Extracting the exponent and mantissa of a Javascript Number

Integer factorization is nowhere near necessary for this.

The exponent is basically going to be the floor of the base-2 logarithm, which isn't that hard to compute.

The following code passes QuickCheck tests, as well as tests on infinity and negative infinity:

minNormalizedDouble :: Double
minNormalizedDouble = 2 ^^ (-1022)

powers :: [(Int, Double)]
powers = [(b, 2.0 ^^ fromIntegral b) | i <- [9, 8..0], let b = bit i]

exponentOf :: Double -> Int
exponentOf d
  | d < 0   = exponentOf (-d)
  | d < minNormalizedDouble = -1024
  | d < 1   = 
      let go (dd, accum) (p, twoP)
            | dd * twoP < 1 = (dd * twoP, accum - p)
            | otherwise = (dd, accum)
      in snd $ foldl' go (d, 0) powers
  | otherwise   =
      let go (x, accum) (p, twoP)
            | x * twoP <= d = (x * twoP, accum + p)
            | otherwise = (x, accum)
    in 1 + (snd $ foldl' go (1.0, 0) powers)


decode :: Double -> (Integer, Int)
decode 0.0 = (0, 0)
decode d
  | isInfinite d, d > 0 = (4503599627370496, 972)
  | isInfinite d, d < 0 = (-4503599627370496, 972)
  | isNaN d             = (-6755399441055744, 972)
  | otherwise       =
      let
        e = exponentOf d - 53
        twoE = 2.0 ^^ e
         in (round (d / twoE), e)

I tested it using quickCheck (\ d -> decodeFloat d == decode d), and explicitly tested it separately on positive and negative infinities.

The only primitive operations used here are left-shift, double multiplication, double division, and infinity and NaN testing, which Javascript supports to the best of my knowledge.

Using the new ArrayBuffer access arrays, it is actually possible to retrieve the exact mantissa and exponent, by extracting them from the Uint8Array. If you need more speed, consider reusing the Float64Array.

function getNumberParts(x)
{
    var float = new Float64Array(1),
        bytes = new Uint8Array(float.buffer);

    float[0] = x;

    var sign = bytes[7] >> 7,
        exponent = ((bytes[7] & 0x7f) << 4 | bytes[6] >> 4) - 0x3ff;

    bytes[7] = 0x3f;
    bytes[6] |= 0xf0;

    return {
        sign: sign,
        exponent: exponent,
        mantissa: float[0],
    }
}

I've also created some test cases. 0 fails, since there is another representation for 2^-1023.

var tests = [1, -1, .123, -.123, 1.5, -1.5, 1e100, -1e100, 
                    1e-100, -1e-100, Infinity, -Infinity];

tests.forEach(function(x)
{
    var parts = getNumberParts(x),
        value = Math.pow(-1, parts.sign) *
                    Math.pow(2, parts.exponent) *
                    parts.mantissa;

    console.log("Testing: " + x + " " + value);
    console.assert(x === value);
});

console.log("Tests passed");

ECMAScript doesn't define any straightforward way to do this; but for what it's worth, this isn't a "factorization problem" in the same sense as prime factorization.

What you want can theoretically be done very quickly by first handling the sign, then using a binary-tree approach (or logarithm) to find the exponent, and lastly dividing by the relevant power of two to get the mantissa; but unfortunately, it can be somewhat tricky to implement this in practice (what with special cases such as denormalized numbers). I recommend you read through section 8.5 of the ECMAScript specification to get a sense of what cases you'll have to handle.

For base 10 you can get mantissa and exponent in an array with

   var myarray = (number.toExponential() + '').split("e");
   // then ...
   var mantissa = parseFloat(myarray[0]);
   var exponent = parseInt(myarray[1]);

If you don't care if the result parts are text instead of numbers and if there might be a plus sign on the front of the exponent part, then you can skip the parseFloat and parseInt steps and just take the parts directly from the array at [0] and [1].