SSE rms calculation

I want to calculation the rms with the Intel sse intrinsic. Like this:

float rms( float *a, float *b , int l)
{
    int n=0;
    float r=0.0;
    for(int i=0;i<l;i++)
    {
        if(finitef(a[i]) && finitef(b[i]))
        {
            n++;
            tmp = a[i] - b[i];
            r += tmp*tmp;
        }
    }
    r /= n;
    return r;
}

But how to check which elements are NaN? And how to count n?

You can test a value for NaN by comparing the value with itself. x == x will return false if x is a NaN. So for a SSE vector of 4 x float values, vx:

    vmask = _mm_cmpeq_ps(vx, vx);

will give you a mask vector with all 0s for NaN elements in vx and all 1s for non-NaN elements. You can use the mask to zero out the NaNs. You can also use the mask to count the number of valid data points by treating it as a vector of 32 bit ints and accumulating.

Here is a working, tested example - note that it assumes n is a multiple of 4, that a, b are not 16 byte aligned, and note also that it requires SSE4.

float rms(const float *a, const float *b , int n)
{
    int count;
    float sum;
    __m128i vcount = _mm_set1_epi32(0);
    __m128 vsum = _mm_set1_ps(0.0f);
    assert((n & 3) == 0);
    for (int i = 0; i < n; i += 4)
    {
        __m128 va = _mm_loadu_ps(&a[i]);
        __m128 vb = _mm_loadu_ps(&b[i]);
        __m128 vmaska = _mm_cmpeq_ps(va, va);
        __m128 vmaskb = _mm_cmpeq_ps(vb, vb);
        __m128 vmask = _mm_and_ps(vmaska, vmaskb);
        __m128 vtmp = _mm_sub_ps(va, vb);
        vtmp = _mm_and_ps(vtmp, vmask);
        vtmp = _mm_mul_ps(vtmp, vtmp);
        vsum = _mm_add_ps(vsum, vtmp);
        vcount = _mm_sub_epi32(vcount, (__m128i)vmask);
    }
    vsum = _mm_hadd_ps(vsum, vsum);
    vsum = _mm_hadd_ps(vsum, vsum);
    _mm_store_ss(&sum, vsum);
    vcount = _mm_hadd_epi32(vcount, vcount);
    vcount = _mm_hadd_epi32(vcount, vcount);
    count = _mm_extract_epi32(vcount, 0);
    return count > 0 ? sum / (float)count : 0.0f;
}