大数运算（一）

Author：水如烟

一时兴起做做看看，发现真的不简单，花时间，头大。不过体会也相应深些。

运算单元改了又改。在基本运算单元中，变量能简则简，条件检测尽可能的放在外围。

下面的代码是关于大数值的存储和分割。其中把握好地址是关键。因为数值是分块运算的，如果地址转换不正确，最后合并结果时肯定也不正确的了。这个稍经修改，可以用来写文件切合器。区别是，处理对象不同，一是字符，一是字节。

整体的我还没做好。也是一个单元一个单元的做。如往后需要修改补充，以最后供下载的代码为准。

Friend Class Information
    Private Sub New()
    End Sub

    Private Shared gUnitMaxSize As Integer
    Private Shared gUnitDataType As TypeCode

    ''' <summary>
    ''' 运算单元最大位数
    ''' </summary>
    Public Shared ReadOnly Property UnitMaxSize() As Integer
        Get
            Return 1 '测试,不用太大。gUnitMaxSize
        End Get
    End Property

    ''' <summary>
    ''' 运算单元数据类型
    ''' </summary>
    ''' <value></value>
    Public Shared ReadOnly Property UnitDataType() As TypeCode
        Get
            Return gUnitDataType
        End Get
    End Property

    ''' <summary>
    ''' 转换为运算单元数据类型
    ''' </summary>
    ''' <param name="Value">值</param>
    Public Shared Function ConverToUnitDataType(ByVal Value As Object) As Object
        Return System.Convert.ChangeType(Value, UnitDataType)
    End Function

    Public Shared Function ConverToUnitDataTypeFullString(ByVal Value As Object) As String
        Return Value.ToString.PadLeft(UnitMaxSize, "0"c)
    End Function

    Public Shared Function ConverToUnitDataTypeFullString(ByVal Value As Object, ByVal unitNum As Integer) As String
        Return Value.ToString.PadLeft(CInt(UnitMaxSize * Math.Pow(2, unitNum)), "0"c)
    End Function

    Public Shared Function SplitValueToArray(ByVal Value As String) As String()
        Return SplitValueToArray(Value, 0)
    End Function

    Public Shared Function SplitValueToArray(ByVal Value As String, ByVal unitNum As Integer) As String()
        Return CommonFunction.SplitStringToArray(Value, CInt(UnitMaxSize * Math.Pow(2, unitNum)))
    End Function

    Public Shared Function AddressConvertFromAToB(ByVal aAddress As Integer, ByVal aUnitNum As Integer, ByVal bUnitNum As Integer) As Integer
        If (aAddress * Math.Pow(2, aUnitNum)) Mod Math.Pow(2, bUnitNum) > 0 Then Throw New Exception("转换无效")
        Return CInt(aAddress * Math.Pow(2, aUnitNum) / (Math.Pow(2, bUnitNum)))
    End Function

    Public Shared Function IsZero(ByVal value As String) As Boolean
        Return System.Text.RegularExpressions.Regex.IsMatch(value, "^[0]+$")
    End Function

    Public Shared Function GetStringValue(ByVal Value As String) As String
        Dim mResult As String = System.Text.RegularExpressions.Regex.Match(Value, "^[0]{0,}(?<Value>[1-9].*)$").Groups("Value").Value
        If String.IsNullOrEmpty(mResult) Then mResult = "0"
        Return mResult
    End Function

    Public Shared Function GetStringsValue(ByVal valueCollection As Collections.ObjectModel.Collection(Of String), ByVal unitNum As Integer) As String
        Return GetStringsValue(valueCollection, 0, unitNum)
    End Function

    Public Shared Function GetStringsValue(ByVal valueCollection As Collections.ObjectModel.Collection(Of String), ByVal appendEmptyValueCount As Integer, ByVal unitNum As Integer) As String
        Return GetStringsValue(valueCollection, 0, valueCollection.Count - 1, appendEmptyValueCount, unitNum)
    End Function

    Public Shared Function GetStringsValue(ByVal valueCollection As Collections.ObjectModel.Collection(Of String), ByVal firstIndex As Integer, ByVal lastIndex As Integer, ByVal unitNum As Integer) As String
        Return GetStringsValue(valueCollection, firstIndex, lastIndex, 0, unitNum)
    End Function

    Public Shared Function GetStringsValue(ByVal valueCollection As Collections.ObjectModel.Collection(Of String), ByVal firstIndex As Integer, ByVal lastIndex As Integer, ByVal appendEmptyValueCount As Integer, ByVal unitNum As Integer) As String
        Dim b As New System.Text.StringBuilder
        Dim tmp As String

        For i As Integer = firstIndex To lastIndex

            If i = firstIndex Then
                tmp = valueCollection(i)
            Else
                tmp = Information.ConverToUnitDataTypeFullString(valueCollection(i), unitNum)
            End If

            b.Append(tmp)
        Next

        For i As Integer = 0 To appendEmptyValueCount - 1
            tmp = Information.ConverToUnitDataTypeFullString("0", unitNum)
            b.Append(tmp)
        Next

        Return b.ToString
    End Function

    Shared Sub New()

        '寻找可表示为整数的且表示范围最大的数据类型
        Dim mTypeName As String
        Dim mType As Type
        Dim mFieldInfo As Reflection.FieldInfo

        Dim mMaxValue As String = "0"
        Dim mDataTypeCode As TypeCode

        Dim mCurrentTypeMaxValue As String = "0"
        For Each c As TypeCode In [Enum].GetValues(GetType(TypeCode))

            mTypeName = c.ToString
            mType = Type.GetType(String.Format("System.{0}", mTypeName))

            mFieldInfo = mType.GetField("MaxValue")
            If mFieldInfo Is Nothing Then Continue For

            mCurrentTypeMaxValue = mFieldInfo.GetValue(Nothing).ToString

            If IsNumeric(mCurrentTypeMaxValue) Then
                If mCurrentTypeMaxValue.Length > mMaxValue.Length Then
                    mMaxValue = mCurrentTypeMaxValue
                    mDataTypeCode = c
                End If
            End If

        Next

        gUnitDataType = mDataTypeCode

        '确定该数据类型下,可表示的最大位数。保证两数相乘结果仍可表示为整数。
        Dim x As Object
        x = ConverToUnitDataType(mMaxValue)

        Dim mSqrtResult As String = Math.Sqrt(CDbl(x)).ToString '最大数开方

        Dim mPointIndex As Integer = mSqrtResult.IndexOf("."c) '只取整数部分
        If mPointIndex > 0 Then
            mSqrtResult = mSqrtResult.Substring(0, mPointIndex)
        End If

        Dim mDigits As Integer = mSqrtResult.ToString.Length - 1 '可表示的最大位数是最大数开方后整数部分位数减一位

        gUnitMaxSize = mDigits
    End Sub

End Class

Friend Class CommonFunction
    Private Sub New()
    End Sub

    Public Shared Function Clone(Of T)(ByVal obj As T) As T
        Dim tmpT As T

        Dim mFormatter As New System.Runtime.Serialization.Formatters.Binary.BinaryFormatter
        Dim mMemoryStream As New System.IO.MemoryStream

        Using mMemoryStream
            mFormatter.Serialize(mMemoryStream, obj)
            mMemoryStream.Position = 0
            tmpT = CType(mFormatter.Deserialize(mMemoryStream), T)
            mMemoryStream.Close()
        End Using

        Return tmpT
    End Function

    Public Shared Function SplitStringToArray(ByVal line As String, ByVal digits As Integer) As String()
        Dim mLineLength As Integer = line.Length
        Dim mCount As Integer = mLineLength  \ digits
        If (mLineLength Mod digits) > 0 Then mCount += 1

        Dim mResult(mCount - 1) As String

        Dim mCurrentIndex As Integer
        For i As Integer = mCount - 1 To 0 Step -1
            mCurrentIndex = mLineLength - (mCount - i) * digits

            If mCurrentIndex < 0 Then
                mResult(0) = line.Substring(0, mLineLength - (mCount - 1) * digits)
            Else
                mResult(i) = line.Substring(mCurrentIndex, digits)

            End If

        Next

        Return mResult
    End Function

End Class

<Serializable()> _
Public Class AddressInformation
    Private gAddress As Integer = 0
    Private gUnitNum As Integer = 0

    Public Property Address() As Integer
        Get
            Return gAddress
        End Get
        Friend Set(ByVal value As Integer)
            gAddress = value
        End Set
    End Property

    Public ReadOnly Property UnitNum() As Integer
        Get
            Return gUnitNum
        End Get
    End Property

    Friend Sub Add(ByVal value As Integer)
        gAddress += value
    End Sub

    Friend Sub SetZero()
        gAddress = 0
    End Sub

    Friend Sub Increase()
        gAddress += 1
    End Sub

    Friend Sub ResetAddressFrom(ByVal address As Integer, ByVal unitNum As Integer)
        gAddress = AddressConvertFromAToB(address, unitNum, gUnitNum)
    End Sub

    Friend Sub CopyAddressTo(ByRef addressInfo As AddressInformation)
        addressInfo.gAddress = AddressConvertFromAToB(gAddress, gUnitNum, addressInfo.gUnitNum)
    End Sub

    Friend Sub New()
    End Sub

    Friend Sub New(ByVal unitNum As Integer)
        gUnitNum = unitNum
    End Sub

    Public Function Clone() As AddressInformation
        Return CommonFunction.Clone(Of AddressInformation)(Me)
    End Function

    Public Function ConvertTo(ByVal unitNum As Integer) As AddressInformation
        Dim mAddressInfo As New AddressInformation(unitNum)
        CopyAddressTo(mAddressInfo)
        Return mAddressInfo
    End Function

    Private Shared Function AddressConvertFromAToB(ByVal aAddress As Integer, ByVal aUnitNum As Integer, ByVal bUnitNum As Integer) As Integer
        Return Information.AddressConvertFromAToB(aAddress, aUnitNum, bUnitNum)
    End Function

    Public Shadows Function ToString() As String
        Return String.Format("UnitNum :{0}, Address :{1}", gUnitNum, gAddress)
    End Function
End Class

<Serializable()> _
Public Class StringValue
    Private gOrignalAddressInfo As AddressInformation
    Private gFirstAddressInfo As AddressInformation
    Private gLastAddressInfo As AddressInformation

    Private gValueArray As New System.Collections.ObjectModel.Collection(Of String)

    Friend ReadOnly Property ValueCollection() As System.Collections.ObjectModel.Collection(Of String)
        Get
            Return gValueArray
        End Get
    End Property

    Friend ReadOnly Property OrignalAddressInfo() As AddressInformation
        Get
            Return gOrignalAddressInfo
        End Get
    End Property

    Public ReadOnly Property FirstAddressInfo() As AddressInformation
        Get
            Return gFirstAddressInfo
        End Get
    End Property

    Public ReadOnly Property LastAddressInfo() As AddressInformation
        Get
            Return gLastAddressInfo
        End Get
    End Property

    Public ReadOnly Property UnitLength() As Integer
        Get
            Return CInt(Information.UnitMaxSize * Math.Pow(2, gFirstAddressInfo.UnitNum))
        End Get
    End Property

    Public ReadOnly Property Size() As Integer
        Get
            Return gLastAddressInfo.Address - gFirstAddressInfo.Address + 1
        End Get
    End Property

    Public ReadOnly Property FullValue() As String
        Get
            Return GetFullValue()
        End Get
    End Property

    Private Function GetFullValue() As String

        Return Information.GetStringsValue(gValueArray, gFirstAddressInfo.Address - gOrignalAddressInfo.Address, gFirstAddressInfo.UnitNum)
    End Function

    Public ReadOnly Property Value() As String
        Get
            Return GetValue()
        End Get
    End Property

    Private Function GetValue() As String

        Return Information.GetStringsValue(gValueArray, gFirstAddressInfo.UnitNum)
    End Function

    Private Sub Initialize(ByVal value As String)
        gOrignalAddressInfo = gFirstAddressInfo.Clone

        If Information.IsZero(value) Then
            gValueArray.Add("0")
        Else
            '处理这种情形0000000000000000000000000012344505454564646900000000000000000
            Dim tmpValueArray As String() = Information.SplitValueToArray(value, gFirstAddressInfo.UnitNum)

            '忽略前面是零的项；每项，如全是0用一个0表示(000000000000=0)，否则忽略开头的0(00000012300=12300)
            Dim mCurrentValue As String
            Dim mFirstIsZero As Boolean = True

            For i As Integer = 0 To tmpValueArray.Length - 1
                mCurrentValue = Information.GetStringValue(tmpValueArray(i))

                mFirstIsZero = mFirstIsZero And mCurrentValue.Equals("0")
                If Not mFirstIsZero Then
                    gValueArray.Add(mCurrentValue)
                End If
            Next

            '最后面连续项全是0的，当进位处理，地址前移，移去这些项
            Dim mLastIsZero As Boolean = True
            Dim mCount As Integer = 0
            Do Until Not mLastIsZero
                mLastIsZero = mLastIsZero And gValueArray(gValueArray.Count - 1).Equals("0")
                If mLastIsZero Then
                    mCount += 1
                    gValueArray.RemoveAt(gValueArray.Count - 1)
                End If
            Loop

            If mCount > 0 Then gFirstAddressInfo.Add(mCount)
        End If

        gLastAddressInfo = gFirstAddressInfo.Clone
        gLastAddressInfo.Add(gValueArray.Count - 1)
    End Sub

    Friend Sub New(ByVal value As String)
        gFirstAddressInfo = New AddressInformation()

        Initialize(value)
    End Sub

    Friend Sub New(ByVal unitNum As Integer, ByVal address As Integer, ByVal value As String)
        gFirstAddressInfo = New AddressInformation(unitNum)
        gFirstAddressInfo.Address = address

        Initialize(value)
    End Sub

    Friend Sub New(ByVal addressInfo As AddressInformation, ByVal value As String)
        gFirstAddressInfo = addressInfo.Clone

        Initialize(value)
    End Sub

    Public Function Test_OutPutValueInformation() As String
        Dim mFormat As String = "({0},{1})"

        Dim b As New System.Text.StringBuilder
        For i As Integer = 0 To Size - 1

            b.Append(String.Format(mFormat, gLastAddressInfo.Address - i, gValueArray(i)))
        Next

        Return b.ToString
    End Function

    Private Function GetAddress(ByVal index As Integer) As Integer
        Return gLastAddressInfo.Address - index
    End Function

    Private Function GetIndex(ByVal Address As Integer) As Integer
        Return gLastAddressInfo.Address - Address
    End Function

    Public Function CopyToByIndex(ByVal unitNum As Integer, ByVal index As Integer) As StringValue

        Return CopyToByIndex(unitNum, index, index)
    End Function

    Public Function CopyToByIndex(ByVal unitNum As Integer, ByVal firstIndex As Integer, ByVal lastIndex As Integer) As StringValue
        If (firstIndex > lastIndex) OrElse (firstIndex < 0 OrElse lastIndex > Me.Size) Then Throw New Exception("引用索引无效")

        Dim mAddressInfo As AddressInformation = gFirstAddressInfo.ConvertTo(unitNum)
        mAddressInfo.ResetAddressFrom(GetAddress(lastIndex), gFirstAddressInfo.UnitNum) '地址以lastIndex地址为参照

        Dim mValue As String
        mValue = Information.GetStringsValue(gValueArray, firstIndex, lastIndex, gFirstAddressInfo.UnitNum)

        Return New StringValue(mAddressInfo, mValue)
    End Function

    Public Function CopyToByAddress(ByVal unitNum As Integer, ByVal address As Integer) As StringValue
        Return CopyToByIndex(unitNum, GetIndex(address))
    End Function

    Public Function CopyToByAddress(ByVal unitNum As Integer, ByVal firstAddress As Integer, ByVal lastAddress As Integer) As StringValue
        Return CopyToByIndex(unitNum, GetIndex(lastAddress), GetIndex(firstAddress))
    End Function

    Public Function CopyTo(ByVal unitNum As Integer) As StringValue
        Return New StringValue(gFirstAddressInfo.ConvertTo(unitNum), Me.Value)
    End Function

    Public Function Clone() As StringValue
        Return CommonFunction.Clone(Of StringValue)(Me)
    End Function
End Class

测试代码：

    Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click
        BigIntLibrary.Test.Run()
    End Sub

Public Class Test
    Public Shared Sub Run()
        Dim addressInfo As New AddressInformation(6)
        addressInfo.Address = 0
        Dim Value As String = "700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000"
        Console.WriteLine(Value)

        Dim Result As New StringValue(addressInfo, Value)
        OutPut(Result)

        OutPut(Result.CopyTo(0))

        OutPut(Result.CopyTo(1))

        OutPut(Result.CopyTo(2))

        OutPut(Result.CopyTo(3))

        OutPut(Result.CopyTo(4))

        OutPut(Result.CopyTo(5))

        OutPut(Result.CopyTo(6))

        OutPut(Result.CopyTo(5).CopyToByIndex(2, 0))
        OutPut(Result.CopyTo(5).CopyToByIndex(2, 0, 1))

    End Sub

    Private Shared Sub OutPut(ByVal info As StringValue)
        Console.WriteLine()
        With info
            Console.WriteLine("存储指数:{0},单位大小:{1},起始地址:{2}", .FirstAddressInfo.UnitNum, .UnitLength, .FirstAddressInfo.Address)
            Console.WriteLine("值:{0}", .Value)
            Console.WriteLine("存储情形:")
            Console.WriteLine(.Test_OutPutValueInformation)
        End With

    End Sub
End Class

结果：

700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000

存储指数:6,单位大小:64,起始地址:0
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000
存储情形:
(1,70000000000080000000000000001111111111011111111111111)(0,7880000000000000000000000088000000000000000000000000000000000000)

存储指数:0,单位大小:1,起始地址:36
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088
存储情形:
(116,7)(115,0)(114,0)(113,0)(112,0)(111,0)(110,0)(109,0)(108,0)(107,0)(106,0)(105,0)(104,8)(103,0)(102,0)(101,0)(100,0)(99,0)(98,0)(97,0)(96,0)(95,0)(94,0)(93,0)(92,0)(91,0)(90,0)(89,0)(88,1)(87,1)(86,1)(85,1)(84,1)(83,1)(82,1)(81,1)(80,1)(79,1)(78,0)(77,1)(76,1)(75,1)(74,1)(73,1)(72,1)(71,1)(70,1)(69,1)(68,1)(67,1)(66,1)(65,1)(64,1)(63,7)(62,8)(61,8)(60,0)(59,0)(58,0)(57,0)(56,0)(55,0)(54,0)(53,0)(52,0)(51,0)(50,0)(49,0)(48,0)(47,0)(46,0)(45,0)(44,0)(43,0)(42,0)(41,0)(40,0)(39,0)(38,0)(37,8)(36,8)

存储指数:1,单位大小:2,起始地址:18
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088
存储情形:
(58,7)(57,0)(56,0)(55,0)(54,0)(53,0)(52,8)(51,0)(50,0)(49,0)(48,0)(47,0)(46,0)(45,0)(44,1)(43,11)(42,11)(41,11)(40,11)(39,10)(38,11)(37,11)(36,11)(35,11)(34,11)(33,11)(32,11)(31,78)(30,80)(29,0)(28,0)(27,0)(26,0)(25,0)(24,0)(23,0)(22,0)(21,0)(20,0)(19,0)(18,88)

存储指数:2,单位大小:4,起始地址:9
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088
存储情形:
(29,7)(28,0)(27,0)(26,8)(25,0)(24,0)(23,0)(22,1)(21,1111)(20,1111)(19,1011)(18,1111)(17,1111)(16,1111)(15,7880)(14,0)(13,0)(12,0)(11,0)(10,0)(9,88)

存储指数:3,单位大小:8,起始地址:4
值:7000000000008000000000000000111111111101111111111111178800000000000000000000000880000
存储情形:
(14,70000)(13,8)(12,0)(11,1)(10,11111111)(9,10111111)(8,11111111)(7,78800000)(6,0)(5,0)(4,880000)

存储指数:4,单位大小:16,起始地址:2
值:7000000000008000000000000000111111111101111111111111178800000000000000000000000880000
存储情形:
(7,70000)(6,800000000)(5,111111111)(4,1011111111111111)(3,7880000000000000)(2,880000)

存储指数:5,单位大小:32,起始地址:1
值:7000000000008000000000000000111111111101111111111111178800000000000000000000000880000
存储情形:
(3,700000000000800000000)(2,1111111111011111111111111)(1,78800000000000000000000000880000)

存储指数:2,单位大小:4,起始地址:26
值:7000000000008
存储情形:
(29,7)(28,0)(27,0)(26,8)

存储指数:2,单位大小:4,起始地址:16
值:70000000000080000000000000001111111111011111111111111
存储情形:
(29,7)(28,0)(27,0)(26,8)(25,0)(24,0)(23,0)(22,1)(21,1111)(20,1111)(19,1011)(18,1111)(17,1111)(16,1111)

如果：

修改一下测试代码：

Public Class Test
    Public Shared Sub Run()
        Dim addressInfo As New AddressInformation(6)
        addressInfo.Address = 0
        Dim Value As String = "700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000"
        Console.WriteLine(Value)

        Dim Result As New StringValue(addressInfo, Value)
        OutPut(Result)

        OutPut(Result.CopyTo(0))

        OutPut(Result.CopyTo(1))

        OutPut(Result.CopyTo(2))

        OutPut(Result.CopyTo(3))

        OutPut(Result.CopyTo(4))

        OutPut(Result.CopyTo(5))

        OutPut(Result.CopyTo(6))

        Result = Result.CopyTo(5)
        OutPut(Result.CopyToByIndex(2, Result.Size - 1))
        OutPut(Result.CopyToByIndex(2, 0, Result.Size - 1))
        OutPut(Result.CopyToByAddress(2, Result.FirstAddressInfo.Address, Result.LastAddressInfo.Address))

结果是：

700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000

存储指数:6,单位大小:896,起始地址:0
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000
存储情形:
(0,700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000)

存储指数:0,单位大小:14,起始地址:2
值:70000000000080000000000000001111111111011111111111111788000000000000000000000008800000000
存储情形:
(8,70000)(7,8000000)(6,11111)(5,11111011111111)(4,11111178800000)(3,0)(2,8800000000)

存储指数:1,单位大小:28,起始地址:1
值:70000000000080000000000000001111111111011111111111111788000000000000000000000008800000000
存储情形:
(4,70000)(3,800000000000000011111)(2,1111101111111111111178800000)(1,8800000000)

存储指数:2,单位大小:56,起始地址:0
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000
存储情形:
(2,70000)(1,8000000000000000111111111101111111111111178800000)(0,88000000000000000000000000000000000000)

存储指数:3,单位大小:112,起始地址:0
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000
存储情形:
(1,70000)(0,800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000)

存储指数:4,单位大小:224,起始地址:0
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000
存储情形:
(0,700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000)

存储指数:5,单位大小:448,起始地址:0
值:700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000
存储情形:
(0,700000000000800000000000000011111111110111111111111117880000000000000000000000088000000000000000000000000000000000000)

存储指数:6,单位大小:896,起始地址:0
值:700000000000800000000000000011111111110111111111111117880000000000