[Haskell-cafe] fast integer base-2 log function?

[Jens Blanck]

> {-# 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 :)

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?

{-# LANGUAGE MagicHash #-}
import GHC.Exts
import Data.Bits

limbSize = bitSize (0 :: Int)

ilog2 k x = case limbSize of
              64 -> ilog2i0 k (fromIntegral x)
              32 -> ilog2i1 k (fromIntegral x)
              _ -> undefined

-- experiment with using a LUT here (hint: FFI + static arrays in C)
ilog2i0, ilog2i1, ilog2i2, ilog2i3, ilog2i4, ilog2i5 :: Int -> Word -> Int
ilog2i0 k x | x .&. 0xFFFFFFFF00000000 /= 0 = ilog2i1 (k + 32) (x `shiftR`
32)
            | otherwise             = ilog2i1 k x
ilog2i1 k x | x .&. 0xFFFF0000 /= 0 = ilog2i2 (k + 16) (x `shiftR` 16)
            | otherwise             = ilog2i2 k x
ilog2i2 k x | x .&. 0xFF00 /= 0     = ilog2i3 (k + 8)  (x `shiftR` 8)
            | otherwise             = ilog2i3 k x
ilog2i3 k x | x .&. 0xF0 /= 0       = ilog2i4 (k + 4)  (x `shiftR` 4)
            | otherwise             = ilog2i4 k x
ilog2i4 k x | x .&. 0xC /= 0        = ilog2i5 (k + 2)  (x `shiftR` 2)
            | otherwise             = ilog2i5 k x
ilog2i5 k x | x .&. 0x2 /= 0        = k + 1 + fromIntegral (x `shiftR` 1)
            | otherwise             = k + fromIntegral x

log2i :: Integer -> Int  -- actually returns bit length
log2i (J# len adr) = ilog2 0 (I# (indexIntArray# adr (len -# 1#))) + I# (32#
*# (len -# 1#))
log2i (S# sml) = ilog2 0 (I# sml)
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