二个巨大数的三則運算

lolmuta · 发表于 2014-4-1 17:41

本帖最后由 lolmuta 于 2014-4-2 11:14 编辑

二个巨大数的+-x 除还在研究中
虽然原理只是小学的数学，但也弄了好一阵子......

Sub test()
Dim sgg As String
sgg = BigNumMultiplication("1230981204973453434534510732", "64569845695683295334534534534586")
Debug.Print sgg '79484266459422178553419202408729802785262572401684842176952
sgg = BigNumAdd("1230981204973453434534510732", "64569845695683295334534534534586")
Debug.Print sgg '64571076676888268787969069045318
sgg = BigNumSubtract("1230981204973453434534510732", "64569845695683295334534534534586")
Debug.Print sgg '-64568614714478321881100000023854
End Sub

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'相乘 A>0 B>0

Public Function BigNumMultiplication(A As String, B As String) As String
Dim Result() As String
ReDim Result(0 To Len(A) - 1)
Dim i As Integer, j As Integer
Dim NextNo As Integer
For i = Len(A) To 1 Step -1
Dim t As Integer
t = CInt(Mid(A, i, 1))
Dim Dig As Integer
Dig = Len(A) - i
For k = 1 To Dig
Result(Dig) = Result(Dig) & "0"
Next
For j = Len(B) To 1 Step -1
Dim s As Integer
s = CInt(Mid(B, j, 1))
'Debug.Print t & " " & s
'保留各位數
Dim s_t As Integer
s_t = s * t + NextNo
If j > 1 Then
Dim S_digits As String
S_digits = s_t Mod 10
'進位要給下一個
NextNo = s_t \ 10
Result(Dig) = S_digits & Result(Dig)
Else
Result(Dig) = s_t & Result(Dig)
End If
Next
NextNo = 0
Next
Dim AddAllNo As String
AddAllNo = "0"
For i = LBound(Result) To UBound(Result)
AddAllNo = BigNumAdd(AddAllNo, Result(i))
Next
BigNumMultiplication = AddAllNo
End Function

复制代码

'相加

Public Function BigNumAdd(A As String, B As String) As String
Dim i As Integer, j As Integer
Dim NoI As Integer
Dim NextNo As Integer
Dim s As Integer, t As Integer
Dim Result As String
Do
NoI = NoI + 1
If (Len(A) - NoI) < 0 And (Len(B) - NoI) < 0 Then
If NextNo > 0 Then
Result = NextNo & Result
End If
Exit Do
End If
If (Len(A) - NoI) < 0 Then
s = 0
Else
s = Mid(A, Len(A) - NoI + 1, 1)
End If
If (Len(B) - NoI) < 0 Then
t = 0
Else
t = Mid(B, Len(B) - NoI + 1, 1)
End If
Dim s_t As Integer
s_t = s + t + NextNo
NextNo = s_t \ 10
Dim S_digits As String
S_digits = CStr(s_t Mod 10)
Result = S_digits & Result
Loop
BigNumAdd = Result
End Function

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'相減

'相減… A>0 B>0
Public Function BigNumSubtract(A As String, B As String) As String
Dim NoI As Integer
Dim NextNo As Integer
Dim s As Integer, t As Integer
Dim Result() As Integer
Dim Ri As Integer
Ri = -1
Do
NoI = NoI + 1
If (Len(A) - NoI) < 0 And (Len(B) - NoI) < 0 Then
Exit Do
End If
If (Len(A) - NoI) < 0 Then
s = 0
Else
s = Mid(A, Len(A) - NoI + 1, 1)
End If
If (Len(B) - NoI) < 0 Then
t = 0
Else
t = Mid(B, Len(B) - NoI + 1, 1)
End If
Dim s_t As Integer
s_t = s - t
Ri = Ri + 1
ReDim Preserve Result(Ri)
Result(Ri) = s_t
Loop
Dim AllNum As String
Dim i As Integer, j As Integer
Dim k As Integer
Dim Postive As Boolean
'chk if positve or not
Do
If (UBound(Result) - k) < 0 Then
BigNumSubtract = "0"
Exit Function
Exit Do
End If
Dim u As Integer
u = Result(UBound(Result) - k)
If u > 0 Then
Postive = True
Exit Do
ElseIf u < 0 Then
Postive = False
Exit Do
ElseIf u = 0 Then
k = k + 1
End If
Loop
'正數
If Postive Then
For i = LBound(Result) To UBound(Result)
If Result(i) < 0 Then
If UBound(Result) >= (i + 1) Then
Result(i + 1) = Result(i + 1) - 1
Result(i) = 10 + Result(i)
End If
End If
Next
For j = UBound(Result) To LBound(Result) Step -1
AllNum = AllNum & CStr(Result(j))
Next
Debug.Print AllNum
'負數
Else
For i = LBound(Result) To UBound(Result)
If Result(i) > 0 Then
If UBound(Result) >= (i + 1) Then
Result(i + 1) = Result(i + 1) + 1
Result(i) = -10 + Result(i)
End If
End If
Next
AllNum = "-"
For j = UBound(Result) To LBound(Result) Step -1
AllNum = AllNum & CStr(Abs(Result(j)))
Next
' Debug.Print AllNum
End If
BigNumSubtract = AllNum
End Function

复制代码

liucqa · 发表于 2014-4-1 21:04

乘法好弄，做个除法吧

东亚五金 · 发表于 2014-4-1 21:15

问一下,在立即窗口显示出来的2位数字是啥意思呢

lolmuta · 发表于 2014-4-1 21:51

东亚五金发表于 2014-4-1 21:15
问一下,在立即窗口显示出来的2位数字是啥意思呢

just for debug...

lolmuta · 发表于 2014-4-2 11:08

更新+ -

香川群子 · 发表于 2014-4-2 13:13

除法确实是最难的……

除法运算中至少还需要包含长数位数值(巨大数)的乘法运算和减法运算。

相当于对前面加法、减法、乘法的综合计算。

请看我的附件。

我的长数位除法自定义函数=DV(Na,Nb,[商或余],[小数位])
其中，小数位指定可以是负数，即分别向上取十位、百位、千位、万位……取整的意思。

欢迎各位测试，有bug告诉我。

香川群子 · 发表于 2014-4-2 14:59

x = 1230981204973453434534510732
y = 64569845695683295334534534534586

Run Count: 1,000
Test1: 0.1094s  香川kagawa加算快1.5倍
Test2: 0.1836s  楼主lolmuta加算

Test3: 0.0391s  香川kagawa减算快2倍
Test4: 0.0977s  楼主lolmuta减算

Test5: 0.0820s  香川kagawa乘算快50倍
Test6: 4.5156s  楼主lolmuta乘算
--End--

楼主的乘法肯定有问题。太慢了。

加入了楼主的代码。

lee1892 · 发表于 2014-11-19 23:49

这个我觉得在计算根号2那个贴子里讨论的已经比较充分了，见开放式竞赛区

aoe1981 · 发表于 2022-2-20 21:32

香川群子发表于 2014-4-2 14:59
x = 1230981204973453434534510732
y = 64569845695683295334534534534586

附件中了除法我检测出了两道出错的情况：
（1）8.954÷0.087（这一道是偶然发现的）
（2）9876543214567000001÷98765432145670（这一道是我凭感觉构造的，被除数中间那串0再多一些还是出错，少到2个以后变正确）

最近也在思考如何优化巨大数除法，也想一次求得12位商，但在算理上还有一些不清楚的地方。想以您的参照，还是有点想不通……

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