The problem

We want to look for the maximum value in an array, this array is composed of int16_t mono audio samples. The maximum value of the array will be the peak value during the audio interval being analysed, this peak is known as sample peak and should not be interpreted as the real peak of the audio which is the true peak (there is a very good explanation about the differences here).

A basic(?) solution

Ok, we have to look for the maximum value in an array and we focus on functionality, this is quite simple actually…

int16_t max = buff [0];
for(i = 1; i < size; i++) {
>....if(max < buff[i]) {
>....>....max = buff[i];
>....}
}

 The intrinsics

These are a series of functions which implement many MMX, SSE and AVX instructions, they are mapped directly to C functions and are also further optimized with gcc. Most of the instructions use vector operations, and you can work with 128, 256 or 512 bit vectors depending on the architecture and the compiler. There is a very detailed guide here and you can see a full list of the funcions here.

You will need to include the headers depending on what functions you want to call, or just include x86intrin.h, which will include all the available ones. Then, you will need to add the appropiate flag to the gcc compile line, in this specific case I’m using -maxv2. If you want to check the supported functions you may use the following command to list you the corresponding includes that gcc will use.

$ gcc -mavx2 -dM -E - < /dev/null | egrep "SSE|AVX"
#define __AVX__ 1
#define __AVX2__ 1
#define __SSE__ 1
#define __SSE2__ 1
#define __SSE2_MATH__ 1
#define __SSE3__ 1
#define __SSE4_1__ 1
#define __SSE4_2__ 1
#define __SSE_MATH__ 1
#define __SSSE3__ 1


The code

What I’m going to do is compare two buffers of 128 bits, one of them has the max value (initialized to 0, if there are all negative values the result will be wrong)  and the other will be the input buffer, this is done using: _mm_max_epi16() which will compare 8 values (int16_t) at a time. This is one of the reasons why the intrinsics increase the performance.

After going through the whole input buffer, I will have in maxval array the maximum value, but I don’t know the position. For the sake of the example I am doing two redundant things here. First, using _mm_shufflelo_epi16()/_mm_shufflehi_epi16() and the _mm_max_epi16()  I will compare values inside the vector and rotate them so the whole buffer has the maximum value, being 16 bit values I can’t shuffle the whole buffer so the shuffle is done in the high bits and the low bits separately.

Finally I will store the final vector in a int16_t array with _mm_store_si128() and I’ll look for the maximum inside it (I could have done this before, but I wanted to show the shuffle which might be useful if the samples were not 16 bit, and the shuffles were not partial).

int16_t find_max(int16_t* buff, int size)
{
    int16_t maxmax[8];
    int i;
    int16_t max = buff[0];

    __m128i *f8 = (__m128i*)buff;
    __m128i maxval = _mm_setzero_si128();
    __m128i maxval2 = _mm_setzero_si128();
    for (i = 0; i < size / 16; i++) {
        maxval = _mm_max_epi16(maxval, f8[i]);
    }
    maxval2 = maxval;
    for (i = 0; i < 3; i++) {
        maxval = _mm_max_epi16(maxval, _mm_shufflehi_epi16(maxval, 0x3));
        _mm_store_si128(&maxmax, maxval);
        maxval2 = _mm_max_epi16(maxval2, _mm_shufflelo_epi16(maxval2, 0x3));
        _mm_store_si128(&maxmax, maxval2);
    }
    _mm_store_si128(&maxmax, maxval);
    for(i = 0; i < 8; i++)
        if(max < maxmax[i])
            max = maxmax[i];
    return max;
}

Some numbers

I’m going to compare 3 different cases, and find the maximum value in random (pseudo random) arrays of 10000 and 1000000 samples.

• Using an intuitive for loop as the one shown before
• Same loop as before but with compiler optimizations
• Using SSE instructions via intrinsics (sample code).

This table shows the total delay in us (micro seconds) that the different functions take.

As you can see, the code gets much faster with the Intrinsics, and even faster with the optimizations.

Afterwords

• You will see an improvement in most cases, and consider that it gets better when the arrays are larger
• It gets even better with optimizations (-O2)
• There is still a difference with smaller arrays (10000 element ones)
• The key factor is to look for repetitive operations in large arrays
• You may lose some portability, as some functions may not be available in every microprocessor
• There are some transition penalties when switching between AVX and SSE, so when mixing both this should be considered

Hope you guys liked the post, please feel free to ask any questions and if I can/know, I will answer you.