math | Arbitrary-precision arithmetic library for PHP

This problem should be solved easily using a trie.

The trie node should basically keep a track of 2 things:

1. Child nodes
2. Count of prefixes ending at current node

Insert all strings in the trie, which will be done in O(string length * number of strings). After that, simply traversing the trie, you can hash the prefixes based on the count as per your use case. For suffixes, you can use the same approach, just start traversing the strings in reverse order.

Edit:
On second thought, trie might be the most efficient way, but a simple hashmap implementation should also work here. Here's an example to generate all prefixes with count > 1.

This seems to be caused by a JVM intrinsic function for Math.cos, which is described in the related issue JDK-8242461. The behavior experienced there is not considered an issue:

The returned results reported in this bug are indeed adjacent floating-point values [this is the case here as well]

[...]

Therefore, while it is possible one or the other of the returned values is outside of the accuracy bounds, just have different return values for Math.cos is not in and of itself evidence of a problem.

For reproducible results, use the StrictMath.cos instead.

And indeed, disabling the intrinsics using -XX:+UnlockDiagnosticVMOptions -XX:DisableIntrinsic=_dcos (as proposed in the linked issue), causes Math.cos to have the same (expected) result as StrictMath.cos.

So it appears the behavior you are seeing here is most likely compliant with the Math documentation as well.

For the C code, change %f to %.99g to show more digits. This reveals erf(4) returns 0.9999999845827420852373279558378271758556365966796875.

%f requests six digits after the decimal point. The value is rounded to fit that format. %.numberf requests number digits after the decimal point and always used the “fixed” format. %.numberg requests number significant digits and uses a a “general” format that switches to exponential notation when appropriate.

For the Raku code, if you want output of “1.0” or “1.000000”, you will need to apply some formatting request to the output. I do not practice Raku, but a brief search shows Raku has printf-like features you can use, so requesting the %f format with it should duplicate the C output.

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.

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.

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

Since you're already using Docker, I'd suggest using a multi-stage build. Using a standard docker image like golang one can build an executable asset which is guaranteed to work with other docker linux images:

There are a few ways to approach this but what I'd probably do – and a generally useful pattern – is to use a subset to create a slightly over-inclusive multi and then redispatch the case you shouldn't have included. For the example you provided, that might look a bit like:

Not a perfect solution, I must admit. But it's simple and comes pretty close.
I create 5 vectors that are gonna span the space of the matrix and create random linear combinations to fill the rest of the matrix. My initial thought was that a trivial solution will be to copy those vectors 20 times.
To improve that, I created linear combinations of them with weights drawn from a uniform distribution, but then the distribution of the entries in the matrix becomes normal because the weighted mean basically causes the central limit theorm to take effect.
A middle point between the trivial approach and the second approach that doesn't work is to use sets of weights that favor one of the vectors over the others. And you can generate these sorts of weight vectors by passing any vector through the softmax function with an appropriately high temperature parameter.
The distribution is almost uniform, but the vectors are still very close to the base vectors. You can play with the temperature parameter to find a sweet spot that suits your purpose.