实际上我们已经远离了轨道，在一个编程论坛讨论数学问题，有点偏离主题。
我其实对vb6一知半解。我一般是编写vfp程序获得数据。把笔算开平方发在了vfp编程论坛板块，20分的悬赏，可是快到期了，无一人问津，只好撤掉悬赏。

我们是不是可以先把多位数拆分，比如1234567890，表示成a=0，b=9，c=8，d=7，....，从个位倒着用字母表示，也可以统一用x1=0，x2=9，x3=8，....；用y1，y2，y3，....；来表示另一个整数，然后，就是它们分别相乘了，获得xi*yj个数据，用其角码表是位数（所以角码从0开始），这样角码之和就是位数（另角码之和加1确定），然后计算所有的角码之和相同的和，这样就完成笔算多位数相乘的汇总结果，最后把临近位再做处理（之和大于9的部分），最后输出一个处理好的数字文本（把各个位上的数字做倒排列而成）。
    只是一个初步设想，能不能实现是个问题。

主要涉及算法，把算法搞清楚，再编程不难

这个问题从发出悬赏就没有人问津，我一个把多位数拆分成多个单元的想法也没人实现，所以，只能自己抽空解决了。自己买坑，自己跳。

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大数快速四则计算,（除法很耗时，最好转化为乘法再计算）
ll_Add     ： 加 +
ll_Sub     ： 减 -
ll_Mult    ： 乘 *
ll_Div     ： 除 /
ll_Mod     ： 模 %/Mod()
ll_Less    ： 小于 >
ll_IntSqrt ： 平方根 SQRT()
ll_power   ： 乘幂 ^/**
ll_pl      ： 排列
ll_zh      ： 组合


调用方法
? ll_mult("4", "4")  && 4x4
endtext

?
? "1000000位长度的 4 + 1000000位长度的 7 的运算结果："
? "================================================"
m.a = Replicate("1244", 200)
m.b = Replicate("7457", 2)
m.sc = Seconds()
FOR i=1 TO 100
m.c = ll_add(m.a, m.b)
next
? "耗时 (秒)     ：", Seconds() - m.sc
? "结果长度      ：", Len(m.c)
? "左20位运算结果：", Left(m.c, 20)
?m.c
? "================================================"

*!* Function ll_add adds two integers, represented by strings m.s1 and m.s2
Function ll_add
    Lparameter m.s1, m.s2

    If Left(m.s1,1)="-"
        Return ll_sub(m.s2, Substr(m.s1,2))
    Endif

    If Left(m.s2,1)="-"
        Return ll_sub(m.s1, Substr(m.s2,2))
    Endif

    *!* Uncomment next rows if you want some additional data checking,
    *!* but this may dramaticaly reduce performance on large strings
    *!* local m.ln1, m.ln2, m.ln3, m.s3
    *!* if len(chrtran(m.s1, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s1"
    *!* return ""
    *!* endif

    *!* if len(chrtran(m.s2, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s2"
    *!* return ""
    *!* endif

    Local m.ln1, m.ln2, m.ln3, m.s3
    m.ln1=Len(m.s1)
    m.ln2=Len(m.s2)
    m.ln3 = Max(m.ln1, m.ln2)+1
    m.s1 = Padl(m.s1, m.ln3, "0")
    m.s2 = Padl(m.s2, m.ln3, "0")

    m.s3 = Repl("0", m.ln3)

    Local m.hhnd, m.ptr, m.st2, m.rez

    If !Pemstatus(_Screen,"ll_add",5) Or _Screen.ll_add=0
        Declare Integer HeapCreate In Win32Api Integer, Integer, Integer
        Declare Integer HeapAlloc In Win32Api Integer, Integer, Integer
        Declare RtlMoveMemory In Win32API Integer, String, Integer Cnt

        m.st2 = ;
            chr(0x55)+Chr(0x89)+Chr(0xE5)+Chr(0x57)+Chr(0x56)+Chr(0x50)+Chr(0x53)+Chr(0x51)+ ;
            chr(0x52)+Chr(0x8B)+Chr(0x75)+Chr(0x08)+Chr(0x8B)+Chr(0x5D)+Chr(0x0C)+Chr(0x8B)+ ;
            chr(0x4D)+Chr(0x10)+Chr(0x8B)+Chr(0x7D)+Chr(0x14)+Chr(0x8A)+Chr(0x04)+Chr(0x0E)+ ;
            chr(0x02)+Chr(0x04)+Chr(0x0B)+Chr(0x02)+Chr(0x04)+Chr(0x0F)+Chr(0x2C)+Chr(0x60)+ ;
            chr(0x3C)+Chr(0x39)+Chr(0x7E)+Chr(0x06)+Chr(0x2C)+Chr(0x0A)+Chr(0xFE)+Chr(0x44)+ ;
            chr(0x0F)+Chr(0xFF)+Chr(0x88)+Chr(0x04)+Chr(0x0F)+Chr(0x49)+Chr(0x75)+Chr(0xE5)+ ;
            chr(0x5A)+Chr(0x59)+Chr(0x5B)+Chr(0x58)+Chr(0x5E)+Chr(0x5F)+Chr(0x89)+Chr(0xEC)+ ;
            chr(0x5D)+Chr(0xC2)+Chr(0x10)+Chr(0x00)

        m.hhnd=HeapCreate(0x40000,1024,1024)
        m.ptr=HeapAlloc(m.hhnd,0,Len(m.st2)+16)
        RtlMoveMemory(m.ptr,m.st2,Len(m.st2))
        _Screen.AddProperty("ll_add",m.ptr)

    Endif

    Declare CallWindowProc In Win32API Integer, String, String, Integer, String @

    CallWindowProc(_Screen.ll_add, m.s1, m.s2, m.ln3-1, @m.s3)

    Return Chrtran(Ltrim(Chrtran(m.s3, "0", " ")), " ", "0")


    *!* Function ll_sub substracts integer, represented by strings m.s2 from the
    *!* integer, epresented by m.s1
Function ll_sub
    Lparameter m.s1, m.s2

    If Left(m.s2,1)="-"
        Return ll_add(m.s1, Substr(m.s2,2))
    Endif
    If Left(m.s1,1)="-"
        Return "-"+ll_add(Substr(m.s1,2), m.s2)
    Endif


    *!* Uncomment next rows if you want some additional data checking,
    *!* but this may dramaticaly reduce performance on large strings
    *!* local m.ln1, m.ln2, m.ln3, m.s3
    *!* if len(chrtran(m.s1, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s1"
    *!* return ""
    *!* endif

    *!* if len(chrtran(m.s2, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s2"
    *!* return ""
    *!* endif

    Local m.ln1, m.ln2, m.ln3, m.s3
    m.ln1=Len(m.s1)
    m.ln2=Len(m.s2)
    m.ln3 = Max(m.ln1, m.ln2)+1
    m.s1 = Padl(m.s1, m.ln3, "0")
    m.s2 = Padl(m.s2, m.ln3, "0")

    If m.s1 < m.s2
        Return "-"+ll_sub(m.s2, m.s1)
    Endif

    m.s3 = Repl("0", m.ln3)


    Local m.hhnd, m.ptr, m.st2, m.rez

    If !Pemstatus(_Screen,"ll_sub",5) Or _Screen.ll_sub=0
        Declare Integer HeapCreate In Win32Api Integer, Integer, Integer
        Declare Integer HeapAlloc In Win32Api Integer, Integer, Integer
        Declare RtlMoveMemory In Win32API Integer, String, Integer Cnt

        m.st2 = ;
            chr(0x55)+Chr(0x89)+Chr(0xE5)+Chr(0x57)+Chr(0x56)+Chr(0x50)+Chr(0x53)+Chr(0x51)+ ;
            chr(0x52)+Chr(0x8B)+Chr(0x75)+Chr(0x08)+Chr(0x8B)+Chr(0x5D)+Chr(0x0C)+Chr(0x8B)+ ;
            chr(0x4D)+Chr(0x10)+Chr(0x8B)+Chr(0x7D)+Chr(0x14)+Chr(0xBA)+Chr(0x00)+Chr(0x00)+ ;
            chr(0x00)+Chr(0x00)+Chr(0x8A)+Chr(0x04)+Chr(0x0E)+Chr(0x00)+Chr(0x14)+Chr(0x0B)+ ;
            chr(0x2A)+Chr(0x04)+Chr(0x0B)+Chr(0x7D)+Chr(0x06)+Chr(0xB2)+Chr(0x01)+Chr(0x04)+ ;
            chr(0x0A)+Chr(0xEB)+Chr(0x02)+Chr(0xB2)+Chr(0x00)+Chr(0x04)+Chr(0x30)+Chr(0x88)+ ;
            chr(0x04)+Chr(0x0F)+Chr(0x49)+Chr(0x75)+Chr(0xE5)+Chr(0x5A)+Chr(0x59)+Chr(0x5B)+ ;
            chr(0x58)+Chr(0x5E)+Chr(0x5F)+Chr(0x89)+Chr(0xEC)+Chr(0x5D)+Chr(0xC2)+Chr(0x10)+ ;
            chr(0x00)

        m.hhnd=HeapCreate(0x40000,1024,1024)
        m.ptr=HeapAlloc(m.hhnd,0,Len(m.st2)+16)
        RtlMoveMemory(m.ptr,m.st2,Len(m.st2))
        _Screen.AddProperty("ll_sub",m.ptr)

    Endif

    Declare CallWindowProc In Win32API Integer, String, String, Integer, String @

    CallWindowProc(_Screen.ll_sub, m.s1, m.s2, m.ln3-1, @m.s3)
    Return Chrtran(Ltrim(Chrtran(m.s3, "0", " ")), " ", "0")


    *!* Function ll_mult multiplies two integers, represented by strings m.s1 and m.s2
Function ll_mult
    Lparameter m.s1, m.s2

    Do Case
        Case Left(m.s1,1) = "-" And Left(m.s2,1) <> "-"
            Return "-" + ll_mult(Substr(m.s1,2), m.s2)
        Case Left(m.s1,1) <> "-" And Left(m.s2,1) = "-"
            Return "-" + ll_mult(m.s1, Substr(m.s2,2))
        Case Left(m.s1,1) = "-" And Left(m.s2,1) = "-"
            Return ll_mult(Substr(m.s1,2), Substr(m.s2,2))
    Endcase


    *!* Uncomment next rows if you want some additional data checking,
    *!* but this may dramaticaly reduce performance on large strings
    *!* local m.ln2, m.sm, m.i
    *!* if len(chrtran(m.s1, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s1"
    *!* return ""
    *!* endif

    *!* if len(chrtran(m.s2, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s2"
    *!* return ""
    *!* endif

    Local m.ln2, m.sm, m.i
    m.ln2 = Len(m.s2)

    m.sm = "0"

    For i = 1 To m.ln2
        m.sm = ll_add(m.sm, ll_mult1(m.s1, Int(Val(Substr(m.s2, m.ln2-i+1, 1)))) + Repl("0", i-1))
    Next

    Return m.sm



    *!* Function ll_mult1 multiplies integers, represented by strings m.s1 and one digit integer m.n2
    *!* Is used by function ll_mult
Function ll_mult1
    Lparameter m.s1, m.n2

    *!* Uncomment next rows if you want some additional data checking,
    *!* but this may dramaticaly reduce performance on large strings
    *!* if len(chrtran(m.s1, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s1"
    *!* return ""
    *!* endif

    Local m.ln1, m.s3
    m.ln1 = Len(m.s1)+1
    m.s1="0"+m.s1

    m.s3 = Repl("0", m.ln1)


    Local m.hhnd, m.ptr, m.st2, m.rez

    If !Pemstatus(_Screen,"ll_mult1",5) Or _Screen.ll_mult1=0
        Declare Integer HeapCreate In Win32Api Integer, Integer, Integer
        Declare Integer HeapAlloc In Win32Api Integer, Integer, Integer
        Declare RtlMoveMemory In Win32API Integer, String, Integer Cnt

        m.st2 = ;
            chr(0x55)+Chr(0x89)+Chr(0xE5)+Chr(0x57)+Chr(0x56)+Chr(0x50)+Chr(0x53)+Chr(0x51)+ ;
            chr(0x52)+Chr(0x8B)+Chr(0x75)+Chr(0x08)+Chr(0x8B)+Chr(0x5D)+Chr(0x0C)+Chr(0x8B)+ ;
            chr(0x4D)+Chr(0x10)+Chr(0x8B)+Chr(0x7D)+Chr(0x14)+Chr(0xBA)+Chr(0x0A)+Chr(0x00)+ ;
            chr(0x00)+Chr(0x00)+Chr(0x8A)+Chr(0x04)+Chr(0x0E)+Chr(0x2C)+Chr(0x30)+Chr(0xF6)+ ;
            chr(0xE3)+Chr(0xF6)+Chr(0xF2)+Chr(0x00)+Chr(0x24)+Chr(0x0F)+Chr(0x80)+Chr(0x3C)+ ;
            chr(0x0F)+Chr(0x39)+Chr(0x7E)+Chr(0x08)+Chr(0xFE)+Chr(0x44)+Chr(0x0F)+Chr(0xFF)+ ;
            chr(0x80)+Chr(0x2C)+Chr(0x0F)+Chr(0x0A)+Chr(0x00)+Chr(0x44)+Chr(0x0F)+Chr(0xFF)+ ;
            chr(0x49)+Chr(0x75)+Chr(0xDF)+Chr(0x5A)+Chr(0x59)+Chr(0x5B)+Chr(0x58)+Chr(0x5E)+ ;
            chr(0x5F)+Chr(0x89)+Chr(0xEC)+Chr(0x5D)+Chr(0xC2)+Chr(0x10)+Chr(0x00)

        m.hhnd=HeapCreate(0x40000,1024,1024)
        m.ptr=HeapAlloc(m.hhnd,0,Len(m.st2)+16)
        RtlMoveMemory(m.ptr,m.st2,Len(m.st2))
        _Screen.AddProperty("ll_mult1",m.ptr)

    Endif

    Declare CallWindowProc In Win32API Integer, String, Integer, Integer, String @

    CallWindowProc(_Screen.ll_mult1, m.s1, m.n2, m.ln1-1, @m.s3)
    Return Chrtran(Ltrim(Chrtran(m.s3, "0", " ")), " ", "0")
  *!* Function ll_div divides integer, represented by strings m.s1 by the
    *!* integer, epresented by m.s1. (int(m.s1/m.s2)). If parameter m.md is
    *!* passed by reference, mod(m.s1,m.s2) is returned in m.md
Function ll_div
    Lparameter m.s1, m.s2, m.md

    Do Case
        Case Left(m.s1,1) = "-" And Left(m.s2,1) <> "-"
            Return "-" + ll_div(Substr(m.s1,2), m.s2)
        Case Left(m.s1,1) <> "-" And Left(m.s2,1) = "-"
            Return "-" + ll_div(m.s1, Substr(m.s2,2))
        Case Left(m.s1,1) = "-" And Left(m.s2,1) = "-"
            Return ll_div(Substr(m.s1,2), Substr(m.s2,2))
    Endcase


    *!* Uncomment next rows if you want some additional data checking,
    *!* but this may dramaticaly reduce performance on large strings
    *!* local m.ln1, m.ln2, m.sm, m.i, m.ts1, m.ts1e,
    *!* if len(chrtran(m.s1, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s1"
    *!* return ""
    *!* endif

    *!* if len(chrtran(m.s2, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s2"
    *!* return ""
    *!* endif

    If ll_less(m.s1, m.s2)
        m.md = m.s1
        Return "0"
    Endif

    Local m.ln1, m.ln2, m.sm, m.i, m.ts1, m.ts1e,
    m.ln2 = Len(m.s2)
    m.sm = ""
    m.ts1 = Left(m.s1, m.ln2)
    m.ts1e = Substr(m.s1, m.ln2 + 1)
    m.ln1 = Len(m.ts1e)
    For m.i = 1 To m.ln1 +1
         = 0
        Do While !ll_less(m.ts1, m.s2)
            m.ts1 = ll_sub(m.ts1, m.s2)
             = + 1
        Enddo
        m.sm = m.sm + Allt(Str())
        m.ts1 = m.ts1 + Left(m.ts1e, 1)
        m.ts1e = Substr(m.ts1e, 2)
    Next

    m.sm = tr0(m.sm)
    m.md = m.ts1
    Return m.sm



    *!* Function ll_mod returns mod(m.s1, m.s2)
Function ll_mod
    Lparameter m.s1, m.s2

    Do Case
        Case Left(m.s1,1) = "-" And Left(m.s2,1) <> "-"
            Return ""
        Case Left(m.s1,1) <> "-" And Left(m.s2,1) = "-"
            Return ""
        Case Left(m.s1,1) = "-" And Left(m.s2,1) = "-"
            Return ""
    Endcase

    Local m.md
    ll_div(m.s1, m.s2, @m.md)
    Return m.md


    *!* Function ll_less compare two integers, represented by m.s1 and m.s2.
    *!* .t. is returned if m.s1 < m.s2
Function ll_less
    Lparameter m.s1, m.s2
    Do Case
        Case Left(m.s1,1) = "-" And Left(m.s2,1) <> "-"
            Return .T.
        Case Left(m.s1,1) <> "-" And Left(m.s2,1) = "-"
            Return .F.
        Case Left(m.s1,1) = "-" And Left(m.s2,1) = "-"
            Return ll_less(Substr(m.s2,2), Substr(m.s1,2))
    Endcase

    m.s1 = tr0(m.s1)
    m.s2 = tr0(m.s2)

    Return Len(m.s1) < Len(m.s2) Or (Len(m.s1) = Len(m.s2) And m.s1 < m.s2)

    *!* Function tr0 is used by function ll_less
Function tr0
    Lparameter m.s1
    Do While Left(m.s1, 1) = "0" And Len(m.s1) > 1
        m.s1 = Substr(m.s1, 2)
    Enddo
    Return m.s1


    *!* Funnction ll_intsqrt returns mod(m.s1, m.s2)
Function ll_intsqrt
    Lparameter m.s1

    *!* Uncomment next rows if you want some additional data checking,
    *!* but this may dramaticaly reduce performance on large strings
    *!* if len(chrtran(m.s1, "0123456789", "")) > 0
    *!* wait window "Long_ar: error in s1"
    *!* return ""
    *!* endif

    Local m.ln, m.chet, m.tln, m.sq, m.i, m.j, m.tsq, m.tkv, m.tnkv
    m.ln = Len(m.s1)
    If m.ln <= 16
        Return Allt(Str(Int(Sqrt(Val(m.s1)))))
    Endif
    m.chet = m.ln%2
    m.tln = m.ln - 16 + m.chet
    m.sq = Allt(Str(Int(Sqrt(Val(Left(m.s1, m.ln - m.tln))))))

    For m.i = 1 To m.tln/2
        m.tkv = Left(m.s1, m.ln - m.tln + m.i*2)
        For m.j = 9 To 0 Step -1
            m.tsq = m.sq+Allt(Str(m.j))
            m.tnkv = ll_mult(m.tsq, m.tsq)
            If ll_less(m.tnkv, m.tkv) Or m.tnkv == m.tkv
                Exit
            Endif
        Next
        m.sq = m.sq + Allt(Str(m.j))
    Next
    Return m.sq



Function ll_add_dec
    Lparameter m.s1, m.s2, m.dec
    Local m.pos1, m.pos2
    m.pos1 = Rat(".", m.s1)
    If m.pos1 = 0
        m.s1 = m.s1 + Repl("0", m.dec)
    Else
        m.s1 = Left(m.s1, m.pos1 - 1) + Padr(Substr(m.s1, m.pos1 + 1), m.dec, "0")
    Endif

    m.pos2 = Rat(".", m.s2)
    If m.pos2 = 0
        m.s2 = m.s2 + Repl("0", m.dec)
    Else
        m.s2 = Left(m.s2, m.pos2 - 1) + Padr(Substr(m.s2, m.pos2 + 1), m.dec, "0")
    Endif

    m.res = ll_add(m.s1, m.s2)
    If Len(m.res) > m.dec
        Return Left(m.res, Len(m.res) - m.dec) + "." + Right(m.res, m.dec)
    Else
        Return "0."+Padl(m.res, m.dec, "0")
    Endif


Function ll_power
    Lparameter m.s1, m.s2
    m.pow = m.s1
    For I = 1 To Val(m.s2) - 1
    m.pow = ll_Mult(m.pow, m.s1)
    Endfor
    Return m.pow



Function ll_pl
    Lparameter m.s1, m.s2
    m.pow = m.s1
    For I = 1 To Val(m.s2) - 1
    m.pow = ll_Mult(m.pow, LTRIM(STR(VAL(m.s1)-i)))
    Endfor
    Return m.pow


Function ll_zh
    Lparameter m.s1, m.s2
    Return ll_div(ll_pl(m.s1,m.s2),ll_pl(m.s2,m.s2))

我用PYTHON写出来了，不足50行代码
下面是测试结果
PS D:\wpp> & C:/Programs/Python/python.exe d:/wpp/sqrt.py
对1进行开平方，我的=1.0000   电脑的=1.0000
对2进行开平方，我的=1.4142   电脑的=1.4142
对3进行开平方，我的=1.7320   电脑的=1.7321
对4进行开平方，我的=2.0000   电脑的=2.0000
对5进行开平方，我的=2.2360   电脑的=2.2361
对6进行开平方，我的=2.4494   电脑的=2.4495
对7进行开平方，我的=2.6457   电脑的=2.6458
对8进行开平方，我的=2.8284   电脑的=2.8284
对9进行开平方，我的=3.0000   电脑的=3.0000
PS D:\wpp>

精英人才还是有的。不能局限于一种算法，要横向对比。

FOR i=1 TO 10
    FOR j=1 TO 10 STEP 2
        ? ROUND(SQRT(i/j),2), ROUND(QSqrt(i/j),2)
    ENDFOR
ENDFOR

FUNCTION QSqrt(x as Single)
    LOCAL xf as Single, xi as Integer 
    xf = 0.5*x
    xi = CTOBIN(BINTOC(x,"4FS"),"4RS")
    xi = 1597463007 - BITRSHIFT(xi,1)
    x  = CTOBIN(BINTOC(xi,"4RS"),"4NS")
    RETURN 1/(x*(1.5-xf*x*x))
ENDFUNC

各位大佬都给出了，我还没有去运用。