-#!/usr/bin/perl -w
+
+#
+# "Tax the rat farms." - Lord Vetinari
+#
# The following hash values are used:
# sign : +,-,NaN,+inf,-inf
# _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_02;
+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 $div_scale);
+use vars qw($VERSION @ISA $PACKAGE $upgrade $downgrade
+ $accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf);
@ISA = qw(Exporter Math::BigFloat);
-@EXPORT_OK = qw();
-$VERSION = '0.06';
+$VERSION = '0.12';
+
+use overload; # inherit from Math::BigFloat
-use overload; # inherit from Math::BigFloat
+BEGIN { *objectify = \&Math::BigInt::objectify; }
##############################################################################
# global constants, flags and accessory
-use constant MB_NEVER_ROUND => 0x0001;
-
$accuracy = $precision = undef;
$round_mode = 'even';
$div_scale = 40;
$upgrade = undef;
$downgrade = undef;
+# these are internally, and not to be used from the outside
+
+use constant MB_NEVER_ROUND => 0x0001;
+
+$_trap_nan = 0; # are NaNs ok? set w/ config()
+$_trap_inf = 0; # are infs ok? set w/ config()
+
my $nan = 'NaN';
-my $class = 'Math::BigRat';
my $MBI = 'Math::BigInt';
+my $CALC = 'Math::BigInt::Calc';
+my $class = 'Math::BigRat';
+my $IMPORT = 0;
sub isa
{
UNIVERSAL::isa(@_);
}
+sub BEGIN
+ {
+ *AUTOLOAD = \&Math::BigFloat::AUTOLOAD;
+ }
+
sub _new_from_float
{
- # turn a single float input into a rational (like '0.1')
+ # turn a single float input into a rational number (like '0.1')
my ($self,$f) = @_;
return $self->bnan() if $f->is_nan();
- return $self->binf('-inf') if $f->{sign} eq '-inf';
- return $self->binf('+inf') if $f->{sign} eq '+inf';
+ return $self->binf($f->{sign}) if $f->{sign} =~ /^[+-]inf$/;
- #print "f $f caller", join(' ',caller()),"\n";
- $self->{_n} = $f->{_m}->copy(); # mantissa
+ 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->{sign} = $f->{sign}; $self->{_n}->{sign} = '+';
- if ($f->{_e}->{sign} eq '-')
+ $self->{sign} = $f->{sign} || '+';
+ if ($f->{_es} eq '-')
{
# something like Math::BigRat->new('0.1');
- $self->{_d}->blsft($f->{_e}->copy()->babs(),10); # 1 / 1 => 1/10
+ # 1 / 1 => 1/10
+ $self->{_d}->blsft( $MBI->new($CALC->_str ( $f->{_e} )),10);
}
else
{
# something like Math::BigRat->new('10');
# 1 / 1 => 10/1
- $self->{_n}->blsft($f->{_e},10) unless $f->{_e}->is_zero();
+ $self->{_n}->blsft( $MBI->new($CALC->_str($f->{_e})),10) unless
+ $CALC->_is_zero($f->{_e});
}
-# print "float new $self->{_n} / $self->{_d}\n";
$self;
}
my $self = { }; bless $self,$class;
-# print "ref ",ref($n),"\n";
-# if (ref($n))
-# {
-# print "isa float " if $n->isa('Math::BigFloat');
-# print "isa int " if $n->isa('Math::BigInt');
-# print "isa rat " if $n->isa('Math::BigRat');
-# print "isa lite " if $n->isa('Math::BigInt::Lite');
-# }
-# else
-# {
-# print "scalar $n\n";
-# }
# input like (BigInt,BigInt) or (BigFloat,BigFloat) not handled yet
if ((!defined $d) && (ref $n) && (!$n->isa('Math::BigRat')))
{
-# print "is ref, but not rat\n";
if ($n->isa('Math::BigFloat'))
{
- # print "is ref, and float\n";
- return $self->_new_from_float($n)->bnorm();
+ $self->_new_from_float($n);
}
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} = '+';
- return $self->bnorm();
}
if ($n->isa('Math::BigInt::Lite'))
{
-# print "is ref, and lite\n";
- $self->{_n} = $MBI->new($$n); # "mantissa" = $n
+ # TODO: trap NaN, inf
+ $self->{sign} = '+'; $self->{sign} = '-' if $$n < 0;
+ $self->{_n} = $MBI->new(abs($$n),undef,undef); # "mantissa" = $n
$self->{_d} = $MBI->bone();
- $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+';
- return $self->bnorm();
}
+ return $self->bnorm();
}
return $n->copy() if ref $n;
-
-# print "is string\n";
if (!defined $n)
{
- $self->{_n} = $MBI->bzero(); # undef => 0
+ $self->{_n} = $MBI->bzero(); # undef => 0
$self->{_d} = $MBI->bone();
$self->{sign} = '+';
return $self->bnorm();
# string input with / delimiter
if ($n =~ /\s*\/\s*/)
{
- return Math::BigRat->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid
- return Math::BigRat->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid
+ return $class->bnan() if $n =~ /\/.*\//; # 1/2/3 isn't valid
+ return $class->bnan() if $n =~ /\/\s*$/; # 1/ isn't valid
($n,$d) = split (/\//,$n);
# try as BigFloats first
if (($n =~ /[\.eE]/) || ($d =~ /[\.eE]/))
{
# one of them looks like a float
- $self->_new_from_float(Math::BigFloat->new($n));
+ # 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;
+
+ 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} ) );
+
# now correct $self->{_n} due to $n
- my $f = Math::BigFloat->new($d);
- if ($f->{_e}->{sign} eq '-')
+ my $f = Math::BigFloat->new($d,undef,undef);
+ return $self->bnan() if $f->is_nan();
+ $self->{_d} = $MBI->new( $CALC->_str( $f->{_m} ) );
+
+ # calculate the difference between nE and dE
+ my $diff_e = $MBI->new ($nf->exponent())->bsub ( $f->exponent);
+ if ($diff_e->is_negative())
+ {
+ # < 0: mul d with it
+ $self->{_d}->blsft($diff_e->babs(),10);
+ }
+ elsif (!$diff_e->is_zero())
{
- # 10 / 0.1 => 100/1
- $self->{_n}->blsft($f->{_e}->copy()->babs(),10);
+ # > 0: mul n with it
+ $self->{_n}->blsft($diff_e,10);
}
- else
- {
- $self->{_d}->blsft($f->{_e},10); # 1 / 1 => 10/1
- }
}
else
{
- $self->{_n} = $MBI->new($n);
- $self->{_d} = $MBI->new($d);
- return $self->bnan() if $self->{_n}->is_nan() || $self->{_d}->is_nan();
- # inf handling is missing here
+ # 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())
+ {
+ 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();
+ }
- $self->{sign} = $self->{_n}->{sign}; $self->{_n}->{sign} = '+';
+ $self->{sign} = $self->{_n}->{sign}; $self->{_n}->babs();
# if $d is negative, flip sign
$self->{sign} =~ tr/+-/-+/ if $self->{_d}->{sign} eq '-';
- $self->{_d}->{sign} = '+'; # normalize
+ $self->{_d}->babs(); # normalize
}
+
return $self->bnorm();
}
# simple string input
if (($n =~ /[\.eE]/))
{
- # looks like a float
-# print "float-like string $d\n";
- $self->_new_from_float(Math::BigFloat->new($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->{sign} = 'NaN';
+ $self->_new_from_float(Math::BigFloat->new($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} = '+';
+ $self->{sign} = $self->{_n}->{sign}; $self->{_n}->babs();
+ return $self->bnan() if $self->{sign} eq 'NaN';
+ return $self->binf($self->{sign}) if $self->{sign} =~ /^[+-]inf$/;
}
$self->bnorm();
}
-###############################################################################
+sub copy
+ {
+ my ($c,$x);
+ if (@_ > 1)
+ {
+ # if two arguments, the first one is the class to "swallow" subclasses
+ ($c,$x) = @_;
+ }
+ else
+ {
+ $x = shift;
+ $c = ref($x);
+ }
+ return unless ref($x); # only for objects
+
+ my $self = {}; bless $self,$c;
+
+ $self->{sign} = $x->{sign};
+ $self->{_d} = $x->{_d}->copy();
+ $self->{_n} = $x->{_n}->copy();
+ $self->{_a} = $x->{_a} if defined $x->{_a};
+ $self->{_p} = $x->{_p} if defined $x->{_p};
+ $self;
+ }
+
+##############################################################################
+
+sub config
+ {
+ # return (later set?) configuration data as hash ref
+ my $class = shift || 'Math::BigFloat';
+
+ my $cfg = $class->SUPER::config(@_);
+
+ # now we need only to override the ones that are different from our parent
+ $cfg->{class} = $class;
+ $cfg->{with} = $MBI;
+ $cfg;
+ }
+
+##############################################################################
sub bstr
{
- my ($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;
}
-# print "bstr $x->{sign} $x->{_n} $x->{_d}\n";
- 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 $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
+ $s . $x->{_n}->bstr() . '/' . $x->{_d}->bstr();
}
sub bnorm
# don't reduce again)
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- # both parts must be BigInt's
- die ("n is not $MBI but (".ref($x->{_n}).')')
- if ref($x->{_n}) ne $MBI;
- die ("d is not $MBI but (".ref($x->{_d}).')')
- if ref($x->{_d}) ne $MBI;
+ # both parts must be BigInt's (or whatever we are using today)
+ if (ref($x->{_n}) ne $MBI)
+ {
+ require Carp; Carp::croak ("n is not $MBI but (".ref($x->{_n}).')');
+ }
+ if (ref($x->{_d}) ne $MBI)
+ {
+ require Carp; Carp::croak ("d is not $MBI but (".ref($x->{_d}).')');
+ }
# 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()
- $x->{_d}->{_a} = undef; $x->{_n}->{_a} = undef;
- $x->{_d}->{_p} = undef; $x->{_n}->{_p} = undef;
-
-# print "$x->{sign} $x->{_n} / $x->{_d} => ";
+ 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 $x->{sign} !~ /^[+-]$/;
if (($x->{sign} =~ /^[+-]$/) &&
($x->{_n}->is_zero()))
{
- $x->{sign} = '+'; # never -0
+ $x->{sign} = '+'; # never -0
$x->{_d} = $MBI->bone() unless $x->{_d}->is_one();
return $x;
}
- return $x if $x->{_d}->is_one();
+ return $x if $x->{_d}->is_one(); # no need to reduce
# reduce other numbers
- # print "bgcd $x->{_n} (",ref($x->{_n}),") $x->{_d} (",ref($x->{_d}),")\n";
# 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())
{
-# print "normalize $x->{_d} / $x->{_n} => ";
$x->{_n}->bdiv($gcd);
$x->{_d}->bdiv($gcd);
-# print "$x->{_d} / $x->{_n}\n";
}
-# print "$x->{_n} / $x->{_d}\n";
$x;
}
sub _bnan
{
- # used by parent class bone() to initialize number to 1
+ # used by parent class bnan() to initialize number to NaN
my $self = shift;
- $self->{_n} = Math::BigInt->bzero();
- $self->{_d} = Math::BigInt->bzero();
+
+ if ($_trap_nan)
+ {
+ require Carp;
+ my $class = ref($self);
+ Carp::croak ("Tried to set $self to NaN in $class\::_bnan()");
+ }
+ $self->{_n} = $MBI->bzero();
+ $self->{_d} = $MBI->bzero();
}
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} = Math::BigInt->bzero();
- $self->{_d} = Math::BigInt->bzero();
+
+ if ($_trap_inf)
+ {
+ require Carp;
+ my $class = ref($self);
+ Carp::croak ("Tried to set $self to inf in $class\::_binf()");
+ }
+ $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} = Math::BigInt->bone();
- $self->{_d} = Math::BigInt->bone();
+ $self->{_n} = $MBI->bone();
+ $self->{_d} = $MBI->bone();
}
sub _bzero
{
- # used by parent class bone() to initialize number to 1
+ # used by parent class bzero() to initialize number to 0
my $self = shift;
- $self->{_n} = Math::BigInt->bzero();
- $self->{_d} = Math::BigInt->bone();
+ $self->{_n} = $MBI->bzero();
+ $self->{_d} = $MBI->bone();
}
##############################################################################
sub badd
{
- # add two rationals
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ # add two rational numbers
+
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,@_);
+ }
-# print "rat badd\n";
-# print "ref($x) = ",ref($x),"\n";
-# print "ref($y) = ",ref($y),"\n";
$x = $self->new($x) unless $x->isa($self);
$y = $self->new($y) unless $y->isa($self);
-# print "ref($x) = ",ref($x),"\n";
-# print "ref($y) = ",ref($y),"\n";
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);
$x->{_d}->bmul($y->{_d});
- # calculate new sign
+ # calculate sign of result and norm our _n part
$x->{sign} = $x->{_n}->{sign}; $x->{_n}->{sign} = '+';
- $x->bnorm()->round($a,$p,$r);
+ $x->bnorm()->round(@r);
}
sub bsub
{
- # subtract two rationals
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ # subtract two rational numbers
- $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
-
- my $gcd = $x->{_d}->bgcd($y->{_d});
-
- my $aa = $x->{_d}->copy();
- my $bb = $y->{_d}->copy();
- if ($gcd->is_one())
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
{
- $bb->bdiv($gcd); $aa->bdiv($gcd);
+ ($self,$x,$y,@r) = objectify(2,@_);
}
- $x->{_n}->bmul($bb); $x->{_n}->{sign} = $x->{sign};
- my $m = $y->{_n}->copy()->bmul($aa);
- $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} = '+';
- $x->bnorm()->round($a,$p,$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
+ $x;
}
sub bmul
{
- # multiply two rationals
- my ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ # multiply two rational numbers
+
+ # set up parameters
+ my ($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);
+ $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');
# 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,@_);
- $x = $class->new($x) unless $x->isa($class);
- $y = $class->new($y) unless $y->isa($class);
+ # 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);
-# print "rat bdiv $x $y ",ref($x)," ",ref($y),"\n";
return $self->_div_inf($x,$y)
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
# 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});
-# print "result $x->{_d} $x->{_n}\n";
# compute new sign
$x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-';
- $x->bnorm()->round($a,$p,$r);
-# print "result $x->{_d} $x->{_n}\n";
+ $x->bnorm()->round(@r);
$x;
}
+sub bmod
+ {
+ # compute "remainder" (in Perl way) of $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,@_);
+ }
+
+ $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());
+
+ return $x if $x->is_zero(); # 0 / 7 = 0, mod 0
+
+ # 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())
+ {
+ $u->{_n}->bdiv($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
+ }
+
+ # compute $y * $u
+ $u->{_d} = $y->{_d}; # 1 * $y->{_d}, see floor above
+ $u->{_n}->bmul($y->{_n});
+
+ my $xsign = $x->{sign}; $x->{sign} = '+'; # remember sign and make abs
+ # compute $x - $u
+ $x->bsub($u);
+ $x->{sign} = $xsign; # put sign back
+
+ $x->bnorm()->round(@r);
+ }
+
+##############################################################################
+# bdec/binc
+
+sub bdec
+ {
+ # decrement value (subtract 1)
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ 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
+ }
+ else
+ {
+ if ($x->{_n}->bacmp($x->{_d}) < 0)
+ {
+ # 1/3 -- => -2/3
+ $x->{_n} = $x->{_d} - $x->{_n};
+ $x->{sign} = '-';
+ }
+ else
+ {
+ $x->{_n}->bsub($x->{_d}); # 5/2 => 3/2
+ }
+ }
+ $x->bnorm()->round(@r);
+ }
+
+sub binc
+ {
+ # increment value (add 1)
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ 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)
+ {
+ # -1/3 ++ => 2/3 (overflow at 0)
+ $x->{_n} = $x->{_d} - $x->{_n};
+ $x->{sign} = '+';
+ }
+ else
+ {
+ $x->{_n}->bsub($x->{_d}); # -5/2 => -3/2
+ }
+ }
+ else
+ {
+ $x->{_n}->badd($x->{_d}); # 5/2 => 7/2
+ }
+ $x->bnorm()->round(@r);
+ }
+
##############################################################################
# is_foo methods (the rest is inherited)
sub is_int
{
# return true if arg (BRAT or num_str) is an integer
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't
- $x->{_d}->is_one(); # 1e-1 => no integer
+ $x->{_d}->is_one(); # x/y && y != 1 => no integer
0;
}
sub is_zero
{
# return true if arg (BRAT or num_str) is zero
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if $x->{sign} eq '+' && $x->{_n}->is_zero();
0;
sub is_one
{
# return true if arg (BRAT or num_str) is +1 or -1 if signis given
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- my $sign = shift || ''; $sign = '+' if $sign ne '-';
+ my $sign = $_[2] || ''; $sign = '+' if $sign ne '-';
return 1
if ($x->{sign} eq $sign && $x->{_n}->is_one() && $x->{_d}->is_one());
0;
sub is_odd
{
# return true if arg (BFLOAT or num_str) is odd or false if even
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't
($x->{_d}->is_one() && $x->{_n}->is_odd()); # x/2 is not, but 3/1
sub is_even
{
# return true if arg (BINT or num_str) is even or false if odd
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
return 1 if ($x->{_d}->is_one() # x/3 is never
0;
}
-BEGIN
- {
- *objectify = \&Math::BigInt::objectify;
- }
-
##############################################################################
# parts() and friends
sub numerator
{
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
-
+
+ return $MBI->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/);
+
my $n = $x->{_n}->copy(); $n->{sign} = $x->{sign};
$n;
}
{
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ return $MBI->new($x->{sign}) if ($x->{sign} !~ /^[+-]$/);
$x->{_d}->copy();
}
{
my ($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 $n = $x->{_n}->copy();
$n->{sign} = $x->{sign};
- return ($x->{_n}->copy(),$x->{_d}->copy());
+ return ($n,$x->{_d}->copy());
}
sub length
{
- return 0;
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return $nan unless $x->is_int();
+ $x->{_n}->length(); # length(-123/1) => length(123)
}
sub digit
{
- return 0;
+ my ($self,$x,$n) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return $nan unless $x->is_int();
+ $x->{_n}->digit($n); # digit(-123/1,2) => digit(123,2)
}
##############################################################################
return $x unless $x->{sign} =~ /^[+-]$/;
return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0
- $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1
+ 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;
}
return $x unless $x->{sign} =~ /^[+-]$/;
return $x if $x->{_d}->is_one(); # 22/1 => 22, 0/1 => 0
- $x->{_n}->bdiv($x->{_d}); # 22/7 => 3/1
+ 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
$x;
sub bfac
{
- return Math::BigRat->bnan();
+ my ($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();
+ return $x->round(@r);
+ }
+ $x->bnan();
}
sub bpow
{
- my ($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;
# 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())
+ {
+ # shortcut for x/1 and y/1
+ if ($x->{_d}->is_one())
+ {
+ $x->{_n}->bpow($y->{_n}); # x/1 ** y/1 => (x ** y)/1
+ if ($y->{sign} eq '-')
+ {
+ # 0.2 ** -3 => 1/(0.2 ** 3)
+ ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap
+ }
+ # correct sign; + ** + => +
+ if ($x->{sign} eq '-')
+ {
+ # - * - => +, - * - * - => -
+ $x->{sign} = '+' if $y->{_n}->is_even();
+ }
+ 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});
+ if ($y->{sign} eq '-')
+ {
+ # 0.2 ** -3 => 1/(0.2 ** 3)
+ ($x->{_n},$x->{_d}) = ($x->{_d},$x->{_n}); # swap
+ }
+ # correct sign; + ** + => +
+ if ($x->{sign} eq '-')
+ {
+ # - * - => +, - * - * - => -
+ $x->{sign} = '+' if $y->{_n}->is_even();
+ }
+ return $x->round(@r);
+ }
+
+ # regular calculation (this is wrong for d/e ** f/g)
my $pow2 = $self->__one();
- my $y1 = Math::BigInt->new($y->{_n}/$y->{_d})->babs();
- my $two = Math::BigInt->new(2);
+ my $y1 = $MBI->new($y->{_n}/$y->{_d})->babs();
+ my $two = $MBI->new(2);
while (!$y1->is_one())
{
- print "at $y1 (= $x)\n";
$pow2->bmul($x) if $y1->is_odd();
$y1->bdiv($two);
$x->bmul($x);
$x->bmul($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);
+ $x->bnorm()->round(@r);
}
sub blog
{
- return Math::BigRat->bnan();
+ # set up parameters
+ my ($self,$x,$y,@r) = (ref($_[0]),@_);
+
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,@r) = objectify(2,$class,@_);
+ }
+
+ # blog(1,Y) => 0
+ return $x->bzero() if $x->is_one() && $y->{sign} eq '+';
+
+ # $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));
+ }
+
+ # do it with floats
+ $x->_new_from_float( $x->_as_float()->blog(Math::BigFloat->new("$y"),@r) );
+ }
+
+sub _as_float
+ {
+ my $x = shift;
+
+ local $Math::BigFloat::upgrade = undef;
+ local $Math::BigFloat::accuracy = undef;
+ local $Math::BigFloat::precision = undef;
+ # 22/7 => 3.142857143..
+ Math::BigFloat->new($x->{_n})->bdiv($x->{_d}, $x->accuracy());
+ }
+
+sub broot
+ {
+ # set up parameters
+ my ($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));
+ }
+
+ # do it with floats
+ $x->_new_from_float( $x->_as_float()->broot($y,@r) );
+ }
+
+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");
+ $x->bnan();
}
sub bsqrt
{
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+ return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0
+ return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf
+ return $x->round(@r) if $x->is_zero() || $x->is_one();
+
+ local $Math::BigFloat::upgrade = undef;
+ local $Math::BigFloat::downgrade = undef;
+ local $Math::BigFloat::precision = undef;
+ local $Math::BigFloat::accuracy = undef;
+ local $Math::BigInt::upgrade = undef;
+ local $Math::BigInt::precision = undef;
+ local $Math::BigInt::accuracy = undef;
- return $x->bnan() if $x->{sign} ne '+'; # inf, NaN, -1 etc
- $x->{_d}->bsqrt($a,$p,$r);
- $x->{_n}->bsqrt($a,$p,$r);
- $x->bnorm();
+ $x->{_d} = Math::BigFloat->new($x->{_d})->bsqrt();
+ $x->{_n} = Math::BigFloat->new($x->{_n})->bsqrt();
+
+ # 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($x->{_d}->{_m})); # 7.1/45.1 => 71/45.1
+ }
+ # if sqrt(N) was not integer
+ if ($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
+ }
+
+ # 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);
+ $x->bnorm()->round(@r);
}
sub blsft
{
- my ($self,$x,$y,$b,$a,$p,$r) = objectify(3,@_);
+ my ($self,$x,$y,$b,@r) = objectify(3,@_);
- $x->bmul( $b->copy()->bpow($y), $a,$p,$r);
+ $b = 2 unless defined $b;
+ $b = $self->new($b) unless ref ($b);
+ $x->bmul( $b->copy()->bpow($y), @r);
$x;
}
sub brsft
{
- my ($self,$x,$y,$b,$a,$p,$r) = objectify(2,@_);
+ my ($self,$x,$y,$b,@r) = objectify(2,@_);
- $x->bdiv( $b->copy()->bpow($y), $a,$p,$r);
+ $b = 2 unless defined $b;
+ $b = $self->new($b) unless ref ($b);
+ $x->bdiv( $b->copy()->bpow($y), @r);
$x;
}
sub bcmp
{
- my ($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,$y) = objectify(2,$class,@_);
+ }
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} * $y->{_d};
##############################################################################
# output conversation
-sub as_number
+sub numify
{
+ # convert 17/8 => float (aka 2.125)
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, NaN, etc
- return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf etc
+ # N/1 => N
+ return $x->{_n}->numify() if $x->{_d}->is_one();
+
+ # N/D
+ my $neg = 1; $neg = -1 if $x->{sign} ne '+';
+ $neg * $x->{_n}->numify() / $x->{_d}->numify(); # return sign * N/D
+ }
+
+sub as_number
+ {
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return $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};
$t;
}
+sub as_bin
+ {
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return $x unless $x->is_int();
+
+ my $s = $x->{sign}; $s = '' if $s eq '+';
+ $s . $x->{_n}->as_bin();
+ }
+
+sub as_hex
+ {
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return $x unless $x->is_int();
+
+ my $s = $x->{sign}; $s = '' if $s eq '+';
+ $s . $x->{_n}->as_hex();
+ }
+
sub import
{
my $self = shift;
my $l = scalar @_;
my $lib = ''; my @a;
+ $IMPORT++;
+
for ( my $i = 0; $i < $l ; $i++)
{
# print "at $_[$i] (",$_[$i+1]||'undef',")\n";
push @a, $_[$i];
}
}
- # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work
+ # let use Math::BigInt lib => 'GMP'; use Math::BigRat; still work
my $mbilib = eval { Math::BigInt->config()->{lib} };
if ((defined $mbilib) && ($MBI eq 'Math::BigInt'))
{
}
else
{
- # MBI not loaded, or with ne "Math::BigInt"
+ # MBI not loaded, or not with "Math::BigInt"
$lib .= ",$mbilib" if defined $mbilib;
-# my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt
-# my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
-# $file = File::Spec->catfile (@parts, $file);
-
if ($] < 5.006)
{
# Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is
eval $rc;
}
}
- die ("Couldn't load $MBI: $! $@") if $@;
+ if ($@)
+ {
+ require Carp; Carp::croak ("Couldn't load $MBI: $! $@");
+ }
+ $CALC = Math::BigFloat->config()->{lib};
+
# any non :constant stuff is handled by our parent, Exporter
# even if @_ is empty, to give it a chance
$self->SUPER::import(@a); # for subclasses
=head1 NAME
-Math::BigRat - arbitrarily big rationals
+Math::BigRat - arbitrarily big rational numbers
=head1 SYNOPSIS
- use Math::BigRat;
+ use Math::BigRat;
+
+ my $x = Math::BigRat->new('3/7'); $x += '5/9';
+
+ print $x->bstr(),"\n";
+ print $x ** 2,"\n";
- $x = Math::BigRat->new('3/7');
+ my $y = Math::BigRat->new('inf');
+ print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\n";
- print $x->bstr(),"\n";
+ my $z = Math::BigRat->new(144); $z->bsqrt();
=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 rational numbers.
=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('inf'); # infinity
+ $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()
-Returns a copy of the object as BigInt by truncating it to integer.
+ $x = Math::BigRat->new('13/7');
+ print $x->as_number(),"\n"; # '1'
-=head2 bfac()/blog()
+Returns a copy of the object as BigInt trunced it to integer.
-Are not yet implemented.
+=head2 bfac()
+
+ $x->bfac();
+
+Calculates the factorial of $x. For instance:
+
+ print Math::BigRat->new('3/1')->bfac(),"\n"; # 1*2*3
+ print Math::BigRat->new('5/1')->bfac(),"\n"; # 1*2*3*4*5
+
+Works currently only for integers.
+
+=head2 blog()
+
+Is not yet implemented.
=head2 bround()/round()/bfround()
Are not yet implemented.
+=head2 bmod()
+
+ use Math::BigRat;
+ my $x = Math::BigRat->new('7/4');
+ my $y = Math::BigRat->new('4/3');
+ print $x->bmod($y);
+
+Set $x to the remainder of the division of $x by $y.
+
+=head2 is_one()
+
+ print "$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.
+
+=head2 bsqrt()
+
+ $x->bsqrt();
+
+Calculate the square root of $x.
+
+=head2 config
+
+ use Data::Dumper;
+
+ print Dumper ( Math::BigRat->config() );
+ print Math::BigRat->config()->{lib},"\n";
+
+Returns a hash containing the configuration, e.g. the version number, lib
+loaded etc. The following hash keys are currently filled in with the
+appropriate information.
+
+ key RO/RW Description
+ Example
+ ============================================================
+ lib RO Name of the Math library
+ Math::BigInt::Calc
+ lib_version RO Version of 'lib'
+ 0.30
+ class RO The class of config you just called
+ Math::BigRat
+ version RO version number of the class you used
+ 0.10
+ upgrade RW To which class numbers are upgraded
+ undef
+ downgrade RW To which class numbers are downgraded
+ undef
+ precision RW Global precision
+ undef
+ accuracy RW Global accuracy
+ undef
+ round_mode RW Global round mode
+ even
+ div_scale RW Fallback acccuracy for div
+ 40
+ trap_nan RW Trap creation of NaN (undef = no)
+ undef
+ trap_inf RW Trap creation of +inf/-inf (undef = no)
+ undef
+
+By passing a reference to a hash you may set the configuration values. This
+works only for values that a marked with a C<RW> above, anything else is
+read-only.
=head1 BUGS
+Some things are not yet implemented, or only implemented half-way:
+
=over 2
-=item perl -Mbigrat -le 'print 1 + 2/3'
+=item inf handling (partial)
-This produces wrongly NaN. It is unclear why. The following variants all work:
+=item NaN handling (partial)
- perl -Mbigrat -le 'print 1/3 + 2/3'
- perl -Mbigrat -le 'print 1/3 + 2'
+=item rounding (not implemented except for bceil/bfloor)
-This also does not work:
+=item $x ** $y where $y is not an integer
- perl -Mbigrat -le 'print 1+3+1/2'
+=item bmod(), blog(), bmodinv() and bmodpow() (partial)
=back
-Please see also L<Math::BigInt>.
-
=head1 LICENSE
This program is free software; you may redistribute it and/or modify it under
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
-(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 / blobdiff