# _a : accuracy
# _p : precision
-$VERSION = '1.47';
+$VERSION = '1.51';
require 5.005;
require Exporter;
$downgrade = undef;
# the package we are using for our private parts, defaults to:
# Math::BigInt->config()->{lib}
-my $MBI = 'Math::BigInt::Calc';
+my $MBI = 'Math::BigInt::FastCalc';
# are NaNs ok? (otherwise it dies when encountering an NaN) set w/ config()
$_trap_nan = 0;
# valid method aliases for AUTOLOAD
my %methods = map { $_ => 1 }
qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm
- fint facmp fcmp fzero fnan finf finc fdec flog ffac
+ fint facmp fcmp fzero fnan finf finc fdec flog ffac fneg
fceil ffloor frsft flsft fone flog froot
/;
# valid method's that can be hand-ed up (for AUTOLOAD)
my %hand_ups = map { $_ => 1 }
qw / is_nan is_inf is_negative is_positive is_pos is_neg
- accuracy precision div_scale round_mode fneg fabs fnot
+ accuracy precision div_scale round_mode fabs fnot
objectify upgrade downgrade
bone binf bnan bzero
/;
# else: got a string
# handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]?inf$/)
+ if ($wanted =~ /^[+-]?inf\z/)
{
return $downgrade->new($wanted) if $downgrade;
- $self->{_e} = $MBI->_zero();
- $self->{_es} = '+';
- $self->{_m} = $MBI->_zero();
- $self->{sign} = $wanted;
- $self->{sign} = '+inf' if $self->{sign} eq 'inf';
- return $self->bnorm();
+ $self->{sign} = $wanted; # set a default sign for bstr()
+ return $self->binf($wanted);
}
# shortcut for simple forms like '12' that neither have trailing nor leading
my $z = $MBI->_new($zeros);
# turn '120e2' into '12e3'
$MBI->_rsft ( $self->{_m}, $z, 10);
- _e_add ( $self->{_e}, $z, $self->{_es}, '+');
+ ($self->{_e}, $self->{_es}) =
+ _e_add ( $self->{_e}, $z, $self->{_es}, '+');
}
}
$self->{sign} = $$mis;
# for something like 0Ey, set y to 1, and -0 => +0
- # Check $$miv for beeing '0' and $$mfv eq '', because otherwise _m could not
+ # Check $$miv for being '0' and $$mfv eq '', because otherwise _m could not
# have become 0. That's faster than to call $MBI->_is_zero().
$self->{sign} = '+', $self->{_e} = $MBI->_one()
if $$miv eq '0' and $$mfv eq '';
# (ref to BFLOAT or num_str ) return num_str
# Convert number from internal format to (non-scientific) string format.
# internal format is always normalized (no leading zeros, "-0" => "+0")
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
if ($x->{sign} !~ /^[+-]$/)
{
# (ref to BFLOAT or num_str ) return num_str
# Convert number from internal format to scientific string format.
# internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
if ($x->{sign} !~ /^[+-]$/)
{
##############################################################################
# public stuff (usually prefixed with "b")
+sub bneg
+ {
+ # (BINT or num_str) return BINT
+ # negate number or make a negated number from string
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+ return $x if $x->modify('bneg');
+
+ # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN'
+ $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $MBI->_is_zero($x->{_m}));
+ $x;
+ }
+
# tels 2001-08-04
# XXX TODO this must be overwritten and return NaN for non-integer values
# band(), bior(), bxor(), too
my ($self,@arg) = objectify(0,@_);
my $x = $self->new(shift @arg);
- while (@arg) { $x = _lcm($x,shift @arg); }
+ while (@arg) { $x = Math::BigInt::__lcm($x,shift @arg); }
$x;
}
-sub bgcd
- {
- # (BFLOAT or num_str, BFLOAT or num_str) return BINT
+sub bgcd
+ {
+ # (BINT or num_str, BINT or num_str) return BINT
# does not modify arguments, but returns new object
- # GCD -- Euclids algorithm Knuth Vol 2 pg 296
-
- my ($self,@arg) = objectify(0,@_);
- my $x = $self->new(shift @arg);
- while (@arg) { $x = _gcd($x,shift @arg); }
+
+ my $y = shift;
+ $y = __PACKAGE__->new($y) if !ref($y);
+ my $self = ref($y);
+ my $x = $y->copy()->babs(); # keep arguments
+
+ return $x->bnan() if $x->{sign} !~ /^[+-]$/ # x NaN?
+ || !$x->is_int(); # only for integers now
+
+ while (@_)
+ {
+ my $t = shift; $t = $self->new($t) if !ref($t);
+ $y = $t->copy()->babs();
+
+ return $x->bnan() if $y->{sign} !~ /^[+-]$/ # y NaN?
+ || !$y->is_int(); # only for integers now
+
+ # greatest common divisor
+ while (! $y->is_zero())
+ {
+ ($x,$y) = ($y->copy(), $x->copy()->bmod($y));
+ }
+
+ last if $x->is_one();
+ }
$x;
}
$scale = $ly if $ly > $scale;
my $diff = $ly - $lx;
$scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx!
-
- # cases like $x /= $x (but not $x /= $y!) were wrong due to modifying $x
- # twice below)
- require Scalar::Util;
- if (Scalar::Util::refaddr($x) == Scalar::Util::refaddr($y))
+
+ # already handled inf/NaN/-inf above:
+
+ # check that $y is not 1 nor -1 and cache the result:
+ my $y_not_one = !($MBI->_is_zero($y->{_e}) && $MBI->_is_one($y->{_m}));
+
+ # flipping the sign of $y will also flip the sign of $x for the special
+ # case of $x->bsub($x); so we can catch it below:
+ my $xsign = $x->{sign};
+ $y->{sign} =~ tr/+-/-+/;
+
+ if ($xsign ne $x->{sign})
{
- $x->bone(); # x/x => 1, rem 0
+ # special case of $x /= $x results in 1
+ $x->bone(); # "fixes" also sign of $y, since $x is $y
}
else
{
-
+ # correct $y's sign again
+ $y->{sign} =~ tr/+-/-+/;
+ # continue with normal div code:
+
# make copy of $x in case of list context for later reminder calculation
- if (wantarray && !$y->is_one())
+ if (wantarray && $y_not_one)
{
$rem = $x->copy();
}
$x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+';
# check for / +-1 ( +/- 1E0)
- if (!$y->is_one())
+ if ($y_not_one)
{
# promote BigInts and it's subclasses (except when already a BigFloat)
$y = $self->new($y) unless $y->isa('Math::BigFloat');
if (wantarray)
{
- if (!$y->is_one())
+ if ($y_not_one)
{
$rem->bmod($y,@params); # copy already done
}
return $x->bnan() if $x->is_zero();
return $x;
}
- return $x->bzero() if $y->is_one() || $x->is_zero();
+
+ return $x->bzero() if $x->is_zero()
+ || ($x->is_int() &&
+ # check that $y == +1 or $y == -1:
+ ($MBI->_is_zero($y->{_e}) && $MBI->_is_one($y->{_m})));
my $cmp = $x->bacmp($y); # equal or $x < $y?
return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0
# expects and returns normalized numbers!
my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x);
- return $x if $x->modify('bfround');
-
- my ($scale,$mode) = $x->_scale_p($self->precision(),$self->round_mode(),@_);
- return $x if !defined $scale; # no-op
+ my ($scale,$mode) = $x->_scale_p(@_);
+ return $x if !defined $scale || $x->modify('bfround'); # no-op
# never round a 0, +-inf, NaN
if ($x->is_zero())
require Carp; Carp::croak ('bround() needs positive accuracy');
}
- my ($scale,$mode) = $x->_scale_a($self->accuracy(),$self->round_mode(),@_);
- return $x if !defined $scale; # no-op
-
- return $x if $x->modify('bround');
+ my ($scale,$mode) = $x->_scale_a(@_);
+ return $x if !defined $scale || $x->modify('bround'); # no-op
# scale is now either $x->{_a}, $accuracy, or the user parameter
# test whether $x already has lower accuracy, do nothing in this case
# but do round if the accuracy is the same, since a math operation might
# want to round a number with A=5 to 5 digits afterwards again
- return $x if defined $_[0] && defined $x->{_a} && $x->{_a} < $_[0];
+ return $x if defined $x->{_a} && $x->{_a} < $scale;
# scale < 0 makes no sense
+ # scale == 0 => keep all digits
# never round a +-inf, NaN
- return $x if ($scale < 0) || $x->{sign} !~ /^[+-]$/;
+ return $x if ($scale <= 0) || $x->{sign} !~ /^[+-]$/;
- # 1: $scale == 0 => keep all digits
- # 2: never round a 0
- # 3: if we should keep more digits than the mantissa has, do nothing
- if ($scale == 0 || $x->is_zero() || $MBI->_len($x->{_m}) <= $scale)
+ # 1: never round a 0
+ # 2: if we should keep more digits than the mantissa has, do nothing
+ if ($x->is_zero() || $MBI->_len($x->{_m}) <= $scale)
{
$x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale;
return $x;
}
}
+ $lib =~ tr/a-zA-Z0-9,://cd; # restrict to sane characters
# let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work
my $mbilib = eval { Math::BigInt->config()->{lib} };
if ((defined $mbilib) && ($MBI eq 'Math::BigInt::Calc'))
{
require Carp; Carp::croak ("Couldn't load $lib: $! $@");
}
+ # find out which one was actually loaded
$MBI = Math::BigInt->config()->{lib};
+ # register us with MBI to get notified of future lib changes
+ Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } );
+
# 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
# The following all modify their first argument. If you want to preserve
# $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is
- # neccessary when mixing $a = $b assigments with non-overloaded math.
+ # necessary when mixing $a = $b assignments with non-overloaded math.
# set
$x->bzero(); # set $i to 0
=head1 DESCRIPTION
-All operators (inlcuding basic math operations) are overloaded if you
+All operators (including basic math operations) are overloaded if you
declare your big floating point numbers as
$i = new Math::BigFloat '12_3.456_789_123_456_789E-2';
=back
-all with optional leading and trailing zeros and/or spaces. Additonally,
+all with optional leading and trailing zeros and/or spaces. Additionally,
numbers are allowed to have an underscore between any two digits.
Empty strings as well as other illegal numbers results in 'NaN'.
See also: L<Rounding|Rounding>.
-Math::BigFloat supports both precision and accuracy. For a full documentation,
-examples and tips on these topics please see the large section in
-L<Math::BigInt>.
+Math::BigFloat supports both precision (rounding to a certain place before or
+after the dot) and accuracy (rounding to a certain number of digits). For a
+full documentation, examples and tips on these topics please see the large
+section about rounding in L<Math::BigInt>.
-Since things like sqrt(2) or 1/3 must presented with a limited precision lest
-a operation consumes all resources, each operation produces no more than
-the requested number of digits.
+Since things like C<sqrt(2)> or C<1 / 3> must presented with a limited
+accuracy lest a operation consumes all resources, each operation produces
+no more than the requested number of digits.
-Please refer to BigInt's documentation for the precedence rules of which
-accuracy/precision setting will be used.
-
-If there is no gloabl precision set, B<and> the operation inquestion was not
-called with a requested precision or accuracy, B<and> the input $x has no
-accuracy or precision set, then a fallback parameter will be used. For
-historical reasons, it is called C<div_scale> and can be accessed via:
+If there is no gloabl precision or accuracy set, B<and> the operation in
+question was not called with a requested precision or accuracy, B<and> the
+input $x has no accuracy or precision set, then a fallback parameter will
+be used. For historical reasons, it is called C<div_scale> and can be accessed
+via:
$d = Math::BigFloat->div_scale(); # query
Math::BigFloat->div_scale($n); # set to $n digits
-The default value is 40 digits.
+The default value for C<div_scale> is 40.
-In case the result of one operation has more precision than specified,
+In case the result of one operation has more digits than specified,
it is rounded. The rounding mode taken is either the default mode, or the one
supplied to the operation after the I<scale>:
$x = Math::BigFloat->new(2);
- Math::BigFloat->precision(5); # 5 digits max
- $y = $x->copy()->bdiv(3); # will give 0.66666
- $y = $x->copy()->bdiv(3,6); # will give 0.666666
- $y = $x->copy()->bdiv(3,6,'odd'); # will give 0.666667
+ Math::BigFloat->accuracy(5); # 5 digits max
+ $y = $x->copy()->bdiv(3); # will give 0.66667
+ $y = $x->copy()->bdiv(3,6); # will give 0.666667
+ $y = $x->copy()->bdiv(3,6,undef,'odd'); # will give 0.666667
Math::BigFloat->round_mode('zero');
- $y = $x->copy()->bdiv(3,6); # will give 0.666666
+ $y = $x->copy()->bdiv(3,6); # will also give 0.666667
+
+Note that C<< Math::BigFloat->accuracy() >> and C<< Math::BigFloat->precision() >>
+set the global variables, and thus B<any> newly created number will be subject
+to the global rounding B<immediately>. This means that in the examples above, the
+C<3> as argument to C<bdiv()> will also get an accuracy of B<5>.
+
+It is less confusing to either calculate the result fully, and afterwards
+round it explicitly, or use the additional parameters to the math
+functions like so:
+
+ use Math::BigFloat;
+ $x = Math::BigFloat->new(2);
+ $y = $x->copy()->bdiv(3);
+ print $y->bround(5),"\n"; # will give 0.66667
+
+ or
+
+ use Math::BigFloat;
+ $x = Math::BigFloat->new(2);
+ $y = $x->copy()->bdiv(3,5); # will give 0.66667
+ print "$y\n";
=head2 Rounding
$x = Math::BigFloat->new(2.5);
$y = $x->as_number('odd'); # $y = 3
-=head1 EXAMPLES
-
- # not ready yet
+=head1 METHODS
+
+=head2 accuracy
+
+ $x->accuracy(5); # local for $x
+ CLASS->accuracy(5); # global for all members of CLASS
+ # Note: This also applies to new()!
+
+ $A = $x->accuracy(); # read out accuracy that affects $x
+ $A = CLASS->accuracy(); # read out global accuracy
+
+Set or get the global or local accuracy, aka how many significant digits the
+results have. If you set a global accuracy, then this also applies to new()!
+
+Warning! The accuracy I<sticks>, e.g. once you created a number under the
+influence of C<< CLASS->accuracy($A) >>, all results from math operations with
+that number will also be rounded.
+
+In most cases, you should probably round the results explicitly using one of
+L<round()>, L<bround()> or L<bfround()> or by passing the desired accuracy
+to the math operation as additional parameter:
+
+ my $x = Math::BigInt->new(30000);
+ my $y = Math::BigInt->new(7);
+ print scalar $x->copy()->bdiv($y, 2); # print 4300
+ print scalar $x->copy()->bdiv($y)->bround(2); # print 4300
+
+=head2 precision()
+
+ $x->precision(-2); # local for $x, round at the second digit right of the dot
+ $x->precision(2); # ditto, round at the second digit left of the dot
+
+ CLASS->precision(5); # Global for all members of CLASS
+ # This also applies to new()!
+ CLASS->precision(-5); # ditto
+
+ $P = CLASS->precision(); # read out global precision
+ $P = $x->precision(); # read out precision that affects $x
+
+Note: You probably want to use L<accuracy()> instead. With L<accuracy> you
+set the number of digits each result should have, with L<precision> you
+set the place where to round!
=head1 Autocreating constants
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
+(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
require Math::BigFloat;
-This will load the neccessary things (like BigInt) when they are needed, and
+This will load the necessary things (like BigInt) when they are needed, and
automatically.
Use the lib, Luke! And see L<Using Math::BigInt::Lite> for more details than
don't specify it onem but if you specify one, it will try to load them.
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
+"Foo,Bar,Baz,Calc", but independent of which lib exists, the result is the
same as trying the latter load alone, except for the fact that one of Bar or
-Baz might be loaded needlessly in an intermidiate step (and thus hang around
+Baz might be loaded needlessly in an intermediate step (and thus hang around
and waste memory). If neither Bar nor Baz exist (or don't work/compile), they
will still be tried to be loaded, but this is not as time/memory consuming as
actually loading one of them. Still, this type of usage is not recommended due
print $c->bdiv(123.456),"\n";
It prints both quotient and reminder since print works in list context. Also,
-bdiv() will modify $c, so be carefull. You probably want to use
+bdiv() will modify $c, so be careful. You probably want to use
print $c / 123.456,"\n";
print scalar $c->bdiv(123.456),"\n"; # or if you want to modify $c
print $x->bpow($i),"\n"; # ditto
print $x ** $i,"\n"; # leave $x alone
+=item precision() vs. accuracy()
+
+A common pitfall is to use L<precision()> when you want to round a result to
+a certain number of digits:
+
+ use Math::BigFloat;
+
+ Math::BigFloat->precision(4); # does not do what you think it does
+ my $x = Math::BigFloat->new(12345); # rounds $x to "12000"!
+ print "$x\n"; # print "12000"
+ my $y = Math::BigFloat->new(3); # rounds $y to "0"!
+ print "$y\n"; # print "0"
+ $z = $x / $y; # 12000 / 0 => NaN!
+ print "$z\n";
+ print $z->precision(),"\n"; # 4
+
+Replacing L<precision> with L<accuracy> is probably not what you want, either:
+
+ use Math::BigFloat;
+
+ Math::BigFloat->accuracy(4); # enables global rounding:
+ my $x = Math::BigFloat->new(123456); # rounded immediately to "12350"
+ print "$x\n"; # print "123500"
+ my $y = Math::BigFloat->new(3); # rounded to "3
+ print "$y\n"; # print "3"
+ print $z = $x->copy()->bdiv($y),"\n"; # 41170
+ print $z->accuracy(),"\n"; # 4
+
+What you want to use instead is:
+
+ use Math::BigFloat;
+
+ my $x = Math::BigFloat->new(123456); # no rounding
+ print "$x\n"; # print "123456"
+ my $y = Math::BigFloat->new(3); # no rounding
+ print "$y\n"; # print "3"
+ print $z = $x->copy()->bdiv($y,4),"\n"; # 41150
+ print $z->accuracy(),"\n"; # undef
+
+In addition to computing what you expected, the last example also does B<not>
+"taint" the result with an accuracy or precision setting, which would
+influence any further operation.
+
=back
=head1 SEE ALSO
=head1 AUTHORS
Mark Biggar, overloaded interface by Ilya Zakharevich.
-Completely rewritten by Tels http://bloodgate.com in 2001, 2002, and still
-at it in 2003.
+Completely rewritten by Tels L<http://bloodgate.com> in 2001 - 2004, and still
+at it in 2005.
=cut
projects / p5sagit/p5-mst-13.2.git / blobdiff