I'm trying to do some comparisons on different methods for calculating dot products using SSE Intrinsics, but since the methods are only a few cycles long, I have to run the instructions trillions of times for it to take more than a tiny fraction of a second. The only problem with that is that gcc with the -O3 flag is "optimizing" my main method into an infinite loop.
My code is
#include <immintrin.h>
#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <inttypes.h>
#define NORMAL 0
struct _Vec3 {
float x;
float y;
float z;
float w;
};
typedef struct _Vec3 Vec3;
__m128 singleDot(__m128 a, __m128 b) {
return _mm_dp_ps(a, b, 0b00001111);
}
int main(int argc, char** argv) {
for (uint16_t j = 0; j < (1L << 16); j++) {
for (uint64_t i = 0; i < (1L << 62); i++) {
Vec3 a = {i, i + 0.5, i + 1, 0.0};
Vec3 b = {i, i - 0.5, i - 1, 0.0};
#if NORMAL
float ans = normalDot(a, b); // naive implementation
#else
// float _c[4] = {a.x, a.y, a.z, 0.0};
// float _d[4] = {b.x, b.y, b.z, 0.0};
__m128 c = _mm_load_ps((float*)&a);
__m128 d = _mm_load_ps((float*)&b);
__m128 ans = singleDot(c, d);
#endif
}
}
}
but when I compile with gcc -std=c11 -march=native -O3 main.c and run objdump -d, it turns main into
0000000000400400 <main>:
400400: eb fe jmp 400400 <main>
is there an alternative for timing different approaches?
That's because this:
for (uint16_t j = 0; j < (1L << 16); j++) {
is an infinte loop -- the maximum value for a uint16_t is 65535 (216-1), after which it will wrap back to 0. So the test will always be true.
Even after fixing the uint16_t instead of uint64_t typo that makes your loop infinite, the actual work would still be optimized away because nothing uses the result.
You can use Google Benchmark's DoNotOptimize to stop your unused ans result from being optimized away. e.g. functions like "Escape" and "Clobber" that this Q&A is asking about. That works in GCC, and that question links to a relevant youtube video from a clang developer's CppCon talk.
Another worse way is to assign the result to a volatile variable. But keep in mind that common-subexpression elimination can still optimize away earlier parts of the calculation, whether you use volatile or an inline-asm macro to make sure the compiler materializes the actual final result somewhere. Micro-benchmarking is hard. You need the compiler to do exactly the amount of work that would happen in the real use-case, but not more.
See Idiomatic way of performance evaluation? for that and more.
Keep in mind exactly what you're measuring here.
Probably a bunch of loop overhead and probably store-forwarding stalls depending on whether the compiler vectorizes those initializers or not, but even if it does; conversion of integer to FP and 2x SIMD FP additions are comparable in cost a dpps in terms of throughput cost. (Which is what you're measuring, not latency; the difference matters a lot on CPUs with out-of-order execution depending on the context of your real use case).
Performance is not 1-dimensional at the scale of a couple instructions. Slapping a repeat loop around some work can measure the throughput or latency, depending on whether you make the input dependent on the previous output (a loop-carried dependency chain). But if your work ends up bound on front-end throughput, then loop overhead is an important part. Plus you might end up with effects due to how the machine code for your loop lines up with 32-byte boundaries for the uop cache.
For something this short and simple, static analysis is usually good. Count uops for the front-end, and ports in the back end, and analyze latency. What considerations go into predicting latency for operations on modern superscalar processors and how can I calculate them by hand?. LLVM-MCA can do this for you, so can IACA. You can also measure as part of your real loop that uses dot products.
See also RDTSCP in NASM always returns the same value for some discussion of what you can measure about a single instruction.
I have to run the instructions trillions of times for it to take more than a tiny fraction of a second
Current x86 CPUs can loop at best one iteration per clock cycle for a tiny loop. It's impossible to write a loop that runs faster than that. 4 billion iterations (in asm) will take at least a whole second on a 4GHz CPU.
Of course an optimizing C compiler could unroll your loop and be doing as many source iterations as it wants per asm jump.
I am new to SSE intrinsics and try to optimise my code by it. Here is my program about counting array elements which are equal to the given value.
I changed my code to SSE version but the speed almost doesn't change. I am wondering whether I use SSE in a wrong way...
This code is for an assignment where we're not allowed to enable compiler optimization options.
No SSE version:
int get_freq(const float* matrix, float value) {
int freq = 0;
for (ssize_t i = start; i < end; i++) {
if (fabsf(matrix[i] - value) <= FLT_EPSILON) {
freq++;
}
}
return freq;
}
SSE version:
#include <immintrin.h>
#include <math.h>
#include <float.h>
#define GETLOAD(n) __m128 load##n = _mm_load_ps(&matrix[i + 4 * n])
#define GETEQU(n) __m128 check##n = _mm_and_ps(_mm_cmpeq_ps(load##n, value), and_value)
#define GETCOUNT(n) count = _mm_add_ps(count, check##n)
int get_freq(const float* matrix, float givenValue, ssize_t g_elements) {
int freq = 0;
int i;
__m128 value = _mm_set1_ps(givenValue);
__m128 count = _mm_setzero_ps();
__m128 and_value = _mm_set1_ps(0x00000001);
for (i = 0; i + 15 < g_elements; i += 16) {
GETLOAD(0); GETLOAD(1); GETLOAD(2); GETLOAD(3);
GETEQU(0); GETEQU(1); GETEQU(2); GETEQU(3);
GETCOUNT(0);GETCOUNT(1);GETCOUNT(2);GETCOUNT(3);
}
__m128 shuffle_a = _mm_shuffle_ps(count, count, _MM_SHUFFLE(1, 0, 3, 2));
count = _mm_add_ps(count, shuffle_a);
__m128 shuffle_b = _mm_shuffle_ps(count, count, _MM_SHUFFLE(2, 3, 0, 1));
count = _mm_add_ps(count, shuffle_b);
freq = _mm_cvtss_si32(count);
for (; i < g_elements; i++) {
if (fabsf(matrix[i] - givenValue) <= FLT_EPSILON) {
freq++;
}
}
return freq;
}
If you need to compile with -O0, then do as much as possible in a single statement. In normal code, int a=foo(); bar(a); will compile to the same asm as bar(foo()), but in -O0 code, the second version will probably be faster, because it doesn't store the result to memory and then reload it for the next statement.
-O0 is designed to give the most predictable results from debugging, which is why everything is stored to memory after every statement. This is obviously horrible for performance.
I wrote a big answer a while ago for a different question from someone else with a stupid assignment like yours that required them to optimize for -O0. Some of that may help.
Don't try too hard on this assignment. Probably most of the "tricks" that you figure out that make your code run faster with -O0 will only matter for -O0, but make no difference with optimization enabled.
In real life, code is typically compiled with clang or gcc -O2 at least, and sometimes -O3 -march=haswell or whatever to auto-vectorize. (Once it's debugged and you're ready to optimize.)
Re: your update:
Now it compiles, and the horrible asm from the SSE version can be seen. I put it on godbolt along with a version of the scalar code that actually compiles, too. Intrinsics usually compile very badly with optimization disabled, with the inline functions still having args and return values that result in actual load/store round trips (store-forwarding latency) even with __attribute__((always_inline)). See Demonstrator code failing to show 4 times faster SIMD speed with optimization disabled for example.
The scalar version comes out a lot less bad. Its source does everything in one expression, so temporaries stay in registers. The loop counter is still in memory, though, bottlenecking it to at best one iteration per 6 cycles on Haswell, for example. (See the x86 tag wiki for optimization resources.)
BTW, a vectorized fabsf() is easy, see Fastest way to compute absolute value using SSE. That and an SSE compare for less-than should do the trick to give you the same semantics as your scalar code. (But makes it even harder to get -O0 to not suck).
You might do better just manually unrolling your scalar version one or two times, because -O0 sucks too much.
Some compilers are pretty good about doing optimization of vectors. Did you check the generated assembly of optimized build of both versions? Isn't the "naive" version actually using SIMD or other optimization techniques?
I understand the concept of unrolling loops however, can someone explain to me how to unroll a simple loop?
It would be great if you would show me a loop, and then a unrolled version of that loop with explanations of what is happening.
I think it's important to clarify when loop unrolling is most effective: with dependency chains. A dependency chain is a series of operations where each calculation depends on the previous calculation. For example, the following loop has a dependency chain.
for(i=0; i<n; i++) sum += a[i];
Most modern processors can do multiple out-of-order operations per cycle. This increases the instruction throughput. However, out-of-order operations can't do this in a dependency chain. In the loop above each calculation is bound by the latency of the addition operation.
In the loop above we can unroll it into two dependency chains like this
sum1 = 0, sum2 = 0;
for(i=0; i<n/2; i+=2) sum1 += a[2*i], sum2 += a[2*i+1];
for(i=(n/2)*2; i<n; i++) sum += a[i]; // clean up for n odd
sum += sum1 + sum2;
Now an out-of-order processor could operate on either chain independently and depending on the processor simultaneously.
In general you should unroll by an amount equal to the latency of the operation times the number of those operations that can be done per clock cycle. For example with a x86_64 processor it can perform at least one SSE addition per clock cycle and the SSE addition has a latency of 3 so you should unroll three times. With a Haswell processor it can do two FMA operations per clock cycle and each FMA operations has a latency of 5 so you would need to unroll 10 times to get the maximum throughput.
As far as compilers go GCC does not unroll dependency chains (even with -funroll-loops). You have to unroll yourself with GCC. With Clang it unrolls four times which is generally pretty good (in some cases on Haswell and Broadwell you would need to unroll 10 times and with Skylake 8 times).
Another reason to unroll is when the number of operations in a loop exceeds the number of instructions which can be push through per clock cycle. For example in the following loop
for(i=0; i<n; i++) b[i] += 3.14159*a[i];
there is no dependency chain so there is no problem with out-of-order execution. But let's consider an instruction set which needs the following operations per iteration.
2 SIMD load
1 SIMD store
1 SIMD multiply
1 SIMD addition
1 scalar addition for the loop counter
1 conditional jump
Let's also assume the the processor can push through five of these instructions per cycle. In this case there are seven instructions per iteration but only five can be done per cycle. Loop unrolling can then be used to amortize the cost of the scalar addition to the counter i and the conditional jump. For example if you fully unrolled the loop these instruction would not be necessary.
For amortizing the cost of the loop counter and jump -funroll-loops works fine with GCC . It unrolls eight times which means the counter addition and jump has to be done once every eight iteration instead of every iteration.
The process of unrolling loops utilizes an essential concept in computer science: the space-time tradeoff, where increasing the space used can often lead to decreasing the time of an algorithm.
Let's say we have a simple loop,
const int n = 1000;
for (int i = 0; i < n; ++i) {
foo();
}
This is compiled to assembly looking something like this:
mov eax, 0
loop:
call foo
inc eax
cmp eax, 1000
jne loop
So the space-time trade-off is 5 lines of assembly for ~(4 * 1000) = ~4000 instructions executed.
So, let's try and unroll the loop a bit.
for (int i = 0; i < n; i += 10) {
foo();
foo();
foo();
foo();
foo();
foo();
foo();
foo();
foo();
foo();
}
And its assembly:
mov eax, 0
loop:
call foo
call foo
call foo
call foo
call foo
call foo
call foo
call foo
call foo
call foo
add eax, 10
cmp eax, 1000
jne loop
The space-time trade-off is 14 lines of assembly for ~(14 * 100) = ~1400 instructions executed.
We can do a total unrolling, like this:
foo();
foo();
// ...
// 996 foo()'s
// ...
foo();
foo();
Which compiles in assembly as 1000 call instructions.
This gives a space-time trade-off of 1000 lines of assembly for 1000 instructions.
As you can see, the general trend is that to reduce the amount of instructions executed by the CPU, we must increase the space required.
It is not efficient to totally unroll a loop, as the space required becomes extremely large. Partial unrolling gives huge benefits with greatly diminishing returns the more you unroll the loop.
While it's a good idea to understand loop unrolling, keep in mind that the compiler is smart and will do it for you.
Rolled (regular):
#define N 44
int main() {
int A[N], B[N];
int i;
// fill A with stuff ...
for(i = 0; i < N; i++) {
B[i] = A[i] * (100 % i);
}
// do stuff with B ...
}
Unrolled:
#define N 44
int main() {
int A[N], B[N];
int i;
// fill A with stuff ...
for(i = 0; i < N; i += 4) {
B[i] = A[i] * (100 % i);
B[i+1] = A[i+1] * (100 % i+1);
B[i+2] = A[i+2] * (100 % i+2);
B[i+3] = A[i+3] * (100 % i+3);
}
// do stuff with B ...
}
Unrolling can potentially increase performance at the cost of a larger program size. Performance increases could be due to a reduction in branch penalties, cache misses and execution instructions. Some disadvantages are obvious, like an increase in the amount of code and a decrease in readability, and some are not so obvious.
I need to optimize some for-loops for speed (for a school assignment) without using compiler optimization flags.
Given a specific Linux server (owned by the school), a satisfactory improvement is to make it run under 7 seconds, and a great improvement is to make it run under 5 seconds. This code that I have right here gets about 5.6 seconds. I am thinking I may need to use pointers with this in some way to get it to go faster, but I'm not really sure. What options do I have?
The file must remain 50 lines or less (not counting comments).
#include <stdio.h>
#include <stdlib.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 ...
register double sum1 = 0, sum2 = 0, sum3 = 0, sum4 = 0, sum5 = 0, sum6 = 0, sum7 = 0, sum8 = 0, sum9 = 0;
register int j;
// ... and this one.
printf("CS201 - Asgmt 4 - \n");
for (i = 0; i < N_TIMES; i++)
{
// You can change anything between this comment ...
for (j = 0; j < ARRAY_SIZE; j += 10)
{
sum += array[j];
sum1 += array[j + 1];
sum2 += array[j + 2];
sum3 += array[j + 3];
sum4 += array[j + 4];
sum5 += array[j + 5];
sum6 += array[j + 6];
sum7 += array[j + 7];
sum8 += array[j + 8];
sum9 += array[j + 9];
}
// ... and this one. But your inner loop must do the same
// number of additions as this one does.
}
// You can add some final code between this comment ...
sum += sum1 + sum2 + sum3 + sum4 + sum5 + sum6 + sum7 + sum8 + sum9;
// ... and this one.
return 0;
}
Re-posting a modified version of my answer from optimized sum of an array of doubles in C, since that question got voted down to -5. The OP of the other question phrased it more as "what else is possible", so I took him at his word and info-dumped about vectorizing and tuning for current CPU hardware. :)
The OP of that question eventually said he wasn't allowed to use compiler options higher than -O0, which I guess is the case here, too.
Summary:
Why using -O0 distorts things (unfairly penalizes things that are fine in normal code for a normal compiler). Using -O0 (the gcc/clang default) so your loops don't optimize away is not a valid excuse or a useful way to find out what will be faster with normal optimization enabled. (See also Idiomatic way of performance evaluation? for more about benchmark methods and pitfalls, like ways to enable optimization but still stop the compiler from optimizing away the work you want to measure.)
Stuff that's wrong with the assignment.
Types of optimizations. FP latency vs. throughput, and dependency chains. Link to Agner Fog's site. (Essential reading for optimization).
Experiments getting the compiler to optimize it (after fixing it to not optimize away). Best result with auto-vectorization (no source changes): gcc: half as fast as an optimal vectorized loop. clang: same speed as a hand-vectorized loop.
Some more comments on why bigger expressions are a perf win with -O0 only.
Source changes to get good performance without -ffast-math, making the code closer to what we want the compiler to do. Also some rules-lawyering ideas that would be useless in the real-world.
Vectorizing the loop with GCC architecture-neutral vectors, to see how close the auto-vectorizing compilers came to matching the performance of ideal asm code (since I checked the compiler output).
I think the point of the assignment is to sort of teach assembly-language performance optimizations using C with no compiler optimizations. This is silly. It's mixing up things the compiler will do for you in real life with things that do require source-level changes.
See Why does clang produce inefficient asm with -O0 (for this simple floating point sum)?
-O0 doesn't just "not optimize", it makes the compiler store variables to memory after every statement instead of keeping them in registers. It does this so you get the "expected" results if you set a breakpoint with gdb and modify the value (in memory) of a C variable. Or even if you jump to another line in the same function. So each C statement has to be compiled to an independent block of asm that starts and ends with all variables in memory. For a modern portable compiler like gcc which already transforms through multiple internal representations of program flow on the way from source to asm, this part of -O0 requires explicitly de-optimizing its graph of data flow back into separate C statements. These store/reloads lengthen every loop-carried dependency chain so it's horrible for tiny loops if the loop counter is kept in memory. (e.g. 1 cycle per iteration for inc reg vs. 6c for inc [mem], creating a bottleneck on loop counter updates in tight loops).
With gcc -O0, the register keyword lets gcc keep a var in a register instead of memory, and thus can make a big difference in tight loops (Example on the Godbolt Compiler explorer). But that's only with -O0. In real code, register is meaningless: the compiler attempts to optimally use the available registers for variables and temporaries. register is already deprecated in ISO C++11 (but not C11), and there's a proposal to remove it from the language along with other obsolete stuff like trigraphs.
With an extra variables involved, -O0 hurts array indexing a bit more than pointer incrementing.
Array indexing usually makes code easier to read. Compilers sometimes fail to optimize stuff like array[i*width + j*width*height], so it's a good idea to change the source to do the strength-reduction optimization of turning the multiplies into += adds.
At an asm level, array indexing vs. pointer incrementing are close to the same performance. (x86 for example has addressing modes like [rsi + rdx*4] which are as fast as [rdi]. except on Sandybridge and later.) It's the compiler's job to optimize your code by using pointer incrementing even when the source uses array indexing, when that's faster.
For good performance, you have to be aware of what compilers can and can't do. Some optimizations are "brittle", and a small seemingly-innocent change to the source will stop the compiler from doing an optimization that was essential for some code to run fast. (e.g. pulling a constant computation out of a loop, or proving something about how different branch conditions are related to each other, and simplifying.)
Besides all that, it's a 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.
(You can fix this by printing sum at the end. gcc and clang don't seem to realize that calloc returns zeroed memory, and optimize it away to 0.0. See my code below.)
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, the other version of this question had an uninitialized variable kicking around. It looks like long int help was introduced by the OP of that question, not the prof. So I will have to downgrade my "utter nonsense" to merely "silly", because the code doesn't even print the result at the end. That's the most common way of getting the compiler not to optimize everything away in a microbenchmark like this.
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. 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.
Instead of just unrolling, keep multiple accumulators which you only add up at the end, like you're doing with the sum0..sum9 unroll-by-10. FP instructions have medium latency but high throughput, so you need to keep multiple FP operations in flight to keep the floating point execution units saturated.
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
Lets start by seeing what the compiler can do for us.
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: it collects the sums every time, instead of giving each thread 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. profile-guided optimization is a good idea when you can exercise all the relevant code-paths, so the compiler can make better unrolling / inlining decisions.
clang-3.5 -Ofast -march=native -ffast-math: 1.070s. (clang 3.5 is too old to support -march=sandybridge. You should prefer to use a compiler version that's new enough to know about the target architecture you're tuning for, esp. if using -march to make code that doesn't need to run on older architectures.)
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. It knows that calloc only returns 16-byte aligned memory (on x86-64 System V), and when tuning for Sandybridge (before Haswell) it knows that 32-byte loads have a big penalty when misaligned. And that splitting them isn't too expensive since a 32-byte load takes 2 cycles in a load port anyway.
vmovupd -0x60(%rbx,%rcx,8),%xmm4
vinsertf128 $0x1,-0x50(%rbx,%rcx,8),%ymm4,%ymm4
This is worse on later CPUs, especially when the data does happen to be aligned at run-time; see Why doesn't gcc resolve _mm256_loadu_pd as single vmovupd? about GCC versions where -mavx256-split-unaligned-load was on by default with -mtune=generic.
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.) In that case it uses a tight loop of 4x vaddpd mem, %ymm, %ymm. It only runs about 0.65 insns per cycle (and 0.93 uops / cycle), according to perf, so the bottleneck isn't front-end.
I checked with a debugger, and calloc is indeed returning a pointer that's an odd multiple of 16. (glibc for large allocations tends to allocate new pages, and put bookkeeping info in the initial bytes, always misaligning to any boundary wider than 16.) So half the 32B memory accesses are crossing a cache line, causing a big slowdown. It is slightly faster to do two separate 16B loads when your pointer is 16B-aligned but not 32B-aligned, on Sandybridge. (gcc enables -mavx256-split-unaligned-load and ...-store for -march=sandybridge, and also for the default tune=generic with -mavx, which is not so good especially for Haswell or with memory that's usually aligned by the compiler doesn't know about it.)
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 (from the other question) 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. 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 accumulator variables 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 the godbolt compiler explorer. The -xc compiler option compiles as C, not C++. The inner loop is from .L3 to jne .L3. See the x86 tag wiki for x86 asm links. See also this q&a about micro-fusion not happening on SnB-family, which Agner Fog's guides don't cover).
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.
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 bandwidth was the problem after all. There aren't enough line-fill buffers to keep enough misses in flight to sustain the peak throughput every cycle. L2 sustained bandwidth is less than peak on Intel SnB / Haswell / Skylake CPUs.
See also Single Threaded Memory Bandwidth on Sandy Bridge (Intel forum thread, with much discussion about what limits throughput, and how latency * max_concurrency is one possible bottleneck. See also the "Latency Bound Platforms" part of the answer to Enhanced REP MOVSB for memcpy limited memory concurrency is a bottleneck for loads as well as stores, but for loads prefetch into L2 does mean you might not be limited purely by Line Fill buffers for outstanding L1D misses.
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.) 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 64kiB L1D on an AMD K10 (Istanbul) CPU, but not Bulldozer-family (16kiB L1D) or Ryzen (32kiB L1D).
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.
You may be on the right track, though you'll need to measure it to be certain (my normal advice to measure, not guess seems a little superfluous here since the whole point of the assignment is to measure).
Optimising compilers will probably not see much of a difference since they're pretty clever about that sort of stuff but, since we don't know what optimisation level it will be compiling at, you may get a substantial improvement.
To use pointers in the inner loop is a simple matter of first adding a pointer variable:
register double *pj;
then changing the loop to:
for (pj = &(array[0]); pj < &(array[ARRAY_SIZE]); j++) {
sum += *j++;
sum1 += *j++;
sum2 += *j++;
sum3 += *j++;
sum4 += *j++;
sum5 += *j++;
sum6 += *j++;
sum7 += *j++;
sum8 += *j++;
sum9 += *j;
}
This keeps the amount of additions the same within the loop (assuming you're counting += and ++ as addition operators, of course) but basically uses pointers rather than array indexes.
With no optimisation1 on my system, this drops it from 9.868 seconds (CPU time) to 4.84 seconds. Your mileage may vary.
1 With optimisation level -O3, both are reported as taking 0.001 seconds so, as mentioned, the optimisers are pretty clever. However, given you're seeing 5+ seconds, I'd suggest it wasn't been compiled with optimisation on.
As an aside, this is a good reason why it's usually advisable to write your code in a readable manner and let the compiler take care of getting it running faster. While my meager attempts at optimisation roughly doubled the speed, using -O3 made it run some ten thousand times faster :-)
Before anything else, try to change compiler settings to produce faster code. There is general optimisation, and the compiler might do auto vectorisation.
What you would always do is try several approaches and check what is fastest. As a target, try to get to one cycle per addition or better.
Number of iterations per loop: You add up 10 sums simultaneously. It might be that your processor doesn't have enough registers for that, or it has more. I'd measure the time for 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14... sums per loop.
Number of sums: Having more than one sum means that latency doesn't bite you, just throughput. But more than four or six might not be helpful. Try four sums, with 4, 8, 12, 16 iterations per loop. Or six sums, with 6, 12, 18 iterations.
Caching: You are running through an array of 80,000 bytes. Probably more than L1 cache. Split the array into 2 or 4 parts. Do an outer loop iterating over the two or four subarrays, the next loop from 0 to N_TIMES - 1, and the inner loop adding up values.
And then you can try using vector operations, or multi-threading your code, or using the GPU to do the work.
And if you are forced to use no optimisation, then the "register" keyword might actually work.
I've spent the past few days reading about autovectorization with gcc 4.7. I followed some examples I saw online, and the setup seems to be correct. But when I actually run with the code and compare between vectorization on or off, there isn't a noticeable difference in runtime.
Here's the code I've been working with:
#include <string.h>
#include <stdlib.h>
#include <emmintrin.h>
#include <stdio.h>
#include <math.h>
int main(int argc, char** argv) {
long b = strtol(argv[2], NULL, 0);
unsigned long long int i;
unsigned long long int n = (int)pow(2,29);
float total = 0;
float *__restrict__ x1;
float *__restrict__ y1;
posix_memalign((void *)&x1, 16, sizeof(float)*n);
posix_memalign((void *)&y1, 16, sizeof(float)*n);
float *__restrict__ x = __builtin_assume_aligned(x1,16);
float *__restrict__ y = __builtin_assume_aligned(y1,16);
for (i=0;i<n;i++) {
x[i] = i;
y[i] = i;
}
for (i=0; i<n; i++) {
y[i] += x[i];
}
printf("y[%li]: \t\t\t\t%f\n", b,y[b]);
printf("correct answer: \t\t\t%f\n", (b)*2);
return 0;
}
Some of this stuff seems redundant to me, but was necessary to get the compiler to understand what was going on (especially the fact that the data were aligned). The "b" variable that's read from command line is just there because I was paranoid about the compiler optimizing away the loop entirely.
Here is the compiler command when vectorizeration is enabled:
gcc47 -ftree-vectorizer-verbose=3 -msse2 -lm -O2 -finline-functions -funswitch-loops -fpredictive-commoning -fgcse-after-reload -fipa-cp-clone test.c -ftree-vectorize -o v
Basically, this is equivalent to just using -O3. I put the flags in myself so that all I needed to do was remove "ftree-vectorize" and be able to test the result sans vectorization.
Here is the output of the ftree-vectorize-verbose flag, to show that the code is in fact being vectorized:
Analyzing loop at test.c:29
29: vect_model_load_cost: aligned.
29: vect_model_load_cost: inside_cost = 1, outside_cost = 0 .
29: vect_model_load_cost: aligned.
29: vect_model_load_cost: inside_cost = 1, outside_cost = 0 .
29: vect_model_simple_cost: inside_cost = 1, outside_cost = 0 .
29: vect_model_store_cost: aligned.
29: vect_model_store_cost: inside_cost = 1, outside_cost = 0 .
29: cost model: Adding cost of checks for loop versioning aliasing.
29: Cost model analysis:
Vector inside of loop cost: 4
Vector outside of loop cost: 4
Scalar iteration cost: 4
Scalar outside cost: 1
prologue iterations: 0
epilogue iterations: 0
Calculated minimum iters for profitability: 2
29: Profitability threshold = 3
Vectorizing loop at test.c:29
29: Profitability threshold is 3 loop iterations.
29: created 1 versioning for alias checks.
29: LOOP VECTORIZED.
Analyzing loop at test.c:24
24: vect_model_induction_cost: inside_cost = 2, outside_cost = 2 .
24: vect_model_simple_cost: inside_cost = 2, outside_cost = 0 .
24: not vectorized: relevant stmt not supported: D.5806_18 = (float) D.5823_58;
test.c:7: note: vectorized 1 loops in function.
Note that the vectorization is profitable after 3 iterations, and I'm running with 2^29~=500,000,000 iterations. So I should expect a vastly different runtime with vectorization turned off, right?
Well, here are the runtimes of the code (I ran it 20 times in a row):
59.082s
79.385s
57.557s
57.264s
53.588s
54.300s
53.645s
69.044s
57.238s
59.366s
56.314s
55.224s
57.308s
57.682s
56.083s
369.590s
59.963s
55.683s
54.979s
62.309s
Throwing away that weird ~370s outlier, that gives a mean runtime of 58.7s, with a standard deviation of 6.0s.
Next, I'll compile with the same command as before, but with no -ftree-vectorize flag:
gcc47 -ftree-vectorizer-verbose=3 -msse2 -lm -O2 -finline-functions -funswitch-loops -fpredictive-commoning -fgcse-after-reload -fipa-cp-clone test.c -o nov
Again running the program 20 times in a row yields the following times:
69.471s
57.134s
56.240s
57.040s
55.787s
56.530s
60.010s
60.187s
324.227s
56.377s
55.337s
54.110s
56.164s
59.919s
493.468s
63.876s
57.389s
55.553s
54.908s
56.828s
Again throwing away outliers, this gives a mean runtimee of 57.9s with a standard deviation of 3.6s.
So these two versions have statistically indistinguishable runtimes.
Can anyone point me to what I'm doing wrong? Does the "profitability threshold" spit out by the compiler not mean what I think it means? I really appreciate any help people can give me, I've been trying to figure this out for the past week.
EDIT:
I implemented the change that #nilspipenbrinck suggested, and it seems to have worked. I stuck the vectorized loop in a function, and called that function a boatload of times. The relative run-times are now 24.0s (sigma of <0.1s) for no vectorization vs 20.8s (sigma of <0.2s) for vectorization, or a 13% speed improvement. Not as much as I was hoping for, but at least now I know its working! Thanks for taking the time to look at my question and write an answer, I really appreciate it.
You don't do much arithmetic. Therefore the runtime of your test code is memory bound. E.g. you spend most of the time by moving the data between the CPU and memory.
Furthermore your n is very large with 2^29 elements. Therefore you don't benefit from the first and second level cache in any way.
If you want to see improvements with SSE, use a smaller n such that you only touch 8 or 16 kilobyte of data. Also make sure that the data is 'hot' e.g. it has recently been accessed by the CPU. That way the data does not have to be moved from main memory but it gets moved from the caches which is several magnitudes faster.
As an alternative you could also do a lot more arithmetic. This would give the memory prefetch system a chance to fetch the data from main memory in the background while you utilize the CPU doing math.
Summarized: If the arithmetic is faster than your system can move the memory around you will not see any benefits. Memory access times will be the bottleneck and the few cycles you save using the SSE instruction set will get lost in the noise of memory access timings.
There are several factors that determine how profitable will be to vectorize code. In this case (basing this on the output you provided) the compiler is only vectorizing one loop, I would think that's the second one because the first one would be typically ignored since there is not enough computation being done for it to be profitable to vectorize.
The running times you are posting are for the whole code, not for the loop alone, so there is only so much vectorizing will do for the overall running time. If you really want to see how much improvement is there from vectorization I would suggest running a profiler such as AMD Code XL, Intel Vtune, OProfile and such, it will tell you specifically for that loop how much improvement in terms of time and performance you are making.
Right now I'm working in evaluation of vectorizing compilers, and I would code running upt to 60 times faster with vectorization, other times the speedup is not as impressive, and it all depends on the loop, the compiler and the architecture you are using.