Kahan summation algorithm has big computing error when it is compiled by GCC

Question

I use Kahan summation algorithm:

inline void KahanSum(float value, float & sum, float & correction)
{
    float term = value - correction;
    fl         


        

Answer 1

I suppouse, that it's a result of aggresive compiler optimization. So GCC can reduce the expression from:

    float term = value - correction;
    float temp = sum + term;
    correction = (temp - sum) - term;
    sum = temp;

to

    float term = value - correction;
    correction = 0;
    sum += term;

because this transformation is mathematically correct, but this optimization kills Kahan algorithm.

In order to avoid this problem you can use "-O1" GCC compiler options to compile the code. It will be something like this:

#if defined(__GNUC__)
#  pragma GCC push_options
#  pragma GCC optimize ("O1")
#endif 
inline void KahanSum(float value, float & sum, float & correction)
{
    float term = value - correction;
    float temp = sum + term;
    correction = (temp - sum) - term;
    sum = temp; 
}

float KahanSum(const float * ptr, size_t size)
{
    float sum = 0, correction = 0;
    for(size_t i = 0; i < size; ++i)
        KahanSum(ptr[i], sum, correction);
    return sum;
}
#if defined(__GNUC__)
#  pragma GCC pop_options
#endif