Haskell logbase error

Question

I am trying to calculate the length of an Integer in Haskell, using the fact that the length is equal to truncate (log10(x)+1).

Using Integers I created:

len :: Integer -> Integer
len i = toInteger (truncate (logBase 10 (fromIntegral i)) + 1)

Unfortunately, not all numbers get the correct length. I tried a few different cases and found that:

logBase 10 10         = 1.0
logBase 10 100        = 2.0
logBase 10 1000       = 2.9999..6
logBase 10 10000      = 4.0
logBase 10 100000     = 5.0
logBase 10 1000000    = 5.9999999

Is there a reason why logBase 10 1000 doesn't return 3.0? How do I get the correct log-value for 1000 in base 10?

Answer 1

There is an integer log base function in GHC modules which has type Integer -> Integer -> Int#.

Example usage:

{-# LANGUAGE MagicHash #-}

import Control.Monad
import GHC.Integer.Logarithms ( integerLogBase# )
import GHC.Exts (Int(..))

main = do
  forM_ [(1::Int)..20] $ \n -> do
    let a = 10^n-1
        la = I# (integerLogBase# 10 a)
        b = 10^n
        lb = I# (integerLogBase# 10 b)
    putStrLn $ show a ++ " -> " ++ show la
    putStrLn $ show b ++ " -> " ++ show lb

Output:

9 -> 0
10 -> 1
99 -> 1
100 -> 2
999 -> 2
1000 -> 3
9999 -> 3
10000 -> 4
99999 -> 4
100000 -> 5
999999 -> 5
1000000 -> 6
9999999 -> 6
...
9999999999999999999 -> 18
10000000000000000000 -> 19
99999999999999999999 -> 19
100000000000000000000 -> 20