Effects of cache on performance

It is not clear to me, why is Node.js so amazyingly slow on a Raspberry Pi (article 1, article 2)?

Is it because of the small cache (16kb+128kb)? Is Node.js emitting poor code on ARM? Well, I decided to investigate the cache issue. The 128kb cache of the Raspberry Pi is supposed to be primarily used by the GPU; is it actually effective at all?

A suitable test algorithm
To understand what I test, and because of the fun of it, I wanted to implement a suitable test program. I can imagine a good test program for cache testing would:

  • be reasonably slow/fast, so measuring execution time is practical and meaningful
  • have working data sets in sizes 10kb-10Mb
  • the same problem should be solvable with different work set sizes, in a way that the theoretical execution time should be the same, but the difference is because of cache only
  • be reasonably simple to implement and understand, while not so trivial that the optimizer just gets rid of the problem entirely

Finally, I think it is fun if the program does something slightly meaningful.

I found that Bubblesort (and later Selectionsort) were good problems, if combined with a quasi twist. Original bubble sort:

Array to sort: G A F C B D H E   ( N=8 )
Sorted array:  A B C D E F G H
Theoretical cost: O(N2) = 64/2 = 32
Actual cost: 7+6+5+4+3+2+1     = 28 (compares and conditional swaps)

I invented the following cache-optimized Bubble-Twist-Sort:

Array to sort:                G A F C B D H E
Sort halves using Bubblesort: A C F G B D E H
Now, the twist:                                 ( G>B : swap )
                              A C F B G D E H   ( D>F : swap )
                              A C D B G F E H   ( C<E : done )
Sort halves using Bubblesort: A B C D E F G H
Theoretical cost = 16/2 + 16/2 (first two bubbelsort)
                 + 4/2         (expected number of twist-swaps)
                 + 16/2 + 16/2 (second two bubbelsort)
                 = 34
Actual cost: 4*(3+2+1) + 2 = 26

Anyway, for larger arrays the actual costs get very close. The idea here is that I can run a bubbelsort on 1000 elements (effectively using 1000 memory units of memory intensively for ~500000 operations). But instead of doing that, I can replace it with 4 runs on 500 elements (4* ~12500 operations + ~250 operations). So I am solving the same problem, using the same algorithm, but optimizing for smaller cache sizes.

Enough of Bubblesort… you are probably either lost in details or disgusted with this horribly stupid idea of optimizing and not optimizing Bubblesort at the same time.

I made a Selectionsort option. And for a given data size I allowed it either to sort bytes or 32-bit words (which is 16 times faster, for same data size).

The test machines
I gathered 10 different test machines, with different cache sizes and instructions sets:

	QNAP	wdr3600	ac20i	Rpi	Rpi 2	wdr4900	G4	Celeron	Xeon	Athlon	i5
								~2007   ~2010   ~2013
============================================================================================
L1	32	32	32	16	?	32	64	32	32	128	32
L2				128	?	256	256	512	6M	1024	256
L3							1024				6M
Mhz	500	560	580	700	900	800	866	900	2800	3000	3100
CPU	ARMv5	Mips74K	Mips24K	ARMv6	ARMv7	PPC	PPC	x86	x64	x64	x64
OS	Debian	OpenWrt	OpenWrt	OpenWrt	OpenWrt	OpenWrt	Debian	Ubuntu	MacOSX	Ubuntu	Windows

Note that for the multi-core machines (Xeon, Athlon, i5) the L2/L3 caches may be shared or not between cores and the numbers above are a little ambigous. The sizes should be for Data cache when separate from Instruction cache.

The benchmarks
I ran Bubblesort for sizes 1000000 bytes down to 1000000/512. For Selectionsort I just ran three rounds. For Bubblesort I also ran for 2000000 and 4000000 but those times are divided by 4 and 16 to be comparable. All times are in seconds.

Bubblesort

	QNAP	wdr3600	ac20i	rpi	rpi2	wdr4900	G4	Celeron	Xeon	Athlon	i5
============================================================================================
4000000	1248	1332	997	1120	396	833		507	120	104	93
2000000	1248	1332	994	1118	386	791	553	506	114	102	93
1000000	1274	1330	1009	1110	367	757	492	504	113	96	93
500000	1258	1194	959	1049	352	628	389	353	72	74	63
250000	1219	1116	931	911	351	445	309	276	53	61	48
125000	1174	1043	902	701	349	397	287	237	44	56	41
62500	941	853	791	573	349	373	278	218	38	52	37
31250	700	462	520	474	342	317	260	208	36	48	36
15625	697	456	507	368	340	315	258	204	35	49	35
7812	696	454	495	364	340	315	256	202	34	49	35
3906	696	455	496	364	340	315	257	203	34	47	35
1953	698	456	496	365	342	320	257	204	35	45	35

Selectionsort

	QNAP	wdr3600	ac20i	rpi	rpi2	wdr4900	G4	Celeron	Xeon	Athlon	i5
============================================================================================
1000000	1317	996	877	1056	446	468	296	255	30	45	19
31250	875	354	539	559	420	206	147	245	28	40	21
1953	874	362	520	457	422	209	149	250	30	41	23

Theoretically, all timings for a single machine should be equal. The differences can be explained much by cache sizes, but obviously there are more things happening here.

Findings
Mostly the data makes sense. The caches creates plateaus and the L1 size can almost be prediced by the data. I would have expected even bigger differences between best/worse-cases; now it is in the range 180%-340%. The most surprising thing (?) is the Selectionsort results. They are sometimes a lot faster (G4, i5) and sometimes significantly slower! This is strange: I have no idea.

I believe the i5 superior performance of Selectionsort 1000000 is due to cache and branch prediction.

I note that the QNAP and Archer C20i both have DDRII memory, while the RPi has SDRAM. This seems to make a difference when work sizes get bigger.

I have also made other Benchmarks where the WDR4900 were faster than the G4 – not this time.

The Raspberry Pi
What did I learn about the Raspberry Pi? Well, memory is slow and branch prediction seems bad. It is typically 10-15 times slower than the modern (Xeon, Athlon, i5) CPUs. But for large selectionsort problems the difference is up to 40x. This starts getting close to the Node.js crap speed. It is not hard to imagine that Node.js benefits heavily from great branch prediction and large cache sizes – both things that the RPi lacks.

What about the 128k cache? Does it work? Well, compared to the L1-only machines, performance of RPi degrades sligthly slower, perhaps. Not impressed.

Bubblesort vs Selectionsort
It really puzzles me that Bubblesort ever beats Selectionsort:

void bubbelsort_uint32_t(uint32_t* array, size_t len) {
  size_t i, j, jm1;
  uint32_t tmp;
  for ( i=len ; i>1 ; i-- ) {
    for ( j=1 ; j<i ; j++ ) {
      jm1 = j-1;
      if ( array[jm1] > array[j] ) {
        tmp = array[jm1];
        array[jm1] = array[j];
        array[j] = tmp;
      }
    }
  }
}

void selectionsort_uint32_t(uint32_t* array, size_t len) {
  size_t i, j, best;
  uint32_t tmp;
  for ( i=1 ; i<len ; i++ ) {
    best = i-1;
    for ( j=i ; j<len ; j++ ) {
      if ( array[best] > array[j] ) {
        best = j;
      }
    }
    tmp = array[i-1];
    array[i-1] = array[best];
    array[best] = tmp;
  } 
}

Essentially, the difference is how the swap takes place outside the inner loop (once) instead of all the time. The Selectionsort should also be able of benefit from easier branch prediction and much fewer writes to memory. Perhaps compiling to assembly code would reveal something odd going on.

Power of 2 aligned data sets
I avoided using a datasize with the size an exact power of two: 1024×1024 vs 1000×1000. I did this becuase caches are supposed to work better this way. Perhaps I will make some 1024×1024 runs some day.

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