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?
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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