units | Measuring stuff usually involves dealing with units

Looking into UTF8 decoding performance, I noticed the performance of protobuf's UnsafeProcessor::decodeUtf8 is better than String(byte[] bytes, int offset, int length, Charset charset) for the following non ascii string: "Quizdeltagerne spiste jordbær med flØde, mens cirkusklovnen".

I tried to figure out why, so I copied the relevant code in String and replaced the array accesses with unsafe array accesses, same as UnsafeProcessor::decodeUtf8. Here are the JMH benchmark results:

(Note! This question particularly covers the state of C++14, before the introduction of inline variables in C++17)

• What constitutes odr-use of a constexpr variable used in the definition of an inline function, such that multiple definitions of the function violates [basic.def.odr]/6?

(... likely [basic.def.odr]/3; but could this silently introduce UB in a program as soon as, say, the address of such a constexpr variable is taken in the context of the inline function's definition?)

TLDR example: does a program where doMath() defined as follows:

I've got data with time (seconds) on the x axis and intensity (in relative fluorescent units, or rfu) on the y-axis. It's generated by watching fragments of DNA pass a camera - the bigger the DNA fragment the bigger the time. There are 23 fragments of known size (in DNA base pair units, bp), and therefore there should be 23 peaks. As I know the size of the DNA fragments in bp, I want to recalibrate the x-axis from time (seconds) to base pairs (bp) using a linear model.

Unfortunately there is quite a lot of noise in the data that produces spurious peaks. The only way to confidently tell the true ones from the false ones is that the false ones don't fit the expected pattern in DNA base pairs.

I've provided data from one sample at this link in a data frame called demo. Unfortunately it's too large to paste below.

https://1drv.ms/t/s!AvBi5ipmBYfrhf0v_kvWuN2foLyBgg?e=RWfdXZ

I can pick out all the peaks as follows.

I borrowed the R code from the link and produced the following graph:

Using the same idea, I tried with my data as follows:

(Disclaimer: I'm not 100% sure how codatatype works, especially when not referring to terminal algebras).

Consider the "category of types", something like Hask but with whatever adjustment that fits the discussion. Within such a category, it is said that (1) the initial algebras define datatypes, and (2) terminal algebras define codatatypes.

I'm struggling to convince myself of (2).

Consider the functor T(t) = 1 + a * t. I agree that the initial T-algebra is well-defined and indeed defines [a], the list of a. By definition, the initial T-algebra is a type X together with a function f :: 1+a*X -> X, such that for any other type Y and function g :: 1+a*Y -> Y, there is exactly one function m :: X -> Y such that m . f = g . T(m) (where . denotes the function combination operator as in Haskell). With f interpreted as the list constructor(s), g the initial value and the step function, and T(m) the recursion operation, the equation essentially asserts the unique existance of the function m given any initial value and any step function defined in g, which necessitates an underlying well-behaved fold together with the underlying type, the list of a.

For example, g :: Unit + (a, Nat) -> Nat could be () -> 0 | (_,n) -> n+1, in which case m defines the length function, or g could be () -> 0 | (_,n) -> 0, then m defines a constant zero function. An important fact here is that, for whatever g, m can always be uniquely defined, just as fold does not impose any contraint on its arguments and always produce a unique well-defined result.

This does not seem to hold for terminal algebras.

Consider the same functor T defined above. The definition of the terminal T-algebra is the same as the initial one, except that m is now of type X -> Y and the equation now becomes m . g = f . T(m). It is said that this should define a potentially infinite list.

I agree that this is sometimes true. For example, when g :: Unit + (Unit, Int) -> Int is defined as () -> 0 | (_,n) -> n+1 like before, m then behaves such that m(0) = () and m(n+1) = Cons () m(n). For non-negative n, m(n) should be a finite list of units. For any negative n, m(n) should be of infinite length. It can be verified that the equation above holds for such g and m.

With any of the two following modified definition of g, however, I don't see any well-defined m anymore.

First, when g is again () -> 0 | (_,n) -> n+1 but is of type g :: Unit + (Bool, Int) -> Int, m must satisfy that m(g((b,i))) = Cons b m(g(i)), which means that the result depends on b. But this is impossible, because m(g((b,i))) is really just m(i+1) which has no mentioning of b whatsoever, so the equation is not well-defined.

Second, when g is again of type g :: Unit + (Unit, Int) -> Int but is defined as the constant zero function g _ = 0, m must satisfy that m(g(())) = Nil and m(g(((),i))) = Cons () m(g(i)), which are contradictory because their left hand sides are the same, both being m(0), while the right hand sides are never the same.

In summary, there are T-algebras that have no morphism into the supposed terminal T-algebra, which implies that the terminal T-algebra does not exist. The theoretical modeling of the codatatype Stream (or infinite list), if any, cannot be based on the nonexistant terminal algebra of the functor T(t) = 1 + a * t.

Many thanks to any hint of any flaw in the story above.

The undesired functionality
In Chrome 95 there was introduced new functionality where the user can hover and click on the unit part of a css value to hotswap the unit.
The feature is part of a package solution that has been labeled "Length Authoring Tools" in the release notes, and can be seen in action and described in detail in the release notes on the official blog.

How can this feature be disabled?

Issue 1:

If a css-line in the inspector says padding: 0 10px; then the user can click the px-part of the line and open a selector that let's the user swap px to other units such as rem,vmax or in.
Clicking this part of the value no longer lets the user edit the entire value quickly. Most users already know what unit they desire to use beforehand, so they do not need to be helped to accidentally select pt or vw when working exclusively with px everywhere else.

Issue 2:

When selecting and copying properties from the inspector there is now inserted whitespaces/new lines between the value and the unit since the unit portion seems to be considered a separate element. This makes prototyping in the devtools and copy/pasting to external documents very tedious and broken.

I have downloaded a list of all the towns and cities etc in the US from the census bureau. Here is a random sample:

Consider a program with the following two translation units:

I am working with OSM data to create vector street maps. For the roads, I use line geometry provided by OSM and add a buffer to convert the line to geometry that looks like a road.

My question is related to geometry, not OSM, so I will use basic lines for simplicity.