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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