my $class = "Math::BigInt";
require 5.005;
-$VERSION = '1.60';
+$VERSION = '1.63';
use Exporter;
@ISA = qw( Exporter );
@EXPORT_OK = qw( objectify _swap bgcd blcm);
my $self = bless {}, $class;
# shortcut for "normal" numbers
- if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*$/))
+ if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/))
{
$self->{sign} = $1 || '+';
my $ref = \$wanted;
if ($wanted =~ /^[+-]/)
{
- # remove sign without touching wanted
+ # remove sign without touching wanted to make it work with constants
my $t = $wanted; $t =~ s/^[+-]//; $ref = \$t;
}
$self->{value} = $CALC->_new($ref);
return 'inf'; # +inf
}
my ($m,$e) = $x->parts();
- # e can only be positive
- my $sign = 'e+';
- # MBF: my $s = $e->{sign}; $s = '' if $s eq '-'; my $sep = 'e'.$s;
+ my $sign = 'e+'; # e can only be positive
return $m->bstr().$sign.$e->bstr();
}
{
# Make a "normal" scalar from a BigInt object
my $x = shift; $x = $class->new($x) unless ref $x;
- return $x->{sign} if $x->{sign} !~ /^[+-]$/;
+
+ return $x->bstr() if $x->{sign} !~ /^[+-]$/;
my $num = $CALC->_num($x->{value});
return -$num if $x->{sign} eq '-';
$num;
($self,$x,$y) = objectify(2,@_);
}
+ return $upgrade->bcmp($x,$y) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
+
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
# handle +-inf and NaN
($self,$x,$y) = objectify(2,@_);
}
+ return $upgrade->bacmp($x,$y) if defined $upgrade &&
+ ((!$x->isa($self)) || (!$y->isa($self)));
+
if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
{
# handle +-inf and NaN
sub bmodinv
{
- # modular inverse. given a number which is (hopefully) relatively
+ # Modular inverse. given a number which is (hopefully) relatively
# prime to the modulus, calculate its inverse using Euclid's
- # alogrithm. if the number is not relatively prime to the modulus
+ # alogrithm. If the number is not relatively prime to the modulus
# (i.e. their gcd is not one) then NaN is returned.
# set up parameters
my ($self,$x,$y,@r) = (ref($_[0]),@_);
- # objectify is costly, so avoid it
+ # objectify is costly, so avoid it
if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
{
($self,$x,$y,@r) = objectify(2,@_);
- }
+ }
return $x if $x->modify('bmodinv');
return $x->bnan()
- if ($y->{sign} ne '+' # -, NaN, +inf, -inf
- || $x->is_zero() # or num == 0
- || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf
+ if ($y->{sign} ne '+' # -, NaN, +inf, -inf
+ || $x->is_zero() # or num == 0
+ || $x->{sign} !~ /^[+-]$/ # or num NaN, inf, -inf
);
# put least residue into $x if $x was negative, and thus make it positive
if ($CALC->can('_modinv'))
{
- $x->{value} = $CALC->_modinv($x->{value},$y->{value});
- $x->bnan() if !defined $x->{value} ; # in case there was none
+ my $sign;
+ ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value});
+ $x->bnan() if !defined $x->{value}; # in case no GCD found
+ return $x if !defined $sign; # already real result
+ $x->{sign} = $sign; # flip/flop see below
+ $x->bmod($y); # calc real result
return $x;
}
-
my ($u, $u1) = ($self->bzero(), $self->bone());
my ($a, $b) = ($y->copy(), $x->copy());
# a case with 28 loops still gains about 3% with this layout.
my $q;
($a, $q, $b) = ($b, $a->bdiv($b)); # step #1
- # Euclid's Algorithm
- while (!$b->is_zero())
+ # Euclid's Algorithm (calculate GCD of ($a,$b) in $a and also calculate
+ # two values in $u and $u1, we use only $u1 afterwards)
+ my $sign = 1; # flip-flop
+ while (!$b->is_zero()) # found GCD if $b == 0
{
- ($u, $u1) = ($u1, $u->bsub($u1->copy()->bmul($q))); # step #2
+ # the original algorithm had:
+ # ($u, $u1) = ($u1, $u->bsub($u1->copy()->bmul($q))); # step #2
+ # The following creates exact the same sequence of numbers in $u1,
+ # except for the sign ($u1 is now always positive). Since formerly
+ # the sign of $u1 was alternating between '-' and '+', the $sign
+ # flip-flop will take care of that, so that at the end of the loop
+ # we have the real sign of $u1. Keeping numbers positive gains us
+ # speed since badd() is faster than bsub() and makes it possible
+ # to have the algorithmn in Calc for even more speed.
+
+ ($u, $u1) = ($u1, $u->badd($u1->copy()->bmul($q))); # step #2
+ $sign = - $sign; # flip sign
+
($a, $q, $b) = ($b, $a->bdiv($b)); # step #1 again
}
- # if the gcd is not 1, then return NaN! It would be pointless to
- # have called bgcd to check this first, because we would then be performing
- # the same Euclidean Algorithm *twice*
+ # If the gcd is not 1, then return NaN! It would be pointless to
+ # have called bgcd to check this first, because we would then be
+ # performing the same Euclidean Algorithm *twice*.
return $x->bnan() unless $a->is_one();
- $u1->bmod($y);
- $x->{value} = $u1->{value};
- $x->{sign} = $u1->{sign};
+ $u1->bneg() if $sign != 1; # need to flip?
+
+ $u1->bmod($y); # calc result
+ $x->{value} = $u1->{value}; # and copy over to $x
+ $x->{sign} = $u1->{sign}; # to modify in place
$x;
}
my $lastlast = $x+$two;
while ($last != $x && $lastlast != $x)
{
- $lastlast = $last; $last = $x;
- $x += $y / $x;
- $x /= $two;
+ $lastlast = $last; $last = $x->copy();
+ $x->badd($y / $x);
+ $x->bdiv($two);
}
- $x-- if $x * $x > $y; # overshot?
+ $x->bdec() if $x * $x > $y; # overshot?
$x->round(@r);
}
# we have fewer digits than we want to scale to
my $len = $x->length();
+ # convert $scale to a scalar in case it is an object (put's a limit on the
+ # number length, but this would already limited by memory constraints), makes
+ # it faster
+ $scale = $scale->numify() if ref ($scale);
+
# scale < 0, but > -len (not >=!)
if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
{
my $xs = $CALC->_str($x->{value});
my $pl = -$pad-1;
-
+
# pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
# pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3
$digit_round = '0'; $digit_round = substr($$xs,$pl,1) if $pad <= $len;
if ($round_up) # what gave test above?
{
$put_back = 1;
- $pad = $len, $$xs = '0'x$pad if $scale < 0; # tlr: whack 0.51=>1.0
+ $pad = $len, $$xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0
# we modify directly the string variant instead of creating a number and
# adding it, since that is faster (we already have the string)
$$x =~ s/\s+$//g; # strip white space at end
# shortcut, if nothing to split, return early
- if ($$x =~ /^[+-]?\d+$/)
+ if ($$x =~ /^[+-]?\d+\z/)
{
$$x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
return (\$sign, $x, \'', \'', \0);
# 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2
# .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2
- return if $$x =~ /[Ee].*[Ee]/; # more than one E => error
+ #return if $$x =~ /[Ee].*[Ee]/; # more than one E => error
- my ($m,$e) = split /[Ee]/,$$x;
+ my ($m,$e,$last) = split /[Ee]/,$$x;
+ return if defined $last; # last defined => 1e2E3 or others
$e = '0' if !defined $e || $e eq "";
+
# sign,value for exponent,mantint,mantfrac
my ($es,$ev,$mis,$miv,$mfv);
# valid exponent?
$es = $1; $ev = $2;
# valid mantissa?
return if $m eq '.' || $m eq '';
- my ($mi,$mf,$last) = split /\./,$m;
- return if defined $last; # last defined => 1.2.3 or others
+ my ($mi,$mf,$lastf) = split /\./,$m;
+ return if defined $lastf; # last defined => 1.2.3 or others
$mi = '0' if !defined $mi;
$mi .= '0' if $mi =~ /^[\-\+]?$/;
$mf = '0' if !defined $mf || $mf eq '';
$one = Math::BigInt->bone(); # create a +1
$one = Math::BigInt->bone('-'); # create a -1
- # Testing
- $x->is_zero(); # true if arg is +0
- $x->is_nan(); # true if arg is NaN
- $x->is_one(); # true if arg is +1
- $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_inf(sign); # true if +inf, or -inf (sign is default '+')
- $x->is_int(); # true if $x is an integer (not a float)
-
- $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
- $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
- $x->sign(); # return the sign, either +,- or NaN
- $x->digit($n); # return the nth digit, counting from right
- $x->digit(-$n); # return the nth digit, counting from left
+ # Testing (don't modify their arguments)
+ # (return true if the condition is met, otherwise false)
+
+ $x->is_zero(); # if $x is +0
+ $x->is_nan(); # if $x is NaN
+ $x->is_one(); # if $x is +1
+ $x->is_one('-'); # if $x is -1
+ $x->is_odd(); # if $x is odd
+ $x->is_even(); # if $x is even
+ $x->is_positive(); # if $x >= 0
+ $x->is_negative(); # if $x < 0
+ $x->is_inf(sign); # if $x is +inf, or -inf (sign is default '+')
+ $x->is_int(); # if $x is an integer (not a float)
+
+ # comparing and digit/sign extration
+ $x->bcmp($y); # compare numbers (undef,<0,=0,>0)
+ $x->bacmp($y); # compare absolutely (undef,<0,=0,>0)
+ $x->sign(); # return the sign, either +,- or NaN
+ $x->digit($n); # return the nth digit, counting from right
+ $x->digit(-$n); # return the nth digit, counting from left
# The following all modify their first argument:
- # set
- $x->bzero(); # set $x to 0
- $x->bnan(); # set $x to NaN
- $x->bone(); # set $x to +1
- $x->bone('-'); # set $x to -1
- $x->binf(); # set $x to inf
- $x->binf('-'); # set $x to -inf
-
- $x->bneg(); # negation
- $x->babs(); # absolute value
- $x->bnorm(); # normalize (no-op)
- $x->bnot(); # two's complement (bit wise not)
- $x->binc(); # increment x by 1
- $x->bdec(); # decrement x by 1
+ $x->bzero(); # set $x to 0
+ $x->bnan(); # set $x to NaN
+ $x->bone(); # set $x to +1
+ $x->bone('-'); # set $x to -1
+ $x->binf(); # set $x to inf
+ $x->binf('-'); # set $x to -inf
+
+ $x->bneg(); # negation
+ $x->babs(); # absolute value
+ $x->bnorm(); # normalize (no-op in BigInt)
+ $x->bnot(); # two's complement (bit wise not)
+ $x->binc(); # increment $x by 1
+ $x->bdec(); # decrement $x by 1
- $x->badd($y); # addition (add $y to $x)
- $x->bsub($y); # subtraction (subtract $y from $x)
- $x->bmul($y); # multiplication (multiply $x by $y)
- $x->bdiv($y); # divide, set $x to quotient
- # return (quo,rem) or quo if scalar
-
- $x->bmod($y); # modulus (x % y)
- $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod))
- $x->bmodinv($mod); # the inverse of $x in the given modulus $mod
-
- $x->bpow($y); # power of arguments (x ** y)
- $x->blsft($y); # left shift
- $x->brsft($y); # right shift
- $x->blsft($y,$n); # left shift, by base $n (like 10)
- $x->brsft($y,$n); # right shift, by base $n (like 10)
+ $x->badd($y); # addition (add $y to $x)
+ $x->bsub($y); # subtraction (subtract $y from $x)
+ $x->bmul($y); # multiplication (multiply $x by $y)
+ $x->bdiv($y); # divide, set $x to quotient
+ # return (quo,rem) or quo if scalar
+
+ $x->bmod($y); # modulus (x % y)
+ $x->bmodpow($exp,$mod); # modular exponentation (($num**$exp) % $mod))
+ $x->bmodinv($mod); # the inverse of $x in the given modulus $mod
+
+ $x->bpow($y); # power of arguments (x ** y)
+ $x->blsft($y); # left shift
+ $x->brsft($y); # right shift
+ $x->blsft($y,$n); # left shift, by base $n (like 10)
+ $x->brsft($y,$n); # right shift, by base $n (like 10)
- $x->band($y); # bitwise and
- $x->bior($y); # bitwise inclusive or
- $x->bxor($y); # bitwise exclusive or
- $x->bnot(); # bitwise not (two's complement)
+ $x->band($y); # bitwise and
+ $x->bior($y); # bitwise inclusive or
+ $x->bxor($y); # bitwise exclusive or
+ $x->bnot(); # bitwise not (two's complement)
- $x->bsqrt(); # calculate square-root
- $x->bfac(); # factorial of $x (1*2*3*4*..$x)
+ $x->bsqrt(); # calculate square-root
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
- $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r
- $x->bround($N); # accuracy: preserve $N digits
- $x->bfround($N); # round to $Nth digit, no-op for BigInts
+ $x->round($A,$P,$mode); # round to accuracy or precision using mode $r
+ $x->bround($N); # accuracy: preserve $N digits
+ $x->bfround($N); # round to $Nth digit, no-op for BigInts
- # The following do not modify their arguments in BigInt, but do in BigFloat:
- $x->bfloor(); # return integer less or equal than $x
- $x->bceil(); # return integer greater or equal than $x
+ # The following do not modify their arguments in BigInt,
+ # but do so in BigFloat:
+
+ $x->bfloor(); # return integer less or equal than $x
+ $x->bceil(); # return integer greater or equal than $x
# The following do not modify their arguments:
- bgcd(@values); # greatest common divisor (no OO style)
- blcm(@values); # lowest common multiplicator (no OO style)
+ bgcd(@values); # greatest common divisor (no OO style)
+ blcm(@values); # lowest common multiplicator (no OO style)
- $x->length(); # return number of digits in number
- ($x,$f) = $x->length(); # length of number and length of fraction part,
- # latter is always 0 digits long for BigInt's
-
- $x->exponent(); # return exponent as BigInt
- $x->mantissa(); # return (signed) mantissa as BigInt
- $x->parts(); # return (mantissa,exponent) as BigInt
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
- $x->as_number(); # return as BigInt (in BigInt: same as copy())
+ $x->length(); # return number of digits in number
+ ($x,$f) = $x->length(); # length of number and length of fraction part,
+ # latter is always 0 digits long for BigInt's
+
+ $x->exponent(); # return exponent as BigInt
+ $x->mantissa(); # return (signed) mantissa as BigInt
+ $x->parts(); # return (mantissa,exponent) as BigInt
+ $x->copy(); # make a true copy of $x (unlike $y = $x;)
+ $x->as_number(); # return as BigInt (in BigInt: same as copy())
- # conversation to string
- $x->bstr(); # normalized string
- $x->bsstr(); # normalized string in scientific notation
- $x->as_hex(); # as signed hexadecimal string with prefixed 0x
- $x->as_bin(); # as signed binary string with prefixed 0b
+ # conversation to string (do not modify their argument)
+ $x->bstr(); # normalized string
+ $x->bsstr(); # normalized string in scientific notation
+ $x->as_hex(); # as signed hexadecimal string with prefixed 0x
+ $x->as_bin(); # as signed binary string with prefixed 0b
- Math::BigInt->config(); # return hash containing configuration/version
# precision and accuracy (see section about rounding for more)
- $x->precision(); # return P of $x (or global, if P of $x undef)
- $x->precision($n); # set P of $x to $n
- $x->accuracy(); # return A of $x (or global, if A of $x undef)
- $x->accuracy($n); # set P $x to $n
+ $x->precision(); # return P of $x (or global, if P of $x undef)
+ $x->precision($n); # set P of $x to $n
+ $x->accuracy(); # return A of $x (or global, if A of $x undef)
+ $x->accuracy($n); # set A $x to $n
- Math::BigInt->precision(); # get/set global P for all BigInt objects
- Math::BigInt->accuracy(); # get/set global A for all BigInt objects
+ # Global methods
+ Math::BigInt->precision(); # get/set global P for all BigInt objects
+ Math::BigInt->accuracy(); # get/set global A for all BigInt objects
+ Math::BigInt->config(); # return hash containing configuration
=head1 DESCRIPTION
=head1 METHODS
-Each of the methods below accepts three additional parameters. These arguments
-$A, $P and $R are accuracy, precision and round_mode. Please see more in the
-section about ACCURACY and ROUNDIND.
+Each of the methods below (except config(), accuracy() and precision())
+accepts three additional parameters. These arguments $A, $P and $R are
+accuracy, precision and round_mode. Please see the section about
+L<ACCURACY and PRECISION> for more information.
=head2 config
use Data::Dumper;
print Dumper ( Math::BigInt->config() );
+ print Math::BigInt->config()->{lib},"\n";
Returns a hash containing the configuration, e.g. the version number, lib
-loaded etc.
+loaded etc. The following hash keys are currently filled in with the
+appropriate information.
+
+ key Description
+ Example
+ ============================================================
+ lib Name of the Math library
+ Math::BigInt::Calc
+ lib_version Version of 'lib'
+ 0.30
+ class The class of config you just called
+ Math::BigInt
+ upgrade To which class numbers are upgraded
+ Math::BigFloat
+ downgrade To which class numbers are downgraded
+ undef
+ precision Global precision
+ undef
+ accuracy Global accuracy
+ undef
+ round_mode Global round mode
+ even
+ version version number of the class you used
+ 1.61
+ div_scale Fallback acccuracy for div
+ 40
+
+It is currently not supported to set the configuration parameters by passing
+a hash ref to C<config()>.
=head2 accuracy
$x->accuracy(5); # local for $x
- $class->accuracy(5); # global for all members of $class
+ CLASS->accuracy(5); # global for all members of CLASS
+ $A = $x->accuracy(); # read out
+ $A = CLASS->accuracy(); # read out
Set or get the global or local accuracy, aka how many significant digits the
-results have. Please see the section about L<ACCURACY AND PRECISION> for
-further details.
+results have.
+
+Please see the section about L<ACCURACY AND PRECISION> for further details.
Value must be greater than zero. Pass an undef value to disable it:
print $x->accuracy(),"\n"; # still 4
print $y->accuracy(),"\n"; # 5, since global is 5
+Note: Works also for subclasses like Math::BigFloat. Each class has it's own
+globals separated from Math::BigInt, but it is possible to subclass
+Math::BigInt and make the globals of the subclass aliases to the ones from
+Math::BigInt.
+
+=head2 precision
+
+ $x->precision(-2); # local for $x, round right of the dot
+ $x->precision(2); # ditto, but round left of the dot
+ CLASS->accuracy(5); # global for all members of CLASS
+ CLASS->precision(-5); # ditto
+ $P = CLASS->precision(); # read out
+ $P = $x->precision(); # read out
+
+Set or get the global or local precision, aka how many digits the result has
+after the dot (or where to round it when passing a positive number). In
+Math::BigInt, passing a negative number precision has no effect since no
+numbers have digits after the dot.
+
+Please see the section about L<ACCURACY AND PRECISION> for further details.
+
+Value must be greater than zero. Pass an undef value to disable it:
+
+ $x->precision(undef);
+ Math::BigInt->precision(undef);
+
+Returns the current precision. For C<$x->precision()> it will return either the
+local precision of $x, or if not defined, the global. This means the return
+value represents the accuracy that will be in effect for $x:
+
+ $y = Math::BigInt->new(1234567); # unrounded
+ print Math::BigInt->precision(4),"\n"; # set 4, print 4
+ $x = Math::BigInt->new(123456); # will be automatically rounded
+
+Note: Works also for subclasses like Math::BigFloat. Each class has it's own
+globals separated from Math::BigInt, but it is possible to subclass
+Math::BigInt and make the globals of the subclass aliases to the ones from
+Math::BigInt.
+
=head2 brsft
$x->brsft($y,$n);
=head2 bnorm
- $x->bnorm(); # normalize (no-op)
+ $x->bnorm(); # normalize (no-op)
=head2 bnot
- $x->bnot(); # two's complement (bit wise not)
+ $x->bnot(); # two's complement (bit wise not)
=head2 binc
- $x->binc(); # increment x by 1
+ $x->binc(); # increment x by 1
=head2 bdec
- $x->bdec(); # decrement x by 1
+ $x->bdec(); # decrement x by 1
=head2 badd
- $x->badd($y); # addition (add $y to $x)
+ $x->badd($y); # addition (add $y to $x)
=head2 bsub
- $x->bsub($y); # subtraction (subtract $y from $x)
+ $x->bsub($y); # subtraction (subtract $y from $x)
=head2 bmul
- $x->bmul($y); # multiplication (multiply $x by $y)
+ $x->bmul($y); # multiplication (multiply $x by $y)
=head2 bdiv
- $x->bdiv($y); # divide, set $x to quotient
- # return (quo,rem) or quo if scalar
+ $x->bdiv($y); # divide, set $x to quotient
+ # return (quo,rem) or quo if scalar
=head2 bmod
- $x->bmod($y); # modulus (x % y)
+ $x->bmod($y); # modulus (x % y)
=head2 bmodinv
- $num->bmodinv($mod); # modular inverse
+ num->bmodinv($mod); # modular inverse
Returns the inverse of C<$num> in the given modulus C<$mod>. 'C<NaN>' is
returned unless C<$num> is relatively prime to C<$mod>, i.e. unless
=head2 bmodpow
- $num->bmodpow($exp,$mod); # modular exponentation ($num**$exp % $mod)
+ $num->bmodpow($exp,$mod); # modular exponentation
+ # ($num**$exp % $mod)
Returns the value of C<$num> taken to the power C<$exp> in the modulus
C<$mod> using binary exponentation. C<bmodpow> is far superior to
writing
- $num ** $exp % $mod
+ $num ** $exp % $mod
because C<bmodpow> is much faster--it reduces internal variables into
the modulus whenever possible, so it operates on smaller numbers.
C<bmodpow> also supports negative exponents.
- bmodpow($num, -1, $mod)
+ bmodpow($num, -1, $mod)
is exactly equivalent to
- bmodinv($num, $mod)
+ bmodinv($num, $mod)
=head2 bpow
- $x->bpow($y); # power of arguments (x ** y)
+ $x->bpow($y); # power of arguments (x ** y)
=head2 blsft
- $x->blsft($y); # left shift
- $x->blsft($y,$n); # left shift, by base $n (like 10)
+ $x->blsft($y); # left shift
+ $x->blsft($y,$n); # left shift, in base $n (like 10)
=head2 brsft
- $x->brsft($y); # right shift
- $x->brsft($y,$n); # right shift, by base $n (like 10)
+ $x->brsft($y); # right shift
+ $x->brsft($y,$n); # right shift, in base $n (like 10)
=head2 band
- $x->band($y); # bitwise and
+ $x->band($y); # bitwise and
=head2 bior
- $x->bior($y); # bitwise inclusive or
+ $x->bior($y); # bitwise inclusive or
=head2 bxor
- $x->bxor($y); # bitwise exclusive or
+ $x->bxor($y); # bitwise exclusive or
=head2 bnot
- $x->bnot(); # bitwise not (two's complement)
+ $x->bnot(); # bitwise not (two's complement)
=head2 bsqrt
- $x->bsqrt(); # calculate square-root
+ $x->bsqrt(); # calculate square-root
=head2 bfac
- $x->bfac(); # factorial of $x (1*2*3*4*..$x)
+ $x->bfac(); # factorial of $x (1*2*3*4*..$x)
=head2 round
- $x->round($A,$P,$round_mode); # round to accuracy or precision using mode $r
+ $x->round($A,$P,$round_mode);
+
+Round $x to accuracy C<$A> or precision C<$P> using the round mode
+C<$round_mode>.
=head2 bround
- $x->bround($N); # accuracy: preserve $N digits
+ $x->bround($N); # accuracy: preserve $N digits
=head2 bfround
- $x->bfround($N); # round to $Nth digit, no-op for BigInts
+ $x->bfround($N); # round to $Nth digit, no-op for BigInts
=head2 bfloor
=head2 bgcd
- bgcd(@values); # greatest common divisor (no OO style)
+ bgcd(@values); # greatest common divisor (no OO style)
=head2 blcm
- blcm(@values); # lowest common multiplicator (no OO style)
+ blcm(@values); # lowest common multiplicator (no OO style)
head2 length
=head2 parts
- $x->parts(); # return (mantissa,exponent) as BigInt
+ $x->parts(); # return (mantissa,exponent) as BigInt
=head2 copy
- $x->copy(); # make a true copy of $x (unlike $y = $x;)
+ $x->copy(); # make a true copy of $x (unlike $y = $x;)
=head2 as_number
- $x->as_number(); # return as BigInt (in BigInt: same as copy())
+ $x->as_number(); # return as BigInt (in BigInt: same as copy())
=head2 bsrt
- $x->bstr(); # normalized string
+ $x->bstr(); # return normalized string
=head2 bsstr
- $x->bsstr(); # normalized string in scientific notation
+ $x->bsstr(); # normalized string in scientific notation
=head2 as_hex
- $x->as_hex(); # as signed hexadecimal string with prefixed 0x
+ $x->as_hex(); # as signed hexadecimal string with prefixed 0x
=head2 as_bin
- $x->as_bin(); # as signed binary string with prefixed 0b
+ $x->as_bin(); # as signed binary string with prefixed 0b
=head1 ACCURACY and PRECISION
projects / p5sagit/p5-mst-13.2.git / blobdiff