double 소수점 계산 관련 문의

hlowd

안녕하세요.

qt 5.12.x 버전 사용중에 있고 소수점 계산 중에 궁금한 부분이 있어 문의드립니다.

double a = 0.00025;
double sum = 0.0;

for(int i = 0; i < 100000; i++)
{
sum += a;
}

이렇게 계산을 할 경우 0.00025씩 증가하여야 하는데 값을 출력해보면 0.827998 이런식으로 깨져서 표시됩니다.

아래와 같이 ceil이나 round 함수를 사용해도 0.00025씩 동일하게 증가하여 표시되게 하는 좋은 방법이 없을까요?

ceil(a * 1000000) / 1000000;
round(a * 1000000) / 1000000;

ps) window 10, ubuntu 20.04 버전 동일합니다.

Paul Colby

Hi @hlowd, what you are seeing here an accumulative floating point error that comes from the fact that floating point numbers cannot represent every possible number exactly.

The solution is to use a fixed-point approach instead of floating - ie using integers, but where the integers represent a decimal fraction instead of whole units.

Easier explained with an example:

This doesn't work, as you've shown already:

#include <iostream>

int main() {
  double a = 0.00025;
  double sum = 0.0;
  for(int i = 0; i < 100000; i++) {
    sum += a;
    std::cout << sum << std::endl;
  }
}

Outputs:

But this version:

#include <iomanip>
#include <iostream>

int main() {   
  uint64_t a = 25; 
  uint64_t sum = 0;
  for(int i = 0; i < 100000; i++) {
    sum += a;
    std::cout << (sum/100000) << '.' << std::setfill('0') << std::setw(5) << (sum%10000) << std::endl;
  }
}

Outputs what you want (if I understand you correctly):

Of course, the std::* stuff can be replaced with Qt-specific equivalents, but the problem is not specific to Qt (indeed, not specific to C++ either, but modern FPUs).

Cheers.

hlowd

@Paul-Colby
안녕하세요.

우선 바쁘신 와중에 답변주셔서 감사합니다.

답변해주신 부분에 대해 추가적으로 궁금한 내용이 있습니다.

더해지는 값을 double 형 변수에 저장하는 것은 어려울까요?

Paul Colby

@hlowd said in double 소수점 계산 관련 문의:

더해지는 값을 double 형 변수에 저장하는 것은 어려울까요?

Sure, you can convert the results to floating point numbers at any stage - eg inside the loop, or a the very end. For example:

#include <iomanip>
#include <iostream>

int main() {   
  uint64_t a = 25; 
  uint64_t sum = 0;
  for(int i = 0; i < 100000; i++) {
    sum += a;
    const double sumAsFloat = sum/100000.0;
    std::cout << (sum/100000) << '.' << std::setfill('0') << std::setw(5) << (sum%100000)
              << std::setprecision(10) << "  \t[" << sumAsFloat << ']' << std::endl;
  }
}

Outputs:

0.00025         [0.00025]
0.00050         [0.0005]
0.00075         [0.00075]
0.00100         [0.001]
0.00125         [0.00125]
24.99900        [24.999]
24.99925        [24.99925]
24.99950        [24.9995]
24.99975        [24.99975]
25.00000        [25]

Cheers.

PS: In printing both the uint64_t and double versions side-by-side, I realised there's was a small error in my previous reply, where the (sum%10000) should have had another 0, ie (sum%100000). I fixed that in the code in this reply :)