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Math::BigFloat(3pm)    Perl Programmers Reference Guide    Math::BigFloat(3pm)


       Math::BigFloat - Arbitrary size floating point math package


        use Math::BigFloat;

        # Number creation
        my $x = Math::BigFloat->new($str);     # defaults to 0
        my $y = $x->copy();                    # make a true copy
        my $nan  = Math::BigFloat->bnan();     # create a NotANumber
        my $zero = Math::BigFloat->bzero();    # create a +0
        my $inf = Math::BigFloat->binf();      # create a +inf
        my $inf = Math::BigFloat->binf('-');   # create a -inf
        my $one = Math::BigFloat->bone();      # create a +1
        my $mone = Math::BigFloat->bone('-');  # create a -1
        my $x = Math::BigFloat->bone('-');     #

        my $x = Math::BigFloat->from_hex('0xc.afep+3');    # from hexadecimal
        my $x = Math::BigFloat->from_bin('0b1.1001p-4');   # from binary
        my $x = Math::BigFloat->from_oct('1.3267p-4');     # from octal

        my $pi = Math::BigFloat->bpi(100);     # PI to 100 digits

        # the following examples compute their result to 100 digits accuracy:
        my $cos  = Math::BigFloat->new(1)->bcos(100);        # cosinus(1)
        my $sin  = Math::BigFloat->new(1)->bsin(100);        # sinus(1)
        my $atan = Math::BigFloat->new(1)->batan(100);       # arcus tangens(1)

        my $atan2 = Math::BigFloat->new(  1 )->batan2( 1 ,100); # batan(1)
        my $atan2 = Math::BigFloat->new(  1 )->batan2( 8 ,100); # batan(1/8)
        my $atan2 = Math::BigFloat->new( -2 )->batan2( 1 ,100); # batan(-2)

        # 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_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)
        $x->bacmp($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. If you want to pre-
        # serve $x, use $z = $x->copy()->bXXX($y); See under L</CAVEATS> for
        # necessary when mixing $a = $b assignments with non-overloaded math.

        # set
        $x->bzero();            # set $i to 0
        $x->bnan();             # set $i 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

        $x->badd($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)
        $x->bpow($y);           # power of arguments ($x ** $y)
        $x->bmodpow($exp,$mod); # modular exponentiation (($num**$exp) % $mod))
        $x->blsft($y, $n);      # left shift by $y places in base $n
        $x->brsft($y, $n);      # right shift by $y places in base $n
                                # returns (quo,rem) or quo if in scalar context

        $x->blog();             # logarithm of $x to base e (Euler's number)
        $x->blog($base);        # logarithm of $x to base $base (f.i. 2)
        $x->bexp();             # calculate e ** $x where e is Euler's number

        $x->band($y);           # bit-wise and
        $x->bior($y);           # bit-wise inclusive or
        $x->bxor($y);           # bit-wise exclusive or
        $x->bnot();             # bit-wise not (two's complement)

        $x->bsqrt();            # calculate square-root
        $x->broot($y);          # $y'th root of $x (e.g. $y == 3 => cubic root)
        $x->bfac();             # factorial of $x (1*2*3*4*..$x)

        $x->bround($N);         # accuracy: preserve $N digits
        $x->bfround($N);        # precision: round to the $Nth digit

        $x->bfloor();           # return integer less or equal than $x
        $x->bceil();            # return integer greater or equal than $x
        $x->bint();             # round towards zero

         # The following do not modify their arguments:

        bgcd(@values);          # greatest common divisor
        blcm(@values);          # lowest common multiplicator

        $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

        $x->length();           # number of digits (w/o sign and '.')
        ($l,$f) = $x->length(); # number of digits, and length of fraction

        $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

        # these get/set the appropriate global value for all BigFloat objects
        Math::BigFloat->precision();   # Precision
        Math::BigFloat->accuracy();    # Accuracy
        Math::BigFloat->round_mode();  # rounding mode


       All operators (including basic math operations) are overloaded if you
       declare your big floating point numbers as

         $i = Math::BigFloat -> new('12_3.456_789_123_456_789E-2');

       Operations with overloaded operators preserve the arguments, which is
       exactly what you expect.

       Input to these routines are either BigFloat objects, or strings of the
       following four forms:

       o   "/^[+-]\d+$/"

       o   "/^[+-]\d+\.\d*$/"

       o   "/^[+-]\d+E[+-]?\d+$/"

       o   "/^[+-]\d*\.\d+E[+-]?\d+$/"

       all with optional leading and trailing zeros and/or spaces.
       Additionally, numbers are allowed to have an underscore between any two

       Empty strings as well as other illegal numbers results in 'NaN'.

       bnorm() on a BigFloat object is now effectively a no-op, since the
       numbers are always stored in normalized form. On a string, it creates a
       BigFloat object.

       Output values are BigFloat objects (normalized), except for bstr() and

       The string output will always have leading and trailing zeros stripped
       and drop a plus sign. "bstr()" will give you always the form with a
       decimal point, while "bsstr()" (s for scientific) gives you the
       scientific notation.

               Input                   bstr()          bsstr()
               '-0'                    '0'             '0E1'
               '  -123 123 123'        '-123123123'    '-123123123E0'
               '00.0123'               '0.0123'        '123E-4'
               '123.45E-2'             '1.2345'        '12345E-4'
               '10E+3'                 '10000'         '1E4'

       Some routines ("is_odd()", "is_even()", "is_zero()", "is_one()",
       "is_nan()") return true or false, while others ("bcmp()", "bacmp()")
       return either undef, <0, 0 or >0 and are suited for sort.

       Actual math is done by using the class defined with "with => Class;"
       (which defaults to BigInts) to represent the mantissa and exponent.

       The sign "/^[+-]$/" is stored separately. The string 'NaN' is used to
       represent the result when input arguments are not numbers, and 'inf'
       and '-inf' are used to represent positive and negative infinity,

   mantissa(), exponent() and parts()
       mantissa() and exponent() return the said parts of the BigFloat as
       BigInts such that:

               $m = $x->mantissa();
               $e = $x->exponent();
               $y = $m * ( 10 ** $e );
               print "ok\n" if $x == $y;

       "($m,$e) = $x->parts();" is just a shortcut giving you both of them.

       Currently the mantissa is reduced as much as possible, favouring higher
       exponents over lower ones (e.g. returning 1e7 instead of 10e6 or
       10000000e0).  This might change in the future, so do not depend on it.

   Accuracy vs. Precision
       See also: Rounding.

       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 Math::BigInt.

       Since things like sqrt(2) or "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.

       If there is no global precision or accuracy set, and the operation in
       question was not called with a requested precision or accuracy, and the
       input $x has no accuracy or precision set, then a fallback parameter
       will be used. For historical reasons, it is called "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 for "div_scale" is 40.

       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 scale:

           $x = Math::BigFloat->new(2);
           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
           $y = $x->copy()->bdiv(3,6);               # will also give 0.666667

       Note that "Math::BigFloat->accuracy()" and
       "Math::BigFloat->precision()" set the global variables, and thus any
       newly created number will be subject to the global rounding
       immediately. This means that in the examples above, the 3 as argument
       to "bdiv()" will also get an accuracy of 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


               use Math::BigFloat;
               $x = Math::BigFloat->new(2);
               $y = $x->copy()->bdiv(3,5);             # will give 0.66667
               print "$y\n";

       bfround ( +$scale )
           Rounds to the $scale'th place left from the '.', counting from the
           dot.  The first digit is numbered 1.

       bfround ( -$scale )
           Rounds to the $scale'th place right from the '.', counting from the

       bfround ( 0 )
           Rounds to an integer.

       bround  ( +$scale )
           Preserves accuracy to $scale digits from the left (aka significant
           digits) and pads the rest with zeros. If the number is between 1
           and -1, the significant digits count from the first non-zero after
           the '.'

       bround  ( -$scale ) and bround ( 0 )
           These are effectively no-ops.

       All rounding functions take as a second parameter a rounding mode from
       one of the following: 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or

       The default rounding mode is 'even'. By using
       "Math::BigFloat->round_mode($round_mode);" you can get and set the
       default mode for subsequent rounding. The usage of
       "$Math::BigFloat::$round_mode" is no longer supported.  The second
       parameter to the round functions then overrides the default

       The "as_number()" function returns a BigInt from a Math::BigFloat. It
       uses 'trunc' as rounding mode to make it equivalent to:

               $x = 2.5;
               $y = int($x) + 2;

       You can override this by passing the desired rounding mode as parameter
       to "as_number()":

               $x = Math::BigFloat->new(2.5);
               $y = $x->as_number('odd');      # $y = 3


       Math::BigFloat supports all methods that Math::BigInt supports, except
       it calculates non-integer results when possible. Please see
       Math::BigInt for a full description of each method. Below are just the
       most important differences:

                 $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 sticks, e.g. once you created a number under
           the influence of "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 "round()" in Math::BigInt, "bround()" in Math::BigInt
           or "bfround()" in Math::BigInt 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

                 $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 "accuracy()" instead. With
           "accuracy()" you set the number of digits each result should have,
           with "precision()" you set the place where to round!

                   $q = $x->bdiv($y);
                   ($q, $r) = $x->bdiv($y);

           In scalar context, divides $x by $y and returns the result to the
           given or default accuracy/precision. In list context, does floored
           division (F-division), returning an integer $q and a remainder $r
           so that $x = $q * $y + $r. The remainer (modulo) is equal to what
           is returned by "$x-"bmod($y)>.


           Returns $x modulo $y. When $x is finite, and $y is finite and non-
           zero, the result is identical to the remainder after floored
           division (F-division). If, in addition, both $x and $y are
           integers, the result is identical to the result from Perl's %

                   $x->bexp($accuracy);            # calculate e ** X

           Calculates the expression "e ** $x" where "e" is Euler's number.

           This method was added in v1.82 of Math::BigInt (April 2007).

                   $x->bnok($y);   # x over y (binomial coefficient n over k)

           Calculates the binomial coefficient n over k, also called the
           "choose" function. The result is equivalent to:

                   ( n )      n!
                   | - |  = -------
                   ( k )    k!(n-k)!

           This method was added in v1.84 of Math::BigInt (April 2007).

                   print Math::BigFloat->bpi(100), "\n";

           Calculate PI to N digits (including the 3 before the dot). The
           result is rounded according to the current rounding mode, which
           defaults to "even".

           This method was added in v1.87 of Math::BigInt (June 2007).

                   my $x = Math::BigFloat->new(1);
                   print $x->bcos(100), "\n";

           Calculate the cosinus of $x, modifying $x in place.

           This method was added in v1.87 of Math::BigInt (June 2007).

                   my $x = Math::BigFloat->new(1);
                   print $x->bsin(100), "\n";

           Calculate the sinus of $x, modifying $x in place.

           This method was added in v1.87 of Math::BigInt (June 2007).

                   my $y = Math::BigFloat->new(2);
                   my $x = Math::BigFloat->new(3);
                   print $y->batan2($x), "\n";

           Calculate the arcus tanges of $y divided by $x, modifying $y in
           place.  See also "batan()".

           This method was added in v1.87 of Math::BigInt (June 2007).

                   my $x = Math::BigFloat->new(1);
                   print $x->batan(100), "\n";

           Calculate the arcus tanges of $x, modifying $x in place. See also

           This method was added in v1.87 of Math::BigInt (June 2007).


           Multiply $x by $y, and then add $z to the result.

           This method was added in v1.87 of Math::BigInt (June 2007).

           This method is called when Math::BigFloat encounters an object it
           doesn't know how to handle. For instance, assume $x is a
           Math::BigFloat, or subclass thereof, and $y is defined, but not a
           Math::BigFloat, or subclass thereof. If you do

               $x -> badd($y);

           $y needs to be converted into an object that $x can deal with. This
           is done by first checking if $y is something that $x might be
           upgraded to. If that is the case, no further attempts are made. The
           next is to see if $y supports the method "as_float()". The method
           "as_float()" is expected to return either an object that has the
           same class as $x, a subclass thereof, or a string that
           "ref($x)->new()" can parse to create an object.

           In Math::BigFloat, "as_float()" has the same effect as "copy()".

               $x -> from_hex("0x1.921fb54442d18p+1");
               $x = Math::BigFloat -> from_hex("0x1.921fb54442d18p+1");

           Interpret input as a hexadecimal string.A prefix ("0x", "x",
           ignoring case) is optional. A single underscore character ("_") may
           be placed between any two digits. If the input is invalid, a NaN is
           returned. The exponent is in base 2 using decimal digits.

           If called as an instance method, the value is assigned to the

               $x -> from_bin("0b1.1001p-4");
               $x = Math::BigFloat -> from_bin("0b1.1001p-4");

           Interpret input as a hexadecimal string. A prefix ("0b" or "b",
           ignoring case) is optional. A single underscore character ("_") may
           be placed between any two digits. If the input is invalid, a NaN is
           returned. The exponent is in base 2 using decimal digits.

           If called as an instance method, the value is assigned to the

               $x -> from_oct("1.3267p-4");
               $x = Math::BigFloat -> from_oct("1.3267p-4");

           Interpret input as an octal string. A single underscore character
           ("_") may be placed between any two digits. If the input is
           invalid, a NaN is returned. The exponent is in base 2 using decimal

           If called as an instance method, the value is assigned to the

Autocreating constants

       After "use Math::BigFloat ':constant'" all the floating point constants
       in the given scope are converted to "Math::BigFloat". This conversion
       happens at compile time.

       In particular

         perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"'

       prints the value of "2E-100". Note that without conversion of constants
       the expression 2E-100 will be calculated as normal floating point

       Please note that ':constant' does not affect integer constants, nor
       binary nor hexadecimal constants. Use bignum or Math::BigInt to get
       this to work.

   Math library
       Math with the numbers is done (by default) by a module called
       Math::BigInt::Calc. This is equivalent to saying:

               use Math::BigFloat lib => 'Calc';

       You can change this by using:

               use Math::BigFloat lib => 'GMP';

       Note: General purpose packages should not be explicit about the library
       to use; let the script author decide which is best.

       Note: The keyword 'lib' will warn when the requested library could not
       be loaded. To suppress the warning use 'try' instead:

               use Math::BigFloat try => 'GMP';

       If your script works with huge numbers and Calc is too slow for them,
       you can also for the loading of one of these libraries and if none of
       them can be used, the code will die:

               use Math::BigFloat only => 'GMP,Pari';

       The following would first try to find Math::BigInt::Foo, then
       Math::BigInt::Bar, and when this also fails, revert to

               use Math::BigFloat lib => 'Foo,Math::BigInt::Bar';

       See the respective low-level library documentation for further details.

       Please note that Math::BigFloat does not use the denoted library
       itself, but it merely passes the lib argument to Math::BigInt. So,
       instead of the need to do:

               use Math::BigInt lib => 'GMP';
               use Math::BigFloat;

       you can roll it all into one line:

               use Math::BigFloat lib => 'GMP';

       It is also possible to just require Math::BigFloat:

               require Math::BigFloat;

       This will load the necessary things (like BigInt) when they are needed,
       and automatically.

       See Math::BigInt for more details than you ever wanted to know about
       using a different low-level library.

   Using Math::BigInt::Lite
       For backwards compatibility reasons it is still possible to request a
       different storage class for use with Math::BigFloat:

               use Math::BigFloat with => 'Math::BigInt::Lite';

       However, this request is ignored, as the current code now uses the low-
       level math library for directly storing the number parts.


       "Math::BigFloat" exports nothing by default, but can export the "bpi()"

               use Math::BigFloat qw/bpi/;

               print bpi(10), "\n";


       Do not try to be clever to insert some operations in between switching

           require Math::BigFloat;
           my $matter = Math::BigFloat->bone() + 4;    # load BigInt and Calc
           Math::BigFloat->import( lib => 'Pari' );    # load Pari, too
           my $anti_matter = Math::BigFloat->bone()+4; # now use Pari

       This will create objects with numbers stored in two different backend
       libraries, and VERY BAD THINGS will happen when you use these together:

               my $flash_and_bang = $matter + $anti_matter;    # Don't do this!

       stringify, bstr()
           Both stringify and bstr() now drop the leading '+'. The old code
           would return '+1.23', the new returns '1.23'. See the documentation
           in Math::BigInt for reasoning and details.

           The following will probably not print what you expect:

                   print $c->bdiv(123.456),"\n";

           It prints both quotient and remainder since print works in list
           context. Also, bdiv() will modify $c, so be careful. You probably
           want to use

               print $c / 123.456,"\n";
               # or if you want to modify $c:
               print scalar $c->bdiv(123.456),"\n";


           The following will probably not print what you expect:

                   my $c = Math::BigFloat->new('3.14159');
                   print $c->brsft(3,10),"\n";     # prints 0.00314153.1415

           It prints both quotient and remainder, since print calls "brsft()"
           in list context. Also, "$c->brsft()" will modify $c, so be careful.
           You probably want to use

                   print scalar $c->copy()->brsft(3,10),"\n";
                   # or if you really want to modify $c
                   print scalar $c->brsft(3,10),"\n";


       Modifying and =
           Beware of:

                   $x = Math::BigFloat->new(5);
                   $y = $x;

           It will not do what you think, e.g. making a copy of $x. Instead it
           just makes a second reference to the same object and stores it in
           $y. Thus anything that modifies $x will modify $y (except
           overloaded math operators), and vice versa. See Math::BigInt for
           details and how to avoid that.

           "bpow()" now modifies the first argument, unlike the old code which
           left it alone and only returned the result. This is to be
           consistent with "badd()" etc. The first will modify $x, the second
           one won't:

                   print bpow($x,$i),"\n";         # modify $x
                   print $x->bpow($i),"\n";        # ditto
                   print $x ** $i,"\n";            # leave $x alone

       precision() vs. accuracy()
           A common pitfall is to use "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 "precision()" with "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 not "taint" the result with an accuracy or precision setting,
           which would influence any further operation.


       Please report any bugs or feature requests to "bug-math-bigint at", or through the web interface at
       <> (requires
       login).  We will be notified, and then you'll automatically be notified
       of progress on your bug as I make changes.


       You can find documentation for this module with the perldoc command.

           perldoc Math::BigFloat

       You can also look for information at:

       o   RT: CPAN's request tracker


       o   AnnoCPAN: Annotated CPAN documentation


       o   CPAN Ratings


       o   Search CPAN


       o   CPAN Testers Matrix


       o   The Bignum mailing list

           o   Post to mailing list

               "bignum at"

           o   View mailing list


           o   Subscribe/Unsubscribe



       This program is free software; you may redistribute it and/or modify it
       under the same terms as Perl itself.


       Math::BigFloat and Math::BigInt(3) as well as the backends
       Math::BigInt::FastCalc(3), Math::BigInt::GMP(3), and 

       The pragmas bignum(3), bigint(3) and bigrat(3) also might be of
       interest because they solve the autoupgrading/downgrading issue, at
       least partly.


       o   Mark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001.

       o   Completely rewritten by Tels <> in 2001-2008.

       o   Florian Ragwitz, 2010.

       o   Peter John Acklam,, 2011-.

perl v5.24.0                      2016-03-01               Math::BigFloat(3pm)

perl 5.24 - Generated Wed Nov 16 19:09:06 CST 2016
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