Extracting the exponent and mantissa of a Javascript Number

Question

Is there a reasonably fast way to extract the exponent and mantissa from a Number in Javascript?

AFAIK there\'s no way to get at the bits behind a Number in Javascri

Answer 1

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.