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Delphi无限位四则运算的几个函数

时间:2011/9/3 15:36:28 点击:

  核心提示:加法、乘法由zswang编写   function StrLeft(const mStr: string; mDelimiter: string): string;  begin   Result :...
加法、乘法由zswang编写

  function StrLeft(const mStr: string; mDelimiter: string): string;
  begin
    Result := Copy(mStr, 1, Pos(mDelimiter, mStr) - 1);
  end; { StrLeft }

  function StrRight(const mStr: string; mDelimiter: string): string;
  begin
    if Pos(mDelimiter, mStr) <= 0 then
      Result := ''
    else Result := Copy(mStr, Pos(mDelimiter, mStr) + Length(mDelimiter), MaxInt);
  end; { StrRight }

  function formatnum(mNumber: string):string;
  var
    m:integer;
    TemStr:string;
  begin
    Result:='';
    for m:=1 to Length(mNumber) do
    begin
      if mNumber[m]='.' then
        Result:=Result+'.'
      else
        Result:=Result+IntToStr(StrToIntDef(mNumber[m], 0));
    end;
    while Pos('0', Result) = 1 do Delete(Result, 1, 1); //排除整数前无效的0
    if Pos('.', Result )<= 0 then Result := Result + '.'; //没有有小数点补小数点
    TemStr:=StrRight(Result,'.');
    while Copy(TemStr, Length(TemStr), 1) = '0' do Delete(TemStr, Length(TemStr), 1); //排除小数后无效的0
    Result:=StrLeft(Result,'.')+'.'+TemStr;
    if Copy(Result, Length(Result), 1) = '.' then Delete(Result, Length(Result), 1); //排除无效小数点
    if Copy(Result, 1, 1)='.' then Result:='0'+Result;
    if (Result = '') then Result := '0';
  end;

  function InfiniteAdd(mNumberA, mNumberB: string): string; { 无限位数加法 }
  var
    I: Integer;
    T: Integer;
  begin
    Result := '';
    if Pos('.', mNumberA) <= 0 then mNumberA := mNumberA + '.'; //没有有小数点补小数点
    if Pos('.', mNumberB) <= 0 then mNumberB := mNumberB + '.'; //没有有小数点补小数点
    I := Max(Length(StrLeft(mNumberA, '.')), Length(StrLeft(mNumberB, '.'))); //整数部分最大长度
    mNumberA := DupeString('0', I - Length(StrLeft(mNumberA, '.'))) + mNumberA; //整数前补0
    mNumberB := DupeString('0', I - Length(StrLeft(mNumberB, '.'))) + mNumberB; //整数前补0
    T := Max(Length(StrRight(mNumberA, '.')), Length(StrRight(mNumberB, '.'))); //小数部分最大长度
    mNumberA := mNumberA + DupeString('0', T - Length(StrRight(mNumberA, '.'))); //小数后补0
    mNumberB := mNumberB + DupeString('0', T - Length(StrRight(mNumberB, '.'))); //小数后补0
    I := I + T + 1; //计算总长度//小数长度和整数长度加上小数点长度
    T := 0; //进位数初始化
    for I := I downto 1 do //从后向前扫描
      if [mNumberA[I], mNumberB[I]] <> ['.'] then begin //不是小数点时
        T := StrToIntDef(mNumberA[I], 0) + T; //累加当前数位
        T := StrToIntDef(mNumberB[I], 0) + T; //累加当前数位
        Result := IntToStr(T mod 10) + Result; //计算当前数位上的数字
        T := T div 10; //计算进位数
      end else Result := '.' + Result; //加上小数点
    if T <> 0 then Result := IntToStr(T mod 10) + Result; //处理进位数
    while Pos('0', Result) = 1 do Delete(Result, 1, 1); //排除整数前无效的0
    while Copy(Result, Length(Result), 1) = '0' do
      Delete(Result, Length(Result), 1); //排除小数后无效的0
    if Copy(Result, Length(Result), 1) = '.' then
      Delete(Result, Length(Result), 1); //排除无效小数点
    if Copy(Result, 1, 1) = '.' then Result := '0' + Result; //处理无0小数情况
    if (Result = '') then Result := '0'; //处理空字符情况
  end; { InfiniteAdd }

  function InfiniteMult(mNumberA, mNumberB: string): string; { 无限位数乘法 }

    function fMult(mNumber: string; mByte: Byte): string; { 无限位数乘法子函数 }
    var
      I: Integer;
      T: Integer;
    begin
      Result := '';
      T := 0;
      for I := Length(mNumber) downto 1 do begin //从后向前扫描
        T := StrToIntDef(mNumber[I], 0) * mByte + T; //累加当前数位
        Result := IntToStr(T mod 10) + Result; //计算当前数位上的数字
        T := T div 10; //计算进位数
      end;
      if T <> 0 then Result := IntToStr(T mod 10) + Result; //处理进位数
    end; { fMult }

  var
    I: Integer;
    vDecimal: Integer; //小数位数
    T: string;
  begin
    Result := '';
    ///////Begin 处理小数
    if Pos('.', mNumberA) <= 0 then mNumberA := mNumberA + '.'; //没有有小数点补小数点
    if Pos('.', mNumberB) <= 0 then mNumberB := mNumberB + '.'; //没有有小数点补小数点
    vDecimal := Length(StrRight(mNumberA, '.')) + Length(StrRight(mNumberB, '.')); //计算小数位数
    mNumberA := StrLeft(mNumberA, '.') + StrRight(mNumberA, '.'); //删除小数点
    mNumberB := StrLeft(mNumberB, '.') + StrRight(mNumberB, '.'); //删除小数点
    ///////End 处理小数
    T := '';
    for I := Length(mNumberB) downto 1 do begin
      Result := InfiniteAdd(Result, fMult(mNumberA, StrToIntDef(mNumberB[I], 0)) + T);
      T := T + '0';
    end;
    Insert('.', Result, Length(Result) - vDecimal + 1);
    while Pos('0', Result) = 1 do Delete(Result, 1, 1); //排除整数前无效的0
    while Copy(Result, Length(Result), 1) = '0' do
      Delete(Result, Length(Result), 1); //排除小数后无效的0
    if Copy(Result, Length(Result), 1) = '.' then
      Delete(Result, Length(Result), 1); //排除无效小数点
    if Copy(Result, 1, 1) = '.' then Result := '0' + Result; //处理无0小数情况
    if (Result = '') then Result := '0'; //处理空字符情况
  end; { InfiniteMult }

  function InfiniteSub(mNumberA, mNumberB: string): string; { 无限位数减法 }
  var
    I: Integer;
    T: Integer;
    TemNumA:String;
    minus:Boolean;
  begin
    Result := '';
    mNumberA:=formatnum(mNumberA);
    mNumberB:=formatnum(mNumberB);
    if Pos('.', mNumberA) <= 0 then mNumberA := mNumberA + '.'; //没有有小数点补小数点
    if Pos('.', mNumberB) <= 0 then mNumberB := mNumberB + '.'; //没有有小数点补小数点
    I := Max(Length(StrLeft(mNumberA, '.')), Length(StrLeft(mNumberB, '.'))); //整数部分最大长度
    mNumberA := DupeString('0', I - Length(StrLeft(mNumberA, '.'))) + mNumberA; //整数前补0
    mNumberB := DupeString('0', I - Length(StrLeft(mNumberB, '.'))) + mNumberB; //整数前补0
    T := Max(Length(StrRight(mNumberA, '.')), Length(StrRight(mNumberB, '.'))); //小数部分最大长度
    if ((Length(StrLeft(mNumberA, '.'))) > (Length(StrLeft(mNumberB, '.')))) or(((Length(StrLeft(mNumberA, '.'))) = (Length(StrLeft(mNumberB, '.'))))and(mNumberB>mNumberA))then
    begin
      TemNumA := mNumberA;
      mNumberA := mNumberB + DupeString('0', T - Length(StrRight(mNumberB, '.'))); //小数后补0
      mNumberB := TemNumA + DupeString('0', T - Length(StrRight(TemNumA, '.'))); //小数后补0
      minus:=True;
    end
    else
    begin
      mNumberA := mNumberA + DupeString('0', T - Length(StrRight(mNumberA, '.'))); //小数后补0
      mNumberB := mNumberB + DupeString('0', T - Length(StrRight(mNumberB, '.'))); //小数后补0
      minus:=False;
    end;
    I := I + T + 1; //计算总长度//小数长度和整数长度加上小数点长度
    T := 0; //进位数初始化
    for I := I downto 1 do //从后向前扫描
      if [mNumberA[I], mNumberB[I]] <> ['.'] then begin //不是小数点时
        T := StrToIntDef(mNumberB[I], 0) - T; //累加当前数位
        T := StrToIntDef(mNumberA[I], 0) - T; //累加当前数位
        if (T<0) and (I<>1) then
        begin
          T:=T+10;
          Result := IntToStr(T mod 10) + Result; //计算当前数位上的数字
          T := -1; //计算进位数
        end
        else
        begin
          Result := IntToStr(T mod 10) + Result; //计算当前数位上的数字
          T := T div 10; //计算进位数
        end;
      end else Result := '.' + Result; //加上小数点
    if T <> 0 then Result := IntToStr(T mod 10) + Result; //处理进位数
    while Pos('0', Result) = 1 do Delete(Result, 1, 1); //排除整数前无效的0
    while Copy(Result, Length(Result), 1) = '0' do
      Delete(Result, Length(Result), 1); //排除小数后无效的0
    if Copy(Result, Length(Result), 1) = '.' then
      Delete(Result, Length(Result), 1); //排除无效小数点
    if Copy(Result, 1, 1) = '.' then Result := '0' + Result; //处理无0小数情况
    if (Result = '') then Result := '0'; //处理空字符情况
    if minus then Result:='-'+Result;
  end; { InfiniteSub}

  function InfiniteDiv(mNumberA, mNumberB: string;n:integer): string; { 无限位数除法 }
  //n为有效数字个数

   function vDecimal(mNumber: string):integer;
   var m,x:integer;
   begin
     x:=0;
     if Pos('.', mNumber) <= 0 then
     begin
       for m:=Length(mNumber) downto 1 do
       begin
         if mNumber[m]='0' then x:=x+1 else Break;
       end;
       Result:=-x;
     end
     else
       Result:=Length(StrRight(mNumber, '.'));
   end;

   function formatnum2(mNumber: string):string;
   begin
     Result:=mNumber;
     if Pos('.', Result )<= 0 then Result := Result + '.';
     Result:=StrLeft(Result,'.')+StrRight(Result,'.');
     while Pos('0', Result) = 1 do
       Delete(Result, 1, 1);//排除整数前无效的0
     while Copy(Result, Length(Result), 1) = '0' do
       Delete(Result, Length(Result), 1);//排除小数后无效的0
   end;

  var
    I,J,t,v,y,Len: Integer;
    TemSub,TemNum: string;
  begin
    Result := '';
    mNumberA:=formatnum(mNumberA);
    mNumberB:=formatnum(mNumberB);
    v:=vDecimal(mNumberA)-vDecimal(mNumberB);
    mNumberA:=formatnum2(mNumberA);
    mNumberB:=formatnum2(mNumberB);
    if mNumberB='' then
      Result:='Err'
    else if mNumberA='' then
      Result:='0'
    else
    begin
    I:=0;
    if Length(mNumberA)>Length(mNumberB) then
      Len:=Length(mNumberB)
    else
      Len:=Length(mNumberA);
    if Copy(mNumberA,1,Len)>=Copy(mNumberB,1,Len) then
      J:=Length(mNumberB)
    else
      J:=Length(mNumberB)+1;
    for y:=1 to J do
    begin
      if Length(mNumberA)>=y then
        TemSub:=TemSub+mNumberA[y]
      else
      begin
        TemSub:=TemSub+'0';
        v:=v+1;
      end;
    end;
    while I<=n-1 do
    begin
      if TemSub[1]>mNumberB[1] then
        t:=StrToInt(TemSub[1]) Div StrToInt(mNumberB[1])
      else
        t:=StrToInt(TemSub[1]+TemSub[2]) Div StrToInt(mNumberB[1]);
      TemNum:=InfiniteMult(mNumberB,IntToStr(t));
      while (Length(TemNum)>Length(TemSub)) or ((Length(TemNum)=Length(TemSub))and(TemNum>TemSub)) do
      begin
        t:=t-1;
        TemNum:=InfiniteMult(mNumberB,IntToStr(t));
      end;
      Result:=Result+IntToStr(t);
      I:=I+1;
      TemSub:=InfiniteSub(TemSub,TemNum);
      if (TemSub='0') and (Length(mNumberA)<J) then
      begin
        v:=v+1;
        Break;
      end;
      if TemSub='0' then TemSub:='';
      J:=J+1;
      if Length(mNumberA)>=J then
      begin
        TemSub:=TemSub+mNumberA[J];
      end
      else
      begin
        TemSub:=TemSub+'0';
        v:=v+1;
      end;
    end;
    if Length(mNumberA)>=J then
      v:=v-(Length(mNumberA)-J)-1
    else
      v:=v-1;
    while Copy(Result, Length(Result), 1) = '0' do
    begin
      v:=v-1;
      Delete(Result, Length(Result), 1);
    end;
    if v>Length(Result) then
      Result:='.'+DupeString('0',v-Length(Result)) + Result
    else if v>0 then
      Insert('.', Result, Length(Result) - v +1); //插入小数点
    if v<0 then Result:=Result+DupeString('0',0-v);
    if Copy(Result, 1, 1)='.' then Result:='0'+Result; //小数前面补0
    end;
  end; { InfiniteDiv}

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