# _a : accuracy
# _p : precision
# _f : flags, used by MBR to flag parts of a rational as untouchable
+# You should not look at the innards of a BigRat - use the methods for this.
package Math::BigRat;
require 5.005_03;
use strict;
-use Exporter;
+require Exporter;
use Math::BigFloat;
use vars qw($VERSION @ISA $PACKAGE @EXPORT_OK $upgrade $downgrade
$accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf);
@ISA = qw(Exporter Math::BigFloat);
@EXPORT_OK = qw();
-$VERSION = '0.10';
+$VERSION = '0.11';
use overload; # inherit from Math::BigFloat
sub _new_from_float
{
- # turn a single float input into a rational (like '0.1')
+ # turn a single float input into a rational number (like '0.1')
my ($self,$f) = @_;
return $self->bnan() if $f->is_nan();
{
if ($n->isa('Math::BigFloat'))
{
- return $self->_new_from_float($n)->bnorm();
+ $self->_new_from_float($n);
}
if ($n->isa('Math::BigInt'))
{
$self->{_n} = $n->copy(); # "mantissa" = $n
$self->{_d} = $MBI->bone();
$self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+';
- return $self->bnorm();
}
if ($n->isa('Math::BigInt::Lite'))
{
$self->{sign} = '+'; $self->{sign} = '-' if $$n < 0;
$self->{_n} = $MBI->new(abs($$n),undef,undef); # "mantissa" = $n
$self->{_d} = $MBI->bone();
- return $self->bnorm();
}
+ return $self->bnorm();
}
return $n->copy() if ref $n;
# inf/inf => NaN
return $self->bnan() if
($self->{_n}->is_inf() && $self->{_d}->is_inf());
- # +-inf/123 => +-inf
- return $self->binf($self->{sign}) if $self->{_n}->is_inf();
+ if ($self->{_n}->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);
+ }
# 123/inf => 0
return $self->bzero();
}
sub bstr
{
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
if ($x->{sign} !~ /^[+-]$/) # inf, NaN etc
{
return $s;
}
- my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3
+ my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # '+3/2' => '3/2'
- return $s.$x->{_n}->bstr() if $x->{_d}->is_one();
- return $s.$x->{_n}->bstr() . '/' . $x->{_d}->bstr();
+ return $s . $x->{_n}->bstr() if $x->{_d}->is_one();
+ $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
}
sub bsstr
}
my $s = ''; $s = $x->{sign} if $x->{sign} ne '+'; # +3 vs 3
- return $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
+ $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
}
sub bnorm
$x->{_d}->{_f} = MB_NEVER_ROUND;
$x->{_n}->{_f} = MB_NEVER_ROUND;
# 'forget' that parts were rounded via MBI::bround() in MBF's bfround()
- $x->{_d}->{_a} = undef; $x->{_n}->{_a} = undef;
- $x->{_d}->{_p} = undef; $x->{_n}->{_p} = undef;
+ 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 $x->{sign} !~ /^[+-]$/;
sub badd
{
- # add two rationals
+ # add two rational numbers
# set up parameters
my ($self,$x,$y,@r) = (ref($_[0]),@_);
$x->{_d}->bmul($y->{_d});
- # calculate new sign
+ # calculate sign of result and norm our _n part
$x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+';
$x->bnorm()->round(@r);
sub bsub
{
- # subtract two rationals
+ # subtract two rational numbers
# set up parameters
my ($self,$x,$y,@r) = (ref($_[0]),@_);
($self,$x,$y,@r) = objectify(2,@_);
}
- # TODO: $self instead or $class??
- $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
- # - - - = --------- = --
- # 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
-
- 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
- $x->{_n}->bsub($m);
-
- $x->{_d}->bmul($y->{_d});
-
- # calculate new sign
- $x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+';
-
- $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
+ $x->{sign} =~ tr/+-/-+/
+ unless $x->{sign} eq '+' && $x->{_n}->is_zero(); # not -0
+ $x;
}
sub bmul
{
- # multiply two rationals
+ # multiply two rational numbers
# set up parameters
my ($self,$x,$y,@r) = (ref($_[0]),@_);
{
my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+ # if $x is an integer
if (($x->{sign} eq '+') && ($x->{_d}->is_one()))
{
$x->{_n}->bfac();
sub blog
{
- return Math::BigRat->bnan();
+ # set up parameters
+ my ($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 <= 0 => NaN
+ return $x->bnan() if $x->is_zero() || $x->{sign} ne '+' || $y->{sign} ne '+';
+
+ if ($x->is_int() && $y->is_int())
+ {
+ return $self->new($x->as_number()->blog($y->as_number(),@r));
+ }
+
+ warn ("blog() not fully implemented");
+ $x->bnan();
+ }
+
+sub broot
+ {
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
+
+ if ($x->is_int() && $y->is_int())
+ {
+ return $self->new($x->as_number()->broot($y->as_number(),@r));
+ }
+
+ warn ("broot() not fully implemented");
+ $x->bnan();
+ }
+
+sub bmodpow
+ {
+ # set up parameters
+ my ($self,$x,$y,$m,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,$m,@r) = objectify(3,@_);
+ }
+
+ # $x or $y or $m are NaN or +-inf => NaN
+ return $x->bnan()
+ if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/ ||
+ $m->{sign} !~ /^[+-]$/;
+
+ if ($x->is_int() && $y->is_int() && $m->is_int())
+ {
+ return $self->new($x->as_number()->bmodpow($y->as_number(),$m,@r));
+ }
+
+ warn ("bmodpow() not fully implemented");
+ $x->bnan();
+ }
+
+sub bmodinv
+ {
+ # set up parameters
+ my ($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 or $y are NaN or +-inf => NaN
+ return $x->bnan()
+ if $x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/;
+
+ if ($x->is_int() && $y->is_int())
+ {
+ return $self->new($x->as_number()->bmodinv($y->as_number(),@r));
+ }
+
+ warn ("bmodinv() not fully implemented");
+ $x->bnan();
}
sub bsqrt
sub bcmp
{
- my ($self,$x,$y) = objectify(2,@_);
+ # compare two signed numbers
+
+ # 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,@_);
+ }
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
sub bacmp
{
- my ($self,$x,$y) = objectify(2,@_);
+ # compare two numbers (as unsigned)
+
+ # set up parameters
+ my ($self,$x,$y) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y) = objectify(2,@_);
+ }
if (($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; # inf is always bigger
+ return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
+ return -1;
}
my $t = $x->{_n} * $y->{_d};
=head1 NAME
-Math::BigRat - arbitrarily big rationals
+Math::BigRat - arbitrarily big rational numbers
=head1 SYNOPSIS
use Math::BigRat;
- $x = Math::BigRat->new('3/7'); $x += '5/9';
+ my $x = Math::BigRat->new('3/7'); $x += '5/9';
print $x->bstr(),"\n";
print $x ** 2,"\n";
+ my $y = Math::BigRat->new('inf');
+ print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n";
+
+ my $z = Math::BigRat->new(144); $z->bsqrt();
+
=head1 DESCRIPTION
Math::BigRat complements Math::BigInt and Math::BigFloat by providing support
-for arbitrarily big rationals.
+for arbitrarily big rational numbers.
=head2 MATH LIBRARY
Create a new Math::BigRat object. Input can come in various forms:
$x = Math::BigRat->new(123); # scalars
+ $x = Math::BigRat->new('inf'); # infinity
$x = Math::BigRat->new('123.3'); # float
$x = Math::BigRat->new('1/3'); # simple string
$x = Math::BigRat->new('1 / 3'); # spaced
Truncate $x to an integer value.
+=head2 bsqrt()
+
+ $x->bsqrt();
+
+Calculate the square root of $x.
+
=head2 config
use Data::Dumper;
=item $x ** $y where $y is not an integer
+=item bmod(), blog(), bmodinv() and bmodpow() (partial)
+
=back
=head1 LICENSE
=head1 AUTHORS
-(C) by Tels L<http://bloodgate.com/> 2001-2002.
+(C) by Tels L<http://bloodgate.com/> 2001, 2002, 2003, 2004.
=cut
projects / p5sagit/p5-mst-13.2.git / commitdiff