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 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.

Configuration methods

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()" in Math::BigInt, "bround()" in Math::BigInt or "bfround()" in Math::BigInt or by passing the desired accuracy to the math operation as additional parameter:

    my $x = Math::BigInt->new(30000);
    my $y = Math::BigInt->new(7);
    print scalar $x->copy()->bdiv($y, 2);           # print 4300
    print scalar $x->copy()->bdiv($y)->bround(2);   # print 4300
    

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!

Constructor methods

from_hex()

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

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

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

from_oct()

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

Interpret input as an octal string. A single underscore character ("_") may be placed between any two digits. If the input is invalid, a NaN is returned. The exponent is in base 2 using decimal 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 -> 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;
        $mbf = Math::BigFloat -> from_ieee754($bytes, "binary64");
    

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).

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 (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 (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).

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).

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).

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).

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).

as_float()

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

    $x -> badd($y);
    

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

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

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 -> bpi(30);
    $b = $x -> to_ieee754("binary64");  # encode as 8 bytes
    $h = unpack "H*", $b;               # "400921fb54442d18"
    # 3.141592653589793115997963...
    $y = Math::BigFloat -> from_ieee754($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 supports both precision (rounding to a certain place before or after the dot) and accuracy (rounding to a certain number of digits). For a full documentation, examples and tips on these topics please see the large section about rounding in Math::BigInt.

Since things like sqrt(2) or "1 / 3" must presented with a limited accuracy lest a operation consumes all resources, each operation produces no more than the requested number of digits.

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

    $d = Math::BigFloat->div_scale();       # query
    Math::BigFloat->div_scale($n);          # set to $n digits

The default value for "div_scale" is 40.

In case the result of one operation has more digits than specified, it is rounded. The rounding mode taken is either the default mode, or the one supplied to the operation after the scale:

    $x = Math::BigFloat->new(2);
    Math::BigFloat->accuracy(5);              # 5 digits max
    $y = $x->copy()->bdiv(3);                 # 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->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";               # gives 0.66667
    or
    use Math::BigFloat;
    $x = Math::BigFloat->new(2);
    $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->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

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. 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.

See Math::BigInt for more details about using a different low-level library.

Using Math::BigInt::Lite

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

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

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