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authorafresh1 <afresh1@openbsd.org>2017-02-05 00:31:51 +0000
committerafresh1 <afresh1@openbsd.org>2017-02-05 00:31:51 +0000
commitb8851fcc53cbe24fd20b090f26dd149e353f6174 (patch)
tree4b7c1695865f00ab7a0da30b5632d514848ea3a2 /gnu/usr.bin/perl/dist/Math-BigInt/lib/Math/BigInt.pm
parentAdd option PCIVERBOSE. (diff)
downloadwireguard-openbsd-b8851fcc53cbe24fd20b090f26dd149e353f6174.tar.xz
wireguard-openbsd-b8851fcc53cbe24fd20b090f26dd149e353f6174.zip
Fix merge issues, remove excess files - match perl-5.24.1 dist
Diffstat (limited to 'gnu/usr.bin/perl/dist/Math-BigInt/lib/Math/BigInt.pm')
-rw-r--r--gnu/usr.bin/perl/dist/Math-BigInt/lib/Math/BigInt.pm5376
1 files changed, 0 insertions, 5376 deletions
diff --git a/gnu/usr.bin/perl/dist/Math-BigInt/lib/Math/BigInt.pm b/gnu/usr.bin/perl/dist/Math-BigInt/lib/Math/BigInt.pm
deleted file mode 100644
index a2aabc18648..00000000000
--- a/gnu/usr.bin/perl/dist/Math-BigInt/lib/Math/BigInt.pm
+++ /dev/null
@@ -1,5376 +0,0 @@
-package Math::BigInt;
-
-#
-# "Mike had an infinite amount to do and a negative amount of time in which
-# to do it." - Before and After
-#
-
-# The following hash values are used:
-# value: unsigned int with actual value (as a Math::BigInt::Calc or similar)
-# sign : +,-,NaN,+inf,-inf
-# _a : accuracy
-# _p : precision
-# _f : flags, used by MBF to flag parts of a float as untouchable
-
-# Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
-# underlying lib might change the reference!
-
-my $class = "Math::BigInt";
-use 5.006002;
-
-$VERSION = '1.9993';
-
-@ISA = qw(Exporter);
-@EXPORT_OK = qw(objectify bgcd blcm);
-
-# _trap_inf and _trap_nan are internal and should never be accessed from the
-# outside
-use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode
- $upgrade $downgrade $_trap_nan $_trap_inf/;
-use strict;
-
-# Inside overload, the first arg is always an object. If the original code had
-# it reversed (like $x = 2 * $y), then the third parameter is true.
-# In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes
-# no difference, but in some cases it does.
-
-# For overloaded ops with only one argument we simple use $_[0]->copy() to
-# preserve the argument.
-
-# Thus inheritance of overload operators becomes possible and transparent for
-# our subclasses without the need to repeat the entire overload section there.
-
-# We register ops that are not registerable yet, so suppress warnings
-{ no warnings;
-use overload
-'=' => sub { $_[0]->copy(); },
-
-# some shortcuts for speed (assumes that reversed order of arguments is routed
-# to normal '+' and we thus can always modify first arg. If this is changed,
-# this breaks and must be adjusted.)
-'+=' => sub { $_[0]->badd($_[1]); },
-'-=' => 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]); },
-'<<=' => sub { $_[0]->blsft($_[1]); },
-'>>=' => sub { $_[0]->brsft($_[1]); },
-
-# not supported by Perl yet
-'..' => \&_pointpoint,
-
-'<=>' => sub { my $rc = $_[2] ?
- ref($_[0])->bcmp($_[1],$_[0]) :
- $_[0]->bcmp($_[1]);
- $rc = 1 unless defined $rc;
- $rc <=> 0;
- },
-# we need '>=' to get things like "1 >= NaN" right:
-'>=' => sub { my $rc = $_[2] ?
- ref($_[0])->bcmp($_[1],$_[0]) :
- $_[0]->bcmp($_[1]);
- # if there was a NaN involved, return false
- return '' unless defined $rc;
- $rc >= 0;
- },
-'cmp' => sub {
- $_[2] ?
- "$_[1]" cmp $_[0]->bstr() :
- $_[0]->bstr() cmp "$_[1]" },
-
-'cos' => sub { $_[0]->copy->bcos(); },
-'sin' => sub { $_[0]->copy->bsin(); },
-'atan2' => sub { $_[2] ?
- ref($_[0])->new($_[1])->batan2($_[0]) :
- $_[0]->copy()->batan2($_[1]) },
-
-# are not yet overloadable
-#'hex' => sub { print "hex"; $_[0]; },
-#'oct' => sub { print "oct"; $_[0]; },
-
-# log(N) is log(N, e), where e is Euler's number
-'log' => sub { $_[0]->copy()->blog($_[1], undef); },
-'exp' => sub { $_[0]->copy()->bexp($_[1]); },
-'int' => sub { $_[0]->copy(); },
-'neg' => sub { $_[0]->copy()->bneg(); },
-'abs' => sub { $_[0]->copy()->babs(); },
-'sqrt' => sub { $_[0]->copy()->bsqrt(); },
-'~' => sub { $_[0]->copy()->bnot(); },
-
-# for subtract it's a bit tricky to not modify b: b-a => -a+b
-'-' => sub { my $c = $_[0]->copy; $_[2] ?
- $c->bneg()->badd( $_[1]) :
- $c->bsub( $_[1]) },
-'+' => sub { $_[0]->copy()->badd($_[1]); },
-'*' => sub { $_[0]->copy()->bmul($_[1]); },
-
-'/' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bdiv($_[0]) : $_[0]->copy->bdiv($_[1]);
- },
-'%' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bmod($_[0]) : $_[0]->copy->bmod($_[1]);
- },
-'**' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bpow($_[0]) : $_[0]->copy->bpow($_[1]);
- },
-'<<' => sub {
- $_[2] ? ref($_[0])->new($_[1])->blsft($_[0]) : $_[0]->copy->blsft($_[1]);
- },
-'>>' => sub {
- $_[2] ? ref($_[0])->new($_[1])->brsft($_[0]) : $_[0]->copy->brsft($_[1]);
- },
-'&' => sub {
- $_[2] ? ref($_[0])->new($_[1])->band($_[0]) : $_[0]->copy->band($_[1]);
- },
-'|' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bior($_[0]) : $_[0]->copy->bior($_[1]);
- },
-'^' => sub {
- $_[2] ? ref($_[0])->new($_[1])->bxor($_[0]) : $_[0]->copy->bxor($_[1]);
- },
-
-# can modify arg of ++ and --, so avoid a copy() for speed, but don't
-# use $_[0]->bone(), it would modify $_[0] to be 1!
-'++' => sub { $_[0]->binc() },
-'--' => sub { $_[0]->bdec() },
-
-# if overloaded, O(1) instead of O(N) and twice as fast for small numbers
-'bool' => sub {
- # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/
- # v5.6.1 dumps on this: return !$_[0]->is_zero() || undef; :-(
- my $t = undef;
- $t = 1 if !$_[0]->is_zero();
- $t;
- },
-
-# the original qw() does not work with the TIESCALAR below, why?
-# Order of arguments insignificant
-'""' => sub { $_[0]->bstr(); },
-'0+' => sub { $_[0]->numify(); }
-;
-} # no warnings scope
-
-##############################################################################
-# global constants, flags and accessory
-
-# These vars are public, but their direct usage is not recommended, use the
-# accessor methods instead
-
-$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
-$accuracy = undef;
-$precision = undef;
-$div_scale = 40;
-
-$upgrade = undef; # default is no upgrade
-$downgrade = undef; # default is no downgrade
-
-# These are internally, and not to be used from the outside at all
-
-$_trap_nan = 0; # are NaNs ok? set w/ config()
-$_trap_inf = 0; # are infs ok? set w/ config()
-my $nan = 'NaN'; # constants for easier life
-
-my $CALC = 'Math::BigInt::Calc'; # module to do the low level math
- # default is Calc.pm
-my $IMPORT = 0; # was import() called yet?
- # used to make require work
-my %WARN; # warn only once for low-level libs
-my %CAN; # cache for $CALC->can(...)
-my %CALLBACKS; # callbacks to notify on lib loads
-my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math
-
-##############################################################################
-# the old code had $rnd_mode, so we need to support it, too
-
-$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 to enable $rnd_mode to work transparently
- tie $rnd_mode, 'Math::BigInt';
-
- # set up some handy alias names
- *as_int = \&as_number;
- *is_pos = \&is_positive;
- *is_neg = \&is_negative;
- }
-
-##############################################################################
-
-sub round_mode
- {
- no strict 'refs';
- # make Class->round_mode() work
- my $self = shift;
- my $class = ref($self) || $self || __PACKAGE__;
- if (defined $_[0])
- {
- my $m = shift;
- if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
- {
- require Carp; Carp::croak ("Unknown round mode '$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)
- {
- return ${"${class}::upgrade"} = $_[0];
- }
- ${"${class}::upgrade"};
- }
-
-sub downgrade
- {
- no strict 'refs';
- # make Class->downgrade() work
- my $self = shift;
- my $class = ref($self) || $self || __PACKAGE__;
- # need to set new value?
- if (@_ > 0)
- {
- return ${"${class}::downgrade"} = $_[0];
- }
- ${"${class}::downgrade"};
- }
-
-sub div_scale
- {
- no strict 'refs';
- # make Class->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"} = $_[0];
- }
- ${"${class}::div_scale"};
- }
-
-sub accuracy
- {
- # $x->accuracy($a); ref($x) $a
- # $x->accuracy(); ref($x)
- # Class->accuracy(); class
- # Class->accuracy($a); class $a
-
- my $x = shift;
- my $class = ref($x) || $x || __PACKAGE__;
-
- no strict 'refs';
- # need to set new value?
- if (@_ > 0)
- {
- 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
- delete $x->{_p}; # clear P
- $a = ${"${class}::accuracy"} unless defined $a; # proper return value
- }
- else
- {
- ${"${class}::accuracy"} = $a; # set global A
- ${"${class}::precision"} = undef; # clear global P
- }
- return $a; # shortcut
- }
-
- my $a;
- # $object->accuracy() or fallback to global
- $a = $x->{_a} if ref($x);
- # but don't return global undef, when $x's accuracy is 0!
- $a = ${"${class}::accuracy"} if !defined $a;
- $a;
- }
-
-sub precision
- {
- # $x->precision($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__;
-
- 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
- delete $x->{_a}; # clear A
- $p = ${"${class}::precision"} unless defined $p; # proper return value
- }
- else
- {
- ${"${class}::precision"} = $p; # set global P
- ${"${class}::accuracy"} = undef; # clear global A
- }
- return $p; # shortcut
- }
-
- my $p;
- # $object->precision() or fallback to global
- $p = $x->{_p} if ref($x);
- # but don't return global undef, when $x's precision is 0!
- $p = ${"${class}::precision"} if !defined $p;
- $p;
- }
-
-sub config
- {
- # return (or set) configuration data as hash ref
- my $class = shift || 'Math::BigInt';
-
- no strict 'refs';
- if (@_ > 1 || (@_ == 1 && (ref($_[0]) eq 'HASH')))
- {
- # try to set given options as arguments from hash
-
- my $args = $_[0];
- if (ref($args) ne 'HASH')
- {
- $args = { @_ };
- }
- # these values can be "set"
- my $set_args = {};
- foreach my $key (
- qw/trap_inf trap_nan
- upgrade downgrade precision accuracy round_mode div_scale/
- )
- {
- $set_args->{$key} = $args->{$key} if exists $args->{$key};
- delete $args->{$key};
- }
- if (keys %$args > 0)
- {
- require Carp;
- Carp::croak ("Illegal key(s) '",
- join("','",keys %$args),"' passed to $class\->config()");
- }
- foreach my $key (keys %$set_args)
- {
- if ($key =~ /^trap_(inf|nan)\z/)
- {
- ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0);
- next;
- }
- # use a call instead of just setting the $variable to check argument
- $class->$key($set_args->{$key});
- }
- }
-
- # now return actual configuration
-
- my $cfg = {
- lib => $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}::$key"};
- };
- if (@_ == 1 && (ref($_[0]) ne 'HASH'))
- {
- # calls of the style config('lib') return just this value
- return $cfg->{$_[0]};
- }
- $cfg;
- }
-
-sub _scale_a
- {
- # select accuracy parameter based on precedence,
- # used by bround() and bfround(), may return undef for scale (means no op)
- my ($x,$scale,$mode) = @_;
-
- $scale = $x->{_a} unless defined $scale;
-
- no strict 'refs';
- my $class = ref($x);
-
- $scale = ${ $class . '::accuracy' } unless defined $scale;
- $mode = ${ $class . '::round_mode' } unless defined $mode;
-
- if (defined $scale)
- {
- $scale = $scale->can('numify') ? $scale->numify() : "$scale" if ref($scale);
- $scale = int($scale);
- }
-
- ($scale,$mode);
- }
-
-sub _scale_p
- {
- # select precision parameter based on precedence,
- # used by bround() and bfround(), may return undef for scale (means no op)
- my ($x,$scale,$mode) = @_;
-
- $scale = $x->{_p} unless defined $scale;
-
- no strict 'refs';
- my $class = ref($x);
-
- $scale = ${ $class . '::precision' } unless defined $scale;
- $mode = ${ $class . '::round_mode' } unless defined $mode;
-
- if (defined $scale)
- {
- $scale = $scale->can('numify') ? $scale->numify() : "$scale" if ref($scale);
- $scale = int($scale);
- }
-
- ($scale,$mode);
- }
-
-##############################################################################
-# constructors
-
-sub copy
- {
- # if two arguments, the first one is the class to "swallow" subclasses
- if (@_ > 1)
- {
- my $self = bless {
- sign => $_[1]->{sign},
- value => $CALC->_copy($_[1]->{value}),
- }, $_[0] if @_ > 1;
-
- $self->{_a} = $_[1]->{_a} if defined $_[1]->{_a};
- $self->{_p} = $_[1]->{_p} if defined $_[1]->{_p};
- return $self;
- }
-
- my $self = bless {
- sign => $_[0]->{sign},
- value => $CALC->_copy($_[0]->{value}),
- }, ref($_[0]);
-
- $self->{_a} = $_[0]->{_a} if defined $_[0]->{_a};
- $self->{_p} = $_[0]->{_p} if defined $_[0]->{_p};
- $self;
- }
-
-sub new
- {
- # create a new BigInt object from a string or another BigInt object.
- # see hash keys documented at top
-
- # the argument could be an object, so avoid ||, && etc on it, this would
- # cause costly overloaded code to be called. The only allowed ops are
- # ref() and defined.
-
- my ($class,$wanted,$a,$p,$r) = @_;
-
- # 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} = $1 || '+';
-
- if ($wanted =~ /^[+-]/)
- {
- # remove sign without touching wanted to make it work with constants
- my $t = $wanted; $t =~ s/^[+-]//;
- $self->{value} = $CALC->_new($t);
- }
- else
- {
- $self->{value} = $CALC->_new($wanted);
- }
- no strict 'refs';
- if ( (defined $a) || (defined $p)
- || (defined ${"${class}::precision"})
- || (defined ${"${class}::accuracy"})
- )
- {
- $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p);
- }
- return $self;
- }
-
- # handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]?inf\z/)
- {
- $self->{sign} = $wanted; # set a default sign for bstr()
- return $self->binf($wanted);
- }
- # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign
- my ($mis,$miv,$mfv,$es,$ev) = _split($wanted);
- if (!ref $mis)
- {
- if ($_trap_nan)
- {
- require Carp; Carp::croak("$wanted is not a number in $class");
- }
- $self->{value} = $CALC->_zero();
- $self->{sign} = $nan;
- return $self;
- }
- if (!ref $miv)
- {
- # _from_hex or _from_bin
- $self->{value} = $mis->{value};
- $self->{sign} = $mis->{sign};
- return $self; # throw away $mis
- }
- # make integer from mantissa by adjusting exp, then convert to bigint
- $self->{sign} = $$mis; # store sign
- $self->{value} = $CALC->_zero(); # for all the NaN cases
- my $e = int("$$es$$ev"); # exponent (avoid recursion)
- if ($e > 0)
- {
- my $diff = $e - CORE::length($$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 $$miv\n";
- $$miv = $$miv . ($$mfv . '0' x $diff);
- }
- }
- else
- {
- 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)
- {
- # xE-y, and empty mfv
- #print "xE-y\n";
- $e = abs($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} =~ /^[+-]$/;
- # if any of the globals is set, use them to round and store them inside $self
- # do not round for new($x,undef,undef) since that is used by MBF to signal
- # no rounding
- $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p;
- $self;
- }
-
-sub bnan
- {
- # create a bigint 'NaN', if given a BigInt, set it to 'NaN'
- my $self = shift;
- $self = $class if !defined $self;
- if (!ref($self))
- {
- 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');
- 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
- $self;
- }
-
-sub binf
- {
- # create a bigint '+-inf', if given a BigInt, set it to '+-inf'
- # the sign is either '+', or if given, used from there
- my $self = shift;
- my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/;
- $self = $class if !defined $self;
- if (!ref($self))
- {
- my $c = $self; $self = {}; bless $self, $c;
- }
- no strict 'refs';
- if (${"${class}::_trap_inf"})
- {
- require Carp;
- Carp::croak ("Tried to set $self to +-inf in $class\::binf()");
- }
- $self->import() if $IMPORT == 0; # make require work
- return if $self->modify('binf');
- 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
- $self;
- }
-
-sub bzero
- {
- # create a bigint '+0', if given a BigInt, set it to 0
- my $self = shift;
- $self = __PACKAGE__ if !defined $self;
-
- if (!ref($self))
- {
- my $c = $self; $self = {}; bless $self, $c;
- }
- $self->import() if $IMPORT == 0; # make require work
- return if $self->modify('bzero');
-
- if ($self->can('_bzero'))
- {
- # use subclass to initialize
- $self->_bzero();
- }
- else
- {
- # otherwise do our own thing
- $self->{value} = $CALC->_zero();
- }
- $self->{sign} = '+';
- if (@_ > 0)
- {
- if (@_ > 3)
- {
- # call like: $x->bzero($a,$p,$r,$y);
- ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
- }
- else
- {
- $self->{_a} = $_[0]
- if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
- $self->{_p} = $_[1]
- if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
- }
- }
- $self;
- }
-
-sub bone
- {
- # create a bigint '+1' (or -1 if given sign '-'),
- # if given a BigInt, set it to +1 or -1, respectively
- my $self = shift;
- my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
- $self = $class if !defined $self;
-
- if (!ref($self))
- {
- my $c = $self; $self = {}; bless $self, $c;
- }
- $self->import() if $IMPORT == 0; # make require work
- return if $self->modify('bone');
-
- if ($self->can('_bone'))
- {
- # use subclass to initialize
- $self->_bone();
- }
- else
- {
- # otherwise do our own thing
- $self->{value} = $CALC->_one();
- }
- $self->{sign} = $sign;
- if (@_ > 0)
- {
- if (@_ > 3)
- {
- # call like: $x->bone($sign,$a,$p,$r,$y);
- ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
- }
- else
- {
- # call like: $x->bone($sign,$a,$p,$r);
- $self->{_a} = $_[0]
- if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
- $self->{_p} = $_[1]
- if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
- }
- }
- $self;
- }
-
-##############################################################################
-# string conversion
-
-sub bsstr
- {
- # (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) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- if ($x->{sign} !~ /^[+-]$/)
- {
- return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
- return 'inf'; # +inf
- }
- my ($m,$e) = $x->parts();
- #$m->bstr() . 'e+' . $e->bstr(); # e can only be positive in BigInt
- # 'e+' because E can only be positive in BigInt
- $m->bstr() . 'e+' . $CALC->_str($e->{value});
- }
-
-sub bstr
- {
- # make a string from bigint object
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- if ($x->{sign} !~ /^[+-]$/)
- {
- return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
- return 'inf'; # +inf
- }
- my $es = ''; $es = $x->{sign} if $x->{sign} eq '-';
- $es.$CALC->_str($x->{value});
- }
-
-sub numify
- {
- # Make a "normal" scalar from a BigInt object
- my $x = shift; $x = $class->new($x) unless ref $x;
-
- return $x->bstr() if $x->{sign} !~ /^[+-]$/;
- my $num = $CALC->_num($x->{value});
- return -$num if $x->{sign} eq '-';
- $num;
- }
-
-##############################################################################
-# public stuff (usually prefixed with "b")
-
-sub sign
- {
- # return the sign of the number: +/-/-inf/+inf/NaN
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- $x->{sign};
- }
-
-sub _find_round_parameters
- {
- # After any operation or when calling round(), the result is rounded by
- # regarding the A & P from arguments, local parameters, or globals.
-
- # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!!
-
- # This procedure finds the round parameters, but it is for speed reasons
- # duplicated in round. Otherwise, it is tested by the testsuite and used
- # by fdiv().
-
- # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P
- # were requested/defined (locally or globally or both)
-
- my ($self,$a,$p,$r,@args) = @_;
- # $a accuracy, if given by caller
- # $p precision, if given by caller
- # $r round_mode, if given by caller
- # @args all 'other' arguments (0 for unary, 1 for binary ops)
-
- my $c = ref($self); # find out class of argument(s)
- no strict 'refs';
-
- # convert to normal scalar for speed and correctness in inner parts
- $a = $a->can('numify') ? $a->numify() : "$a" if defined $a && ref($a);
- $p = $p->can('numify') ? $p->numify() : "$p" if defined $p && ref($p);
-
- # now pick $a or $p, but only if we have got "arguments"
- if (!defined $a)
- {
- foreach ($self,@args)
- {
- # take the defined one, or if both defined, the one that is smaller
- $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
- }
- }
- if (!defined $p)
- {
- # even if $a is defined, take $p, to signal error for both defined
- foreach ($self,@args)
- {
- # take the defined one, or if both defined, the one that is bigger
- # -2 > -3, and 3 > 2
- $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
- }
- }
- # if still none defined, use globals (#2)
- $a = ${"$c\::accuracy"} unless defined $a;
- $p = ${"$c\::precision"} unless defined $p;
-
- # 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|common)$/)
- {
- require Carp; Carp::croak ("Unknown round mode '$r'");
- }
-
- $a = int($a) if defined $a;
- $p = int($p) if defined $p;
-
- ($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 embedded 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)
-
- my $c = ref($self); # find out class of argument(s)
- no strict 'refs';
-
- # now pick $a or $p, but only if we have got "arguments"
- if (!defined $a)
- {
- foreach ($self,@args)
- {
- # take the defined one, or if both defined, the one that is smaller
- $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
- }
- }
- if (!defined $p)
- {
- # even if $a is defined, take $p, to signal error for both defined
- foreach ($self,@args)
- {
- # take the defined one, or if both defined, the one that is bigger
- # -2 > -3, and 3 > 2
- $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
- }
- }
- # if still none defined, use globals (#2)
- $a = ${"$c\::accuracy"} unless defined $a;
- $p = ${"$c\::precision"} unless defined $p;
-
- # 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|common)$/)
- {
- require Carp; Carp::croak ("Unknown round mode '$r'");
- }
-
- # now round, by calling either fround or ffround:
- if (defined $a)
- {
- $self->bround(int($a),$r) if !defined $self->{_a} || $self->{_a} >= $a;
- }
- else # both can't be undefined due to early out
- {
- $self->bfround(int($p),$r) if !defined $self->{_p} || $self->{_p} <= $p;
- }
- # bround() or bfround() already called bnorm() if nec.
- $self;
- }
-
-sub bnorm
- {
- # (numstr or BINT) return BINT
- # Normalize number -- no-op here
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- $x;
- }
-
-sub babs
- {
- # (BINT or num_str) return BINT
- # make number absolute, or return absolute BINT from string
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- return $x if $x->modify('babs');
- # post-normalized abs for internal use (does nothing for NaN)
- $x->{sign} =~ s/^-/+/;
- $x;
- }
-
-sub bsgn {
- # Signum function.
-
- my $self = shift;
-
- return $self if $self->modify('bsgn');
-
- return $self -> bone("+") if $self -> is_pos();
- return $self -> bone("-") if $self -> is_neg();
- return $self; # zero or NaN
-}
-
-sub bneg
- {
- # (BINT or num_str) return BINT
- # negate number or make a negated number from string
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- return $x if $x->modify('bneg');
-
- # for +0 do not negate (to have always normalized +0). Does nothing for 'NaN'
- $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value}));
- $x;
- }
-
-sub bcmp
- {
- # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
- # (BINT or num_str, BINT or num_str) return cond_code
-
- # set up parameters
- my ($self,$x,$y) = (ref($_[0]),@_);
-
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y) = objectify(2,@_);
- }
-
- return $upgrade->bcmp($x,$y) if defined $upgrade &&
- ((!$x->isa($self)) || (!$y->isa($self)));
-
- if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
- {
- # handle +-inf and NaN
- return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
- return +1 if $x->{sign} eq '+inf';
- return -1 if $x->{sign} eq '-inf';
- return -1 if $y->{sign} eq '+inf';
- return +1;
- }
- # check sign for speed first
- return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y
- return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
-
- # have same sign, so compare absolute values. Don't make tests for zero here
- # because it's actually slower than testing 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}); # swapped acmp (lib returns 0,1,-1)
- }
-
-sub bacmp
- {
- # Compares 2 values, ignoring their signs.
- # Returns one of undef, <0, =0, >0. (suitable for sort)
- # (BINT, BINT) return cond_code
-
- # set up parameters
- my ($self,$x,$y) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y) = objectify(2,@_);
- }
-
- return $upgrade->bacmp($x,$y) if defined $upgrade &&
- ((!$x->isa($self)) || (!$y->isa($self)));
-
- if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
- {
- # handle +-inf and NaN
- return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
- return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
- return -1;
- }
- $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
-
- # 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($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade &&
- ((!$x->isa($self)) || (!$y->isa($self)));
-
- $r[3] = $y; # no push!
- # inf and NaN handling
- if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
- {
- # NaN first
- return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
- # inf handling
- if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
- {
- # +inf++inf or -inf+-inf => same, rest is NaN
- return $x if $x->{sign} eq $y->{sign};
- return $x->bnan();
- }
- # +-inf + something => +inf
- # something +-inf => +-inf
- $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
- return $x;
- }
-
- my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
-
- if ($sx eq $sy)
- {
- $x->{value} = $CALC->_add($x->{value},$y->{value}); # same sign, abs add
- }
- else
- {
- my $a = $CALC->_acmp ($y->{value},$x->{value}); # absolute compare
- if ($a > 0)
- {
- $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap
- $x->{sign} = $sy;
- }
- elsif ($a == 0)
- {
- # speedup, if equal, set result to 0
- $x->{value} = $CALC->_zero();
- $x->{sign} = '+';
- }
- else # a < 0
- {
- $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
- }
- }
- $x->round(@r);
- }
-
-sub bsub
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # subtract second arg from first, modify first
-
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
-
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
- }
-
- return $x if $x->modify('bsub');
-
- return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade &&
- ((!$x->isa($self)) || (!$y->isa($self)));
-
- return $x->round(@r) if $y->is_zero();
-
- # To correctly handle the lone special case $x->bsub($x), we note the sign
- # of $x, then flip the sign from $y, and if the sign of $x did change, too,
- # then we caught the special case:
- my $xsign = $x->{sign};
- $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
- if ($xsign ne $x->{sign})
- {
- # special case of $x->bsub($x) results in 0
- return $x->bzero(@r) if $xsign =~ /^[+-]$/;
- return $x->bnan(); # NaN, -inf, +inf
- }
- $x->badd($y,@r); # badd does not leave internal zeros
- $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
- $x; # already rounded by badd() or no round nec.
- }
-
-sub binc
- {
- # increment arg by one
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x if $x->modify('binc');
-
- if ($x->{sign} eq '+')
- {
- $x->{value} = $CALC->_inc($x->{value});
- return $x->round($a,$p,$r);
- }
- elsif ($x->{sign} eq '-')
- {
- $x->{value} = $CALC->_dec($x->{value});
- $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
- return $x->round($a,$p,$r);
- }
- # inf, nan handling etc
- $x->badd($self->bone(),$a,$p,$r); # badd does round
- }
-
-sub bdec
- {
- # decrement arg by one
- my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x if $x->modify('bdec');
-
- if ($x->{sign} eq '-')
- {
- # x already < 0
- $x->{value} = $CALC->_inc($x->{value});
- }
- else
- {
- return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf or NaN
- # >= 0
- if ($CALC->_is_zero($x->{value}))
- {
- # == 0
- $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1
- }
- else
- {
- # > 0
- $x->{value} = $CALC->_dec($x->{value});
- }
- }
- $x->round(@r);
- }
-
-sub blog
- {
- # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base
- # $base of $x)
-
- # set up parameters
- my ($self,$x,$base,@r) = (undef,@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$base,@r) = objectify(2,@_);
- }
-
- return $x if $x->modify('blog');
-
- $base = $self->new($base) if defined $base && !ref $base;
-
- # inf, -inf, NaN, <0 => NaN
- return $x->bnan()
- if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+');
-
- return $upgrade->blog($upgrade->new($x),$base,@r) if
- defined $upgrade;
-
- # fix for bug #24969:
- # the default base is e (Euler's number) which is not an integer
- if (!defined $base)
- {
- require Math::BigFloat;
- my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int();
- # modify $x in place
- $x->{value} = $u->{value};
- $x->{sign} = $u->{sign};
- return $x;
- }
-
- my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value});
- return $x->bnan() unless defined $rc; # not possible to take log?
- $x->{value} = $rc;
- $x->round(@r);
- }
-
-sub bnok
- {
- # Calculate n over k (binomial coefficient or "choose" function) as integer.
- # 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('bnok');
- return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN';
- return $x->binf() if $x->{sign} eq '+inf';
-
- # k > n or k < 0 => 0
- my $cmp = $x->bacmp($y);
- return $x->bzero() if $cmp < 0 || $y->{sign} =~ /^-/;
- # k == n => 1
- return $x->bone(@r) if $cmp == 0;
-
- if ($CALC->can('_nok'))
- {
- $x->{value} = $CALC->_nok($x->{value},$y->{value});
- }
- else
- {
- # ( 7 ) 7! 1*2*3*4 * 5*6*7 5 * 6 * 7 6 7
- # ( - ) = --------- = --------------- = --------- = 5 * - * -
- # ( 3 ) (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3 2 3
-
- if (!$y->is_zero())
- {
- my $z = $x - $y;
- $z->binc();
- my $r = $z->copy(); $z->binc();
- my $d = $self->new(2);
- while ($z->bacmp($x) <= 0) # f <= x ?
- {
- $r->bmul($z); $r->bdiv($d);
- $z->binc(); $d->binc();
- }
- $x->{value} = $r->{value}; $x->{sign} = '+';
- }
- else { $x->bone(); }
- }
- $x->round(@r);
- }
-
-sub bexp
- {
- # Calculate e ** $x (Euler's number to the power of X), truncated to
- # an integer value.
- my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x if $x->modify('bexp');
-
- # inf, -inf, NaN, <0 => NaN
- return $x->bnan() if $x->{sign} eq 'NaN';
- return $x->bone() if $x->is_zero();
- return $x if $x->{sign} eq '+inf';
- return $x->bzero() if $x->{sign} eq '-inf';
-
- my $u;
- {
- # run through Math::BigFloat unless told otherwise
- require Math::BigFloat unless defined $upgrade;
- local $upgrade = 'Math::BigFloat' unless defined $upgrade;
- # calculate result, truncate it to integer
- $u = $upgrade->bexp($upgrade->new($x),@r);
- }
-
- if (!defined $upgrade)
- {
- $u = $u->as_int();
- # modify $x in place
- $x->{value} = $u->{value};
- $x->round(@r);
- }
- else { $x = $u; }
- }
-
-sub blcm
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does not modify arguments, but returns new object
- # Lowest Common Multiple
-
- my $y = shift; my ($x);
- if (ref($y))
- {
- $x = $y->copy();
- }
- else
- {
- $x = $class->new($y);
- }
- my $self = ref($x);
- while (@_)
- {
- my $y = shift; $y = $self->new($y) if !ref ($y);
- $x = __lcm($x,$y);
- }
- $x;
- }
-
-sub bgcd
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does not modify arguments, but returns new object
- # GCD -- Euclid's algorithm, variant C (Knuth Vol 3, pg 341 ff)
-
- my $y = shift;
- $y = $class->new($y) if !ref($y);
- my $self = ref($y);
- my $x = $y->copy()->babs(); # keep arguments
- return $x->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN?
-
- while (@_)
- {
- $y = shift; $y = $self->new($y) if !ref($y);
- return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
- $x->{value} = $CALC->_gcd($x->{value},$y->{value});
- last if $CALC->_is_one($x->{value});
- }
- $x;
- }
-
-sub bnot
- {
- # (num_str or BINT) return BINT
- # represent ~x as twos-complement number
- # 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->binc()->bneg(); # binc already does round
- }
-
-##############################################################################
-# is_foo test routines
-# we don't need $self, so undef instead of ref($_[0]) make it slightly faster
-
-sub is_zero
- {
- # return true if arg (BINT or num_str) is zero (array '+', '0')
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
- $CALC->_is_zero($x->{value});
- }
-
-sub is_nan
- {
- # return true if arg (BINT or num_str) is NaN
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- $x->{sign} eq $nan ? 1 : 0;
- }
-
-sub is_inf
- {
- # return true if arg (BINT or num_str) is +-inf
- my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- if (defined $sign)
- {
- $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf
- $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-'
- return $x->{sign} =~ /^$sign$/ ? 1 : 0;
- }
- $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity
- }
-
-sub is_one
- {
- # return true if arg (BINT or num_str) is +1, or -1 if sign is given
- my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- $sign = '+' if !defined $sign || $sign ne '-';
-
- return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
- $CALC->_is_one($x->{value});
- }
-
-sub is_odd
- {
- # return true when arg (BINT or num_str) is odd, false for even
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
- $CALC->_is_odd($x->{value});
- }
-
-sub is_even
- {
- # return true when arg (BINT or num_str) is even, false for odd
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
- $CALC->_is_even($x->{value});
- }
-
-sub is_positive
- {
- # return true when arg (BINT or num_str) is positive (> 0)
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- return 1 if $x->{sign} eq '+inf'; # +inf is positive
-
- # 0+ is neither positive nor negative
- ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0;
- }
-
-sub is_negative
- {
- # return true when arg (BINT or num_str) is negative (< 0)
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not
- }
-
-sub is_int
- {
- # return true when arg (BINT or num_str) is an integer
- # always true for BigInt, but different for BigFloats
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't
- }
-
-###############################################################################
-
-sub bmul
- {
- # multiply the first number by the second number
- # (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,$upgrade->new($y),@r)
- if defined $upgrade && !$y->isa($self);
-
- $r[3] = $y; # no push here
-
- $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
-
- $x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
- $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0
-
- $x->round(@r);
- }
-
-sub bmuladd
- {
- # multiply two numbers and then add the third to the result
- # (BINT or num_str, BINT or num_str, BINT or num_str) return BINT
-
- # set up parameters
- my ($self,$x,$y,$z,@r) = objectify(3,@_);
-
- return $x if $x->modify('bmuladd');
-
- return $x->bnan() if ($x->{sign} eq $nan) ||
- ($y->{sign} eq $nan) ||
- ($z->{sign} eq $nan);
-
- # inf handling of x and y
- 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('-');
- }
- # inf handling x*y and z
- if (($z->{sign} =~ /^[+-]inf$/))
- {
- # something +-inf => +-inf
- $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/;
- }
-
- return $upgrade->bmuladd($x,$upgrade->new($y),$upgrade->new($z),@r)
- if defined $upgrade && (!$y->isa($self) || !$z->isa($self) || !$x->isa($self));
-
- # TODO: what if $y and $z have A or P set?
- $r[3] = $z; # 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
-
- my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); # get signs
-
- if ($sx eq $sz)
- {
- $x->{value} = $CALC->_add($x->{value},$z->{value}); # same sign, abs add
- }
- else
- {
- my $a = $CALC->_acmp ($z->{value},$x->{value}); # absolute compare
- if ($a > 0)
- {
- $x->{value} = $CALC->_sub($z->{value},$x->{value},1); # abs sub w/ swap
- $x->{sign} = $sz;
- }
- elsif ($a == 0)
- {
- # speedup, if equal, set result to 0
- $x->{value} = $CALC->_zero();
- $x->{sign} = '+';
- }
- else # a < 0
- {
- $x->{value} = $CALC->_sub($x->{value}, $z->{value}); # abs sub
- }
- }
- $x->round(@r);
- }
-
-sub _div_inf
- {
- # helper function that handles +-inf cases for bdiv()/bmod() to reuse code
- my ($self,$x,$y) = @_;
-
- # NaN if x == NaN or y == NaN or x==y==0
- return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
- if (($x->is_nan() || $y->is_nan()) ||
- ($x->is_zero() && $y->is_zero()));
-
- # +-inf / +-inf == NaN, remainder 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 (! $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} = '+'; # do not leave -0
- }
- $rem->round(@r);
- return ($x,$rem);
- }
-
- $x->{value} = $CALC->_div($x->{value},$y->{value});
- $x->{sign} = '+' if $CALC->_is_zero($x->{value});
-
- $x->round(@r);
- }
-
-###############################################################################
-# modulus functions
-
-sub bmod
- {
- # modulus (or remainder)
- # (BINT or num_str, BINT or num_str) return BINT
-
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
- }
-
- return $x if $x->modify('bmod');
- $r[3] = $y; # no push!
- if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
- {
- my ($d,$r) = $self->_div_inf($x,$y);
- $x->{sign} = $r->{sign};
- $x->{value} = $r->{value};
- return $x->round(@r);
- }
-
- # calc new sign and in case $y == +/- 1, return $x
- $x->{value} = $CALC->_mod($x->{value},$y->{value});
- if (!$CALC->_is_zero($x->{value}))
- {
- $x->{value} = $CALC->_sub($y->{value},$x->{value},1) # $y-$x
- if ($x->{sign} ne $y->{sign});
- $x->{sign} = $y->{sign};
- }
- else
- {
- $x->{sign} = '+'; # do not leave -0
- }
- $x->round(@r);
- }
-
-sub bmodinv
- {
- # Return modular multiplicative inverse: z is the modular inverse of x (mod
- # y) if and only if x*z (mod y) = 1 (mod y). If the modulus y is larger than
- # one, x and z are relative primes (i.e., their greatest common divisor is
- # one).
- #
- # If no modular multiplicative inverse exists, NaN is returned.
-
- # set up parameters
- my ($self,$x,$y,@r) = (undef,@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$x,$y,@r) = objectify(2,@_);
- }
-
- return $x if $x->modify('bmodinv');
-
- # Return NaN if one or both arguments is +inf, -inf, or nan.
-
- return $x->bnan() if ($y->{sign} !~ /^[+-]$/ ||
- $x->{sign} !~ /^[+-]$/);
-
- # Return NaN if $y is zero; 1 % 0 makes no sense.
-
- return $x->bnan() if $y->is_zero();
-
- # Return 0 in the trivial case. $x % 1 or $x % -1 is zero for all finite
- # integers $x.
-
- return $x->bzero() if ($y->is_one() ||
- $y->is_one('-'));
-
- # Return NaN if $x = 0, or $x modulo $y is zero. The only valid case when
- # $x = 0 is when $y = 1 or $y = -1, but that was covered above.
- #
- # Note that computing $x modulo $y here affects the value we'll feed to
- # $CALC->_modinv() below when $x and $y have opposite signs. E.g., if $x =
- # 5 and $y = 7, those two values are fed to _modinv(), but if $x = -5 and
- # $y = 7, the values fed to _modinv() are $x = 2 (= -5 % 7) and $y = 7.
- # The value if $x is affected only when $x and $y have opposite signs.
-
- $x->bmod($y);
- return $x->bnan() if $x->is_zero();
-
- # Compute the modular multiplicative inverse of the absolute values. We'll
- # correct for the signs of $x and $y later. Return NaN if no GCD is found.
-
- ($x->{value}, $x->{sign}) = $CALC->_modinv($x->{value}, $y->{value});
- return $x->bnan() if !defined $x->{value};
-
- # Library inconsistency workaround: _modinv() in Math::BigInt::GMP versions
- # <= 1.32 return undef rather than a "+" for the sign.
-
- $x->{sign} = '+' unless defined $x->{sign};
-
- # When one or both arguments are negative, we have the following
- # relations. If x and y are positive:
- #
- # modinv(-x, -y) = -modinv(x, y)
- # modinv(-x, y) = y - modinv(x, y) = -modinv(x, y) (mod y)
- # modinv( x, -y) = modinv(x, y) - y = modinv(x, y) (mod -y)
-
- # We must swap the sign of the result if the original $x is negative.
- # However, we must compensate for ignoring the signs when computing the
- # inverse modulo. The net effect is that we must swap the sign of the
- # result if $y is negative.
-
- $x -> bneg() if $y->{sign} eq '-';
-
- # Compute $x modulo $y again after correcting the sign.
-
- $x -> bmod($y) if $x->{sign} ne $y->{sign};
-
- return $x;
- }
-
-sub bmodpow
- {
- # Modular exponentiation. Raises a very large number to a very large exponent
- # in a given very large modulus quickly, thanks to binary exponentiation.
- # Supports negative exponents.
- my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
-
- return $num if $num->modify('bmodpow');
-
- # When the exponent 'e' is negative, use the following relation, which is
- # based on finding the multiplicative inverse 'd' of 'b' modulo 'm':
- #
- # b^(-e) (mod m) = d^e (mod m) where b*d = 1 (mod m)
-
- $num->bmodinv($mod) if ($exp->{sign} eq '-');
-
- # Check for valid input. All operands must be finite, and the modulus must be
- # non-zero.
-
- return $num->bnan() if ($num->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
- $exp->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
- $mod->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf
- $mod->is_zero());
-
- # Compute 'a (mod m)', ignoring the signs on 'a' and 'm'. If the resulting
- # value is zero, the output is also zero, regardless of the signs on 'a' and
- # 'm'.
-
- my $value = $CALC->_modpow($num->{value}, $exp->{value}, $mod->{value});
- my $sign = '+';
-
- # If the resulting value is non-zero, we have four special cases, depending
- # on the signs on 'a' and 'm'.
-
- unless ($CALC->_is_zero($value)) {
-
- # There is a negative sign on 'a' (= $num**$exp) only if the number we
- # are exponentiating ($num) is negative and the exponent ($exp) is odd.
-
- if ($num->{sign} eq '-' && $exp->is_odd()) {
-
- # When both the number 'a' and the modulus 'm' have a negative sign,
- # use this relation:
- #
- # -a (mod -m) = -(a (mod m))
-
- if ($mod->{sign} eq '-') {
- $sign = '-';
- }
-
- # When only the number 'a' has a negative sign, use this relation:
- #
- # -a (mod m) = m - (a (mod m))
-
- else {
- # Use copy of $mod since _sub() modifies the first argument.
- my $mod = $CALC->_copy($mod->{value});
- $value = $CALC->_sub($mod, $value);
- $sign = '+';
- }
-
- } else {
-
- # When only the modulus 'm' has a negative sign, use this relation:
- #
- # a (mod -m) = (a (mod m)) - m
- # = -(m - (a (mod m)))
-
- if ($mod->{sign} eq '-') {
- # Use copy of $mod since _sub() modifies the first argument.
- my $mod = $CALC->_copy($mod->{value});
- $value = $CALC->_sub($mod, $value);
- $sign = '-';
- }
-
- # When neither the number 'a' nor the modulus 'm' have a negative
- # sign, directly return the already computed value.
- #
- # (a (mod m))
-
- }
-
- }
-
- $num->{value} = $value;
- $num->{sign} = $sign;
-
- return $num;
- }
-
-###############################################################################
-
-sub bfac
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # compute factorial number from $x, modify $x in place
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf
- return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN
-
- $x->{value} = $CALC->_fac($x->{value});
- $x->round(@r);
- }
-
-sub bpow
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # compute power of two numbers -- stolen from Knuth Vol 2 pg 233
- # modifies first argument
-
- # 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 $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
-
- # inf handling
- if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
- {
- if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
- {
- # +-inf ** +-inf
- return $x->bnan();
- }
- # +-inf ** Y
- if ($x->{sign} =~ /^[+-]inf/)
- {
- # +inf ** 0 => NaN
- return $x->bnan() if $y->is_zero();
- # -inf ** -1 => 1/inf => 0
- return $x->bzero() if $y->is_one('-') && $x->is_negative();
-
- # +inf ** Y => inf
- return $x if $x->{sign} eq '+inf';
-
- # -inf ** Y => -inf if Y is odd
- return $x if $y->is_odd();
- return $x->babs();
- }
- # X ** +-inf
-
- # 1 ** +inf => 1
- return $x if $x->is_one();
-
- # 0 ** inf => 0
- return $x if $x->is_zero() && $y->{sign} =~ /^[+]/;
-
- # 0 ** -inf => inf
- return $x->binf() if $x->is_zero();
-
- # -1 ** -inf => NaN
- return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/;
-
- # -X ** -inf => 0
- return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/;
-
- # -1 ** inf => NaN
- return $x->bnan() if $x->{sign} eq '-';
-
- # X ** inf => inf
- return $x->binf() if $y->{sign} =~ /^[+]/;
- # X ** -inf => 0
- return $x->bzero();
- }
-
- return $upgrade->bpow($upgrade->new($x),$y,@r)
- if defined $upgrade && (!$y->isa($self) || $y->{sign} eq '-');
-
- $r[3] = $y; # no push!
-
- # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu
-
- my $new_sign = '+';
- $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+');
-
- # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf
- return $x->binf()
- if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value});
- # 1 ** -y => 1 / (1 ** |y|)
- # so do test for negative $y after above's clause
- return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value});
-
- $x->{value} = $CALC->_pow($x->{value},$y->{value});
- $x->{sign} = $new_sign;
- $x->{sign} = '+' if $CALC->_is_zero($y->{value});
- $x->round(@r);
- }
-
-sub blsft
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # compute x << y, base n, y >= 0
-
- # 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 '-';
-
- $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n);
- $x->round(@r);
- }
-
-sub brsft
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # compute x >> y, base n, y >= 0
-
- # 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 '-';
-
- # 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 ($y >= CORE::length($bin))
- {
- $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 < 0, n == 2, y == 1
- $x->bdec(); # n == 2, but $y == 1: this fixes it
- }
-
- $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n);
- $x->round(@r);
- }
-
-sub band
- {
- #(BINT or num_str, BINT or num_str) return BINT
- # compute x & y
-
- # 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!
-
- return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
-
- my $sx = $x->{sign} eq '+' ? 1 : -1;
- my $sy = $y->{sign} eq '+' ? 1 : -1;
-
- if ($sx == 1 && $sy == 1)
- {
- $x->{value} = $CALC->_and($x->{value},$y->{value});
- return $x->round(@r);
- }
-
- if ($CAN{signed_and})
- {
- $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy);
- return $x->round(@r);
- }
-
- require $EMU_LIB;
- __emu_band($self,$x,$y,$sx,$sy,@r);
- }
-
-sub bior
- {
- #(BINT or num_str, BINT or num_str) return BINT
- # compute x | y
-
- # 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!
-
- return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
-
- my $sx = $x->{sign} eq '+' ? 1 : -1;
- my $sy = $y->{sign} eq '+' ? 1 : -1;
-
- # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior()
-
- # don't use lib for negative values
- if ($sx == 1 && $sy == 1)
- {
- $x->{value} = $CALC->_or($x->{value},$y->{value});
- return $x->round(@r);
- }
-
- # if lib can do negative values, let it handle this
- if ($CAN{signed_or})
- {
- $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy);
- return $x->round(@r);
- }
-
- require $EMU_LIB;
- __emu_bior($self,$x,$y,$sx,$sy,@r);
- }
-
-sub bxor
- {
- #(BINT or num_str, BINT or num_str) return BINT
- # compute x ^ y
-
- # 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!
-
- return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
-
- my $sx = $x->{sign} eq '+' ? 1 : -1;
- my $sy = $y->{sign} eq '+' ? 1 : -1;
-
- # don't use lib for negative values
- if ($sx == 1 && $sy == 1)
- {
- $x->{value} = $CALC->_xor($x->{value},$y->{value});
- return $x->round(@r);
- }
-
- # if lib can do negative values, let it handle this
- if ($CAN{signed_xor})
- {
- $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy);
- return $x->round(@r);
- }
-
- require $EMU_LIB;
- __emu_bxor($self,$x,$y,$sx,$sy,@r);
- }
-
-sub length
- {
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- my $e = $CALC->_len($x->{value});
- wantarray ? ($e,0) : $e;
- }
-
-sub digit
- {
- # return the nth decimal digit, negative values count backward, 0 is right
- my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- $n = $n->numify() if ref($n);
- $CALC->_digit($x->{value},$n||0);
- }
-
-sub _trailing_zeros
- {
- # return the amount of trailing zeros in $x (as scalar)
- my $x = shift;
- $x = $class->new($x) unless ref $x;
-
- return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc
-
- $CALC->_zeros($x->{value}); # must handle odd values, 0 etc
- }
-
-sub bsqrt
- {
- # calculate square root of $x
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- return $x if $x->modify('bsqrt');
-
- return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN
- return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf
-
- return $upgrade->bsqrt($x,@r) if defined $upgrade;
-
- $x->{value} = $CALC->_sqrt($x->{value});
- $x->round(@r);
- }
-
-sub broot
- {
- # calculate $y'th root of $x
-
- # set up parameters
- my ($self,$x,$y,@r) = (ref($_[0]),@_);
-
- $y = $self->new(2) unless defined $y;
-
- # objectify is costly, so avoid it
- if ((!ref($x)) || (ref($x) ne ref($y)))
- {
- ($self,$x,$y,@r) = objectify(2,$self || $class,@_);
- }
-
- return $x if $x->modify('broot');
-
- # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
- return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
- $y->{sign} !~ /^\+$/;
-
- return $x->round(@r)
- if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
-
- return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade;
-
- $x->{value} = $CALC->_root($x->{value},$y->{value});
- $x->round(@r);
- }
-
-sub exponent
- {
- # return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
-
- if ($x->{sign} !~ /^[+-]$/)
- {
- my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf,+inf => NaN or inf
- return $self->new($s);
- }
- return $self->bone() if $x->is_zero();
-
- # 12300 => 2 trailing zeros => exponent is 2
- $self->new( $CALC->_zeros($x->{value}) );
- }
-
-sub mantissa
- {
- # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
-
- if ($x->{sign} !~ /^[+-]$/)
- {
- # for NaN, +inf, -inf: keep the sign
- return $self->new($x->{sign});
- }
- my $m = $x->copy(); delete $m->{_p}; delete $m->{_a};
-
- # that's a bit inefficient:
- my $zeros = $CALC->_zeros($m->{value});
- $m->brsft($zeros,10) if $zeros != 0;
- $m;
- }
-
-sub parts
- {
- # return a copy of both the exponent and the mantissa
- my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
-
- ($x->mantissa(),$x->exponent());
- }
-
-##############################################################################
-# rounding functions
-
-sub bfround
- {
- # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
- # $n == 0 || $n == 1 => round to integer
- my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x;
-
- my ($scale,$mode) = $x->_scale_p(@_);
-
- return $x if !defined $scale || $x->modify('bfround'); # no-op
-
- # no-op for BigInts if $n <= 0
- $x->bround( $x->length()-$scale, $mode) if $scale > 0;
-
- delete $x->{_a}; # delete to save memory
- $x->{_p} = $scale; # store new _p
- $x;
- }
-
-sub _scan_for_nonzero
- {
- # internal, used by bround() to scan for non-zeros after a '5'
- my ($x,$pad,$xs,$len) = @_;
-
- return 0 if $len == 1; # "5" is trailed by invisible zeros
- my $follow = $pad - 1;
- return 0 if $follow > $len || $follow < 1;
-
- # use the string form to check whether only '0's follow or not
- substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0;
- }
-
-sub fround
- {
- # Exists to make life easier for switch between MBF and MBI (should we
- # autoload fxxx() like MBF does for bxxx()?)
- my $x = shift; $x = $class->new($x) unless ref $x;
- $x->bround(@_);
- }
-
-sub bround
- {
- # accuracy: +$n preserve $n digits from left,
- # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF)
- # 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(@_);
- return $x if !defined $scale || $x->modify('bround'); # no-op
-
- 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();
- # 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;
-
- # do not use digit(), it is very costly for binary => decimal
- # getting the entire string is also costly, but we need to do it only once
- my $xs = $CALC->_str($x->{value});
- my $pl = -$pad-1;
-
- # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
- # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
- $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len;
- $pl++; $pl ++ if $pad >= $len;
- $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
- my $round_up = 1; # default round up
- $round_up -- if
- ($mode eq 'trunc') || # trunc by round down
- ($digit_after =~ /[01234]/) || # round down anyway,
- # 6789 => round up
- ($digit_after eq '5') && # not 5000...0000
- ($x->_scan_for_nonzero($pad,$xs,$len) == 0) &&
- (
- ($mode eq 'even') && ($digit_round =~ /[24680]/) ||
- ($mode eq 'odd') && ($digit_round =~ /[13579]/) ||
- ($mode eq '+inf') && ($x->{sign} eq '-') ||
- ($mode eq '-inf') && ($x->{sign} eq '+') ||
- ($mode eq 'zero') # round down if zero, sign adjusted below
- );
- my $put_back = 0; # not yet modified
-
- if (($pad > 0) && ($pad <= $len))
- {
- substr($xs,-$pad,$pad) = '0' x $pad; # replace with '00...'
- $put_back = 1; # need to put back
- }
- elsif ($pad > $len)
- {
- $x->bzero(); # round to '0'
- }
-
- if ($round_up) # what gave test above?
- {
- $put_back = 1; # need to put back
- $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
-
- # we modify directly the string variant instead of creating a number and
- # adding it, since that is faster (we already have the string)
- my $c = 0; $pad ++; # for $pad == $len case
- while ($pad <= $len)
- {
- $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10';
- substr($xs,-$pad,1) = $c; $pad++;
- last if $c != 0; # no overflow => early out
- }
- $xs = '1'.$xs if $c == 0;
-
- }
- $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed
-
- $x->{_a} = $scale if $scale >= 0;
- if ($scale < 0)
- {
- $x->{_a} = $len+$scale;
- $x->{_a} = 0 if $scale < -$len;
- }
- $x;
- }
-
-sub bfloor
- {
- # round towards minus infinity; no-op since it's already integer
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- $x->round(@r);
- }
-
-sub bceil
- {
- # round towards plus infinity; no-op since it's already int
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- $x->round(@r);
- }
-
-sub bint {
- # round towards zero; no-op since it's already integer
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- $x->round(@r);
-}
-
-sub as_number
- {
- # An object might be asked to return itself as bigint on certain overloaded
- # operations. This does exactly this, so that sub classes can simple inherit
- # it or override with their own integer conversion routine.
- $_[0]->copy();
- }
-
-sub as_hex
- {
- # return as hex string, with prefixed 0x
- my $x = shift; $x = $class->new($x) if !ref($x);
-
- return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
-
- my $s = '';
- $s = $x->{sign} if $x->{sign} eq '-';
- $s . $CALC->_as_hex($x->{value});
- }
-
-sub as_bin
- {
- # return as binary string, with prefixed 0b
- my $x = shift; $x = $class->new($x) if !ref($x);
-
- return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
-
- my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
- return $s . $CALC->_as_bin($x->{value});
- }
-
-sub as_oct
- {
- # return as octal string, with prefixed 0
- my $x = shift; $x = $class->new($x) if !ref($x);
-
- return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
-
- my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
- return $s . $CALC->_as_oct($x->{value});
- }
-
-##############################################################################
-# private stuff (internal use only)
-
-sub objectify {
- # Convert strings and "foreign objects" to the objects we want.
-
- # The first argument, $count, is the number of following arguments that
- # objectify() looks at and converts to objects. The first is a classname.
- # If the given count is 0, all arguments will be used.
-
- # After the count is read, objectify obtains the name of the class to which
- # the following arguments are converted. If the second argument is a
- # reference, use the reference type as the class name. Otherwise, if it is
- # a string that looks like a class name, use that. Otherwise, use $class.
-
- # Caller: Gives us:
- #
- # $x->badd(1); => ref x, scalar y
- # Class->badd(1,2); => classname x (scalar), scalar x, scalar y
- # Class->badd(Class->(1),2); => classname x (scalar), ref x, scalar y
- # Math::BigInt::badd(1,2); => scalar x, scalar y
-
- # A shortcut for the common case $x->unary_op():
-
- return (ref($_[1]), $_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
-
- # Check the context.
-
- unless (wantarray) {
- require Carp;
- Carp::croak ("${class}::objectify() needs list context");
- }
-
- # Get the number of arguments to objectify.
-
- my $count = shift;
- $count ||= @_;
-
- # Initialize the output array.
-
- my @a = @_;
-
- # If the first argument is a reference, use that reference type as our
- # class name. Otherwise, if the first argument looks like a class name,
- # then use that as our class name. Otherwise, use the default class name.
-
- {
- if (ref($a[0])) { # reference?
- unshift @a, ref($a[0]);
- last;
- }
- if ($a[0] =~ /^[A-Z].*::/) { # string with class name?
- last;
- }
- unshift @a, $class; # default class name
- }
-
- no strict 'refs';
-
- # What we upgrade to, if anything.
-
- my $up = ${"$a[0]::upgrade"};
-
- # Disable downgrading, because Math::BigFloat -> foo('1.0','2.0') needs
- # floats.
-
- my $down;
- if (defined ${"$a[0]::downgrade"}) {
- $down = ${"$a[0]::downgrade"};
- ${"$a[0]::downgrade"} = undef;
- }
-
- for my $i (1 .. $count) {
- my $ref = ref $a[$i];
-
- # If it is an object of the right class, all is fine.
-
- if ($ref eq $a[0]) {
- next;
- }
-
-# # Don't do anything with undefs.
-#
-# unless (defined($a[$i])) {
-# next;
-# }
- $a[$i] //= 0;
-
- # Perl scalars are fed to the appropriate constructor.
-
- unless ($ref) {
- $a[$i] = $a[0] -> new($a[$i]);
- next;
- }
-
- # Upgrading is OK, so skip further tests if the argument is upgraded.
-
- if (defined $up && $ref eq $up) {
- next;
- }
-
- # If we want a Math::BigInt, see if the object can become one.
- # Support the old misnomer as_number().
-
- if ($a[0] eq 'Math::BigInt') {
- if ($a[$i] -> can('as_int')) {
- $a[$i] = $a[$i] -> as_int();
- next;
- }
- if ($a[$i] -> can('as_number')) {
- $a[$i] = $a[$i] -> as_number();
- next;
- }
- }
-
- # If we want a Math::BigFloat, see if the object can become one.
-
- if ($a[0] eq 'Math::BigFloat') {
- if ($a[$i] -> can('as_float')) {
- $a[$i] = $a[$i] -> as_float();
- next;
- }
- }
-
- # Last resort.
-
- $a[$i] = $a[0] -> new($a[$i]);
- }
-
- # Reset the downgrading.
-
- ${"$a[0]::downgrade"} = $down;
-
- return @a;
-}
-
-sub _register_callback
- {
- my ($class,$callback) = @_;
-
- if (ref($callback) ne 'CODE')
- {
- require Carp;
- Carp::croak ("$callback is not a coderef");
- }
- $CALLBACKS{$class} = $callback;
- }
-
-sub import
- {
- my $self = shift;
-
- $IMPORT++; # remember we did import()
- my @a; my $l = scalar @_;
- my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die
- 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) },
- binary => sub { $self->new(shift) };
- }
- elsif ($_[$i] eq 'upgrade')
- {
- # this causes upgrading
- $upgrade = $_[$i+1]; # or undef to disable
- $i++;
- }
- elsif ($_[$i] =~ /^(lib|try|only)\z/)
- {
- # this causes a different low lib to take care...
- $CALC = $_[$i+1] || '';
- # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback)
- $warn_or_die = 1 if $_[$i] eq 'lib';
- $warn_or_die = 2 if $_[$i] eq 'only';
- $i++;
- }
- else
- {
- push @a, $_[$i];
- }
- }
- # any non :constant stuff is handled by our parent, Exporter
- if (@a > 0)
- {
- require Exporter;
-
- $self->SUPER::import(@a); # need it for subclasses
- $self->export_to_level(1,$self,@a); # need it for MBF
- }
-
- # try to load core math lib
- my @c = split /\s*,\s*/,$CALC;
- foreach (@c)
- {
- $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters
- }
- push @c, \'Calc' # if all fail, try these
- if $warn_or_die < 2; # but not for "only"
- $CALC = ''; # signal error
- foreach my $l (@c)
- {
- # fallback libraries are "marked" as \'string', extract string if nec.
- my $lib = $l; $lib = $$l if ref($l);
-
- next if ($lib || '') eq '';
- $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
- $lib =~ s/\.pm$//;
- if ($] < 5.006)
- {
- # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is
- # used in the same script, or eval("") inside import().
- my @parts = split /::/, $lib; # Math::BigInt => Math BigInt
- my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
- require File::Spec;
- $file = File::Spec->catfile (@parts, $file);
- eval { require "$file"; $lib->import( @c ); }
- }
- else
- {
- eval "use $lib qw/@c/;";
- }
- if ($@ eq '')
- {
- my $ok = 1;
- # loaded it ok, see if the api_version() is high enough
- if ($lib->can('api_version') && $lib->api_version() >= 1.0)
- {
- $ok = 0;
- # api_version matches, check if it really provides anything we need
- for my $method (qw/
- one two ten
- str num
- add mul div sub dec inc
- acmp len digit is_one is_zero is_even is_odd
- is_two is_ten
- zeros new copy check
- from_hex from_oct from_bin as_hex as_bin as_oct
- rsft lsft xor and or
- mod sqrt root fac pow modinv modpow log_int gcd
- /)
- {
- if (!$lib->can("_$method"))
- {
- if (($WARN{$lib}||0) < 2)
- {
- require Carp;
- Carp::carp ("$lib is missing method '_$method'");
- $WARN{$lib} = 1; # still warn about the lib
- }
- $ok++; last;
- }
- }
- }
- if ($ok == 0)
- {
- $CALC = $lib;
- if ($warn_or_die > 0 && ref($l))
- {
- require Carp;
- my $msg = "Math::BigInt: couldn't load specified math lib(s), fallback to $lib";
- Carp::carp ($msg) if $warn_or_die == 1;
- Carp::croak ($msg) if $warn_or_die == 2;
- }
- last; # found a usable one, break
- }
- else
- {
- if (($WARN{$lib}||0) < 2)
- {
- my $ver = eval "\$$lib\::VERSION" || 'unknown';
- require Carp;
- Carp::carp ("Cannot load outdated $lib v$ver, please upgrade");
- $WARN{$lib} = 2; # never warn again
- }
- }
- }
- }
- if ($CALC eq '')
- {
- require Carp;
- if ($warn_or_die == 2)
- {
- Carp::croak ("Couldn't load specified math lib(s) and fallback disallowed");
- }
- else
- {
- Carp::croak ("Couldn't load any math lib(s), not even fallback to Calc.pm");
- }
- }
-
- # notify callbacks
- foreach my $class (keys %CALLBACKS)
- {
- &{$CALLBACKS{$class}}($CALC);
- }
-
- # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib
- # functions
-
- %CAN = ();
- for my $method (qw/ signed_and signed_or signed_xor /)
- {
- $CAN{$method} = $CALC->can("_$method") ? 1 : 0;
- }
-
- # import done
- }
-
-sub from_hex {
- # Create a bigint from a hexadecimal string.
-
- my ($self, $str) = @_;
-
- if ($str =~ s/
- ^
- ( [+-]? )
- (0?x)?
- (
- [0-9a-fA-F]*
- ( _ [0-9a-fA-F]+ )*
- )
- $
- //x)
- {
- # Get a "clean" version of the string, i.e., non-emtpy and with no
- # underscores or invalid characters.
-
- my $sign = $1;
- my $chrs = $3;
- $chrs =~ tr/_//d;
- $chrs = '0' unless CORE::length $chrs;
-
- # Initialize output.
-
- my $x = Math::BigInt->bzero();
-
- # The library method requires a prefix.
-
- $x->{value} = $CALC->_from_hex('0x' . $chrs);
-
- # Place the sign.
-
- if ($sign eq '-' && ! $CALC->_is_zero($x->{value})) {
- $x->{sign} = '-';
- }
-
- return $x;
- }
-
- # CORE::hex() parses as much as it can, and ignores any trailing garbage.
- # For backwards compatibility, we return NaN.
-
- return $self->bnan();
-}
-
-sub from_oct {
- # Create a bigint from an octal string.
-
- my ($self, $str) = @_;
-
- if ($str =~ s/
- ^
- ( [+-]? )
- (
- [0-7]*
- ( _ [0-7]+ )*
- )
- $
- //x)
- {
- # Get a "clean" version of the string, i.e., non-emtpy and with no
- # underscores or invalid characters.
-
- my $sign = $1;
- my $chrs = $2;
- $chrs =~ tr/_//d;
- $chrs = '0' unless CORE::length $chrs;
-
- # Initialize output.
-
- my $x = Math::BigInt->bzero();
-
- # The library method requires a prefix.
-
- $x->{value} = $CALC->_from_oct('0' . $chrs);
-
- # Place the sign.
-
- if ($sign eq '-' && ! $CALC->_is_zero($x->{value})) {
- $x->{sign} = '-';
- }
-
- return $x;
- }
-
- # CORE::oct() parses as much as it can, and ignores any trailing garbage.
- # For backwards compatibility, we return NaN.
-
- return $self->bnan();
-}
-
-sub from_bin {
- # Create a bigint from a binary string.
-
- my ($self, $str) = @_;
-
- if ($str =~ s/
- ^
- ( [+-]? )
- (0?b)?
- (
- [01]*
- ( _ [01]+ )*
- )
- $
- //x)
- {
- # Get a "clean" version of the string, i.e., non-emtpy and with no
- # underscores or invalid characters.
-
- my $sign = $1;
- my $chrs = $3;
- $chrs =~ tr/_//d;
- $chrs = '0' unless CORE::length $chrs;
-
- # Initialize output.
-
- my $x = Math::BigInt->bzero();
-
- # The library method requires a prefix.
-
- $x->{value} = $CALC->_from_bin('0b' . $chrs);
-
- # Place the sign.
-
- if ($sign eq '-' && ! $CALC->_is_zero($x->{value})) {
- $x->{sign} = '-';
- }
-
- return $x;
- }
-
- # For consistency with from_hex() and from_oct(), we return NaN when the
- # input is invalid.
-
- return $self->bnan();
-}
-
-sub _split
- {
- # input: num_str; output: undef for invalid or
- # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,\$exp_sign,\$exp_value)
- # Internal, take apart a string and return the pieces.
- # Strip leading/trailing whitespace, leading zeros, underscore and reject
- # invalid input.
- my $x = shift;
-
- # strip white space at front, also extraneous leading zeros
- $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2'
- $x =~ s/^\s+//; # but this will
- $x =~ s/\s+$//g; # strip white space at end
-
- # shortcut, if nothing to split, return early
- if ($x =~ /^[+-]?[0-9]+\z/)
- {
- $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
- return (\$sign, \$x, \'', \'', \0);
- }
-
- # invalid starting char?
- return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
-
- return Math::BigInt->from_hex($x) if $x =~ /^[+-]?0x/; # hex string
- return Math::BigInt->from_bin($x) if $x =~ /^[+-]?0b/; # binary string
-
- # strip underscores between digits
- $x =~ s/([0-9])_([0-9])/$1$2/g;
- $x =~ s/([0-9])_([0-9])/$1$2/g; # do twice for 1_2_3
-
- # some possible inputs:
- # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
- # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999
-
- my ($m,$e,$last) = split /[Ee]/,$x;
- return if defined $last; # last defined => 1e2E3 or others
- $e = '0' if !defined $e || $e eq "";
-
- # sign,value for exponent,mantint,mantfrac
- my ($es,$ev,$mis,$miv,$mfv);
- # valid exponent?
- if ($e =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros
- {
- $es = $1; $ev = $2;
- # valid mantissa?
- return if $m eq '.' || $m eq '';
- my ($mi,$mf,$lastf) = split /\./,$m;
- return if defined $lastf; # lastf 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*([0-9]+)$/) # strip leading zeros
- {
- $mis = $1||'+'; $miv = $2;
- return unless ($mf =~ /^([0-9]*?)0*$/); # strip trailing zeros
- $mfv = $1;
- # handle the 0e999 case here
- $ev = 0 if $miv eq '0' && $mfv eq '';
- return (\$mis,\$miv,\$mfv,\$es,\$ev);
- }
- }
- return; # NaN, not a number
- }
-
-##############################################################################
-# internal calculation routines (others are in Math::BigInt::Calc etc)
-
-sub __lcm
- {
- # (BINT or num_str, BINT or num_str) return BINT
- # does modify first argument
- # LCM
-
- my ($x,$ty) = @_;
- return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan);
- my $method = ref($x) . '::bgcd';
- no strict 'refs';
- $x * $ty / &$method($x,$ty);
- }
-
-###############################################################################
-# trigonometric functions
-
-sub bpi
- {
- # Calculate PI to N digits. Unless upgrading is in effect, returns the
- # result truncated to an integer, that is, always returns '3'.
- my ($self,$n) = @_;
- if (@_ == 1)
- {
- # called like Math::BigInt::bpi(10);
- $n = $self; $self = $class;
- }
- $self = ref($self) if ref($self);
-
- return $upgrade->new($n) if defined $upgrade;
-
- # hard-wired to "3"
- $self->new(3);
- }
-
-sub bcos
- {
- # Calculate cosinus(x) to N digits. Unless upgrading is in effect, returns the
- # result truncated to an integer.
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- return $x if $x->modify('bcos');
-
- return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
-
- return $upgrade->new($x)->bcos(@r) if defined $upgrade;
-
- require Math::BigFloat;
- # calculate the result and truncate it to integer
- my $t = Math::BigFloat->new($x)->bcos(@r)->as_int();
-
- $x->bone() if $t->is_one();
- $x->bzero() if $t->is_zero();
- $x->round(@r);
- }
-
-sub bsin
- {
- # Calculate sinus(x) to N digits. Unless upgrading is in effect, returns the
- # result truncated to an integer.
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- return $x if $x->modify('bsin');
-
- return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
-
- return $upgrade->new($x)->bsin(@r) if defined $upgrade;
-
- require Math::BigFloat;
- # calculate the result and truncate it to integer
- my $t = Math::BigFloat->new($x)->bsin(@r)->as_int();
-
- $x->bone() if $t->is_one();
- $x->bzero() if $t->is_zero();
- $x->round(@r);
- }
-
-sub batan2
- {
- # calculate arcus tangens of ($y/$x)
-
- # set up parameters
- my ($self,$y,$x,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
- {
- ($self,$y,$x,@r) = objectify(2,@_);
- }
-
- return $y if $y->modify('batan2');
-
- return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan);
-
- # Y X
- # != 0 -inf result is +- pi
- if ($x->is_inf() || $y->is_inf())
- {
- # upgrade to BigFloat etc.
- return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
- if ($y->is_inf())
- {
- if ($x->{sign} eq '-inf')
- {
- # calculate 3 pi/4 => 2.3.. => 2
- $y->bone( substr($y->{sign},0,1) );
- $y->bmul($self->new(2));
- }
- elsif ($x->{sign} eq '+inf')
- {
- # calculate pi/4 => 0.7 => 0
- $y->bzero();
- }
- else
- {
- # calculate pi/2 => 1.5 => 1
- $y->bone( substr($y->{sign},0,1) );
- }
- }
- else
- {
- if ($x->{sign} eq '+inf')
- {
- # calculate pi/4 => 0.7 => 0
- $y->bzero();
- }
- else
- {
- # PI => 3.1415.. => 3
- $y->bone( substr($y->{sign},0,1) );
- $y->bmul($self->new(3));
- }
- }
- return $y;
- }
-
- return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
-
- require Math::BigFloat;
- my $r = Math::BigFloat->new($y)->batan2(Math::BigFloat->new($x),@r)->as_int();
-
- $x->{value} = $r->{value};
- $x->{sign} = $r->{sign};
-
- $x;
- }
-
-sub batan
- {
- # Calculate arcus tangens of x to N digits. Unless upgrading is in effect, returns the
- # result truncated to an integer.
- my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
-
- return $x if $x->modify('batan');
-
- return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN
-
- return $upgrade->new($x)->batan(@r) if defined $upgrade;
-
- # calculate the result and truncate it to integer
- my $t = Math::BigFloat->new($x)->batan(@r);
-
- $x->{value} = $CALC->_new( $x->as_int()->bstr() );
- $x->round(@r);
- }
-
-###############################################################################
-# this method returns 0 if the object can be modified, or 1 if not.
-# We use a fast constant sub() here, to avoid costly calls. Subclasses
-# may override it with special code (f.i. Math::BigInt::Constant does so)
-
-sub modify () { 0; }
-
-1;
-__END__
-
-=pod
-
-=head1 NAME
-
-Math::BigInt - Arbitrary size integer/float math package
-
-=head1 SYNOPSIS
-
- use Math::BigInt;
-
- # or make it faster with huge numbers: install (optional)
- # Math::BigInt::GMP and always use (it will fall back to
- # pure Perl if the GMP library is not installed):
- # (See also the L<MATH LIBRARY> section!)
-
- # will warn if Math::BigInt::GMP cannot be found
- use Math::BigInt lib => 'GMP';
-
- # to suppress the warning use this:
- # use Math::BigInt try => 'GMP';
-
- # dies if GMP cannot be loaded:
- # use Math::BigInt only => 'GMP';
-
- my $str = '1234567890';
- my @values = (64,74,18);
- my $n = 1; my $sign = '-';
-
- # Number creation
- my $x = Math::BigInt->new($str); # defaults to 0
- my $y = $x->copy(); # make a true copy
- my $nan = Math::BigInt->bnan(); # create a NotANumber
- my $zero = Math::BigInt->bzero(); # create a +0
- my $inf = Math::BigInt->binf(); # create a +inf
- my $inf = Math::BigInt->binf('-'); # create a -inf
- my $one = Math::BigInt->bone(); # create a +1
- my $mone = Math::BigInt->bone('-'); # create a -1
-
- my $pi = Math::BigInt->bpi(); # returns '3'
- # see Math::BigFloat::bpi()
-
- $h = Math::BigInt->new('0x123'); # from hexadecimal
- $b = Math::BigInt->new('0b101'); # from binary
- $o = Math::BigInt->from_oct('0101'); # from octal
-
- # Testing (don't modify their arguments)
- # (return true if the condition is met, otherwise false)
-
- $x->is_zero(); # if $x is +0
- $x->is_nan(); # if $x is NaN
- $x->is_one(); # if $x is +1
- $x->is_one('-'); # if $x is -1
- $x->is_odd(); # if $x is odd
- $x->is_even(); # if $x is even
- $x->is_pos(); # if $x > 0
- $x->is_neg(); # if $x < 0
- $x->is_inf($sign); # if $x is +inf, or -inf (sign is default '+')
- $x->is_int(); # if $x is an integer (not a float)
-
- # comparing and digit/sign extraction
- $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
- $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
- $x->sign(); # return the sign, either +,- or NaN
- $x->digit($n); # return the nth digit, counting from right
- $x->digit(-$n); # return the nth digit, counting from left
-
- # The following all modify their first argument. If you want to pre-
- # serve $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for
- # why this is necessary when mixing $a = $b assignments with non-over-
- # loaded 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->bsgn(); # sign function (-1, 0, 1, or NaN)
- $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
-
- $x->bmuladd($y,$z); # $x = $x * $y + $z
-
- $x->bmod($y); # modulus (x % y)
- $x->bmodpow($y,$mod); # modular exponentiation (($x ** $y) % $mod)
- $x->bmodinv($mod); # modular multiplicative inverse
- $x->bpow($y); # power of arguments (x ** y)
- $x->blsft($y); # left shift in base 2
- $x->brsft($y); # right shift in base 2
- # returns (quo,rem) or quo if in sca-
- # lar context
- $x->blsft($y,$n); # left shift by $y places in base $n
- $x->brsft($y,$n); # right shift by $y places in base $n
- # returns (quo,rem) or quo if in sca-
- # lar context
-
- $x->band($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)
-
- $x->bnok($y); # x over y (binomial coefficient n over k)
-
- $x->blog(); # logarithm of $x to base e (Euler's number)
- $x->blog($base); # logarithm of $x to base $base (f.i. 2)
- $x->bexp(); # calculate e ** $x where e is Euler's number
-
- $x->round($A,$P,$mode); # round to accuracy or precision using
- # mode $mode
- $x->bround($n); # accuracy: preserve $n digits
- $x->bfround($n); # $n > 0: round $nth digits,
- # $n < 0: round to the $nth digit after the
- # dot, no-op for BigInts
-
- # The following do not modify their arguments in BigInt (are no-ops),
- # but do so in BigFloat:
-
- $x->bfloor(); # round towards minus infinity
- $x->bceil(); # round towards plus infinity
- $x->bint(); # round towards zero
-
- # The following do not modify their arguments:
-
- # greatest common divisor (no OO style)
- my $gcd = Math::BigInt::bgcd(@values);
- # lowest common multiple (no OO style)
- my $lcm = Math::BigInt::blcm(@values);
-
- $x->length(); # return number of digits in number
- ($xl,$f) = $x->length(); # length of number and length of fraction
- # part, latter is always 0 digits long
- # for BigInts
-
- $x->exponent(); # return exponent as BigInt
- $x->mantissa(); # return (signed) mantissa as BigInt
- $x->parts(); # return (mantissa,exponent) as BigInt
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
- $x->as_int(); # return as BigInt (in BigInt: same as copy())
- $x->numify(); # return as scalar (might overflow!)
-
- # conversion to string (do not modify their argument)
- $x->bstr(); # normalized string (e.g. '3')
- $x->bsstr(); # norm. string in scientific notation (e.g. '3E0')
- $x->as_hex(); # as signed hexadecimal string with prefixed 0x
- $x->as_bin(); # as signed binary string with prefixed 0b
- $x->as_oct(); # as signed octal string with prefixed 0
-
-
- # precision and accuracy (see section about rounding for more)
- $x->precision(); # return P of $x (or global, if P of $x undef)
- $x->precision($n); # set P of $x to $n
- $x->accuracy(); # return A of $x (or global, if A of $x undef)
- $x->accuracy($n); # set A $x to $n
-
- # Global methods
- Math::BigInt->precision(); # get/set global P for all BigInt objects
- Math::BigInt->accuracy(); # get/set global A for all BigInt objects
- Math::BigInt->round_mode(); # get/set global round mode, one of
- # 'even', 'odd', '+inf', '-inf', 'zero',
- # 'trunc' or 'common'
- Math::BigInt->config(); # return hash containing configuration
-
-=head1 DESCRIPTION
-
-All operators (including basic math operations) are overloaded if you
-declare your big integers as
-
- $i = new Math::BigInt '123_456_789_123_456_789';
-
-Operations with overloaded operators preserve the arguments which is
-exactly what you expect.
-
-=head2 Input
-
-Input values to these routines may be any string, that looks like a number
-and results in an integer, including hexadecimal and binary numbers.
-
-Scalars holding numbers may also be passed, but note that non-integer numbers
-may already have lost precision due to the conversion to float. Quote
-your input if you want BigInt to see all the digits:
-
- $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.
-
-Hexadecimal (prefixed with "0x") and binary numbers (prefixed with "0b")
-are accepted, too. Please note that octal numbers are not recognized
-by new(), so the following will print "123":
-
- perl -MMath::BigInt -le 'print Math::BigInt->new("0123")'
-
-To convert an octal number, use from_oct();
-
- perl -MMath::BigInt -le 'print Math::BigInt->from_oct("0123")'
-
-Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('')
-results in 'NaN'. This might change in the future, so use always the following
-explicit forms to get a zero or NaN:
-
- $zero = Math::BigInt->bzero();
- $nan = Math::BigInt->bnan();
-
-C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers
-are always stored in normalized form. If passed a string, creates a BigInt
-object from the input.
-
-=head2 Output
-
-Output values are BigInt objects (normalized), except for the methods which
-return a string (see L</SYNOPSIS>).
-
-Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>,
-C<is_nan()>, etc.) return true or false, while others (C<bcmp()>, C<bacmp()>)
-return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort.
-
-=head1 METHODS
-
-Each of the methods below (except config(), accuracy() and precision())
-accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R>
-are C<accuracy>, C<precision> and C<round_mode>. Please see the section about
-L</ACCURACY and PRECISION> for more information.
-
-=over
-
-=item config()
-
- use Data::Dumper;
-
- print Dumper ( Math::BigInt->config() );
- print Math::BigInt->config()->{lib},"\n";
-
-Returns a hash containing the configuration, e.g. the version number, lib
-loaded etc. The following hash keys are currently filled in with the
-appropriate information.
-
- key Description
- Example
- ============================================================
- lib Name of the low-level math library
- Math::BigInt::Calc
- lib_version Version of low-level math library (see 'lib')
- 0.30
- class The class name of config() you just called
- Math::BigInt
- upgrade To which class math operations might be
- upgraded Math::BigFloat
- downgrade To which class math operations might be
- downgraded undef
- precision Global precision
- undef
- accuracy Global accuracy
- undef
- round_mode Global round mode
- even
- version version number of the class you used
- 1.61
- div_scale Fallback accuracy for div
- 40
- trap_nan If true, traps creation of NaN via croak()
- 1
- trap_inf If true, traps creation of +inf/-inf via croak()
- 1
-
-The following values can be set by passing C<config()> a reference to a hash:
-
- trap_inf trap_nan
- upgrade downgrade precision accuracy round_mode div_scale
-
-Example:
-
- $new_cfg = Math::BigInt->config(
- { trap_inf => 1, precision => 5 }
- );
-
-=item accuracy()
-
- $x->accuracy(5); # local for $x
- CLASS->accuracy(5); # global for all members of CLASS
- # Note: This also applies to new()!
-
- $A = $x->accuracy(); # read out accuracy that affects $x
- $A = CLASS->accuracy(); # read out global accuracy
-
-Set or get the global or local accuracy, aka how many significant digits the
-results have. If you set a global accuracy, then this also applies to new()!
-
-Warning! The accuracy I<sticks>, e.g. once you created a number under the
-influence of C<< CLASS->accuracy($A) >>, all results from math operations with
-that number will also be rounded.
-
-In most cases, you should probably round the results explicitly using one of
-L</round()>, L</bround()> or L</bfround()> or by passing the desired accuracy
-to the math operation as additional parameter:
-
- my $x = Math::BigInt->new(30000);
- my $y = Math::BigInt->new(7);
- print scalar $x->copy()->bdiv($y, 2); # print 4300
- print scalar $x->copy()->bdiv($y)->bround(2); # print 4300
-
-Please see the section about L</ACCURACY and PRECISION> for further details.
-
-Value must be greater than zero. Pass an undef value to disable it:
-
- $x->accuracy(undef);
- Math::BigInt->accuracy(undef);
-
-Returns the current accuracy. For C<< $x->accuracy() >> it will return either
-the local accuracy, or if not defined, the global. This means the return value
-represents the accuracy that will be in effect for $x:
-
- $y = Math::BigInt->new(1234567); # unrounded
- print Math::BigInt->accuracy(4),"\n"; # set 4, print 4
- $x = Math::BigInt->new(123456); # $x will be automatic-
- # ally rounded!
- print "$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.
-
-=item precision()
-
- $x->precision(-2); # local for $x, round at the second
- # digit right of the dot
- $x->precision(2); # ditto, round at the second digit
- # left of the dot
-
- CLASS->precision(5); # Global for all members of CLASS
- # This also applies to new()!
- CLASS->precision(-5); # ditto
-
- $P = CLASS->precision(); # read out global precision
- $P = $x->precision(); # read out precision that affects $x
-
-Note: You probably want to use L</accuracy()> instead. With L</accuracy()> you
-set the number of digits each result should have, with L</precision()> you
-set the place where to round!
-
-C<precision()> sets or gets the global or local precision, aka at which digit
-before or after the dot to round all results. A set global precision also
-applies to all newly created numbers!
-
-In Math::BigInt, passing a negative number precision has no effect since no
-numbers have digits after the dot. In L<Math::BigFloat>, it will round all
-results to P digits after the dot.
-
-Please see the section about L</ACCURACY and PRECISION> for further details.
-
-Pass an undef value to disable it:
-
- $x->precision(undef);
- Math::BigInt->precision(undef);
-
-Returns the current precision. For C<< $x->precision() >> it will return either
-the local precision of $x, or if not defined, the global. This means the return
-value represents the prevision that will be in effect for $x:
-
- $y = Math::BigInt->new(1234567); # unrounded
- print Math::BigInt->precision(4),"\n"; # set 4, print 4
- $x = Math::BigInt->new(123456); # will be automatically rounded
- print $x; # print "120000"!
-
-Note: Works also for subclasses like L<Math::BigFloat>. Each class has its
-own globals separated from Math::BigInt, but it is possible to subclass
-Math::BigInt and make the globals of the subclass aliases to the ones from
-Math::BigInt.
-
-=item 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).
-
-=item 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.
-
-=item from_oct()
-
- $x = Math::BigInt->from_oct("0775"); # input is octal
-
-Interpret the input as an octal string and return the corresponding value. A
-"0" (zero) prefix is optional. A single underscore character may be placed
-right after the prefix, if present, or between any two digits. If the input is
-invalid, a NaN is returned.
-
-=item from_hex()
-
- $x = Math::BigInt->from_hex("0xcafe"); # input is hexadecimal
-
-Interpret input as a hexadecimal string. A "0x" or "x" prefix is optional. A
-single underscore character may be placed right after the prefix, if present,
-or between any two digits. If the input is invalid, a NaN is returned.
-
-=item from_bin()
-
- $x = Math::BigInt->from_bin("0b10011"); # input is binary
-
-Interpret the input as a binary string. A "0b" or "b" prefix is optional. A
-single underscore character may be placed right after the prefix, if present,
-or between any two digits. If the input is invalid, a NaN is returned.
-
-=item 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();
-
-=item 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();
-
-=item 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('-');
-
-=item 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
-
-=item 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
- $x->is_inf('-'); # true if -inf (sign is default '+')
-
-These methods all test the BigInt for being one specific value and return
-true or false depending on the input. These are faster than doing something
-like:
-
- if ($x == 0)
-
-=item is_pos()/is_neg()/is_positive()/is_negative()
-
- $x->is_pos(); # true if > 0
- $x->is_neg(); # true if < 0
-
-The methods return true if the argument is positive or negative, respectively.
-C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and
-C<-inf> is negative. A C<zero> is neither positive nor negative.
-
-These methods are only testing the sign, and not the value.
-
-C<is_positive()> and C<is_negative()> are aliases to C<is_pos()> and
-C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were
-introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced
-in v1.68.
-
-=item 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.
-
-In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers.
-
-=item bcmp()
-
- $x->bcmp($y);
-
-Compares $x with $y and takes the sign into account.
-Returns -1, 0, 1 or undef.
-
-=item bacmp()
-
- $x->bacmp($y);
-
-Compares $x with $y while ignoring their sign. Returns -1, 0, 1 or undef.
-
-=item sign()
-
- $x->sign();
-
-Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
-
-If you want $x to have a certain sign, use one of the following methods:
-
- $x->babs(); # '+'
- $x->babs()->bneg(); # '-'
- $x->bnan(); # 'NaN'
- $x->binf(); # '+inf'
- $x->binf('-'); # '-inf'
-
-=item digit()
-
- $x->digit($n); # return the nth digit, counting from right
-
-If C<$n> is negative, returns the digit counting from left.
-
-=item 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.
-
-=item babs()
-
- $x->babs();
-
-Set the number to its absolute value, e.g. change the sign from '-' to '+'
-and from '-inf' to '+inf', respectively. Does nothing for NaN or positive
-numbers.
-
-=item bsgn()
-
- $x->bsgn();
-
-Signum function. Set the number to -1, 0, or 1, depending on whether the
-number is negative, zero, or positive, respectively. Does not modify NaNs.
-
-=item bnorm()
-
- $x->bnorm(); # normalize (no-op)
-
-=item bnot()
-
- $x->bnot();
-
-Two's complement (bitwise not). This is equivalent to
-
- $x->binc()->bneg();
-
-but faster.
-
-=item binc()
-
- $x->binc(); # increment x by 1
-
-=item bdec()
-
- $x->bdec(); # decrement x by 1
-
-=item badd()
-
- $x->badd($y); # addition (add $y to $x)
-
-=item bsub()
-
- $x->bsub($y); # subtraction (subtract $y from $x)
-
-=item bmul()
-
- $x->bmul($y); # multiplication (multiply $x by $y)
-
-=item bmuladd()
-
- $x->bmuladd($y,$z);
-
-Multiply $x by $y, and then add $z to the result,
-
-This method was added in v1.87 of Math::BigInt (June 2007).
-
-=item bdiv()
-
- $x->bdiv($y); # divide, set $x to quotient
- # return (quo,rem) or quo if scalar
-
-=item bmod()
-
- $x->bmod($y); # modulus (x % y)
-
-=item bmodinv()
-
- $x->bmodinv($mod); # modular multiplicative inverse
-
-Returns the multiplicative inverse of C<$x> modulo C<$mod>. If
-
- $y = $x -> copy() -> bmodinv($mod)
-
-then C<$y> is the number closest to zero, and with the same sign as C<$mod>,
-satisfying
-
- ($x * $y) % $mod = 1 % $mod
-
-If C<$x> and C<$y> are non-zero, they must be relative primes, i.e.,
-C<bgcd($y, $mod)==1>. 'C<NaN>' is returned when no modular multiplicative
-inverse exists.
-
-=item bmodpow()
-
- $num->bmodpow($exp,$mod); # modular exponentiation
- # ($num**$exp % $mod)
-
-Returns the value of C<$num> taken to the power C<$exp> in the modulus
-C<$mod> using binary exponentiation. C<bmodpow> is far superior to
-writing
-
- $num ** $exp % $mod
-
-because it is much faster - it reduces internal variables into
-the modulus whenever possible, so it operates on smaller numbers.
-
-C<bmodpow> also supports negative exponents.
-
- bmodpow($num, -1, $mod)
-
-is exactly equivalent to
-
- bmodinv($num, $mod)
-
-=item bpow()
-
- $x->bpow($y); # power of arguments (x ** y)
-
-=item blog()
-
- $x->blog($base, $accuracy); # logarithm of x to the base $base
-
-If C<$base> is not defined, Euler's number (e) is used:
-
- print $x->blog(undef, 100); # log(x) to 100 digits
-
-=item bexp()
-
- $x->bexp($accuracy); # calculate e ** X
-
-Calculates the expression C<e ** $x> where C<e> is Euler's number.
-
-This method was added in v1.82 of Math::BigInt (April 2007).
-
-See also L</blog()>.
-
-=item bnok()
-
- $x->bnok($y); # x over y (binomial coefficient n over k)
-
-Calculates the binomial coefficient n over k, also called the "choose"
-function. The result is equivalent to:
-
- ( n ) n!
- | - | = -------
- ( k ) k!(n-k)!
-
-This method was added in v1.84 of Math::BigInt (April 2007).
-
-=item bpi()
-
- print Math::BigInt->bpi(100), "\n"; # 3
-
-Returns PI truncated to an integer, with the argument being ignored. This means
-under BigInt this always returns C<3>.
-
-If upgrading is in effect, returns PI, rounded to N digits with the
-current rounding mode:
-
- use Math::BigFloat;
- use Math::BigInt upgrade => Math::BigFloat;
- print Math::BigInt->bpi(3), "\n"; # 3.14
- print Math::BigInt->bpi(100), "\n"; # 3.1415....
-
-This method was added in v1.87 of Math::BigInt (June 2007).
-
-=item bcos()
-
- my $x = Math::BigInt->new(1);
- print $x->bcos(100), "\n";
-
-Calculate the cosinus of $x, modifying $x in place.
-
-In BigInt, unless upgrading is in effect, the result is truncated to an
-integer.
-
-This method was added in v1.87 of Math::BigInt (June 2007).
-
-=item bsin()
-
- my $x = Math::BigInt->new(1);
- print $x->bsin(100), "\n";
-
-Calculate the sinus of $x, modifying $x in place.
-
-In BigInt, unless upgrading is in effect, the result is truncated to an
-integer.
-
-This method was added in v1.87 of Math::BigInt (June 2007).
-
-=item batan2()
-
- my $x = Math::BigInt->new(1);
- my $y = Math::BigInt->new(1);
- print $y->batan2($x), "\n";
-
-Calculate the arcus tangens of C<$y> divided by C<$x>, modifying $y in place.
-
-In BigInt, unless upgrading is in effect, the result is truncated to an
-integer.
-
-This method was added in v1.87 of Math::BigInt (June 2007).
-
-=item batan()
-
- my $x = Math::BigFloat->new(0.5);
- print $x->batan(100), "\n";
-
-Calculate the arcus tangens of $x, modifying $x in place.
-
-In BigInt, unless upgrading is in effect, the result is truncated to an
-integer.
-
-This method was added in v1.87 of Math::BigInt (June 2007).
-
-=item blsft()
-
- $x->blsft($y); # left shift in base 2
- $x->blsft($y,$n); # left shift, in base $n (like 10)
-
-=item brsft()
-
- $x->brsft($y); # right shift in base 2
- $x->brsft($y,$n); # right shift, in base $n (like 10)
-
-=item band()
-
- $x->band($y); # bitwise and
-
-=item bior()
-
- $x->bior($y); # bitwise inclusive or
-
-=item bxor()
-
- $x->bxor($y); # bitwise exclusive or
-
-=item bnot()
-
- $x->bnot(); # bitwise not (two's complement)
-
-=item bsqrt()
-
- $x->bsqrt(); # calculate square-root
-
-=item broot()
-
- $x->broot($N);
-
-Calculates the N'th root of C<$x>.
-
-=item bfac()
-
- $x->bfac(); # factorial of $x (1*2*3*4*..$x)
-
-=item round()
-
- $x->round($A,$P,$round_mode);
-
-Round $x to accuracy C<$A> or precision C<$P> using the round mode
-C<$round_mode>.
-
-=item bround()
-
- $x->bround($N); # accuracy: preserve $N digits
-
-=item bfround()
-
- $x->bfround($N);
-
-If N is > 0, rounds to the Nth digit from the left. If N < 0, rounds to
-the Nth digit after the dot. Since BigInts are integers, the case N < 0
-is a no-op for them.
-
-Examples:
-
- Input N Result
- ===================================================
- 123456.123456 3 123500
- 123456.123456 2 123450
- 123456.123456 -2 123456.12
- 123456.123456 -3 123456.123
-
-=item bfloor()
-
- $x->bfloor();
-
-Round $x towards minus infinity (i.e., set $x to the largest integer less than
-or equal to $x). This is a no-op in BigInt, but changes $x in BigFloat, if $x
-is not an integer.
-
-=item bceil()
-
- $x->bceil();
-
-Round $x towards plus infinity (i.e., set $x to the smallest integer greater
-than or equal to $x). This is a no-op in BigInt, but changes $x in BigFloat, if
-$x is not an integer.
-
-=item bint()
-
- $x->bint();
-
-Round $x towards zero. This is a no-op in BigInt, but changes $x in BigFloat,
-if $x is not an integer.
-
-=item bgcd()
-
- bgcd(@values); # greatest common divisor (no OO style)
-
-=item blcm()
-
- blcm(@values); # lowest common multiple (no OO style)
-
-=item 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.
-
-=item exponent()
-
- $x->exponent();
-
-Return the exponent of $x as BigInt.
-
-=item mantissa()
-
- $x->mantissa();
-
-Return the signed mantissa of $x as BigInt.
-
-=item parts()
-
- $x->parts(); # return (mantissa,exponent) as BigInt
-
-=item copy()
-
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
-
-=item as_int()/as_number()
-
- $x->as_int();
-
-Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as
-C<copy()>.
-
-C<as_number()> is an alias to this method. C<as_number> was introduced in
-v1.22, while C<as_int()> was only introduced in v1.68.
-
-=item bstr()
-
- $x->bstr();
-
-Returns a normalized string representation of C<$x>.
-
-=item bsstr()
-
- $x->bsstr(); # normalized string in scientific notation
-
-=item as_hex()
-
- $x->as_hex(); # as signed hexadecimal string with prefixed 0x
-
-=item as_bin()
-
- $x->as_bin(); # as signed binary string with prefixed 0b
-
-=item as_oct()
-
- $x->as_oct(); # as signed octal string with prefixed 0
-
-=item numify()
-
- print $x->numify();
-
-This returns a normal Perl scalar from $x. It is used automatically
-whenever a scalar is needed, for instance in array index operations.
-
-This loses precision, to avoid this use L<as_int()|/"as_int()/as_number()"> instead.
-
-=item modify()
-
- $x->modify('bpowd');
-
-This method returns 0 if the object can be modified with the given
-operation, or 1 if not.
-
-This is used for instance by L<Math::BigInt::Constant>.
-
-=item upgrade()/downgrade()
-
-Set/get the class for downgrade/upgrade operations. Thuis is used
-for instance by L<bignum>. The defaults are '', thus the following
-operation will create a BigInt, not a BigFloat:
-
- my $i = Math::BigInt->new(123);
- my $f = Math::BigFloat->new('123.1');
-
- print $i + $f,"\n"; # print 246
-
-=item div_scale()
-
-Set/get the number of digits for the default precision in divide
-operations.
-
-=item round_mode()
-
-Set/get the current round mode.
-
-=back
-
-=head1 ACCURACY and PRECISION
-
-Since version v1.33, Math::BigInt and Math::BigFloat have full support for
-accuracy and precision based rounding, both automatically after every
-operation, as well as manually.
-
-This section describes the accuracy/precision handling in Math::Big* as it
-used to be and as it is now, complete with an explanation of all terms and
-abbreviations.
-
-Not yet implemented things (but with correct description) are marked with '!',
-things that need to be answered are marked with '?'.
-
-In the next paragraph follows a short description of terms used here (because
-these may differ from terms used by others people or documentation).
-
-During the rest of this document, the shortcuts A (for accuracy), P (for
-precision), F (fallback) and R (rounding mode) will be used.
-
-=head2 Precision P
-
-A fixed number of digits before (positive) or after (negative)
-the decimal point. For example, 123.45 has a precision of -2. 0 means an
-integer like 123 (or 120). A precision of 2 means two digits to the left
-of the decimal point are zero, so 123 with P = 1 becomes 120. Note that
-numbers with zeros before the decimal point may have different precisions,
-because 1200 can have p = 0, 1 or 2 (depending on what the initial value
-was). It could also have p < 0, when the digits after the decimal point
-are zero.
-
-The string output (of floating point numbers) will be padded with zeros:
-
- Initial value P A Result String
- ------------------------------------------------------------
- 1234.01 -3 1000 1000
- 1234 -2 1200 1200
- 1234.5 -1 1230 1230
- 1234.001 1 1234 1234.0
- 1234.01 0 1234 1234
- 1234.01 2 1234.01 1234.01
- 1234.01 5 1234.01 1234.01000
-
-For BigInts, no padding occurs.
-
-=head2 Accuracy A
-
-Number of significant digits. Leading zeros are not counted. A
-number may have an accuracy greater than the non-zero digits
-when there are zeros in it or trailing zeros. For example, 123.456 has
-A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3.
-
-The string output (of floating point numbers) will be padded with zeros:
-
- Initial value P A Result String
- ------------------------------------------------------------
- 1234.01 3 1230 1230
- 1234.01 6 1234.01 1234.01
- 1234.1 8 1234.1 1234.1000
-
-For BigInts, no padding occurs.
-
-=head2 Fallback F
-
-When both A and P are undefined, this is used as a fallback accuracy when
-dividing numbers.
-
-=head2 Rounding mode R
-
-When rounding a number, different 'styles' or 'kinds'
-of rounding are possible. (Note that random rounding, as in
-Math::Round, is not implemented.)
-
-=over
-
-=item 'trunc'
-
-truncation invariably removes all digits following the
-rounding place, replacing them with zeros. Thus, 987.65 rounded
-to tens (P=1) becomes 980, and rounded to the fourth sigdig
-becomes 987.6 (A=4). 123.456 rounded to the second place after the
-decimal point (P=-2) becomes 123.46.
-
-All other implemented styles of rounding attempt to round to the
-"nearest digit." If the digit D immediately to the right of the
-rounding place (skipping the decimal point) is greater than 5, the
-number is incremented at the rounding place (possibly causing a
-cascade of incrementation): e.g. when rounding to units, 0.9 rounds
-to 1, and -19.9 rounds to -20. If D < 5, the number is similarly
-truncated at the rounding place: e.g. when rounding to units, 0.4
-rounds to 0, and -19.4 rounds to -19.
-
-However the results of other styles of rounding differ if the
-digit immediately to the right of the rounding place (skipping the
-decimal point) is 5 and if there are no digits, or no digits other
-than 0, after that 5. In such cases:
-
-=item 'even'
-
-rounds the digit at the rounding place to 0, 2, 4, 6, or 8
-if it is not already. E.g., when rounding to the first sigdig, 0.45
-becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5.
-
-=item 'odd'
-
-rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if
-it is not already. E.g., when rounding to the first sigdig, 0.45
-becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6.
-
-=item '+inf'
-
-round to plus infinity, i.e. always round up. E.g., when
-rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5,
-and 0.4501 also becomes 0.5.
-
-=item '-inf'
-
-round to minus infinity, i.e. always round down. E.g., when
-rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6,
-but 0.4501 becomes 0.5.
-
-=item 'zero'
-
-round to zero, i.e. positive numbers down, negative ones up.
-E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55
-becomes -0.5, but 0.4501 becomes 0.5.
-
-=item 'common'
-
-round up if the digit immediately to the right of the rounding place
-is 5 or greater, otherwise round down. E.g., 0.15 becomes 0.2 and
-0.149 becomes 0.1.
-
-=back
-
-The handling of A & P in MBI/MBF (the old core code shipped with Perl
-versions <= 5.7.2) is like this:
-
-=over
-
-=item Precision
-
- * ffround($p) is able to round to $p number of digits after the decimal
- point
- * otherwise P is unused
-
-=item Accuracy (significant digits)
-
- * fround($a) rounds to $a significant digits
- * only fdiv() and fsqrt() take A as (optional) parameter
- + other operations simply create the same number (fneg etc), or
- more (fmul) of digits
- + rounding/truncating is only done when explicitly calling one
- of fround or ffround, and never for BigInt (not implemented)
- * fsqrt() simply hands its accuracy argument over to fdiv.
- * the documentation and the comment in the code indicate two
- different ways on how fdiv() determines the maximum number
- of digits it should calculate, and the actual code does yet
- another thing
- POD:
- max($Math::BigFloat::div_scale,length(dividend)+length(divisor))
- Comment:
- result has at most max(scale, length(dividend), length(divisor)) digits
- Actual code:
- scale = max(scale, length(dividend)-1,length(divisor)-1);
- scale += length(divisor) - length(dividend);
- So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10
- So for lx = 3, ly = 9, scale = 10, scale will actually be 16
- (10+9-3). Actually, the 'difference' added to the scale is cal-
- culated from the number of "significant digits" in dividend and
- divisor, which is derived by looking at the length of the man-
- tissa. Which is wrong, since it includes the + sign (oops) and
- actually gets 2 for '+100' and 4 for '+101'. Oops again. Thus
- 124/3 with div_scale=1 will get you '41.3' based on the strange
- assumption that 124 has 3 significant digits, while 120/7 will
- get you '17', not '17.1' since 120 is thought to have 2 signif-
- icant digits. The rounding after the division then uses the
- remainder and $y to determine whether it must round up or down.
- ? I have no idea which is the right way. That's why I used a slightly more
- ? simple scheme and tweaked the few failing testcases to match it.
-
-=back
-
-This is how it works now:
-
-=over
-
-=item Setting/Accessing
-
- * You can set the A global via Math::BigInt->accuracy() or
- Math::BigFloat->accuracy() or whatever class you are using.
- * You can also set P globally by using Math::SomeClass->precision()
- likewise.
- * Globals are classwide, and not inherited by subclasses.
- * to undefine A, use Math::SomeCLass->accuracy(undef);
- * to undefine P, use Math::SomeClass->precision(undef);
- * 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, use Math::SomeClass->accuracy()
- * to find out the current global P, use Math::SomeClass->precision()
- * use $x->accuracy() respective $x->precision() for the local
- setting of $x.
- * Please note that $x->accuracy() respective $x->precision()
- return eventually defined global A or P, when $x's A or P is not
- set.
-
-=item Creating numbers
-
- * When you create a number, you can give the desired A or P via:
- $x = Math::BigInt->new($number,$A,$P);
- * Only one of A or P can be defined, otherwise the result is NaN
- * If no A or P is give ($x = Math::BigInt->new($number) form), then the
- globals (if set) will be used. Thus changing the global defaults later on
- will not change the A or P of previously created numbers (i.e., A and P of
- $x will be what was in effect when $x was created)
- * If given undef for A and P, NO rounding will occur, and the globals will
- NOT be used. This is used by subclasses to create numbers without
- suffering rounding in the parent. Thus a subclass is able to have its own
- globals enforced upon creation of a number by using
- $x = Math::BigInt->new($number,undef,undef):
-
- use Math::BigInt::SomeSubclass;
- use Math::BigInt;
-
- Math::BigInt->accuracy(2);
- Math::BigInt::SomeSubClass->accuracy(3);
- $x = Math::BigInt::SomeSubClass->new(1234);
-
- $x is now 1230, and not 1200. A subclass might choose to implement
- this otherwise, e.g. falling back to the parent's A and P.
-
-=item Usage
-
- * If A or P are enabled/defined, they are used to round the result of each
- operation according to the rules below
- * Negative P is ignored in Math::BigInt, since BigInts never have digits
- after the decimal point
- * Math::BigFloat uses Math::BigInt internally, but setting A or P inside
- Math::BigInt as globals does not tamper with the parts of a BigFloat.
- A flag is used to mark all Math::BigFloat numbers as 'never round'.
-
-=item Precedence
-
- * It only makes sense that a number has only one of A or P at a time.
- If you set either A or P on one object, or globally, the other one will
- be automatically cleared.
- * If two objects are involved in an operation, and one of them has A in
- effect, and the other P, this results in an error (NaN).
- * A takes precedence over P (Hint: A comes before P).
- If neither of them is defined, nothing is used, i.e. the result will have
- as many digits as it can (with an exception for fdiv/fsqrt) and will not
- be rounded.
- * There is another setting for fdiv() (and thus for fsqrt()). If neither of
- A or P is defined, fdiv() will use a fallback (F) of $div_scale digits.
- If either the dividend's or the divisor's mantissa has more digits than
- the value of F, the higher value will be used instead of F.
- This is to limit the digits (A) of the result (just consider what would
- happen with unlimited A and P in the case of 1/3 :-)
- * fdiv will calculate (at least) 4 more digits than required (determined by
- A, P or F), and, if F is not used, round the result
- (this will still fail in the case of a result like 0.12345000000001 with A
- or P of 5, but this can not be helped - or can it?)
- * Thus you can have the math done by on Math::Big* class in two modi:
- + never round (this is the default):
- This is done by setting A and P to undef. No math operation
- will round the result, with fdiv() and fsqrt() as exceptions to guard
- against overflows. You must explicitly call bround(), bfround() or
- round() (the latter with parameters).
- Note: Once you have rounded a number, the settings will 'stick' on it
- and 'infect' all other numbers engaged in math operations with it, since
- local settings have the highest precedence. So, to get SaferRound[tm],
- use a copy() before rounding like this:
-
- $x = Math::BigFloat->new(12.34);
- $y = Math::BigFloat->new(98.76);
- $z = $x * $y; # 1218.6984
- print $x->copy()->fround(3); # 12.3 (but A is now 3!)
- $z = $x * $y; # still 1218.6984, without
- # copy would have been 1210!
-
- + round after each op:
- After each single operation (except for testing like is_zero()), the
- method round() is called and the result is rounded appropriately. By
- setting proper values for A and P, you can have all-the-same-A or
- all-the-same-P modes. For example, Math::Currency might set A to undef,
- and P to -2, globally.
-
- ?Maybe an extra option that forbids local A & P settings would be in order,
- ?so that intermediate rounding does not 'poison' further math?
-
-=item Overriding globals
-
- * you will be able to give A, P and R as an argument to all the calculation
- routines; the second parameter is A, the third one is P, and the fourth is
- R (shift right by one for binary operations like badd). P is used only if
- the first parameter (A) is undefined. These three parameters override the
- globals in the order detailed as follows, i.e. the first defined value
- wins:
- (local: per object, global: global default, parameter: argument to sub)
- + parameter A
- + parameter P
- + local A (if defined on both of the operands: smaller one is taken)
- + local P (if defined on both of the operands: bigger one is taken)
- + global A
- + global P
- + global F
- * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two
- arguments (A and P) instead of one
-
-=item Local settings
-
- * You can set A or P locally by using $x->accuracy() or
- $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
-
- * the rounding routines will use the respective global or local settings.
- fround()/bround() is for accuracy rounding, while ffround()/bfround()
- is for precision
- * the two rounding functions take as the second parameter one of the
- following rounding modes (R):
- 'even', 'odd', '+inf', '-inf', 'zero', 'trunc', 'common'
- * you can set/get the global R by using Math::SomeClass->round_mode()
- or by setting $Math::SomeClass::round_mode
- * after each operation, $result->round() is called, and the result may
- eventually be rounded (that is, if A or P were set either locally,
- globally or as parameter to the operation)
- * to manually round a number, call $x->round($A,$P,$round_mode);
- this will round the number by using the appropriate rounding function
- and then normalize it.
- * rounding modifies the local settings of the number:
-
- $x = Math::BigFloat->new(123.456);
- $x->accuracy(5);
- $x->bround(4);
-
- Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy()
- will be 4 from now on.
-
-=item Default values
-
- * R: 'even'
- * F: 40
- * A: undef
- * P: undef
-
-=item Remarks
-
- * The defaults are set up so that the new code gives the same results as
- the old code (except in a few cases on fdiv):
- + Both A and P are undefined and thus will not be used for rounding
- after each operation.
- + round() is thus a no-op, unless given extra parameters A and P
-
-=back
-
-=head1 Infinity and Not a Number
-
-While BigInt has extensive handling of inf and NaN, certain quirks remain.
-
-=over
-
-=item oct()/hex()
-
-These perl routines currently (as of Perl v.5.8.6) cannot handle passed
-inf.
-
- te@linux:~> perl -wle 'print 2 ** 3333'
- inf
- te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333'
- 1
- te@linux:~> perl -wle 'print oct(2 ** 3333)'
- 0
- te@linux:~> perl -wle 'print hex(2 ** 3333)'
- Illegal hexadecimal digit 'i' ignored at -e line 1.
- 0
-
-The same problems occur if you pass them Math::BigInt->binf() objects. Since
-overloading these routines is not possible, this cannot be fixed from BigInt.
-
-=item ==, !=, <, >, <=, >= with NaNs
-
-BigInt's bcmp() routine currently returns undef to signal that a NaN was
-involved in a comparison. However, the overload code turns that into
-either 1 or '' and thus operations like C<< NaN != NaN >> might return
-wrong values.
-
-=item log(-inf)
-
-C<< log(-inf) >> is highly weird. Since log(-x)=pi*i+log(x), then
-log(-inf)=pi*i+inf. However, since the imaginary part is finite, the real
-infinity "overshadows" it, so the number might as well just be infinity.
-However, the result is a complex number, and since BigInt/BigFloat can only
-have real numbers as results, the result is NaN.
-
-=item exp(), cos(), sin(), atan2()
-
-These all might have problems handling infinity right.
-
-=back
-
-=head1 INTERNALS
-
-The actual numbers are stored as unsigned big integers (with separate sign).
-
-You should neither care about nor depend on the internal representation; it
-might change without notice. Use B<ONLY> method calls like C<< $x->sign(); >>
-instead relying on the internal representation.
-
-=head2 MATH LIBRARY
-
-Math with the numbers is done (by default) by a module called
-C<Math::BigInt::Calc>. This is equivalent to saying:
-
- use Math::BigInt try => 'Calc';
-
-You can change this backend library by using:
-
- use Math::BigInt try => 'GMP';
-
-B<Note>: General purpose packages should not be explicit about the library
-to use; let the script author decide which is best.
-
-If your script works with huge numbers and Calc is too slow for them,
-you can also for the loading of one of these libraries and if none
-of them can be used, the code will die:
-
- use Math::BigInt only => 'GMP,Pari';
-
-The following would first try to find Math::BigInt::Foo, then
-Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
-
- use Math::BigInt try => 'Foo,Math::BigInt::Bar';
-
-The library that is loaded last will be used. Note that this can be
-overwritten at any time by loading a different library, and numbers
-constructed with different libraries cannot be used in math operations
-together.
-
-=head3 What library to use?
-
-B<Note>: General purpose packages should not be explicit about the library
-to use; let the script author decide which is best.
-
-L<Math::BigInt::GMP> and L<Math::BigInt::Pari> are in cases involving big
-numbers much faster than Calc, however it is slower when dealing with very
-small numbers (less than about 20 digits) and when converting very large
-numbers to decimal (for instance for printing, rounding, calculating their
-length in decimal etc).
-
-So please select carefully what library you want to use.
-
-Different low-level libraries use different formats to store the numbers.
-However, you should B<NOT> depend on the number having a specific format
-internally.
-
-See the respective math library module documentation for further details.
-
-=head2 SIGN
-
-The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
-
-A sign of 'NaN' is used to represent the result when input arguments are not
-numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
-minus infinity. You will get '+inf' when dividing a positive number by 0, and
-'-inf' when dividing any negative number by 0.
-
-=head2 mantissa(), exponent() and parts()
-
-C<mantissa()> and C<exponent()> return the said parts of the BigInt such
-that:
-
- $m = $x->mantissa();
- $e = $x->exponent();
- $y = $m * ( 10 ** $e );
- print "ok\n" if $x == $y;
-
-C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them
-in one go. Both the returned mantissa and exponent have a sign.
-
-Currently, for BigInts C<$e> is always 0, except +inf and -inf, where it is
-C<+inf>; and for NaN, where it is C<NaN>; and for C<$x == 0>, where it is C<1>
-(to be compatible with Math::BigFloat's internal representation of a zero as
-C<0E1>).
-
-C<$m> is currently just a copy of the original number. The relation between
-C<$e> and C<$m> will stay always the same, though their real values might
-change.
-
-=head1 EXAMPLES
-
- use Math::BigInt;
-
- sub bigint { Math::BigInt->new(shift); }
-
- $x = Math::BigInt->bstr("1234") # string "1234"
- $x = "$x"; # same as bstr()
- $x = Math::BigInt->bneg("1234"); # BigInt "-1234"
- $x = Math::BigInt->babs("-12345"); # BigInt "12345"
- $x = Math::BigInt->bnorm("-0.00"); # BigInt "0"
- $x = bigint(1) + bigint(2); # BigInt "3"
- $x = bigint(1) + "2"; # ditto (auto-BigIntify of "2")
- $x = bigint(1); # BigInt "1"
- $x = $x + 5 / 2; # BigInt "3"
- $x = $x ** 3; # BigInt "27"
- $x *= 2; # BigInt "54"
- $x = Math::BigInt->new(0); # BigInt "0"
- $x--; # BigInt "-1"
- $x = Math::BigInt->badd(4,5) # BigInt "9"
- print $x->bsstr(); # 9e+0
-
-Examples for rounding:
-
- use Math::BigFloat;
- use Test;
-
- $x = Math::BigFloat->new(123.4567);
- $y = Math::BigFloat->new(123.456789);
- Math::BigFloat->accuracy(4); # no more A than 4
-
- ok ($x->copy()->fround(),123.4); # even rounding
- print $x->copy()->fround(),"\n"; # 123.4
- Math::BigFloat->round_mode('odd'); # round to odd
- print $x->copy()->fround(),"\n"; # 123.5
- Math::BigFloat->accuracy(5); # no more A than 5
- Math::BigFloat->round_mode('odd'); # round to odd
- print $x->copy()->fround(),"\n"; # 123.46
- $y = $x->copy()->fround(4),"\n"; # A = 4: 123.4
- print "$y, ",$y->accuracy(),"\n"; # 123.4, 4
-
- Math::BigFloat->accuracy(undef); # A not important now
- Math::BigFloat->precision(2); # P important
- print $x->copy()->bnorm(),"\n"; # 123.46
- print $x->copy()->fround(),"\n"; # 123.46
-
-Examples for converting:
-
- my $x = Math::BigInt->new('0b1'.'01' x 123);
- print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n";
-
-=head1 Autocreating constants
-
-After C<use Math::BigInt ':constant'> all the B<integer> decimal, 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
-constants the expression 2**100 will be calculated as perl scalar.
-
-Please note that strings and floating point constants are not affected,
-so that
-
- use Math::BigInt qw/:constant/;
-
- $x = 1234567890123456789012345678901234567890
- + 123456789123456789;
- $y = '1234567890123456789012345678901234567890'
- + '123456789123456789';
-
-do not work. You need an explicit Math::BigInt->new() around one of the
-operands. You should also quote large constants to protect loss of precision:
-
- use Math::BigInt;
-
- $x = Math::BigInt->new('1234567889123456789123456789123456789');
-
-Without the quotes Perl would convert the large number to a floating point
-constant at compile time and then hand the result to BigInt, which results in
-an truncated result or a NaN.
-
-This also applies to integers that look like floating point constants:
-
- use Math::BigInt ':constant';
-
- print ref(123e2),"\n";
- print ref(123.2e2),"\n";
-
-will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat>
-to get this to work.
-
-=head1 PERFORMANCE
-
-Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x
-must be made in the second case. For long numbers, the copy can eat up to 20%
-of the work (in the case of addition/subtraction, less for
-multiplication/division). If $y is very small compared to $x, the form
-$x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes
-more time then the actual addition.
-
-With a technique called copy-on-write, the cost of copying with overload could
-be minimized or even completely avoided. A test implementation of COW did show
-performance gains for overloaded math, but introduced a performance loss due
-to a constant overhead for all other operations. So Math::BigInt does currently
-not COW.
-
-The rewritten version of this module (vs. v0.01) is slower on certain
-operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it
-does now more work and handles much more cases. The time spent in these
-operations is usually gained in the other math operations so that code on
-the average should get (much) faster. If they don't, please contact the author.
-
-Some operations may be slower for small numbers, but are significantly faster
-for big numbers. Other operations are now constant (O(1), like C<bneg()>,
-C<babs()> etc), instead of O(N) and thus nearly always take much less time.
-These optimizations were done on purpose.
-
-If you find the Calc module to slow, try to install any of the replacement
-modules and see if they help you.
-
-=head2 Alternative math libraries
-
-You can use an alternative library to drive Math::BigInt. See the section
-L</MATH LIBRARY> for more information.
-
-For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>.
-
-=head1 SUBCLASSING
-
-=head2 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
-
-=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 its own C<new()> and can
-store additional hash keys in the object. There are also some package globals
-that must be defined, e.g.:
-
- # Globals
- $accuracy = undef;
- $precision = -2; # round to 2 decimal places
- $round_mode = 'even';
- $div_scale = 40;
-
-Additionally, you might want to provide the following two globals to allow
-auto-upgrading and auto-downgrading to work correctly:
-
- $upgrade = undef;
- $downgrade = undef;
-
-This allows Math::BigInt to correctly retrieve package globals from the
-subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or
-t/Math/BigFloat/SubClass.pm completely functional subclass examples.
-
-Don't forget to
-
- use overload;
-
-in your subclass to automatically inherit the overloading from the parent. If
-you like, you can change part of the overloading, look at Math::String for an
-example.
-
-=head1 UPGRADING
-
-When used like this:
-
- use Math::BigInt upgrade => 'Foo::Bar';
-
-certain operations will 'upgrade' their calculation and thus the result to
-the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat:
-
- use Math::BigInt upgrade => 'Math::BigFloat';
-
-As a shortcut, you can use the module L<bignum>:
-
- use bignum;
-
-Also good for one-liners:
-
- 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
-
-=item bsqrt()
-
-=item div()
-
-=item blog()
-
-=item bexp()
-
-=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 EXPORTS
-
-C<Math::BigInt> exports nothing by default, but can export the following methods:
-
- bgcd
- blcm
-
-=head1 CAVEATS
-
-Some things might not work as you expect them. Below is documented what is
-known to be troublesome:
-
-=over
-
-=item bstr(), bsstr() and 'cmp'
-
-Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now
-drop the leading '+'. The old code would return '+3', the new returns '3'.
-This is to be consistent with Perl and to make C<cmp> (especially with
-overloading) to work as you expect. It also solves problems with C<Test.pm>,
-because its C<ok()> uses 'eq' internally.
-
-Mark Biggar said, when asked about to drop the '+' altogether, or make only
-C<cmp> work:
-
- I agree (with the first alternative), don't add the '+' on positive
- numbers. It's not as important anymore with the new internal
- form for numbers. It made doing things like abs and neg easier,
- but those have to be done differently now anyway.
-
-So, the following examples will now work all as expected:
-
- use Test;
- BEGIN { plan tests => 1 }
- use Math::BigInt;
-
- my $x = new Math::BigInt 3*3;
- my $y = new Math::BigInt 3*3;
-
- ok ($x,3*3);
- print "$x eq 9" if $x eq $y;
- print "$x eq 9" if $x eq '9';
- print "$x eq 9" if $x eq 3*3;
-
-Additionally, the following still works:
-
- print "$x == 9" if $x == $y;
- print "$x == 9" if $x == 9;
- print "$x == 9" if $x == 3*3;
-
-There is now a C<bsstr()> method to get the string in scientific notation aka
-C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr()
-for comparison, but Perl will represent some numbers as 100 and others
-as 1e+308. If in doubt, convert both arguments to Math::BigInt before
-comparing them as strings:
-
- use Test;
- BEGIN { plan tests => 3 }
- use Math::BigInt;
-
- $x = Math::BigInt->new('1e56'); $y = 1e56;
- ok ($x,$y); # will fail
- ok ($x->bsstr(),$y); # okay
- $y = Math::BigInt->new($y);
- ok ($x,$y); # okay
-
-Alternatively, simply use C<< <=> >> for comparisons, this will get it
-always right. There is not yet a way to get a number automatically represented
-as a string that matches exactly the way Perl represents it.
-
-See also the section about L<Infinity and Not a Number> for problems in
-comparing NaNs.
-
-=item int()
-
-C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a
-Perl scalar:
-
- $x = Math::BigInt->new(123);
- $y = int($x); # BigInt 123
- $x = Math::BigFloat->new(123.45);
- $y = int($x); # BigInt 123
-
-In all Perl versions you can use C<as_number()> or C<as_int> for the same
-effect:
-
- $x = Math::BigFloat->new(123.45);
- $y = $x->as_number(); # BigInt 123
- $y = $x->as_int(); # ditto
-
-This also works for other subclasses, like Math::String.
-
-If you want a real Perl scalar, use C<numify()>:
-
- $y = $x->numify(); # 123 as scalar
-
-This is seldom necessary, though, because this is done automatically, like
-when you access an array:
-
- $z = $array[$x]; # does work automatically
-
-=item length()
-
-The following will probably not do what you expect:
-
- $c = Math::BigInt->new(123);
- print $c->length(),"\n"; # prints 30
-
-It prints both the number of digits in the number and in the fraction part
-since print calls C<length()> in list context. Use something like:
-
- print scalar $c->length(),"\n"; # prints 3
-
-=item bdiv()
-
-The following will probably not do what you expect:
-
- print $c->bdiv(10000),"\n";
-
-It prints both quotient and remainder since print calls C<bdiv()> in list
-context. Also, C<bdiv()> will modify $c, so be careful. You probably want
-to use
-
- print $c / 10000,"\n";
-
-or, if you want to modify $c instead,
-
- print scalar $c->bdiv(10000),"\n";
-
-The quotient is always the greatest integer less than or equal to the
-real-valued quotient of the two operands, and the remainder (when it is
-non-zero) 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)
- -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
-manpage), and the equation
-
- $x == ($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. 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 behind this.
-
-Perl's 'use integer;' changes the behaviour of % and / for scalars, but will
-not change BigInt's way to do things. This is because under 'use integer' Perl
-will do what the underlying C thinks is right and this is different for each
-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:
-
- $x = Math::BigFloat->new(5);
- $y = $x;
-
-It will not do what you think, e.g. making a copy of $x. Instead it just makes
-a second reference to the B<same> object and stores it in $y. Thus anything
-that modifies $x (except overloaded operators) will modify $y, and vice versa.
-Or in other words, C<=> is only safe if you modify your BigInts only via
-overloaded math. As soon as you use a method call it breaks:
-
- $x->bmul(2);
- print "$x, $y\n"; # prints '10, 10'
-
-If you want a true copy of $x, use:
-
- $y = $x->copy();
-
-You can also chain the calls like this, this will make first a copy and then
-multiply it by 2:
-
- $y = $x->copy()->bmul(2);
-
-See also the documentation for overload.pm regarding C<=>.
-
-=item bpow
-
-C<bpow()> (and the rounding functions) now modifies the first argument and
-returns it, unlike the old code which left it alone and only returned the
-result. This is to be consistent with C<badd()> etc. The first three will
-modify $x, the last one won't:
-
- print bpow($x,$i),"\n"; # modify $x
- print $x->bpow($i),"\n"; # ditto
- print $x **= $i,"\n"; # the same
- print $x ** $i,"\n"; # leave $x alone
-
-The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though.
-
-=item Overloading -$x
-
-The following:
-
- $x = -$x;
-
-is slower than
-
- $x->bneg();
-
-since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant
-needs to preserve $x since it does not know that it later will get overwritten.
-This makes a copy of $x and takes O(N), but $x->bneg() is O(1).
-
-=item Mixing different object types
-
-In Perl you will get a floating point value if you do one of the following:
-
- $float = 5.0 + 2;
- $float = 2 + 5.0;
- $float = 5 / 2;
-
-With overloaded math, only the first two variants will result in a BigFloat:
-
- use Math::BigInt;
- use Math::BigFloat;
-
- $mbf = Math::BigFloat->new(5);
- $mbi2 = Math::BigInteger->new(5);
- $mbi = Math::BigInteger->new(2);
-
- # what actually gets called:
- $float = $mbf + $mbi; # $mbf->badd()
- $float = $mbf / $mbi; # $mbf->bdiv()
- $integer = $mbi + $mbf; # $mbi->badd()
- $integer = $mbi2 / $mbi; # $mbi2->bdiv()
- $integer = $mbi2 / $mbf; # $mbi2->bdiv()
-
-This is because math with overloaded operators follows the first (dominating)
-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.
-
-To get a Math::BigFloat you either need to call the operation manually,
-make sure the operands are already of the proper type or casted to that type
-via Math::BigFloat->new():
-
- $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5
-
-Beware of simple "casting" the entire expression, this would only convert
-the already computed result:
-
- $float = Math::BigFloat->new($mbi2 / $mbi); # = 2.0 thus wrong!
-
-Beware also of the order of more complicated expressions like:
-
- $integer = ($mbi2 + $mbi) / $mbf; # int / float => int
- $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto
-
-If in doubt, break the expression into simpler terms, or cast all operands
-to the desired resulting type.
-
-Scalar values are a bit different, since:
-
- $float = 2 + $mbf;
- $float = $mbf + 2;
-
-will both result in the proper type due to the way the overloaded math works.
-
-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 a big integer, e.g. the square
-root of 144 is 12, but from 12 the square root is 3, regardless of rounding
-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->round_mode('even');
- print $x->copy->bsqrt(),"\n"; # 4
-
- 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
-
-This program is free software; you may redistribute it and/or modify it under
-the same terms as Perl itself.
-
-=head1 SEE ALSO
-
-L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as
-L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
-
-The pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest
-because they solve the autoupgrading/downgrading issue, at least partly.
-
-The package at
-L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
-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 - 2006
-and still at it in 2007.
-
-Many people contributed in one or more ways to the final beast, see the file
-CREDITS for an (incomplete) list. If you miss your name, please drop me a
-mail. Thank you!
-
-=cut
Copyright © 1996 – 2023 Jason A. Donenfeld. All Rights Reverse Engineered.