wiki | 🤣 | Wiki library

This problem has a fun O(n) solution.

If you draw a graph of cumulative sum vs index, then:

The average value in the subarray between any two indexes is the slope of the line between those points on the graph.

The first highest-average-prefix will end at the point that makes the highest angle from 0. The next highest-average-prefix must then have a smaller average, and it will end at the point that makes the highest angle from the first ending. Continuing to the end of the array, we find that...

These segments of highest average are exactly the segments in the upper convex hull of the cumulative sum graph.

Find these segments using the monotone chain algorithm. Since the points are already sorted, it takes O(n) time.

Typeclass laws are not part of the Haskell language, so they are not subject to the same kind of language-theoretic semantic analysis as the language itself.

Instead, these laws are typically presented as an informal mathematical notation. Most presentations do not need a more detailed mathematical exposition, so they do not provide one.

The indexing operation doesn't have an identity element. The domain and range of indexing is not necessarily the same -- the domain is arrays and objects, but the range is any type of object, since array elements and object properties can hold any type. If you have an array of integers, the domain is Array, while the range is Integer, so it's not possible for there to be an identity. a[x] will always be an integer, which can never be equal to the array itself.

And even if you have an array of arrays, there's no reason to expect any of the elements to be a reference to the array itself. It's possible to create self-referential arrays like this, but most are not. And even if it is, the self-reference could be in any index, so there's no unique identity value.

node-fetch v3 recently stopped support for the require way of importing it in favor of ES Modules. You'll need to use ESM imports now, like:

The JNDI feature was added into Log4j 2.0-beta9.

Log4j 1.x thus does not have the vulnerable code.

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.

Go to your package.json file and delete as many dependencies as you can until the project builds successfully. Then start adding back the dependencies one by one to detect which ones have troubles.

Then you can manually patch those dependencies by acceding them on node_modules/[dependencie]/android/build.gradle and setting androidx.core:core-ktx: or androidx.core:core: to a specific version (1.6.0 in my case).

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.,

(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).