Haskell日志库错误 [英] Haskell logbase error

问题描述

我试图计算Haskell中Integer的长度，使用长度等于 truncate（log10（x）+1）的事实。 p>

使用我创建的整数：

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

不幸的是，并非所有的数字都得到正确的长度。我试了几个不同的案例，发现：

  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 
  

为什么 logBase 10 1000 不返回3.0？如何以10为基数获得1000的正确对数值？

解决方案

GHC模块中有一个整数对数基函数其中键入整数 - >整数 - >

  { - ＃LANGUAGE MagicHash＃ - } 
 
 import Control.Monad 
 import GHC.Integer.Logarithms（integerLogBase＃）
 import GHC.Exts（Int（..） ）
 
 main = do 
 forM_ [（1 :: Int）.. 20] $ \\\
  - >做
让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 
  

输出：

  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 
  

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?

解决方案

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

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