# _a : accuracy
# _p : precision
# _f : flags, used by MBF to flag parts of a float as untouchable
-# _cow : copy on write: number of objects that share the data (NRY)
# Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
# underlying lib might change the reference!
my $class = "Math::BigInt";
require 5.005;
-$VERSION = '1.41';
+$VERSION = '1.47';
use Exporter;
@ISA = qw( Exporter );
@EXPORT_OK = qw( bneg babs bcmp badd bmul bdiv bmod bnorm bsub
- bgcd blcm
- bround
+ bgcd blcm bround
blsft brsft band bior bxor bnot bpow bnan bzero
bacmp bstr bsstr binc bdec binf bfloor bceil
is_odd is_even is_zero is_one is_nan is_inf sign
is_positive is_negative
- length as_number
- objectify _swap
+ length as_number objectify _swap
);
#@EXPORT = qw( );
-use vars qw/$rnd_mode $accuracy $precision $div_scale/;
+use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/;
use strict;
# Inside overload, the first arg is always an object. If the original code had
'-=' => sub { $_[0]->bsub($_[1]); },
'*=' => sub { $_[0]->bmul($_[1]); },
'/=' => sub { scalar $_[0]->bdiv($_[1]); },
+'%=' => sub { $_[0]->bmod($_[1]); },
+'^=' => sub { $_[0]->bxor($_[1]); },
+'&=' => sub { $_[0]->band($_[1]); },
+'|=' => sub { $_[0]->bior($_[1]); },
'**=' => sub { $_[0]->bpow($_[1]); },
+'..' => \&_pointpoint,
+
'<=>' => sub { $_[2] ?
- $class->bcmp($_[1],$_[0]) :
- $class->bcmp($_[0],$_[1])},
-'cmp' => sub {
+ ref($_[0])->bcmp($_[1],$_[0]) :
+ ref($_[0])->bcmp($_[0],$_[1])},
+'cmp' => sub {
$_[2] ?
$_[1] cmp $_[0]->bstr() :
$_[0]->bstr() cmp $_[1] },
return $t;
},
-qw(
-"" bstr
-0+ numify), # Order of arguments unsignificant
+# the original qw() does not work with the TIESCALAR below, why?
+# Order of arguments unsignificant
+'""' => sub { $_[0]->bstr(); },
+'0+' => sub { $_[0]->numify(); }
;
##############################################################################
my $CALC = 'Math::BigInt::Calc'; # module to do low level math
sub _core_lib () { return $CALC; } # for test suite
-# Rounding modes, one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
-$rnd_mode = 'even';
-$accuracy = undef;
-$precision = undef;
-$div_scale = 40;
+$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'
+$accuracy = undef;
+$precision = undef;
+$div_scale = 40;
+
+##############################################################################
+# the old code had $rnd_mode, so we need to support it, too
+
+$rnd_mode = 'even';
+sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; }
+sub FETCH { return $round_mode; }
+sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
+
+BEGIN { tie $rnd_mode, 'Math::BigInt'; }
+
+##############################################################################
sub round_mode
{
+ no strict 'refs';
# make Class->round_mode() work
- my $self = shift || $class;
- # shift @_ if defined $_[0] && $_[0] eq $class;
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
if (defined $_[0])
{
my $m = shift;
die "Unknown round mode $m"
if $m !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
- $rnd_mode = $m; return;
+ ${"${class}::round_mode"} = $m; return $m;
}
- return $rnd_mode;
+ return ${"${class}::round_mode"};
+ }
+
+sub div_scale
+ {
+ no strict 'refs';
+ # make Class->round_mode() work
+ my $self = shift;
+ my $class = ref($self) || $self || __PACKAGE__;
+ if (defined $_[0])
+ {
+ die ('div_scale must be greater than zero') if $_[0] < 0;
+ ${"${class}::div_scale"} = shift;
+ }
+ return ${"${class}::div_scale"};
}
sub accuracy
{
- # $x->accuracy($a); ref($x) a
- # $x->accuracy(); ref($x);
- # Class::accuracy(); # not supported
- #print "MBI @_ ($class)\n";
- my $x = shift;
+ # $x->accuracy($a); ref($x) $a
+ # $x->accuracy(); ref($x)
+ # Class->accuracy(); class
+ # Class->accuracy($a); class $a
- die ("accuracy() needs reference to object as first parameter.")
- if !ref $x;
+ my $x = shift;
+ my $class = ref($x) || $x || __PACKAGE__;
+ no strict 'refs';
+ # need to set new value?
if (@_ > 0)
{
- $x->{_a} = shift;
- $x->round() if defined $x->{_a};
+ my $a = shift;
+ die ('accuracy must not be zero') if defined $a && $a == 0;
+ if (ref($x))
+ {
+ # $object->accuracy() or fallback to global
+ $x->bround($a) if defined $a;
+ $x->{_a} = $a; # set/overwrite, even if not rounded
+ $x->{_p} = undef; # clear P
+ }
+ else
+ {
+ # set global
+ ${"${class}::accuracy"} = $a;
+ }
+ return $a; # shortcut
+ }
+
+ if (ref($x))
+ {
+ # $object->accuracy() or fallback to global
+ return $x->{_a} || ${"${class}::accuracy"};
}
- return $x->{_a};
+ return ${"${class}::accuracy"};
}
sub precision
{
- my $x = shift;
+ # $x->precision($p); ref($x) $p
+ # $x->precision(); ref($x)
+ # Class->precision(); class
+ # Class->precision($p); class $p
- die ("precision() needs reference to object as first parameter.")
- if !ref $x;
+ my $x = shift;
+ my $class = ref($x) || $x || __PACKAGE__;
+ no strict 'refs';
+ # need to set new value?
if (@_ > 0)
{
- $x->{_p} = shift;
- $x->round() if defined $x->{_p};
+ my $p = shift;
+ if (ref($x))
+ {
+ # $object->precision() or fallback to global
+ $x->bfround($p) if defined $p;
+ $x->{_p} = $p; # set/overwrite, even if not rounded
+ $x->{_a} = undef; # clear P
+ }
+ else
+ {
+ # set global
+ ${"${class}::precision"} = $p;
+ }
+ return $p; # shortcut
+ }
+
+ if (ref($x))
+ {
+ # $object->precision() or fallback to global
+ return $x->{_p} || ${"${class}::precision"};
}
- return $x->{_p};
+ return ${"${class}::precision"};
}
sub _scale_a
{
if ($k eq 'value')
{
- $self->{$k} = $CALC->_copy($x->{$k});
+ $self->{value} = $CALC->_copy($x->{value});
}
elsif (ref($x->{$k}) eq 'SCALAR')
{
my $self = {}; bless $self, $class;
# handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]inf$/)
+ if ($wanted =~ /^[+-]?inf$/)
{
$self->{value} = $CALC->_zero();
- $self->{sign} = $wanted;
+ $self->{sign} = $wanted; $self->{sign} = '+inf' if $self->{sign} eq 'inf';
return $self;
}
# split str in m mantissa, e exponent, i integer, f fraction, v value, s sign
}
$self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0
$self->{value} = $CALC->_new($miv) if $self->{sign} =~ /^[+-]$/;
- #print "$wanted => $self->{sign}\n";
# if any of the globals is set, use them to round and store them inside $self
- $self->round($accuracy,$precision,$rnd_mode)
+ $self->round($accuracy,$precision,$round_mode)
if defined $accuracy || defined $precision;
return $self;
}
return if $self->modify('bzero');
$self->{value} = $CALC->_zero();
$self->{sign} = '+';
- #print "result: $self\n";
return $self;
}
my $self = shift;
my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
$self = $class if !defined $self;
- #print "bone $self\n";
if (!ref($self))
{
return if $self->modify('bone');
$self->{value} = $CALC->_one();
$self->{sign} = $sign;
- #print "result: $self\n";
return $self;
}
# (ref to BFLOAT or num_str ) return num_str
# Convert number from internal format to scientific string format.
# internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
- my ($self,$x) = objectify(1,@_);
+ my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
+ # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
if ($x->{sign} !~ /^[+-]$/)
{
sub bstr
{
# make a string from bigint object
- my $x = shift; $x = $class->new($x) unless ref $x;
+ my $x = shift; $class = ref($x) || $x; $x = $class->new(shift) if !ref($x);
+ # my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
if ($x->{sign} !~ /^[+-]$/)
{
return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
sub sign
{
# return the sign of the number: +/-/NaN
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
return $x->{sign};
}
-sub round
+sub _find_round_parameters
{
# After any operation or when calling round(), the result is rounded by
# regarding the A & P from arguments, local parameters, or globals.
my @args = @_; # all 'other' arguments (0 for unary, 1 for binary ops)
$self = new($self) unless ref($self); # if not object, make one
- my $c = ref($args[0]); # find out class of argument
+ my $c = ref($self); # find out class of argument(s)
unshift @args,$self; # add 'first' argument
# leave bigfloat parts alone
- return $self if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
+ return ($self) if exists $self->{_f} && $self->{_f} & MB_NEVER_ROUND != 0;
no strict 'refs';
- my $z = "$c\::accuracy"; my $aa = $$z; my $ap = undef;
- if (!defined $aa)
- {
- $z = "$c\::precision"; $ap = $$z;
- }
# now pick $a or $p, but only if we have got "arguments"
if ((!defined $a) && (!defined $p) && (@args > 0))
{
foreach (@args)
{
- # take the defined one, or if both defined, the one that is smaller
- $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} < $p);
+ # take the defined one, or if both defined, the one that is bigger
+ # -2 > -3, and 3 > 2
+ $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
}
# if none defined, use globals (#2)
if (!defined $p)
{
- $a = $aa; $p = $ap; # save the check: if !defined $a;
+ my $z = "$c\::accuracy"; my $a = $$z;
+ if (!defined $a)
+ {
+ $z = "$c\::precision"; $p = $$z;
+ }
}
} # endif !$a
} # endif !$a || !$P && args > 0
- # for clearity, this is not merged at place (#2)
+ my @params = ($self);
+ if (defined $a || defined $p)
+ {
+ $r = $r || ${"$c\::round_mode"};
+ die "Unknown round mode '$r'"
+ if $r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/;
+ push @params, ($a,$p,$r);
+ }
+ return @params;
+ }
+
+sub round
+ {
+ # round $self according to given parameters, or given second argument's
+ # parameters or global defaults
+ my $self = shift;
+
+ my @params = $self->_find_round_parameters(@_);
+ return $self->bnorm() if @params == 1; # no-op
+
# now round, by calling fround or ffround:
- if (defined $a)
+ if (defined $params[1])
{
- $self->{_a} = $a; $self->bround($a,$r);
+ $self->bround($params[1],$params[3]);
}
- elsif (defined $p)
+ else
{
- $self->{_p} = $p; $self->bfround($p,$r);
+ $self->bfround($params[2],$params[3]);
}
- return $self->bnorm();
+ return $self->bnorm(); # after round, normalize
}
sub bnorm
{
- # (num_str or BINT) return BINT
+ # (numstr or BINT) return BINT
# Normalize number -- no-op here
- return $_[0];
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ return $x;
}
sub babs
{
# (BINT or num_str) return BINT
# make number absolute, or return absolute BINT from string
- my $x = shift; $x = $class->new($x) unless ref $x;
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
return $x if $x->modify('babs');
# post-normalized abs for internal use (does nothing for NaN)
$x->{sign} =~ s/^-/+/;
{
# (BINT or num_str) return BINT
# negate number or make a negated number from string
- my $x = shift; $x = $class->new($x) unless ref $x;
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
return $x if $x->modify('bneg');
# for +0 dont negate (to have always normalized)
return $x if $x->is_zero();
return 0 if $xz && $yz; # 0 <=> 0
return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y
return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0
- # normal compare now
- &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0;
+
+ # post-normalized compare for internal use (honors signs)
+ if ($x->{sign} eq '+')
+ {
+ return 1 if $y->{sign} eq '-'; # 0 check handled above
+ return $CALC->_acmp($x->{value},$y->{value});
+ }
+
+ # $x->{sign} eq '-'
+ return -1 if $y->{sign} eq '+';
+ return $CALC->_acmp($y->{value},$x->{value}); # swaped
+
+ # &cmp($x->{value},$y->{value},$x->{sign},$y->{sign}) <=> 0;
}
sub bacmp
my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
return $x if $x->modify('bsub');
- $x->badd($y->bneg()); # badd does not leave internal zeros
- $y->bneg(); # refix y, assumes no one reads $y in between
- return $x->round($a,$p,$r,$y);
+
+ if (!$y->is_zero()) # don't need to do anything if $y is 0
+ {
+ $y->{sign} =~ tr/+\-/-+/; # does nothing for NaN
+ $x->badd($y,$a,$p,$r); # badd does not leave internal zeros
+ $y->{sign} =~ tr/+\-/-+/; # refix $y (does nothing for NaN)
+ }
+ $x; # already rounded by badd()
}
sub binc
{
# increment arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
- # my $x = shift; $x = $class->new($x) unless ref $x; my $self = ref($x);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('binc');
- $x->badd($self->__one())->round($a,$p,$r);
+
+ if ($x->{sign} eq '+')
+ {
+ $x->{value} = $CALC->_inc($x->{value});
+ return $x->round($a,$p,$r);
+ }
+ elsif ($x->{sign} eq '-')
+ {
+ $x->{value} = $CALC->_dec($x->{value});
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+ return $x->round($a,$p,$r);
+ }
+ # inf, nan handling etc
+ $x->badd($self->__one(),$a,$p,$r); # does round
}
sub bdec
{
# decrement arg by one
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
return $x if $x->modify('bdec');
- $x->badd($self->__one('-'))->round($a,$p,$r);
+
+ my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+';
+ # <= 0
+ if (($x->{sign} eq '-') || $zero)
+ {
+ $x->{value} = $CALC->_inc($x->{value});
+ $x->{sign} = '-' if $zero; # 0 => 1 => -1
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+ return $x->round($a,$p,$r);
+ }
+ # > 0
+ elsif ($x->{sign} eq '+')
+ {
+ $x->{value} = $CALC->_dec($x->{value});
+ return $x->round($a,$p,$r);
+ }
+ # inf, nan handling etc
+ $x->badd($self->__one('-'),$a,$p,$r); # does round
}
sub blcm
{
$x = $class->new($y);
}
- while (@_) { $x = _lcm($x,shift); }
+ while (@_) { $x = __lcm($x,shift); }
$x;
}
# does not modify arguments, but returns new object
# GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff)
- my $y = shift; my ($x);
- if (ref($y))
- {
- $x = $y->copy();
- }
- else
- {
- $x = $class->new($y);
- }
-
+ my $y = shift;
+ $y = __PACKAGE__->new($y) if !ref($y);
+ my $self = ref($y);
+ my $x = $y->copy(); # keep arguments
if ($CALC->can('_gcd'))
{
while (@_)
{
- $y = shift; $y = $class->new($y) if !ref($y);
+ $y = shift; $y = $self->new($y) if !ref($y);
next if $y->is_zero();
return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN?
$x->{value} = $CALC->_gcd($x->{value},$y->{value}); last if $x->is_one();
{
while (@_)
{
- $x = __gcd($x,shift); last if $x->is_one(); # _gcd handles NaN
+ $y = shift; $y = $self->new($y) if !ref($y);
+ $x = __gcd($x,$y->copy()); last if $x->is_one(); # _gcd handles NaN
}
}
$x->babs();
}
-sub bmod
- {
- # modulus
- # (BINT or num_str, BINT or num_str) return BINT
- my ($self,$x,$y) = objectify(2,@_);
-
- return $x if $x->modify('bmod');
- (&bdiv($self,$x,$y))[1];
- }
-
sub bnot
{
# (num_str or BINT) return BINT
# represent ~x as twos-complement number
- my ($self,$x) = objectify(1,@_);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
return $x if $x->modify('bnot');
- $x->bneg(); $x->bdec(); # was: bsub(-1,$x);, time it someday
- $x;
+ $x->bneg(); $x->bdec(); # was: bsub(-1,$x);, time it someday
+ return $x->round($a,$p,$r);
}
sub is_zero
{
# return true if arg (BINT or num_str) is zero (array '+', '0')
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't
$CALC->_is_zero($x->{value});
- #return $CALC->_is_zero($x->{value});
}
sub is_nan
{
# return true if arg (BINT or num_str) is NaN
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} eq $nan);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ return 1 if $x->{sign} eq $nan;
+ return 0;
}
sub is_inf
{
# return true if arg (BINT or num_str) is +-inf
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- my $sign = shift || '';
+ my ($self,$x,$sign) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- return $x->{sign} =~ /^[+-]inf$/ if $sign eq '';
- return $x->{sign} =~ /^[$sign]inf$/;
+ $sign = '' if !defined $sign;
+ return 0 if $sign !~ /^([+-]|)$/;
+
+ if ($sign eq '')
+ {
+ return 1 if ($x->{sign} =~ /^[+-]inf$/);
+ return 0;
+ }
+ $sign = quotemeta($sign.'inf');
+ return 1 if ($x->{sign} =~ /^$sign$/);
+ return 0;
}
sub is_one
{
# return true if arg (BINT or num_str) is +1
# or -1 if sign is given
- #my ($self,$x) = objectify(1,@_);
- my $x = shift; $x = $class->new($x) unless ref $x;
- my $sign = shift || ''; $sign = '+' if $sign ne '-';
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+ $sign = '' if !defined $sign; $sign = '+' if $sign ne '-';
- return 0 if $x->{sign} ne $sign;
+ return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either
return $CALC->_is_one($x->{value});
}
sub is_odd
{
# return true when arg (BINT or num_str) is odd, false for even
- my $x = shift; $x = $class->new($x) unless ref $x;
- #my ($self,$x) = objectify(1,@_);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
return $CALC->_is_odd($x->{value});
sub is_even
{
# return true when arg (BINT or num_str) is even, false for odd
- my $x = shift; $x = $class->new($x) unless ref $x;
- #my ($self,$x) = objectify(1,@_);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
return $CALC->_is_even($x->{value});
sub is_positive
{
# return true when arg (BINT or num_str) is positive (>= 0)
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} =~ /^\+/);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return 1 if $x->{sign} =~ /^\+/;
+ return 0;
}
sub is_negative
{
# return true when arg (BINT or num_str) is negative (< 0)
- my $x = shift; $x = $class->new($x) unless ref $x;
- return ($x->{sign} =~ /^-/);
+ # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return 1 if ($x->{sign} =~ /^-/);
+ return 0;
}
###############################################################################
}
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
+
$x->{value} = $CALC->_mul($x->{value},$y->{value}); # do actual math
return $x->round($a,$p,$r,$y);
}
+sub _div_inf
+ {
+ # helper function that handles +-inf cases for bdiv()/bmod() to reuse code
+ my ($self,$x,$y) = @_;
+
+ # NaN if x == NaN or y == NaN or x==y==0
+ return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
+ if (($x->is_nan() || $y->is_nan()) ||
+ ($x->is_zero() && $y->is_zero()));
+
+ # +inf / +inf == -inf / -inf == 1, remainder is 0 (A / A = 1, remainder 0)
+ if (($x->{sign} eq $y->{sign}) &&
+ ($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return wantarray ? ($x->bone(),$self->bzero()) : $x->bone();
+ }
+ # +inf / -inf == -inf / +inf == -1, remainder 0
+ if (($x->{sign} ne $y->{sign}) &&
+ ($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+ {
+ return wantarray ? ($x->bone('-'),$self->bzero()) : $x->bone('-');
+ }
+ # x / +-inf => 0, remainder x (works even if x == 0)
+ if ($y->{sign} =~ /^[+-]inf$/)
+ {
+ my $t = $x->copy(); # binf clobbers up $x
+ return wantarray ? ($x->bzero(),$t) : $x->bzero()
+ }
+
+ # 5 / 0 => +inf, -6 / 0 => -inf
+ # +inf / 0 = inf, inf, and -inf / 0 => -inf, -inf
+ # exception: -8 / 0 has remainder -8, not 8
+ # exception: -inf / 0 has remainder -inf, not inf
+ if ($y->is_zero())
+ {
+ # +-inf / 0 => special case for -inf
+ return wantarray ? ($x,$x->copy()) : $x if $x->is_inf();
+ if (!$x->is_zero() && !$x->is_inf())
+ {
+ my $t = $x->copy(); # binf clobbers up $x
+ return wantarray ?
+ ($x->binf($x->{sign}),$t) : $x->binf($x->{sign})
+ }
+ }
+
+ # last case: +-inf / ordinary number
+ my $sign = '+inf';
+ $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign};
+ $x->{sign} = $sign;
+ return wantarray ? ($x,$self->bzero()) : $x;
+ }
+
sub bdiv
{
# (dividend: BINT or num_str, divisor: BINT or num_str) return
return $x if $x->modify('bdiv');
- # x / +-inf => 0, reminder x
- return wantarray ? ($x->bzero(),$x->copy()) : $x->bzero()
- if $y->{sign} =~ /^[+-]inf$/;
-
- # NaN if x == NaN or y == NaN or x==y==0
- return wantarray ? ($x->bnan(),bnan()) : $x->bnan()
- if (($x->is_nan() || $y->is_nan()) ||
- ($x->is_zero() && $y->is_zero()));
-
- # 5 / 0 => +inf, -6 / 0 => -inf
- return wantarray
- ? ($x->binf($x->{sign}),$self->bnan()) : $x->binf($x->{sign})
- if ($x->{sign} =~ /^[+-]$/ && $y->is_zero());
-
- # old code: always NaN if /0
- #return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
- # if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ || $y->is_zero());
+ return $self->_div_inf($x,$y)
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
# 0 / something
return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero();
}
# calc new sign and in case $y == +/- 1, return $x
+ my $xsign = $x->{sign}; # keep
$x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+');
# check for / +-1 (cant use $y->is_one due to '-'
- if (($y == 1) || ($y == -1)) # slow!
- #if ((@{$y->{value}} == 1) && ($y->{value}->[0] == 1))
+ if (($y == 1) || ($y == -1)) # slow!
{
return wantarray ? ($x,$self->bzero()) : $x;
}
# call div here
my $rem = $self->bzero();
- $rem->{sign} = $y->{sign};
- #($x->{value},$rem->{value}) = div($x->{value},$y->{value});
($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
- # do not leave rest "-0";
- # $rem->{sign} = '+' if (@{$rem->{value}} == 1) && ($rem->{value}->[0] == 0);
- $rem->{sign} = '+' if $CALC->_is_zero($rem->{value});
- if (($x->{sign} eq '-') and (!$rem->is_zero()))
- {
- $x->bdec();
- }
+ # do not leave result "-0";
+ $x->{sign} = '+' if $CALC->_is_zero($x->{value});
$x->round($a,$p,$r,$y);
+
if (wantarray)
{
- $rem->round($a,$p,$r,$x,$y);
- return ($x,$y-$rem) if $x->{sign} eq '-'; # was $x,$rem
+ if (! $CALC->_is_zero($rem->{value}))
+ {
+ $rem->{sign} = $y->{sign};
+ $rem = $y-$rem if $xsign ne $y->{sign}; # one of them '-'
+ }
+ else
+ {
+ $rem->{sign} = '+'; # dont leave -0
+ }
+ $rem->round($a,$p,$r,$x,$y);
return ($x,$rem);
}
return $x;
}
+sub bmod
+ {
+ # modulus (or remainder)
+ # (BINT or num_str, BINT or num_str) return BINT
+ my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ return $x if $x->modify('bmod');
+ if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
+ {
+ my ($d,$r) = $self->_div_inf($x,$y);
+ return $r;
+ }
+
+ if ($CALC->can('_mod'))
+ {
+ # calc new sign and in case $y == +/- 1, return $x
+ $x->{value} = $CALC->_mod($x->{value},$y->{value});
+ my $xsign = $x->{sign};
+ if (!$CALC->_is_zero($x->{value}))
+ {
+ $x->{sign} = $y->{sign};
+ $x = $y-$x if $xsign ne $y->{sign}; # one of them '-'
+ }
+ else
+ {
+ $x->{sign} = '+'; # dont leave -0
+ }
+ }
+ else
+ {
+ $x = (&bdiv($self,$x,$y))[1]; # slow way
+ }
+ $x->bround($a,$p,$r);
+ }
+
sub bpow
{
# (BINT or num_str, BINT or num_str) return BINT
$x->{value} = $CALC->_pow($x->{value},$y->{value});
return $x->round($a,$p,$r);
}
- # based on the assumption that shifting in base 10 is fast, and that mul
- # works faster if numbers are small: we count trailing zeros (this step is
- # O(1)..O(N), but in case of O(N) we save much more time due to this),
- # stripping them out of the multiplication, and add $count * $y zeros
- # afterwards like this:
- # 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6
- # creates deep recursion?
+
+# based on the assumption that shifting in base 10 is fast, and that mul
+# works faster if numbers are small: we count trailing zeros (this step is
+# O(1)..O(N), but in case of O(N) we save much more time due to this),
+# stripping them out of the multiplication, and add $count * $y zeros
+# afterwards like this:
+# 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6
+# creates deep recursion?
# my $zeros = $x->_trailing_zeros();
# if ($zeros > 0)
# {
my $pow2 = $self->__one();
my $y1 = $class->new($y);
- my ($res);
+ my $two = $self->new(2);
while (!$y1->is_one())
{
- #print "bpow: p2: $pow2 x: $x y: $y1 r: $res\n";
- #print "len ",$x->length(),"\n";
- ($y1,$res)=&bdiv($y1,2);
- if (!$res->is_zero()) { &bmul($pow2,$x); }
- if (!$y1->is_zero()) { &bmul($x,$x); }
- #print "$x $y\n";
+ $pow2->bmul($x) if $y1->is_odd();
+ $y1->bdiv($two);
+ $x->bmul($x);
}
- #print "bpow: e p2: $pow2 x: $x y: $y1 r: $res\n";
- &bmul($x,$pow2) if (!$pow2->is_one());
- #print "bpow: e p2: $pow2 x: $x y: $y1 r: $res\n";
+ $x->bmul($pow2) unless $pow2->is_one();
return $x->round($a,$p,$r);
}
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- my $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft');
+ my $t; $t = $CALC->_lsft($x->{value},$y->{value},$n) if $CALC->can('_lsft');
if (defined $t)
{
$x->{value} = $t; return $x;
$n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
- my $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft');
+ my $t; $t = $CALC->_rsft($x->{value},$y->{value},$n) if $CALC->can('_rsft');
if (defined $t)
{
$x->{value} = $t; return $x;
$x->badd( bmul( $class->new(
abs($sx*int($xr->numify()) | $sy*int($yr->numify()))),
$m));
-# $x->badd( bmul( $class->new(int($xr->numify()) | int($yr->numify())), $m));
$m->bmul($x10000);
}
$x->bneg() if $sign;
$x->badd( bmul( $class->new(
abs($sx*int($xr->numify()) ^ $sy*int($yr->numify()))),
$m));
-# $x->badd( bmul( $class->new(int($xr->numify()) ^ int($yr->numify())), $m));
$m->bmul($x10000);
}
$x->bneg() if $sign;
sub length
{
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
my $e = $CALC->_len($x->{value});
- # # fallback, since we do not know the underlying representation
- #my $es = "$x"; my $c = 0; $c = 1 if $es =~ /^[+-]/; # if lib returns '+123'
- #my $e = CORE::length($es)-$c;
return wantarray ? ($e,0) : $e;
}
my $x = shift;
$x = $class->new($x) unless ref $x;
- return 0 if $x->is_zero() || $x->{sign} !~ /^[+-]$/;
+ return 0 if $x->is_zero() || $x->is_odd() || $x->{sign} !~ /^[+-]$/;
return $CALC->_zeros($x->{value}) if $CALC->can('_zeros');
sub bsqrt
{
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
return $x->bnan() if $x->{sign} =~ /\-|$nan/; # -x or NaN => NaN
return $x->bzero() if $x->is_zero(); # 0 => 0
sub exponent
{
# return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
- my ($self,$x) = objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return bnan() if $x->is_nan();
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ my $s = $x->{sign}; $s =~ s/^[+-]//;
+ return $self->new($s); # -inf,+inf => inf
+ }
my $e = $class->bzero();
return $e->binc() if $x->is_zero();
$e += $x->_trailing_zeros();
sub mantissa
{
- # return a copy of the mantissa (here always $self)
- my ($self,$x) = objectify(1,@_);
+ # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return bnan() if $x->is_nan();
+ if ($x->{sign} !~ /^[+-]$/)
+ {
+ my $s = $x->{sign}; $s =~ s/^[+]//;
+ return $self->new($s); # +inf => inf
+ }
my $m = $x->copy();
# that's inefficient
my $zeros = $m->_trailing_zeros();
sub parts
{
- # return a copy of both the exponent and the mantissa (here 0 and self)
- my $self = shift;
- $self = $class->new($self) unless ref $self;
+ # return a copy of both the exponent and the mantissa
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return ($self->mantissa(),$self->exponent());
+ return ($x->mantissa(),$x->exponent());
}
##############################################################################
sub bfround
{
# precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
- # $n == 0 => round to integer
+ # $n == 0 || $n == 1 => round to integer
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_p($precision,$rnd_mode,@_);
+ my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_);
return $x if !defined $scale; # no-op
# no-op for BigInts if $n <= 0
- return $x if $scale <= 0;
+ if ($scale <= 0)
+ {
+ $x->{_p} = $scale; return $x;
+ }
$x->bround( $x->length()-$scale, $mode);
+ $x->{_a} = undef; # bround sets {_a}
+ $x->{_p} = $scale; # so correct it
+ $x;
}
sub _scan_for_nonzero
# and overwrite the rest with 0's, return normalized number
# do not return $x->bnorm(), but $x
my $x = shift; $x = $class->new($x) unless ref $x;
- my ($scale,$mode) = $x->_scale_a($accuracy,$rnd_mode,@_);
+ my ($scale,$mode) = $x->_scale_a($x->accuracy(),$x->round_mode(),@_);
return $x if !defined $scale; # no-op
# print "MBI round: $x to $scale $mode\n";
- # -scale means what? tom? hullo? -$scale needed by MBF round, but what for?
return $x if $x->{sign} !~ /^[+-]$/ || $x->is_zero() || $scale == 0;
# we have fewer digits than we want to scale to
my $len = $x->length();
- # print "$len $scale\n";
- return $x if $len < abs($scale);
+ # print "$scale $len\n";
+ # scale < 0, but > -len (not >=!)
+ if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
+ {
+ $x->{_a} = $scale if !defined $x->{_a}; # if not yet defined overwrite
+ return $x;
+ }
# count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
my ($pad,$digit_round,$digit_after);
$pad = $len - $scale;
- $pad = abs($scale)+1 if $scale < 0;
+ $pad = abs($scale-1) if $scale < 0;
+
# do not use digit(), it is costly for binary => decimal
#$digit_round = '0'; $digit_round = $x->digit($pad) if $pad < $len;
#$digit_after = '0'; $digit_after = $x->digit($pad-1) if $pad > 0;
+
my $xs = $CALC->_str($x->{value});
my $pl = -$pad-1;
+
+ # print "pad $pad pl $pl scale $scale len $len\n";
# pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
# pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
$digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len;
$pl++; $pl ++ if $pad >= $len;
$digit_after = '0'; $digit_after = substr($$xs,$pl,1)
if $pad > 0;
-
- #my $d_round = '0'; $d_round = $x->digit($pad) if $pad < $len;
- #my $d_after = '0'; $d_after = $x->digit($pad-1) if $pad > 0;
- # print "$pad $pl $$xs $digit_round:$d_round $digit_after:$d_after\n";
+
+ # print "$pad $pl $$xs dr $digit_round da $digit_after\n";
# in case of 01234 we round down, for 6789 up, and only in case 5 we look
# closer at the remaining digits of the original $x, remember decision
{
$x->bzero(); # round to '0'
}
- # print "res $pad $len $x $$xs\n";
+ # print "res $pad $len $x $$xs\n";
}
# move this later on after the inc of the string
#$x->{value} = $CALC->_new($xs); # put back in
if ($round_up) # what gave test above?
{
+ #print " $pad => ";
$pad = $len if $scale < 0; # tlr: whack 0.51=>1.0
# modify $x in place, undef, undef to avoid rounding
# str creation much faster than 10 ** something
+ #print " $pad, $x => ";
$x->badd( Math::BigInt->new($x->{sign}.'1'.'0'x$pad) );
+ #print "$x\n";
# increment string in place, to avoid dec=>hex for the '1000...000'
# $xs ...blah foo
}
# to here:
#$x->{value} = $CALC->_new($xs); # put back in
+
+ $x->{_a} = $scale if $scale >= 0;
+ if ($scale < 0)
+ {
+ $x->{_a} = $len+$scale;
+ $x->{_a} = 0 if $scale < -$len;
+ }
$x;
}
{
# return integer less or equal then number, since it is already integer,
# always returns $self
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
# not needed: return $x if $x->modify('bfloor');
-
return $x->round($a,$p,$r);
}
{
# return integer greater or equal then number, since it is already integer,
# always returns $self
- my ($self,$x,$a,$p,$r) = objectify(1,@_);
+ my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
# not needed: return $x if $x->modify('bceil');
-
return $x->round($a,$p,$r);
}
{
# internal speedup, set argument to 1, or create a +/- 1
my $self = shift;
- my $x = $self->bzero(); $x->{value} = $CALC->_one();
+ my $x = $self->bone(); # $x->{value} = $CALC->_one();
$x->{sign} = shift || '+';
return $x;
}
# $class,1,2. (We can not take '1' as class ;o)
# badd($class,1) is not supported (it should, eventually, try to add undef)
# currently it tries 'Math::BigInt' + 1, which will not work.
-
+
+ # some shortcut for the common cases
+
+ # $x->unary_op();
+ return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
+ # $x->binary_op($y);
+ #return (ref($_[1]),$_[1],$_[2]) if (@_ == 3) && ($_[0]||0 == 2)
+ # && ref($_[1]) && ref($_[2]);
+
+# print "obj '",join ("' '", @_),"'\n";
+
my $count = abs(shift || 0);
- #print caller(),"\n";
+# print "MBI ",caller(),"\n";
my @a; # resulting array
if (ref $_[0])
#print "$count\n";
$count--;
$k = shift;
+# print "$k (",ref($k),") => \n";
if (!ref($k))
{
$k = $a[0]->new($k);
# foreign object, try to convert to integer
$k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
}
+ # print "$k (",ref($k),")\n";
push @a,$k;
}
push @a,@_; # return other params, too
}
# any non :constant stuff is handled by our parent, Exporter
# even if @_ is empty, to give it a chance
- #$self->SUPER::import(@a); # does not work
- $self->export_to_level(1,$self,@a); # need this instead
+ $self->SUPER::import(@a); # need it for subclasses
+ $self->export_to_level(1,$self,@a); # need it for MBF
# try to load core math lib
my @c = split /\s*,\s*/,$CALC;
# used in the same script, or eval inside import().
(my $mod = $lib . '.pm') =~ s!::!/!g;
# require does not automatically :: => /, so portability problems arise
- eval { require $mod; $lib->import(); }
+ eval { require $mod; $lib->import( @c ); }
}
else
{
- eval "use $lib;";
+ eval "use $lib @c;";
}
- $CALC = $lib, last if $@ eq '';
+ $CALC = $lib, last if $@ eq ''; # no error in loading lib?
}
}
{
# (ref to num_str) return num_str
# internal, take apart a string and return the pieces
- # strip leading/trailing whitespace, leading zeros, underscore, reject
+ # strip leading/trailing whitespace, leading zeros, underscore and reject
# invalid input
my $x = shift;
# 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
# .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2
- #print "input: '$$x' ";
+ return if $$x =~ /[Ee].*[Ee]/; # more than one E => error
+
my ($m,$e) = split /[Ee]/,$$x;
$e = '0' if !defined $e || $e eq "";
# print "m '$m' e '$e'\n";
$self->copy();
}
-##############################################################################
-# internal calculation routines (others are in Math::BigInt::Calc etc)
+sub as_hex
+ {
+ # return as hex string, with prefixed 0x
+ my $x = shift; $x = $class->new($x) if !ref($x);
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ return '0x0' if $x->is_zero();
+
+ my $es = ''; my $s = '';
+ $s = $x->{sign} if $x->{sign} eq '-';
+ if ($CALC->can('_as_hex'))
+ {
+ $es = ${$CALC->_as_hex($x->{value})};
+ }
+ else
+ {
+ my $x1 = $x->copy()->babs(); my $xr;
+ my $x100 = Math::BigInt->new (0x100);
+ while (!$x1->is_zero())
+ {
+ ($x1, $xr) = bdiv($x1,$x100);
+ $es .= unpack('h2',pack('C',$xr->numify()));
+ }
+ $es = reverse $es;
+ $es =~ s/^[0]+//; # strip leading zeros
+ $s .= '0x';
+ }
+ $s . $es;
+ }
-sub cmp
+sub as_bin
{
- # post-normalized compare for internal use (honors signs)
- # input: ref to value, ref to value, sign, sign
- # output: <0, 0, >0
- my ($cx,$cy,$sx,$sy) = @_;
+ # return as binary string, with prefixed 0b
+ my $x = shift; $x = $class->new($x) if !ref($x);
- if ($sx eq '+')
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
+ return '0b0' if $x->is_zero();
+
+ my $es = ''; my $s = '';
+ $s = $x->{sign} if $x->{sign} eq '-';
+ if ($CALC->can('_as_bin'))
{
- return 1 if $sy eq '-'; # 0 check handled above
- return $CALC->_acmp($cx,$cy);
+ $es = ${$CALC->_as_bin($x->{value})};
}
else
{
- # $sx eq '-'
- return -1 if $sy eq '+';
- return $CALC->_acmp($cy,$cx);
+ my $x1 = $x->copy()->babs(); my $xr;
+ my $x100 = Math::BigInt->new (0x100);
+ while (!$x1->is_zero())
+ {
+ ($x1, $xr) = bdiv($x1,$x100);
+ $es .= unpack('b8',pack('C',$xr->numify()));
+ }
+ $es = reverse $es;
+ $es =~ s/^[0]+//; # strip leading zeros
+ $s .= '0b';
}
- 0; # equal
+ $s . $es;
}
-sub _lcm
+##############################################################################
+# internal calculation routines (others are in Math::BigInt::Calc etc)
+
+sub __lcm
{
# (BINT or num_str, BINT or num_str) return BINT
# does modify first argument
sub __gcd
{
# (BINT or num_str, BINT or num_str) return BINT
- # does modify first arg
+ # does modify both arguments
# GCD -- Euclids algorithm E, Knuth Vol 2 pg 296
-
- my $x = shift; my $ty = $class->new(shift); # preserve y, but make class
+ my ($x,$ty) = @_;
+
return $x->bnan() if $x->{sign} !~ /^[+-]$/ || $ty->{sign} !~ /^[+-]$/;
while (!$ty->is_zero())
# The following do not modify their arguments:
- bgcd(@values); # greatest common divisor
- blcm(@values); # lowest common multiplicator
-
- $x->bstr(); # normalized string
- $x->bsstr(); # normalized string in scientific notation
+ bgcd(@values); # greatest common divisor (no OO style)
+ blcm(@values); # lowest common multiplicator (no OO style)
+
$x->length(); # return number of digits in number
- ($x,$f) = $x->length(); # length of number and length of fraction part
+ ($x,$f) = $x->length(); # length of number and length of fraction part,
+ # latter is always 0 digits long for BigInt's
$x->exponent(); # return exponent as BigInt
- $x->mantissa(); # return mantissa as BigInt
+ $x->mantissa(); # return (signed) mantissa as BigInt
$x->parts(); # return (mantissa,exponent) as BigInt
$x->copy(); # make a true copy of $x (unlike $y = $x;)
$x->as_number(); # return as BigInt (in BigInt: same as copy())
+
+ # conversation to string
+ $x->bstr(); # normalized string
+ $x->bsstr(); # normalized string in scientific notation
+ $x->as_hex(); # as signed hexadecimal string with prefixed 0x
+ $x->as_bin(); # as signed binary string with prefixed 0b
=head1 DESCRIPTION
again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange
assumption that 124 has 3 significant digits, while 120/7 will get you
'17', not '17.1' since 120 is thought to have 2 significant digits.
- The rounding after the division then uses the reminder and $y to determine
+ The rounding after the division then uses the remainder and $y to determine
wether it must round up or down.
? I have no idea which is the right way. That's why I used a slightly more
? simple scheme and tweaked the few failing testcases to match it.
following rounding modes (R):
'even', 'odd', '+inf', '-inf', 'zero', 'trunc'
* you can set and get the global R by using Math::SomeClass->round_mode()
- or by setting $Math::SomeClass::rnd_mode
+ or by setting $Math::SomeClass::round_mode
* after each operation, $result->round() is called, and the result may
eventually be rounded (that is, if A or P were set either locally,
globally or as parameter to the operation)
- * to manually round a number, call $x->round($A,$P,$rnd_mode);
+ * to manually round a number, call $x->round($A,$P,$round_mode);
this will round the number by using the appropriate rounding function
and then normalize it.
* rounding modifies the local settings of the number:
print $x->copy()->bnorm(),"\n"; # 123.46
print $x->copy()->fround(),"\n"; # 123.46
+Examples for converting:
+
+ my $x = Math::BigInt->new('0b1'.'01' x 123);
+ print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n";
+
=head1 Autocreating constants
After C<use Math::BigInt ':constant'> all the B<integer> decimal constants
It is yet unlcear whether overloaded int() should return a scalar or a BigInt.
+=item length
+
+The following will probably not do what you expect:
+
+ $c = Math::BigInt->new(123);
+ print $c->length(),"\n"; # prints 30
+
+It prints both the number of digits in the number and in the fraction part
+since print calls C<length()> in list context. Use something like:
+
+ print scalar $c->length(),"\n"; # prints 3
+
=item bdiv
The following will probably not do what you expect:
print $c->bdiv(10000),"\n";
-It prints both quotient and reminder since print calls C<bdiv()> in list
+It prints both quotient and remainder since print calls C<bdiv()> in list
context. Also, C<bdiv()> will modify $c, so be carefull. You probably want
to use
nonzero) always has the same sign as the second operand; so, for
example,
- 1 / 4 => ( 0, 1)
- 1 / -4 => (-1,-3)
- -3 / 4 => (-1, 1)
- -3 / -4 => ( 0,-3)
+ 1 / 4 => ( 0, 1)
+ 1 / -4 => (-1,-3)
+ -3 / 4 => (-1, 1)
+ -3 / -4 => ( 0,-3)
+ -11 / 2 => (-5,1)
+ 11 /-2 => (-5,-1)
As a consequence, the behavior of the operator % agrees with the
behavior of Perl's built-in % operator (as documented in the perlop
$x == ($x / $y) * $y + ($x % $y)
holds true for any $x and $y, which justifies calling the two return
-values of bdiv() the quotient and remainder.
+values of bdiv() the quotient and remainder. The only exception to this rule
+are when $y == 0 and $x is negative, then the remainder will also be
+negative. See below under "infinity handling" for the reasoning behing this.
Perl's 'use integer;' changes the behaviour of % and / for scalars, but will
not change BigInt's way to do things. This is because under 'use integer' Perl
system. If you need BigInt's behaving exactly like Perl's 'use integer', bug
the author to implement it ;)
+=item infinity handling
+
+Here are some examples that explain the reasons why certain results occur while
+handling infinity:
+
+The following table shows the result of the division and the remainder, so that
+the equation above holds true. Some "ordinary" cases are strewn in to show more
+clearly the reasoning:
+
+ A / B = C, R so that C * B + R = A
+ =========================================================
+ 5 / 8 = 0, 5 0 * 8 + 5 = 5
+ 0 / 8 = 0, 0 0 * 8 + 0 = 0
+ 0 / inf = 0, 0 0 * inf + 0 = 0
+ 0 /-inf = 0, 0 0 * -inf + 0 = 0
+ 5 / inf = 0, 5 0 * inf + 5 = 5
+ 5 /-inf = 0, 5 0 * -inf + 5 = 5
+ -5/ inf = 0, -5 0 * inf + -5 = -5
+ -5/-inf = 0, -5 0 * -inf + -5 = -5
+ inf/ 5 = inf, 0 inf * 5 + 0 = inf
+ -inf/ 5 = -inf, 0 -inf * 5 + 0 = -inf
+ inf/ -5 = -inf, 0 -inf * -5 + 0 = inf
+ -inf/ -5 = inf, 0 inf * -5 + 0 = -inf
+ 5/ 5 = 1, 0 1 * 5 + 0 = 5
+ -5/ -5 = 1, 0 1 * -5 + 0 = -5
+ inf/ inf = 1, 0 1 * inf + 0 = inf
+ -inf/-inf = 1, 0 1 * -inf + 0 = -inf
+ inf/-inf = -1, 0 -1 * -inf + 0 = inf
+ -inf/ inf = -1, 0 1 * -inf + 0 = -inf
+ 8/ 0 = inf, 8 inf * 0 + 8 = 8
+ inf/ 0 = inf, inf inf * 0 + inf = inf
+ 0/ 0 = NaN
+
+These cases below violate the "remainder has the sign of the second of the two
+arguments", since they wouldn't match up otherwise.
+
+ A / B = C, R so that C * B + R = A
+ ========================================================
+ -inf/ 0 = -inf, -inf -inf * 0 + inf = -inf
+ -8/ 0 = -inf, -8 -inf * 0 + 8 = -8
+
=item Modifying and =
Beware of:
=head1 SEE ALSO
-L<Math::BigFloat> and L<Math::Big>.
+L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>,
+L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
-L<Math::BigInt::BitVect> and L<Math::BigInt::Pari>.
+The package at
+L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
+more documentation including a full version history, testcases, empty
+subclass files and benchmarks.
=head1 AUTHORS
projects / p5sagit/p5-mst-13.2.git / blobdiff