require Exporter;
use Math::BigFloat;
-use vars qw($VERSION @ISA $PACKAGE $upgrade $downgrade
+use vars qw($VERSION @ISA $upgrade $downgrade
$accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf);
@ISA = qw(Exporter Math::BigFloat);
-$VERSION = '0.12';
+$VERSION = '0.13';
-use overload; # inherit from Math::BigFloat
+use overload; # inherit overload from Math::BigFloat
-BEGIN { *objectify = \&Math::BigInt::objectify; }
+BEGIN
+ {
+ *objectify = \&Math::BigInt::objectify; # inherit this from BigInt
+ *AUTOLOAD = \&Math::BigFloat::AUTOLOAD; # can't inherit AUTOLOAD
+ # we inherit these from BigFloat because currently it is not possible
+ # that MBF has a different $MBI variable than we, because MBF also uses
+ # Math::BigInt::config->('lib'); (there is always only one library loaded)
+ *_e_add = \&Math::BigFloat::_e_add;
+ *_e_sub = \&Math::BigFloat::_e_sub;
+ }
##############################################################################
-# global constants, flags and accessory
+# Global constants and flags. Access these only via the accessor methods!
$accuracy = $precision = undef;
$round_mode = 'even';
$upgrade = undef;
$downgrade = undef;
-# these are internally, and not to be used from the outside
-
-use constant MB_NEVER_ROUND => 0x0001;
+# 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()
+# the package we are using for our private parts, defaults to:
+# Math::BigInt->config()->{lib}
+my $MBI = 'Math::BigInt::Calc';
+
my $nan = 'NaN';
-my $MBI = 'Math::BigInt';
-my $CALC = 'Math::BigInt::Calc';
my $class = 'Math::BigRat';
my $IMPORT = 0;
UNIVERSAL::isa(@_);
}
-sub BEGIN
- {
- *AUTOLOAD = \&Math::BigFloat::AUTOLOAD;
- }
+##############################################################################
sub _new_from_float
{
return $self->bnan() if $f->is_nan();
return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/;
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
- $self->{_n} = $MBI->new($CALC->_str ( $f->{_m} ),undef,undef);# mantissa
- $self->{_d} = $MBI->bone();
+ $self->{_n} = $MBI->_copy( $f->{_m} ); # mantissa
+ $self->{_d} = $MBI->_one();
$self->{sign} = $f->{sign} || '+';
if ($f->{_es} eq '-')
{
# something like Math::BigRat->new('0.1');
# 1 / 1 => 1/10
- $self->{_d}->blsft( $MBI->new($CALC->_str ( $f->{_e} )),10);
+ $MBI->_lsft ( $self->{_d}, $f->{_e} ,10);
}
else
{
# something like Math::BigRat->new('10');
# 1 / 1 => 10/1
- $self->{_n}->blsft( $MBI->new($CALC->_str($f->{_e})),10) unless
- $CALC->_is_zero($f->{_e});
+ $MBI->_lsft ( $self->{_n}, $f->{_e} ,10) unless
+ $MBI->_is_zero($f->{_e});
}
$self;
}
if ($n->isa('Math::BigInt'))
{
# TODO: trap NaN, inf
- $self->{_n} = $n->copy(); # "mantissa" = $n
- $self->{_d} = $MBI->bone();
- $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+';
+ $self->{_n} = $MBI->_copy($n->{value}); # "mantissa" = $n
+ $self->{_d} = $MBI->_one(); # d => 1
+ $self->{sign} = $n->{sign};
}
if ($n->isa('Math::BigInt::Lite'))
{
# TODO: trap NaN, inf
$self->{sign} = '+'; $self->{sign} = '-' if $$n < 0;
- $self->{_n} = $MBI->new(abs($$n),undef,undef); # "mantissa" = $n
- $self->{_d} = $MBI->bone();
+ $self->{_n} = $MBI->_new(abs($$n)); # "mantissa" = $n
+ $self->{_d} = $MBI->_one(); # d => 1
}
- return $self->bnorm();
+ return $self->bnorm(); # normalize (120/1 => 12/10)
}
- return $n->copy() if ref $n;
+ return $n->copy() if ref $n; # already a BigRat
if (!defined $n)
{
- $self->{_n} = $MBI->bzero(); # undef => 0
- $self->{_d} = $MBI->bone();
+ $self->{_n} = $MBI->_zero(); # undef => 0
+ $self->{_d} = $MBI->_one();
$self->{sign} = '+';
- return $self->bnorm();
+ return $self;
}
+
# string input with / delimiter
if ($n =~ /\s*\/\s*/)
{
# try as BigFloats first
if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/))
{
- # one of them looks like a float
- # Math::BigFloat($n,undef,undef) does not what it is supposed to do, so:
local $Math::BigFloat::accuracy = undef;
local $Math::BigFloat::precision = undef;
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
+ # one of them looks like a float
my $nf = Math::BigFloat->new($n,undef,undef);
$self->{sign} = '+';
return $self->bnan() if $nf->is_nan();
- $self->{_n} = $MBI->new( $CALC->_str( $nf->{_m} ) );
+ $self->{_n} = $MBI->_copy( $nf->{_m} ); # get mantissa
# now correct $self->{_n} due to $n
my $f = Math::BigFloat->new($d,undef,undef);
return $self->bnan() if $f->is_nan();
- $self->{_d} = $MBI->new( $CALC->_str( $f->{_m} ) );
+ $self->{_d} = $MBI->_copy( $f->{_m} );
# calculate the difference between nE and dE
- my $diff_e = $MBI->new ($nf->exponent())->bsub ( $f->exponent);
+ # XXX TODO: check that exponent() makes a copy to avoid copy()
+ my $diff_e = $nf->exponent()->copy()->bsub( $f->exponent);
if ($diff_e->is_negative())
{
# < 0: mul d with it
- $self->{_d}->blsft($diff_e->babs(),10);
+ $MBI->_lsft( $self->{_d}, $MBI->_new( $diff_e->babs()), 10);
}
elsif (!$diff_e->is_zero())
{
# > 0: mul n with it
- $self->{_n}->blsft($diff_e,10);
+ $MBI->_lsft( $self->{_n}, $MBI->_new( $diff_e), 10);
}
}
else
{
- # both d and n are (big)ints
- $self->{_n} = $MBI->new($n,undef,undef);
- $self->{_d} = $MBI->new($d,undef,undef);
- $self->{sign} = '+';
- return $self->bnan() if $self->{_n}->{sign} eq $nan ||
- $self->{_d}->{sign} eq $nan;
- # handle inf and NAN cases:
- if ($self->{_n}->is_inf() || $self->{_d}->is_inf())
- {
- # inf/inf => NaN
- return $self->bnan() if
- ($self->{_n}->is_inf() && $self->{_d}->is_inf());
- if ($self->{_n}->is_inf())
+ # both d and n look like (big)ints
+
+ $self->{sign} = '+'; # no sign => '+'
+ $self->{_n} = undef;
+ $self->{_d} = undef;
+ if ($n =~ /^([+-]?)0*(\d+)\z/) # first part ok?
+ {
+ $self->{sign} = $1 || '+'; # no sign => '+'
+ $self->{_n} = $MBI->_new($2 || 0);
+ }
+
+ if ($d =~ /^([+-]?)0*(\d+)\z/) # second part ok?
+ {
+ $self->{sign} =~ tr/+-/-+/ if ($1 || '') eq '-'; # negate if second part neg.
+ $self->{_d} = $MBI->_new($2 || 0);
+ }
+
+ if (!defined $self->{_n} || !defined $self->{_d})
+ {
+ $d = Math::BigInt->new($d,undef,undef) unless ref $d;
+ $n = Math::BigInt->new($n,undef,undef) unless ref $n;
+
+ if ($n->{sign} =~ /^[+-]$/ && $d->{sign} =~ /^[+-]$/)
+ {
+ # both parts are ok as integers (wierd things like ' 1e0'
+ $self->{_n} = $MBI->_copy($n->{value});
+ $self->{_d} = $MBI->_copy($d->{value});
+ $self->{sign} = $n->{sign};
+ $self->{sign} =~ tr/+-/-+/ if $d->{sign} eq '-'; # -1/-2 => 1/2
+ return $self->bnorm();
+ }
+
+ $self->{sign} = '+'; # a default sign
+ return $self->bnan() if $n->is_nan() || $d->is_nan();
+
+ # handle inf cases:
+ if ($n->is_inf() || $d->is_inf())
{
- my $s = '+'; # '+inf/+123' or '-inf/-123'
- $s = '-' if substr($self->{_n}->{sign},0,1) ne $self->{_d}->{sign};
- # +-inf/123 => +-inf
- return $self->binf($s);
+ if ($n->is_inf())
+ {
+ return $self->bnan() if $d->is_inf(); # both are inf => NaN
+ my $s = '+'; # '+inf/+123' or '-inf/-123'
+ $s = '-' if substr($n->{sign},0,1) ne $d->{sign};
+ # +-inf/123 => +-inf
+ return $self->binf($s);
+ }
+ # 123/inf => 0
+ return $self->bzero();
}
- # 123/inf => 0
- return $self->bzero();
- }
-
- $self->{sign} = $self->{_n}->{sign}; $self->{_n}->babs();
- # if $d is negative, flip sign
- $self->{sign} =~ tr/+-/-+/ if $self->{_d}->{sign} eq '-';
- $self->{_d}->babs(); # normalize
+ }
}
return $self->bnorm();
if (($n =~ /[\.eE]/))
{
# looks like a float, quacks like a float, so probably is a float
- # Math::BigFloat($n,undef,undef) does not what it is supposed to do, so:
+ $self->{sign} = 'NaN';
local $Math::BigFloat::accuracy = undef;
local $Math::BigFloat::precision = undef;
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
- $self->{sign} = 'NaN';
$self->_new_from_float(Math::BigFloat->new($n,undef,undef));
}
else
{
- $self->{_n} = $MBI->new($n,undef,undef);
- $self->{_d} = $MBI->bone();
- $self->{sign} = $self->{_n}->{sign}; $self->{_n}->babs();
- return $self->bnan() if $self->{sign} eq 'NaN';
- return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/;
+ # for simple forms, use $MBI directly
+ if ($n =~ /^([+-]?)0*(\d+)\z/)
+ {
+ $self->{sign} = $1 || '+';
+ $self->{_n} = $MBI->_new($2 || 0);
+ $self->{_d} = $MBI->_one();
+ }
+ else
+ {
+ my $n = Math::BigInt->new($n,undef,undef);
+ $self->{_n} = $MBI->_copy($n->{value});
+ $self->{_d} = $MBI->_one();
+ $self->{sign} = $n->{sign};
+ return $self->bnan() if $self->{sign} eq 'NaN';
+ return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/;
+ }
}
$self->bnorm();
}
}
return unless ref($x); # only for objects
- my $self = {}; bless $self,$c;
+ my $self = bless {}, $c;
$self->{sign} = $x->{sign};
- $self->{_d} = $x->{_d}->copy();
- $self->{_n} = $x->{_n}->copy();
+ $self->{_d} = $MBI->_copy($x->{_d});
+ $self->{_n} = $MBI->_copy($x->{_n});
$self->{_a} = $x->{_a} if defined $x->{_a};
$self->{_p} = $x->{_p} if defined $x->{_p};
$self;
my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2'
- return $s . $x->{_n}->bstr() if $x->{_d}->is_one();
- $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
+ return $s . $MBI->_str($x->{_n}) if $MBI->_is_one($x->{_d});
+ $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d});
}
sub bsstr
}
my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3
- $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
+ $s . $MBI->_str($x->{_n}) . '/' . $MBI->_str($x->{_d});
}
sub bnorm
{
- # reduce the number to the shortest form and remember this (so that we
- # don't reduce again)
+ # reduce the number to the shortest form
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- # both parts must be BigInt's (or whatever we are using today)
- if (ref($x->{_n}) ne $MBI)
+ # Both parts must be objects of whatever we are using today.
+ # Second check because Calc.pm has ARRAY res as unblessed objects.
+ if (ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY')
{
- require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).')');
+ require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).') in bnorm()');
}
- if (ref($x->{_d}) ne $MBI)
+ if (ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY')
{
- require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).')');
+ require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).') in bnorm()');
}
- # this is to prevent automatically rounding when MBI's globals are set
- $x->{_d}->{_f} = MB_NEVER_ROUND;
- $x->{_n}->{_f} = MB_NEVER_ROUND;
- # 'forget' that parts were rounded via MBI::bround() in MBF's bfround()
- delete $x->{_d}->{_a}; delete $x->{_n}->{_a};
- delete $x->{_d}->{_p}; delete $x->{_n}->{_p};
-
# no normalize for NaN, inf etc.
return $x if $x->{sign} !~ /^[+-]$/;
# normalize zeros to 0/1
- if (($x->{sign} =~ /^[+-]$/) &&
- ($x->{_n}->is_zero()))
+ if ($MBI->_is_zero($x->{_n}))
{
- $x->{sign} = '+'; # never -0
- $x->{_d} = $MBI->bone() unless $x->{_d}->is_one();
+ $x->{sign} = '+'; # never leave a -0
+ $x->{_d} = $MBI->_one() unless $MBI->_is_one($x->{_d});
return $x;
}
- return $x if $x->{_d}->is_one(); # no need to reduce
+ return $x if $MBI->_is_one($x->{_d}); # no need to reduce
# reduce other numbers
- # disable upgrade in BigInt, otherwise deep recursion
- local $Math::BigInt::upgrade = undef;
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
- my $gcd = $x->{_n}->bgcd($x->{_d});
-
- if (!$gcd->is_one())
+ my $gcd = $MBI->_copy($x->{_n});
+ $gcd = $MBI->_gcd($gcd,$x->{_d});
+
+ if (!$MBI->_is_one($gcd))
{
- $x->{_n}->bdiv($gcd);
- $x->{_d}->bdiv($gcd);
+ $x->{_n} = $MBI->_div($x->{_n},$gcd);
+ $x->{_d} = $MBI->_div($x->{_d},$gcd);
}
$x;
}
my $class = ref($self);
Carp::croak ("Tried to set $self to NaN in $class\::_bnan()");
}
- $self->{_n} = $MBI->bzero();
- $self->{_d} = $MBI->bzero();
+ $self->{_n} = $MBI->_zero();
+ $self->{_d} = $MBI->_zero();
}
sub _binf
my $class = ref($self);
Carp::croak ("Tried to set $self to inf in $class\::_binf()");
}
- $self->{_n} = $MBI->bzero();
- $self->{_d} = $MBI->bzero();
+ $self->{_n} = $MBI->_zero();
+ $self->{_d} = $MBI->_zero();
}
sub _bone
{
# used by parent class bone() to initialize number to +1/-1
my $self = shift;
- $self->{_n} = $MBI->bone();
- $self->{_d} = $MBI->bone();
+ $self->{_n} = $MBI->_one();
+ $self->{_d} = $MBI->_one();
}
sub _bzero
{
# used by parent class bzero() to initialize number to 0
my $self = shift;
- $self->{_n} = $MBI->bzero();
- $self->{_d} = $MBI->bone();
+ $self->{_n} = $MBI->_zero();
+ $self->{_d} = $MBI->_one();
}
##############################################################################
($self,$x,$y,@r) = objectify(2,@_);
}
- $x = $self->new($x) unless $x->isa($self);
- $y = $self->new($y) unless $y->isa($self);
+ # +inf + +inf => +inf, -inf + -inf => -inf
+ return $x->binf(substr($x->{sign},0,1))
+ if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
- return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN');
- # TODO: inf handling
+ # +inf + -inf or -inf + +inf => NaN
+ return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
# 1 1 gcd(3,4) = 1 1*3 + 1*4 7
# - + - = --------- = --
# - + - = --------- = --
# 4 3 4*3 12
- # the gcd() calculation and reducing is then done in bnorm()
+ # and bnorm() will then take care of the rest
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
+ $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d});
- $x->{_n}->bmul($y->{_d}); $x->{_n}->{sign} = $x->{sign};
- my $m = $y->{_n}->copy()->bmul($x->{_d});
- $m->{sign} = $y->{sign}; # 2/1 - 2/1
- $x->{_n}->badd($m);
+ my $m = $MBI->_mul( $MBI->_copy( $y->{_n} ), $x->{_d} );
- $x->{_d}->bmul($y->{_d});
+ ($x->{_n}, $x->{sign}) = _e_add( $x->{_n}, $m, $x->{sign}, $y->{sign});
- # calculate sign of result and norm our _n part
- $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+';
+ $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d});
+ # normalize and round
$x->bnorm()->round(@r);
}
# flip sign of $x, call badd(), then flip sign of result
$x->{sign} =~ tr/+-/-+/
- unless $x->{sign} eq '+' && $x->{_n}->is_zero(); # not -0
- $x->badd($y,@r); # does norm and round
+ unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0
+ $x->badd($y,@r); # does norm and round
$x->{sign} =~ tr/+-/-+/
- unless $x->{sign} eq '+' && $x->{_n}->is_zero(); # not -0
+ unless $x->{sign} eq '+' && $MBI->_is_zero($x->{_n}); # not -0
$x;
}
($self,$x,$y,@r) = objectify(2,@_);
}
- $x = $self->new($x) unless $x->isa($self);
- $y = $self->new($y) unless $y->isa($self);
-
return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN');
# inf handling
# x== 0 # also: or y == 1 or y == -1
return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero();
- # According to Knuth, this can be optimized by doingtwice gcd (for d and n)
- # and reducing in one step)
+ # XXX TODO:
+ # According to Knuth, this can be optimized by doing gcd twice (for d and n)
+ # and reducing in one step. This would save us the bnorm() at the end.
- # 1 1 2 1
- # - * - = - = -
- # 4 3 12 6
+ # 1 2 1 * 2 2 1
+ # - * - = ----- = - = -
+ # 4 3 4 * 3 12 6
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
- $x->{_n}->bmul($y->{_n});
- $x->{_d}->bmul($y->{_d});
+ $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_n});
+ $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_d});
# compute new sign
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-';
($self,$x,$y,@r) = objectify(2,@_);
}
- $x = $self->new($x) unless $x->isa($self);
- $y = $self->new($y) unless $y->isa($self);
-
return $self->_div_inf($x,$y)
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
# x== 0 # also: or y == 1 or y == -1
return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero();
- # TODO: list context, upgrade
+ # XXX TODO: list context, upgrade
+ # According to Knuth, this can be optimized by doing gcd twice (for d and n)
+ # and reducing in one step. This would save us the bnorm() at the end.
# 1 1 1 3
# - / - == - * -
# 4 3 4 1
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
- $x->{_n}->bmul($y->{_d});
- $x->{_d}->bmul($y->{_n});
+ $x->{_n} = $MBI->_mul( $x->{_n}, $y->{_d});
+ $x->{_d} = $MBI->_mul( $x->{_d}, $y->{_n});
# compute new sign
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-';
($self,$x,$y,@r) = objectify(2,@_);
}
- $x = $self->new($x) unless $x->isa($self);
- $y = $self->new($y) unless $y->isa($self);
-
- return $self->_div_inf($x,$y)
- if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
-
return $self->_div_inf($x,$y)
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
# compute $x - $y * floor($x/$y), keeping the sign of $x
- # locally disable these, since they would interfere
- local $Math::BigInt::upgrade = undef;
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
-
- my $u = $x->copy()->babs();
- # first, do a "normal" division ($x/$y)
- $u->{_d}->bmul($y->{_n});
- $u->{_n}->bmul($y->{_d});
-
- # compute floor
- if (!$u->{_d}->is_one())
+ # copy x to u, make it positive and then do a normal division ($u/$y)
+ my $u = bless { sign => '+' }, $self;
+ $u->{_n} = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d} );
+ $u->{_d} = $MBI->_mul( $MBI->_copy($x->{_d}), $y->{_n} );
+
+ # compute floor(u)
+ if (! $MBI->_is_one($u->{_d}))
{
- $u->{_n}->bdiv($u->{_d}); # 22/7 => 3/1 w/ truncate
- # no need to set $u->{_d} to 1, since later we set it to $y->{_d}
- #$x->{_n}->binc() if $x->{sign} eq '-'; # -22/7 => -4/1
+ $u->{_n} = $MBI->_div($u->{_n},$u->{_d}); # 22/7 => 3/1 w/ truncate
+ # no need to set $u->{_d} to 1, since below we set it to $y->{_d} anyway
}
- # compute $y * $u
- $u->{_d} = $y->{_d}; # 1 * $y->{_d}, see floor above
- $u->{_n}->bmul($y->{_n});
+ # now compute $y * $u
+ $u->{_d} = $MBI->_copy($y->{_d}); # 1 * $y->{_d}, see floor above
+ $u->{_n} = $MBI->_mul($u->{_n},$y->{_n});
- my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make abs
+ my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make x positive
# compute $x - $u
$x->bsub($u);
$x->{sign} = $xsign; # put sign back
return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
if ($x->{sign} eq '-')
{
- $x->{_n}->badd($x->{_d}); # -5/2 => -7/2
+ $x->{_n} = $MBI->_add( $x->{_n}, $x->{_d}); # -5/2 => -7/2
}
else
{
- if ($x->{_n}->bacmp($x->{_d}) < 0)
+ if ($MBI->_acmp($x->{_n},$x->{_d}) < 0) # n < d?
{
# 1/3 -- => -2/3
- $x->{_n} = $x->{_d} - $x->{_n};
+ $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n});
$x->{sign} = '-';
}
else
{
- $x->{_n}->bsub($x->{_d}); # 5/2 => 3/2
+ $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # 5/2 => 3/2
}
}
$x->bnorm()->round(@r);
return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
if ($x->{sign} eq '-')
{
- if ($x->{_n}->bacmp($x->{_d}) < 0)
+ if ($MBI->_acmp($x->{_n},$x->{_d}) < 0)
{
# -1/3 ++ => 2/3 (overflow at 0)
- $x->{_n} = $x->{_d} - $x->{_n};
+ $x->{_n} = $MBI->_sub( $MBI->_copy($x->{_d}), $x->{_n});
$x->{sign} = '+';
}
else
{
- $x->{_n}->bsub($x->{_d}); # -5/2 => -3/2
+ $x->{_n} = $MBI->_sub($x->{_n}, $x->{_d}); # -5/2 => -3/2
}
}
else
{
- $x->{_n}->badd($x->{_d}); # 5/2 => 7/2
+ $x->{_n} = $MBI->_add($x->{_n},$x->{_d}); # 5/2 => 7/2
}
$x->bnorm()->round(@r);
}
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't
- $x->{_d}->is_one(); # x/y && y != 1 => no integer
+ $MBI->_is_one($x->{_d}); # x/y && y != 1 => no integer
0;
}
# return true if arg (BRAT or num_str) is zero
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- return 1 if $x->{sign} eq '+' && $x->{_n}->is_zero();
+ return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_n});
0;
}
my $sign = $_[2] || ''; $sign = '+' if $sign ne '-';
return 1
- if ($x->{sign} eq $sign && $x->{_n}->is_one() && $x->{_d}->is_one());
+ if ($x->{sign} eq $sign && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d}));
0;
}
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't
- ($x->{_d}->is_one() && $x->{_n}->is_odd()); # x/2 is not, but 3/1
+ ($MBI->_is_one($x->{_d}) && $MBI->_is_odd($x->{_n})); # x/2 is not, but 3/1
0;
}
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
- return 1 if ($x->{_d}->is_one() # x/3 is never
- && $x->{_n}->is_even()); # but 4/1 is
+ return 1 if ($MBI->_is_one($x->{_d}) # x/3 is never
+ && $MBI->_is_even($x->{_n})); # but 4/1 is
0;
}
{
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return $MBI->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/);
+ # NaN, inf, -inf
+ return Math::BigInt->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/);
- my $n = $x->{_n}->copy(); $n->{sign} = $x->{sign};
+ my $n = Math::BigInt->new($MBI->_str($x->{_n})); $n->{sign} = $x->{sign};
$n;
}
{
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return $MBI->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/);
- $x->{_d}->copy();
+ # NaN
+ return Math::BigInt->new($x->{sign}) if $x->{sign} eq 'NaN';
+ # inf, -inf
+ return Math::BigInt->bone() if $x->{sign} !~ /^[+-]$/;
+
+ Math::BigInt->new($MBI->_str($x->{_d}));
}
sub parts
{
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return ($self->bnan(),$self->bnan()) if $x->{sign} eq 'NaN';
- return ($self->binf(),$self->binf()) if $x->{sign} eq '+inf';
- return ($self->binf('-'),$self->binf()) if $x->{sign} eq '-inf';
+ my $c = 'Math::BigInt';
+
+ return ($c->bnan(),$c->bnan()) if $x->{sign} eq 'NaN';
+ return ($c->binf(),$c->binf()) if $x->{sign} eq '+inf';
+ return ($c->binf('-'),$c->binf()) if $x->{sign} eq '-inf';
- my $n = $x->{_n}->copy();
+ my $n = $c->new( $MBI->_str($x->{_n}));
$n->{sign} = $x->{sign};
- return ($n,$x->{_d}->copy());
+ my $d = $c->new( $MBI->_str($x->{_d}));
+ ($n,$d);
}
sub length
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return $nan unless $x->is_int();
- $x->{_n}->length(); # length(-123/1) => length(123)
+ $MBI->_len($x->{_n}); # length(-123/1) => length(123)
}
sub digit
{
- my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+ my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0],$_[1]) : objectify(1,@_);
return $nan unless $x->is_int();
- $x->{_n}->digit($n); # digit(-123/1,2) => digit(123,2)
+ $MBI->_digit($x->{_n},$n || 0); # digit(-123/1,2) => digit(123,2)
}
##############################################################################
{
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return $x unless $x->{sign} =~ /^[+-]$/;
- return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0
+ return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf
+ $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0
- local $Math::BigInt::upgrade = undef;
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
- $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 w/ truncate
- $x->{_d}->bone();
- $x->{_n}->binc() if $x->{sign} eq '+'; # +22/7 => 4/1
- $x->{sign} = '+' if $x->{_n}->is_zero(); # -0 => 0
+ $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate
+ $x->{_d} = $MBI->_one(); # d => 1
+ $x->{_n} = $MBI->_inc($x->{_n})
+ if $x->{sign} eq '+'; # +22/7 => 4/1
+ $x->{sign} = '+' if $MBI->_is_zero($x->{_n}); # -0 => 0
$x;
}
{
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return $x unless $x->{sign} =~ /^[+-]$/;
- return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0
+ return $x if $x->{sign} !~ /^[+-]$/ || # not for NaN, inf
+ $MBI->_is_one($x->{_d}); # 22/1 => 22, 0/1 => 0
- local $Math::BigInt::upgrade = undef;
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
- $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1 w/ truncate
- $x->{_d}->bone();
- $x->{_n}->binc() if $x->{sign} eq '-'; # -22/7 => -4/1
+ $x->{_n} = $MBI->_div($x->{_n},$x->{_d}); # 22/7 => 3/1 w/ truncate
+ $x->{_d} = $MBI->_one(); # d => 1
+ $x->{_n} = $MBI->_inc($x->{_n})
+ if $x->{sign} eq '-'; # -22/7 => -4/1
$x;
}
{
my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- # if $x is an integer
- if (($x->{sign} eq '+') && ($x->{_d}->is_one()))
+ # if $x is not an integer
+ if (($x->{sign} ne '+') || (!$MBI->_is_one($x->{_d})))
{
- $x->{_n}->bfac();
- return $x->round(@r);
+ return $x->bnan();
}
- $x->bnan();
+
+ $x->{_n} = $MBI->_fac($x->{_n});
+ # since _d is 1, we don't need to reduce/norm the result
+ $x->round(@r);
}
sub bpow
return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
return $x->bone(@r) if $y->is_zero();
return $x->round(@r) if $x->is_one() || $y->is_one();
- if ($x->{sign} eq '-' && $x->{_n}->is_one() && $x->{_d}->is_one())
+
+ if ($x->{sign} eq '-' && $MBI->_is_one($x->{_n}) && $MBI->_is_one($x->{_d}))
{
# if $x == -1 and odd/even y => +1/-1
return $y->is_odd() ? $x->round(@r) : $x->babs()->round(@r);
}
# 1 ** -y => 1 / (1 ** |y|)
# so do test for negative $y after above's clause
- # return $x->bnan() if $y->{sign} eq '-';
+
return $x->round(@r) if $x->is_zero(); # 0**y => 0 (if not y <= 0)
# shortcut y/1 (and/or x/1)
- if ($y->{_d}->is_one())
+ if ($MBI->_is_one($y->{_d}))
{
# shortcut for x/1 and y/1
- if ($x->{_d}->is_one())
+ if ($MBI->_is_one($x->{_d}))
{
- $x->{_n}->bpow($y->{_n}); # x/1 ** y/1 => (x ** y)/1
+ $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # x/1 ** y/1 => (x ** y)/1
if ($y->{sign} eq '-')
{
# 0.2 ** -3 => 1/(0.2 ** 3)
if ($x->{sign} eq '-')
{
# - * - => +, - * - * - => -
- $x->{sign} = '+' if $y->{_n}->is_even();
+ $x->{sign} = '+' if $MBI->_is_even($y->{_n});
}
return $x->round(@r);
}
# x/z ** y/1
- $x->{_n}->bpow($y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y
- $x->{_d}->bpow($y->{_n});
+ $x->{_n} = $MBI->_pow($x->{_n},$y->{_n}); # 5/2 ** y/1 => 5 ** y / 2 ** y
+ $x->{_d} = $MBI->_pow($x->{_d},$y->{_n});
if ($y->{sign} eq '-')
{
# 0.2 ** -3 => 1/(0.2 ** 3)
if ($x->{sign} eq '-')
{
# - * - => +, - * - * - => -
- $x->{sign} = '+' if $y->{_n}->is_even();
+ $x->{sign} = '+' if $MBI->_is_even($y->{_n});
}
return $x->round(@r);
}
# regular calculation (this is wrong for d/e ** f/g)
- my $pow2 = $self->__one();
- my $y1 = $MBI->new($y->{_n}/$y->{_d})->babs();
- my $two = $MBI->new(2);
- while (!$y1->is_one())
+ my $pow2 = $self->bone();
+ my $y1 = $MBI->_div ( $MBI->_copy($y->{_n}), $y->{_d});
+ my $two = $MBI->_two();
+
+ while (!$MBI->_is_one($y1))
{
- $pow2->bmul($x) if $y1->is_odd();
- $y1->bdiv($two);
+ $pow2->bmul($x) if $MBI->_is_odd($y1);
+ $MBI->_div($y1, $two);
$x->bmul($x);
}
$x->bmul($pow2) unless $pow2->is_one();
$x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) );
}
+sub _float_from_part
+ {
+ my $x = shift;
+
+ my $f = Math::BigFloat->bzero();
+ $f->{_m} = $MBI->_copy($x);
+ $f->{_e} = $MBI->_zero();
+
+ $f;
+ }
+
sub _as_float
{
my $x = shift;
local $Math::BigFloat::accuracy = undef;
local $Math::BigFloat::precision = undef;
# 22/7 => 3.142857143..
- Math::BigFloat->new($x->{_n})->bdiv($x->{_d}, $x->accuracy());
+
+ my $a = $x->accuracy() || 0;
+ if ($a != 0 || !$MBI->_is_one($x->{_d}))
+ {
+ # n/d
+ return Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}))->bdiv( $MBI->_str($x->{_d}), $x->accuracy());
+ }
+ # just n
+ Math::BigFloat->new($x->{sign} . $MBI->_str($x->{_n}));
}
sub broot
local $Math::BigInt::precision = undef;
local $Math::BigInt::accuracy = undef;
- $x->{_d} = Math::BigFloat->new($x->{_d})->bsqrt();
- $x->{_n} = Math::BigFloat->new($x->{_n})->bsqrt();
+ $x->{_n} = _float_from_part( $x->{_n} )->bsqrt();
+ $x->{_d} = _float_from_part( $x->{_d} )->bsqrt();
+
+ # XXX TODO: we probably can optimze this:
# if sqrt(D) was not integer
if ($x->{_d}->{_es} ne '+')
{
$x->{_n}->blsft($x->{_d}->exponent()->babs(),10); # 7.1/4.51 => 7.1/45.1
- $x->{_d} = $MBI->new($CALC->_str($x->{_d}->{_m})); # 7.1/45.1 => 71/45.1
+ $x->{_d} = $MBI->_copy( $x->{_d}->{_m} ); # 7.1/45.1 => 71/45.1
}
# if sqrt(N) was not integer
if ($x->{_n}->{_es} ne '+')
{
$x->{_d}->blsft($x->{_n}->exponent()->babs(),10); # 71/45.1 => 710/45.1
- $x->{_n} = $MBI->new($CALC->_str($x->{_n}->{_m})); # 710/45.1 => 710/451
+ $x->{_n} = $MBI->_copy( $x->{_n}->{_m} ); # 710/45.1 => 710/451
}
-
+
# convert parts to $MBI again
- $x->{_n} = $x->{_n}->as_number() unless $x->{_n}->isa($MBI);
- $x->{_d} = $x->{_d}->as_number() unless $x->{_d}->isa($MBI);
+ $x->{_n} = $MBI->_lsft( $MBI->_copy( $x->{_n}->{_m} ), $x->{_n}->{_e}, 10)
+ if ref($x->{_n}) ne $MBI && ref($x->{_n}) ne 'ARRAY';
+ $x->{_d} = $MBI->_lsft( $MBI->_copy( $x->{_d}->{_m} ), $x->{_d}->{_e}, 10)
+ if ref($x->{_d}) ne $MBI && ref($x->{_d}) ne 'ARRAY';
+
$x->bnorm()->round(@r);
}
sub brsft
{
- my ($self,$x,$y,$b,@r) = objectify(2,@_);
+ my ($self,$x,$y,$b,@r) = objectify(3,@_);
$b = 2 unless defined $b;
$b = $self->new($b) unless ref ($b);
return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0
# shortcut
- my $xz = $x->{_n}->is_zero();
- my $yz = $y->{_n}->is_zero();
+ my $xz = $MBI->_is_zero($x->{_n});
+ my $yz = $MBI->_is_zero($y->{_n});
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
- my $t = $x->{_n} * $y->{_d}; $t->{sign} = $x->{sign};
- my $u = $y->{_n} * $x->{_d}; $u->{sign} = $y->{sign};
- $t->bcmp($u);
+ my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d});
+ my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d});
+
+ my $cmp = $MBI->_acmp($t,$u); # signs are equal
+ $cmp = -$cmp if $x->{sign} eq '-'; # both are '-' => reverse
+ $cmp;
}
sub bacmp
return -1;
}
- my $t = $x->{_n} * $y->{_d};
- my $u = $y->{_n} * $x->{_d};
- $t->bacmp($u);
+ my $t = $MBI->_mul( $MBI->_copy($x->{_n}), $y->{_d});
+ my $u = $MBI->_mul( $MBI->_copy($y->{_n}), $x->{_d});
+ $MBI->_acmp($t,$u); # ignore signs
}
##############################################################################
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc
# N/1 => N
- return $x->{_n}->numify() if $x->{_d}->is_one();
+ return $MBI->_num($x->{_n}) if $MBI->_is_one($x->{_d});
# N/D
my $neg = 1; $neg = -1 if $x->{sign} ne '+';
- $neg * $x->{_n}->numify() / $x->{_d}->numify(); # return sign * N/D
+ $neg * $MBI->_num($x->{_n}) / $MBI->_num($x->{_d}); # return sign * N/D
}
sub as_number
{
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf etc
+ return Math::BigInt->new($x) if $x->{sign} !~ /^[+-]$/; # NaN, inf etc
- # need to disable these, otherwise bdiv() gives BigRat again
- local $Math::BigInt::upgrade = undef;
- local $Math::BigInt::accuracy = undef;
- local $Math::BigInt::precision = undef;
- my $t = $x->{_n}->copy()->bdiv($x->{_d}); # 22/7 => 3
- $t->{sign} = $x->{sign};
- $t;
+ my $u = Math::BigInt->bzero();
+ $u->{sign} = $x->{sign};
+ $u->{value} = $MBI->_div( $MBI->_copy($x->{_n}), $x->{_d}); # 22/7 => 3
+ $u;
}
sub as_bin
return $x unless $x->is_int();
my $s = $x->{sign}; $s = '' if $s eq '+';
- $s . $x->{_n}->as_bin();
+ $s . $MBI->_as_bin($x->{_n});
}
sub as_hex
return $x unless $x->is_int();
my $s = $x->{sign}; $s = '' if $s eq '+';
- $s . $x->{_n}->as_hex();
+ $s . $MBI->_as_hex($x->{_n});
}
sub import
require Carp; Carp::croak ("Couldn't load $MBI: $! $@");
}
- $CALC = Math::BigFloat->config()->{lib};
+ $MBI = Math::BigFloat->config()->{lib};
# any non :constant stuff is handled by our parent, Exporter
# even if @_ is empty, to give it a chance
https://perl5.git.perl.org / perl5.git / blobdiff