“无限”位四则运算

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}

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