# _p: precision
# _f: flags, used to signal MBI not to touch our private parts
-$VERSION = '1.30';
+$VERSION = '1.31';
require 5.005;
use Exporter;
-use Math::BigInt qw/objectify/;
+use File::Spec;
+# use Math::BigInt;
@ISA = qw( Exporter Math::BigInt);
use strict;
use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/;
-use vars qw/$upgrade $downgrade/;
+use vars qw/$upgrade $downgrade $MBI/;
my $class = "Math::BigFloat";
use overload
$upgrade = undef;
$downgrade = undef;
+$MBI = 'Math::BigInt'; # the package we are using for our private parts
+ # changable by use Math::BigFloat with => 'package'
##############################################################################
# the old code had $rnd_mode, so we need to support it, too
-$rnd_mode = 'even';
sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; }
sub FETCH { return $round_mode; }
sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); }
-BEGIN { tie $rnd_mode, 'Math::BigFloat'; }
+BEGIN
+ {
+ $rnd_mode = 'even';
+ tie $rnd_mode, 'Math::BigFloat';
+ }
##############################################################################
if ((ref($wanted)) && (ref($wanted) ne $class))
{
$self->{_m} = $wanted->as_number(); # get us a bigint copy
- $self->{_e} = Math::BigInt->bzero();
+ $self->{_e} = $MBI->bzero();
$self->{_m}->babs();
$self->{sign} = $wanted->sign();
return $self->bnorm();
{
return $downgrade->new($wanted) if $downgrade;
- $self->{_e} = Math::BigInt->bzero();
- $self->{_m} = Math::BigInt->bzero();
+ $self->{_e} = $MBI->bzero();
+ $self->{_m} = $MBI->bzero();
$self->{sign} = $wanted;
$self->{sign} = '+inf' if $self->{sign} eq 'inf';
return $self->bnorm();
return $downgrade->bnan() if $downgrade;
- $self->{_e} = Math::BigInt->bzero();
- $self->{_m} = Math::BigInt->bzero();
+ $self->{_e} = $MBI->bzero();
+ $self->{_m} = $MBI->bzero();
$self->{sign} = $nan;
}
else
{
# make integer from mantissa by adjusting exp, then convert to bigint
# undef,undef to signal MBI that we don't need no bloody rounding
- $self->{_e} = Math::BigInt->new("$$es$$ev",undef,undef); # exponent
- $self->{_m} = Math::BigInt->new("$$miv$$mfv",undef,undef); # create mant.
+ $self->{_e} = $MBI->new("$$es$$ev",undef,undef); # exponent
+ $self->{_m} = $MBI->new("$$miv$$mfv",undef,undef); # create mant.
# 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5
$self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0;
$self->{sign} = $$mis;
{
# used by parent class bone() to initialize number to 1
my $self = shift;
- $self->{_m} = Math::BigInt->bzero();
- $self->{_e} = Math::BigInt->bzero();
+ $self->{_m} = $MBI->bzero();
+ $self->{_e} = $MBI->bzero();
}
sub _binf
{
# used by parent class bone() to initialize number to 1
my $self = shift;
- $self->{_m} = Math::BigInt->bzero();
- $self->{_e} = Math::BigInt->bzero();
+ $self->{_m} = $MBI->bzero();
+ $self->{_e} = $MBI->bzero();
}
sub _bone
{
# used by parent class bone() to initialize number to 1
my $self = shift;
- $self->{_m} = Math::BigInt->bone();
- $self->{_e} = Math::BigInt->bzero();
+ $self->{_m} = $MBI->bone();
+ $self->{_e} = $MBI->bzero();
}
sub _bzero
{
# used by parent class bone() to initialize number to 1
my $self = shift;
- $self->{_m} = Math::BigInt->bzero();
- $self->{_e} = Math::BigInt->bone();
+ $self->{_m} = $MBI->bzero();
+ $self->{_e} = $MBI->bone();
}
sub isa
{
my ($self,$class) = @_;
- return if $class eq 'Math::BigInt'; # we aren't
- return UNIVERSAL::isa($self,$class);
+ return if $class =~ /^Math::BigInt/; # we aren't one of these
+ UNIVERSAL::isa($self,$class);
}
##############################################################################
my $zeros = -$x->{_p} + $cad;
$es .= $dot.'0' x $zeros if $zeros > 0;
}
- return $es;
+ $es;
}
sub bsstr
}
my $sign = $x->{_e}->{sign}; $sign = '' if $sign eq '-';
my $sep = 'e'.$sign;
- return $x->{_m}->bstr().$sep.$x->{_e}->bstr();
+ $x->{_m}->bstr().$sep.$x->{_e}->bstr();
}
sub numify
# Make a number from a BigFloat object
# simple return string and let Perl's atoi()/atof() handle the rest
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- return $x->bsstr();
+ $x->bsstr();
}
##############################################################################
return $x if $x->{sign} eq $y->{sign};
return $x->bnan();
}
- # +-inf + something => +inf
- # something +-inf => +-inf
+ # +-inf + something => +inf; something +-inf => +-inf
$x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
return $x;
}
# take lower of the two e's and adapt m1 to it to match m2
my $e = $y->{_e};
- $e = Math::BigInt::bzero() if !defined $e; # if no BFLOAT ?
- $e = $e->copy(); # make copy (didn't do it yet)
+ $e = $MBI->bzero() if !defined $e; # if no BFLOAT ?
+ $e = $e->copy(); # make copy (didn't do it yet)
$e->bsub($x->{_e});
my $add = $y->{_m}->copy();
-# if ($e < 0) # < 0
if ($e->{sign} eq '-') # < 0
{
my $e1 = $e->copy()->babs();
$x->{_m}->blsft($e1,10);
$x->{_e} += $e; # need the sign of e
}
-# if ($e > 0) # > 0
elsif (!$e->is_zero()) # > 0
{
#$add *= (10 ** $e);
{
$x->{_m}->blsft($x->{_e},10);
}
- $x->{_e} = Math::BigInt->bzero() unless $x->{_e}->is_zero();
+ $x->{_e} = $MBI->bzero() unless $x->{_e}->is_zero();
$x->{_e}->bsub($shiftx) if $shiftx != 0;
$x->{_e}->bsub($shifty) if $shifty != 0;
# now mantissas are equalized, exponent of $x is adjusted, so calc result
-# $ym->{sign} = '-' if $neg; # bmod() will make the correction for us
$x->{_m}->bmod($ym);
&& ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head?
{
# exact result
- $x->{_m} = $gs; $x->{_e} = Math::BigInt->bzero(); $x->bnorm();
+ $x->{_m} = $gs; $x->{_e} = $MBI->bzero(); $x->bnorm();
# shortcut to not run trough _find_round_parameters again
if (defined $params[1])
{
$x->bnorm()->round(@r);
}
+sub _pow2
+ {
+ # Calculate a power where $y is a non-integer, like 2 ** 0.5
+ my ($x,$y,$a,$p,$r) = @_;
+ my $self = ref($x);
+
+ # we need to limit the accuracy to protect against overflow
+ my $fallback = 0;
+ my $scale = 0;
+ my @params = $x->_find_round_parameters($a,$p,$r);
+
+ # no rounding at all, so must use fallback
+ if (scalar @params == 1)
+ {
+ # simulate old behaviour
+ $params[1] = $self->div_scale(); # and round to it as accuracy
+ $scale = $params[1]+4; # at least four more for proper round
+ $params[3] = $r; # round mode by caller or undef
+ $fallback = 1; # to clear a/p afterwards
+ }
+ else
+ {
+ # the 4 below is empirical, and there might be cases where it is not
+ # enough...
+ $scale = abs($params[1] || $params[2]) + 4; # take whatever is defined
+ }
+
+ # when user set globals, they would interfere with our calculation, so
+ # disable then and later re-enable them
+ no strict 'refs';
+ my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+ my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+ # we also need to disable any set A or P on $x (_find_round_parameters took
+ # them already into account), since these would interfere, too
+ delete $x->{_a}; delete $x->{_p};
+ # need to disable $upgrade in BigInt, to avoid deep recursion
+ local $Math::BigInt::upgrade = undef;
+
+ # split the second argument into its integer and fraction part
+ # we calculate the result then from these two parts, like in
+ # 2 ** 2.4 == (2 ** 2) * (2 ** 0.4)
+ my $c = $self->new($y->as_number()); # integer part
+ my $d = $y-$c; # fractional part
+ my $xc = $x->copy(); # a temp. copy
+
+ # now calculate binary fraction from the decimal fraction on the fly
+ # f.i. 0.654:
+ # 0.654 * 2 = 1.308 > 1 => 0.1 ( 1.308 - 1 = 0.308)
+ # 0.308 * 2 = 0.616 < 1 => 0.10
+ # 0.616 * 2 = 1.232 > 1 => 0.101 ( 1.232 - 1 = 0.232)
+ # and so on...
+ # The process stops when the result is exactly one, or when we have
+ # enough accuracy
+
+ # From the binary fraction we calculate the result as follows:
+ # we assume the fraction ends in 1, and we remove this one first.
+ # For each digit after the dot, assume 1 eq R and 0 eq XR, where R means
+ # take square root and X multiply with the original X.
+
+ my $i = 0;
+ while ($i++ < 50)
+ {
+ $d->badd($d); # * 2
+ last if $d->is_one(); # == 1
+ $x->bsqrt(); # 0
+ if ($d > 1)
+ {
+ $x->bsqrt(); $x->bmul($xc); $d->bdec(); # 1
+ }
+ print "at $x\n";
+ }
+ # assume fraction ends in 1
+ $x->bsqrt(); # 1
+ if (!$c->is_one())
+ {
+ $x->bmul( $xc->bpow($c) );
+ }
+ elsif (!$c->is_zero())
+ {
+ $x->bmul( $xc );
+ }
+ # done
+
+ # shortcut to not run trough _find_round_parameters again
+ if (defined $params[1])
+ {
+ $x->bround($params[1],$params[3]); # then round accordingly
+ }
+ else
+ {
+ $x->bfround($params[2],$params[3]); # then round accordingly
+ }
+ if ($fallback)
+ {
+ # clear a/p after round, since user did not request it
+ $x->{_a} = undef; $x->{_p} = undef;
+ }
+ # restore globals
+ $$abr = $ab; $$pbr = $pb;
+ $x;
+ }
+
sub _pow
{
# Calculate a power where $y is a non-integer, like 2 ** 0.5
return $x->bone() if $y->is_zero();
return $x if $x->is_one() || $y->is_one();
- return $x->_pow($y,$a,$p,$r) if !$y->is_int(); # non-integer power
+ return $x->_pow2($y,$a,$p,$r) if !$y->is_int(); # non-integer power
my $y1 = $y->as_number(); # make bigint
# if ($x == -1)
}
# try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx()
$name =~ s/^f/b/;
- return &{'Math::BigInt'."::$name"}(@_);
+ return &{"$MBI"."::$name"}(@_);
}
my $bname = $name; $bname =~ s/^f/b/;
*{$class."::$name"} = \&$bname;
{
my $self = shift;
my $l = scalar @_; my $j = 0; my @a = @_;
+ my $lib = '';
for ( my $i = 0; $i < $l ; $i++, $j++)
{
if ( $_[$i] eq ':constant' )
my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
splice @a, $j, $s; $j -= $s;
}
+ elsif ($_[$i] eq 'lib')
+ {
+ $lib = $_[$i+1] || ''; # default Calc
+ my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
+ splice @a, $j, $s; $j -= $s;
+ }
+ elsif ($_[$i] eq 'with')
+ {
+ $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt
+ my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
+ splice @a, $j, $s; $j -= $s;
+ }
}
+ my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt
+ my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
+ $file = File::Spec->catdir (@parts, $file);
+ # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work
+ my $mbilib = eval { Math::BigInt->config()->{lib} };
+ $lib .= ",$mbilib" if defined $mbilib;
+ require $file;
+ $MBI->import ( lib => $lib, 'objectify' );
+
# 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
$len += $x->{_e} if $x->{_e}->sign() eq '+';
if (wantarray())
{
- my $t = Math::BigInt::bzero();
+ my $t = $MBI->bzero();
$t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-';
return ($len,$t);
}
perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"'
-prints the value of C<2E-100>. Note that without conversion of
+prints the value of C<2E-100>. Note that without conversion of
constants the expression 2E-100 will be calculated as normal floating point
number.
+Please note that ':constant' does not affect integer constants, nor binary
+nor hexadecimal constants. Use L<bignum> or L<Math::BigInt> to get this to
+work.
+
+=head2 Math library
+
+Math with the numbers is done (by default) by a module called
+Math::BigInt::Calc. This is equivalent to saying:
+
+ use Math::BigFloat lib => 'Calc';
+
+You can change this by using:
+
+ use Math::BigFloat lib => 'BitVect';
+
+The following would first try to find Math::BigInt::Foo, then
+Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
+
+ use Math::BigFloat 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
+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.
+
+Please note that Math::BigFloat does B<not> use the denoted library itself,
+but it merely passes the lib argument to Math::BigInt. So, instead of the need
+to do:
+
+ use Math::BigInt lib => 'GMP';
+ use Math::BigFloat;
+
+you can roll it all into one line:
+
+ use Math::BigFloat lib => 'GMP';
+
+Use the lib, Luke! And see L<Using Math::BigInt::Lite> for more details.
+
+=head2 Using Math::BigInt::Lite
+
+It is possible to use L<Math::BigInt::Lite> with Math::BigFloat:
+
+ # 1
+ use Math::BigFloat with => 'Math::BigInt::Lite';
+
+There is no need to "use Math::BigInt" or "use Math::BigInt::Lite", but you
+can combine these if you want. For instance, you may want to use
+Math::BigInt objects in your main script, too.
+
+ # 2
+ use Math::BigInt;
+ use Math::BigFloat with => 'Math::BigInt::Lite';
+
+Of course, you can combine this with the C<lib> parameter.
+
+ # 3
+ use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';
+
+If you want to use Math::BigInt's, too, simple add a Math::BigInt B<before>:
+
+ # 4
+ use Math::BigInt;
+ use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';
+
+Notice that the module with the last C<lib> will "win" and thus
+it's lib will be used if the lib is available:
+
+ # 5
+ use Math::BigInt lib => 'Bar,Baz';
+ use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo';
+
+That would try to load Foo, Bar, Baz and Calc (in that order). Or in other
+words, Math::BigFloat will try to retain previously loaded libs when you
+don't specify it one.
+
+Actually, the lib loading order would be "Bar,Baz,Calc", and then
+"Foo,Bar,Baz,Calc", but independend of which lib exists, the result is the
+same as trying the latter load alone, except for the fact that Bar or Baz
+might be loaded needlessly in an intermidiate step
+
+The old way still works though:
+
+ # 6
+ use Math::BigInt lib => 'Bar,Baz';
+ use Math::BigFloat;
+
+But B<examples #3 and #4 are recommended> for usage.
+
=head1 BUGS
=over 2
projects / p5sagit/p5-mst-13.2.git / blobdiff