';
if ($CALC->can('_as_bin'))
{
- $es = $CALC->_as_bin($x->{value});
+ $es = ${$CALC->_as_bin($x->{value})};
}
else
{
- my $x1 = $x->copy()->babs(); my $xr;
- my $x100 = Math::BigInt->new (0x100);
+ return '0b0' if $x->is_zero();
+ my $x1 = $x->copy()->babs(); my ($xr,$x10000,$b);
+ if ($] >= 5.006)
+ {
+ $x10000 = Math::BigInt->new (0x10000); $b = 'b16';
+ }
+ else
+ {
+ $x10000 = Math::BigInt->new (0x1000); $b = 'b12';
+ }
while (!$x1->is_zero())
{
- ($x1, $xr) = bdiv($x1,$x100);
- $es .= unpack('b8',pack('C',$xr->numify()));
+ ($x1, $xr) = bdiv($x1,$x10000);
+ $es .= unpack($b,pack('v',$xr->numify()));
}
- $es = reverse $es;
- $es =~ s/^[0]+//; # strip leading zeros
- }
- $s . $es;
- }
-
-##############################################################################
-# internal calculation routines (others are in Math::BigInt::Calc etc)
-
-sub cmp
- {
- # post-normalized compare for internal use (honors signs)
- # input: ref to value, ref to value, sign, sign
- # output: <0, 0, >0
- my ($cx,$cy,$sx,$sy) = @_;
-
- if ($sx eq '+')
- {
- return 1 if $sy eq '-'; # 0 check handled above
- return $CALC->_acmp($cx,$cy);
- }
- else
- {
- # $sx eq '-'
- return -1 if $sy eq '+';
- return $CALC->_acmp($cy,$cx);
+ $es = reverse $es;
+ $es =~ s/^[0]+//; # strip leading zeros
+ $s .= '0b';
}
- 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())
use Math::BigInt;
+ # or make it faster: install (optional) Math::BigInt::GMP
+ # and always use (it will fall back to pure Perl if the
+ # GMP library is not installed):
+
+ use Math::BigInt lib => 'GMP';
+
# Number creation
$x = Math::BigInt->new($str); # defaults to 0
$nan = Math::BigInt->bnan(); # create a NotANumber
$one = Math::BigInt->bone(); # create a +1
$one = Math::BigInt->bone('-'); # create a -1
- # Testing
- $x->is_zero(); # true if arg is +0
- $x->is_nan(); # true if arg is NaN
- $x->is_one(); # true if arg is +1
- $x->is_one('-'); # true if arg is -1
- $x->is_odd(); # true if odd, false for even
- $x->is_even(); # true if even, false for odd
- $x->is_positive(); # true if >= 0
- $x->is_negative(); # true if < 0
- $x->is_inf(sign); # true if +inf, or -inf (sign is default '+')
-
- $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
- $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
- $x->sign(); # return the sign, either +,- or NaN
- $x->digit($n); # return the nth digit, counting from right
- $x->digit(-$n); # return the nth digit, counting from left
-
- # The following all modify their first argument:
-
- # set
- $x->bzero(); # set $x to 0
- $x->bnan(); # set $x to NaN
- $x->bone(); # set $x to +1
- $x->bone('-'); # set $x to -1
-
- $x->bneg(); # negation
- $x->babs(); # absolute value
- $x->bnorm(); # normalize (no-op)
- $x->bnot(); # two's complement (bit wise not)
- $x->binc(); # increment x by 1
- $x->bdec(); # decrement x by 1
+ # Testing (don't modify their arguments)
+ # (return true if the condition is met, otherwise false)
+
+ $x->is_zero(); # if $x is +0
+ $x->is_nan(); # if $x is NaN
+ $x->is_one(); # if $x is +1
+ $x->is_one('-'); # if $x is -1
+ $x->is_odd(); # if $x is odd
+ $x->is_even(); # if $x is even
+ $x->is_positive(); # if $x >= 0
+ $x->is_negative(); # if $x < 0
+ $x->is_inf(sign); # if $x is +inf, or -inf (sign is default '+')
+ $x->is_int(); # if $x is an integer (not a float)
+
+ # comparing and digit/sign extration
+ $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
+ $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
+ $x->sign(); # return the sign, either +,- or NaN
+ $x->digit($n); # return the nth digit, counting from right
+ $x->digit(-$n); # return the nth digit, counting from left
+
+ # The following all modify their first argument. If you want to preserve
+ # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is
+ # neccessary when mixing $a = $b assigments with non-overloaded math.
+
+ $x->bzero(); # set $x to 0
+ $x->bnan(); # set $x to NaN
+ $x->bone(); # set $x to +1
+ $x->bone('-'); # set $x to -1
+ $x->binf(); # set $x to inf
+ $x->binf('-'); # set $x to -inf
+
+ $x->bneg(); # negation
+ $x->babs(); # absolute value
+ $x->bnorm(); # normalize (no-op in BigInt)
+ $x->bnot(); # two's complement (bit wise not)
+ $x->binc(); # increment $x by 1
+ $x->bdec(); # decrement $x by 1
- $x->badd($y); # addition (add $y to $x)
- $x->bsub($y); # subtraction (subtract $y from $x)
- $x->bmul($y); # multiplication (multiply $x by $y)
- $x->bdiv($y); # divide, set $x to quotient
- # return (quo,rem) or quo if scalar
-
- $x->bmod($y); # modulus (x % y)
- $x->bpow($y); # power of arguments (x ** y)
- $x->blsft($y); # left shift
- $x->brsft($y); # right shift
- $x->blsft($y,$n); # left shift, by base $n (like 10)
- $x->brsft($y,$n); # right shift, by base $n (like 10)
+ $x->badd($y); # addition (add $y to $x)
+ $x->bsub($y); # subtraction (subtract $y from $x)
+ $x->bmul($y); # multiplication (multiply $x by $y)
+ $x->bdiv($y); # divide, set $x to quotient
+ # return (quo,rem) or quo if scalar
+
+ $x->bmod($y); # modulus (x % y)
+ $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod))
+ $x->bmodinv($mod); # the inverse of $x in the given modulus $mod
+
+ $x->bpow($y); # power of arguments (x ** y)
+ $x->blsft($y); # left shift
+ $x->brsft($y); # right shift
+ $x->blsft($y,$n); # left shift, by base $n (like 10)
+ $x->brsft($y,$n); # right shift, by base $n (like 10)
- $x->band($y); # bitwise and
- $x->bior($y); # bitwise inclusive or
- $x->bxor($y); # bitwise exclusive or
- $x->bnot(); # bitwise not (two's complement)
+ $x->band($y); # bitwise and
+ $x->bior($y); # bitwise inclusive or
+ $x->bxor($y); # bitwise exclusive or
+ $x->bnot(); # bitwise not (two's complement)
+
+ $x->bsqrt(); # calculate square-root
+ $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root)
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
- $x->bsqrt(); # calculate square-root
+ $x->round($A,$P,$mode); # round to accuracy or precision using mode $mode
+ $x->bround($N); # accuracy: preserve $N digits
+ $x->bfround($N); # round to $Nth digit, no-op for BigInts
- $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r
- $x->bround($N); # accuracy: preserve $N digits
- $x->bfround($N); # round to $Nth digit, no-op for BigInts
+ # The following do not modify their arguments in BigInt (are no-ops),
+ # but do so in BigFloat:
- # The following do not modify their arguments in BigInt, but do in BigFloat:
- $x->bfloor(); # return integer less or equal than $x
- $x->bceil(); # return integer greater or equal than $x
+ $x->bfloor(); # return integer less or equal than $x
+ $x->bceil(); # return integer greater or equal than $x
# The following do not modify their arguments:
- bgcd(@values); # greatest common divisor
- blcm(@values); # lowest common multiplicator
+ bgcd(@values); # greatest common divisor (no OO style)
+ blcm(@values); # lowest common multiplicator (no OO style)
- $x->length(); # return number of digits in number
- ($x,$f) = $x->length(); # length of number and length of fraction part,
- # latter is always 0 digits long for BigInt's
-
- $x->exponent(); # return exponent as BigInt
- $x->mantissa(); # return mantissa as BigInt
- $x->parts(); # return (mantissa,exponent) as BigInt
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
- $x->as_number(); # return as BigInt (in BigInt: same as copy())
+ $x->length(); # return number of digits in number
+ ($x,$f) = $x->length(); # length of number and length of fraction part,
+ # latter is always 0 digits long for BigInt's
+
+ $x->exponent(); # return exponent as BigInt
+ $x->mantissa(); # return (signed) mantissa as BigInt
+ $x->parts(); # return (mantissa,exponent) as BigInt
+ $x->copy(); # make a true copy of $x (unlike $y = $x;)
+ $x->as_number(); # return as BigInt (in BigInt: same as copy())
- # conversation to string
- $x->bstr(); # normalized string
- $x->bsstr(); # normalized string in scientific notation
- $x->as_hex(); # as signed hexadecimal string with prefixed 0x
- $x->as_bin(); # as signed binary string with prefixed 0b
+ # conversation to string (do not modify their argument)
+ $x->bstr(); # normalized string
+ $x->bsstr(); # normalized string in scientific notation
+ $x->as_hex(); # as signed hexadecimal string with prefixed 0x
+ $x->as_bin(); # as signed binary string with prefixed 0b
+
+
+ # precision and accuracy (see section about rounding for more)
+ $x->precision(); # return P of $x (or global, if P of $x undef)
+ $x->precision($n); # set P of $x to $n
+ $x->accuracy(); # return A of $x (or global, if A of $x undef)
+ $x->accuracy($n); # set A $x to $n
+ # Global methods
+ Math::BigInt->precision(); # get/set global P for all BigInt objects
+ Math::BigInt->accuracy(); # get/set global A for all BigInt objects
+ Math::BigInt->config(); # return hash containing configuration
=head1 DESCRIPTION
=over 2
-=item Canonical notation
-
-Big integer values are strings of the form C</^[+-]\d+$/> with leading
-zeros suppressed.
+=item Input
- '-0' canonical value '-0', normalized '0'
- ' -123_123_123' canonical value '-123123123'
- '1_23_456_7890' canonical value '1234567890'
+Input values to these routines may be any string, that looks like a number
+and results in an integer, including hexadecimal and binary numbers.
-=item Input
+Scalars holding numbers may also be passed, but note that non-integer numbers
+may already have lost precision due to the conversation to float. Quote
+your input if you want BigInt to see all the digits.
-Input values to these routines may be either Math::BigInt objects or
-strings of the form C</^\s*[+-]?[\d]+\.?[\d]*E?[+-]?[\d]*$/>.
+ $x = Math::BigInt->new(12345678890123456789); # bad
+ $x = Math::BigInt->new('12345678901234567890'); # good
You can include one underscore between any two digits.
This means integer values like 1.01E2 or even 1000E-2 are also accepted.
-Non integer values result in NaN.
+Non-integer values result in NaN.
-Math::BigInt::new() defaults to 0, while Math::BigInt::new('') results
-in 'NaN'.
+Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('')
+results in 'NaN'.
-bnorm() on a BigInt object is now effectively a no-op, since the numbers
+C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers
are always stored in normalized form. On a string, it creates a BigInt
-object.
+object from the input.
=item Output
=back
+=head1 METHODS
+
+Each of the methods below (except config(), accuracy() and precision())
+accepts three additional parameters. These arguments $A, $P and $R are
+accuracy, precision and round_mode. Please see the section about
+L<ACCURACY and PRECISION> for more information.
+
+=head2 config
+
+ use Data::Dumper;
+
+ print Dumper ( Math::BigInt->config() );
+ print Math::BigInt->config()->{lib},"\n";
+
+Returns a hash containing the configuration, e.g. the version number, lib
+loaded etc. The following hash keys are currently filled in with the
+appropriate information.
+
+ key Description
+ Example
+ ============================================================
+ lib Name of the Math library
+ Math::BigInt::Calc
+ lib_version Version of 'lib'
+ 0.30
+ class The class of config you just called
+ Math::BigInt
+ upgrade To which class numbers are upgraded
+ Math::BigFloat
+ downgrade To which class numbers are downgraded
+ undef
+ precision Global precision
+ undef
+ accuracy Global accuracy
+ undef
+ round_mode Global round mode
+ even
+ version version number of the class you used
+ 1.61
+ div_scale Fallback acccuracy for div
+ 40
+
+The following values can be set by passing config a reference to a hash:
+
+ trap_inf trap_nan
+ upgrade downgrade precision accuracy round_mode div_scale
+
+Example:
+
+ $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } );
+
+=head2 accuracy
+
+ $x->accuracy(5); # local for $x
+ CLASS->accuracy(5); # global for all members of CLASS
+ $A = $x->accuracy(); # read out
+ $A = CLASS->accuracy(); # read out
+
+Set or get the global or local accuracy, aka how many significant digits the
+results have.
+
+Please see the section about L<ACCURACY AND PRECISION> for further details.
+
+Value must be greater than zero. Pass an undef value to disable it:
+
+ $x->accuracy(undef);
+ Math::BigInt->accuracy(undef);
+
+Returns the current accuracy. For C<$x->accuracy()> it will return either the
+local accuracy, or if not defined, the global. This means the return value
+represents the accuracy that will be in effect for $x:
+
+ $y = Math::BigInt->new(1234567); # unrounded
+ print Math::BigInt->accuracy(4),"\n"; # set 4, print 4
+ $x = Math::BigInt->new(123456); # will be automatically rounded
+ print "$x $y\n"; # '123500 1234567'
+ print $x->accuracy(),"\n"; # will be 4
+ print $y->accuracy(),"\n"; # also 4, since global is 4
+ print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5
+ print $x->accuracy(),"\n"; # still 4
+ print $y->accuracy(),"\n"; # 5, since global is 5
+
+Note: Works also for subclasses like Math::BigFloat. Each class has it's own
+globals separated from Math::BigInt, but it is possible to subclass
+Math::BigInt and make the globals of the subclass aliases to the ones from
+Math::BigInt.
+
+=head2 precision
+
+ $x->precision(-2); # local for $x, round right of the dot
+ $x->precision(2); # ditto, but round left of the dot
+ CLASS->accuracy(5); # global for all members of CLASS
+ CLASS->precision(-5); # ditto
+ $P = CLASS->precision(); # read out
+ $P = $x->precision(); # read out
+
+Set or get the global or local precision, aka how many digits the result has
+after the dot (or where to round it when passing a positive number). In
+Math::BigInt, passing a negative number precision has no effect since no
+numbers have digits after the dot.
+
+Please see the section about L<ACCURACY AND PRECISION> for further details.
+
+Value must be greater than zero. Pass an undef value to disable it:
+
+ $x->precision(undef);
+ Math::BigInt->precision(undef);
+
+Returns the current precision. For C<$x->precision()> it will return either the
+local precision of $x, or if not defined, the global. This means the return
+value represents the accuracy that will be in effect for $x:
+
+ $y = Math::BigInt->new(1234567); # unrounded
+ print Math::BigInt->precision(4),"\n"; # set 4, print 4
+ $x = Math::BigInt->new(123456); # will be automatically rounded
+
+Note: Works also for subclasses like Math::BigFloat. Each class has it's own
+globals separated from Math::BigInt, but it is possible to subclass
+Math::BigInt and make the globals of the subclass aliases to the ones from
+Math::BigInt.
+
+=head2 brsft
+
+ $x->brsft($y,$n);
+
+Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and
+2, but others work, too.
+
+Right shifting usually amounts to dividing $x by $n ** $y and truncating the
+result:
+
+
+ $x = Math::BigInt->new(10);
+ $x->brsft(1); # same as $x >> 1: 5
+ $x = Math::BigInt->new(1234);
+ $x->brsft(2,10); # result 12
+
+There is one exception, and that is base 2 with negative $x:
+
+
+ $x = Math::BigInt->new(-5);
+ print $x->brsft(1);
+
+This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the
+result).
+
+=head2 new
+
+ $x = Math::BigInt->new($str,$A,$P,$R);
+
+Creates a new BigInt object from a scalar or another BigInt object. The
+input is accepted as decimal, hex (with leading '0x') or binary (with leading
+'0b').
+
+See L<Input> for more info on accepted input formats.
+
+=head2 bnan
+
+ $x = Math::BigInt->bnan();
+
+Creates a new BigInt object representing NaN (Not A Number).
+If used on an object, it will set it to NaN:
+
+ $x->bnan();
+
+=head2 bzero
+
+ $x = Math::BigInt->bzero();
+
+Creates a new BigInt object representing zero.
+If used on an object, it will set it to zero:
+
+ $x->bzero();
+
+=head2 binf
+
+ $x = Math::BigInt->binf($sign);
+
+Creates a new BigInt object representing infinity. The optional argument is
+either '-' or '+', indicating whether you want infinity or minus infinity.
+If used on an object, it will set it to infinity:
+
+ $x->binf();
+ $x->binf('-');
+
+=head2 bone
+
+ $x = Math::BigInt->binf($sign);
+
+Creates a new BigInt object representing one. The optional argument is
+either '-' or '+', indicating whether you want one or minus one.
+If used on an object, it will set it to one:
+
+ $x->bone(); # +1
+ $x->bone('-'); # -1
+
+=head2 is_one()/is_zero()/is_nan()/is_inf()
+
+
+ $x->is_zero(); # true if arg is +0
+ $x->is_nan(); # true if arg is NaN
+ $x->is_one(); # true if arg is +1
+ $x->is_one('-'); # true if arg is -1
+ $x->is_inf(); # true if +inf
+ $x->is_inf('-'); # true if -inf (sign is default '+')
+
+These methods all test the BigInt for beeing one specific value and return
+true or false depending on the input. These are faster than doing something
+like:
+
+ if ($x == 0)
+
+=head2 is_positive()/is_negative()
+
+ $x->is_positive(); # true if >= 0
+ $x->is_negative(); # true if < 0
+
+The methods return true if the argument is positive or negative, respectively.
+C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and
+C<-inf> is negative. A C<zero> is positive.
+
+These methods are only testing the sign, and not the value.
+
+=head2 is_odd()/is_even()/is_int()
+
+ $x->is_odd(); # true if odd, false for even
+ $x->is_even(); # true if even, false for odd
+ $x->is_int(); # true if $x is an integer
+
+The return true when the argument satisfies the condition. C<NaN>, C<+inf>,
+C<-inf> are not integers and are neither odd nor even.
+
+=head2 bcmp
+
+ $x->bcmp($y);
+
+Compares $x with $y and takes the sign into account.
+Returns -1, 0, 1 or undef.
+
+=head2 bacmp
+
+ $x->bacmp($y);
+
+Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef.
+
+=head2 sign
+
+ $x->sign();
+
+Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
+
+=head2 bcmp
+
+ $x->digit($n); # return the nth digit, counting from right
+
+=head2 bneg
+
+ $x->bneg();
+
+Negate the number, e.g. change the sign between '+' and '-', or between '+inf'
+and '-inf', respectively. Does nothing for NaN or zero.
+
+=head2 babs
+
+ $x->babs();
+
+Set the number to it's absolute value, e.g. change the sign from '-' to '+'
+and from '-inf' to '+inf', respectively. Does nothing for NaN or positive
+numbers.
+
+=head2 bnorm
+
+ $x->bnorm(); # normalize (no-op)
+
+=head2 bnot
+
+ $x->bnot(); # two's complement (bit wise not)
+
+=head2 binc
+
+ $x->binc(); # increment x by 1
+
+=head2 bdec
+
+ $x->bdec(); # decrement x by 1
+
+=head2 badd
+
+ $x->badd($y); # addition (add $y to $x)
+
+=head2 bsub
+
+ $x->bsub($y); # subtraction (subtract $y from $x)
+
+=head2 bmul
+
+ $x->bmul($y); # multiplication (multiply $x by $y)
+
+=head2 bdiv
+
+ $x->bdiv($y); # divide, set $x to quotient
+ # return (quo,rem) or quo if scalar
+
+=head2 bmod
+
+ $x->bmod($y); # modulus (x % y)
+
+=head2 bmodinv
+
+ num->bmodinv($mod); # modular inverse
+
+Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is
+returned unless C<$num> is relatively prime to C<$mod>, i.e. unless
+C<bgcd($num, $mod)==1>.
+
+=head2 bmodpow
+
+ $num->bmodpow($exp,$mod); # modular exponentation
+ # ($num**$exp % $mod)
+
+Returns the value of C<$num> taken to the power C<$exp> in the modulus
+C<$mod> using binary exponentation. C<bmodpow> is far superior to
+writing
+
+ $num ** $exp % $mod
+
+because C<bmodpow> is much faster--it reduces internal variables into
+the modulus whenever possible, so it operates on smaller numbers.
+
+C<bmodpow> also supports negative exponents.
+
+ bmodpow($num, -1, $mod)
+
+is exactly equivalent to
+
+ bmodinv($num, $mod)
+
+=head2 bpow
+
+ $x->bpow($y); # power of arguments (x ** y)
+
+=head2 blsft
+
+ $x->blsft($y); # left shift
+ $x->blsft($y,$n); # left shift, in base $n (like 10)
+
+=head2 brsft
+
+ $x->brsft($y); # right shift
+ $x->brsft($y,$n); # right shift, in 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 $x to accuracy C<$A> or precision C<$P> using the round mode
+C<$round_mode>.
+
+=head2 bround
+
+ $x->bround($N); # accuracy: preserve $N digits
+
+=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(); # return 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->bneg("1234"); # BigInt "-1234"
+ $x = Math::BigInt->babs("-12345"); # BigInt "12345"
$x = Math::BigInt->bnorm("-0 00"); # BigInt "0"
$x = bint(1) + bint(2); # BigInt "3"
$x = bint(1) + "2"; # ditto (auto-BigIntify of "2")
$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:
=head1 Autocreating constants
-After C<use Math::BigInt ':constant'> all the B<integer> decimal constants
-in the given scope are converted to C<Math::BigInt>. This conversion
-happens at compile time.
+After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal
+and binary constants in the given scope are converted to C<Math::BigInt>.
+This conversion happens at compile time.
In particular,
perl -MMath::BigInt=:constant -e 'print 2**100,"\n"'
-prints the integer value of C<2**100>. Note that without conversion of
+prints the integer value of C<2**100>. Note that without conversion of
constants the expression 2**100 will be calculated as perl scalar.
Please note that strings and floating point constants are not affected,
+ '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.
+
+This also applies to integers that look like floating point constants:
+
+ use Math::BigInt ':constant';
+
+ print ref(123e2),"\n";
+ print ref(123.2e2),"\n";
+
+will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat>
+to get this to work.
=head1 PERFORMANCE
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
- my $x = Math::BigInt->new(2);
- print $x ** (1024*1024);
+ use overload;
-For more benchmark results see http://bloodgate.com/perl/benchmarks.html
+in your subclass to automatically inherit the overloading from the parent. If
+you like, you can change part of the overloading, look at Math::String for an
+example.
+
+=head1 UPGRADING
+
+When used like this:
+
+ use Math::BigInt upgrade => 'Foo::Bar';
+
+certain operations will 'upgrade' their calculation and thus the result to
+the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat:
+
+ use Math::BigInt upgrade => 'Math::BigFloat';
+
+As a shortcut, you can use the module C<bignum>:
+
+ use bignum;
+
+Also good for oneliners:
+
+ perl -Mbignum -le 'print 2 ** 255'
+
+This makes it possible to mix arguments of different classes (as in 2.5 + 2)
+as well es preserve accuracy (as in sqrt(3)).
+
+Beware: This feature is not fully implemented yet.
+
+=head2 Auto-upgrade
+
+The following methods upgrade themselves unconditionally; that is if upgrade
+is in effect, they will always hand up their work:
+
+=over 2
+
+=item bsqrt()
+
+=item div()
+
+=item blog()
+
+=back
+
+Beware: This list is not complete.
+
+All other methods upgrade themselves only when one (or all) of their
+arguments are of the class mentioned in $upgrade (This might change in later
+versions to a more sophisticated scheme):
=head1 BUGS
=over 2
+=item broot() does not work
+
+The broot() function in BigInt may only work for small values. This will be
+fixed in a later version.
+
=item Out of Memory!
Under Perl prior to 5.6.0 having an C<use Math::BigInt ':constant';> and
$y = Math::BigInt->new($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 bdiv
+=item length
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:
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 autoupgrading|upgrading. See the
+pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this.
+
=item bsqrt()
-C<bsqrt()> works only good if the result is 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.
+mode. The reason is that the result is always truncated to an integer.
If you want a better approximation of the square root, then use:
$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>, L<Math::BigRat> 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 pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest
+because they solve the autoupgrading/downgrading issue, at least partly.
+
+The package at
+L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
+more documentation including a full version history, testcases, empty
+subclass files and benchmarks.
=head1 AUTHORS
Original code by Mark Biggar, overloaded interface by Ilya Zakharevich.
-Completely rewritten by Tels http://bloodgate.com in late 2000, 2001.
+Completely rewritten by Tels http://bloodgate.com in late 2000, 2001, 2002
+and still at it in 2003.
+
+Many people contributed in one or more ways to the final beast, see the file
+CREDITS for an (uncomplete) list. If you miss your name, please drop me a
+mail. Thank you!
=cut