[Haskell-cafe] fast integer base-2 log function?
Stefan O'Rear
stefanor at cox.net
Tue Feb 26 20:29:02 EST 2008
On Tue, Feb 26, 2008 at 09:33:57PM +0000, Jens Blanck wrote:
> > {-# 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)
> >
> >
> I tried the above but I got wrong results on 2^31..2^32-1 because in the
> additions in ilog2i4, the number x was -1 because of sign extension
> performed by the shifts all the way (thanks for the ghci debugger). (So,
> yes, I do care somewhat about garbage on negatives :)
This is what you get for only testing on 100 and 2^34, I guess :)
If you change all the Int to Word (unsigned) it should work. Should.
> I modified to the following hoping also to use both on 32 and 64 bit
> machines. Have I shot myself in the foot anyway? For example, is there a
> guarantee that the most significant limb is non-zero? Is there any
> possibility of this or some related function being added to Data.Bits?
> [snip code]
It's still not going to be portable because I'm hardwiring the GMP "nail
count" parameter to 0. As for going standard - if you want this,
propose it! I can't think of a sane implementation of Integer that
doesn't support some kind of approximate logarithm.
Stefan
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