“无限”位四则运算_delphi教程

由于标准的数字变量类型取值有限，如果需要进行运算的数字超过了范围，用标准的数字变量类型就显得无能为力了！下面的四个函数利用Delphi中的字符串对象实现了大数运算。

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}

一时消遣娱乐之作~~~