random | The most random module on npm

There is much debate about unsigned. Without going too much into subjective territory, consider the following: What matters is not whether the value returned from rand() cannot be negative. What matters is that rand() returns a value of a certain type and that type determines what you can do with that value. rand() never returns a negative value, but does it make sense to apply operations on the value that make the value negative? Certainly yes. For example you might want to do:

I think this gets you pretty close; might just need to adjust the various name columns and drop the extra data (I kept the grouping column).

The main idea is to recursively use pd.json_normalize with pd.concat for all availalable children levels.

EDIT: Put everything into a single function and added section to collapse the name columns like the expected output.

This is a good question... and I would have hoped there would be a practical guide somewhere. One could question if SO would be a good place to ask this question, but regardless, here's my attempt to summarize the various scale_color_*() and scale_fill_*() functions built into ggplot2. Here, we'll describe the range of functions using scale_color_*(); however, the same general rules will apply for scale_fill_*() functions.

There are 22 functions in all, but happily we can group them intelligently based on practical usage scenarios. There are three key criteria that can be used to define practically how to use each of the scale_color_*() functions:

1. Nature of the mapping data. Is the data mapped to the color aesthetic discrete or continuous? CONTINUOUS data is something that can be explained via real numbers: time, temperature, lengths - these are all continuous because even if your observations are 1 and 2, there can exist something that would have a theoretical value of 1.5. DISCRETE data is just the opposite: you cannot express this data via real numbers. Take, for example, if your observations were: "Model A" and "Model B". There is no obvious way to express something in-between those two. As such, you can only represent these as single colors or numbers.

2. The Colorspace. The color palette used to draw onto the plot. By default, ggplot2 uses (I believe) a color palette based on evenly-spaced hue values. There are other functions built into the library that use either Brewer palettes or Viridis colorspaces.

3. The level of Specification. Generally, once you have defined if the scale function is continuous and in what colorspace, you have variation on the level of control or specification the user will need or can specify. A good example of this is the functions: *_continuous(), *_gradient(), *_gradient2(), and *_gradientn().

We can start off with continuous scales. These functions are all used when applied to observations that are continuous variables (see above). The functions here can further be defined if they are either binned or not binned. "Binning" is just a way of grouping ranges of a continuous variable to all be assigned to a particular color. You'll notice the effect of "binning" is to change the legend keys from a "colorbar" to a "steps" legend.

The continuous example (colorbar legend):

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 reason is this breaking change:

DeflateStream, GZipStream, and CryptoStream diverged from typical Stream.Read and Stream.ReadAsync behavior in two ways:

They didn't complete the read operation until either the buffer passed to the read operation was completely filled or the end of the stream was reached.

And the new behaviour is:

Starting in .NET 6, when Stream.Read or Stream.ReadAsync is called on one of the affected stream types with a buffer of length N, the operation completes when:

At least one byte has been read from the stream, or The underlying stream they wrap returns 0 from a call to its read, indicating no more data is available.

In your case you are affected because of this code in Decrypt method:

If you're just going to reuse a property from a superclass but treat it as a narrower type, you should probably use the declare property modifier in the subclass instead of re-declaring the field:

The real reason is in V8 memory optimization. When you store integers - it stores the 32 bit number in place, But when you store double-number - it is stored differently (as an object) - so yValues array contains the reference but the actual value stored in heap. So in your example you just used all heap memory. To see the limit, use: console.memory and you'll see something like this:

Cache misses. When N int objects are allocated back-to-back, the memory reserved to hold them tends to be in a contiguous chunk. So crawling over the list in allocation order tends to access the memory holding the ints' values in sequential, contiguous, increasing order too.

Shuffle it, and the access pattern when crawling over the list is randomized too. Cache misses abound, provided there are enough different int objects that they don't all fit in cache.

At r==1, and r==2, CPython happens to treat such small ints as singletons, so, e.g., despite that you have 10 million elements in the list, at r==2 it contains only (at most) 100 distinct int objects. All the data for those fit in cache simultaneously.

Beyond that, though, you're likely to get more, and more, and more distinct int objects. Hardware caches become increasingly useless then when the access pattern is random.

Illustrating: