各位老师好！求助编辑一个大整数的快速乘除法可调用程序

朋友的注释共有17张图片，我注释了4张，发了末尾3张，还有10张没有弄懂看不清楚没有发，不懂原理，通过末尾3张注释看大致是：把乘数被乘数由多项式系数表示法变为点值表示，通过快速fft，再相乘，结果变为系数表示法，用快速逆fft变换。不懂vc语句，有懂的感兴趣的老师朋友，请给与指导，谢谢！

下面是计算和判断梅森数的程序，仅发主程序供大家参考，希望得到快速乘法除法程序以提高这个程序的速度：（判断法采用卢卡斯-莱莫测试法）
 Private Sub Command1_Click()
Dim a
a = Val(Text1)
B = 1
Do While C <= a - 1
B = MbC(Trim(B), 2)
C = C + 1
Loop
Text2 = MPC(Trim(B), 1)
End Sub

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

End Sub
 

Private Sub Command3_Click()
Dim a
B = Trim(Text1)
B1 = 1
Do While C <= B - 1
B1 = MbC(Trim(B1), 2)
C = C + 1
Loop
a = MPC(Trim(B1), 1)

If Len(a) <= 11 Then
Text3 = fenjieyinzi(Trim(a))
Else
Text3 = fenjieyinzi1(Trim(a), Val(B))
End If
End Sub

Private Function fenjieyinzi1(sa As String, sb As String) As String
Dim X, B
X = Trim(sa)

 B = Val(sb)
 s = 4
 B1 = 0
Do While B1 <= B
If InStr(MCC1(Trim(s), Trim(X)), "/") = 0 Then
a = True
Else
a = a
End If
B1 = B1 + 1
s1 = zhengchuqyushu(MCC1(Trim(s), Trim(X)))
s2 = s2 & s1 & "(" & B1 & ")" & vbCrLf
s = MPC(MbC(Trim(s1), Trim(s1)), 2)
Loop
If a = True Then
fenjieyinzi1 = "这是素数" & s2
Else
fenjieyinzi1 = "2*2" & s2
End If

End Function

如下为网上搜索到的快速乘法的c语言程序，请老师看看能不能运行？能不能翻译成vb程序？
迭代型：(共119行，乱了，再整理一下）
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <conio.h>
#define N 150010const double pi = 3.141592653;
char s1[N>>1], s2[N>>1];
double rea[N], ina[N], reb[N], inb[N];
int ans[N>>1];
 void Swap(double *x, double *y)
{
    double t = *x;
    *x = *y;
    *y = t;
}
 int Rev(int x, int len)
{
    int ans = 0;
    int i;
   for(i = 0;
 i < len; i++)
{
       ans <<= 1;
        ans |= (x & 1);
        x >>= 1;
    }
    return ans;
}
 void FFT(double *reA, double *inA, int n, bool flag)
{
   int s;
    double lgn = log((double)n) / log((double)2);
    int i;
    for(i = 0; i < n; i++)
{  
      int j = Rev(i, lgn);
        if(j > i)
{
            Swap(&reA[i], &reA[j]);
            Swap(&inA[i], &inA[j]);
        }
    }
   for(s = 1; s <= lgn; s++)
{   
     int m = (1<<s);
        double reWm = cos(2*pi/m), inWm = sin(2*pi/m);
        if(flag) inWm = -inWm;
        int k;
        for(k = 0; k < n; k += m)
{  
          double reW = 1.0, inW = 0.0;
            int j;
           for(j = 0; j < m / 2; j++)
{  
              int tag = k+j+m/2;
                double reT = reW * reA[tag] - inW * inA[tag];
                double inT = reW * inA[tag] + inW * reA[tag];
               double reU = reA[k+j], inU = inA[k+j];
                reA[k+j] = reU + reT;
                inA[k+j] = inU + inT;
                reA[tag] = reU - reT;
               inA[tag] = inU - inT;
               double rew_t = reW * reWm - inW * inWm;
                 double inw_t = reW * inWm + inW * reWm;
                reW = rew_t;
               inW = inw_t;
           }
        }
    }
    if(flag)
{
        for(i = 0;
 i < n; i++)
{
            reA[i] /= n;
            inA[i] /= n;
        }
   }
}
 int main()
{
#if 0
   freopen("in.txt","r",stdin);
#endif
   while(~scanf("%s%s", s1, s2))
{
       memset(ans, 0 , sizeof(ans));
        memset(rea, 0 , sizeof(rea));
        memset(ina, 0 , sizeof(ina));
        memset(reb, 0 , sizeof(reb));
        memset(inb, 0 , sizeof(inb));
        int i, lent, len = 1, len1, len2;
        len1 = strlen(s1);
        len2 = strlen(s2);
        lent = (len1 > len2 ? len1 : len2);
        while(len < lent) len <<= 1;
        len <<= 1;
        for(i = 0;
 i < len; i++)
{
           if(i < len1) rea[i] = (double)s1[len1-i-1] - '0';
            if(i < len2) reb[i] = (double)s2[len2-i-1] - '0';
            ina[i] = inb[i] = 0.0;
        }
        FFT(rea, ina, len, 0);
        FFT(reb, inb, len, 0);
        for(i = 0; i < len; i++)
{
           double rec = rea[i] * reb[i] - ina[i] * inb[i];
            double inc = rea[i] * inb[i] + ina[i] * reb[i];
            rea[i] = rec; ina[i] = inc;
        }
        FFT(rea, ina, len, 1);
        for(i = 0; i < len; i++)
           ans[i] = (int)(rea[i] + 0.4);
        for(i = 0; i < len; i++)
{
           ans[i+1] += ans[i] / 10;
            ans[i] %= 10;
        }
        int len_ans = len1 + len2 + 2;
        while(ans[len_ans] == 0 && len_ans > 0)
 len_ans--;
        for(i = len_ans; i >= 0; i--)
            printf("%d", ans[i]);
       printf("\n");
    }
    return 0;
}
————————————————
迭代型比递归型稍快一点。
发帖时间 昨天 09:18
        

朋友说前面的c语言程序缺少图中下面画红线的库，谁知道？怎么补？哪里找？

这个是用我的模仿手工乘法的程序计算结果：（比快速傅里叶变换的还快？）
111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111*111111111=12345678999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999987654321有221位,用时0.0078125秒.

把数据设定提到前面，省略了中间的重复部分，居然速度又提高了一点：
111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111*111111111=12345678999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999987654321有221位,用时0.734375秒.

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还不如106#楼的模仿手工计算的程序快呢，咋回事？

速度基本无法再提高了，改一下算法，改为8位一组试试，如何呢？如下是优化后的代码（还没有改成8位一组的）：
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

Private Sub Command1_Click()
  Dim xr() As Double, a As String
  a = Trim(Text1)
  b = Trim(Text3)
  ts = Timer
  sb1 = Len(a) + Len(b)
  sb2 = Log(sb1) / Log(2)
  If InStr(sb2, ".") = 0 Then
  sb2 = sb2
  Else
  sb2 = Int(sb2) + 1
  End If
  sb = 2 ^ sb2
  Print sb
  If Len(a) = Len(b) And 2 ^ (Int(Log(Len(a)) / Log(2))) = Len(a) Then
    a = String(Val(sb) - Len(a), "0") & a
  b = String(Val(sb) - Len(b), "0") & b
  a = dxcx0(Trim(a), Val(sb)): b = dxcx0(Trim(b), Val(sb))
  Else

  a = String(Val(sb) - Len(a), "0") & a
  b = String(Val(sb) - Len(b), "0") & b
  a = dxcx0(Trim(a), Val(sb)): b = dxcx0(Trim(b), Val(sb))
  End If
  ReDim xr(0 To Len(a) - 1): ReDim yr(0 To Len(b) - 1): ReDim zr(0 To Len(b) - 1)
  For i1 = 0 To Len(a) - 1
  xr(i1) = Mid(a, i1 + 1, 1)
  yr(i1) = Mid(b, i1 + 1, 1)

     Next
  
  Dim xi(): Dim yi(): Dim zi()
  n = Len(a) '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
     
      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)
      

      s = s & "/" & zr(i)
      s1 = s1 & "/" & zi(i)
      Next
     s2 = nifft(dxcx1(Trim(s)), dxcx1(Trim(s1)), Trim(sb1))
     
      Text2 = s2 & "有" & Len(s2) & "位，用时" & Timer - ts & "秒"
  End Sub

  Private Sub Command2_Click()
  Text1 = ""
  Text2 = ""
  Text3 = ""
  Form1.Cls
  End Sub

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 nifft(sa As String, sb As String, sb1 As String) As String
  
  Dim xi(): Dim yi(): Dim zi()
  Dim xr(), yr(), zr()
  s2 = Split(sa, "/")
  s3 = Split(sb, "/")
      j = UBound(s2)
      n = j
     For k = 1 To j
         n1 = n1 + 1
          ReDim Preserve xr(0 To n1 - 1)
          ReDim Preserve yr(0 To n1 - 1)
         xr(n1 - 1) = s2(n1): yr(n1 - 1) = s3(n1)
       Next
     

  ReDim zr(0 To j - 1)

  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 = -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
     
      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) - yi(i)) / n
      
     
      s1 = Int(Val(zr(i) + 0.5))
      s = "/" & s1 & s
      zr(i) = s1
      Next
      For i1 = 1 To Val(j - sb1 + 1)
      zr(sb1 + i1 - 2) = 0
      Next
      
     
     
      For i1 = 0 To n - 1
      If zr(i1) < 0 Then
      zr(i1) = 0
      Else
      zr(i1) = zr(i1)
      End If
      
      
      If i1 = 0 Then
      s6 = Int(zr(i1)) \ 10
      s8 = Int(zr(i1)) Mod 10
      ElseIf Val(zr(i1)) >= 0 Then
      s7 = Int(zr(i1)) + Val(s6)
      s10 = Val(s7) Mod 10
      s11 = s10 & s11
      s6 = Val(s7) \ 10
      Else
      s6 = Val(s6)
      End If
     
      Next
      s9 = s6 & s11 & s8
     
  nifft = qdqd0(Trim(s9))

  End Function

  Private Function dxcx0(sa As String, sb As String) As String

  Dim x_() As Double, a As String
    a = Trim(sa)
    ReDim x_(1 To sb)
    For i1 = 1 To sb
    x_(i1) = Mid(a, sb - i1 + 1, 1)
      Next
    Dim n As Integer, i As Long, j As Long, mn As Long, lh As Long, t As Double, 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
    s = s & x_(j + 1)
    Next
    dxcx0 = x_(1) & x_(1 + sb / 2) & s
   

  End Function

  Private Function dxcx1(sa As String) As String

  Dim x_() As Double, a As String
    a = Trim(sa)
     

  s2 = Split(sa, "/")
  s3 = Split(sb, "/")
      j = UBound(s2)
      sb = j
     
       ReDim x_(1 To sb)
     For k = 1 To j
         n1 = n1 + 1
          ReDim Preserve x_(1 To n1)
        
         x_(n1) = s2(n1)
       Next
    Dim n As Integer, i As Long, mn As Long, lh As Long, t As Double
    '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
    s = s & "/" & x_(j + 1)
    Next
    dxcx1 = "/" & x_(1) & "/" & x_(1 + sb / 2) & s
   
    End Function

[此贴子已经被作者于2021-3-19 20:44编辑过]

147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369*36985214=
1.931.931.931.931.931.931.931.931.931.931.931.931.931.931.93688410879246E+159896E+150488E+154032E+15175005115893E+156033E+155133E+15838062999246E+159896E+150488E+154032E+15175005135893E+156033E+155133E+15838062969246E+159896E+150488E+154032E+15175005105893E+156033E+155133E+15838062959246E+159896E+150488E+154032E+15175005135893E+156033E+155133E+15838062999246E+159896E+150488E+154032E+15175005155893E+156033E+155133E+15838062989246E+159896E+150318E+1507871970有460位，用时0.1953125秒

真是奇怪的结果，可能是无法摆脱科学计数法的缘故，咋弄？咋就不用科学计数法了？改成4位一组试试？

51750801837147361345408953922231823615475578427966187002956389087112242842559611794590895524485015222232340190036677951157401229518412775512617768569186939216558814320044037671525512763073762127357272238470370174050144130962253437215369727381909754581075278888137687950749577751967083233227932391898438489520107788418593104216764745143648165875043861634459264809523254076330115365651752264033578829280651927862062277153553168278640509846511729608378923480331705134467105387853440058108864733429085916392927954109944314725590758950098556991513109760871599045355054258610189920009222629391227784118536578933067532162200768112408111142115021110731900107445187734955403922470144187293970602024056652942406064101184615113779243566842311336047149767396006622923831778833173731302325162741660053390002572456069410383734906953419854919650114722834689335022576764661864630532595250136417800041415827379233503655173380741283758557001102498493237113089198106283487003030225058520047964863929279622015825870972146222540614667928697270131499340362072956956518213266361286372027834000838185920579641835952404678850816456467012890793914108776148483471455515695596694573035435841962871983614397882366460940068418989292218104650923374259244879331938925143014431488635252724366437874702141802712286424754174951797598162531093933772708024046029028652425912112434874797404878317364682580259997737809632860143160557722236459697738869857870982308547756781808568834445404196611833859447257611721058384661943492980180884154939581533269700568975940675513953240040220315659784214936947443784598154082110443748171557676558299300252057475022409541083454882202785077569281268346332901357829843950754331120530978456454396022570647840977328115888711408099894489014427119253061839770890965114853246067272044090282103668762164047374624856119676063310166566519499552342907590495696658359542582469176737197423550084705962160477441546453931948920780829433665262356431973422034925001341330921812806939990688094288773216182971976433480031438271163051341645350474631300965486818841553843112688792803367397276204832936049162335586140151875524537720425345701193713093955432559579831822084761702059241698184717469616732582600658006352069963017377661059372648121969448644394344799369193952197519795756182552461838014896498816263546256621347748100920475049252091842372001283217811864786225692344297842649982716736752004086642881662614773154743879410328420184057019873899911520017723788801*
51750801837147361345408953922231823615475578427966187002956389087112242842559611794590895524485015222232340190036677951157401229518412775512617768569186939216558814320044037671525512763073762127357272238470370174050144130962253437215369727381909754581075278888137687950749577751967083233227932391898438489520107788418593104216764745143648165875043861634459264809523254076330115365651752264033578829280651927862062277153553168278640509846511729608378923480331705134467105387853440058108864733429085916392927954109944314725590758950098556991513109760871599045355054258610189920009222629391227784118536578933067532162200768112408111142115021110731900107445187734955403922470144187293970602024056652942406064101184615113779243566842311336047149767396006622923831778833173731302325162741660053390002572456069410383734906953419854919650114722834689335022576764661864630532595250136417800041415827379233503655173380741283758557001102498493237113089198106283487003030225058520047964863929279622015825870972146222540614667928697270131499340362072956956518213266361286372027834000838185920579641835952404678850816456467012890793914108776148483471455515695596694573035435841962871983614397882366460940068418989292218104650923374259244879331938925143014431488635252724366437874702141802712286424754174951797598162531093933772708024046029028652425912112434874797404878317364682580259997737809632860143160557722236459697738869857870982308547756781808568834445404196611833859447257611721058384661943492980180884154939581533269700568975940675513953240040220315659784214936947443784598154082110443748171557676558299300252057475022409541083454882202785077569281268346332901357829843950754331120530978456454396022570647840977328115888711408099894489014427119253061839770890965114853246067272044090282103668762164047374624856119676063310166566519499552342907590495696658359542582469176737197423550084705962160477441546453931948920780829433665262356431973422034925001341330921812806939990688094288773216182971976433480031438271163051341645350474631300965486818841553843112688792803367397276204832936049162335586140151875524537720425345701193713093955432559579831822084761702059241698184717469616732582600658006352069963017377661059372648121969448644394344799369193952197519795756182552461838014896498816263546256621347748100920475049252091842372001283217811864786225692344297842649982716736752004086642881662614773154743879410328420184057019873899911520017723788801=
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时间不慢，末尾几位不对了好像是，再说吧，晚安！！

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9999601699994313999943589999789299997708999974319999641999998089999958939999675199996811999956919999719399996813999977089999651199996415999949539999534499997113999967909999623599998245999980579999658399997295999964669999755999998804999974659999778999996331999952439999666999995769999982499999830599997981999977939999719199997465999972679999708499998447999971249999790999999520999968419999711499996541999968179999835799998299999982699999638699997903999967379999643199996664999984499999799599997593999981699999793799996277999956959999653499997919999977569999870599998236999976859999772099998551999980979999937999999435999987859999774899997791999986159999779999997534999982739999865399998075999981459999807999998646999978039999785799999197999994709999863999997478999982699999727599999591999971200000292200001699000022160000210000001398000017570000222600001000000031900000194400002546000017080000127600001807000026340000095600002202000023310000253600001483000028700000302200003064000015000000358600002660000031200000268700003164000012850000280800002028000032320000424300005122000026870000410200003518000046040000274800003856000034860000389200003281000040360000235800003482000023160000377800003988000035880000300100005022000032830000370600002662000041600000366900005128000030320000479600002813000048380000232000004564000058110000535400004560000048840000573200006024000045520000696800006236000062500000539400006284000052090000448200004161000063720000515600007394000033750000628600006071000063100000245600007404000048880000648400005147000054640000343800007388000067790000655000006479000067180000624100006088000053520000785400006812000068800000672700009064000056400000662200007102000085300000671900007436000064510000835000007332000079600000850300008924000050740000801000008739000094880000693900008706000061660001023400007652000084920000761300009160000079530001053800007187000094940000736800009696000085940000906000008243000106460000704700009268000068890000906200006883000112060000628300010330000072710000875000007188000095720000720400010862000078920000894400008743000101460000970100009982000074650000996400007992000088960000774900010898000090920000994200008629000115940000694000008740000081360001108000008338000092640000845800012686000090790001038200010632000111560000777600009636000082150001103200007912000103060000988100011934000103390000828600009333000117000000749200009780000119490001289400008948000104680001071700012804000084610001265600010581000118280001030900010738000079430001212400008555000110100001104700010708000095240001072200008944000138580000902700011068000100790001283200013475000103120000863200011022000075790001017000009164000106400001010600011736000080500001313600007906000103740000828100012010000102970000934000009132000118040000925100010440000100020001070600007697000102680000819200012340000086540001160600008759000123960001104600009446000086510001214600008440000113920001161400011968000096020001081800011073000102240000967300011480000090810001360200010897000101100000763000010982000102150001031000010177000101360000887200010414000081380001029200009063000115500000882000012442000126430000953000009026000090240000815400008750000089920001058200008833000102760000824100011644000072500000832400007204000101980000991400006042000079620001111800008454000098500000931100008768000073260000951000007308000087820000729000008716000065490001142200009350000057440000543100007010000055200000707200007959000078340000564800007404000065510000757800006639000081360000593100007900000069120000555000004869000090180000582200005460000073540000724800005544000078900000585000008294000065850000670600005061000076220000992100004896000051960000528400005422000040400000632300005306000061290000723600004077000073860000420700005548000054960000819400005415000040320000294100007546000043570000540000004707000068840000381500005588000036810000468000004691000071280000471200005760000056250000344400002460000043400000217200003268000015660000363200002697000035260000242700002742000017320000350800002345000046860000365400002300000016340000560000000995000018160000148700002954000025630000390600001214000025420000175700002164000016940000361400004869000004839999979700002354000023270000126200001116000034980000266400000816000007750000339000001648000007540000058400001634000013900000020999999328000034020000202900001290000007670000238600000303000016340000049400001174000012400000131000000062000030440000157999999289999994570000027199999074999996079999985900000827999997630000064799998608000009200000217700001442000007110000143800001696999990659999897200000749999989380000007399999029999996439999927000000631999990000000055400001377999999179999948900000336000019479999991599998679999994979999989299998765999989349999957200000768000007459999891399999453999985349999972399999369999997460000182399997953999988219999953600000185999994919999958700000106000007189999896799999365000002940000000899999681999980810000028000000016.

看起来二者差得很多，这个算法不对了，少了很多。

11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111（329位，329个1）*101=11111111111111111111111111111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222211有377位，用时0.2773438秒（331位是正确的，多了46个1）。

[此贴子已经被作者于2021-3-20 08:10编辑过]

147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369147852369*36985214=5465465465465465465465465465465465465465465465465465465465465465465465465465465465465468351513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317513340317507871966有487位，用时0.5390625秒（末尾数字是与实际相同的，最高位咋又多了好多位？）

看看这样不行，无法调整了，把一位一组的程序再优化一下吧。

修改了一下程序，这回可能对了，程序速度和模仿手工计算的相似，还能提高，希望老师能优化一下程序，前面的一位一组是对的，速度太慢能否优化？这个待优化的快速程序代码如下：

Private Sub Command1_Click()
  Dim xr() As String, a As String
  a = Trim(Text1)
  b = Trim(Text3)
  ts = Timer
  x = Len(a) \ 4: Y = Len(b) \ 4
  If Val(4 * x) = Len(a) Then
  a = a
  ElseIf Val(4 * Y) = Len(b) Then
  b = b
  Else
  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
  End If
  
  
  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
  Print sb
  

  a = String(Val(sb) * 4 - Len(a), "0") & a
  b = String(Val(sb) * 4 - Len(b), "0") & b
  a = dxcx0(Trim(a), Val(sb)): b = dxcx0(Trim(b), Val(sb))
  Print a
  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
  For i1 = 0 To (Len(a) - 4) \ 4
  xr(i1) = Mid(a, (i1 + 1) * 4 - 3, 4)
  yr(i1) = Mid(b, (i1 + 1) * 4 - 3, 4)

     Next
     End If
  
  Dim xi(): Dim yi(): Dim zi()
  n = Len(a) \ 4 '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")
     Print xr(p), xr(q)
      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
     s2 = nifft(dxcx1(Trim(s)), dxcx1(Trim(s1)), Trim(sb1))
     
      Text2 = s2 & "有" & Len(s2) & "位，用时" & Timer - ts & "秒"
  End Sub

  Private Sub Command2_Click()
  Text1 = ""
  Text2 = ""
  Text3 = ""
  Form1.Cls
  End Sub

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 nifft(sa As String, sb As String, sb1 As String) As String
  
  Dim xi(): Dim yi(): Dim zi()
  Dim xr(), yr()
  Dim zr() As String
  
  s2 = Split(sa, "/")
  s3 = Split(sb, "/")
      J = UBound(s2)
      n = J
     For k = 1 To J
         n1 = n1 + 1
          ReDim Preserve xr(0 To n1 - 1)
          ReDim Preserve yr(0 To n1 - 1)
         xr(n1 - 1) = s2(n1): yr(n1 - 1) = s3(n1)
         xr(n1 - 1) = Format(Val(xr(n1 - 1)), "0.000000"): yr(n1 - 1) = Format(Val(yr(n1 - 1)), "0.000000")

       Next
     

  ReDim zr(0 To J - 1)

  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 = -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 > 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) - yi(I)) / n
      zr(I) = Format(Val(zr(I) + 0.5), "0.000000")
     If InStr(zr(I), ".") = 0 Then
     s1 = zr(I)
     Else
     s1 = Left(zr(I), InStr(zr(I), ".") - 1)
      End If
      s = "/" & s1 & s
      zr(I) = s1
      Next
      For i1 = 1 To Val(J - sb1 + 1)
      zr(sb1 + i1 - 2) = 0
      Next
      
     
     
      For i1 = 0 To n - 1
      If zr(i1) < 0 Then
      zr(i1) = "00000000"
      Else
      zr(i1) = zr(i1)
      End If
      s5 = s5 & "/" & zr(i1)
      
      If i1 = 0 Then
      If Len(zr(i1)) < 4 Then
      zr(i1) = String(4 - Len(zr(i1)), "0") & zr(i1)
      Else
      zr(i1) = zr(i1)
      End If
      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 = MPC1(Trim(zr(i1)), Trim(s6))
      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 = "00000000"
      Else
      s7 = s7
      s6 = Val(Left(s7, Len(s7) - 4))
      End If
      Else
      s6 = s6
      End If
     
      Next
      s9 = s6 & s11 & s8
     
  nifft = qdqd0(Trim(s9))

  End Function

  Private Function dxcx0(sa As String, sb As String) As String

  Dim x_() As String, a As String
    a = Trim(sa)
    ReDim x_(1 To sb)
    For i1 = 1 To sb
    x_(i1) = Mid(a, (sb - i1 + 1) * 4 - 3, 4)
    If Len(x_(i1)) < 4 Then
    x_(i1) = String(4 - Len(x_(i1)), "0") & x_(i1)
    Else
    x_(i1) = x_(i1)
    End If
   
      Next
    Dim n As Integer, I As Long, J As Long, mn As Long, lh As Long, t As Double, 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
    s = s & x_(J + 1)
    Next
    dxcx0 = x_(1) & x_(1 + sb / 2) & s
   
   

  End Function

  Private Function dxcx1(sa As String) As String

  Dim x_() As Double, a As String
    a = Trim(sa)
     

  s2 = Split(sa, "/")
  s3 = Split(sb, "/")
      J = UBound(s2)
      sb = J
     
       ReDim x_(1 To sb)
     For k = 1 To J
         n1 = n1 + 1
          ReDim Preserve x_(1 To n1)
        
         x_(n1) = Format(Val(s2(n1)), "0.000000")
       Next
    Dim n As Integer, I As Long, mn As Long, lh As Long, t As Double
    '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
x_(J + 1) = Format(Val(x_(J + 1)), "0.000000")
    s = s & "/" & x_(J + 1)
    Next
    x_(1) = Format(Val(x_(1)), "0.000000"): x_(1 + sb / 2) = Format(Val(x_(1 + sb / 2)), "0.000000")
    dxcx1 = "/" & x_(1) & "/" & x_(1 + sb / 2) & s
   
    End Function

Public Function MPC1(D1 As String, D2 As String) As String 'jiafa
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): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
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 = 0 '进位清0
B1(J) = Mid$(D4, J, 1) '每位数
For I = x To 1 Step -1  'D1
   a(I) = Mid$(d3, I, 1) '每位数
   C1(I) = a(I) + B1(I) + JW '计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  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
  
End Function

[此贴子已经被作者于2021-3-20 10:24编辑过]

111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111*111111111=12345678999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999987654321有221位，用时0.3984375秒（结果是对的，速度提高了一点，可能还有提升空间，希望帮助优化，谢谢各位老师！）

这是模仿手工计算的程序结果，看上去比傅立叶变换的程序还快？结果如下：
51750801837147361345408953922231823615475578427966187002956389087112242842559611794590895524485015222232340190036677951157401229518412775512617768569186939216558814320044037671525512763073762127357272238470370174050144130962253437215369727381909754581075278888137687950749577751967083233227932391898438489520107788418593104216764745143648165875043861634459264809523254076330115365651752264033578829280651927862062277153553168278640509846511729608378923480331705134467105387853440058108864733429085916392927954109944314725590758950098556991513109760871599045355054258610189920009222629391227784118536578933067532162200768112408111142115021110731900107445187734955403922470144187293970602024056652942406064101184615113779243566842311336047149767396006622923831778833173731302325162741660053390002572456069410383734906953419854919650114722834689335022576764661864630532595250136417800041415827379233503655173380741283758557001102498493237113089198106283487003030225058520047964863929279622015825870972146222540614667928697270131499340362072956956518213266361286372027834000838185920579641835952404678850816456467012890793914108776148483471455515695596694573035435841962871983614397882366460940068418989292218104650923374259244879331938925143014431488635252724366437874702141802712286424754174951797598162531093933772708024046029028652425912112434874797404878317364682580259997737809632860143160557722236459697738869857870982308547756781808568834445404196611833859447257611721058384661943492980180884154939581533269700568975940675513953240040220315659784214936947443784598154082110443748171557676558299300252057475022409541083454882202785077569281268346332901357829843950754331120530978456454396022570647840977328115888711408099894489014427119253061839770890965114853246067272044090282103668762164047374624856119676063310166566519499552342907590495696658359542582469176737197423550084705962160477441546453931948920780829433665262356431973422034925001341330921812806939990688094288773216182971976433480031438271163051341645350474631300965486818841553843112688792803367397276204832936049162335586140151875524537720425345701193713093955432559579831822084761702059241698184717469616732582600658006352069963017377661059372648121969448644394344799369193952197519795756182552461838014896498816263546256621347748100920475049252091842372001283217811864786225692344297842649982716736752004086642881662614773154743879410328420184057019873899911520017723788801*
51750801837147361345408953922231823615475578427966187002956389087112242842559611794590895524485015222232340190036677951157401229518412775512617768569186939216558814320044037671525512763073762127357272238470370174050144130962253437215369727381909754581075278888137687950749577751967083233227932391898438489520107788418593104216764745143648165875043861634459264809523254076330115365651752264033578829280651927862062277153553168278640509846511729608378923480331705134467105387853440058108864733429085916392927954109944314725590758950098556991513109760871599045355054258610189920009222629391227784118536578933067532162200768112408111142115021110731900107445187734955403922470144187293970602024056652942406064101184615113779243566842311336047149767396006622923831778833173731302325162741660053390002572456069410383734906953419854919650114722834689335022576764661864630532595250136417800041415827379233503655173380741283758557001102498493237113089198106283487003030225058520047964863929279622015825870972146222540614667928697270131499340362072956956518213266361286372027834000838185920579641835952404678850816456467012890793914108776148483471455515695596694573035435841962871983614397882366460940068418989292218104650923374259244879331938925143014431488635252724366437874702141802712286424754174951797598162531093933772708024046029028652425912112434874797404878317364682580259997737809632860143160557722236459697738869857870982308547756781808568834445404196611833859447257611721058384661943492980180884154939581533269700568975940675513953240040220315659784214936947443784598154082110443748171557676558299300252057475022409541083454882202785077569281268346332901357829843950754331120530978456454396022570647840977328115888711408099894489014427119253061839770890965114853246067272044090282103668762164047374624856119676063310166566519499552342907590495696658359542582469176737197423550084705962160477441546453931948920780829433665262356431973422034925001341330921812806939990688094288773216182971976433480031438271163051341645350474631300965486818841553843112688792803367397276204832936049162335586140151875524537720425345701193713093955432559579831822084761702059241698184717469616732582600658006352069963017377661059372648121969448644394344799369193952197519795756182552461838014896498816263546256621347748100920475049252091842372001283217811864786225692344297842649982716736752004086642881662614773154743879410328420184057019873899911520017723788801=
2678145490787694710138406683675886762424440548647327525594133873038347266950777818028529804877891353347244255046176220880989519574806598935727647635506939520211209794328712328126947740602255036264392628020291100698432900022333877728824270241063030019536831205264726059774673235680796770108334187808344470141093691232926021244583649747591446066921535333854157441330339217364515328375889937313870826987520723914810358707312468857074455945610038118763873992681688857200178452843740327143990247797893489008808544535536081089994800692174759199578596435124153437689121057209523619989593900355037400039597165241729693472001589594642879166693443994939359639600558001937547209387175085119128575833396037478944824322315197771750730768383267287661855880237549141571520374996029107650341071074081501632143441365461865431362023790463469688071768208320226561675630348708531708110373889241713511809029065048200924851629507265095151843687852114948736130517024578482059771284515915597919026074110811882700307150650858080695566672584075215926450360584738705106755945308199980660478183563586945902705730231409948938478910176292179410952310592864745025373902249844607078729230098512959498522851990040833671698873183076996740726479481352429756295966452788332789259316653805673821716832204368483794501474641036177256005810416507649770210480747056764697918800240201155395628561684853684747063434500664449114760179367086926249813006056735202795763742271472136500817313178050955623517148960973128433455798444839070215800699075256371341531892841721456473301085595261371522078416420399702683504171019191363372883472415693921509069484448792009627325245658854979159002549542769741504596589556474585723101403486046952706847309188488390899096649210853675228464611999630360164703837131620319658277117300208326944026347808645954842782309633205645471959842390075986572806483755223497552549948718545978420793425036666212191832327909389117021539426917904222971515424022606157676379417252939026404363841301595348953340657745965591468370831371449860774296757556463049237248472613472436666799615694672489600751763956185893123579218797539971253828850163437053164723845196089466298000486042246621634263064752906475198879616484926366053597071510886820878425907736453843197228282179943365206039514850477377542684361730162273246709577442085159313947668552462343596819299335060863266863059421286080919061657175757802930378698062290163092494909661982639303946271889619023417245433500782685534406291391527022657608608130680134939380126048353657648559735671562230714451258764762350451448379438849319710473631625533527602085050858633346936315115309333355986556546113134787213610042970405680162084678021281774169131725296977361816657904233850711837826724976507876061043779177845550646612327663283839673950405472039432309339110648301347672597370034346896334064135099613033528785924976781865447506814375627647103020761819104412269362847848884053177378762432543285984193091289854949394023586451139393716370633759317698908834326333339634557238526607966375935960004339535161203546369910853171524516945554862019134684985868547068709986010719120259421723270478586992153989283736650948010894951434857207445141886625290777550599700738909777829412358941157674866550887608199469723859806486384262574182811908513849905040209776132986875560077482527819093584150609347560543627976011009349905362597935257895287412087233810106693141683912683308201407373637490835862452911394718399632093441745957478079754723679119343225931665785380948807114301164623717144211285944154289093317610519159281033583963015810556464180819928345256832572962092994993950655913067768151113345566231088759030148164710287289335782462899525700500822021472132532771242198844498579102733028256523810973405350508253183399668290339844052874956694050028526577775764032598023622192221226501334606994447870277619118208162133562541678250491647671042612088902952091163094215645902682086024337098910110924115381788866213335441814530141911754446270296630426675020592640816713810936850961517475097707179713115856513919631998747192606018612535436009162735908155778165736923393260822217415131632296810207091918499370220533980666393617256227781299273913099896641458499949922475383775878771011361417556799406151773618626138749998464514570482965286184387350245762317271666329142667987131139265167425606863654107927682419958167046956962340419295394058625063862272314570914511355913547470055072878835349142049813368019960713974852351833144227544851625677753419141348585495260230041111323576432417502998832485027071744397105338790364666312325483218209150368759120749671419554589928540715813531144241705501211397506662448276056294585639532800634727428900861538486753011006379264618338782036690340859441153926551954112364946638768223012718907190897165613382555036872673785444132692292217184974818914501886689736449912131900762592363447945036085692999163815947845753538999001633767986447907729462453017601有4888位，用时3.929688秒

111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111*111111111=12345678999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999987654321有221位，用时0.0859375秒（这个快，是4位一组的程序，还有可以优化的空间）

4位一组的程序重发如下，是修改好的，还有提升空间，希望老师指点，谢谢！代码如下：

Private Sub Command1_Click()
  Dim xr() As String, a As String
  a = Trim(Text1)
  b = Trim(Text3)
  ts = Timer
  x = Len(a) \ 4: Y = Len(b) \ 4
  If Val(4 * x) = Len(a) Then
  a = a
  ElseIf Val(4 * Y) = Len(b) Then
  b = b
  Else
  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
  End If
  
  
  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
  Print sb
  

  a = String(Val(sb) * 4 - Len(a), "0") & a
  b = String(Val(sb) * 4 - Len(b), "0") & b
  a = dxcx0(Trim(a), Val(sb)): b = dxcx0(Trim(b), Val(sb))
  Print a
  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
  For i1 = 0 To (Len(a) - 4) \ 4
  xr(i1) = Mid(a, (i1 + 1) * 4 - 3, 4)
  yr(i1) = Mid(b, (i1 + 1) * 4 - 3, 4)

     Next
     End If
  
  Dim xi(): Dim yi(): Dim zi()
  n = Len(a) \ 4 '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")
     Print xr(p), xr(q)
      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
     s2 = nifft(dxcx1(Trim(s)), dxcx1(Trim(s1)), Trim(sb1))
     
      Text2 = s2 & "有" & Len(s2) & "位，用时" & Timer - ts & "秒"
  End Sub

  Private Sub Command2_Click()
  Text1 = ""
  Text2 = ""
  Text3 = ""
  Form1.Cls
  End Sub

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 nifft(sa As String, sb As String, sb1 As String) As String
  
  Dim xi(): Dim yi(): Dim zi()
  Dim xr(), yr()
  Dim zr() As String
  
  s2 = Split(sa, "/")
  s3 = Split(sb, "/")
      J = UBound(s2)
      n = J
     For k = 1 To J
         n1 = n1 + 1
          ReDim Preserve xr(0 To n1 - 1)
          ReDim Preserve yr(0 To n1 - 1)
         xr(n1 - 1) = s2(n1): yr(n1 - 1) = s3(n1)
         xr(n1 - 1) = Format(Val(xr(n1 - 1)), "0.000000"): yr(n1 - 1) = Format(Val(yr(n1 - 1)), "0.000000")

       Next
     

  ReDim zr(0 To J - 1)

  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 = -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 > 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) - yi(I)) / n
      zr(I) = Format(Val(zr(I) + 0.5), "0.000000")
     If InStr(zr(I), ".") = 0 Then
     s1 = zr(I)
     Else
     s1 = Left(zr(I), InStr(zr(I), ".") - 1)
      End If
      s = "/" & s1 & s
      zr(I) = s1
      Next
      For i1 = 1 To Val(J - 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 = MPC1(Trim(zr(i1)), Trim(s6))
      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
     
  nifft = qdqd0(Trim(s9))

  End Function

  Private Function dxcx0(sa As String, sb As String) As String

  Dim x_() As String, a As String
    a = Trim(sa)
    ReDim x_(1 To sb)
    For i1 = 1 To sb
    x_(i1) = Mid(a, (sb - i1 + 1) * 4 - 3, 4)
    If Len(x_(i1)) < 4 Then
    x_(i1) = String(4 - Len(x_(i1)), "0") & x_(i1)
    Else
    x_(i1) = x_(i1)
    End If
   
      Next
    Dim n As Integer, I As Long, J As Long, mn As Long, lh As Long, t As Double, 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
    s = s & x_(J + 1)
    Next
    dxcx0 = x_(1) & x_(1 + sb / 2) & s
   
   

  End Function

  Private Function dxcx1(sa As String) As String

  Dim x_() As Double, a As String
    a = Trim(sa)
     

  s2 = Split(sa, "/")
  s3 = Split(sb, "/")
      J = UBound(s2)
      sb = J
     
       ReDim x_(1 To sb)
     For k = 1 To J
         n1 = n1 + 1
          ReDim Preserve x_(1 To n1)
        
         x_(n1) = Format(Val(s2(n1)), "0.000000")
       Next
    Dim n As Integer, I As Long, mn As Long, lh As Long, t As Double
    '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
x_(J + 1) = Format(Val(x_(J + 1)), "0.000000")
    s = s & "/" & x_(J + 1)
    Next
    x_(1) = Format(Val(x_(1)), "0.000000"): x_(1 + sb / 2) = Format(Val(x_(1 + sb / 2)), "0.000000")
    dxcx1 = "/" & x_(1) & "/" & x_(1 + sb / 2) & s
   
    End Function

Public Function MPC1(D1 As String, D2 As String) As String 'jiafa
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): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
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 = 0 '进位清0
B1(J) = Mid$(D4, J, 1) '每位数
For I = x To 1 Step -1  'D1
   a(I) = Mid$(d3, I, 1) '每位数
   C1(I) = a(I) + B1(I) + JW '计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  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
  
End Function

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可能会用到如下可调用程序（谁知道加上这么多辅助程序是否会影响速度，当然有的可能就用不上，有的是不必要，尽量不用，移动小数点是必须的）
发出来，明天再弄吧，做个50位一组的验证一下，各位老师晚安！发一下程序：
'移动小数点的程序
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

'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 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

'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

'减法程序（必须大的减去小的不输出负值）：（这个收集进来这回就全了，可以组装起来成为快速程序了）
 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): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
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, 1) ';每位数
For I = x To 1 Step -1  ';D1
   a(I) = Mid(d3, I, 1) ';每位数
   C1(I) = 10 + a(I) - B1(I) - 1 + JW ';计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  Next
  Next
  For r = 1 To x
  MPC = MPC & E1(r)
  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

'比较大小的程序
Public Function MBJC(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2021-3-22 09:05编辑过]

优化了一下程序，3位一组的，把3位当一位数计算，去掉了快速逆变换可调用程序，直接把逆变换加再主程序中，居然速度提高了。下面发一下这个代码：

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

Private Sub Command1_Click()
  Dim xr() As Double, a As String
  a = Trim(Text1)
  b = Trim(Text3)
  ts = Timer
  
  x = Len(a) \ 3: Y = Len(b) \ 3
  a = String(Val(x * 3 + 3 - Len(a)), "0") & a
  b = String(Val(Y * 3 + 3 - 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
  Print sb
  a = String(Val(sb) * 3 - Len(a), "0") & a
  b = String(Val(sb) * 3 - Len(b), "0") & b
  Print a
  
  
  
   ReDim x_(1 To sb): ReDim y_(1 To sb)
    For i1 = 1 To sb
    x_(i1) = Mid(a, (sb - i1 + 1) * 3 - 2, 3): y_(i1) = Mid(b, (sb - i1 + 1) * 3 - 2, 3)
    If Len(x_(i1)) < 3 Then
    x_(i1) = String(3 - Len(x_(i1)), "0") & x_(i1)
    ElseIf Len(y_(i1)) < 3 Then
    y_(i1) = String(3 - Len(y_(i1)), "0") & y_(i1)
    Else
    x_(i1) = x_(i1): y_(i1) = y_(i1)
    End If
   
      Next
    Dim n As Integer, I As Long, J As Long, mn As Long, lh As Long, t As Double, 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
    s = s & x_(J + 1)
    s1 = s1 & y_(J + 1)
    Next
    a = x_(1) & x_(1 + sb / 2) & s
    b = y_(1) & y_(1 + sb / 2) & s1
  
  ReDim xr(0 To (Len(a) - 3) \ 3): ReDim yr(0 To (Len(b) - 3) \ 3): ReDim zr(0 To (Len(b) - 3) \ 3)
  If Len(a) = 3 Then
  xr(0) = a: yr(0) = b
  Else
  For i1 = 0 To (Len(a) - 3) \ 3
  xr(i1) = Mid(a, (i1 + 1) * 3 - 2, 3)
  yr(i1) = Mid(b, (i1 + 1) * 3 - 2, 3)

     Next
     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) \ 3: 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) = "000"
      ElseIf Len(zr(i1)) < 3 Then
      zr(i1) = String(3 - 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)) - 3))
      If Len(s6) < 3 Then
      s6 = String(3 - Len(s6), "0") & s6
      Else
      s6 = s6
      End If
      s8 = Right(zr(i1), 3)
      ElseIf Val(zr(i1)) >= 0 Then
      s7 = MPC1(Trim(zr(i1)), Trim(s6))
      s10 = Right(s7, 3)
      s11 = s10 & s11
      If Len(s7) < 3 Then
      s7 = String(3 - Len(s7), "0") & s7
      ElseIf Len(s7) = 3 Then
      s6 = "000"
      Else
      s7 = s7
      s6 = Val(Left(s7, Len(s7) - 3))
      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))
      Text2 = s9 & "有" & Len(s9) & "位，用时" & Timer - ts & "秒"
  End Sub

  Private Sub Command2_Click()
  Text1 = ""
  Text2 = ""
  Text3 = ""
  Form1.Cls
  End Sub

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 dxcx0(sa As String, sb As String) As String

  Dim x_() As Double, a As String
    a = Trim(sa)
    ReDim x_(1 To sb)
    For i1 = 1 To sb
    x_(i1) = Mid(a, sb - i1 + 1, 1)
      Next
    Dim n As Integer, I As Long, J As Long, mn As Long, lh As Long, t As Double, 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
    s = s & x_(J + 1)
    Next
    dxcx0 = x_(1) & x_(1 + sb / 2) & s
   

  End Function

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

  Private Function dxcx1(sa As String) As String

  Dim x_() As Double, a As String
    a = Trim(sa)
     

  s2 = Split(sa, "/")
  s3 = Split(sb, "/")
      J = UBound(s2)
      sb = J
     
       ReDim x_(1 To sb)
     For k = 1 To J
         n1 = n1 + 1
          ReDim Preserve x_(1 To n1)
        
         x_(n1) = s2(n1)
       Next
    Dim n As Integer, I As Long, mn As Long, lh As Long, t As Double
    '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
    s = s & "/" & x_(J + 1)
    Next
    dxcx1 = "/" & x_(1) & "/" & x_(1 + sb / 2) & s
   
    End Function
    Public Function MPC1(D1 As String, D2 As String) As String 'jiafa
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): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
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 = 0 '进位清0
B1(J) = Mid$(D4, J, 1) '每位数
For I = x To 1 Step -1  'D1
   a(I) = Mid$(d3, I, 1) '每位数
   C1(I) = a(I) + B1(I) + JW '计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  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
  
End Function

   
   
    '移动小数点的程序
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

'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 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

'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

'减法程序（必须大的减去小的不输出负值）：（这个收集进来这回就全了，可以组装起来成为快速程序了）
 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): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
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, 1) ';每位数
For I = x To 1 Step -1  ';D1
   a(I) = Mid(d3, I, 1) ';每位数
   C1(I) = 10 + a(I) - B1(I) - 1 + JW ';计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  Next
  Next
  For r = 1 To x
  MPC = MPC & E1(r)
  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

'比较大小的程序
Public Function MBJC(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2021-3-29 14:28编辑过]

111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111*111111111=12345678999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999987654321有221位，用时6.640625E-02秒（这是4位一组的程序结果，又快了一点点）

把4位一组的快速程序代码发一下，代码如下：

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

Private Sub Command1_Click()
  Dim xr() As Double, a As String
  a = Trim(Text1)
  b = Trim(Text3)
  ts = Timer
  
  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
  Print sb
  a = String(Val(sb) * 4 - Len(a), "0") & a
  b = String(Val(sb) * 4 - Len(b), "0") & b
  Print a
  
  
  
   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
    Dim n As Integer, I As Long, J As Long, mn As Long, lh As Long, t As Double, 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
    s = s & x_(J + 1)
    s1 = s1 & y_(J + 1)
    Next
    a = x_(1) & x_(1 + sb / 2) & s
    b = y_(1) & y_(1 + sb / 2) & s1
  
  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
  For i1 = 0 To (Len(a) - 4) \ 4
  xr(i1) = Mid(a, (i1 + 1) * 4 - 3, 4)
  yr(i1) = Mid(b, (i1 + 1) * 4 - 3, 4)

     Next
     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 = MPC1(Trim(zr(i1)), Trim(s6))
      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))
      Text2 = s9 & "有" & Len(s9) & "位，用时" & Timer - ts & "秒"
  End Sub

  Private Sub Command2_Click()
  Text1 = ""
  Text2 = ""
  Text3 = ""
  Form1.Cls
  End Sub

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 dxcx0(sa As String, sb As String) As String

  Dim x_() As Double, a As String
    a = Trim(sa)
    ReDim x_(1 To sb)
    For i1 = 1 To sb
    x_(i1) = Mid(a, sb - i1 + 1, 1)
      Next
    Dim n As Integer, I As Long, J As Long, mn As Long, lh As Long, t As Double, 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
    s = s & x_(J + 1)
    Next
    dxcx0 = x_(1) & x_(1 + sb / 2) & s
   

  End Function

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

  Private Function dxcx1(sa As String) As String

  Dim x_() As Double, a As String
    a = Trim(sa)
     

  s2 = Split(sa, "/")
  s3 = Split(sb, "/")
      J = UBound(s2)
      sb = J
     
       ReDim x_(1 To sb)
     For k = 1 To J
         n1 = n1 + 1
          ReDim Preserve x_(1 To n1)
        
         x_(n1) = s2(n1)
       Next
    Dim n As Integer, I As Long, mn As Long, lh As Long, t As Double
    '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
    s = s & "/" & x_(J + 1)
    Next
    dxcx1 = "/" & x_(1) & "/" & x_(1 + sb / 2) & s
   
    End Function
    Public Function MPC1(D1 As String, D2 As String) As String 'jiafa
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): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
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 = 0 '进位清0
B1(J) = Mid$(D4, J, 1) '每位数
For I = x To 1 Step -1  'D1
   a(I) = Mid$(d3, I, 1) '每位数
   C1(I) = a(I) + B1(I) + JW '计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  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
  
End Function

   
   
    '移动小数点的程序
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

'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 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

'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

'减法程序（必须大的减去小的不输出负值）：（这个收集进来这回就全了，可以组装起来成为快速程序了）
 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): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
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, 1) ';每位数
For I = x To 1 Step -1  ';D1
   a(I) = Mid(d3, I, 1) ';每位数
   C1(I) = 10 + a(I) - B1(I) - 1 + JW ';计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  Next
  Next
  For r = 1 To x
  MPC = MPC & E1(r)
  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

'比较大小的程序
Public Function MBJC(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2021-3-29 14:16编辑过]

4999999999999999999999999有25位，用时2.197266E-02秒（这个是我的程序计算的60度的余弦值点后25位，可以用于8位一组的利用快速傅里叶变换的乘法程序，50位的就慢些（可用于16位一组的快速乘法），大约0.15秒，150位的（可用于48位一组的快速乘法）更慢大约4.5秒，要想提高计算正弦余弦的速度看来必须改变算法，可以用到秦九韶算法，用到秦九韶多项式，就是把泰勒级数展开式写成秦九韶多项式，就是有多层括号的多项式，由内向外逐层计算，迭代几次就可以达到精度，希望老师指点！欢迎指导，欢迎提供更好的方法。）

50000000000000000000000000000000000000000000000001有50位，用时0.1572266秒

500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000有150位，用时4.741211秒

有空试试8位一组的就是把8位当作1位数，看看能不能提高速度（因为要多次用到正弦余弦值，前面的速度还是不够快，得不偿失的话，速度不一定能快），有空再试试吧。
各位老师晚安！！

秦九韶算法：把一个一元n次多项式改写成秦九韶多项式，求多项式的值时，首先计算最内层括号内一次多项式的值，然后由内向外逐层计算一次多项式的值，这样，求n次多项式f(x)的值就转化为求n个一次多项式的值。上述方法称为秦九韶算法。直到今天，这种算法仍是多项式求值比较先进的算法。

可见老祖宗留下的方法还是好的，珍贵的有用的，在当时是先进的！

反复提取公因子后，原函数可以写成秦九韶多项式，可以用来加快计算速度。

对于一个n次的多项式函数，用常规方法（用重复乘法计算幂，再把各项相加）计算出结果最多需要n次加法和[n*(n+1)]/2次乘法。若用x迭代的方法计算幂则需要n次加法和2n+1次乘法。如果计算中的数值数据是以字节方式储存的，那么常规方法约需要x占用的字节的2n倍空间。

而使用秦九韶算法时，至多只需作n次加法和n次乘法，最多需要x占用的字节的n倍空间。

该算法看似简单，其最大的意义在于将求n次多项式的值转化为求n个一次多项式的值。在人工计算时，利用秦九韶算法和其中的系数表可以大幅简化运算；对于计算机程序算法而言，加法比乘法的计算效率要高很多，因此该算法仍有极大的意义，用于减少CPU运算时间。

该算法看似简单，其最大的意义在于将求n次多项式的值转化为求n个一次多项式的值。在人工计算时，利用秦九韶算法和其中的系数表可以大幅简化运算；对于计算机程序算法而言，加法比乘法的计算效率要高很多，因此该算法仍有极大的意义，对于计算机来说，做一次乘法运算所用的时间比作一次加法运算要长得多，所以此算法极大地缩短了CPU运算时间。