Quantity type can be changed with a quantity_cast<ToQS>. As those are separate casts with different side effects, we do not have the cast taking the entire quantity type as a target as this would potentially require casting the value (rep and unit) and quantity type (quantity spec).

Furthermore, I argue that qp.point_for(ToPO) is in fact also a cast of the same style: changing the representation without changing the meaning, but potentially raising truncation issues. Thus, I propose to add a value_cast to the overload set.

I am not so sure if a translation between vector spaces is a cast operation?

quantity_cast<ToQS> does something different: It allows changing the quantity type. What I was suggesting precisely was that value_cast<ToQ>(q) shall be equivalent to value_cast<ToQ::unit,ToQ::rep>(q) precisely iff the quantity type of q and ToQ is the same (or implicitly convertible), or else shall fail to compile. Thus, if I do value_cast<ToQ>, I'm guaranteed not to change the interpretation, just the representation.

I am not so sure if a translation between vector spaces is a cast operation?

Here, my line of though is again in "representation" vs "semantic meaning". For me qp.point_for(ToQP) is not a change of vector space, but a change of "coordinate system". If I want to describe to you where I live, I could chose any popular city's city-hall that you know, and tell you how many meters east I live. I could instead tell you a number of miles with respect to the same city. Or I could choose a different city. Every time, I need to adjust the number that I give you, but we're always talking about the same point, my home. Thus, in addition to the "number", I need two things of metadata to tell you what this number represents; the reference point and the unit of measurements. Furthermore, if I write down the number on paper, I could either choose scientific notation (1.23 x 10^4) or an integer (12300). So the number representation is just the third choice I have in the representation.

Of course, this only applies as long as the reference points are all embedded in the same vector space; exactly the same requirement as for point_for(ToPO). I'm not saying that point_for(ToPO) is not valuable, or even that value_cast<ToPO> would be particularly intuitive. But I do think that value_cast<Q> and value_cast<QP> are valuable (I need them all over our code): I usually start from a narrow integer representation using a custom unit and reference point as read out by a piece of hardware (say, an uint16 measuring in units of 2^-7 degree Celsius, with zero corresponding to -45 degree Celsius). I keep that representation around for as long as possible, but eventually, it may go into a feedback loop, which expects a completely different representation (floating point, units of 1 degree Celsius, reference point + 30 degree Celsius). At this point, I don't care anymore that I started off with a specific sensor's representation, I just want that temperature point here. I'm aware that my sensor has a different measurement resolution and value range than the target quantity point, but I'm fine with that. So I ask my chosen units library to please do the conversion for me, I still want the same temperature point, up to small rounding issues.

Sure, I understand. Do you have good motivating examples for such a use case, as I will need to defend this in the ISO C++ Committee? Said otherwise, do you often change both a unit and a representation type?

We cross-posted, but the second paragraph (minus the point-origin discussion) also is the motivating example for the value_cast<ToQ> use-case: Starting-off from a representation close to the sensor hardware, which is typically not exactly represented in SI units (but defined with respect to an SI unit), going to a unit that is an actual SI unit; widening the representation in the process (often just float - but only because my microcontroller does in fact have a floating-point coprocessor).

E.g. a lidar sensor could output as quantity<isq::distance[pow<2,-25>*si::second*si::speed_of_light],uint16> (counting time using a 32 MHz clock), but eventually, I may want to have quantity<si::milli<si::metre>,int32>. The source type often comes in as a generic function argument, and the output type may be specified as part of a member variable, so I may not actually know the exact choice of unit nor representation type in that part of the code, and instead rely on the people choosing the sensor and architecting the API to choose sensible units.

OK, so we can consider adding those overloads. I would prefer to be conservative first and require quantity specs to be exactly the same. Unless you have a good motivation example for the implicitly convertible ones?

Unfortunately, I am unable to implement those things now as we have an ISO C++ Committee mailing deadline 12 days from now, and I scope on writing the next revisions of the papers. It sucks, but most of my time lately is spent on writing those papers instead of extending the library. And the backlog of things to design and implement grows all the time...

Can you provide a PR?

I'll try. I do have a deadline for this refactor myself (a customer needs a firmware update in just 7 days from now).

Thanks a lot! And good luck. A week for a refactor is not that much at all.

How do I test "equality" of quantity specs?

Just use op==.