benchmark | A microbenchmark support library | Performance Testing library

Code readability, short-circuiting and it is not guaranteed that Ord will always outperform a || operand. Computer systems are more complicated than expected, even though they are man-made.

There was a case where a for loop with a much more complicated condition ran faster on an IBM. The CPU didn't cool and thus instructions were executed faster, that was a possible reason. What I am trying to say, focus on other areas to improve code than fighting small-cases which will differ depending on the CPU and the boolean evaluation (compiler optimizations).

Those samples depend on JDK internals.

Looks like since JDK 9 and JDK-8152907, Math.log is no longer intrinsified into C2 intermediate representation. Instead, a direct call to a quick LIBM-backed stub is made. This is usually faster for the code that actually uses the result. Notice how measureCorrect is faster in JDK 17 output in your case.

But for JMH samples, it limits the the compiler optimizations around the Math.log, and dead code / folding samples do not work properly. The fix it to make samples that do not rely on JDK internals without a good reason, and instead use a custom written payload.

This is being done in JMH here:

• https://bugs.openjdk.java.net/browse/CODETOOLS-7903094
• https://github.com/openjdk/jmh/pull/60

To measure the branch you are interested in and particularly the scenario when while loop becomes hot, I've used the following benchmark:

Your split splits the list in two ordered halves, so merge consumes its first argument first and then just produces the second half in full. In other words it is equivalent to ++, doing redundant comparisons on the first half which always turn out to be True.

In the true mergesort the merge actually does twice the work on random data because the two parts are not ordered.

The split though spends some work on the partitioning whereas an online bottom-up mergesort would spend no work there at all. But the built-in sort tries to detect ordered runs in the input, and apparently that extra work is not negligible.

Zen2 has 3 cycle latency for vaddpd, 5 cycle latency for vfma...pd. (https://uops.info/).

Your code with 8 accumulators has enough ILP that you'd expect close to two FMA per clock, about 8 per 5 clocks (if there aren't other bottlenecks) which is a bit less than the 10/5 theoretical max.

vaddpd and vmulpd actually run on different ports on Zen2 (unlike Intel), port FP2/3 and FP0/1 respectively, so it can in theory sustain 2/clock vaddpd and vmulpd. Since the latency of the loop-carried dependency is shorter, 8 accumulators are enough to hide the vaddpd latency if scheduling doesn't let one dep chain get behind. (But at least multiplies aren't stealing cycles from it.)

Zen2's front-end is 5 instructions wide (or 6 uops if there are any multi-uop instructions), and it can decode memory-source instructions as a single uop. So it might well be doing 2/clock each multiply and add with the non-FMA version.

If you can unroll by 10 or 12, that might hide enough FMA latency and make it equal to the non-FMA version, but with less power consumption and more SMT-friendly to code running on the other logical core. (10 = 5 x 2 would be just barely enough, which means any scheduling imperfections lose progress on a dep chain which is on the critical path. See Why does mulss take only 3 cycles on Haswell, different from Agner's instruction tables? (Unrolling FP loops with multiple accumulators) for some testing on Intel.)

(By comparison, Intel Skylake runs vaddpd/vmulpd on the same ports with the same latency as vfma...pd, all with 4c latency, 0.5c throughput.)

I didn't look at your code super carefully, but 10 YMM vectors might be a tradeoff between touching two pairs of cache lines vs. touching 5 total lines, which might be worse if a spatial prefetcher tries to complete an aligned pair. Or might be fine. 12 YMM vectors would be three pairs, which should be fine.

Depending on matrix size, out-of-order exec may be able to overlap inner loop dep chains between separate iterations of the outer loop, especially if the loop exit condition can execute sooner and resolve the mispredict (if there is one) while FP work is still in flight. That's an advantage to having fewer total uops for the same work, favouring FMA.

You can see the cost of instructions on most mainstream architecture here and there. Based on that and assuming you use for example an Intel Skylake processor, you can see that one 32-bit imul instruction can be computed per cycle but with a latency of 3 cycles. In the optimized code, 2 lea instructions (which are very cheap) can be executed per cycle with a 1 cycle latency. The same thing apply for the sal instruction (2 per cycle and 1 cycle of latency).

This means that the optimized version can be executed with only 2 cycle of latency while the first one takes 3 cycle of latency (not taking into account load/store instructions that are the same). Moreover, the second version can be better pipelined since the two instructions can be executed for two different input data in parallel thanks to a superscalar out-of-order execution. Note that two loads can be executed in parallel too although only one store can be executed in parallel per cycle. This means that the execution is bounded by the throughput of store instructions. Overall, only 1 value can only computed per cycle. AFAIK, recent Intel Icelake processors can do two stores in parallel like new AMD Ryzen processors. The second one is expected to be as fast or possibly faster on the chosen use-case (Intel Skylake processors). It should be significantly faster on very recent x86-64 processors.

Note that the lea instruction is very fast because the multiply-add is done on a dedicated CPU unit (hard-wired shifters) and it only supports some specific constant for the multiplication (supported factors are 1, 2, 4 and 8, which mean that lea can be used to multiply an integer by the constants 2, 3, 4, 5, 8 and 9). This is why lea is faster than imul/mul.

I can reproduce the slower execution with -O2 using GCC 11.2 (on Linux with a i5-9600KF processor).

The main source of source of slowdown comes from the higher number of micro-operations (uops) to be executed in the -O2 version certainly combined with the saturation of some execution ports certainly due to a bad micro-operation scheduling.

Here is the assembly of the loop with -Os:

First off, you can further reduce the theoretical cycles to 6 by replacing the first mul with uzp1 and doing the following smull and smlal the other way around: mul, mul, smull, smlal => smull, uzp1, mul, smlal This also heavily reduces the register pressure so that we can do an even deeper unrolling (up to 32 per iteration)

And you don't need v2 coefficents, but you can pack them to the higher part of v1

Let's rule out everything by unrolling this deep and writing it in assembly:

Here's the code in question, from the Python 3.10 branch (in ceval.c, and called from the same file's implementation of the BINARY_ADD opcode). As @jasonharper noted in a comment, it peeks ahead to see whether the result of the BINARY_ADD will next be bound to the same name from which the left-hand addend came. In fast(), it is (operand came from s and result stored into s), but in slow() it isn't (operand came from s but stored into t).

There's no guarantee this optimization will persist, though. For example, I noticed that your fast() is no faster than your slow() on the current development CPython main branch (which is the current work-in-progress toward an eventual 3.11 release).

As noted, there's no guarantee this optimization will persist. "Serious" Python programmers should know better than to rely on dodgy CPython-specific tricks, and, indeed, PEP 8 explicitly warns against relying on this specific one:

Code should be written in a way that does not disadvantage other implementations of Python (PyPy, Jython, IronPython, Cython, Psyco, and such).

For example, do not rely on CPython's efficient implementation of in-place string concatenation for statements in the form a += b or a = a + b ...

By default MEX compiles with the gfortran option -fdefault-integer-8. The way gfortran handles this results in what you see.

Consider the non-MEX program