FASTER | Fast persistent recoverable log and key-value store | Key Value Database library

From the cpython source code for sum sum initially seems to attempt a fast path that assumes all inputs are the same type. If that fails it will just iterate:

This worked as suggeted by nextJS docs but it takes away Rust compiler and all its benefits... Here is what I did for those who eventually get stuck...

Step 1. add this line or edit next.json.js

The math module from the standard library has a sqrt function to calculate the square root of a number. It takes any type that can be converted to float (which includes int) as an argument and returns a float.

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).

The functions provided in the Python re module do not optimize based on anchors. In particular, functions that try to apply a regex at every position - .search, .sub, .findall etc. - will do so even when the regex can only possibly match at the beginning. I.e., even without multi-line mode specified, such that ^ can only match at the beginning of the string, the call is not re-routed internally. Thus:

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.

It looks like GCC's naïveté about store-forwarding stalls is hurting its auto-vectorization strategy here. See also Store forwarding by example for some practical benchmarks on Intel with hardware performance counters, and What are the costs of failed store-to-load forwarding on x86? Also Agner Fog's x86 optimization guides.

(gcc -O3 enables -ftree-vectorize and a few other options not included by -O2, e.g. if-conversion to branchless cmov, which is another way -O3 can hurt with data patterns GCC didn't expect. By comparison, Clang enables auto-vectorization even at -O2, although some of its optimizations are still only on at -O3.)

It's doing 64-bit loads (and branching to store or not) on pairs of ints. This means, if we swapped the last iteration, this load comes half from that store, half from fresh memory, so we get a store-forwarding stall after every swap. But bubble sort often has long chains of swapping every iteration as an element bubbles far, so this is really bad.

(Bubble sort is bad in general, especially if implemented naively without keeping the previous iteration's second element around in a register. It can be interesting to analyze the asm details of exactly why it sucks, so it is fair enough for wanting to try.)

Anyway, this is pretty clearly an anti-optimization you should report on GCC Bugzilla with the "missed-optimization" keyword. Scalar loads are cheap, and store-forwarding stalls are costly. (Can modern x86 implementations store-forward from more than one prior store? no, nor can microarchitectures other than in-order Atom efficiently load when it partially overlaps with one previous store, and partially from data that has to come from the L1d cache.)

Even better would be to keep buf[x+1] in a register and use it as buf[x] in the next iteration, avoiding a store and load. (Like good hand-written asm bubble sort examples, a few of which exist on Stack Overflow.)

If it wasn't for the store-forwarding stalls (which AFAIK GCC doesn't know about in its cost model), this strategy might be about break-even. SSE 4.1 for a branchless pmind / pmaxd comparator might be interesting, but that would mean always storing and the C source doesn't do that.

If this strategy of double-width load had any merit, it would be better implemented with pure integer on a 64-bit machine like x86-64, where you can operate on just the low 32 bits with garbage (or valuable data) in the upper half. E.g.,

The original code can be re-written in the following way:

(fastest methods, 3 and 4, are at the end)

In a fast NumPy method you need to specify dtype=np.object so that NumPy does not convert Python int to its own dtypes (np.int64 or others). It will now give you correct results (checked it up to N=100000).