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

NAME
       Math::BigFloat - Arbitrary size floating point math package

SYNOPSIS
         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 $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 preserve
         # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is
         # 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,$mod);       # modular exponentation (($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

         # 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

DESCRIPTION
       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';

       Operations with overloaded operators preserve the arguments, 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.
       Additionally, numbers are allowed to have an underscore 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'

       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 (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 gloabl 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
               Math::BigFloat->round_mode('zero');
               $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

               or

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

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

       ffround ( -$scale )
         Rounds to the $scale'th place right from the '.', counting 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 rounding mode from
       one of the following: 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or
       'common'.

       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.

       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

METHODS
       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:

   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 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(), bround() or 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

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

   bexp()
               $x->bexp($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).

   bnok()
               $x->bnok($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).

   bpi()
               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).

   bcos()
               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).

   bsin()
               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).

   batan2()
               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).

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

       Calculate the arcus tanges of $x, modifying $x in place. See also
       batan2().

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

   bmuladd()
               $x->bmuladd($y,$z);

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

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

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 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
       Math::BigInt::Calc:

               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 libary for directly storing the number parts.

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

               use Math::BigFloat qw/bpi/;

               print bpi(10), "\n";

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

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

               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.

       bdiv
        The following will probably not print 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 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

        instead.

       brsft
        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";

        instead.

       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
        "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.

SEE ALSO
       Math::BigInt, Math::BigRat and Math::Big as well as
       Math::BigInt::BitVect, Math::BigInt::Pari and  Math::BigInt::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/~tels/Math-BigInt
       <http://search.cpan.org/~tels/Math-BigInt> contains more documentation
       including a full version history, testcases, empty subclass 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 - 2006, and still at
       it in 2007.

perl v5.12.1                      2010-04-26               Math::BigFloat(3pm)
 

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