Programming Praxis – Bit Hacks

In today’s Programming Praxis exercise, our goal is to write three functions that use bit twiddling, namely one to determine a numbers sign, one to determine of the signs of two numbers are equal and one to take the absolute value of a number without using branching. Let’s get started, shall we?

import Data.Bits
import Data.Composition

To determine whether or not a number is negative we can simply look at the highest bit.

negative :: Int -> Bool
negative n = testBit n (bitSize n - 1)

To check whether two numbers have the same sign we use an xor operation, which will produce a 0 in the highest bit when they are the same and a 1 when they’re not. We then test that bit to produce the result.

sameSign :: Int -> Int -> Bool
sameSign = (not . negative) .: xor

For the absolute function I used the provided algorithm. When testing I thought I’d found a mistake since abs(minBound) was not equal to maxBound. Turns out this is correct behaviour: minBound is equal to -2147483648, whereas maxBound is equal to 2147483647. Note the difference in the last number. Taking the absolute of minBound produces a value that cannot be expressed in 32 bits and thus loops right back around to minBound.

absolute :: Int -> Int
absolute n = xor (n + mask) mask where mask = shiftR n (bitSize n - 1)

Some tests to see if everything is working properly:

main :: IO ()
main = do print $       negative minBound
          print $       negative (-100)
          print $       negative   (-1)
          print $ not $ negative     0
          print $ not $ negative     1
          print $ not $ negative   100
          print $ not $ negative maxBound
          print $       sameSign minBound minBound
          print $       sameSign (-1) (-1)
          print $ not $ sameSign (-1)   1
          print $ not $ sameSign   1  (-1)
          print $       sameSign   1    1
          print $       sameSign maxBound maxBound
          print $ absolute minBound == minBound
          print $ absolute   (-100) ==      100
          print $ absolute       0  ==        0
          print $ absolute     100  ==      100
          print $ absolute maxBound == maxBound

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