关于天文数字十进制与十六进制间的转换

对于一般的整型数字，16进制与10进制 间的转化可以用CLNG（），HEX（）函数解决，但遇上天文数字，这些函数就无能为力了。下面是笔者写的几个函数，演示了天文数字计算中的一些技巧。

Dim largehex As String, largedec As String, start As Long, Y(20) As String

'预备函数
Function sums(ByVal X As String, ByVal Y As String) As String ' sum of two hugehexnum（两个大数之和）
Dim max As Long, temp As Long, I As Long, result As Variant
max = IIf(Len(X) >= Len(Y), Len(X), Len(Y))
X = Right(String(max, "0") & X, max)
Y = Right(String(max, "0") & Y, max)
ReDim result(0 To max)
For I = max To 1 Step -1
result(I) = Val(Mid(X, I, 1)) + Val(Mid(Y, I, 1))
Next
For I = max To 1 Step -1
temp = result(I) \ 10
result(I) = result(I) Mod 10
result(I - 1) = result(I - 1) + temp
Next
If result(0) = 0 Then result(0) = ""
sums = Join(result, "")
Erase result

End Function

Function multi(ByVal X As String, ByVal Y As String) As String 'multi of two huge hexnum（两个大数之积）
Dim result As Variant
Dim xl As Long, yl As Long, temp As Long, I As Long
xl = Len(Trim(X))
yl = Len(Trim(Y))
 
ReDim result(1 To xl + yl)
For I = 1 To xl
For temp = 1 To yl
result(I + temp) = result(I + temp) + Val(Mid(X, I, 1)) * Val(Mid(Y, temp, 1))
Next
Next

For I = xl + yl To 2 Step -1
temp = result(I) \ 10
result(I) = result(I) Mod 10
result(I - 1) = result(I - 1) + temp
Next

If result(1) = "0" Then result(1) = ""
multi = Join(result, "")
Erase result

End Function
Function POWERS(ByVal X As Integer) As String ' GET 16777216^X,ie 16^(6*x)（16777216的X 次方）
POWERS = 1
Dim I As Integer
For I = 1 To X
POWERS = multi(POWERS, CLng(&H1000000))
Next
End Function
Function half(ByVal X As String) As String 'get half of x（取半）
X = 0 & X
Dim I As Long
ReDim result(2 To Len(X)) As String
For I = 2 To Len(X)
result(I) = CStr(Val(Mid(X, I, 1)) \ 2 + IIf(Val(Mid(X, I - 1, 1)) Mod 2 = 1, 5, 0))
Next
half = Join(result, "")
If Left(half, 1) = "0" Then half = Right(half, Len(half) - 1) ' no zero ahead
End Function

'另一个有用的函数：
Function POWERXY(ByVal X As Integer, ByVal Y As Integer) As String 'GET  X^Y（X 的 Y 次方）
Dim I As Integer
POWERXY = X
For I = 2 To Y
POWERXY = multi(POWERXY, X)
Next
End Function

'进制转换函数：

'16 to 10
Function HEXTODEC(ByVal X As String) As String
Dim A() As String, I As Long, UNIT As Integer
For I = 1 To Len(X)
If Not IsNumeric("&h" & Mid(X, I, 1)) Then MsgBox "NOT A HEX FORMAT!", 64, "INFO": Exit Function
Next
X = String((6 - Len(X) Mod 6) Mod 6, "0") & X

UNIT = Len(X) \ 6 - 1
ReDim A(UNIT)
For I = 0 To UNIT
A(I) = CLng("&h" & Mid(X, I * 6 + 1, 6))
Next
For I = 0 To UNIT
A(I) = multi(A(I), POWERS(UNIT - I))
HEXTODEC = sums(HEXTODEC, A(I))
Next
End Function

 

 

 

' 10 to 16
Function dectohex(ByVal hugenum As String) As String ' trans hugenum to hex
Do While Len(hugenum) > 2
dectohex = Hex(Val(Right(hugenum, 4)) Mod 16) & dectohex
For I = 1 To 4 'devide hugenum  by 16
hugenum = half(hugenum)
Next
Loop
dectohex = Hex(Val(hugenum)) & dectohex
End Function

 

Private Sub Form_Load()
For I = 0 To 20
Y(I) = "1234567890ABCDEF"
Next

largehex = Join(Y, "")
End Sub

 

'hextodec
Private Sub Command1_Click()
start = Timer
largedec = HEXTODEC(largehex)
Debug.Print largedec
MsgBox "hex(" & Len(largehex) & " 位): " & largehex & vbCrLf & vbCrLf & "dec(" & Len(largedec) & " 位): " & largedec, 64, "用时" & Format((Timer - start), "0.0000") & " 秒！"
End Sub

'dectohex
Private Sub Command2_Click()
largedec = "27305594525408320787401222904174795936368587913861811995606068514338921239280447480038845811151419865392100570221250636783105942723266982313358992551204806603060637911792055430458953651997903849585424629638958641829173494438455892966522070157613386886352421847833413821003678138295449221439062614172249927946884678471687751616589458280098503446100701588657220466765694306218356144887228155732857434394095"

start = Timer
largehex = dectohex(largedec)
MsgBox "dec(" & Len(largedec) & " 位): " & largedec & vbCrLf & vbCrLf & "hex(" & Len(largehex) & " 位): " & largehex, 64, "用时" & Format((Timer - start), "0.0000") & " 秒！"
End Sub

'get x^y
Private Sub Command3_Click()
start = Timer
MsgBox "2^3000=" & POWERXY(2, 3000), 64, "用时" & Format((Timer - start), "0.0000") & " 秒！"
End Sub