I posted an improved version of this answer on a duplicate of this: C loop optimization help for final assignment. It was originally just a repost, but then I made some changes to answer the differences in that question. I forget what's different, but you should probably read that one instead. Maybe I should just delete this one.
See also other optimization guides in the x86 tag wiki.
First of all, it's a really crap sample because it doesn't have anything to stop a smart compiler from optimizing away the entire thing. It doesn't even print the sum. Even gcc -O1 (instead of -O3) threw away some of the looping.
Normally you'd put your code in a function, and call it in a loop from main() in another file. And compile them separately, without whole-program cross-file optimisation, so the compiler can't do optimisations based on the compile-time constants you call it with. The repeat-loop being wrapped so tightly around the actual loop over the array is causing havoc with gcc's optimizer (see below).
Also:
gcc -Wall -O3 -march=native fast-loop-cs201.c -o fl
fast-loop-cs201.c: In function ‘main’:
fast-loop-cs201.c:17:14: warning: ‘help’ is used uninitialized in this function [-Wuninitialized]
long int help;
I have to agree with EOF's disparaging remarks about your prof. Giving out code that optimizes away to nothing, and with uninitialized variables, is utter nonsense.
Some people are saying in comments that "the compiler doesn't matter", and that you're supposed to do optimize your C source for the CPU microarchitecture, rather than letting the compiler do it. This is crap: for good performance, you have to be aware of what compilers can do, and can't do. Some optimizations are "brittle", and a small seemingly-innocent change to the source will stop the compiler from doing something.
I assume your prof mentioned a few things about performance. There are a crapton of different things that could come into play here, many of which I assume didn't get mentioned in a 2nd-year CS class.
Besides multithreading with openmp, there's vectorizing with SIMD. There are also optimizations for modern pipelined CPUs: specifically, avoid having one long dependency chain.
Further essential reading:
- Agner Fog's guides for optimizing C and asm for x86. Some of it applies to all CPUs.
- What Every Programmer Should Know About Memory
Your compiler manual is also essential, esp. for floating point code. Floating point has limited precision, and is not associative. The final sum does depend on which order you do the additions in. However, usually the difference in rounding error is small. So the compiler can get a big speedup by re-ordering things if you use -ffast-math to allow it. This may have been what your unroll-by-10 allowed.
Instead of just unrolling, keeping multiple accumulators which you only add up at the end can keep the floating point execution units saturated, because FP instructions have latency != throughput. If you need the result of the last op to be complete before the next one can start, you're limited by latency. For FP add, that's one per 3 cycles. In Intel Sandybridge, IvB, Haswell, and Broadwell, the throughput of FP add is one per cycle. So you need to keep at least 3 independent ops that can be in flight at once to saturate the machine. For Skylake, it's 2 per cycle with latency of 4 clocks. (On the plus side for Skylake, FMA is down to 4 cycle latency.)
In this case, there's also basic stuff like pulling things out of the loop, e.g. help += ARRAY_SIZE.
compiler options
I started out with the original inner loop, with just help += ARRAY_SIZE pulled out, and adding a printf at the end so gcc doesn't optimize everything away. Let's try some compiler options and see what we can achieve with gcc 4.9.2 (on my i5 2500k Sandybridge. 3.8GHz max turbo (slight OC), 3.3GHz sustained (irrelevant for this short benchmark)):
gcc -O0 fast-loop-cs201.c -o fl: 16.43s performance is a total joke. Variables are stored to memory after every operation, and re-loaded before the next. This is a bottleneck, and adds a lot of latency. Not to mention losing out on actual optimisations. Timing / tuning code with -O0 is not useful.-O1: 4.87s-O2: 4.89s-O3: 2.453s (uses SSE to do 2 at once. I'm of course using a 64bit system, so hardware support for -msse2 is baseline.)-O3 -ffast-math -funroll-loops: 2.439s-O3 -march=sandybridge -ffast-math -funroll-loops: 1.275s (uses AVX to do 4 at once.) -Ofast ...: no gain-O3 -ftree-parallelize-loops=4 -march=sandybridge -ffast-math -funroll-loops: 0m2.375s real, 0m8.500s user. Looks like locking overhead killed it. It only spawns the 4 threads total, but the inner loop is too short for it to be a win (because it collects the sums every time, instead of giving one thread the first 1/4 of the outer loop iterations).-Ofast -fprofile-generate -march=sandybridge -ffast-math, run it, then
-Ofast -fprofile-use -march=sandybridge -ffast-math: 1.275s
clang-3.5 -Ofast -march=native -ffast-math: 1.070s. (clang doesn't support -march=sandybridge).
gcc -O3 vectorizes in a hilarious way: The inner loop does 2 (or 4) iterations of the outer loop in parallel, by broadcasting one array element to all elements of an xmm (or ymm) register, and doing an addpd on that. So it sees the same values are being added repeatedly, but even -ffast-math doesn't let gcc just turn it into a multiply. Or switch the loops.
clang-3.5 vectorizes a lot better: it vectorizes the inner loop, instead of the outer, so it doesn't need to broadcast. It even uses 4 vector registers as 4 separate accumulators. However, it doesn't assume that calloc returns aligned memory, and for some reason it thinks the best bet is a pair of 128b loads.
vmovupd -0x60(%rbx,%rcx,8),%xmm4`
vinsertf128 $0x1,-0x50(%rbx,%rcx,8),%ymm4,%ymm4
It's actually slower when I tell it that the array is aligned. (with a stupid hack like array = (double*)((ptrdiff_t)array & ~31); which actually generates an instruction to mask off the low 5 bits, because clang-3.5 doesn't support gcc's __builtin_assume_aligned.) I think the way the tight loop of 4x vaddpd mem, %ymmX,%ymmX is aligned puts cmp $0x271c,%rcx crossing a 32B boundary, so it can't macro-fuse with jne. uop throughput shouldn't be an issue, though, since this code is only getting 0.65insns per cycle (and 0.93 uops / cycle), according to perf.
Ahh, I checked with a debugger, and calloc is only returning a 16B-aligned pointer. So half the 32B memory accesses are crossing a cache line, causing a big slowdown. I guess it is slightly faster to do two separate 16B loads when your pointer is 16B-aligned but not 32B-aligned, on Sandybridge. The compiler is making a good choice here.
Source level changes
As we can see from clang beating gcc, multiple accumulators are excellent. The most obvious way to do this would be:
for (j = 0; j < ARRAY_SIZE; j+=4) { // unroll 4 times
sum0 += array[j];
sum1 += array[j+1];
sum2 += array[j+2];
sum3 += array[j+3];
}
and then don't collect the 4 accumulators into one until after the end of the outer loop.
Your source change of
sum += j[0]+j[1]+j[2]+j[3]+j[4]+j[5]+j[6]+j[7]+j[8]+j[9];
actually has a similar effect, thanks to out-of-order execution. Each group of 10 is a separate dependency chain. order-of-operations rules say the j values get added together first, and then added to sum. So the loop-carried dependency chain is still only the latency of one FP add, and there's lots of independent work for each group of 10. Each group is a separate dependency chain of 9 adds, and takes few enough instructions for the out-of-order execution hardware to see the start of the next chain and, and find the parallelism to keep those medium latency, high throughput FP execution units fed.
With -O0, as your silly assignment apparently requires, values are stored to RAM at the end of every statement. (Technically, at every "sequence point", as the C standards call it.) Writing longer expressions without updating any variables, even temporaries, will make -O0 run faster, but it's not a useful optimisation. Don't waste your time on changes that only help with -O0, esp. not at the expense of readability.
Using 4-accumulators and not adding them together until the end of the outer loop defeats clang's auto-vectorizer. It still runs in only 1.66s (vs. 4.89 for gcc's non-vectorized -O2 with one accumulator). Even gcc -O2 without -ffast-math also gets 1.66s for this source change. Note that ARRAY_SIZE is known to be a multiple of 4, so I didn't include any cleanup code to handle the last up-to-3 elements (or to avoid reading past the end of the array, which would happen as written now). It's really easy to get something wrong and read past the end of the array when doing this.
gcc, on the other hand, does vectorize this, but it also pessimises (un-optimises) the inner loop into a single dependency chain. I think it's doing multiple iterations of the outer loop, again.
Using gcc's platform-independent vector extensions, I wrote a version which compiles into apparently-optimal code:
// compile with gcc -g -Wall -std=gnu11 -Ofast -fno-tree-vectorize -march=native fast-loop-cs201.vec.c -o fl3-vec
#include <stdio.h>
#include <stdlib.h>
#include <stddef.h>
#include <assert.h>
#include <string.h>
// You are only allowed to make changes to this code as specified by the comments in it.
// The code you submit must have these two values.
#define N_TIMES 600000
#define ARRAY_SIZE 10000
int main(void)
{
double *array = calloc(ARRAY_SIZE, sizeof(double));
double sum = 0;
int i;
// You can add variables between this comment ...
long int help = 0;
typedef double v4df __attribute__ ((vector_size (8*4)));
v4df sum0={0}, sum1={0}, sum2={0}, sum3={0};
const size_t array_bytes = ARRAY_SIZE*sizeof(double);
double *aligned_array = NULL;
// this more-than-declaration could go in an if(i == 0) block for strict compliance with the rules
if ( posix_memalign((void**)&aligned_array, 32, array_bytes) ) {
exit (1);
}
memcpy(aligned_array, array, array_bytes); // In this one case: faster to align once and have no extra overhead for N_TIMES through the loop
// ... and this one.
// Please change 'your name' to your actual name.
printf("CS201 - Asgmt 4 - I. Forgot\n");
for (i = 0; i < N_TIMES; i++) {
// You can change anything between this comment ...
/*
#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__) >= 407 // GCC 4.7 or later.
array = __builtin_assume_aligned(array, 32);
#else
// force-align for other compilers. This loop-invariant will be done outside the loop.
array = (double*) ((ptrdiff_t)array & ~31);
#endif
*/
assert ( ARRAY_SIZE / (4*4) == (ARRAY_SIZE+15) / (4*4) ); // We don't have a cleanup loop to handle where the array size isn't a multiple of 16
// incrementing pointers can be more efficient than indexing arrays
// esp. on recent Intel where micro-fusion only works with one-register addressing modes
// of course, the compiler can always generate pointer-incrementing asm from array-indexing source
const double *start = aligned_array;
while ( (ptrdiff_t)start & 31 ) {
// annoying loops like this are the reason people use aligned buffers
sum += *start++; // scalar until we reach 32B alignment
// in practice, this loop doesn't run, because we copy into an aligned buffer
// This will also require a cleanup loop, and break our multiple-of-16 doubles assumption.
}
const v4df *end = (v4df *)(aligned_array+ARRAY_SIZE);
for (const v4df *p = (v4df *)start ; p+3 < end; p+=4) {
sum0 += p[0]; // p+=4 increments the pointer by 4 * 4 * 8 bytes
sum1 += p[1]; // make sure you keep track of what you're incrementing
sum2 += p[2];
sum3 += p[3];
}
// the compiler might be smart enough to pull this out of the inner loop
// in fact, gcc turns this into a 64bit movabs outside of both loops :P
help+= ARRAY_SIZE;
// ... and this one. But your inner loop must do the same
// number of additions as this one does.
/* You could argue legalese and say that
if (i == 0) {
for (j ...)
sum += array[j];
sum *= N_TIMES;
}
* still does as many adds in its *INNER LOOP*, but it just doesn't run it as often
*/
}
// You can add some final code between this comment ...
sum0 = (sum0 + sum1) + (sum2 + sum3);
sum += sum0[0] + sum0[1] + sum0[2] + sum0[3];
printf("sum = %g; help=%ld\n", sum, help); // defeat the compiler.
free (aligned_array);
free (array); // not strictly necessary, because this is the end of main(). Leaving it out for this special case is a bad example for a CS class, though.
// ... and this one.
return 0;
}
The inner loop compiles to:
4007c0: c5 e5 58 19 vaddpd (%rcx),%ymm3,%ymm3
4007c4: 48 83 e9 80 sub $0xffffffffffffff80,%rcx # subtract -128, because -128 fits in imm8 instead of requiring an imm32 to encode add $128, %rcx
4007c8: c5 f5 58 49 a0 vaddpd -0x60(%rcx),%ymm1,%ymm1 # one-register addressing mode can micro-fuse
4007cd: c5 ed 58 51 c0 vaddpd -0x40(%rcx),%ymm2,%ymm2
4007d2: c5 fd 58 41 e0 vaddpd -0x20(%rcx),%ymm0,%ymm0
4007d7: 4c 39 c1 cmp %r8,%rcx # compare with end with p
4007da: 75 e4 jne 4007c0 <main+0xb0>
(For more, see online compiler output at godbolt. Note I had to cast the return value of calloc, because godbolt uses C++ compilers, not C compilers. The inner loop is from .L3 to jne .L3. See https://stackoverflow.com/tags/x86/info for x86 asm links. See also Micro fusion and addressing modes, because this Sandybridge change hasn't made it into Agner Fog's manuals yet.).
performance:
$ perf stat -e task-clock,cycles,instructions,r1b1,r10e,stalled-cycles-frontend,stalled-cycles-backend,L1-dcache-load-misses,cache-misses ./fl3-vec
CS201 - Asgmt 4 - I. Forgot
sum = 0; help=6000000000
Performance counter stats for './fl3-vec':
1086.571078 task-clock (msec) # 1.000 CPUs utilized
4,072,679,849 cycles # 3.748 GHz
2,629,419,883 instructions # 0.65 insns per cycle
# 1.27 stalled cycles per insn
4,028,715,968 r1b1 # 3707.733 M/sec # unfused uops
2,257,875,023 r10e # 2077.982 M/sec # fused uops. lower than insns because of macro-fusion
3,328,275,626 stalled-cycles-frontend # 81.72% frontend cycles idle
1,648,011,059 stalled-cycles-backend # 40.47% backend cycles idle
751,736,741 L1-dcache-load-misses # 691.843 M/sec
18,772 cache-misses # 0.017 M/sec
1.086925466 seconds time elapsed
I still don't know why it's getting such low instructions per cycle. The inner loop is using 4 separate accumulators, and I checked with gdb that the pointers are aligned. So cache-bank conflicts shouldn't be the problem. Sandybridge L2 cache can sustain one 32B transfers per cycle, which should keep up with the one 32B FP vector add per cycle.
Loads 32B loads from L1 take 2 cycles (it wasn't until Haswell that Intel made 32B loads a single-cycle operation). However, there are 2 load ports, so the sustained throughput is 32B per cycle (which we're not reaching).
Perhaps the loads need to be pipelined ahead of when they're used, to minimize having the ROB (re-order buffer) fill up when a load stalls? But the perf counters indicate a fairly high L1 cache hit rate, so hardware prefetch from L2 to L1 seems to be doing its job.
0.65 instructions per cycle is only about half way to saturating the vector FP adder. This is frustrating. Even IACA says the loop should run in 4 cycles per iteration. (i.e. saturate the load ports and port1 (where the FP adder lives)) :/
update: I guess L2 latency was the problem after all. Reducing ARRAY_SIZE to 1008 (multiple of 16), and increasing N_TIMES by a factor of 10, brought the runtime down to 0.5s. That's 1.68 insns per cycle. (The inner loop is 7 total instructions for 4 FP adds, thus we are finally saturating the vector FP add unit, and the load ports.) IDK why the HW prefetcher can't get ahead after one stall, and then stay ahead. Possibly software prefetch could help? Maybe somehow avoid having the HW prefetcher run past the array, and instead start prefetching the start of the array again. (loop tiling is a much better solution, see below.)
Intel CPUs only have 32k each L1-data and L1-instruction caches. I think your array would just barely fit in the L1 on an AMD CPU.
Gcc's attempt to vectorize by broadcasting the same value into a parallel add doesn't seem so crazy. If it had managed to get this right (using multiple accumulators to hide latency), that would have allowed it to saturate the vector FP adder with only half the memory bandwidth. As-is, it was pretty much a wash, probably because of overhead in broadcasting.
Also, it's pretty silly. The N_TIMES is a just a make-work repeat. We don't actually want to optimize for doing the identical work multiple times. Unless we want to win at silly assignments like this. A source-level way to do this would be to increment i in the part of the code we're allowed to modify:
for (...) {
sum += a[j] + a[j] + a[j] + a[j];
}
i += 3; // The inner loop does 4 total iterations of the outer loop
More realistically, to deal with this you could interchange your loops (loop over the array once, adding each value N_TIMES times). I think I've read that Intel's compiler will sometimes do that for you.
A more general technique is called cache blocking, or loop tiling. The idea is to work on your input data in small blocks that fit in cache. Depending on your algorithm, it can be possible to do various stages of thing on a chunk, then repeat for the next chunk, instead of having each stage loop over the whole input. As always, once you know the right name for a trick (and that it exists at all), you can google up a ton of info.
You could rules-lawyer your way into putting an interchanged loop inside an if (i == 0) block in the part of the code you're allowed to modify. It would still do the same number of additions, but in a more cache-optimal order.
