# phpman > perldoc > Math::BigFloat

## NAME
    [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) - Arbitrary size floating point math package

## SYNOPSIS
      use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown);

      # Configuration methods (may be used as class methods and instance methods)

      [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->accuracy();     # get class accuracy
      [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->accuracy($n);   # set class accuracy
      [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->precision();    # get class precision
      [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->precision($n);  # set class precision
      [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->round_mode();   # get class rounding mode
      [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->round_mode($m); # set global round mode, must be one of
                                      # 'even', 'odd', '+inf', '-inf', 'zero',
                                      # 'trunc', or 'common'
      [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->config("lib");  # name of backend math library

      # Constructor methods (when the class methods below are used as instance
      # methods, the value is assigned the invocand)

      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->new($str);               # defaults to 0
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->new('0x123');            # from hexadecimal
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->new('0o377');            # from octal
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->new('0b101');            # from binary
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_hex('0xc.afep+3');  # from hex
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_hex('cafe');        # ditto
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_oct('1.3267p-4');   # from octal
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_oct('01.3267p-4');  # ditto
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_oct('0o1.3267p-4'); # ditto
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_oct('0377');        # ditto
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_bin('0b1.1001p-4'); # from binary
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_bin('0101');        # ditto
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->from_ieee754($b, "binary64");  # from IEEE-754 bytes
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->bzero();                 # create a +0
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->bone();                  # create a +1
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->bone('-');               # create a -1
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->binf();                  # create a +inf
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->binf('-');               # create a -inf
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->bnan();                  # create a Not-A-Number
      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->bpi();                   # returns pi

      $y = $x->copy();        # make a copy (unlike $y = $x)
      $y = $x->as_int();      # return as BigInt

      # Boolean methods (these don't modify the invocand)

      $x->is_zero();          # if $x is 0
      $x->is_one();           # if $x is +1
      $x->is_one("+");        # ditto
      $x->is_one("-");        # if $x is -1
      $x->is_inf();           # if $x is +inf or -inf
      $x->is_inf("+");        # if $x is +inf
      $x->is_inf("-");        # if $x is -inf
      $x->is_nan();           # if $x is NaN

      $x->is_positive();      # if $x > 0
      $x->is_pos();           # ditto
      $x->is_negative();      # if $x < 0
      $x->is_neg();           # ditto

      $x->is_odd();           # if $x is odd
      $x->is_even();          # if $x is even
      $x->is_int();           # if $x is an integer

      # Comparison methods

      $x->bcmp($y);           # compare numbers (undef, < 0, == 0, > 0)
      $x->bacmp($y);          # compare absolutely (undef, < 0, == 0, > 0)
      $x->beq($y);            # true if and only if $x == $y
      $x->bne($y);            # true if and only if $x != $y
      $x->blt($y);            # true if and only if $x < $y
      $x->ble($y);            # true if and only if $x <= $y
      $x->bgt($y);            # true if and only if $x > $y
      $x->bge($y);            # true if and only if $x >= $y

      # Arithmetic methods

      $x->bneg();             # negation
      $x->babs();             # absolute value
      $x->bsgn();             # sign function (-1, 0, 1, or NaN)
      $x->bnorm();            # normalize (no-op)
      $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)
      $x->bmuladd($y,$z);     # $x = $x * $y + $z
      $x->bdiv($y);           # division (floored), set $x to quotient
                              # return (quo,rem) or quo if scalar
      $x->btdiv($y);          # division (truncated), set $x to quotient
                              # return (quo,rem) or quo if scalar
      $x->bmod($y);           # modulus (x % y)
      $x->btmod($y);          # modulus (truncated)
      $x->bmodinv($mod);      # modular multiplicative inverse
      $x->bmodpow($y,$mod);   # modular exponentiation (($x ** $y) % $mod)
      $x->bpow($y);           # power of arguments (x ** y)
      $x->blog();             # logarithm of $x to base e (Euler's number)
      $x->blog($base);        # logarithm of $x to base $base (e.g., base 2)
      $x->bexp();             # calculate e ** $x where e is Euler's number
      $x->bnok($y);           # x over y (binomial coefficient n over k)
      $x->bsin();             # sine
      $x->bcos();             # cosine
      $x->batan();            # inverse tangent
      $x->batan2($y);         # two-argument inverse tangent
      $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)

      $x->blsft($n);          # left shift $n places in base 2
      $x->blsft($n,$b);       # left shift $n places in base $b
                              # returns (quo,rem) or quo (scalar context)
      $x->brsft($n);          # right shift $n places in base 2
      $x->brsft($n,$b);       # right shift $n places in base $b
                              # returns (quo,rem) or quo (scalar context)

      # Bitwise methods

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

      # Rounding methods
      $x->round($A,$P,$mode); # round to accuracy or precision using
                              # rounding mode $mode
      $x->bround($n);         # accuracy: preserve $n digits
      $x->bfround($n);        # $n > 0: round to $nth digit left of dec. point
                              # $n < 0: round to $nth digit right of dec. point
      $x->bfloor();           # round towards minus infinity
      $x->bceil();            # round towards plus infinity
      $x->bint();             # round towards zero

      # Other mathematical methods

      $x->bgcd($y);            # greatest common divisor
      $x->blcm($y);            # least common multiple

      # Object property methods (do not modify the invocand)

      $x->sign();              # the sign, either +, - or NaN
      $x->digit($n);           # the nth digit, counting from the right
      $x->digit(-$n);          # the nth digit, counting from the left
      $x->length();            # return number of digits in number
      ($xl,$f) = $x->length(); # length of number and length of fraction
                               # part, latter is always 0 digits long
                               # for [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) objects
      $x->mantissa();          # return (signed) mantissa as BigInt
      $x->exponent();          # return exponent as BigInt
      $x->parts();             # return (mantissa,exponent) as BigInt
      $x->sparts();            # mantissa and exponent (as integers)
      $x->nparts();            # mantissa and exponent (normalised)
      $x->eparts();            # mantissa and exponent (engineering notation)
      $x->dparts();            # integer and fraction part
      $x->fparts();            # numerator and denominator
      $x->numerator();         # numerator
      $x->denominator();       # denominator

      # Conversion methods (do not modify the invocand)

      $x->bstr();         # decimal notation, possibly zero padded
      $x->bsstr();        # string in scientific notation with integers
      $x->bnstr();        # string in normalized notation
      $x->bestr();        # string in engineering notation
      $x->bdstr();        # string in decimal notation
      $x->as_hex();       # as signed hexadecimal string with prefixed 0x
      $x->as_bin();       # as signed binary string with prefixed 0b
      $x->as_oct();       # as signed octal string with prefixed 0
      $x->to_ieee754($format); # to bytes encoded according to IEEE 754-2008

      # Other conversion methods

      $x->numify();           # return as scalar (might overflow or underflow)

## DESCRIPTION
    [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) provides support for arbitrary precision floating point. Overloading is also
    provided for Perl operators.

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

      $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) -> new('12_3.456_789_123_456_789E-2');

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

### Input
    Input values to these routines may be any scalar number or string that looks like a number.
    Anything that is accepted by Perl as a literal numeric constant should be accepted by this
    module.

    *   Leading and trailing whitespace is ignored.

    *   Leading zeros are ignored, except for floating point numbers with a binary exponent, in
        which case the number is interpreted as an octal floating point number. For example,
        "01.4p+0" gives 1.5, "00.4p+0" gives 0.5, but "0.4p+0" gives a NaN. And while "0377" gives
        255, "0377p0" gives 255.

    *   If the string has a "0x" or "0X" prefix, it is interpreted as a hexadecimal number.

    *   If the string has a "0o" or "0O" prefix, it is interpreted as an octal number. A floating
        point literal with a "0" prefix is also interpreted as an octal number.

    *   If the string has a "0b" or "0B" prefix, it is interpreted as a binary number.

    *   Underline characters are allowed in the same way as they are allowed in literal numerical
        constants.

    *   If the string can not be interpreted, NaN is returned.

    *   For hexadecimal, octal, and binary floating point numbers, the exponent must be separated
        from the significand (mantissa) by the letter "p" or "P", not "e" or "E" as with decimal
        numbers.

    Some examples of valid string input

        Input string                Resulting value

        123                         123
        1.23e2                      123
        12300e-2                    123

        67_538_754                  67538754
        -4_5_6.7_8_9e+0_1_0         -4567890000000

        0x13a                       314
        0x13ap0                     314
        0x1.3ap+8                   314
        0x0.00013ap+24              314
        0x13a000p-12                314

        0o472                       314
        0o1.164p+8                  314
        0o0.0001164p+20             314
        0o1164000p-10               314

        0472                        472     Note!
        01.164p+8                   314
        00.0001164p+20              314
        01164000p-10                314

        0b100111010                 314
        0b1.0011101p+8              314
        0b0.00010011101p+12         314
        0b100111010000p-3           314

        0x1.921fb5p+1               3.14159262180328369140625e+0
        0o1.2677025p1               2.71828174591064453125
        01.2677025p1                2.71828174591064453125
        0b1.1001p-4                 9.765625e-2

### Output
    Output values are usually [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) objects.

    Boolean operators "is_zero()", "is_one()", "is_inf()", etc. return true or false.

    Comparison operators "bcmp()" and "bacmp()") return -1, 0, 1, or undef.

## METHODS
    [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) supports all methods that [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) supports, except it calculates non-integer
    results when possible. Please see [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) for a full description of each method. Below are
    just the most important differences:

### Configuration methods
### accuracy
            $x->[accuracy(5)](https://www.chedong.com/phpMan.php/man/accuracy/5/markdown);           # local for $x
            CLASS->[accuracy(5)](https://www.chedong.com/phpMan.php/man/accuracy/5/markdown);        # 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown), "bround()" in [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) or "bfround()" in [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) or by passing the
        desired accuracy to the math operation as additional parameter:

            my $x = [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown)->[new(30000)](https://www.chedong.com/phpMan.php/man/new/30000/markdown);
            my $y = [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown)->[new(7)](https://www.chedong.com/phpMan.php/man/new/7/markdown);
            print scalar $x->copy()->bdiv($y, 2);           # print 4300
            print scalar $x->copy()->bdiv($y)->[bround(2)](https://www.chedong.com/phpMan.php/man/bround/2/markdown);   # print 4300

### precision
            $x->precision(-2);        # local for $x, round at the second
                                      # digit right of the dot
            $x->[precision(2)](https://www.chedong.com/phpMan.php/man/precision/2/markdown);         # ditto, round at the second digit
                                      # left of the dot

            CLASS->[precision(5)](https://www.chedong.com/phpMan.php/man/precision/5/markdown);      # 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!

### Constructor methods
### from_hex
            $x -> from_hex("0x1.921fb54442d18p+1");
            $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) -> 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 invocand.

### from_oct
            $x -> from_oct("1.3267p-4");
            $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) -> 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 digits.

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

### from_bin
            $x -> from_bin("0b1.1001p-4");
            $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) -> 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 invocand.

### from_ieee754
        Interpret the input as a value encoded as described in IEEE754-2008. The input can be given
        as a byte string, hex string or binary string. The input is assumed to be in big-endian
        byte-order.

                # both $dbl and $mbf are 3.141592...
                $bytes = "\x40\x09\x21\xfb\x54\x44\x2d\x18";
                $dbl = unpack "d>", $bytes;
                $mbf = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) -> from_ieee754($bytes, "binary64");

### bpi
            print [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[bpi(100)](https://www.chedong.com/phpMan.php/man/bpi/100/markdown), "\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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) (June 2007).

### Arithmetic methods
### 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) (June 2007).

### bdiv
            $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)".

### bmod
            $x->bmod($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 % operator.

### 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) (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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) (April 2007).

### bsin
            my $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(1)](https://www.chedong.com/phpMan.php/man/new/1/markdown);
            print $x->[bsin(100)](https://www.chedong.com/phpMan.php/man/bsin/100/markdown), "\n";

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

        This method was added in v1.87 of [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) (June 2007).

### bcos
            my $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(1)](https://www.chedong.com/phpMan.php/man/new/1/markdown);
            print $x->[bcos(100)](https://www.chedong.com/phpMan.php/man/bcos/100/markdown), "\n";

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

        This method was added in v1.87 of [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) (June 2007).

### batan
            my $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(1)](https://www.chedong.com/phpMan.php/man/new/1/markdown);
            print $x->[batan(100)](https://www.chedong.com/phpMan.php/man/batan/100/markdown), "\n";

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

        This method was added in v1.87 of [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) (June 2007).

### batan2
            my $y = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(2)](https://www.chedong.com/phpMan.php/man/new/2/markdown);
            my $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(3)](https://www.chedong.com/phpMan.php/man/new/3/markdown);
            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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) (June 2007).

### as_float
        This method is called when [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) encounters an object it doesn't know how to
        handle. For instance, assume $x is a [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown), or subclass thereof, and $y is defined,
        but not a [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown), 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown), "as_float()" has the same effect as "copy()".

### to_ieee754
        Encodes the invocand as a byte string in the given format as specified in IEEE 754-2008.
        Note that the encoded value is the nearest possible representation of the value. This value
        might not be exactly the same as the value in the invocand.

            # $x = 3.1415926535897932385
            $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) -> [bpi(30)](https://www.chedong.com/phpMan.php/man/bpi/30/markdown);

            $b = $x -> to_ieee754("binary64");  # encode as 8 bytes
            $h = unpack "H*", $b;               # "400921fb54442d18"

            # 3.141592653589793115997963...
            $y = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) -> from_ieee754($h, "binary64");

        All binary formats in IEEE 754-2008 are accepted. For convenience, som aliases are
        recognized: "half" for "binary16", "single" for "binary32", "double" for "binary64",
        "quadruple" for "binary128", "octuple" for "binary256", and "sexdecuple" for "binary512".

        See also <<https://en.wikipedia.org/wiki/IEEE_754>>.

  ACCURACY AND PRECISION
    See also: Rounding.

    [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown).

    Since things like [sqrt(2)](https://www.chedong.com/phpMan.php/man/sqrt/2/markdown) 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:

        $d = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->div_scale();       # query
        [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->div_scale($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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(2)](https://www.chedong.com/phpMan.php/man/new/2/markdown);
        [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[accuracy(5)](https://www.chedong.com/phpMan.php/man/accuracy/5/markdown);              # 5 digits max
        $y = $x->copy()->[bdiv(3)](https://www.chedong.com/phpMan.php/man/bdiv/3/markdown);                 # gives 0.66667
        $y = $x->copy()->bdiv(3,6);               # gives 0.666667
        $y = $x->copy()->bdiv(3,6,undef,'odd');   # gives 0.666667
        [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->round_mode('zero');
        $y = $x->copy()->bdiv(3,6);               # will also give 0.666667

    Note that "[Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->accuracy()" and "[Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown);
        $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(2)](https://www.chedong.com/phpMan.php/man/new/2/markdown);
        $y = $x->copy()->[bdiv(3)](https://www.chedong.com/phpMan.php/man/bdiv/3/markdown);
        print $y->[bround(5)](https://www.chedong.com/phpMan.php/man/bround/5/markdown),"\n";               # gives 0.66667

        or

        use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown);
        $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(2)](https://www.chedong.com/phpMan.php/man/new/2/markdown);
        $y = $x->copy()->bdiv(3,5);             # gives 0.66667
        print "$y\n";

### Rounding
    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 dot.

    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 'common'.

    The default rounding mode is 'even'. By using "[Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->round_mode($round_mode);" you can
    get and set the default mode for subsequent rounding. The usage of
    "$[Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)::$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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown). 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->new(2.5);
        $y = $x->as_number('odd');      # $y = 3

## NUMERIC LITERALS
    After "use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) ':constant'" all numeric literals in the given scope are converted to
    "[Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)" objects. This conversion happens at compile time.

    For example,

        perl -[MMath::BigFloat](https://www.chedong.com/phpMan.php/perldoc/MMath%3A%3ABigFloat/markdown)=:constant -le 'print 2e-150'

    prints the exact value of 2e-150. Note that without conversion of constants the expression
    2e-150 is calculated using Perl scalars, which leads to an inaccuracte result.

    Note that strings are not affected, so that

        use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) qw/:constant/;

        $y = "1234567890123456789012345678901234567890"
                + "123456789123456789";

    does not give you what you expect. You need an explicit [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->new() around at least
    one of the operands. You should also quote large constants to prevent loss of precision:

        use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown);

        $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->new("1234567889123456789123456789123456789");

    Without the quotes Perl converts the large number to a floating point constant at compile time,
    and then converts the result to a [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) object at runtime, which results in an
    inaccurate result.

### Hexadecimal, octal, and binary floating point literals
    Perl (and this module) accepts hexadecimal, octal, and binary floating point literals, but use
    them with care with Perl versions before v5.32.0, because some versions of Perl silently give
    the wrong result. Below are some examples of different ways to write the number decimal 314.

    Hexadecimal floating point literals:

        0x1.3ap+8         0X1.3AP+8
        0x1.3ap8          0X1.3AP8
        0x13a0p-4         0X13A0P-4

    Octal floating point literals (with "0" prefix):

        01.164p+8         01.164P+8
        01.164p8          01.164P8
        011640p-4         011640P-4

    Octal floating point literals (with "0o" prefix) (requires v5.34.0):

        0o1.164p+8        0O1.164P+8
        0o1.164p8         0O1.164P8
        0o11640p-4        0O11640P-4

    Binary floating point literals:

        0b1.0011101p+8    0B1.0011101P+8
        0b1.0011101p8     0B1.0011101P8
        0b10011101000p-2  0B10011101000P-2

### Math library
    Math with the numbers is done (by default) by a module called [Math::BigInt::Calc](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ACalc/markdown). This is
    equivalent to saying:

        use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) lib => "Calc";

    You can change this by using:

        use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) only => "GMP,Pari";

    The following would first try to find [Math::BigInt::Foo](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3AFoo/markdown), then [Math::BigInt::Bar](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ABar/markdown), and when this
    also fails, revert to [Math::BigInt::Calc](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ACalc/markdown):

        use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) lib => "Foo,[Math::BigInt::Bar](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ABar/markdown)";

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

    See [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) for more details about using a different low-level library.

### Using [Math::BigInt::Lite](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ALite/markdown)
    For backwards compatibility reasons it is still possible to request a different storage class
    for use with [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown):

        use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) with => '[Math::BigInt::Lite](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3ALite/markdown)';

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

## EXPORTS
    "[Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)" exports nothing by default, but can export the "bpi()" method:

        use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown) qw/bpi/;

        print [bpi(10)](https://www.chedong.com/phpMan.php/man/bpi/10/markdown), "\n";

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

        require [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown);
        my $matter = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->bone() + 4;    # load BigInt and Calc
        [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->import( lib => 'Pari' );    # load Pari, too
        my $anti_matter = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) for reasoning and details.

### brsft
        The following will probably not print what you expect:

            my $c = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(5)](https://www.chedong.com/phpMan.php/man/new/5/markdown);
            $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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) for details and how
        to avoid that.

### precision
        A common pitfall is to use "precision()" when you want to round a result to a certain number
        of digits:

            use [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown);

            [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[precision(4)](https://www.chedong.com/phpMan.php/man/precision/4/markdown);           # does not do what you
                                                    # think it does
            my $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(12345)](https://www.chedong.com/phpMan.php/man/new/12345/markdown);     # rounds $x to "12000"!
            print "$x\n";                           # print "12000"
            my $y = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(3)](https://www.chedong.com/phpMan.php/man/new/3/markdown);         # 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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown);

            [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[accuracy(4)](https://www.chedong.com/phpMan.php/man/accuracy/4/markdown);          # enables global rounding:
            my $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(123456)](https://www.chedong.com/phpMan.php/man/new/123456/markdown);  # rounded immediately
                                                  #   to "12350"
            print "$x\n";                         # print "123500"
            my $y = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(3)](https://www.chedong.com/phpMan.php/man/new/3/markdown);       # rounded to "3
            print "$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](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown);

            my $x = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(123456)](https://www.chedong.com/phpMan.php/man/new/123456/markdown);    # no rounding
            print "$x\n";                           # print "123456"
            my $y = [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)->[new(3)](https://www.chedong.com/phpMan.php/man/new/3/markdown);         # no rounding
            print "$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.

## BUGS
    Please report any bugs or feature requests to "bug-math-bigint at rt.cpan.org", or through the
    web interface at <<https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt>> (requires login). We
    will be notified, and then you'll automatically be notified of progress on your bug as I make
    changes.

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

        perldoc [Math::BigFloat](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigFloat/markdown)

    You can also look for information at:

    *   GitHub

        <<https://github.com/pjacklam/p5-Math-BigInt>>

    *   RT: CPAN's request tracker

        <<https://rt.cpan.org/Dist/Display.html?Name=Math-BigInt>>

    *   MetaCPAN

        <<https://metacpan.org/release/Math-BigInt>>

    *   CPAN Testers Matrix

        <<http://matrix.cpantesters.org/?dist=Math-BigInt>>

    *   CPAN Ratings

        <<https://cpanratings.perl.org/dist/Math-BigInt>>

    *   The Bignum mailing list

        *   Post to mailing list

            "bignum at lists.scsys.co.uk"

        *   View mailing list

            <<http://lists.scsys.co.uk/pipermail/bignum/>>

        *   Subscribe/Unsubscribe

            <<http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum>>

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

## SEE ALSO
    [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) and [Math::BigInt](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/markdown) as well as the backends [Math::BigInt::FastCalc](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3AFastCalc/markdown), [Math::BigInt::GMP](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3AGMP/markdown),
    and [Math::BigInt::Pari](https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt%3A%3APari/markdown).

    The pragmas bignum, bigint and bigrat.

## AUTHORS
    *   Mark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001.

    *   Completely rewritten by Tels <<http://bloodgate.com>> in 2001-2008.

    *   Florian Ragwitz <<flora@cpan.org>>, 2010.

    *   Peter John Acklam <<pjacklam@gmail.com>>, 2011-.