#
-# "Tax the rat farms."
+# "Tax the rat farms." - Lord Vetinari
#
# The following hash values are used:
# _n : numeraotr (value = _n/_d)
# _a : accuracy
# _p : precision
-# _f : flags, used by MBR to flag parts of a rational as untouchable
+# _f : flags, used by MBR to flag parts of a rationale as untouchable
package Math::BigRat;
@ISA = qw(Exporter Math::BigFloat);
@EXPORT_OK = qw();
-$VERSION = '0.07';
+$VERSION = '0.09';
use overload; # inherit from Math::BigFloat
sub _new_from_float
{
- # turn a single float input into a rational (like '0.1')
+ # turn a single float input into a rationale (like '0.1')
my ($self,$f) = @_;
return $self->bnan() if $f->is_nan();
return $self->binf('-inf') if $f->{sign} eq '-inf';
return $self->binf('+inf') if $f->{sign} eq '+inf';
- #print "f $f caller", join(' ',caller()),"\n";
$self->{_n} = $f->{_m}->copy(); # mantissa
$self->{_d} = $MBI->bone();
$self->{sign} = $f->{sign}; $self->{_n}->{sign} = '+';
}
if ($n->isa('Math::BigInt::Lite'))
{
- $self->{_n} = $MBI->new($$n); # "mantissa" = $n
+ $self->{_n} = $MBI->new($$n,undef,undef); # "mantissa" = $n
$self->{_d} = $MBI->bone();
$self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+';
return $self->bnorm();
if (!defined $n)
{
- $self->{_n} = $MBI->bzero(); # undef => 0
+ $self->{_n} = $MBI->bzero(); # undef => 0
$self->{_d} = $MBI->bone();
$self->{sign} = '+';
return $self->bnorm();
if (($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;
$self->_new_from_float(Math::BigFloat->new($n));
# now correct $self->{_n} due to $n
- my $f = Math::BigFloat->new($d);
+ my $f = Math::BigFloat->new($d,undef,undef);
if ($f->{_e}->{sign} eq '-')
{
# 10 / 0.1 => 100/1
}
else
{
- $self->{_n} = $MBI->new($n);
- $self->{_d} = $MBI->new($d);
+ # both d and n are (big)ints
+ $self->{_n} = $MBI->new($n,undef,undef);
+ $self->{_d} = $MBI->new($d,undef,undef);
return $self->bnan() if $self->{_n}->is_nan() || $self->{_d}->is_nan();
# inf handling is missing here
# simple string input
if (($n =~ /[\.eE]/))
{
- # work around bug in BigFloat that makes 1.1.2 valid
- return $self->bnan() if $n =~ /\..*\./;
- # looks like a float
- $self->_new_from_float(Math::BigFloat->new($n));
+ # 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:
+ local $Math::BigFloat::accuracy = undef;
+ local $Math::BigFloat::precision = undef;
+ local $Math::BigInt::accuracy = undef;
+ local $Math::BigInt::precision = undef;
+ $self->_new_from_float(Math::BigFloat->new($n,undef,undef));
}
else
{
- $self->{_n} = $MBI->new($n);
+ $self->{_n} = $MBI->new($n,undef,undef);
$self->{_d} = $MBI->bone();
$self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+';
return $self->bnan() if $self->{sign} eq 'NaN';
}
my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3
- return $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
+ return $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
}
sub bnorm
# 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())
sub _binf
{
- # used by parent class bone() to initialize number to 1
+ # used by parent class bone() to initialize number to +inf/-inf
my $self = shift;
$self->{_n} = $MBI->bzero();
$self->{_d} = $MBI->bzero();
sub _bone
{
- # used by parent class bone() to initialize number to 1
+ # used by parent class bone() to initialize number to +1/-1
my $self = shift;
$self->{_n} = $MBI->bone();
$self->{_d} = $MBI->bone();
sub _bzero
{
- # used by parent class bone() to initialize number to 1
+ # used by parent class bone() to initialize number to 0
my $self = shift;
$self->{_n} = $MBI->bzero();
$self->{_d} = $MBI->bone();
sub badd
{
- # add two rationals
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ # add two rationales
+
+ # set up parameters
+ my ($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,@_);
+ }
$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');
+ # TODO: inf handling
# 1 1 gcd(3,4) = 1 1*3 + 1*4 7
# - + - = --------- = --
# 4 3 4*3 12
- my $gcd = $x->{_d}->bgcd($y->{_d});
+ # we do not compute the gcd() here, but simple do:
+ # 5 7 5*3 + 7*4 41
+ # - + - = --------- = --
+ # 4 3 4*3 12
+
+ # the gcd() calculation and reducing is then done in bnorm()
- my $aa = $x->{_d}->copy();
- my $bb = $y->{_d}->copy();
- if ($gcd->is_one())
- {
- $bb->bdiv($gcd); $aa->bdiv($gcd);
- }
- $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign};
- my $m = $y->{_n}->copy()->bmul($aa);
+ local $Math::BigInt::accuracy = undef;
+ local $Math::BigInt::precision = undef;
+
+ $x->{_n}->bmul($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);
# calculate new sign
$x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+';
- $x->bnorm()->round($a,$p,$r);
+ $x->bnorm()->round(@r);
}
sub bsub
{
- # subtract two rationals
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ # subtract two rationales
+
+ # set up parameters
+ my ($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,@_);
+ }
$x = $class->new($x) unless $x->isa($class);
$y = $class->new($y) unless $y->isa($class);
return $x->bnan() if ($x->{sign} eq 'NaN' || $y->{sign} eq 'NaN');
# TODO: inf handling
- # 1 1 gcd(3,4) = 1 1*3 + 1*4 7
- # - + - = --------- = --
+ # 1 1 gcd(3,4) = 1 1*3 - 1*4 7
+ # - - - = --------- = --
# 4 3 4*3 12
+
+ # we do not compute the gcd() here, but simple do:
+ # 5 7 5*3 - 7*4 13
+ # - - - = --------- = - --
+ # 4 3 4*3 12
- my $gcd = $x->{_d}->bgcd($y->{_d});
+ local $Math::BigInt::accuracy = undef;
+ local $Math::BigInt::precision = undef;
- my $aa = $x->{_d}->copy();
- my $bb = $y->{_d}->copy();
- if ($gcd->is_one())
- {
- $bb->bdiv($gcd); $aa->bdiv($gcd);
- }
- $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign};
- my $m = $y->{_n}->copy()->bmul($aa);
+ $x->{_n}->bmul($y->{_d}); $x->{_n}->{sign} = $x->{sign};
+ my $m = $y->{_n}->copy()->bmul($x->{_d});
$m->{sign} = $y->{sign}; # 2/1 - 2/1
$x->{_n}->bsub($m);
# calculate new sign
$x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+';
- $x->bnorm()->round($a,$p,$r);
+ $x->bnorm()->round(@r);
}
sub bmul
{
- # multiply two rationals
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ # multiply two rationales
+
+ # set up parameters
+ my ($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,@_);
+ }
$x = $class->new($x) unless $x->isa($class);
$y = $class->new($y) unless $y->isa($class);
# 1 1 2 1
# - * - = - = -
# 4 3 12 6
+
+ local $Math::BigInt::accuracy = undef;
+ local $Math::BigInt::precision = undef;
$x->{_n}->bmul($y->{_n});
$x->{_d}->bmul($y->{_d});
# compute new sign
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-';
- $x->bnorm()->round($a,$p,$r);
+ $x->bnorm()->round(@r);
}
sub bdiv
{
# (dividend: BRAT or num_str, divisor: BRAT or num_str) return
# (BRAT,BRAT) (quo,rem) or BRAT (only rem)
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
$x = $class->new($x) unless $x->isa($class);
$y = $class->new($y) unless $y->isa($class);
# 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});
# compute new sign
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-';
- $x->bnorm()->round($a,$p,$r);
+ $x->bnorm()->round(@r);
$x;
}
}
}
$x->bnorm()->round(@r);
-
- #$x->bsub($self->bone())->round(@r);
}
sub binc
$x->{_n}->badd($x->{_d}); # 5/2 => 7/2
}
$x->bnorm()->round(@r);
-
- #$x->badd($self->bone())->round(@r);
}
##############################################################################
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't
- $x->{_d}->is_one(); # 1e-1 => no integer
+ $x->{_d}->is_one(); # x/y && y != 1 => no integer
0;
}
sub bpow
{
- my ($self,$x,$y,@r) = objectify(2,@_);
+ # power ($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 $x->{sign} =~ /^[+-]inf$/; # -inf/+inf ** x
return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
$x->bmul($pow2) unless $pow2->is_one();
# n ** -x => 1/n ** x
($x->{_d},$x->{_n}) = ($x->{_n},$x->{_d}) if $y->{sign} eq '-';
- $x;
- #$x->round(@r);
+ $x->bnorm()->round(@r);
}
sub blog
##############################################################################
# output conversation
+sub numify
+ {
+ # convert 17/8 => float (aka 2.125)
+ my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc
+
+ my $t = Math::BigFloat->new($x->{_n});
+ $t->bneg() if $x->is_negative();
+ $t->bdiv($x->{_d});
+ $t->numify();
+ }
+
sub as_number
{
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
=head1 NAME
-Math::BigRat - arbitrarily big rationals
+Math::BigRat - arbitrarily big rationales
=head1 SYNOPSIS
- use Math::BigRat;
+ use Math::BigRat;
- $x = Math::BigRat->new('3/7');
+ $x = Math::BigRat->new('3/7'); $x += '5/9';
- print $x->bstr(),"\n";
+ print $x->bstr(),"\n";
+ print $x ** 2,"\n";
=head1 DESCRIPTION
-This is just a placeholder until the real thing is up and running. Watch this
-space...
+Math::BigRat complements Math::BigInt and Math::BigFloat by providing support
+for arbitrarily big rationales.
=head2 MATH LIBRARY
use Math::BigRat lib => 'Foo,Math::BigInt::Bar';
Calc.pm uses as internal format an array of elements of some decimal base
-(usually 1e7, but this might be differen for some systems) with the least
+(usually 1e7, but this might be different for some systems) with the least
significant digit first, while BitVect.pm uses a bit vector of base 2, most
significant bit first. Other modules might use even different means of
representing the numbers. See the respective module documentation for further
details.
+Currently the following replacement libraries exist, search for them at CPAN:
+
+ Math::BigInt::BitVect
+ Math::BigInt::GMP
+ Math::BigInt::Pari
+ Math::BigInt::FastCalc
+
=head1 METHODS
-Any method not listed here is dervied from Math::BigFloat (or
+Any methods not listed here are dervied from Math::BigFloat (or
Math::BigInt), so make sure you check these two modules for further
information.
Create a new Math::BigRat object. Input can come in various forms:
+ $x = Math::BigRat->new(123); # scalars
+ $x = Math::BigRat->new('123.3'); # float
$x = Math::BigRat->new('1/3'); # simple string
$x = Math::BigRat->new('1 / 3'); # spaced
$x = Math::BigRat->new('1 / 0.1'); # w/ floats
=head2 as_number()
+ $x = Math::BigRat->new('13/7');
+ print $x->as_number(),"\n"; # '1'
+
Returns a copy of the object as BigInt by truncating it to integer.
=head2 bfac()
print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3
print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5
-Only works for integers for now.
+Works currently only for integers.
=head2 blog()
Are not yet implemented.
+=head2 is_one()
+
+ print "$x is 1\n" if $x->is_one();
+
+Return true if $x is exactly one, otherwise false.
+
+=head2 is_zero()
+
+ print "$x is 0\n" if $x->is_zero();
+
+Return true if $x is exactly zero, otherwise false.
+
+=head2 is_positive()
+
+ print "$x is >= 0\n" if $x->is_positive();
+
+Return true if $x is positive (greater than or equal to zero), otherwise
+false. Please note that '+inf' is also positive, while 'NaN' and '-inf' aren't.
+
+=head2 is_negative()
+
+ print "$x is < 0\n" if $x->is_negative();
+
+Return true if $x is negative (smaller than zero), otherwise false. Please
+note that '-inf' is also negative, while 'NaN' and '+inf' aren't.
+
+=head2 is_int()
+
+ print "$x is an integer\n" if $x->is_int();
+
+Return true if $x has a denominator of 1 (e.g. no fraction parts), otherwise
+false. Please note that '-inf', 'inf' and 'NaN' aren't integer.
+
+=head2 is_odd()
+
+ print "$x is odd\n" if $x->is_odd();
+
+Return true if $x is odd, otherwise false.
+
+=head2 is_even()
+
+ print "$x is even\n" if $x->is_even();
+
+Return true if $x is even, otherwise false.
+
+=head2 bceil()
+
+ $x->bceil();
+
+Set $x to the next bigger integer value (e.g. truncate the number to integer
+and then increment it by one).
+
+=head2 bfloor()
+
+ $x->bfloor();
+
+Truncate $x to an integer value.
=head1 BUGS
-Some things are not yet implemented, or only implemented half-way.
+Some things are not yet implemented, or only implemented half-way:
+
+=over 2
+
+=item inf handling (partial)
+
+=item NaN handling (partial)
+
+=item rounding (not implemented except for bceil/bfloor)
+
+=item $x ** $y where $y is not an integer
+
+=back
=head1 LICENSE
L<Math::BigFloat> and L<Math::Big> as well as L<Math::BigInt::BitVect>,
L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
-The package at
-L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigRat> may
-contain more documentation and examples as well as testcases.
+See L<http://search.cpan.org/search?dist=bignum> for a way to use
+Math::BigRat.
+
+The package at L<http://search.cpan.org/search?dist=Math%3A%3ABigRat>
+may contain more documentation and examples as well as testcases.
=head1 AUTHORS
projects / p5sagit/p5-mst-13.2.git / blobdiff