[Haskell-cafe] fast integer base-2 log function?
Stefan O'Rear
stefanor at cox.net
Mon Feb 11 02:21:07 EST 2008
On Sun, Feb 10, 2008 at 10:15:58PM -0800, Uwe Hollerbach wrote:
> Hello, haskellers,
>
> Is there a fast integer base-2 log function anywhere in the standard
> libraries? I wandered through the index, but didn't find anything that
> looked right. I need something that's more robust than logBase, it
> needs to handle numbers with a few to many thousands of digits. I
> found a thread from a couple of years ago that suggested there was no
> such routine, and that simply doing "length (show n)" might be the
> best. That seems kind of... less than elegant. I've come up with a
> routine, shown below, that seems reasonably fast (a few seconds of CPU
> time for a million-bit number, likely adequate for my purposes), but
> it seems that something with privileged access to the innards of an
> Integer ought to be even much faster -- it's just a simple walk along
> a list (array?) after all. Any pointers? Thanks!
Even easier.
{-# LANGUAGE MagicHash #-}
import GHC.Exts
import Data.Bits
-- experiment with using a LUT here (hint: FFI + static arrays in C)
ilog2i0, ilog2i1, ilog2i2, ilog2i3, ilog2i4 :: Int -> Int -> Int
ilog2i0 k x | x .&. 0xFFFF0000 /= 0 = ilog2i1 (k + 16) (x `shiftR` 16)
| otherwise = ilog2i1 k x
ilog2i1 k x | x .&. 0xFF00 /= 0 = ilog2i2 (k + 8) (x `shiftR` 8)
| otherwise = ilog2i2 k x
ilog2i2 k x | x .&. 0xF0 /= 0 = ilog2i3 (k + 4) (x `shiftR` 4)
| otherwise = ilog2i3 k x
ilog2i3 k x | x .&. 0xC /= 0 = ilog2i4 (k + 2) (x `shiftR` 2)
| otherwise = ilog2i4 k x
ilog2i4 k x | x .&. 0x2 /= 0 = k + 1 + (x `shiftR` 1)
| otherwise = k + x
log2i :: Integer -> Int -- actually returns bit length, and returns garbage on negatives, but do you care?
log2i (J# len adr) = ilog2i0 0 (I# (indexIntArray# adr (len -# 1#))) + I# (32# *# (len -# 1#))
log2i (S# sml) = ilog2i0 0 (I# sml)
> > powi :: Integer -> Integer -> Integer
> > powi b e | e == 0 = 1
> > | e < 0 = error "negative exponent in powi"
> > | even e = powi (b*b) (e `quot` 2)
> > | otherwise = b * (powi b (e - 1))
>
> > ilog2 :: Integer -> Integer
> > ilog2 n | n < 0 = ilog2 (- n)
> > | n < 2 = 1
> > | otherwise = up n (1 :: Integer)
> > where up n a = if n < (powi 2 a)
> > then bin (quot a 2) a
> > else up n (2*a)
> > bin lo hi = if (hi - lo) <= 1
> > then hi
> > else let av = quot (lo + hi) 2
> > in if n < (powi 2 av)
> > then bin lo av
> > else bin av hi
>
> (This was all properly aligned when I cut'n'pasted; proportional fonts
> might be messing it up here.)
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