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; $VERSION = '1.994'; @ISA = qw(Exporter); @EXPORT_OK = qw(objectify bgcd blcm); # _trap_inf and _trap_nan are internal and should never be accessed from the # outside use vars qw/$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. 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 unsignificant '""' => sub { $_[0]->bstr(); }, '0+' => sub { $_[0]->numify(); } ; ############################################################################## # 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 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 dont 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 testin in Calc (especially w/ Pari et al) # post-normalized compare for internal use (honors signs) if ($x->{sign} eq '+') { # $x and $y both > 0 return $CALC->_acmp($x->{value},$y->{value}); } # $x && $y both < 0 $CALC->_acmp($y->{value},$x->{value}); # swaped 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} = '+'; # dont 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} = '+'; # dont 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 { # return integer less or equal then number; no-op since it's already integer my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_); $x->round(@r); } sub bceil { # return integer greater or equal then number; no-op since it's already int 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 { # check for strings, if yes, return objects instead # the first argument is number of args objectify() should look at it will # return $count+1 elements, the first will be a classname. This is because # overloaded '""' calls bstr($object,undef,undef) and this would result in # useless objects being created and thrown away. So we cannot simple loop # over @_. If the given count is 0, all arguments will be used. # If the second arg is a ref, use it as class. # If not, try to use it as classname, unless undef, then use $class # (aka Math::BigInt). The latter shouldn't happen,though. # 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 # In the last case we check number of arguments to turn it silently into # $class,1,2. (We can not take '1' as class ;o) # badd($class,1) is not supported (it should, eventually, try to add undef) # currently it tries 'Math::BigInt' + 1, which will not work. # some shortcut for the common cases # $x->unary_op(); return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]); my $count = abs(shift || 0); my (@a,$k,$d); # resulting array, temp, and downgrade if (ref $_[0]) { # okay, got object as first $a[0] = ref $_[0]; } else { # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported) $a[0] = $class; $a[0] = shift if $_[0] =~ /^[A-Z].*::/; # classname as first? } no strict 'refs'; # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats if (defined ${"$a[0]::downgrade"}) { $d = ${"$a[0]::downgrade"}; ${"$a[0]::downgrade"} = undef; } my $up = ${"$a[0]::upgrade"}; # print STDERR "# Now in objectify, my class is today $a[0], count = $count\n"; if ($count == 0) { while (@_) { $k = shift; if (!ref($k)) { $k = $a[0]->new($k); } elsif (!defined $up && ref($k) ne $a[0]) { # foreign object, try to convert to integer $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); } push @a,$k; } } else { while ($count > 0) { $count--; $k = shift; if (!ref($k)) { $k = $a[0]->new($k); } elsif (ref($k) ne $a[0] and !defined $up || ref $k ne $up) { # foreign object, try to convert to integer $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k); } push @a,$k; } push @a,@_; # return other params, too } if (! wantarray) { require Carp; Carp::croak ("$class objectify needs list context"); } ${"$a[0]::downgrade"} = $d; @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 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 preserve # $x, use $z = $x->copy()->bXXX($y); See under L for why this is # necessary when mixing $a = $b assignments with non-overloaded math. $x->bzero(); # set $x to 0 $x->bnan(); # set $x to NaN $x->bone(); # set $x to +1 $x->bone('-'); # set $x to -1 $x->binf(); # set $x to inf $x->binf('-'); # set $x to -inf $x->bneg(); # negation $x->babs(); # absolute value $x->bnorm(); # normalize (no-op in BigInt) $x->bnot(); # two's complement (bit wise not) $x->binc(); # increment $x by 1 $x->bdec(); # decrement $x by 1 $x->badd($y); # addition (add $y to $x) $x->bsub($y); # subtraction (subtract $y from $x) $x->bmul($y); # multiplication (multiply $x by $y) $x->bdiv($y); # divide, set $x to quotient # return (quo,rem) or quo if scalar $x->bmuladd($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 scalar 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 scalar 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(); # return integer less or equal than $x $x->bceil(); # return integer greater or equal than $x # 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. =over 2 =item 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(); $nan = Math::BigInt->bnan(); C on a BigInt object is now effectively a no-op, since the numbers are always stored in normalized form. If passed a string, creates a BigInt object from the input. =item Output Output values are BigInt objects (normalized), except for the methods which return a string (see L). Some routines (C, C, C, C, C, etc.) return true or false, while others (C, C) return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort. =back =head1 METHODS Each of the methods below (except config(), accuracy() and precision()) accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R> are C, C and C. Please see the section about L for more information. =head2 config() use Data::Dumper; print Dumper ( Math::BigInt->config() ); print Math::BigInt->config()->{lib},"\n"; Returns a hash containing the configuration, e.g. the version number, lib loaded etc. The following hash keys are currently filled in with the appropriate information. key Description Example ============================================================ lib Name of the 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 a reference to a hash: trap_inf trap_nan upgrade downgrade precision accuracy round_mode div_scale Example: $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } ); =head2 accuracy() $x->accuracy(5); # local for $x CLASS->accuracy(5); # global for all members of CLASS # Note: This also applies to new()! $A = $x->accuracy(); # read out accuracy that affects $x $A = CLASS->accuracy(); # read out global accuracy Set or get the global or local accuracy, aka how many significant digits the results have. If you set a global accuracy, then this also applies to new()! Warning! The accuracy I, e.g. once you created a number under the influence of C<< CLASS->accuracy($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, L or L 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 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); # $x will be automatically rounded! print "$x $y\n"; # '123500 1234567' print $x->accuracy(),"\n"; # will be 4 print $y->accuracy(),"\n"; # also 4, since global is 4 print Math::BigInt->accuracy(5),"\n"; # set to 5, print 5 print $x->accuracy(),"\n"; # still 4 print $y->accuracy(),"\n"; # 5, since global is 5 Note: Works also for subclasses like Math::BigFloat. Each class has it's own globals separated from Math::BigInt, but it is possible to subclass Math::BigInt and make the globals of the subclass aliases to the ones from Math::BigInt. =head2 precision() $x->precision(-2); # local for $x, round 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 instead. With L you set the number of digits each result should have, with L you set the place where to round! C 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, it will round all results to P digits after the dot. Please see the section about L 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. 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. =head2 brsft() $x->brsft($y,$n); Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and 2, but others work, too. Right shifting usually amounts to dividing $x by $n ** $y and truncating the result: $x = Math::BigInt->new(10); $x->brsft(1); # same as $x >> 1: 5 $x = Math::BigInt->new(1234); $x->brsft(2,10); # result 12 There is one exception, and that is base 2 with negative $x: $x = Math::BigInt->new(-5); print $x->brsft(1); This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the result). =head2 new() $x = Math::BigInt->new($str,$A,$P,$R); Creates a new BigInt object from a scalar or another BigInt object. The input is accepted as decimal, hex (with leading '0x') or binary (with leading '0b'). See L