#
# The following hash values are internally used:
-# _e: exponent (BigInt)
-# _m: mantissa (absolute BigInt)
-# sign: +,-,+inf,-inf, or "NaN" if not a number
-# _a: accuracy
-# _p: precision
-# _f: flags, used to signal MBI not to touch our private parts
-
-$VERSION = '1.41';
+# _e : exponent (ref to $CALC object)
+# _m : mantissa (ref to $CALC object)
+# _es : sign of _e
+# sign : +,-,+inf,-inf, or "NaN" if not a number
+# _a : accuracy
+# _p : precision
+
+$VERSION = '1.51';
require 5.005;
-use Exporter;
+
+require Exporter;
@ISA = qw(Exporter Math::BigInt);
use strict;
-use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/;
-use vars qw/$upgrade $downgrade/;
-# the following are internal and should never be accessed from the outside
-use vars qw/$_trap_nan $_trap_inf/;
+# $_trap_inf/$_trap_nan are internal and should never be accessed from outside
+use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode
+ $upgrade $downgrade $_trap_nan $_trap_inf/;
my $class = "Math::BigFloat";
use overload
$upgrade = undef;
$downgrade = undef;
-my $MBI = 'Math::BigInt'; # the package we are using for our private parts
- # changable by use Math::BigFloat with => 'package'
-
-# the following are private and not to be used from the outside:
-
-use constant MB_NEVER_ROUND => 0x0001;
+# the package we are using for our private parts, defaults to:
+# Math::BigInt->config()->{lib}
+my $MBI = 'Math::BigInt::FastCalc';
# are NaNs ok? (otherwise it dies when encountering an NaN) set w/ config()
$_trap_nan = 0;
-# the same for infs
+# the same for infinity
$_trap_inf = 0;
# constant for easier life
my $nan = 'NaN';
-my $IMPORT = 0; # was import() called yet?
- # used to make require work
+my $IMPORT = 0; # was import() called yet? used to make require work
# some digits of accuracy for blog(undef,10); which we use in blog() for speed
my $LOG_10 =
my $LOG_2 =
'0.6931471805599453094172321214581765680755001343602552541206800094933936220';
my $LOG_2_A = length($LOG_2)-1;
+my $HALF = '0.5'; # made into an object if necc.
##############################################################################
# the old code had $rnd_mode, so we need to support it, too
##############################################################################
-# in case we call SUPER::->foo() and this wants to call modify()
-# sub modify () { 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
- accuracy precision div_scale round_mode fneg fabs fnot
+ qw / is_nan is_inf is_negative is_positive is_pos is_neg
+ accuracy precision div_scale round_mode fabs fnot
objectify upgrade downgrade
bone binf bnan bzero
/;
- sub method_alias { return exists $methods{$_[0]||''}; }
- sub method_hand_up { return exists $hand_ups{$_[0]||''}; }
+ sub method_alias { exists $methods{$_[0]||''}; }
+ sub method_hand_up { exists $hand_ups{$_[0]||''}; }
}
##############################################################################
# shortcut for bigints and its subclasses
if ((ref($wanted)) && (ref($wanted) ne $class))
{
- $self->{_m} = $wanted->as_number(); # get us a bigint copy
- $self->{_e} = $MBI->bzero();
- $self->{_m}->babs();
+ $self->{_m} = $wanted->as_number()->{value}; # get us a bigint copy
+ $self->{_e} = $MBI->_zero();
+ $self->{_es} = '+';
$self->{sign} = $wanted->sign();
return $self->bnorm();
}
- # got string
+ # else: got a string
+
# handle '+inf', '-inf' first
- if ($wanted =~ /^[+-]?inf$/)
+ if ($wanted =~ /^[+-]?inf\z/)
{
return $downgrade->new($wanted) if $downgrade;
- $self->{_e} = $MBI->bzero();
- $self->{_m} = $MBI->bzero();
- $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
+ # zeros
+ if ($wanted =~ /^([+-]?)([1-9][0-9]*[1-9])$/)
+ {
+ $self->{_e} = $MBI->_zero();
+ $self->{_es} = '+';
+ $self->{sign} = $1 || '+';
+ $self->{_m} = $MBI->_new($2);
+ return $self->round(@r) if !$downgrade;
}
- #print "new string '$wanted'\n";
- my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted);
+
+ my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split($wanted);
if (!ref $mis)
{
if ($_trap_nan)
return $downgrade->bnan() if $downgrade;
- $self->{_e} = $MBI->bzero();
- $self->{_m} = $MBI->bzero();
+ $self->{_e} = $MBI->_zero();
+ $self->{_es} = '+';
+ $self->{_m} = $MBI->_zero();
$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} = $MBI->new("$$es$$ev",undef,undef); # exponent
- $self->{_m} = $MBI->new("$$miv$$mfv",undef,undef); # create mant.
+ # make integer from mantissa by adjusting exp, then convert to int
+ $self->{_e} = $MBI->_new($$ev); # exponent
+ $self->{_es} = $$es || '+';
+ my $mantissa = "$$miv$$mfv"; # create mant.
+ $mantissa =~ s/^0+(\d)/$1/; # strip leading zeros
+ $self->{_m} = $MBI->_new($mantissa); # create mant.
+
# 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5
- $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0;
+ if (CORE::length($$mfv) != 0)
+ {
+ my $len = $MBI->_new( CORE::length($$mfv));
+ ($self->{_e}, $self->{_es}) =
+ _e_sub ($self->{_e}, $len, $self->{_es}, '+');
+ }
+ # we can only have trailing zeros on the mantissa if $$mfv eq ''
+ else
+ {
+ # Use a regexp to count the trailing zeros in $$miv instead of _zeros()
+ # because that is faster, especially when _m is not stored in base 10.
+ my $zeros = 0; $zeros = CORE::length($1) if $$miv =~ /[1-9](0*)$/;
+ if ($zeros != 0)
+ {
+ my $z = $MBI->_new($zeros);
+ # turn '120e2' into '12e3'
+ $MBI->_rsft ( $self->{_m}, $z, 10);
+ ($self->{_e}, $self->{_es}) =
+ _e_add ( $self->{_e}, $z, $self->{_es}, '+');
+ }
+ }
$self->{sign} = $$mis;
+
+ # for something like 0Ey, set y to 1, and -0 => +0
+ # Check $$miv for being '0' and $$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 '';
+
+ return $self->round(@r) if !$downgrade;
}
# if downgrade, inf, NaN or integers go down
- if ($downgrade && $self->{_e}->{sign} eq '+')
+ if ($downgrade && $self->{_es} eq '+')
{
- #print "downgrading $$miv$$mfv"."E$$es$$ev";
- if ($self->{_e}->is_zero())
+ if ($MBI->_is_zero( $self->{_e} ))
{
- $self->{_m}->{sign} = $$mis; # negative if wanted
- return $downgrade->new($self->{_m});
+ return $downgrade->new($$mis . $MBI->_str( $self->{_m} ));
}
- return $downgrade->new("$$mis$$miv$$mfv"."E$$es$$ev");
+ return $downgrade->new($self->bsstr());
}
- #print "mbf new $self->{sign} $self->{_m} e $self->{_e} ",ref($self),"\n";
$self->bnorm()->round(@r); # first normalize, then round
}
+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->{_es} = $x->{_es};
+ $self->{_m} = $MBI->_copy($x->{_m});
+ $self->{_e} = $MBI->_copy($x->{_e});
+ $self->{_a} = $x->{_a} if defined $x->{_a};
+ $self->{_p} = $x->{_p} if defined $x->{_p};
+ $self;
+ }
+
sub _bnan
{
# used by parent class bone() to initialize number to NaN
}
$IMPORT=1; # call our import only once
- $self->{_m} = $MBI->bzero();
- $self->{_e} = $MBI->bzero();
+ $self->{_m} = $MBI->_zero();
+ $self->{_e} = $MBI->_zero();
+ $self->{_es} = '+';
}
sub _binf
}
$IMPORT=1; # call our import only once
- $self->{_m} = $MBI->bzero();
- $self->{_e} = $MBI->bzero();
+ $self->{_m} = $MBI->_zero();
+ $self->{_e} = $MBI->_zero();
+ $self->{_es} = '+';
}
sub _bone
# used by parent class bone() to initialize number to 1
my $self = shift;
$IMPORT=1; # call our import only once
- $self->{_m} = $MBI->bone();
- $self->{_e} = $MBI->bzero();
+ $self->{_m} = $MBI->_one();
+ $self->{_e} = $MBI->_zero();
+ $self->{_es} = '+';
}
sub _bzero
# used by parent class bone() to initialize number to 0
my $self = shift;
$IMPORT=1; # call our import only once
- $self->{_m} = $MBI->bzero();
- $self->{_e} = $MBI->bone();
+ $self->{_m} = $MBI->_zero();
+ $self->{_e} = $MBI->_one();
+ $self->{_es} = '+';
}
sub isa
# (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} !~ /^[+-]$/)
{
my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.';
# $x is zero?
- my $not_zero = !($x->{sign} eq '+' && $x->{_m}->is_zero());
+ my $not_zero = !($x->{sign} eq '+' && $MBI->_is_zero($x->{_m}));
if ($not_zero)
{
- $es = $x->{_m}->bstr();
+ $es = $MBI->_str($x->{_m});
$len = CORE::length($es);
- my $e = $x->{_e}->numify();
+ my $e = $MBI->_num($x->{_e});
+ $e = -$e if $x->{_es} eq '-';
if ($e < 0)
{
$dot = '';
# if _e is bigger than a scalar, the following will blow your memory
if ($e <= -$len)
{
- #print "style: 0.xxxx\n";
my $r = abs($e) - $len;
$es = '0.'. ('0' x $r) . $es; $cad = -($len+$r);
}
else
{
- #print "insert '.' at $e in '$es'\n";
- substr($es,$e,0) = '.'; $cad = $x->{_e};
+ substr($es,$e,0) = '.'; $cad = $MBI->_num($x->{_e});
+ $cad = -$cad if $x->{_es} eq '-';
}
}
elsif ($e > 0)
$es .= '0' x $e; $len += $e; $cad = 0;
}
} # if not zero
+
$es = '-'.$es if $x->{sign} eq '-';
# if set accuracy or precision, pad with zeros on the right side
if ((defined $x->{_a}) && ($not_zero))
# (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} !~ /^[+-]$/)
{
return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN
return 'inf'; # +inf
}
- # do $esign, because we need '1e+1', since $x->{_e}->bstr() misses the +
- my $esign = $x->{_e}->{sign}; $esign = '' if $esign eq '-';
- my $sep = 'e'.$esign;
+ my $sep = 'e'.$x->{_es};
my $sign = $x->{sign}; $sign = '' if $sign eq '+';
- $sign . $x->{_m}->bstr() . $sep . $x->{_e}->bstr();
+ $sign . $MBI->_str($x->{_m}) . $sep . $MBI->_str($x->{_e});
}
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,@_);
+ # simple return a string and let Perl's atoi()/atof() handle the rest
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
$x->bsstr();
}
##############################################################################
# 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
-# todo: this must be overwritten and return NaN for non-integer values
+# XXX TODO this must be overwritten and return NaN for non-integer values
# band(), bior(), bxor(), too
#sub bnot
# {
sub bcmp
{
# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
- # (BFLOAT or num_str, BFLOAT or num_str) return cond_code
# set up parameters
my ($self,$x,$y) = (ref($_[0]),@_);
return 1 if $yz && $x->{sign} eq '+'; # +x <=> 0
# adjust so that exponents are equal
- my $lxm = $x->{_m}->length();
- my $lym = $y->{_m}->length();
+ my $lxm = $MBI->_len($x->{_m});
+ my $lym = $MBI->_len($y->{_m});
# the numify somewhat limits our length, but makes it much faster
- my $lx = $lxm + $x->{_e}->numify();
- my $ly = $lym + $y->{_e}->numify();
+ my ($xes,$yes) = (1,1);
+ $xes = -1 if $x->{_es} ne '+';
+ $yes = -1 if $y->{_es} ne '+';
+ my $lx = $lxm + $xes * $MBI->_num($x->{_e});
+ my $ly = $lym + $yes * $MBI->_num($y->{_e});
my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-';
return $l <=> 0 if $l != 0;
my $ym = $y->{_m};
if ($diff > 0)
{
- $ym = $y->{_m}->copy()->blsft($diff,10);
+ $ym = $MBI->_copy($y->{_m});
+ $ym = $MBI->_lsft($ym, $MBI->_new($diff), 10);
}
elsif ($diff < 0)
{
- $xm = $x->{_m}->copy()->blsft(-$diff,10);
+ $xm = $MBI->_copy($x->{_m});
+ $xm = $MBI->_lsft($xm, $MBI->_new(-$diff), 10);
}
- my $rc = $xm->bacmp($ym);
+ my $rc = $MBI->_acmp($xm,$ym);
$rc = -$rc if $x->{sign} eq '-'; # -124 < -123
$rc <=> 0;
}
{
# Compares 2 values, ignoring their signs.
# Returns one of undef, <0, =0, >0. (suitable for sort)
- # (BFLOAT or num_str, BFLOAT or num_str) return cond_code
# set up parameters
my ($self,$x,$y) = (ref($_[0]),@_);
return 1 if $yz && !$xz; # +x <=> 0
# adjust so that exponents are equal
- my $lxm = $x->{_m}->length();
- my $lym = $y->{_m}->length();
+ my $lxm = $MBI->_len($x->{_m});
+ my $lym = $MBI->_len($y->{_m});
+ my ($xes,$yes) = (1,1);
+ $xes = -1 if $x->{_es} ne '+';
+ $yes = -1 if $y->{_es} ne '+';
# the numify somewhat limits our length, but makes it much faster
- my $lx = $lxm + $x->{_e}->numify();
- my $ly = $lym + $y->{_e}->numify();
+ my $lx = $lxm + $xes * $MBI->_num($x->{_e});
+ my $ly = $lym + $yes * $MBI->_num($y->{_e});
my $l = $lx - $ly;
return $l <=> 0 if $l != 0;
my $ym = $y->{_m};
if ($diff > 0)
{
- $ym = $y->{_m}->copy()->blsft($diff,10);
+ $ym = $MBI->_copy($y->{_m});
+ $ym = $MBI->_lsft($ym, $MBI->_new($diff), 10);
}
elsif ($diff < 0)
{
- $xm = $x->{_m}->copy()->blsft(-$diff,10);
+ $xm = $MBI->_copy($x->{_m});
+ $xm = $MBI->_lsft($xm, $MBI->_new(-$diff), 10);
}
- $xm->bacmp($ym) <=> 0;
+ $MBI->_acmp($xm,$ym);
}
sub badd
if ($x->is_zero()) # 0+y
{
# make copy, clobbering up x (modify in place!)
- $x->{_e} = $y->{_e}->copy();
- $x->{_m} = $y->{_m}->copy();
+ $x->{_e} = $MBI->_copy($y->{_e});
+ $x->{_es} = $y->{_es};
+ $x->{_m} = $MBI->_copy($y->{_m});
$x->{sign} = $y->{sign} || $nan;
return $x->round($a,$p,$r,$y);
}
# take lower of the two e's and adapt m1 to it to match m2
my $e = $y->{_e};
- $e = $MBI->bzero() if !defined $e; # if no BFLOAT ?
- $e = $e->copy(); # make copy (didn't do it yet)
- $e->bsub($x->{_e}); # Ye - Xe
- my $add = $y->{_m}->copy();
- if ($e->{sign} eq '-') # < 0
+ $e = $MBI->_zero() if !defined $e; # if no BFLOAT?
+ $e = $MBI->_copy($e); # make copy (didn't do it yet)
+
+ my $es;
+
+ ($e,$es) = _e_sub($e, $x->{_e}, $y->{_es} || '+', $x->{_es});
+
+ my $add = $MBI->_copy($y->{_m});
+
+ if ($es eq '-') # < 0
{
- $x->{_e} += $e; # need the sign of e
- $x->{_m}->blsft($e->babs(),10); # destroys copy of _e
+ $MBI->_lsft( $x->{_m}, $e, 10);
+ ($x->{_e},$x->{_es}) = _e_add($x->{_e}, $e, $x->{_es}, $es);
}
- elsif (!$e->is_zero()) # > 0
+ elsif (!$MBI->_is_zero($e)) # > 0
{
- $add->blsft($e,10);
+ $MBI->_lsft($add, $e, 10);
}
# else: both e are the same, so just leave them
- $x->{_m}->{sign} = $x->{sign}; # fiddle with signs
- $add->{sign} = $y->{sign};
- $x->{_m} += $add; # finally do add/sub
- $x->{sign} = $x->{_m}->{sign}; # re-adjust signs
- $x->{_m}->{sign} = '+'; # mantissa always positiv
- # delete trailing zeros, then round
- $x->bnorm()->round($a,$p,$r,$y);
- }
-
-sub bsub
- {
- # (BigFloat or num_str, BigFloat or num_str) return BigFloat
- # subtract second arg from first, modify first
- # set up parameters
- my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
- if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ if ($x->{sign} eq $y->{sign})
{
- ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ # add
+ $x->{_m} = $MBI->_add($x->{_m}, $add);
}
-
- # XXX TODO: remove?
- if ($y->is_zero()) # still round for not adding zero
+ else
{
- return $x->round($a,$p,$r);
+ ($x->{_m}, $x->{sign}) =
+ _e_add($x->{_m}, $add, $x->{sign}, $y->{sign});
}
-
- # $x - $y = -$x + $y
- $y->{sign} =~ tr/+-/-+/; # does nothing for NaN
- $x->badd($y,$a,$p,$r); # badd does not leave internal zeros
- $y->{sign} =~ tr/+-/-+/; # refix $y (does nothing for NaN)
- $x; # already rounded by badd()
+
+ # delete trailing zeros, then round
+ $x->bnorm()->round($a,$p,$r,$y);
}
+# sub bsub is inherited from Math::BigInt!
+
sub binc
{
# increment arg by one
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- if ($x->{_e}->sign() eq '-')
+ if ($x->{_es} eq '-')
{
- return $x->badd($self->bone(),$a,$p,$r); # digits after dot
+ return $x->badd($self->bone(),@r); # digits after dot
}
- if (!$x->{_e}->is_zero())
+ if (!$MBI->_is_zero($x->{_e})) # _e == 0 for NaN, inf, -inf
{
- $x->{_m}->blsft($x->{_e},10); # 1e2 => 100
- $x->{_e}->bzero();
+ # 1e2 => 100, so after the shift below _m has a '0' as last digit
+ $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e},10); # 1e2 => 100
+ $x->{_e} = $MBI->_zero(); # normalize
+ $x->{_es} = '+';
+ # we know that the last digit of $x will be '1' or '9', depending on the
+ # sign
}
# now $x->{_e} == 0
if ($x->{sign} eq '+')
{
- $x->{_m}->binc();
- return $x->bnorm()->bround($a,$p,$r);
+ $MBI->_inc($x->{_m});
+ return $x->bnorm()->bround(@r);
}
elsif ($x->{sign} eq '-')
{
- $x->{_m}->bdec();
- $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0
- return $x->bnorm()->bround($a,$p,$r);
+ $MBI->_dec($x->{_m});
+ $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # -1 +1 => -0 => +0
+ return $x->bnorm()->bround(@r);
}
# inf, nan handling etc
- $x->badd($self->bone(),$a,$p,$r); # does round
+ $x->badd($self->bone(),@r); # badd() does round
}
sub bdec
{
# decrement arg by one
- my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+ my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
- if ($x->{_e}->sign() eq '-')
+ if ($x->{_es} eq '-')
{
- return $x->badd($self->bone('-'),$a,$p,$r); # digits after dot
+ return $x->badd($self->bone('-'),@r); # digits after dot
}
- if (!$x->{_e}->is_zero())
+ if (!$MBI->_is_zero($x->{_e}))
{
- $x->{_m}->blsft($x->{_e},10); # 1e2 => 100
- $x->{_e}->bzero();
+ $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e},10); # 1e2 => 100
+ $x->{_e} = $MBI->_zero(); # normalize
+ $x->{_es} = '+';
}
# now $x->{_e} == 0
my $zero = $x->is_zero();
# <= 0
if (($x->{sign} eq '-') || $zero)
{
- $x->{_m}->binc();
- $x->{sign} = '-' if $zero; # 0 => 1 => -1
- $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0
- return $x->bnorm()->round($a,$p,$r);
+ $MBI->_inc($x->{_m});
+ $x->{sign} = '-' if $zero; # 0 => 1 => -1
+ $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # -1 +1 => -0 => +0
+ return $x->bnorm()->round(@r);
}
# > 0
elsif ($x->{sign} eq '+')
{
- $x->{_m}->bdec();
- return $x->bnorm()->round($a,$p,$r);
+ $MBI->_dec($x->{_m});
+ return $x->bnorm()->round(@r);
}
# inf, nan handling etc
- $x->badd($self->bone('-'),$a,$p,$r); # does round
+ $x->badd($self->bone('-'),@r); # does round
}
sub DEBUG () { 0; }
# also takes care of the "error in _find_round_parameters?" case
return $x->bnan() if $x->{sign} ne '+' || $x->is_zero();
+
# no rounding at all, so must use fallback
if (scalar @params == 0)
{
return $x->bnan() if $base->is_zero() || $base->is_one() ||
$base->{sign} ne '+';
# if $x == $base, we know the result must be 1.0
- return $x->bone('+',@params) if $x->bcmp($base) == 0;
+ if ($x->bcmp($base) == 0)
+ {
+ $x->bone('+',@params);
+ if ($fallback)
+ {
+ # clear a/p after round, since user did not request it
+ delete $x->{_a}; delete $x->{_p};
+ }
+ return $x;
+ }
}
# when user set globals, they would interfere with our calculation, so
$x = Math::BigFloat->new($x);
$self = ref($x);
}
- # first calculate the log to base e (using reduction by 10 (and probably 2))
- $self->_log_10($x,$scale);
-
- # and if a different base was requested, convert it
- if (defined $base)
+
+ my $done = 0;
+
+ # If the base is defined and an integer, try to calculate integer result
+ # first. This is very fast, and in case the real result was found, we can
+ # stop right here.
+ if (defined $base && $base->is_int() && $x->is_int())
+ {
+ my $i = $MBI->_copy( $x->{_m} );
+ $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e});
+ my $int = Math::BigInt->bzero();
+ $int->{value} = $i;
+ $int->blog($base->as_number());
+ # if ($exact)
+ if ($base->as_number()->bpow($int) == $x)
+ {
+ # found result, return it
+ $x->{_m} = $int->{value};
+ $x->{_e} = $MBI->_zero();
+ $x->{_es} = '+';
+ $x->bnorm();
+ $done = 1;
+ }
+ }
+
+ if ($done == 0)
{
- $base = Math::BigFloat->new($base) unless $base->isa('Math::BigFloat');
- # not ln, but some other base (don't modify $base)
- $x->bdiv( $base->copy()->blog(undef,$scale), $scale );
+ # first calculate the log to base e (using reduction by 10 (and probably 2))
+ $self->_log_10($x,$scale);
+
+ # and if a different base was requested, convert it
+ if (defined $base)
+ {
+ $base = Math::BigFloat->new($base) unless $base->isa('Math::BigFloat');
+ # not ln, but some other base (don't modify $base)
+ $x->bdiv( $base->copy()->blog(undef,$scale), $scale );
+ }
}
# shortcut to not run through _find_round_parameters again
if ($fallback)
{
# clear a/p after round, since user did not request it
- $x->{_a} = undef; $x->{_p} = undef;
+ delete $x->{_a}; delete $x->{_p};
}
# restore globals
$$abr = $ab; $$pbr = $pb;
delete $next->{_a}; delete $next->{_p};
$x->badd($next);
- #print "step $x\n ($next - $limit = ",$next - $limit,")\n";
# calculate things for the next term
$over *= $u; $below *= $v; $factor->badd($f);
if (DEBUG)
# log(10) afterwards to get the correct result.
# calculate nr of digits before dot
- my $dbd = $x->{_m}->length() + $x->{_e}->numify();
+ my $dbd = $MBI->_num($x->{_e});
+ $dbd = -$dbd if $x->{_es} eq '-';
+ $dbd += $MBI->_len($x->{_m});
# more than one digit (e.g. at least 10), but *not* exactly 10 to avoid
# infinite recursion
# disable the shortcut for 10, since we need log(10) and this would recurse
# infinitely deep
- if ($x->{_e}->is_one() && $x->{_m}->is_one())
+ if ($x->{_es} eq '+' && $MBI->_is_one($x->{_e}) && $MBI->_is_one($x->{_m}))
{
$dbd = 0; # disable shortcut
# we can use the cached value in these cases
else
{
# disable the shortcut for 2, since we maybe have it cached
- if ($x->{_e}->is_zero() && $x->{_m}->bcmp(2) == 0)
+ if (($MBI->_is_zero($x->{_e}) && $MBI->_is_two($x->{_m})))
{
$dbd = 0; # disable shortcut
# we can use the cached value in these cases
}
# if $x = 0.1, we know the result must be 0-log(10)
- if ($calc != 0 && $x->{_e}->is_one('-') && $x->{_m}->is_one())
+ if ($calc != 0 && $x->{_es} eq '-' && $MBI->_is_one($x->{_e}) &&
+ $MBI->_is_one($x->{_m}))
{
$dbd = 0; # disable shortcut
# we can use the cached value in these cases
if ($scale <= $LOG_10_A)
{
# use cached value
- #print "using cached value for l_10\n";
$l_10 = $LOG_10->copy(); # copy for mul
}
else
# else: slower, compute it (but don't cache it, because it could be big)
# also disable downgrade for this code path
local $Math::BigFloat::downgrade = undef;
- #print "l_10 = $l_10 (self = $self',
- # ", ref(l_10) = ",ref($l_10)," scale $scale)\n";
- #print "calculating value for l_10, scale $scale\n";
$l_10 = $self->new(10)->blog(undef,$scale); # scale+4, actually
}
$dbd-- if ($dbd > 1); # 20 => dbd=2, so make it dbd=1
- # make object
- $dbd = $self->new($dbd);
- #print "dbd $dbd\n";
- $l_10->bmul($dbd); # log(10) * (digits_before_dot-1)
- #print "l_10 = $l_10\n";
- #print "x = $x";
- $x->{_e}->bsub($dbd); # 123 => 1.23
- #print " => $x\n";
- #print "calculating log($x) with scale=$scale\n";
+ $l_10->bmul( $self->new($dbd)); # log(10) * (digits_before_dot-1)
+ my $dbd_sign = '+';
+ if ($dbd < 0)
+ {
+ $dbd = -$dbd;
+ $dbd_sign = '-';
+ }
+ ($x->{_e}, $x->{_es}) =
+ _e_sub( $x->{_e}, $MBI->_new($dbd), $x->{_es}, $dbd_sign); # 123 => 1.23
}
### Since $x in the range 0.5 .. 1.5 is MUCH faster, we do a repeated div
### or mul by 2 (maximum times 3, since x < 10 and x > 0.1)
- my $half = $self->new('0.5');
+ $HALF = $self->new($HALF) unless ref($HALF);
+
my $twos = 0; # default: none (0 times)
my $two = $self->new(2);
- while ($x->bacmp($half) <= 0)
+ while ($x->bacmp($HALF) <= 0)
{
$twos--; $x->bmul($two);
}
{
$twos++; $x->bdiv($two,$scale+4); # keep all digits
}
- #print "$twos\n";
# $twos > 0 => did mul 2, < 0 => did div 2 (never both)
# calculate correction factor based on ln(2)
if ($twos != 0)
if ($scale <= $LOG_2_A)
{
# use cached value
- #print "using cached value for l_10\n";
$l_2 = $LOG_2->copy(); # copy for mul
}
else
# else: slower, compute it (but don't cache it, because it could be big)
# also disable downgrade for this code path
local $Math::BigFloat::downgrade = undef;
- #print "calculating value for l_2, scale $scale\n";
$l_2 = $two->blog(undef,$scale); # scale+4, actually
}
$l_2->bmul($twos); # * -2 => subtract, * 2 => add
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;
}
-###############################################################################
-# is_foo methods (is_negative, is_positive are inherited from BigInt)
+##############################################################################
-sub _is_zero_or_one
+sub _e_add
{
- # internal, return true if BigInt arg is zero or one, saving the
- # two calls to is_zero() and is_one()
- my $x = $_[0];
+ # Internal helper sub to take two positive integers and their signs and
+ # then add them. Input ($CALC,$CALC,('+'|'-'),('+'|'-')),
+ # output ($CALC,('+'|'-'))
+ my ($x,$y,$xs,$ys) = @_;
+
+ # if the signs are equal we can add them (-5 + -3 => -(5 + 3) => -8)
+ if ($xs eq $ys)
+ {
+ $x = $MBI->_add ($x, $y ); # a+b
+ # the sign follows $xs
+ return ($x, $xs);
+ }
+
+ my $a = $MBI->_acmp($x,$y);
+ if ($a > 0)
+ {
+ $x = $MBI->_sub ($x , $y); # abs sub
+ }
+ elsif ($a == 0)
+ {
+ $x = $MBI->_zero(); # result is 0
+ $xs = '+';
+ }
+ else # a < 0
+ {
+ $x = $MBI->_sub ( $y, $x, 1 ); # abs sub
+ $xs = $ys;
+ }
+ ($x,$xs);
+ }
- $x->{sign} eq '+' && ($x->is_zero() || $x->is_one());
+sub _e_sub
+ {
+ # Internal helper sub to take two positive integers and their signs and
+ # then subtract them. Input ($CALC,$CALC,('+'|'-'),('+'|'-')),
+ # output ($CALC,('+'|'-'))
+ my ($x,$y,$xs,$ys) = @_;
+
+ # flip sign
+ $ys =~ tr/+-/-+/;
+ _e_add($x,$y,$xs,$ys); # call add (does subtract now)
}
+###############################################################################
+# is_foo methods (is_negative, is_positive are inherited from BigInt)
+
sub is_int
{
# return true if arg (BFLOAT or num_str) is an integer
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't
- $x->{_e}->{sign} eq '+'; # 1e-1 => no integer
+ $x->{_es} eq '+'; # 1e-1 => no integer
0;
}
# return true if arg (BFLOAT or num_str) is zero
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
- return 1 if $x->{sign} eq '+' && $x->{_m}->is_zero();
+ return 1 if $x->{sign} eq '+' && $MBI->_is_zero($x->{_m});
0;
}
$sign = '+' if !defined $sign || $sign ne '-';
return 1
- if ($x->{sign} eq $sign && $x->{_e}->is_zero() && $x->{_m}->is_one());
+ if ($x->{sign} eq $sign &&
+ $MBI->_is_zero($x->{_e}) && $MBI->_is_one($x->{_m}));
0;
}
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 1 if ($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't
- ($x->{_e}->is_zero() && $x->{_m}->is_odd());
+ ($MBI->_is_zero($x->{_e}) && $MBI->_is_odd($x->{_m}));
0;
}
my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't
- return 1 if ($x->{_e}->{sign} eq '+' # 123.45 is never
- && $x->{_m}->is_even()); # but 1200 is
+ return 1 if ($x->{_es} eq '+' # 123.45 is never
+ && $MBI->_is_even($x->{_m})); # but 1200 is
0;
}
((!$x->isa($self)) || (!$y->isa($self)));
# aEb * cEd = (a*c)E(b+d)
- $x->{_m}->bmul($y->{_m});
- $x->{_e}->badd($y->{_e});
+ $MBI->_mul($x->{_m},$y->{_m});
+ ($x->{_e}, $x->{_es}) = _e_add($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es});
+
# adjust sign:
$x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+';
return $x->bnorm()->round($a,$p,$r,$y);
# enough...
$scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
}
- my $lx = $x->{_m}->length(); my $ly = $y->{_m}->length();
+
+ my $rem; $rem = $self->bzero() if wantarray;
+
+ $y = $self->new($y) unless $y->isa('Math::BigFloat');
+
+ my $lx = $MBI->_len($x->{_m}); my $ly = $MBI->_len($y->{_m});
$scale = $lx if $lx > $scale;
$scale = $ly if $ly > $scale;
my $diff = $ly - $lx;
$scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx!
-
- # make copy of $x in case of list context for later reminder calculation
- my $rem;
- if (wantarray && !$y->is_one())
- {
- $rem = $x->copy();
- }
- $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+';
+ # already handled inf/NaN/-inf above:
- # check for / +-1 ( +/- 1E0)
- if (!$y->is_one())
- {
- # promote BigInts and it's subclasses (except when already a BigFloat)
- $y = $self->new($y) unless $y->isa('Math::BigFloat');
+ # 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}));
- # need to disable $upgrade in BigInt, to avoid deep recursion
- local $Math::BigInt::upgrade = undef; # should be parent class vs MBI
+ # 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/+-/-+/;
- # calculate the result to $scale digits and then round it
- # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d)
- $x->{_m}->blsft($scale,10);
- $x->{_m}->bdiv( $y->{_m} ); # a/c
- $x->{_e}->bsub( $y->{_e} ); # b-d
- $x->{_e}->bsub($scale); # correct for 10**scale
- $x->bnorm(); # remove trailing 0's
+ if ($xsign ne $x->{sign})
+ {
+ # 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_not_one)
+ {
+ $rem = $x->copy();
+ }
+
+ $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+';
+
+ # check for / +-1 ( +/- 1E0)
+ if ($y_not_one)
+ {
+ # promote BigInts and it's subclasses (except when already a BigFloat)
+ $y = $self->new($y) unless $y->isa('Math::BigFloat');
+
+ # calculate the result to $scale digits and then round it
+ # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d)
+ $MBI->_lsft($x->{_m},$MBI->_new($scale),10);
+ $MBI->_div ($x->{_m},$y->{_m}); # a/c
+
+ # correct exponent of $x
+ ($x->{_e},$x->{_es}) = _e_sub($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es});
+ # correct for 10**scale
+ ($x->{_e},$x->{_es}) = _e_sub($x->{_e}, $MBI->_new($scale), $x->{_es}, '+');
+ $x->bnorm(); # remove trailing 0's
+ }
+ } # ende else $x != $y
# shortcut to not run through _find_round_parameters again
if (defined $params[0])
{
- $x->{_a} = undef; # clear before round
+ delete $x->{_a}; # clear before round
$x->bround($params[0],$params[2]); # then round accordingly
}
else
{
- $x->{_p} = undef; # clear before round
+ delete $x->{_p}; # clear before round
$x->bfround($params[1],$params[2]); # then round accordingly
}
if ($fallback)
{
# clear a/p after round, since user did not request it
- $x->{_a} = undef; $x->{_p} = undef;
+ delete $x->{_a}; delete $x->{_p};
}
-
+
if (wantarray)
{
- if (!$y->is_one())
+ if ($y_not_one)
{
$rem->bmod($y,@params); # copy already done
}
- else
- {
- $rem = $self->bzero();
- }
if ($fallback)
{
# clear a/p after round, since user did not request it
- $rem->{_a} = undef; $rem->{_p} = undef;
+ delete $rem->{_a}; delete $rem->{_p};
}
return ($x,$rem);
}
($self,$x,$y,$a,$p,$r) = objectify(2,@_);
}
+ # handle NaN, inf, -inf
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
my ($d,$re) = $self->SUPER::_div_inf($x,$y);
$x->{_m} = $re->{_m};
return $x->round($a,$p,$r,$y);
}
- return $x->bnan() if $x->is_zero() && $y->is_zero();
- return $x if $y->is_zero();
- return $x->bnan() if $x->is_nan() || $y->is_nan();
- return $x->bzero() if $y->is_one() || $x->is_zero();
+ if ($y->is_zero())
+ {
+ return $x->bnan() if $x->is_zero();
+ return $x;
+ }
+
+ 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})));
- # inf handling is missing here
-
my $cmp = $x->bacmp($y); # equal or $x < $y?
return $x->bzero($a,$p) if $cmp == 0; # $x == $y => result 0
$x->{sign} = $y->{sign}; # calc sign first
return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0; # $x < $y => result $x
- my $ym = $y->{_m}->copy();
+ my $ym = $MBI->_copy($y->{_m});
# 2e1 => 20
- $ym->blsft($y->{_e},10) if $y->{_e}->{sign} eq '+' && !$y->{_e}->is_zero();
+ $MBI->_lsft( $ym, $y->{_e}, 10)
+ if $y->{_es} eq '+' && !$MBI->_is_zero($y->{_e});
# if $y has digits after dot
my $shifty = 0; # correct _e of $x by this
- if ($y->{_e}->{sign} eq '-') # has digits after dot
+ if ($y->{_es} eq '-') # has digits after dot
{
# 123 % 2.5 => 1230 % 25 => 5 => 0.5
- $shifty = $y->{_e}->copy()->babs(); # no more digits after dot
- $x->blsft($shifty,10); # 123 => 1230, $y->{_m} is already 25
+ $shifty = $MBI->_num($y->{_e}); # no more digits after dot
+ $MBI->_lsft($x->{_m}, $y->{_e}, 10);# 123 => 1230, $y->{_m} is already 25
}
# $ym is now mantissa of $y based on exponent 0
my $shiftx = 0; # correct _e of $x by this
- if ($x->{_e}->{sign} eq '-') # has digits after dot
+ if ($x->{_es} eq '-') # has digits after dot
{
# 123.4 % 20 => 1234 % 200
- $shiftx = $x->{_e}->copy()->babs(); # no more digits after dot
- $ym->blsft($shiftx,10);
+ $shiftx = $MBI->_num($x->{_e}); # no more digits after dot
+ $MBI->_lsft($ym, $x->{_e}, 10); # 123 => 1230
}
# 123e1 % 20 => 1230 % 20
- if ($x->{_e}->{sign} eq '+' && !$x->{_e}->is_zero())
+ if ($x->{_es} eq '+' && !$MBI->_is_zero($x->{_e}))
{
- $x->{_m}->blsft($x->{_e},10);
+ $MBI->_lsft( $x->{_m}, $x->{_e},10); # es => '+' here
}
- $x->{_e} = $MBI->bzero() unless $x->{_e}->is_zero();
-
- $x->{_e}->bsub($shiftx) if $shiftx != 0;
- $x->{_e}->bsub($shifty) if $shifty != 0;
+
+ $x->{_e} = $MBI->_new($shiftx);
+ $x->{_es} = '+';
+ $x->{_es} = '-' if $shiftx != 0 || $shifty != 0;
+ $MBI->_add( $x->{_e}, $MBI->_new($shifty)) if $shifty != 0;
# now mantissas are equalized, exponent of $x is adjusted, so calc result
- $x->{_m}->bmod($ym);
+ $x->{_m} = $MBI->_mod( $x->{_m}, $ym);
- $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0
+ $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # fix sign for -0
$x->bnorm();
if ($neg != 0) # one of them negative => correct in place
my $r = $y - $x;
$x->{_m} = $r->{_m};
$x->{_e} = $r->{_e};
- $x->{sign} = '+' if $x->{_m}->is_zero(); # fix sign for -0
+ $x->{_es} = $r->{_es};
+ $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # fix sign for -0
$x->bnorm();
}
sub broot
{
# calculate $y'th root of $x
- my ($self,$x,$y,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(2,@_);
+
+ # set up parameters
+ my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+ {
+ ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+ }
# NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
# simulate old behaviour
$params[0] = $self->div_scale(); # and round to it as accuracy
$scale = $params[0]+4; # at least four more for proper round
- $params[2] = $r; # round mode by caller or undef
+ $params[2] = $r; # iound mode by caller or undef
$fallback = 1; # to clear a/p afterwards
}
else
local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI
# remember sign and make $x positive, since -4 ** (1/2) => -2
- my $sign = 0; $sign = 1 if $x->is_negative(); $x->babs();
+ my $sign = 0; $sign = 1 if $x->{sign} eq '-'; $x->{sign} = '+';
- if ($y->bcmp(2) == 0) # normal square root
+ my $is_two = 0;
+ if ($y->isa('Math::BigFloat'))
+ {
+ $is_two = ($y->{sign} eq '+' && $MBI->_is_two($y->{_m}) && $MBI->_is_zero($y->{_e}));
+ }
+ else
+ {
+ $is_two = ($y == 2);
+ }
+
+ # normal square root if $y == 2:
+ if ($is_two)
{
$x->bsqrt($scale+4);
}
# copy private parts over
$x->{_m} = $u->{_m};
$x->{_e} = $u->{_e};
+ $x->{_es} = $u->{_es};
}
else
{
- my $u = $self->bone()->bdiv($y,$scale+4);
- delete $u->{_a}; delete $u->{_p}; # otherwise it conflicts
- $x->bpow($u,$scale+4); # el cheapo
+ # calculate the broot() as integer result first, and if it fits, return
+ # it rightaway (but only if $x and $y are integer):
+
+ my $done = 0; # not yet
+ if ($y->is_int() && $x->is_int())
+ {
+ my $i = $MBI->_copy( $x->{_m} );
+ $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e});
+ my $int = Math::BigInt->bzero();
+ $int->{value} = $i;
+ $int->broot($y->as_number());
+ # if ($exact)
+ if ($int->copy()->bpow($y) == $x)
+ {
+ # found result, return it
+ $x->{_m} = $int->{value};
+ $x->{_e} = $MBI->_zero();
+ $x->{_es} = '+';
+ $x->bnorm();
+ $done = 1;
+ }
+ }
+ if ($done == 0)
+ {
+ my $u = $self->bone()->bdiv($y,$scale+4);
+ delete $u->{_a}; delete $u->{_p}; # otherwise it conflicts
+ $x->bpow($u,$scale+4); # el cheapo
+ }
}
$x->bneg() if $sign == 1;
if ($fallback)
{
# clear a/p after round, since user did not request it
- $x->{_a} = undef; $x->{_p} = undef;
+ delete $x->{_a}; delete $x->{_p};
}
# restore globals
$$abr = $ab; $$pbr = $pb;
# need to disable $upgrade in BigInt, to avoid deep recursion
local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI
- my $xas = $x->as_number();
+ my $i = $MBI->_copy( $x->{_m} );
+ $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e});
+ my $xas = Math::BigInt->bzero();
+ $xas->{value} = $i;
+
my $gs = $xas->copy()->bsqrt(); # some guess
- if (($x->{_e}->{sign} ne '-') # guess can't be accurate if there are
+ if (($x->{_es} ne '-') # guess can't be accurate if there are
# digits after the dot
&& ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head?
{
- # exact result
- $x->{_m} = $gs; $x->{_e} = $MBI->bzero(); $x->bnorm();
+ # exact result, copy result over to keep $x
+ $x->{_m} = $gs->{value}; $x->{_e} = $MBI->_zero(); $x->{_es} = '+';
+ $x->bnorm();
# shortcut to not run through _find_round_parameters again
if (defined $params[0])
{
if ($fallback)
{
# clear a/p after round, since user did not request it
- $x->{_a} = undef; $x->{_p} = undef;
+ delete $x->{_a}; delete $x->{_p};
}
# re-enable A and P, upgrade is taken care of by "local"
${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb;
# sqrt(2) = 1.4 because sqrt(2*100) = 1.4*10; so we can increase the accuracy
# of the result by multipyling the input by 100 and then divide the integer
# result of sqrt(input) by 10. Rounding afterwards returns the real result.
- # this will transform 123.456 (in $x) into 123456 (in $y1)
- my $y1 = $x->{_m}->copy();
+
+ # The following steps will transform 123.456 (in $x) into 123456 (in $y1)
+ my $y1 = $MBI->_copy($x->{_m});
+
+ my $length = $MBI->_len($y1);
+
+ # Now calculate how many digits the result of sqrt(y1) would have
+ my $digits = int($length / 2);
+
+ # But we need at least $scale digits, so calculate how many are missing
+ my $shift = $scale - $digits;
+
+ # That should never happen (we take care of integer guesses above)
+ # $shift = 0 if $shift < 0;
+
+ # Multiply in steps of 100, by shifting left two times the "missing" digits
+ my $s2 = $shift * 2;
+
# We now make sure that $y1 has the same odd or even number of digits than
# $x had. So when _e of $x is odd, we must shift $y1 by one digit left,
# because we always must multiply by steps of 100 (sqrt(100) is 10) and not
# steps of 10. The length of $x does not count, since an even or odd number
# of digits before the dot is not changed by adding an even number of digits
# after the dot (the result is still odd or even digits long).
- my $length = $y1->length();
- $y1->bmul(10) if $x->{_e}->is_odd();
- # now calculate how many digits the result of sqrt(y1) would have
- my $digits = int($length / 2);
- # but we need at least $scale digits, so calculate how many are missing
- my $shift = $scale - $digits;
- # that should never happen (we take care of integer guesses above)
- # $shift = 0 if $shift < 0;
- # multiply in steps of 100, by shifting left two times the "missing" digits
- $y1->blsft($shift*2,10);
+ $s2++ if $MBI->_is_odd($x->{_e});
+
+ $MBI->_lsft( $y1, $MBI->_new($s2), 10);
+
# now take the square root and truncate to integer
- $y1->bsqrt();
+ $y1 = $MBI->_sqrt($y1);
+
# By "shifting" $y1 right (by creating a negative _e) we calculate the final
# result, which is than later rounded to the desired scale.
# calculate how many zeros $x had after the '.' (or before it, depending
- # on sign of $dat, the result should have half as many:
- my $dat = $length + $x->{_e}->numify();
+ # on sign of $dat, the result should have half as many:
+ my $dat = $MBI->_num($x->{_e});
+ $dat = -$dat if $x->{_es} eq '-';
+ $dat += $length;
if ($dat > 0)
{
{
$dat = int(($dat)/2);
}
- $x->{_e}= $MBI->new( $dat - $y1->length() );
-
+ $dat -= $MBI->_len($y1);
+ if ($dat < 0)
+ {
+ $dat = abs($dat);
+ $x->{_e} = $MBI->_new( $dat );
+ $x->{_es} = '-';
+ }
+ else
+ {
+ $x->{_e} = $MBI->_new( $dat );
+ $x->{_es} = '+';
+ }
$x->{_m} = $y1;
+ $x->bnorm();
# shortcut to not run through _find_round_parameters again
if (defined $params[0])
if ($fallback)
{
# clear a/p after round, since user did not request it
- $x->{_a} = undef; $x->{_p} = undef;
+ delete $x->{_a}; delete $x->{_p};
}
# restore globals
$$abr = $ab; $$pbr = $pb;
{
# (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT
# compute factorial number, modifies first argument
- my ($self,$x,@r) = objectify(1,@_);
+ # set up parameters
+ my ($self,$x,@r) = (ref($_[0]),@_);
+ # objectify is costly, so avoid it
+ ($self,$x,@r) = objectify(1,@_) if !ref($x);
+
+ return $x if $x->{sign} eq '+inf'; # inf => inf
return $x->bnan()
if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN
- ($x->{_e}->{sign} ne '+')); # digits after dot?
+ ($x->{_es} ne '+')); # digits after dot?
# use BigInt's bfac() for faster calc
- if (! _is_zero_or_one($x->{_e}))
+ if (! $MBI->_is_zero($x->{_e}))
{
- $x->{_m}->blsft($x->{_e},10); # unnorm
- $x->{_e}->bzero(); # norm again
+ $MBI->_lsft($x->{_m}, $x->{_e},10); # change 12e1 to 120e0
+ $x->{_e} = $MBI->_zero(); # normalize
+ $x->{_es} = '+';
}
- $x->{_m}->blsft($x->{_e},10); # un-norm m
- $x->{_e}->bzero(); # norm again
- $x->{_m}->bfac(); # calculate factorial
+ $MBI->_fac($x->{_m}); # calculate factorial
$x->bnorm()->round(@r); # norm again and round result
}
my $self = ref($x);
# if $y == 0.5, it is sqrt($x)
- return $x->bsqrt($a,$p,$r,$y) if $y->bcmp('0.5') == 0;
+ $HALF = $self->new($HALF) unless ref($HALF);
+ return $x->bsqrt($a,$p,$r,$y) if $y->bcmp($HALF) == 0;
# Using:
# a ** x == e ** (x * ln a)
$below = $v->copy();
$over = $u->copy();
-
+
$limit = $self->new("1E-". ($scale-1));
#my $steps = 0;
while (3 < 5)
$x->badd($next);
# calculate things for the next term
$over *= $u; $below *= $factor; $factor->binc();
+
+ last if $x->{sign} !~ /^[-+]$/;
+
#$steps++;
}
if ($fallback)
{
# clear a/p after round, since user did not request it
- $x->{_a} = undef; $x->{_p} = undef;
+ delete $x->{_a}; delete $x->{_p};
}
# restore globals
$$abr = $ab; $$pbr = $pb;
($self,$x,$y,$a,$p,$r) = objectify(2,@_);
}
- return $x if $x->{sign} =~ /^[+-]inf$/;
return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
- return $x->bone() if $y->is_zero();
+ return $x if $x->{sign} =~ /^[+-]inf$/;
+
+ # -2 ** -2 => NaN
+ return $x->bnan() if $x->{sign} eq '-' && $y->{sign} eq '-';
+
+ # cache the result of is_zero
+ my $y_is_zero = $y->is_zero();
+ 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
+ my $x_is_zero = $x->is_zero();
+ return $x->_pow($y,$a,$p,$r) if !$x_is_zero && !$y->is_int(); # non-integer power
+
+ my $y1 = $y->as_number()->{value}; # make MBI part
- my $y1 = $y->as_number(); # make bigint
# if ($x == -1)
- if ($x->{sign} eq '-' && $x->{_m}->is_one() && $x->{_e}->is_zero())
+ if ($x->{sign} eq '-' && $MBI->_is_one($x->{_m}) && $MBI->_is_zero($x->{_e}))
{
# if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1
- return $y1->is_odd() ? $x : $x->babs(1);
+ return $MBI->_is_odd($y1) ? $x : $x->babs(1);
}
- if ($x->is_zero())
+ if ($x_is_zero)
{
+ return $x->bone() if $y_is_zero;
return $x if $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0)
- # 0 ** -y => 1 / (0 ** y) => / 0! (1 / 0 => +inf)
- $x->binf();
+ # 0 ** -y => 1 / (0 ** y) => 1 / 0! (1 / 0 => +inf)
+ return $x->binf();
}
+ my $new_sign = '+';
+ $new_sign = $MBI->_is_odd($y1) ? '-' : '+' if $x->{sign} ne '+';
+
# calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster)
- $y1->babs();
- $x->{_m}->bpow($y1);
- $x->{_e}->bmul($y1);
- $x->{sign} = $nan if $x->{_m}->{sign} eq $nan || $x->{_e}->{sign} eq $nan;
+ $x->{_m} = $MBI->_pow( $x->{_m}, $y1);
+ $x->{_e} = $MBI->_mul ($x->{_e}, $y1);
+
+ $x->{sign} = $new_sign;
$x->bnorm();
if ($y->{sign} eq '-')
{
# modify $x in place!
- my $z = $x->copy(); $x->bzero()->binc();
+ my $z = $x->copy(); $x->bone();
return $x->bdiv($z,$a,$p,$r); # round in one go (might ignore y's A!)
}
$x->round($a,$p,$r,$y);
# 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())
return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p});
$x->{_p} = $scale; # remember round in any case
- $x->{_a} = undef; # and clear A
+ delete $x->{_a}; # and clear A
if ($scale < 0)
{
# round right from the '.'
- return $x if $x->{_e}->{sign} eq '+'; # e >= 0 => nothing to round
+ return $x if $x->{_es} eq '+'; # e >= 0 => nothing to round
$scale = -$scale; # positive for simplicity
- my $len = $x->{_m}->length(); # length of mantissa
+ my $len = $MBI->_len($x->{_m}); # length of mantissa
# the following poses a restriction on _e, but if _e is bigger than a
# scalar, you got other problems (memory etc) anyway
- my $dad = -($x->{_e}->numify()); # digits after dot
+ my $dad = -(0+ ($x->{_es}.$MBI->_num($x->{_e}))); # digits after dot
my $zad = 0; # zeros after dot
$zad = $dad - $len if (-$dad < -$len); # for 0.00..00xxx style
-
- #print "scale $scale dad $dad zad $zad len $len\n";
+
+ # p rint "scale $scale dad $dad zad $zad len $len\n";
# number bsstr len zad dad
# 0.123 123e-3 3 0 3
# 0.0123 123e-4 3 1 4
# 123 => 100 means length(123) = 3 - $scale (2) => 1
- my $dbt = $x->{_m}->length();
+ my $dbt = $MBI->_len($x->{_m});
# digits before dot
- my $dbd = $dbt + $x->{_e}->numify();
+ my $dbd = $dbt + ($x->{_es} . $MBI->_num($x->{_e}));
# should be the same, so treat it as this
$scale = 1 if $scale == 0;
# shortcut if already integer
}
}
# pass sign to bround for rounding modes '+inf' and '-inf'
- $x->{_m}->{sign} = $x->{sign};
- $x->{_m}->bround($scale,$mode);
- $x->{_m}->{sign} = '+'; # fix sign back
+ my $m = bless { sign => $x->{sign}, value => $x->{_m} }, 'Math::BigInt';
+ $m->bround($scale,$mode);
+ $x->{_m} = $m->{value}; # get our mantissa back
$x->bnorm();
}
{
# accuracy: preserve $N digits, and overwrite the rest with 0's
my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x);
-
+
if (($_[0] || 0) < 0)
{
require Carp; Carp::croak ('bround() needs positive accuracy');
}
- my ($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() || $x->{_m}->length() <= $scale)
+ # 1: never round a 0
+ # 2: if we should keep more digits than the mantissa has, do nothing
+ if ($x->is_zero() || $MBI->_len($x->{_m}) <= $scale)
{
$x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale;
return $x;
}
# pass sign to bround for '+inf' and '-inf' rounding modes
- $x->{_m}->{sign} = $x->{sign};
- $x->{_m}->bround($scale,$mode); # round mantissa
- $x->{_m}->{sign} = '+'; # fix sign back
- # $x->{_m}->{_a} = undef; $x->{_m}->{_p} = undef;
+ my $m = bless { sign => $x->{sign}, value => $x->{_m} }, 'Math::BigInt';
+
+ $m->bround($scale,$mode); # round mantissa
+ $x->{_m} = $m->{value}; # get our mantissa back
$x->{_a} = $scale; # remember rounding
- $x->{_p} = undef; # and clear P
+ delete $x->{_p}; # and clear P
$x->bnorm(); # del trailing zeros gen. by bround()
}
return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf
# if $x has digits after dot
- if ($x->{_e}->{sign} eq '-')
+ if ($x->{_es} eq '-')
{
- $x->{_e}->{sign} = '+'; # negate e
- $x->{_m}->brsft($x->{_e},10); # cut off digits after dot
- $x->{_e}->bzero(); # trunc/norm
- $x->{_m}->binc() if $x->{sign} eq '-'; # decrement if negative
+ $x->{_m} = $MBI->_rsft($x->{_m},$x->{_e},10); # cut off digits after dot
+ $x->{_e} = $MBI->_zero(); # trunc/norm
+ $x->{_es} = '+'; # abs e
+ $MBI->_inc($x->{_m}) if $x->{sign} eq '-'; # increment if negative
}
$x->round($a,$p,$r);
}
return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf
# if $x has digits after dot
- if ($x->{_e}->{sign} eq '-')
+ if ($x->{_es} eq '-')
{
- #$x->{_m}->brsft(-$x->{_e},10);
- #$x->{_e}->bzero();
- #$x++ if $x->{sign} eq '+';
-
- $x->{_e}->{sign} = '+'; # negate e
- $x->{_m}->brsft($x->{_e},10); # cut off digits after dot
- $x->{_e}->bzero(); # trunc/norm
- $x->{_m}->binc() if $x->{sign} eq '+'; # decrement if negative
+ $x->{_m} = $MBI->_rsft($x->{_m},$x->{_e},10); # cut off digits after dot
+ $x->{_e} = $MBI->_zero(); # trunc/norm
+ $x->{_es} = '+'; # abs e
+ $MBI->_inc($x->{_m}) if $x->{sign} eq '+'; # increment if positive
}
$x->round($a,$p,$r);
}
sub DESTROY
{
- # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub
+ # going through AUTOLOAD for every DESTROY is costly, avoid it by empty sub
}
sub AUTOLOAD
# or falling back to MBI::bxxx()
my $name = $AUTOLOAD;
- $name =~ s/.*:://; # split package
+ $name =~ s/(.*):://; # split package
+ my $c = $1 || $class;
no strict 'refs';
- $class->import() if $IMPORT == 0;
+ $c->import() if $IMPORT == 0;
if (!method_alias($name))
{
if (!defined $name)
{
# delayed load of Carp and avoid recursion
require Carp;
- Carp::croak ("Can't call a method without name");
+ Carp::croak ("$c: Can't call a method without name");
}
if (!method_hand_up($name))
{
# delayed load of Carp and avoid recursion
require Carp;
- Carp::croak ("Can't call $class\-\>$name, not a valid method");
+ Carp::croak ("Can't call $c\-\>$name, not a valid method");
}
# try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx()
$name =~ s/^f/b/;
- return &{"$MBI"."::$name"}(@_);
+ return &{"Math::BigInt"."::$name"}(@_);
}
my $bname = $name; $bname =~ s/^f/b/;
- *{$class."::$name"} = \&$bname;
- &$bname; # uses @_
+ $c .= "::$name";
+ *{$c} = \&{$bname};
+ &{$c}; # uses @_
}
sub exponent
if ($x->{sign} !~ /^[+-]$/)
{
my $s = $x->{sign}; $s =~ s/^[+-]//;
- return $self->new($s); # -inf, +inf => +inf
+ return Math::BigInt->new($s); # -inf, +inf => +inf
}
- return $x->{_e}->copy();
+ Math::BigInt->new( $x->{_es} . $MBI->_str($x->{_e}));
}
sub mantissa
if ($x->{sign} !~ /^[+-]$/)
{
my $s = $x->{sign}; $s =~ s/^[+]//;
- return $self->new($s); # -inf, +inf => +inf
+ return Math::BigInt->new($s); # -inf, +inf => +inf
}
- my $m = $x->{_m}->copy(); # faster than going via bstr()
+ my $m = Math::BigInt->new( $MBI->_str($x->{_m}));
$m->bneg() if $x->{sign} eq '-';
$m;
my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//;
return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf
}
- my $m = $x->{_m}->copy(); # faster than going via bstr()
+ my $m = Math::BigInt->bzero();
+ $m->{value} = $MBI->_copy($x->{_m});
$m->bneg() if $x->{sign} eq '-';
- return ($m,$x->{_e}->copy());
+ ($m, Math::BigInt->new( $x->{_es} . $MBI->_num($x->{_e}) ));
}
##############################################################################
elsif ($_[$i] eq 'with')
{
# alternative class for our private parts()
- $MBI = $_[$i+1] || 'Math::BigInt'; # default Math::BigInt
+ # XXX: no longer supported
+ # $MBI = $_[$i+1] || 'Math::BigInt';
$i++;
}
else
}
}
+ $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'))
+ if ((defined $mbilib) && ($MBI eq 'Math::BigInt::Calc'))
{
# MBI already loaded
- $MBI->import('lib',"$lib,$mbilib", 'objectify');
+ Math::BigInt->import('lib',"$lib,$mbilib", 'objectify');
}
else
{
- # MBI not loaded, or with ne "Math::BigInt"
+ # MBI not loaded, or with ne "Math::BigInt::Calc"
$lib .= ",$mbilib" if defined $mbilib;
$lib =~ s/^,//; # don't leave empty
+
# replacement library can handle lib statement, but also could ignore it
- if ($] < 5.006)
- {
- # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is
- # used in the same script, or eval inside import().
- my @parts = split /::/, $MBI; # Math::BigInt => Math BigInt
- my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm
- require File::Spec;
- $file = File::Spec->catfile (@parts, $file);
- eval { require "$file"; };
- $MBI->import( lib => $lib, 'objectify' );
- }
- else
- {
- my $rc = "use $MBI lib => '$lib', 'objectify';";
- eval $rc;
- }
+
+ # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is
+ # used in the same script, or eval inside import(). So we require MBI:
+ require Math::BigInt;
+ Math::BigInt->import( lib => $lib, 'objectify' );
}
if ($@)
{
- require Carp; Carp::croak ("Couldn't load $MBI: $! $@");
+ 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
$self->SUPER::import(@a); # for subclasses
{
# adjust m and e so that m is smallest possible
# round number according to accuracy and precision settings
- my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc
-# if (!$x->{_m}->is_odd())
-# {
- my $zeros = $x->{_m}->_trailing_zeros(); # correct for trailing zeros
- if ($zeros != 0)
+ my $zeros = $MBI->_zeros($x->{_m}); # correct for trailing zeros
+ if ($zeros != 0)
+ {
+ my $z = $MBI->_new($zeros);
+ $x->{_m} = $MBI->_rsft ($x->{_m}, $z, 10);
+ if ($x->{_es} eq '-')
{
- $x->{_m}->brsft($zeros,10); $x->{_e}->badd($zeros);
+ if ($MBI->_acmp($x->{_e},$z) >= 0)
+ {
+ $x->{_e} = $MBI->_sub ($x->{_e}, $z);
+ $x->{_es} = '+' if $MBI->_is_zero($x->{_e});
+ }
+ else
+ {
+ $x->{_e} = $MBI->_sub ( $MBI->_copy($z), $x->{_e});
+ $x->{_es} = '+';
+ }
}
- # for something like 0Ey, set y to 1, and -0 => +0
- $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero();
-# }
- # this is to prevent automatically rounding when MBI's globals are set
- $x->{_m}->{_f} = MB_NEVER_ROUND;
- $x->{_e}->{_f} = MB_NEVER_ROUND;
- # 'forget' that mantissa was rounded via MBI::bround() in MBF's bfround()
- $x->{_m}->{_a} = undef; $x->{_e}->{_a} = undef;
- $x->{_m}->{_p} = undef; $x->{_e}->{_p} = undef;
+ else
+ {
+ $x->{_e} = $MBI->_add ($x->{_e}, $z);
+ }
+ }
+ else
+ {
+ # $x can only be 0Ey if there are no trailing zeros ('0' has 0 trailing
+ # zeros). So, for something like 0Ey, set y to 1, and -0 => +0
+ $x->{sign} = '+', $x->{_es} = '+', $x->{_e} = $MBI->_one()
+ if $MBI->_is_zero($x->{_m});
+ }
+
$x; # MBI bnorm is no-op, so dont call it
}
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
return '0x0' if $x->is_zero();
- return $nan if $x->{_e}->{sign} ne '+'; # how to do 1e-1 in hex!?
+ return $nan if $x->{_es} ne '+'; # how to do 1e-1 in hex!?
- my $z = $x->{_m}->copy();
- if (!$x->{_e}->is_zero()) # > 0
+ my $z = $MBI->_copy($x->{_m});
+ if (! $MBI->_is_zero($x->{_e})) # > 0
{
- $z->blsft($x->{_e},10);
+ $MBI->_lsft( $z, $x->{_e},10);
}
- $z->{sign} = $x->{sign};
+ $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z));
$z->as_hex();
}
return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc
return '0b0' if $x->is_zero();
- return $nan if $x->{_e}->{sign} ne '+'; # how to do 1e-1 in hex!?
+ return $nan if $x->{_es} ne '+'; # how to do 1e-1 in hex!?
- my $z = $x->{_m}->copy();
- if (!$x->{_e}->is_zero()) # > 0
+ my $z = $MBI->_copy($x->{_m});
+ if (! $MBI->_is_zero($x->{_e})) # > 0
{
- $z->blsft($x->{_e},10);
+ $MBI->_lsft( $z, $x->{_e},10);
}
- $z->{sign} = $x->{sign};
+ $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z));
$z->as_bin();
}
# return copy as a bigint representation of this BigFloat number
my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
- my $z = $x->{_m}->copy();
- if ($x->{_e}->{sign} eq '-') # < 0
+ my $z = $MBI->_copy($x->{_m});
+ if ($x->{_es} eq '-') # < 0
{
- $x->{_e}->{sign} = '+'; # flip
- $z->brsft($x->{_e},10);
- $x->{_e}->{sign} = '-'; # flip back
+ $MBI->_rsft( $z, $x->{_e},10);
}
- elsif (!$x->{_e}->is_zero()) # > 0
+ elsif (! $MBI->_is_zero($x->{_e})) # > 0
{
- $z->blsft($x->{_e},10);
+ $MBI->_lsft( $z, $x->{_e},10);
}
- $z->{sign} = $x->{sign};
+ $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z));
$z;
}
my $class = ref($x) || $x;
$x = $class->new(shift) unless ref($x);
- return 1 if $x->{_m}->is_zero();
- my $len = $x->{_m}->length();
- $len += $x->{_e} if $x->{_e}->sign() eq '+';
+ return 1 if $MBI->_is_zero($x->{_m});
+
+ my $len = $MBI->_len($x->{_m});
+ $len += $MBI->_num($x->{_e}) if $x->{_es} eq '+';
if (wantarray())
{
- my $t = $MBI->bzero();
- $t = $x->{_e}->copy()->babs() if $x->{_e}->sign() eq '-';
- return ($len,$t);
+ my $t = 0;
+ $t = $MBI->_num($x->{_e}) if $x->{_es} eq '-';
+ return ($len, $t);
}
$len;
}
$x->is_one('-'); # true if arg is -1
$x->is_odd(); # true if odd, false for even
$x->is_even(); # true if even, false for odd
- $x->is_positive(); # true if >= 0
- $x->is_negative(); # true if < 0
+ $x->is_pos(); # true if >= 0
+ $x->is_neg(); # true if < 0
$x->is_inf(sign); # true if +inf, or -inf (default is '+')
$x->bcmp($y); # compare numbers (undef,<0,=0,>0)
# 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
$x->bstr(); # return string
$x->bsstr(); # return string in scientific notation
-
+
+ $x->as_int(); # return $x as BigInt
$x->exponent(); # return exponent as BigInt
$x->mantissa(); # return mantissa as BigInt
$x->parts(); # return (mantissa,exponent) as BigInt
=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