# _n : numeraotr (value = _n/_d)
# _a : accuracy
# _p : precision
-# _f : flags, used by MBR to flag parts of a rationale as untouchable
+# _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 $div_scale);
+use vars qw($VERSION @ISA $PACKAGE $upgrade $downgrade
+ $accuracy $precision $round_mode $div_scale $_trap_nan $_trap_inf);
@ISA = qw(Exporter Math::BigFloat);
-@EXPORT_OK = qw();
-$VERSION = '0.09';
+$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 $IMPORT = 0;
sub isa
{
UNIVERSAL::isa(@_);
}
+sub BEGIN
+ {
+ *AUTOLOAD = \&Math::BigFloat::AUTOLOAD;
+ }
+
sub _new_from_float
{
- # turn a single float input into a rationale (like '0.1')
+ # turn a single float input into a rational number (like '0.1')
my ($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 $f->{sign} =~ /^[+-]inf$/;
- $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});
}
$self;
}
{
if ($n->isa('Math::BigFloat'))
{
- 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'))
{
- $self->{_n} = $MBI->new($$n,undef,undef); # "mantissa" = $n
+ # TODO: trap NaN, inf
+ $self->{sign} = '+'; $self->{sign} = '-' if $$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 $n;
# string input with / delimiter
if ($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]/))
local $Math::BigFloat::precision = undef;
local $Math::BigInt::accuracy = undef;
local $Math::BigInt::precision = undef;
- $self->_new_from_float(Math::BigFloat->new($n));
+
+ 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,undef,undef);
- if ($f->{_e}->{sign} eq '-')
+ 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
{
# 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
+ $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();
}
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}->{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;
}
- 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() . '/' . $x->{_d}->bstr();
}
sub bnorm
# don't reduce again)
my ($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;
+ 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 _bnan
{
- # used by parent class bone() to initialize number to 1
+ # used by parent class bnan() to initialize number to NaN
my $self = shift;
+
+ if ($_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();
}
{
# used by parent class bone() to initialize number to +inf/-inf
my $self = shift;
+
+ if ($_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 _bzero
{
- # used by parent class bone() to initialize number to 0
+ # used by parent class bzero() to initialize number to 0
my $self = shift;
$self->{_n} = $MBI->bzero();
$self->{_d} = $MBI->bone();
sub badd
{
- # add two rationales
+ # add two rational numbers
# set up parameters
my ($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} = '+';
$x->bnorm()->round(@r);
sub bsub
{
- # subtract two rationales
+ # subtract two rational numbers
# set up parameters
my ($self,$x,$y,@r) = (ref($_[0]),@_);
($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
- # - - - = --------- = --
- # 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
+ $x;
}
sub bmul
{
- # multiply two rationales
+ # multiply two rational numbers
# set up parameters
my ($self,$x,$y,@r) = (ref($_[0]),@_);
($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' || $y->{sign} eq 'NaN');
($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 $self->_div_inf($x,$y)
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
# - / - == - * -
# 4 3 4 1
-# local $Math::BigInt::accuracy = undef;
-# local $Math::BigInt::precision = undef;
+ local $Math::BigInt::accuracy = undef;
+ local $Math::BigInt::precision = undef;
$x->{_n}->bmul($y->{_d});
$x->{_d}->bmul($y->{_n});
$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
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
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)
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
$x->{_d}->is_one(); # x/y && y != 1 => no integer
sub is_zero
{
# return true if arg (BRAT or num_str) is zero
- my ($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 ($x->{_d}->is_one() # x/3 is never
0;
}
-BEGIN
- {
- *objectify = \&Math::BigInt::objectify;
- }
-
##############################################################################
# parts() and friends
sub length
{
- return 0;
+ my ($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
+ 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
return $x unless $x->{sign} =~ /^[+-]$/;
return $x if $x->{_d}->is_one(); # 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 $x->{sign} eq '-'; # -22/7 => -4/1
{
my ($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,$y,@r) = objectify(2,$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};
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();
+ # 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]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- return $x if $x->{sign} !~ /^[+-]$/; # NaN, inf etc
+ 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'))
{
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 rationales
+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 rationales.
+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
$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.
+Returns a copy of the object as BigInt trunced it to integer.
=head2 bfac()
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();
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:
=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 / blobdiff