RFC: SI Units facility for Phobos

[Andrei Alexandrescu]

On 1/5/11 10:32 AM, BCS wrote:
> Andrei Alexandrescu<SeeWebsiteForEmail at erdani.org>  wrote:
[snip]
> Ah. I see what you are getting at. OTOH I'm still not convinced it's any better.
>
> A quick check shows that 1 light years = 9.4605284 ¡Ñ 10^25
> angstroms. A mere 25 orders of magnitude differences, where IEEE754
> doubles have a range of 307 orders of magnitude. As to the issue of
> where to do the conversions: I suspect that the majority of
> computation will be between unit carrying types (particularly if the
> library is used the way I'm intending it to be) and as such, I expect
> that both performance and precision will benefit from having a
> unified internal representation.

People might want to use float for compactness, which has range 1e38 or 
so. But that's not necessarily the largest issue (see below).

> There /might/ be reason to have a very limited set of scaling factors
> (e.g. atomic scale, human scale, astro scale) and define each of the
> other units from one of them. but then you run into issues of what to
> do when you do computations that involve more than one (for example,
> computing the resolution of an X-ray telescope involves all three
> scales).

There are two issues apart from scale. One, creeping errors due to 
conversions. Someone working in miles would not like that after a few 
calculations that look integral they get 67.9999998 miles. Second, let's 
not forget the cost of implicit conversions to and from. The way I see 
it, forcing an internal unit for representation has definite issues that 
reduce its potential applicability.

> When I started writing the library, I looked at these issue just
> enough that I knew sorting it wasn't going to be a fun project. So,
> rather than hash out these issue my self, I copied as much as I could
> from the best units handling tool I know of: MathCAD. As best I can
> tell, it uses the same setup I am.

I don't know MathCAD, but as far as I understand that's a system, not a 
library, and as such might have a slightly different charter. In terms 
of charter Boost units 
(http://www.boost.org/doc/libs/1_38_0/doc/html/boost_units.html) is the 
closest library to this. I haven't looked at it for a while, but indeed 
it does address the issue of scale as I suggested: it allows people to 
store numbers in their own units instead of forcing a specific unit. In 
fact the library makes it a point to distinguish itself from an "SI" 
library as early as its second page:

"While this library attempts to make simple dimensional computations 
easy to code, it is in no way tied to any particular unit system (SI or 
otherwise). Instead, it provides a highly flexible compile-time system 
for dimensional analysis, supporting arbitrary collections of base 
dimensions, rational powers of units, and explicit quantity conversions. 
It accomplishes all of this via template metaprogramming techniques."

Like it or not, Boost units will be the yardstick against which anything 
like it in D will be compared. I hope that D being a superior language 
it will make it considerably easier to implement anything 
metaprogramming-heavy.

>> The crux of the matter is that Radians and Degrees should be distinct
>> types, and that a conversion should be defined taking one to the other.
>> How can we express that in the current library, or what could be added
>> to it to make that possible?
>>
>
> I don't think there /is/ a good solution to that problem because many
> of the computations that result in radians naturally give scalar
> values (arc-length/radius). As a result, the type system has no way
> to determine what the correct type for the expression is without the
> user forcing a cast or the like.

Not a cast, but a conversion. Consider:

void computeFiringSolution(Radians angle)
{
     auto s = sin(angle.value);
     ...
     auto newAngle = Radians(arcsin(s));
}

Much of the point of using units is that there is a good amount of being 
explicit in their handling. The user knows that sin takes a double which 
is meant in Radians. Her program encodes that assumption in a type, but 
is also free to simply fetch the value when using the untyped primitives.

> If angles are treated as an alias for scalar then the conversion to
> degrees can be handled in a reasonable way (but that would also allow
> converting any scalar value to degrees). I again punted on this one
> because people who have put more time than I have available (MathCAD
> again) couldn't come up with anything better.

ArcDegrees and Radians would be two distinct types. You wouldn't be able 
to add Angles to Radians without explicitly stating where you want to be:

ArcDegrees a1;
Radians a2;
auto a = a1 + a2; // error!
auto b = a1 + ArcDegrees(a2); // fine, b is stored in ArcDegrees
auto c = Radians(a1) + a2;    // fine, c is stored in Radians

The same goes about Kilometers and Miles:

Kilometers d1;
Miles d2;
...
auto a = d1 + d2; // error!
auto b = d1 + Kilometers(a2); // fine, b is stored in Kilometers
auto c = Miles(a1) + a2;    // fine, c is stored in Miles

>>> Again, that sounds to me like what the library does. All distance units
>>> are of the same type and internally are encoded as meters, The rest of
>>> the units are converted on access.
>> The issue is that the choice of the unified format may be problematic.
>
> The issue I see is that the choice of a non unified format will be
> problematic. Unless you can show examples (e.i. benchmarks, etc.) of
> where the current solution has precision or performance problems or
> where it's expressive power is inadequate, I will remain reluctant to
> change it.

Examples of precision issues with scaling back and forth by means of a 
multiplier shouldn't be necessary as the problem is obvious. Here's an 
example that took me a couple of minutes to produce:

immutable real metersPerLightyear = 9.4605284e15;
auto a1 = metersPerLightyear * 15.3;
auto a2 = metersPerLightyear * 16.3;
auto a3 = metersPerLightyear * 1;
writeln("Total distance in lightyears: ", (a1 - a2 + a3) / 
metersPerLightyear);
auto b1 = 15.3;
auto b2 = 16.3;
auto b3 = 1;
writeln("Total distance in lightyears: ", (b1 - b2 + b3));

Regarding expressiveness, it is quite clear that there are features 
simply missing: working in Celsius vs. Fahrenheit vs. Kelvin, allowing 
the user to define and use their own units, allowing the user to define 
units with runtime multipliers (monetary) etc. There's always a need to 
stop somewhere as the list could go on forever, but I think the current 
submission stops a bit too early.

If you believe that the library is good as it its, that's definitely 
fine. Don't forget, however, that a good part of the review's purpose is 
to improve the library, not to defend its initial design and 
implementation. A submitter who is willing to go with the library as-is 
although there are beneficial suggested improvements (and that refers to 
everything including e.g. documentation) may be less likely to maintain 
the library in the future. At least that's my perception. In contrast, 
I'm quite hopeful Jonathan will follow through with std.datetime because 
he has been willing to act on all sensible feedback.


Andrei