Part 2: SSE Intrinsics

The intrinsics for SSE (specifically SSE2) are provided in the header file emmintrin.h, which your compiler will automatically provide if it supports compiling code with SSE2. If your compiler supports SSE2, then the macro __SSE2__ will be set, meaning that you can include this header file using;

#ifdef __SSE2__
  #include <emmintrin.h>
#else
  #warning SSE2 is not available. Code will not compile!
#endif

For some compilers, you may need to pass a complier flag to switch on the use of SSE2. For example, gcc and clang use the flag -msse2

Different header files are used for the other versions of SSE. However, for most numerical work, SSE2 is the version you want to use, and it is now widely supported on pretty much any X86- or X86-64-compatible processor that you will use.

The emmintrin.h header file defines a set of data types that represent different types of vectors. These are;

Several functions are defined that operate on __m128 vectors, e.g.

In addition to functions that operate on __m128 float vectors, there are equivalent functions that operate on __m128d double vectors. The functions are named similarly to the float vector functions, except _ps (which stands for “packed single”) is replaced by _pd (which stands for “packed double”). For example;

The above is a lot of information. Let’s now try a simple program that creates two __m128 vectors and calculates their sum. Create a new file called sse.cpp and copy into it;

#include <iostream>

#ifdef __SSE2__
  #include <emmintrin.h>
#else
  #warning SSE2 support is not available. Code will not compile
#endif

int main(int argc, char **argv)
{
    __m128 a = _mm_set_ps(4.0, 3.0, 2.0, 1.0);
    __m128 b = _mm_set_ps(8.0, 7.0, 6.0, 5.0);

    __m128 c = _mm_add_ps(a, b);

    float d[4];
    _mm_storeu_ps(d, c);

    std::cout << "result equals " << d[0] << "," << d[1]
              << "," << d[2] << "," << d[3] << std::endl;

    return 0;
}

Compile and run using

g++ -O2 -msse2 --std=c++14 sse.cpp -o sse
./sse

(note the addition of -msse2 to switch on SSE2 support. Some compilers now do this automatically, but it is still worth adding).

You should see output

result equals 6,8,10,12

This is because we have loaded [1,2,3,4] into a and [5,6,7,8] into b. We calculated the sum, which is [6,8,10,12], which was then printed out.

Try editing sse.cpp to use the other arithmetic functions (i.e. _mm_mul_ps). Is the result what you expect?

Manually vectorising a loop

Now you know how to create and use SSE2 intrinsics, the next step is to use them to vectorise code. We will look here at vectorising the loop.cpp file that we first met in part 1.

Create a new file called sseloop.cpp and copy into it the below;

#include "workshop.h"

#ifdef __SSE2__
  #include <emmintrin.h>
#else
  #warning SSE2 support is not available. Code will not compile.
#endif

int main(int argc, char **argv)
{
    const int size = 512;

    auto a = workshop::Array<float>(size);
    auto b = workshop::Array<float>(size);
    auto c = workshop::Array<float>(size);

    auto sse_a = workshop::AlignedArray<__m128>(size/4);
    auto sse_b = workshop::AlignedArray<__m128>(size/4);
    auto sse_c = workshop::AlignedArray<__m128>(size/4);


    for (int i=0; i<size; ++i)
    {
        a[i] = 1.0*(i+1);
        b[i] = 2.5*(i+1);
        c[i] = 0.0;
    }

    for (int i=0; i<size; i+=4)
    {
        sse_a[i/4] = _mm_set_ps(1.0*(i+3+1),
                                1.0*(i+2+1),
                                1.0*(i+1+1),
                                1.0*(i+0+1));

        sse_b[i/4] = _mm_set_ps(2.5*(i+3+1),
                                2.5*(i+2+1),
                                2.5*(i+1+1),
                                2.5*(i+0+1));

        sse_c[i/4] = _mm_set1_ps(0.0);
    }

    auto timer = workshop::start_timer();

    for (int j=0; j<100000; ++j)
    {
        for (int i=0; i<size; ++i)
        {
            c[i] = a[i] + b[i];
        }
    }

    auto duration = workshop::get_duration(timer);

    timer = workshop::start_timer();

    for (int j=0; j<100000; ++j)
    {    
        for (int i=0; i<size/4; ++i)
        {
            sse_c[i] = _mm_add_ps(sse_a[i], sse_b[i]);
        }
    }

    auto vector_duration = workshop::get_duration(timer);

    std::cout << "The standard loop took " << duration
              << " microseconds to complete." << std::endl;

    std::cout << "The vectorised loop took " << vector_duration
              << " microseconds to complete." << std::endl;

    return 0;
}

Compile and run using

g++ -msse2 -O2 --std=c++14 -Iinclude sseloop.cpp -o sseloop
./sseloop

You should see that the manually vectorised loop is nearly four times faster than the scalar loop. On my computer, the vector loop is about 3.8 times faster than the scalar loop, taking 12.4 ms versus 47.6 ms.

To manually vectorise the loop, we have had to make some changes to the code;

Note that the number of iterations of our loop (512) was evenly divisable by 4. If this was not the case, we would have had to manually add additional scalar iterations of the loop to make up any shortfall. For example, if our loop used 514 iterations, then 512 could be performed using the vector loop, and then code would need to be added to perform the remaining 2 iterations using a scalar loop.

Exercises

Hopefully, you should see the (perhaps surprising) result that vector square root is significantly faster than scalar square root. On my computer, scalar square root takes about 211 ms, while vector square root takes 13.5 ms. This is about a 15 times speed up, which goes beyond the normal four times speed up associated with vectorisation. The reason is that SSE2 has an implementation of square root that is built directly into the processor. This hardware square root is exceptionally fast, and much faster than the scalar square root that is implemented in software. In addition, this hardware square root is an actual processor instruction rather than a function call, meaning that there are no overheads. Indeed, it is that fast that adding in the square root has barely increased the cost of the loop compared to the simple addition.

This shows that if your code uses a lot of square roots, you can get a big performance boost by using manual vectorisation with SSE2 intrinsics.

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