How to compare __m128 types?

The answer to this question also depends on whether you want actual inequality where you'd use something along the lines of what @PaulR has shown:

bool fneq128_a (__m128 const& a, __m128 const& b)
{
    // returns true if at least one element in a is not equal to 
    // the corresponding element in b
    return _mm_movemask_ps(_mm_cmpeq_ps(a, b)) != 0xF;
}

or whether you want to use some epsilon to specify that elements are still considered to be "equal" if they do not differ more than the threshold:

bool fneq128_b (__m128 const& a, __m128 const& b, float epsilon = 1.e-8f)
{
    // epsilon vector
    auto eps = _mm_set1_ps(epsilon);
    // absolute of difference of a and b
    auto abd = _mm_andnot_ps(_mm_set1_ps(-0.0f), _mm_sub_ps(a, b));
    // compare abd to eps
    // returns true if one of the elements in abd is not less than 
    // epsilon
    return _mm_movemask_ps(_mm_cmplt_ps(abd, eps)) != 0xF;
}

Example:

auto a = _mm_set_ps(0.0, 0.0, 0.0, 0.0);
auto b = _mm_set_ps(0.0, 0.0, 0.0, 1.e-15);
std::cout << fneq128_a(a, b) << ' ' << fneq128_b(a, b) << "\n";

Prints:

 1 0

You should probably use _mm_cmpneq_ps. However the interpretation of comparisons is a little different with SIMD code than with scalar code. Do you want to test for any corresponding element not being equal ? Or all corresponding elements not being equal ?

To test the results of the 4 comparisons from _mm_cmpneq_ps you can use _mm_movemask_epi8.

Note that comparing floating point values for equality or inequality is usually a bad idea, except in very specific cases.

__m128i vcmp = (__m128i)_mm_cmpneq_ps(a, b); // compare a, b for inequality
uint16_t test = _mm_movemask_epi8(vcmp); // extract results of comparison
if (test == 0xffff)
    // *all* elements not equal
else if (test != 0)
    // *some* elements not equal
else
    // no elements not equal, i.e. all elements equal

For documentation you want these two volumes from Intel:

Intel® 64 and IA-32 Architectures Software Developer’s Manual Volume 2A: Instruction Set Reference, A-M

Intel® 64 and IA-32 Architectures Software Developer’s Manual Volume 2B: Instruction Set Reference, N-Z