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Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)


NAME
       Math::BigFloat - Arbitrary size floating point math pack-
       age

SYNOPSIS
         use Math::BigFloat;

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

         # 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






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Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)


         $x->badd($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)
         $x->blsft($y);                # left shift
         $x->brsft($y);                # right shift
                                       # return (quo,rem) or quo if scalar

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

         $x->band($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

         # 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







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Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)


         # 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

DESCRIPTION
       All operators (inlcuding basic math operations) are over-
       loaded if you declare your big floating point numbers as

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

       Operations with overloaded operators preserve the argu-
       ments, which is exactly what you expect.

       Canonical notation

       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. Additonally, numbers are allowed to have an under-
       score between any two digits.

       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

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

       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'



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       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, as well as the result of dividing by zero.

       "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.

       A zero is represented and returned as 0E1, not 0E0 (after
       Knuth).

       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 and accuracy. For a
       full documentation, examples and tips on these topics
       please see the large section in 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.

       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, and the operation
       inquestion 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



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       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 is 40 digits.

       In case the result of one operation has more precision
       than specified, it is rounded. The rounding mode taken is
       either the default mode, or the one supplied to the opera-
       tion after the 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->round_mode('zero');
               $y = $x->copy()->bdiv(3,6);             # will give 0.666666

       Rounding


       ffround ( +$scale )
         Rounds to the $scale'th place left from the '.', count-
         ing from the dot.  The first digit is numbered 1.

       ffround ( -$scale )
         Rounds to the $scale'th place right from the '.', count-
         ing from the dot.

       ffround ( 0 )
         Rounds to an integer.

       fround  ( +$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 '.'

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

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

       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 temporarily.



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Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)


       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

EXAMPLES
         # not ready yet

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 number.

       Please note that ':constant' does not affect integer con-
       stants, 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 => 'BitVect';

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

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

       Calc.pm uses as internal format an array of elements of
       some decimal base (usually 1e7, but this might be differen
       for some systems) with the least significant digit first,
       while BitVect.pm uses a bit vector of base 2, most



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Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)


       significant bit first. Other modules might use even dif-
       ferent means of representing the numbers. See the respec-
       tive module 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 neccessary things (like BigInt) when
       they are needed, and automatically.

       Use the lib, Luke! And see "Using Math::BigInt::Lite" for
       more details than you ever wanted to know about loading a
       different library.

       Using Math::BigInt::Lite

       It is possible to use Math::BigInt::Lite with
       Math::BigFloat:

               # 1
               use Math::BigFloat with => 'Math::BigInt::Lite';

       There is no need to "use Math::BigInt" or "use Math::Big-
       Int::Lite", but you can combine these if you want. For
       instance, you may want to use Math::BigInt objects in your
       main script, too.

               # 2
               use Math::BigInt;
               use Math::BigFloat with => 'Math::BigInt::Lite';

       Of course, you can combine this with the "lib" parameter.

               # 3
               use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';

       There is no need for a "use Math::BigInt;" statement, even
       if you want to use Math::BigInt's, since Math::BigFloat
       will needs Math::BigInt and thus always loads it. But if
       you add it, add it before:





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Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)


               # 4
               use Math::BigInt;
               use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'GMP,Pari';

       Notice that the module with the last "lib" will "win" and
       thus it's lib will be used if the lib is available:

               # 5
               use Math::BigInt lib => 'Bar,Baz';
               use Math::BigFloat with => 'Math::BigInt::Lite', lib => 'Foo';

       That would try to load Foo, Bar, Baz and Calc (in that
       order). Or in other words, Math::BigFloat will try to
       retain previously loaded libs when you don't specify it
       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 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 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 actu-
       ally loading one of them. Still, this type of usage is not
       recommended due to these issues.

       The old way (loading the lib only in BigInt) still works
       though:

               # 6
               use Math::BigInt lib => 'Bar,Baz';
               use Math::BigFloat;

       You can even load Math::BigInt afterwards:

               # 7
               use Math::BigFloat;
               use Math::BigInt lib => 'Bar,Baz';

       But this has the same problems like #5, it will first load
       Calc (Math::BigFloat needs Math::BigInt and thus loads it)
       and then later Bar or Baz, depending on which of them
       works and is usable/loadable. Since this loads Calc
       unnecc., it is not recommended.

       Since it also possible to just require Math::BigFloat,
       this poses the question about what libary this will use:

               require Math::BigFloat;
               my $x = Math::BigFloat->new(123); $x += 123;

       It will use Calc. Please note that the call to import() is
       still done, but only when you use for the first time some



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Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)


       Math::BigFloat math (it is triggered via any constructor,
       so the first time you create a Math::BigFloat, the load
       will happen in the background). This means:

               require Math::BigFloat;
               Math::BigFloat->import ( lib => 'Foo,Bar' );

       would be the same as:

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

       But don't try to be clever to insert some operations in
       between:

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

       While this works, it loads Calc needlessly. But maybe you
       just wanted that?

       Examples #3 is highly recommended for daily usage.

BUGS
       Please see the file BUGS in the CPAN distribution
       Math::BigInt for known bugs.

CAVEATS
       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.

       bdiv
        The following will probably not do what you expect:

                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 care-
        full. You probably want to use

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

        instead.

       Modifying and =
        Beware of:

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



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Math::BigFloat(3pPerl Programmers Reference GuiMath::BigFloat(3p)


        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
        "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

SEE ALSO
       Math::BigInt, Math::BigRat and Math::Big as well as
       Math::BigInt::BitVect, Math::BigInt::Pari and  Math::Big-
       Int::GMP.

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

       The package at <http://search.cpan.org/search?mode=mod-
       ule&query=Math%3A%3ABigInt> contains more documentation
       including a full version history, testcases, empty sub-
       class files and benchmarks.

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

AUTHORS
       Mark Biggar, overloaded interface by Ilya Zakharevich.
       Completely rewritten by Tels http://bloodgate.com in 2001,
       2002, and still at it in 2003.


















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