用牛顿迭代法做的快速除法程序

跟直接计算感觉差不多。

例，22222222555552233/7 结果会出现科学计数法数字，和直接计算方法相同。

[此贴子已经被作者于2021-2-6 10:19编辑过]

大整数必须转化成字符串再计算，中间过程可以采用整数，最后再移动小数点。根据验证数据的规律选择精确度，就是小数点后所要求的精确度的2倍可能是，就是要求10的必须精确到20位最后再丢掉末尾10位。

理论上，代码越多，运行速度越慢。

下面计算 1234567891234567 /7

你用你说的这种方法，直接 debug.print它的结果给我写段代码。

我直接debug.print 它的结果。

然后我测试一下这两种代码的运行速度。

牛皮，第一组代码更快。

第一组：
耗时：0.0018毫秒
耗时：0.0016毫秒
耗时：0.0014毫秒

第二组：
耗时：0.0041毫秒
耗时：0.0037毫秒
耗时：0.004毫秒

必须给予大整数的快速乘法基础上才能更快，数据小的没有可比性，没有大整数的快速乘法程序同样很慢。把除法转化成乘以倒数，倒数的精确度靠迭代次数保证的，精确度不是一位一位增长的，而是几位几位增长的，迭代次数小于试商次数，所以速度是快的。
小的数据是无法比较甚至更慢的，因为不管大小都需要迭代，而直接除不用迭代，小数据在计算器中有固化的程序可能是，原理不太清楚或者是转化位二进制（反正和加减法一样直接出结果的），所以反而更快（貌似试商可能原理也不是试商法），再深究我也不知道，说不清楚，等有了学会了快速乘法程序再编程比较一下就明白了。

代码的快慢目前我不敏感，数字不能高精度才是我感兴趣的。比如计算100位数字的加减乘除。

这两个程序（加法和减法）都是仅仅计算整数的，要计算带小数的要移动小数点变化为整数（二者移动的位数必须相同，不够的补0），计算完再把小数点移动回去。

乘法和除法（仅仅计算整数）也发一下，速度太慢仅做参考！
乘法程序：
Public Function MbC(D1 As String, D2 As String) As String '乘法
Dim x, Y '两数长度
x = Len(D1): Y = Len(D2)
Dim a() As Integer
ReDim a(1 To x + Y, 1 To Y)
Dim I, J, C1, C2, CJ, JW
For J = Y To 1 Step -1 'D2
JW = 0 '进位清0
C2 = Mid$(D2, J, 1) '每位数
For I = x To 1 Step -1 'D1
  C1 = Mid$(D1, I, 1) '每位数
  CJ = C1 * C2 + JW '计算乘积
  c = I + J: r = Y + 1 - J
  a(c, r) = CJ Mod 10 '本位
  JW = CJ \ 10 '进位
Next
a(c - 1, r) = JW
Next
Dim b() As Integer
ReDim b(1 To x + Y)
JW = 0
For I = x + Y To 1 Step -1
Bit = JW
For J = 1 To Y
  Bit = Bit + a(I, J)
Next
b(I) = Bit Mod 10
JW = Bit \ 10
Next
If b(1) > 0 Then
MbC = MbC & b(1)
Else
MbC = MbC
End If
For I = 2 To x + Y
MbC = MbC & b(I)
Next
End Function

除法程序：（此程序只用于其中的除数小于8位的）（注意：输出的“/”号后面的是余数）
Public Function MCC(D1 As String, D2 As String) As String ';除数少于8位的除法
If Len(D1) < Len(D2) Then
   MCC = "0" & "/" & D1
   Else
   If Len(D1) < 9 Then
    MCC = Val(D1) \ Val(D2) & "/" & Val(D1) - (Val(D1) \ Val(D2)) * Val(D2)
     If Mid(MCC, InStr(MCC, "/") + 1) = 0 Then
  MCC = Left(MCC, InStr(MCC, "/") - 1)
Else
MCC = MCC
End If
   
    Else
   
   Dim x ';fen duan changdu
   x = Len(D1)
   
     
   
     Dim a() As String
      ReDim a(1 To x)  ';定义数组的储存空间
      For I = 1 To x Step 1  ';把被除数各位放在a()中
       a(I) = Mid(D1, I, 1)
        
      
       Next I
      Dim b() As String
      JW = 0
     ReDim b(1 To x)
     For J = 1 To x Step 1
    b(J) = Val(JW & a(J)) \ Val(D2)
      JW = Val(JW & a(J)) - Val(b(J)) * Val(D2)
       Next J
       For r = 1 To x
       If JW = 0 Then
          MCC = MCC & b(r)
          Else
          CJ = CJ & b(r)
          MCC = CJ & "/" & JW
      
    End If
   
    For I = 1 To Len(MCC)
   If Not Mid(MCC, I, 1) = "0" Then
       Exit For
   End If
Next
strtmp = Mid(MCC, I)
If Len(strtmp) = 0 Then
MCC = "0"
Else
MCC = strtmp
End If
   
   Next
   
   End If
     
     End If
   
End Function

除法程序：（用于除数多于8位的）（注意：输出的“/”号后面的是余数）
Public Function MCC1(D1 As String, D2 As String) As String ';大整数的除法
Dim ss
ss = MBJC(D1, D2)
If ss = -1 Then
MCC1 = "0" & "/" & D1
  Else
  If ss = 0 Then
   MCC1 = 1
   Else
   If Len(D1) = Len(D2) Then
     s = Val(Left(D1, 1)) \ Val(Left(D2, 1))

Do While MBJC(MbC(Trim(s), Trim(D2)), D1) = 1
  s = s - 1
  Loop
  If MBJC(MbC(Trim(s), Trim(D2)), D1) = 0 Then
   MCC1 = s
   Else
   MCC1 = s & "/" & MPC(Trim(D1), MbC(Trim(s), Trim(D2)))

End If
    Else
    If Len(D2) < 9 Then
     MCC1 = MCC(D1, D2)
     Else
    Dim x, Y ';定义分段长度
    x = Len(D1): Y = Len(D2)
   
Dim JW, jcc, jss, jcs

  Dim a() As String, b() As String
  
  ReDim a(1 To x)
  ReDim b(1 To Y)
  For I = 1 To x
  a(I) = Mid(D1, I, 1)
  Next
  For J = 1 To Y
  b(J) = Mid(D2, J, 1)
  Next
  jcc = Val(a(1) & a(2)) \ Val(b(1) & b(2))
   
      
        
  jss = MbC(Trim(jcc), D2)
   For i1 = 1 To Y
    jws = jws & a(i1)
      Next
      
      Do While MBJC(Trim(jws), Trim(jss)) = -1
      jcc = jcc - 1
      jss = MbC(Trim(jcc), D2)
      Loop
  JW = MPC(Trim(jws), Trim(jss))
  
    z = x - Y
   
    Dim c() As String
    ReDim c(1 To z)
    For s = 1 To z
     If MBJC(JW & a(s + Y), D2) = -1 Then
       c(s) = "0"
       Else
     jwc = Val(Left(JW & a(s + Y), 3)) \ Val(Left(D2, 2))
      If Len(jwc) > 1 Then
      c(s) = "9"
       Else
        c(s) = jwc
         End If
      
     Do While MBJC(JW & a(s + Y), MbC(Val(c(s)), D2)) = -1
    c(s) = Right(10000 + Val(c(s) - 1), 1)
     Loop
     End If
   
     JW = MPC(JW & a(s + Y), MbC(Val(c(s)), D2))
     
    jcc = jcc & c(s)
    Next s
    If JW = 0 Then
    MCC1 = jcc
    Else
    MCC1 = jcc & "/" & JW
    End If
   
  For I = 1 To Len(MCC1)
    If Not Mid(MCC1, I, 1) = "0" Then
        Exit For
    End If
Next
strtmp = Mid(MCC1, I)
  If Len(strtmp) = 0 Then
  MCC1 = "0"
  Else
MCC1 = strtmp
End If
   
   
   
    End If
   
   
   
   
   
  
  End If
End If
End If
End Function

比较大小的程序：（注意：除法会调用此程序的，否则除法就无法运行了）

Public Function MBJC(D1 As String, D2 As String) As String ';bijiao
If Len(D1) <= 10 And Len(D2) <= 10 Then
If Val(D1) > Val(D2) Then
MBJC = 1
Else
If Val(D1) = Val(D2) Then
MBJC = 0
Else
MBJC = -1
End If
End If
Else

If Len(D1) > Len(D2) Then
MBJC = 1
Else
If Len(D1) < Len(D2) Then
MBJC = -1
Else
If Len(D1) = Len(D2) Then
Dim x, Y
x = Len(D1) \ 4: Y = Len(D2) \ 4
Dim a() As String, b() As String
ReDim a(4 To 4 * x + 4)
ReDim b(4 To 4 * Y + 4)
If Val(Left(D1, Len(D1) - 4 * x)) > Val(Left(D2, Len(D2) - 4 * Y)) Then
  MBJC = 1
  Else
  If Val(Left(D1, Len(D1) - 4 * x)) < Val(Left(D2, Len(D2) - 4 * Y)) Then
  MBJC = -1
  Else
  For I = 4 To 4 * x Step 4
  a(I) = Mid(D1, Len(D1) - I + 1, 4)
  b(I) = Mid(D2, Len(D2) - I + 1, 4)
  Next
  J = 4 * x
  Do While a(J) = b(J) And J >= 8
  
  J = J - 4
     Loop
     
     
   If Val(a(J)) - Val(b(J)) > 0 Then
   MBJC = 1
   Else
   If Val(a(J)) - Val(b(J)) < 0 Then
   MBJC = -1
   Else
   MBJC = 0
   End If
   
  End If
  
  
  
End If
End If
End If
End If
End If
End If
End Function

如果能写成计算大数，高精度的函数就好了。以后调用方便。

如：

加法函数
减法函数
乘法函数
除法函数
幂函数  如计算：107^101

107^101=9284564683560607824636349236036620084709403829405931331147437307957668341663495926748183799850251378750668211991763528582507888857722224558828540106085807378607424663142945342259084291023976378630973930107有205位

前面都有了，其中除法程序是两种一种是快速的一种慢些仿手工的但可靠。另外有比较大小的函数，必须用到，而快速除法的程序还用到移动和添加小数点的程序。
供您参考试用，谢谢您沟通和指导！新年快乐！（快速程序总算弄好了，修改了移动小数点的位数，关键的一步，否则差距大就费力算不完了。）

[此贴子已经被作者于2021-2-17 23:42编辑过]

这5个函数都有了，那个快速的除法程序也能用了，但速度不快还不如模仿手工计算的快，因为调用的乘法是模仿手工计算的，本身不快，而且加了移动小数点的程序，比如10位的整数，为了保障精确度，移动了小数点相当于算到了几十位的乘法，实际加大了计算量，只有搞出来快速乘法程序速度才能提高。前面已经有一个模仿手工除法的采用试商方法的除法，计算几百位的速度也可以，所以，可以用前面那个程序。
谢谢沟通和指导！

额，还差一个乘幂程序，是吧？我这里有个快速幂程序，送给你供参考！是计算整数的，不考虑带小数的，遇到底数带小数的可以移动小数点，计算完再移动回去，指数则必须是整数的！代码如下：

Private Sub Command1_Click() '快速幂程序
Dim a, b
a = Text1: b = Text2
If b = 1 Then
Text3 = a
ElseIf b = 0 Then
Text3 = 1
Else
a1 = a
Do While b > 1
s = Int(Log(b) / Log(2))
s1 = 0
Do While s1 < s
a = MbC(Trim(a), Trim(a))
s1 = s1 + 1
Loop
a2 = a
b = b - 2 ^ s
a = a1
If s2 > 0 Then
a3 = MbC(Trim(a3), Trim(a2))
Else
a3 = a2
End If
s2 = s2 + 1
Loop
If b = 1 Then
Text3 = MbC(Trim(a3), Trim(a1))
Else
Text3 = a3
End If
s3 = Len(Text3)
Text3 = Text3 & "有" & s3 & "位"
End If
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""

End Sub

Public Function MbC(D1 As String, D2 As String) As String '乘法
Dim x, Y '两数长度
x = Len(D1): Y = Len(D2)
Dim a() As Integer
ReDim a(1 To x + Y, 1 To Y)
Dim I, J, C1, C2, CJ, JW
For J = Y To 1 Step -1 'D2
JW = 0 '进位清0
C2 = Mid$(D2, J, 1) '每位数
For I = x To 1 Step -1 'D1
  C1 = Mid$(D1, I, 1) '每位数
  CJ = C1 * C2 + JW '计算乘积
  c = I + J: r = Y + 1 - J
  a(c, r) = CJ Mod 10 '本位
  JW = CJ \ 10 '进位
Next
a(c - 1, r) = JW
Next
Dim b() As Integer
ReDim b(1 To x + Y)
JW = 0
For I = x + Y To 1 Step -1
Bit = JW
For J = 1 To Y
  Bit = Bit + a(I, J)
Next
b(I) = Bit Mod 10
JW = Bit \ 10
Next
If b(1) > 0 Then
MbC = MbC & b(1)
Else
MbC = MbC
End If
For I = 2 To x + Y
MbC = MbC & b(I)
Next
End Function

下面传一下这个完整的程序代码，代码如下：


Private Sub Command1_Click() '快速除法程序
Dim A, B
  A = Trim(Text1): B = Trim(Text2): b3 = B: a3 = A
  ts = Timer
  If Len(B) = 1 Then
  X1 = Mid(B, 1, 1): X2 = 1 / X1 - 0.01
  Else
  X1 = Mid(B, 1, 2): X2 = 10 / X1 - 0.01
  End If
  x = Mid(X2, 1, 4)
  Y = 0: x3 = 0
  sb = Len(a3) + Len(b3) - 1 + 10
  If Len(a3) = Len(b3) And MBJC(Trim(a3), Trim(b3)) = 0 Then
  a1 = 1
  Text3 = a1
  Else
  If MBJC(Mid(a3, 1, Len(b3)), Trim(b3)) = 0 And Val(Len(qdhz0(Trim(a3)))) = Val(Len(b3)) Then
  a1 = 1 & String(Len(a3) - Len(qdhz0(Trim(a3))), "0")
  Else
  
  A = A & String(10, "0"): B = B & String(10 + Len(a3), "0")
  x = qdqd0(ydxsd(Trim(x), Val(sb)))
  Y1 = 2 & String(Val(sb), "0")
  Do While MBJC(MPC(Trim(x), Trim(x3)), 1) >= 0
  
  s3 = s3 + 1
  Y = mbc2(Trim(x), MPC(Trim(Y1), mbc2(Trim(B), Trim(x), Val(sb))), Val(sb))
  x3 = x
  x = Trim(Y)
  Loop
  a1 = mbc2(Trim(Y), Trim(A), Val(sb))
  s = Len(a3) - Len(b3)
  a1 = qdqd0(Trim(a1))
  
  If MBJC(Mid(a3, 1, Len(b3)), Trim(b3)) < 0 Then
  a1 = tjxsd(Trim(a1), Len(a1) - s)
  Else
  a1 = tjxsd(Trim(a1), Len(a1) - s - 1)
  End If
  End If
  
  If InStr(a1, ".") = 0 Then
  a1 = a1
  Else
  a1 = Left(a1, InStr(a1, ".") - 1)
  End If
  ja = MPC(Trim(a3), MbC4(Trim(b3), Trim(a1)))
  Do While MBJC(Trim(ja), Trim(b3)) >= 0
  ja = MPC(Trim(ja), Trim(b3))
  s5 = s5 + 1
  Loop
  a1 = MPC1(Trim(a1), Trim(s5))
  If ja = 0 Then
  Text3 = a1 & "有" & Len(a1) & "位，用时" & Timer - ts & "秒"
  Else
  Text3 = a1 & "/" & ja & "有" & Len(a1) & "位，用时" & Timer - ts & "秒"
  End If
  End If
  End Sub

  Private Sub Command2_Click()
  Text1 = ""
  Text2 = ""
  Text3 = ""

  End Sub
  
   
        Public Function MbC4(D1 As String, D2 As String) As String '快速乘法
        Dim l As Long, le As Long, le1 As Long, n As Long, r As Long, p As Long, q As Long, m As Byte
  Dim wr As Double, w1 As Double, wlr As Double, wl1 As Double, tr As Double, t1 As Double
  Dim pi As Double, t As Double, tr1 As Double
        
  If Len(D1) + Len(D2) < 30000 Then
  MbC4 = MbC(Trim(D1), Trim(D2))
  Else
Dim xr() As Double, A As String
  A = Trim(D1)
  B = Trim(D2)
  
  x = Len(A) \ 4: Y = Len(B) \ 4
  A = String(Val(x * 4 + 4 - Len(A)), "0") & A
  B = String(Val(Y * 4 + 4 - Len(B)), "0") & B
  x = x + 1: Y = Y + 1
  sb1 = x + Y
  sb2 = Log(sb1) / Log(2)
  If InStr(sb2, ".") = 0 Then
  sb2 = sb2
  Else
  sb2 = Int(sb2) + 1
  End If
  sb = 2 ^ sb2
  A = String(Val(sb) * 4 - Len(A), "0") & A
  B = String(Val(sb) * 4 - Len(B), "0") & B
  
   ReDim x_(1 To sb): ReDim y_(1 To sb)
    For i1 = 1 To sb
    x_(i1) = Mid(A, (sb - i1 + 1) * 4 - 3, 4): y_(i1) = Mid(B, (sb - i1 + 1) * 4 - 3, 4)
    If Len(x_(i1)) < 4 Then
    x_(i1) = String(4 - Len(x_(i1)), "0") & x_(i1)
    ElseIf Len(y_(i1)) < 4 Then
    y_(i1) = String(4 - Len(y_(i1)), "0") & y_(i1)
    Else
    x_(i1) = x_(i1): y_(i1) = y_(i1)
    End If
   
      Next
      ReDim xr(0 To (Len(A) - 4) \ 4): ReDim yr(0 To (Len(B) - 4) \ 4): ReDim zr(0 To (Len(B) - 4) \ 4)
      
       If Len(A) = 4 Then
  xr(0) = A: yr(0) = B
  Else
    Dim I As Long, J As Long, mn As Long, lh As Long, k As Long
    '位序倒置
n = sb '求数组大小，其值必须是2的幂
lh = n / 2
    J = n / 2
    For I = 1 To n - 2


    Debug.Print I, J
    k = lh '下面是向右进位算法
Do
    If k > J Then Exit Do '高位是1吗
J = J - k '是的，高位置0
    k = k / 2 '准备次高位的权
Loop Until k = 0 '次高位的权若非0，则检查新的次高位
J = J + k '非则若最高位是0，则置1
   xr(I + 1) = x_(J + 1): yr(I + 1) = y_(J + 1)
    Next
    xr(0) = x_(1): xr(1) = x_(1 + sb / 2)
    yr(0) = y_(1): yr(1) = y_(1 + sb / 2)
  
     End If
  
  Dim xi(): Dim yi(): Dim zi()
  n = sb '求数组大小，其值必须是2的幂
m = 0
  l = 2
  pi = 3.14159265358979
  Do
  l = l + l
  m = m + 1
  Loop Until l > n
  n = l / 2
  ReDim xi(n - 1): ReDim yi(n - 1): ReDim zi(n - 1)

  l = 1
  Do
    le = 2 ^ l
    le1 = le / 2
    wr = 1
    wi = 0
    If l = 1 Then
    t = 0
    Else
    t = pi / le1
    End If
    w1r = Cos(t)
    w1i = -Sin(t)
    r = 0
  Do
    p = r
    Do
     q = p + le1
     
     tr = xr(q) * wr - xi(q) * wi
     ti = xr(q) * wi + xi(q) * wr
     tr1 = yr(q) * wr - yi(q) * wi
     ti1 = yr(q) * wi + yi(q) * wr
     
     
     xr(q) = xr(p) - tr
     xi(q) = xi(p) - ti
     xr(p) = xr(p) + tr
     xi(p) = xi(p) + ti
     
       yr(q) = yr(p) - tr1
      yi(q) = yi(p) - ti1
      yr(p) = yr(p) + tr1
      yi(p) = yi(p) + ti1
     xr(p) = Format(Val(xr(p)), "0.000000"): xi(p) = Format(Val(xi(p)), "0.000000")
     yr(p) = Format(Val(yr(p)), "0.000000"): yi(p) = Format(Val(yi(p)), "0.000000")
     
      p = p + le
  Loop Until p > n - 1


  wr2 = wr * w1r - wi * w1i
  wi2 = wr * w1i + wi * w1r
  wr = wr2
  wi = wi2
  r = r + 1
  Loop Until r > le1 - 1
  l = l + 1
  Loop Until l > m

  For I = 0 To n - 1 '仅输出模
   zr(I) = xr(I) * yr(I) - xi(I) * yi(I): zi(I) = xr(I) * yi(I) + xi(I) * yr(I)
    zr(I) = Format(Val(zr(I)), "0.000000"): zi(I) = Format(Val(zi(I)), "0.000000")
  

      's = s & "/" & zr(I)
      's1 = s1 & "/" & zi(I)
      Next
      
       J = sb
     
       ReDim x_(1 To sb): ReDim y_(1 To sb)
     For k = 1 To J
         n1 = n1 + 1
          ReDim Preserve x_(1 To n1)
        
         x_(n1) = zr(n1 - 1): y_(n1) = zi(n1 - 1)
         x_(n1) = Format(Val(x_(n1)), "0.000000"): y_(n1) = Format(Val(y_(n1)), "0.000000")
         
       Next
   
    '位序倒置
n = sb '求数组大小，其值必须是2的幂
lh = n / 2
    J = n / 2
   
    For I = 1 To n - 2


    Debug.Print I, J
    k = lh '下面是向右进位算法
Do
    If k > J Then Exit Do '高位是1吗
J = J - k '是的，高位置0
    k = k / 2 '准备次高位的权
Loop Until k = 0 '次高位的权若非0，则检查新的次高位
J = J + k '非则若最高位是0，则置1

xr(I + 1) = x_(J + 1): yr(I + 1) = y_(J + 1)
    'js = js & "/" & x_(J + 1)
    'js1 = js1 & "/" & y_(J + 1)
    Next
    'sx1 = "/" & x_(1) & "/" & x_(1 + sb / 2) & js
    'sy1 = "/" & y_(1) & "/" & y_(1 + sb / 2) & js1
   xr(0) = x_(1): xr(1) = x_(1 + sb / 2)
   yr(0) = y_(1): yr(1) = y_(1 + sb / 2)
   
   
   ns = Len(A) \ 4: Jn = ns
  
      
  

  ReDim zr(0 To ns - 1)

  m = 0
  l = 2
  pi = 3.14159265358979
  Do
  l = l + l
  m = m + 1
  Loop Until l > ns
  ns = l / 2
  ReDim xi(ns - 1): ReDim yi(ns - 1): ReDim zi(ns - 1)

  l = 1
  Do
    le = 2 ^ l
    le1 = le / 2
    wr = 1
    wi = 0
    If l = 1 Then
    t = 0
    Else
    t = -1 * pi / le1
    End If
    w1r = Cos(t)
    w1i = -Sin(t)
    r = 0
  Do
    p = r
    Do
     q = p + le1
     
     tr = xr(q) * wr - xi(q) * wi
     ti = xr(q) * wi + xi(q) * wr
     tr1 = yr(q) * wr - yi(q) * wi
     ti1 = yr(q) * wi + yi(q) * wr
     
     
     xr(q) = xr(p) - tr
     xi(q) = xi(p) - ti
     xr(p) = xr(p) + tr
     xi(p) = xi(p) + ti
     
       yr(q) = yr(p) - tr1
      yi(q) = yi(p) - ti1
      yr(p) = yr(p) + tr1
      yi(p) = yi(p) + ti1
     xr(p) = Format(Val(xr(p)), "0.000000"): xi(p) = Format(Val(xi(p)), "0.000000")
     yr(p) = Format(Val(yr(p)), "0.000000"): yi(p) = Format(Val(yi(p)), "0.000000")
      p = p + le
  Loop Until p > ns - 1


  wr2 = wr * w1r - wi * w1i
  wi2 = wr * w1i + wi * w1r
  wr = wr2
  wi = wi2
  r = r + 1
  Loop Until r > le1 - 1
  l = l + 1
  Loop Until l > m

  For I = 0 To ns - 1 '仅输出模
zr(I) = (xr(I) - yi(I)) / n
      zr(I) = Format(Val(zr(I) + 0.5), "0.000000")
     If InStr(zr(I), ".") = 0 Then
     s121 = zr(I)
     Else
     s121 = Left(zr(I), InStr(zr(I), ".") - 1)
      End If
      's0 = "/" & s121 & s0
      zr(I) = s121
      Next
      For i1 = 1 To Val(Jn - sb1 + 1)
      zr(sb1 + i1 - 2) = 0
      Next
      
     
     
      For i1 = 0 To n - 1
      If zr(i1) < 0 Then
      zr(i1) = "0000"
      ElseIf Len(zr(i1)) < 4 Then
      zr(i1) = String(4 - Len(zr(i1)), "0") & zr(i1)
      Else
      zr(i1) = zr(i1)
      End If
      
      's5 = s5 & "/" & zr(i1)
      
      If i1 = 0 Then
      
      s6 = Val(Left(zr(i1), Len(zr(i1)) - 4))
      If Len(s6) < 4 Then
      s6 = String(4 - Len(s6), "0") & s6
      Else
      s6 = s6
      End If
      s8 = Right(zr(i1), 4)
      ElseIf Val(zr(i1)) >= 0 Then
      s7 = Val(zr(i1)) + Val(s6)
    If Len(s7) = 4 Or Len(s7) = 8 Or Len(s7) = 12 Then
          s7 = s7
          Else
          s7 = String(12 - Len(s7), "0") & s7
         End If
      s10 = Right(s7, 4)
      s11 = s10 & s11
      If Len(s7) < 4 Then
      s7 = String(4 - Len(s7), "0") & s7
      ElseIf Len(s7) = 4 Then
      s6 = "0000"
      Else
      s7 = s7
      s6 = Val(Left(s7, Len(s7) - 4))
      End If
      Else
      s6 = s6
      End If
     
      Next
      s9 = s6 & s11 & s8
     
   
   s9 = qdqd0(Trim(s9))
   
     's2 = nifft(dxcx1(Trim(s)), dxcx1(Trim(s1)), Trim(sb1))
     
     's3 = nifft(Trim(sx1), Trim(sy1), Trim(sb1))
      MbC4 = s9
      End If
  End Function

  
  
  
  
  Private Function mbc2(sa As String, sb As String, sd As String) As String 'chengfa jingdu
  Dim ja

  If Trim(sa) = 0 Or Trim(sb) = 0 Then
  mbc2 = 0
  Else


  ja = MbC4(Trim(sa), Trim(sb))
  If Val(Len(ja)) > Val(sd) Then
  jb = Left(ja, Val(Len(ja)) - Val(sd))
  mbc2 = jb
  Else
  mbc2 = 0
  End If


  End If




  End Function

Private Function qdhz0(sa As String) As String
  A = sa
  Do While Right(A, 1) = "0"
  A = Left(A, Len(A) - 1)
  Loop
  If A = "" Then
  A = 0
  Else
  A = A
  End If
  qdhz0 = A
  End Function


  Private Function qdqd0(sa As String) As String
  A = sa
  Do While Left(A, 1) = "0"
  A = Mid(A, 2)
  Loop
  If A = "" Then
  A = 0
  Else
  A = A
  End If
  qdqd0 = A
  End Function

  Private Function tjxsd(sa As String, sd As String) As String
  If Val(Len(sa)) > Val(sd) Then
  tjxsd = Left(sa, Val(Len(sa)) - Val(sd)) & "." & Mid(sa, Val(Len(sa)) - Val(sd) + 1)
  Else
  If Val(Len(sa)) = Val(sd) Then
    tjxsd = "0." & sa
    Else
    tjxsd = "0." & String(Val(sd) - Val(Len(sa)), "0") & Trim(sa)
    End If
    End If

  End Function

  Private Function ydxsd(sa As String, sd As String) As String
  If Len(sa) = 1 And Val(sa) = 0 Then
    ydxsd = 0
    Else
   
      sc = InStr(sa, ".")
      If Val(sc) = 0 Then
      ydxsd = sa & String(sd, "0")
      Else
      se = Left(sa, Val(sc) - 1)
      sf = Right(sa, Len(sa) - Val(sc))
      If Val(Len(sf)) >= Val(sd) Then
      ydxsd = se & Mid(sf, 1, sd)
        Else
        ydxsd = se & sf & String(Val(sd) - Len(sf), "0")
        End If
        End If
        End If
        End Function
        
       Public Function MbC(D1 As String, D2 As String) As String
Dim j1&, j2&, e&, d&, E1&

   ' 按列法计算C=A*B
m = Trim(D1): n = Trim(D2)
x = Len(m) \ 4: Y = Len(n) \ 4
m = String(4 * x + 4 - Len(m), "0") & m
n = String(4 * Y + 4 - Len(n), "0") & n
x = x + 1: Y = Y + 1
Dim A(), B()
ReDim A(1 To x): ReDim B(1 To Y)
For i1 = 1 To x
A(i1) = Val(Mid(m, i1 * 4 - 3, 4))
Next
For i2 = 1 To Y
B(i2) = Val(Mid(n, i2 * 4 - 3, 4))
Next
ma = x: mb = Y
    MC = ma + mb
    ReDim c(MC)
    E1 = 0
    j1 = ma: j2 = ma
    For I = MC To 2 Step -1
        If I <= ma Then j2 = I - 1
        e = E1: E1 = 0
        For J = j1 To j2
            e = e + A(J) * B(I - J)
            If e > 2040000000 Then '减少进位次数
                e = e - 2040000000
                E1 = E1 + 204000
            End If
        Next J

        If j1 > 1 Then j1 = j1 - 1
base = 10000
        d = e \ base
        c(I) = e - d * base
        If Len(c(I)) < 4 Then
        c(I) = String(4 - Len(c(I)), "0") & c(I)
        Else
        c(I) = c(I)
        End If
jc = c(I) & jc
        E1 = E1 + d
    Next I
    jc = d & jc
   MbC = qqdl(Trim(jc))
End Function

  Public Function MPC(D1 As String, D2 As String) As String ';jianfaqi
  Dim x, Y ';两数长度
If Len(D1) >= Len(D2) Then
  D4 = String(Len(D1) - Len(D2), "0") & D2
  D3 = D1
  Else
  D4 = D2
  D3 = String(Len(D2) - Len(D1), "0") & D1
  End If
  x = Len(D3) \ 8: Y = Len(D4) \ 8
  If Len(D3) > 8 * x Then
  D3 = String(8 * x + 8 - Len(D3), "0") & D3
  D4 = String(8 * Y + 8 - Len(D4), "0") & D4
  x = x + 1: Y = Y + 1
  Else
  x = x: Y = Y
  D3 = D3: D4 = D4
  End If
  
  Dim A() As String, B1() As String, C1() As String, E1() As String
  ReDim A(1 To x)
  ReDim B1(1 To Y)
  ReDim C1(1 To x)
  ReDim E1(1 To x)
  Dim I, J, C2, CJ, JW
  For J = Y To 1 Step -1 ';D2
  JW = 1 ';yu jie weichuzhi
  B1(J) = Mid(D4, J * 8 - 7, 8) ';每位数
For I = x To 1 Step -1  ';D1
     A(I) = Mid(D3, I * 8 - 7, 8) ';每位数
   C1(I) = Val(1 & A(I)) - Val(B1(I)) - Val(1) + Val(JW) ';计算jia
     JW = C1(I) \ 10 ^ 8
     E1(I) = C1(I) Mod 10 ^ 8
     If Len(E1(I)) < 8 Then
     E1(I) = String(8 - Len(E1(I)), "0") & E1(I)
     Else
     E1(I) = E1(I)
     End If
     
    Next
    Next
    For r = 1 To x
    MPC = MPC & E1(r)
    If Len(MPC) > Len(D1) Then
    MPC = Mid(MPC, Len(MPC) - Len(D1) + 1)
    Else
    MPC = MPC
    End If
    For I = 1 To Len(MPC)
      If Not Mid(MPC, I, 1) = "0" Then
          Exit For
      End If
  Next
  strtmp = Mid(MPC, I)
    If Len(strtmp) = 0 Then
    MPC = "0"
    Else
  MPC = strtmp
  End If
    Next
   
   
  End Function
   Public Function MPC1(D1 As String, D2 As String) As String 'jiafa
  Dim x, Y, JW '两数长度

If Len(D1) >= Len(D2) Then
  D4 = String(Len(D1) - Len(D2), "0") & D2
  D3 = D1
  Else
  D4 = D2
  D3 = String(Len(D2) - Len(D1), "0") & D1
  End If
  x = Len(D3) \ 8: Y = Len(D4) \ 8
  If 8 * x < Len(D3) Then
  D3 = String(8 * x + 8 - Len(D3), "0") & D3
  D4 = String(8 * Y + 8 - Len(D4), "0") & D4
  x = x + 1: Y = Y + 1
  Else
  x = x: Y = Y
  D3 = D3: D4 = D4
  End If
  Dim A() As String, B1() As String, C1() As String, E1() As String
  ReDim A(1 To x)
  ReDim B1(1 To Y)
  ReDim C1(1 To x)
  ReDim E1(1 To x)
  Dim I, J, C2, CJ
  For J = Y To 1 Step -1 'D2
  JW = 0 '进位清0
  B1(J) = Mid$(D4, J * 8 - 7, 8) '每位数
For I = x To 1 Step -1  'D1
     A(I) = Mid$(D3, I * 8 - 7, 8) '每位数
   C1(I) = Val(A(I)) + Val(B1(I)) + Val(JW) '计算jia
   If Len(C1(I)) < 8 Then
   C1(I) = String(8 - Len(C1(I)), "0") & C1(I)
   Else
   C1(I) = C1(I)
   End If
     JW = Left(C1(I), Len(C1(I)) - 8)
     E1(I) = Right(C1(I), 8)
    Next
    Next
    For r = 1 To x
    If JW = 0 Then
    MPC1 = MPC1 & E1(r)
    Else
    jc = jc & E1(r)
    MPC1 = JW & jc
    End If
    Next
   MPC1 = qqdl(Trim(MPC1))
  End Function

  Public Function MBJC(D1 As String, D2 As String) As String ';bijiao
  If Len(D1) <= 10 And Len(D2) <= 10 Then
  If Val(D1) > Val(D2) Then
  MBJC = 1
  Else
  If Val(D1) = Val(D2) Then
  MBJC = 0
  Else
  MBJC = -1
  End If
  End If
  Else

  If Len(D1) > Len(D2) Then
  MBJC = 1
  Else
  If Len(D1) < Len(D2) Then
  MBJC = -1
  Else
  If Len(D1) = Len(D2) Then
  Dim x, Y
  x = Len(D1) \ 4: Y = Len(D2) \ 4
  Dim A() As String, B() As String
  ReDim A(4 To 4 * x + 4)
  ReDim B(4 To 4 * Y + 4)
  If Val(Left(D1, Len(D1) - 4 * x)) > Val(Left(D2, Len(D2) - 4 * Y)) Then
     MBJC = 1
     Else
     If Val(Left(D1, Len(D1) - 4 * x)) < Val(Left(D2, Len(D2) - 4 * Y)) Then
     MBJC = -1
     Else
     For I = 4 To 4 * x Step 4
     A(I) = Mid(D1, Len(D1) - I + 1, 4)
     B(I) = Mid(D2, Len(D2) - I + 1, 4)
     Next
     J = 4 * x
     Do While A(J) = B(J) And J >= 8
     
     J = J - 4
        Loop
        
        
      If Val(A(J)) - Val(B(J)) > 0 Then
      MBJC = 1
      Else
      If Val(A(J)) - Val(B(J)) < 0 Then
      MBJC = -1
      Else
      MBJC = 0
      End If
      
     End If
     
     
     
  End If
  End If
  End If
  End If
  End If
  End If
  End Function



'符号运算程序
Private Function fhys(sa As String) As String

 If InStr(sa, "-") = 0 Then
  fhys = 1
   Else
   fhys = -1
 End If
 
   
End Function

'添加符号程序
Private Function tjfh(sa As String, sf As String) As String 'qianjia fuhao
If Val(sf) < 0 Then
tjfh = "-" & sa
Else
tjfh = sa
End If

 
 
   
End Function

'带符号的加法程序
Private Function mpc3(sa As String, sb As String) As String 'jiafa jingdu daifh
Dim ja
fh1 = fhys(sa)
fh2 = fhys(sb)
If Val(fh1) * Val(fh2) > 0 Then
ja = MPC1(qdfh(sa), qdfh(sb))


If Val(fh1) > 0 Then
mpc3 = ja
Else
mpc3 = "-" & ja
End If
Else
xd = MBJC(qdfh(sa), qdfh(sb))
If xd >= 0 Then
jb = qqdl(MPC(qdfh(sa), qdfh(sb)))
Else
jb = qqdl(MPC(qdfh(sb), qdfh(sa)))
End If
If xd >= 0 And Val(fh1) > 0 Then
mpc3 = jb
Else
 If xd > 0 And Val(fh1) < 0 Then
 mpc3 = "-" & jb
 Else
 If Val(fh2) < 0 Then
 mpc3 = "-" & jb
 Else
 mpc3 = jb
 End If
 End If
 End If
 End If
 
End Function

'带符号的减法程序
Private Function mpc2(sa As String, sb As String) As String 'jianfa jingdu daifh
Dim ja
fh1 = fhys(sa)
fh2 = fhys(sb)
xd = MBJC(qqdl(qdfh(sa)), qqdl(qdfh(sb)))
If Val(fh1) * Val(fh2) < 0 Then
ja = MPC1(qdfh(sa), qdfh(sb))


If Val(fh1) > 0 Then
mpc2 = ja
Else

mpc2 = "-" & ja


End If
Else

If xd >= 0 Then
jb = qqdl(MPC(qdfh(sa), qdfh(sb)))
Else
jb = qqdl(MPC(qdfh(sb), qdfh(sa)))
End If
If xd >= 0 And Val(fh1) > 0 Then
mpc2 = jb
Else
 If xd > 0 And Val(fh1) < 0 Then
 mpc2 = "-" & jb
 Else
 If Val(fh2) <= 0 Then
 mpc2 = jb
 Else
 mpc2 = "-" & jb
 End If
 End If
 End If
 End If
 
End Function

'去前导0的程序
Private Function qqdl(sa As String) As String

  
  For I = 1 To Len(sa)
    If Not Mid(sa, I, 1) = "0" Then
        Exit For
    End If
Next
strtmp = Mid(sa, I)
  If Len(strtmp) = 0 Then
  qqdl = "0"
  Else
qqdl = strtmp
 End If
End Function

'带符号的比较大小程序
Private Function mbjc2(sa As String, sb As String) As String 'bi jiao dx daifh
Dim ja
fh1 = fhys(sa)
fh2 = fhys(sb)
If Val(fh1) < Val(fh2) Then
mbjc2 = -1
Else
If Val(fh1) > Val(fh2) Then
mbjc2 = 1
Else

ja = MBJC(qdfh(sa), qdfh(sb))

If Val(fh1) > 0 And Val(ja) > 0 Then
mbjc2 = 1
Else
If Val(fh1) < 0 And Val(ja) > 0 Then
mbjc2 = -1
Else
If Val(fh1) > 0 And Val(ja) < 0 Then
mbjc2 = -1
Else
If Val(fh1) < 0 And Val(ja) < 0 Then
mbjc2 = 1
Else
mbjc2 = 0
End If
End If
End If
End If
End If
End If


 
End Function

'带符号的乘法程序
Private Function mbc6(sa As String, sb As String, sd As String) As String 'chengfa jingdu daifh
Dim ja
fh1 = fhys(sa)
fh2 = fhys(sb)
If sa = 0 Or sb = 0 Then
mbc2 = 0
Else


ja = MbC(qdfh(sa), qdfh(sb))
If Val(Len(ja)) > Val(sd) Then
jb = Left(ja, Val(Len(ja)) - Val(sd))

If Val(fh1) * Val(fh2) > 0 Then
mbc2 = jb
Else
mbc2 = "-" & jb
End If

Else
mbc2 = 0
End If
End If



 
End Function

'去掉符号的程序
Private Function qdfh(sa As String) As String

 If InStr(sa, "-") > 0 Then
 qdfh = Mid(sa, 2)
 Else
 If InStr(sa, "+") > 0 Then
 qdfh = Mid(sa, 2)
 Else
 qdfh = sa
 End If
 End If
   
End Function



'比较大小的程序
Public Function MBJC1(D1 As String, D2 As String) As String 'bijiao
If Len(D1) > Len(D2) Then
MBJC = 1
Else
If Len(D1) < Len(D2) Then
MBJC = -1
Else
If Len(D1) = Len(D2) And Len(D1) >= 10 Then

 
Dim x, Y
x = Len(D1) \ 4: Y = Len(D2) \ 4
Dim A() As String, B() As String
ReDim A(4 To 4 * x + 4)
ReDim B(4 To 4 * Y + 4)
If Val(Left(D1, Len(D1) - 4 * x)) > Val(Left(D2, Len(D2) - 4 * Y)) Then
 MBJC = 1
 Else
 If Val(Left(D1, Len(D1) - 4 * x)) < Val(Left(D2, Len(D2) - 4 * Y)) Then
 MBJC = -1
 Else
 For I = 4 To 4 * x Step 4
 A(I) = Mid(D1, Len(D1) - I + 1, 4)
 B(I) = Mid(D2, Len(D2) - I + 1, 4)
 Next
 J = 4 * x
 Do While A(J) = B(J) And J >= 8
 
 J = J - 4
    Loop
   
   
  If Val(A(J)) - Val(B(J)) > 0 Then
  MBJC = 1
  Else
  If Val(A(J)) - Val(B(J)) < 0 Then
  MBJC = -1
  Else
  MBJC = 0
  End If
  
 End If
 
 
 
 
End If
End If
End If
If Len(D1) < 10 Then
 ja = Val(D1) - Val(D2)
  If ja > 0 Then
   MBJC = 1
   Else
    If ja = 0 Then
     MBJC = 0
    Else
   
  MBJC = -1
 End If
 End If
 End If
 
End If
End If
End Function

[此贴子已经被作者于2021-4-17 23:53编辑过]

改进了一下除法程序，其实是把其中的大数减法可调用程序改进了一下，把其中的一维数组由一位的改为8位的，这样减法速度快了，由于除法程序大量调用大数减法，所以，速度有所提高，下面是验证结果：
9284564683560607824636349236036620084709403829405931331147437307957668341663495926748183799850251378750668211991763528582507888857722224558828540106085807378607424663142945342259084291023976378630973930107/107=86771632556641194622769619028379626959900970368279732066798479513623068613677532025683960746264031577109048710203397463387924194931983407091855515010147732510349763206943414413636301785270807276924990001有203位，用时1.476563秒。

把此程序重新发在前面，就是编辑修改了前楼的程序。

9284564683560607824636349236036620084709403829405931331147437307957668341663495926748183799850251378750668211991763528582507888857722224558828540106085807378607424663142945342259084291023976378630973930107/107=86771632556641194622769619028379626959900970368279732066798479513623068613677532025683960746264031577109048710203397463387924194931983407091855515010147732510349763206943414413636301785270807276924990001有203位，用时0秒（模仿手工计算的居然不需要时间，前面快速程序是有条件的，在大于300位才能显出优势的）

Private Function jspaizh(sd As String) As String '派/2=1+1/3+1*2/3*5+1*2*3/3*5*7+……
'应该是 Pi/4=1-1/3+1/5-1/7+…+（-1）^(n-1)/(2*n-1)吧，呵呵
'派/2=2/1*2/3*4/3*4/5^^^^^=2*2/1*3*4*4/3*5*6*6/5*7*^^^^^^^
Dim s1 As String
s1 = "31415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 32823066470938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 37867831652712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360" _
& "0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724" _
& "8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132" _
& "0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960" _
& "8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035"
s2 = DeleteSpace(s1)
jspaizh = Left(s2, Val(sd) + 1)

End Function

Public Function DeleteSpace(Tmp As String) As String
   Dim Inst As Integer
   Do
       Tmp = Replace(Tmp, " ", "")
       DoEvents
       Inst = InStr(Tmp, " ")
   Loop While Inst > 0
   DeleteSpace = Tmp
End Function

Private Function jcjs(sa As String) As String

Dim s
s = 1
For I = 1 To sa
s = MbC(Trim(s), Val(I))
Next
jcjs = s



   
End Function

这两个程序可能有用发一下。

[此贴子已经被作者于2021-3-24 23:23编辑过]

Private Function mpc3(sa As String, sb As String) As String 'jiafa jingdu daifh
Dim ja
fh1 = fhys(sa)
fh2 = fhys(sb)
If Val(fh1) * Val(fh2) > 0 Then
ja = MPC1(qdfh(sa), qdfh(sb))


If Val(fh1) > 0 Then
mpc3 = ja
Else
mpc3 = "-" & ja
End If
Else
xd = MBJC(qdfh(sa), qdfh(sb))
If xd >= 0 Then
jb = qqdl(MPC(qdfh(sa), qdfh(sb)))
Else
jb = qqdl(MPC(qdfh(sb), qdfh(sa)))
End If
If xd >= 0 And Val(fh1) > 0 Then
mpc3 = jb
Else
If xd > 0 And Val(fh1) < 0 Then
mpc3 = "-" & jb
Else
If Val(fh2) < 0 Then
mpc3 = "-" & jb
Else
mpc3 = jb
End If
End If
End If
End If

End Function

Private Function mpc2(sa As String, sb As String) As String 'jianfa jingdu daifh
Dim ja
fh1 = fhys(sa)
fh2 = fhys(sb)
xd = MBJC(qqdl(qdfh(sa)), qqdl(qdfh(sb)))
If Val(fh1) * Val(fh2) < 0 Then
ja = MPC1(qdfh(sa), qdfh(sb))


If Val(fh1) > 0 Then
mpc2 = ja
Else

mpc2 = "-" & ja


End If
Else

If xd >= 0 Then
jb = qqdl(MPC(qdfh(sa), qdfh(sb)))
Else
jb = qqdl(MPC(qdfh(sb), qdfh(sa)))
End If
If xd >= 0 And Val(fh1) > 0 Then
mpc2 = jb
Else
If xd > 0 And Val(fh1) < 0 Then
mpc2 = "-" & jb
Else
If Val(fh2) <= 0 Then
mpc2 = jb
Else
mpc2 = "-" & jb
End If
End If
End If
End If

End Function

Private Function mbc2(sa As String, sb As String, sd As String) As String 'chengfa jingdu daifh
Dim ja
fh1 = fhys(sa)
fh2 = fhys(sb)
If sa = 0 Or sb = 0 Then
mbc2 = 0
Else


ja = MbC(qdfh(sa), qdfh(sb))
If Val(Len(ja)) > Val(sd) Then
jb = Left(ja, Val(Len(ja)) - Val(sd))

If Val(fh1) * Val(fh2) > 0 Then
mbc2 = jb
Else
mbc2 = "-" & jb
End If

Else
mbc2 = 0
End If
End If




End Function

Private Sub Command1_Click() '快速除法程序
Dim a, B
  a = Trim(Text1): B = Trim(Text2): b3 = B: a3 = a
  ts = Timer
  If Len(B) = 1 Then
  X1 = Mid(B, 1, 1): X2 = 1 / X1 - 0.01
  Else
  X1 = Mid(B, 1, 2): X2 = 10 / X1 - 0.01
  End If
  x = Mid(X2, 1, 4)
  Y = 0: x3 = 0
  sb = Len(a3) + Len(b3) - 1 + 2
  If Len(a3) = Len(b3) And MBJC(Trim(a3), Trim(b3)) = 0 Then
  a1 = 1
  ElseIf MBJC(Mid(a3, 1, Len(b3)), Trim(b3)) = 0 And Val(Len(qdhz0(Trim(a3)))) = Val(Len(b3)) Then
  a1 = 1 & String(Len(a3) - Len(qdhz0(Trim(a3))), "0")
  Else
  
  a = a & String(2, "0"): B = B & String(2 + Len(a3), "0")
  x = qdqd0(ydxsd(Trim(x), Val(sb)))
  Y1 = 2 & String(Val(sb), "0")
  Do While MBJC(MPC(Trim(x), Trim(x3)), 1) >= 0
  
  s3 = s3 + 1
  Y = mbc2(Trim(x), MPC(Trim(Y1), mbc2(Trim(B), Trim(x), Val(sb))), Val(sb))
  x3 = x
  x = Trim(Y)
  Loop
  a1 = mbc2(Trim(Y), Trim(a), Val(sb))
  s = Len(a3) - Len(b3)
  a1 = qdqd0(Trim(a1))
  
  If MBJC(Mid(a3, 1, Len(b3)), Trim(b3)) < 0 Then
  a1 = tjxsd(Trim(a1), Len(a1) - s)
  Else
  a1 = tjxsd(Trim(a1), Len(a1) - s - 1)
  End If
  End If
  
  If InStr(a1, ".") = 0 Then
  a1 = a1
  Else
  a1 = Left(a1, InStr(a1, ".") - 1)
  End If
  ja = MPC(Trim(a3), MbC(Trim(b3), Trim(a1)))
  Do While MBJC(Trim(ja), Trim(b3)) >= 0
  ja = MPC(Trim(ja), Trim(b3))
  s5 = s5 + 1
  Loop
  a1 = MPC1(Trim(a1), Trim(s5))
  If ja = 0 Then
  Text3 = a1 & "用时" & Timer - ts & "秒，有" & Len(a1) & "位"
  Else
  Text3 = a1 & "/" & ja & "用时" & Timer - ts & "秒，整数部分有" & Len(a1) & "位"
  End If
  End Sub

  Private Sub Command2_Click()
  Text1 = ""
  Text2 = ""
  Text3 = ""

  End Sub
  Private Function mbc2(sa As String, sb As String, sd As String) As String 'chengfa jingdu
  Dim ja

  If Trim(sa) = 0 Or Trim(sb) = 0 Then
  mbc2 = 0
  Else


  ja = MbC(Trim(sa), Trim(sb))
  If Val(Len(ja)) > Val(sd) Then
  jb = Left(ja, Val(Len(ja)) - Val(sd))
  mbc2 = jb
  Else
  mbc2 = 0
  End If


  End If




  End Function

Private Function qdhz0(sa As String) As String
  a = sa
  Do While Right(a, 1) = "0"
  a = Left(a, Len(a) - 1)
  Loop
  If a = "" Then
  a = 0
  Else
  a = a
  End If
  qdhz0 = a
  End Function


  Private Function qdqd0(sa As String) As String
  a = sa
  Do While Left(a, 1) = "0"
  a = Mid(a, 2)
  Loop
  If a = "" Then
  a = 0
  Else
  a = a
  End If
  qdqd0 = a
  End Function

  Private Function tjxsd(sa As String, sd As String) As String
  If Val(Len(sa)) > Val(sd) Then
  tjxsd = Left(sa, Val(Len(sa)) - Val(sd)) & "." & Mid(sa, Val(Len(sa)) - Val(sd) + 1)
  Else
  If Val(Len(sa)) = Val(sd) Then
    tjxsd = "0." & sa
    Else
    tjxsd = "0." & String(Val(sd) - Val(Len(sa)), "0") & Trim(sa)
    End If
    End If

  End Function

  Private Function ydxsd(sa As String, sd As String) As String
  If Len(sa) = 1 And Val(sa) = 0 Then
    ydxsd = 0
    Else
   
      sc = InStr(sa, ".")
      If Val(sc) = 0 Then
      ydxsd = sa & String(sd, "0")
      Else
      se = Left(sa, Val(sc) - 1)
      sf = Right(sa, Len(sa) - Val(sc))
      If Val(Len(sf)) >= Val(sd) Then
      ydxsd = se & Mid(sf, 1, sd)
        Else
        ydxsd = se & sf & String(Val(sd) - Len(sf), "0")
        End If
        End If
        End If
        End Function
        
       Public Function MbC(D1 As String, D2 As String) As String
Dim j1&, j2&, e&, d&, E1&, m, n

   ' 按列法计算C=A*B
m = Trim(D1): n = Trim(D2)
x = Len(m) \ 4: Y = Len(n) \ 4
m = String(4 * x + 4 - Len(m), "0") & m
n = String(4 * Y + 4 - Len(n), "0") & n
x = x + 1: Y = Y + 1
Dim a(), B()
ReDim a(1 To x): ReDim B(1 To Y)
For i1 = 1 To x
a(i1) = Val(Mid(m, i1 * 4 - 3, 4))
Next
For i2 = 1 To Y
B(i2) = Val(Mid(n, i2 * 4 - 3, 4))
Next
ma = x: mb = Y
    MC = ma + mb
    ReDim c(MC)
    E1 = 0
    j1 = ma: j2 = ma
    For I = MC To 2 Step -1
        If I <= ma Then j2 = I - 1
        e = E1: E1 = 0
        For J = j1 To j2
            e = e + a(J) * B(I - J)
            If e > 2040000000 Then '减少进位次数
                e = e - 2040000000
                E1 = E1 + 204000
            End If
        Next J

        If j1 > 1 Then j1 = j1 - 1
base = 10000
        d = e \ base
        c(I) = e - d * base
        If Len(c(I)) < 4 Then
        c(I) = String(4 - Len(c(I)), "0") & c(I)
        Else
        c(I) = c(I)
        End If
jc = c(I) & jc
        E1 = E1 + d
    Next I
    jc = d & jc
   MbC = qdqd0(Trim(jc))
End Function
 Public Function MPC(D1 As String, D2 As String) As String ';jianfaqi
  Dim x, Y ';两数长度
  If qdqd0(D2) = "0" Then
  MPC = D1
  Else
If Len(D1) >= Len(D2) Then
  d4 = String(Len(D1) - Len(D2), "0") & D2
  d3 = D1
  Else
  d4 = D2
  d3 = String(Len(D2) - Len(D1), "0") & D1
  End If
  x = Len(d3) \ 8: Y = Len(d4) \ 8
  d3 = String(8 * x + 8 - Len(d3), "0") & d3
  d4 = String(8 * Y + 8 - Len(d4), "0") & d4
  x = x + 1: Y = Y + 1
  
  Dim a() As String, B1() As String, C1() As String, E1() As String
  ReDim a(1 To x)
  ReDim B1(1 To Y)
  ReDim C1(1 To x)
  ReDim E1(1 To x)
  Dim I, J, C2, CJ, jw
  For J = Y To 1 Step -1 ';D2
  jw = 1 ';yu jie weichuzhi
  B1(J) = Mid(d4, J * 8 - 7, 8) ';每位数
For I = x To 1 Step -1  ';D1
     a(I) = Mid(d3, I * 8 - 7, 8) ';每位数
   C1(I) = Val(1 & a(I)) - Val(B1(I)) - Val(1) + Val(jw) ';计算jia
   If Len(C1(I)) <= 8 Then
   jw = 0
   C1(I) = String(8 - Len(C1(I)), "0") & C1(I)
   Else
     jw = Left(C1(I), Len(C1(I)) - 8)
     End If
     E1(I) = Right(C1(I), 8)
     If Len(E1(I)) < 8 Then
     E1(I) = String(8 - Len(E1(I)), "0") & E1(I)
     Else
     E1(I) = E1(I)
     End If
     
    Next
    Next
    For r = 1 To x
    MPC = MPC & E1(r)
    If Len(MPC) > Len(D1) Then
    MPC = Mid(MPC, Len(MPC) - Len(D1) + 1)
    Else
    MPC = MPC
    End If
    For I = 1 To Len(MPC)
      If Not Mid(MPC, I, 1) = "0" Then
          Exit For
      End If
  Next
  strTmp = Mid(MPC, I)
    If Len(strTmp) = 0 Then
    MPC = "0"
    Else
  MPC = strTmp
  End If
    Next
   End If
   
  End Function

   Public Function MPC1(D1 As String, D2 As String) As String 'jiafa
  Dim x, Y, jw '两数长度
If qdqd0(D1) = "0" Then
MPC1 = D2
ElseIf qdqd0(D2) = "0" Then
MPC1 = D1
Else
If Len(D1) >= Len(D2) Then
  d4 = String(Len(D1) - Len(D2), "0") & D2
  d3 = D1
  Else
  d4 = D2
  d3 = String(Len(D2) - Len(D1), "0") & D1
  End If
  x = Len(d3) \ 8: Y = Len(d4) \ 8
  If 8 * x < Len(d3) Then
  d3 = String(8 * x + 8 - Len(d3), "0") & d3
  d4 = String(8 * Y + 8 - Len(d4), "0") & d4
  x = x + 1: Y = Y + 1
  Else
  x = x: Y = Y
  d3 = d3: d4 = d4
  End If
  Dim a() As String, B1() As String, C1() As String, E1() As String
  ReDim a(1 To x)
  ReDim B1(1 To Y)
  ReDim C1(1 To x)
  ReDim E1(1 To x)
  Dim I, J, C2, CJ
  For J = Y To 1 Step -1 'D2
  jw = 0 '进位清0
  B1(J) = Mid$(d4, J * 8 - 7, 8) '每位数
For I = x To 1 Step -1  'D1
     a(I) = Mid$(d3, I * 8 - 7, 8) '每位数
   C1(I) = Val(a(I)) + Val(B1(I)) + Val(jw) '计算jia
   If Len(C1(I)) < 8 Then
   C1(I) = String(8 - Len(C1(I)), "0") & C1(I)
   Else
   C1(I) = C1(I)
   End If
     jw = Left(C1(I), Len(C1(I)) - 8)
     E1(I) = Right(C1(I), 8)
    Next
    Next
    For r = 1 To x
    If jw = 0 Then
    MPC1 = MPC1 & E1(r)
    Else
    jc = jc & E1(r)
    MPC1 = jw & jc
    End If
    Next
   MPC1 = qdqd0(Trim(MPC1))
   End If
  End Function

  Public Function MBJC(D1 As String, D2 As String) As String ';bijiao
  If Len(D1) <= 10 And Len(D2) <= 10 Then
  If Val(D1) > Val(D2) Then
  MBJC = 1
  Else
  If Val(D1) = Val(D2) Then
  MBJC = 0
  Else
  MBJC = -1
  End If
  End If
  Else

  If Len(D1) > Len(D2) Then
  MBJC = 1
  Else
  If Len(D1) < Len(D2) Then
  MBJC = -1
  Else
  If Len(D1) = Len(D2) Then
  Dim x, Y
  x = Len(D1) \ 4: Y = Len(D2) \ 4
  Dim a() As String, B() As String
  ReDim a(4 To 4 * x + 4)
  ReDim B(4 To 4 * Y + 4)
  If Val(Left(D1, Len(D1) - 4 * x)) > Val(Left(D2, Len(D2) - 4 * Y)) Then
     MBJC = 1
     Else
     If Val(Left(D1, Len(D1) - 4 * x)) < Val(Left(D2, Len(D2) - 4 * Y)) Then
     MBJC = -1
     Else
     For I = 4 To 4 * x Step 4
     a(I) = Mid(D1, Len(D1) - I + 1, 4)
     B(I) = Mid(D2, Len(D2) - I + 1, 4)
     Next
     J = 4 * x
     Do While a(J) = B(J) And J >= 8
     
     J = J - 4
        Loop
        
        
      If Val(a(J)) - Val(B(J)) > 0 Then
      MBJC = 1
      Else
      If Val(a(J)) - Val(B(J)) < 0 Then
      MBJC = -1
      Else
      MBJC = 0
      End If
      
     End If
     
     
     
  End If
  End If
  End If
  End If
  End If
  End If
  End Function



（程序稍有改进，就是被除数和除数末尾都少补了8个0，速度稍有提高）

[此贴子已经被作者于2021-4-30 21:45编辑过]

大数除法，一般都是采用减法实现。
如果结合补位、试商、乘法，上面的2000多位数据除法，耗时0.5s以下就可实现，原理如下：

1、补位，有两种情况【需要判断大小在进行补位】【补位后，减法次数从n倍，降低为2数的位长差数】
   情形1：9234/11，补位后：1100（够除，补齐）    【直接减法需要93次，补位减法最多需要3*9次】
   情形2：9234/99，补位后：990（不够除，少补1位）
2、试商+减法+乘法【需要调用大数乘法、大数减法】【试商值=商，减少了减法次数】
   int((92/11)=8  |9234-(1100*8)=434 【直接减法需要93次，补位减法+试商减法，就需要3次】
   int((923)/99)=9|9234-(990*9)=324
3、剩余数---缩位
   434/110
   324/99
4、继续试商+减法+乘法
   int((43/11)=3      434-（110*3）=104
   int((324)/99)=3    324-(99*3)=   27  【不够除结束：9234/99=93 余27】
5、继续试商+减法+乘法
   int(104/11)=9    104-(11*9)=5【不够除结束：9234/11=839 余5】
通过以上算法，2000位-5000位的除法在0.3-0.4秒可以完成。

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（改进版程序，结果可能是对的，速度没有提高多少，稍有提高，继续研究努力！在单位电脑上就快一点，速度与电脑硬件有很大关系的.大量用到乘法和减法，我的减法程序速度太慢，无法用老师说的补0再用减法的程序，改进了一下方法把4位当作一位来处理，试商采用预估的方法，略高于实际的商，多次用到判断大小的程序，主要是减法慢1千位的减法一步就需要超过0.5秒了，总体时间长了，而利用牛顿迭代法的除法更快些，二者各有优缺点，当除数位数不多时利用这个除法感觉更有利。）

[此贴子已经被作者于2021-5-8 18:17编辑过]

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198737927=
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（这是利用牛顿迭代法的快速除法程序计算的结果，可见当除数位数较多时，还是这个利用牛顿迭代法的快速除法速度快些）

字符串比较大小不用那么麻烦
1、先比长度判断大小
2、长度相同，直接比较大小
Public Function MBJC(D1 As String, D2 As String) As String ';bijiao
  If Len(D1) > Len(D2) Then MBJC = 1: Exit Function
  If Len(D1) < Len(D2) Then MBJC = -1: Exit Function
  If D1 > D2 Then MBJC = 1: Exit Function
  If D1 < D2 Then MBJC = -1: Exit Function
  MBJC = 0
End Function

我的比较大小的编程思想就是这样的，只不过，D1>D2和D1<D2无法直接比较，需要一段一段比较的，从高位段到低位段的，程序没有您写的这么简单。

需要学习和消化。