Beating the optimizer

It’s generally believed that it’s far too difficult to beat an optimizing C compiler when producing code, at least for a simple problem. In this post we will see how that’s not true and simple “hand-optimized” code can get large improvements in some cases.

Obviously that doesn’t mean that we should program using intrinsics or assembly most of the time: it still took me far more time to write this code than the time required to compile a C file with optimizations. But it means that, if we are working in a piece of time-critical code and profiling shows us a “hot spot”, it’s reasonable to consider doing such an optimization.

The problem

The problem description is very simple: given a big buffer (many megabytes), count the number of bytes equal to a given one. The prototype of such a function could be the following one:

size_t memcount(const void *s, int c, size_t n);

The baseline solution

Before doing any optimization is important to get a baseline solution and consider how optimal it is. In this case, it’s very easy to write:

size_t memcount_naive(const void *s, int c, size_t n)
{
    const uint8_t *b = (const uint8_t *)s;
    size_t count = 0;
    for (size_t i = 0; i < n; i++)
        if (b[i] == c)
            count++;
    return count;
}

Evaluating the baseline

We are going to do the evaluation with a relatively slow mobile Ivy Bridge core:

$ grep 'processor\|\(model name\)' /proc/cpuinfo 
processor	: 0
model name	: Intel(R) Core(TM) i5-3210M CPU @ 2.50GHz
processor	: 1
model name	: Intel(R) Core(TM) i5-3210M CPU @ 2.50GHz
processor	: 2
model name	: Intel(R) Core(TM) i5-3210M CPU @ 2.50GHz
processor	: 3
model name	: Intel(R) Core(TM) i5-3210M CPU @ 2.50GHz

Timing with clock_gettime(), we get the following results:

$ gcc --version
gcc (Ubuntu 4.8.4-2ubuntu1~14.04) 4.8.4
Copyright (C) 2013 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
$ gcc -march=native -std=c11 -DTEST_NAIVE -O3 memcount.c -o memcount && ./memcount 
Generated random arrays.
Count of character 45 in 'a1' using 'memcount_naive' is: 408978
Elapsed time: 103946325 ns
Count of character 45 in 'a1' using 'memcount_naive' is: 408978
Elapsed time: 104022735 ns
Count of character 45 in 'a2' using 'memcount_naive' is: 409445
Elapsed time: 104278289 ns
Count of character 45 in 'a3' using 'memcount_naive' is: 410593
Elapsed time: 104127038 ns
Count of character 45 in 'a4' using 'memcount_naive' is: 104447433
Elapsed time: 104110155 ns
Count of character 45 in 'a5' using 'memcount_naive' is: 104857613
Elapsed time: 104122294 ns

The measured time to count bytes with a given value in a ~100 MB array is about 100 ms, giving us a processing speed of approximately 1 GB/s. There are no substantial caching effects, as expected given that we are processing a 100 MB array.

Can we do better?

Memory bandwidth

Let’s start by calculating the memory bandwidth. We can get the memory parameters by using the dmidecode command:

$ sudo dmidecode --type 17 | grep '\(Locator\)\|\(Clock\)\|\(Size\)\|\(Type\)'
	Size: 4096 MB
	Locator: ChannelA-DIMM0
	Bank Locator: BANK 0
	Type: DDR3
	Type Detail: Synchronous
	Configured Clock Speed: 1333 MHz
	Size: No Module Installed
	Locator: ChannelA-DIMM1
	Bank Locator: BANK 1
	Type: Unknown
	Type Detail: None
	Configured Clock Speed: Unknown
	Size: 4096 MB
	Locator: ChannelB-DIMM0
	Bank Locator: BANK 2
	Type: DDR3
	Type Detail: Synchronous
	Configured Clock Speed: 1333 MHz
	Size: No Module Installed
	Locator: ChannelB-DIMM1
	Bank Locator: BANK 3
	Type: Unknown
	Type Detail: None
	Configured Clock Speed: Unknown

We have two DDR3 DIMMs in separate channels, running at “1333 MHz”. The expected bandwidth would be:

\displaystyle 1333\,\mathrm{MT}/\mathrm{s} \cdot 128\,\mathrm{bit}/\mathrm{T} \cdot 0.125 \,\mathrm{bit}/\mathrm{byte} \approx 20\,\mathrm{GB}/\mathrm{s},

so we should have plenty of room for improvement. We can get a more realistic upper limit by comparing the performance to a highly optimized normal operation, such as memchr():

$ gcc -march=native -std=c11 -DTEST_MEMCHR -O3 memcount.c -o memcount && ./memcount 
Generated random arrays.
Timing 'memchr()' to get character 13' in 'a5'. Result: (nil)
Elapsed time: 6475968 ns
Timing 'memchr()' to get character 13' in 'a5'. Result: (nil)
Elapsed time: 6919187 ns

Now we know that bandwidths of ~14 GB/s are achievable in this system, so there should be plenty of room for improving performance.

Using SSE intrinsics

My solution (that is probably far from optimal) is the following one:

size_t memcount_sse(const void *s, int c, size_t n)
{
    size_t nb = n / 16;
    size_t count = 0;
    __m128i ct = _mm_set1_epi32(c * ((~0UL) / 0xff));
    __m128i z = _mm_set1_epi32(0);
    __m128i acr = _mm_set1_epi32(0);
    for (size_t i = 0; i < nb; i++)
    {
        __m128i b = _mm_lddqu_si128((const __m128i *)s + i);
        __m128i cr = _mm_cmpeq_epi8 (ct, b);
        acr = _mm_add_epi8(acr, cr);
        if (i % 0xff == 0xfe)
        {
            acr = _mm_sub_epi8(z, acr);
            __m128i sacr = _mm_sad_epu8(acr, z);
            count += _mm_extract_epi64(sacr, 0);
            count += _mm_extract_epi64(sacr, 1);
            acr = _mm_set1_epi32(0);
        }
    }
    acr = _mm_sub_epi8(z, acr);
    __m128i sacr = _mm_sad_epu8(acr, z);
    count += _mm_extract_epi64(sacr, 0);
    count += _mm_extract_epi64(sacr, 1);
    for (size_t i = nb * 16; i < n; i++)
        if (((const uint8_t *)s)[i] == c)
            count++;
    return count;
}

Testing it we get substantially better times:

$ gcc -march=native -std=c11 -DTEST_SSE -O3 memcount.c -o memcount && ./memcount 
Generated random arrays.
Count of character 45 in 'a1' using 'memcount_sse' is: 408978
Elapsed time: 10908773 ns
Count of character 45 in 'a2' using 'memcount_sse' is: 409445
Elapsed time: 11195531 ns
Count of character 45 in 'a3' using 'memcount_sse' is: 410593
Elapsed time: 12147576 ns
Count of character 45 in 'a4' using 'memcount_sse' is: 104447433
Elapsed time: 10930570 ns
Count of character 45 in 'a5' using 'memcount_sse' is: 104857613
Elapsed time: 10856319 ns

The new speeds are between 8 and 9 GB/s, almost an order of magnitude faster than the “naive” code.

Explanation

As this is my first program using intrinsics, it’s probably far from optimal. But, as it can seem pretty impenetrable, let’s explain it step by step.

Initialization

size_t memcount_sse(const void *s, int c, size_t n)
{
    size_t nb = n / 16;
    size_t count = 0;
    __m128i ct = _mm_set1_epi32(c * ((~0UL) / 0xff));
    __m128i z = _mm_set1_epi32(0);
    __m128i acr = _mm_set1_epi32(0);

This section just initializes some variables:

  • nb: we will process the input in blocks of 16 bytes (128 bits), so we use this variable to track the number of blocks to be processed.
  • count: the return value, to be filled with the byte count to be computed.
  • ct: the comparison target, a 128 bit value filled with copies of c, the byte value we are counting.
  • z: a zero 128 bit value.
  • acr: the accumulated comparison result, a 128 bit value that accumulates the comparison results in a special format, to be described later.

Only one intrinsic is used here, _mm_set1_epi32(). It loads repeated copies of a 32 bit value in a 128 bit value.

Comparing and accumulating

    for (size_t i = 0; i < nb; i++)
    {
        __m128i b = _mm_lddqu_si128((const __m128i *)s + i);
        __m128i cr = _mm_cmpeq_epi8 (ct, b);
        acr = _mm_add_epi8(acr, cr);

The loop is self explanatory: we are just iterating over 128 bit blocks. The next intrinsic, _mm_lddqu_si128() just loads a potentially unaligned 128 bit value into the 128 bit variable b.

Now comes the key section: we compare b byte per byte against the comparison target ct, using the intrinsic _mm_cmpeq_epi8(), and we store 0xff when the bytes match and 0x00 when they don’t in the comparison result cr. That result is summed byte per byte in the accumulated counts variable acr, with the intrinsic _mm_add_epi8().

As 0xff is -1 modulo 256, the accumulation works normally, but we could have an overflow after 256 iterations. To avoid that, we need to move this counts to our count variable periodically.

Definitive accumulation

        if (i % 0xff == 0xfe)
        {
            acr = _mm_sub_epi8(z, acr);
            __m128i sacr = _mm_sad_epu8(acr, z);
            count += _mm_extract_epi64(sacr, 0);
            count += _mm_extract_epi64(sacr, 1);
            acr = _mm_set1_epi32(0);
        }

Every 255 iterations (to avoid overflow), we do the following operations:

  • Change the sign of acr by subtracting it from zero to get the positive values of the counts (using the _mm_sub_epi8() intrinsic).
  • Get the absolute value of each byte and sum all these values to get the total count (using the _mm_sad_epu8() intrinsic, that leaves the sum split in the low and high parts of the 128 bit variable).
  • Sum the low and high parts of the 128 bit variable to count, to get the total count, using the _mm_extract_epi64() intrinsic to get those parts.
  • Set the accumulated comparison result acr variable to zero.

After loop accumulation

    acr = _mm_sub_epi8(z, acr);
    __m128i sacr = _mm_sad_epu8(acr, z);
    count += _mm_extract_epi64(sacr, 0);
    count += _mm_extract_epi64(sacr, 1);

Accumulates the value that remains in acr after exiting the main loop.

Bytes after last block

    for (size_t i = nb * 16; i < n; i++)
        if (((const uint8_t *)s)[i] == c)
            count++;
    return count;
}

Handles the bytes that come after the last 16 byte block and returns the total count.

Conclusion

We have seen that a substantial improvement of almost 10x can be obtained over the optimizing compiler results, even in cases where the code to be optimized is quite simple. It would be interesting to see how close to the 20 GB/s we can get with more carefully optimized code…

The code used for these tests is available in Github.

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