为什么 ULong > 16 位数字的数学会变得不稳定？

Question

我正在做一个"简单的";基地转换器来转换ULong基地10一个字符串与任何基础。这里我用64个字符。用例是缩短存储为String的ULong。

Public Class BaseConverter
'base64, but any length would work
Private Shared ReadOnly Characters() As Char = {"0"c, "1"c, "2"c, "3"c, "4"c, "5"c, "6"c, "7"c, "8"c, "9"c,
"a"c, "b"c, "c"c, "d"c, "e"c, "f"c, "g"c, "h"c, "i"c, "j"c, "k"c, "l"c, "m"c, "n"c, "o"c, "p"c, "q"c, "r"c, "s"c, "t"c, "u"c, "v"c, "w"c, "x"c, "y"c, "z"c,
"A"c, "B"c, "C"c, "D"c, "E"c, "F"c, "G"c, "H"c, "I"c, "J"c, "K"c, "L"c, "M"c, "N"c, "O"c, "P"c, "Q"c, "R"c, "S"c, "T"c, "U"c, "V"c, "W"c, "X"c, "Y"c, "Z"c,
"+"c, "-"c}
Public Shared Function Encode(number As ULong) As String
Dim buffer = New Text.StringBuilder()
Dim quotient = number
Dim remainder As ULong
Dim base = Convert.ToUInt64(Characters.LongLength)
Do
remainder = quotient Mod base
quotient = quotient  base
buffer.Insert(0, Characters(remainder).ToString())
Loop While quotient <> 0
Return buffer.ToString()
End Function
Public Shared Function Decode(str As String) As ULong
If String.IsNullOrWhiteSpace(str) Then Return 0
Dim result As ULong = 0
Dim base = Convert.ToUInt64(Characters.LongLength)
Dim nPos As ULong = 0
For i As Integer = str.Length - 1 To 0 Step - 1
Dim cPos As Integer = Array.IndexOf(Of Char)(Characters, str(i))
result += (base ^ nPos) * Convert.ToUInt64(cPos)
nPos += 1
Next
Return result
End Function
End Class

它可以很好地处理16位以内的数字，但当数字有更多的数字时，它开始对进行舍入。

17位的结果为8,18位的结果为32,19位的结果为256。

例如，42347959784570944周围的这些数字不要工作并导致那些块:

42347959784570939 > 2msPWXX00X > 42347959784570936 ERROR
42347959784570940 > 2msPWXX00Y > 42347959784570944 ERROR
42347959784570941 > 2msPWXX00Z > 42347959784570944 ERROR
42347959784570942 > 2msPWXX00+ > 42347959784570944 ERROR
42347959784570943 > 2msPWXX00- > 42347959784570944 ERROR
42347959784570944 > 2msPWXX010 > 42347959784570944
42347959784570945 > 2msPWXX011 > 42347959784570944 ERROR
42347959784570946 > 2msPWXX012 > 42347959784570944 ERROR
42347959784570947 > 2msPWXX013 > 42347959784570944 ERROR
42347959784570948 > 2msPWXX014 > 42347959784570944 ERROR
42347959784570949 > 2msPWXX015 > 42347959784570952 ERROR

问题必须在Decode()函数，因为生成的字符串不同。

我在https://dotnetfiddle.net/7wAGLh上做了一些测试，但我就是找不到问题。

Answer 1

指数运算符^总是返回一个Double.
这意味着整个表达式(base ^ nPos) * Convert.ToUInt64(cPos)被求值并返回为Double(然后无声地塞进ULong)。

这会带来你正在观察的Double不精确。

始终使用Option Strict On是捕获这些错误的好方法。

假设您知道(base ^ nPos)不会超过ULong的最大值(这似乎是假设)，那么修复方法是

result += CULng(base ^ nPos) * Convert.ToUInt64(cPos)