c++ - Kahan求和算法用GCC编译时计算误差大

Question

我用的是Kahan求和算法:

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;
}

如果用MSVS编译可以正常运行，但是用GCC的话会出现很大的计算错误。

问题出在哪里？

Answer 1

我想，这是积极的编译器优化的结果。所以 GCC 可以减少来自的表达式:

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

到

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

因为这个变换在数学上是正确的，但是这个优化杀死了卡汉算法。

为了避免这个问题，您可以使用“-O1”GCC 编译器选项来编译代码。它将是这样的:

#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