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docs: abstractions in the absolute quantities article redesigned + example
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Mateusz Pusz
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@ -82,37 +82,36 @@ Despite the above drawbacks, affine space points are necessary to model some abs
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(e.g., temperatures in degrees Celsius, tared mass measurements, altitudes above some
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reference point, etc.) and do it really well. Constrained affine space arithmetic
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(e.g., preventing accidental addition of points) also improves the safety of our programs.
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This is why it is a very valuable abstraction and should be used even more often than now.
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This is why it is a valuable abstraction and should be used more even often than now.
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To improve the user experience and open the doors for new features in the future, we are
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considering adding a third abstraction for absolute quantities. In terms of properties,
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an absolute quantity will lie between points and deltas.
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| Feature | Point | Absolute | Delta |
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|--------------------------------|:----------------------:|:------------------------:|:----------------------:|
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| **Interpolation** | :white_check_mark: | :white_check_mark: | :white_check_mark: |
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| **Subtraction** | :white_check_mark: | :white_check_mark: | :white_check_mark: |
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| **Addition** | :material-close-thick: | :white_check_mark: | :white_check_mark: |
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| **Multiply/Divide** | :material-close-thick: | :white_check_mark: | :white_check_mark: |
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| **May be non-negative** | :white_check_mark: | :white_check_mark: | :material-close-thick: |
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| **Relative to origin** | Absolute & relative | Absolute (implicit only) | :material-close-thick: |
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| **Can use offset units** | :white_check_mark: | :material-close-thick: | :white_check_mark: |
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| **Conversion to offset units** | With offset | :material-close-thick: | No offset |
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| **Text output** | :material-close-thick: | :white_check_mark: | :white_check_mark: |
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| Feature | Point | Absolute | Delta |
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|--------------------------------|:----------------------:|:-----------------------------:|:----------------------:|
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| **Interpolation** | :white_check_mark: | :white_check_mark: | :white_check_mark: |
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| **Subtraction** | :white_check_mark: | :white_check_mark: | :white_check_mark: |
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| **Addition** | :material-close-thick: | :white_check_mark: | :white_check_mark: |
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| **Multiply/Divide** | :material-close-thick: | :white_check_mark: | :white_check_mark: |
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| **May be non-negative** | :white_check_mark: | :white_check_mark: | :material-close-thick: |
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| **Relative to origin** | Absolute & relative | Measured against nothing/void | :material-close-thick: |
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| **Can use offset units** | :white_check_mark: | :material-close-thick: | :white_check_mark: |
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| **Conversion to offset units** | With offset | :material-close-thick: | No offset |
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| **Text output** | :material-close-thick: | :white_check_mark: | :white_check_mark: |
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As we can see above, absolute quantities have only two limitations, and both are connected
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to the offset units' usage. They can't use those because they must remain absolute
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instead of being measured relative to some custom origin.
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It is also vital to notice that there will be no way to provide a custom origin for
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absolute quantities, even if it is defined in terms of `absolute_point_origin`. Those
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quantities are meant to model abstractions with well-established and unambiguous zero
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origins. If we allow passing absolute point origins, we could define two quantities
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of the same type measured according to different not-related origins, which would be
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too confusing.
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Absolute quantities could be considered delta quantities that represent a whole
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-- the entire entity being measured. This is why we can represent a system mass by adding
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absolute masses of all system elements or a system energy by adding absolute
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temperatures of all the system elements.
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The above also allows us to print them, as we do not need any special text to describe
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their origin.
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As those are more related to deltas than points, it is impossible to specify their origin
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points. This also allows us to print them, as we do not need any special text to describe
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their origin as they are always measured against nothing/void.
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## Interfaces refactoring
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@ -123,9 +122,9 @@ a `quantity_spec` point wrapper. For example, `quantity_point<isq::altitude[m]>`
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`quantity<point<isq::altitude[m]>>`.
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I initially planned `quantity<isq::mass>` to be the same as `quantity<delta<isq::mass>>`,
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but it turns out that deltas probably should not be the default. It is consistent with how we
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write physical expressions on paper, right? Delta symbol (∆) is always "verbose"
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in our equations, it would be nice for the C++ code to do the same. So, deltas will always
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but it turns out that deltas probably should not be the default. It is consistent with how
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we write physical expressions on paper, right? Delta symbol (∆) is always "verbose"
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in physical equations, it would be nice for the C++ code to do the same. So, deltas will always
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need to be explicit.
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And this brings us to absolute quantities. They should actually be the default we are looking
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@ -165,37 +164,90 @@ Affine space arithmetic is well-defined. However, we are adding a new type to th
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that lands between points and deltas. This is why we must agree on the arithmetic for all
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possible combinations.
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Let's try to define them here, assuming that points and absolute values share
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a common origin.
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!!! note
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If points and absolute values do not share a common absolute point origin
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the operation should fail to compile.
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### Addition
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In case of addition, a more constrained type is preserved (except for adding two points,
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which is undefined):
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Absolute quantities are deltas against nothing so adding them to a point yields another point.
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| Lhs \ Rhs | Point | Absolute | Delta |
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|--------------|:----------------------:|:--------:|:--------:|
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| **Point** | :material-close-thick: | Point | Point |
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| **Absolute** | Point | Absolute | Absolute |
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| **Delta** | Point | Absolute | Delta |
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Adding a delta to them yields a delta, as a delta may represent only a part of something and
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a whole, and a part is not a whole. The delta may also be negative and greater
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than the absolute quantity, which may yield a negative value. This is why delta is a good
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result here.
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Only adding whole non-negative entities of the system yields a system being expressed as
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an entire non-negative entity. This is why adding absolute quantities results in an absolute
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quantity.
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| Lhs \ Rhs | Point | Absolute | Delta |
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|--------------|:----------------------:|:--------:|:-----:|
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| **Point** | :material-close-thick: | Point | Point |
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| **Absolute** | Point | Absolute | Delta |
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| **Delta** | Point | Delta | Delta |
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### Subtraction
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Subtraction is more tricky. To verify the logic below, it might be helpful to ask whether
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a result may be negative when two arguments are non-negative. If the answer is true,
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the result should be a delta quantity.
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Similarly, during subtraction, regular affine space arithmetics for deltas apply.
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Subtracting an absolute quantity from a point yields a point, and trying to do the opposite
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does not make physical sense.
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| Lhs \ Rhs | Point | Absolute | Delta |
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|--------------|:----------------------:|:--------:|:--------:|
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| **Point** | Delta | Point | Point |
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| **Absolute** | Delta | Delta | Absolute |
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| **Delta** | :material-close-thick: | Delta | Delta |
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Subtracting two non-negative absolute quantities may yield a negative value if we subtract
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a larger one from the smaller one, so the result should be a delta. A similar result
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may be obtained by subtracting a delta from absolute quantity or absolute quantity from a delta.
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| Lhs \ Rhs | Point | Absolute | Delta |
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|--------------|:----------------------:|:--------:|:-----:|
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| **Point** | Delta | Point | Point |
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| **Absolute** | :material-close-thick: | Delta | Delta |
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| **Delta** | :material-close-thick: | Delta | Delta |
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!!! info
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Based on the above assumptions, one of the lines of the below code can't compile:
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```cpp
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quantity temp1 = 270 * K;
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quantity temp2 = point<K>(300);
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quantity temp3 = temp2 - temp1; // Point
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// quantity temp4 = temp1 - temp2; // Compile-time error
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quantity temp5 = temp1 - temp2.absolute(); // Delta
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```
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### Motivating example
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Let's consider a room with a table and two glasses filled with fluid on top of it.
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Let's also assume that we want to stack one on top of the other and treat them as a system
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we observe.
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{ width="500" }
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```cpp
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// absolute quantities
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quantity<isq::height[cm]> glass1_height = 20 * cm;
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quantity<isq::height[cm]> glass2_height = 15 * cm;
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// delta quantities
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quantity<delta<isq::height>[cm]> fluid_level = 16 * cm;
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// point quantities
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inline constexpr struct floor_level final : absolute_point_origin<isq::height> floor_level;
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quantity<point<isq::height[cm], floor_level>> table_top = floor_level + 1 * m;
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// quantity<point<isq::height[cm]>> glass1_top(glass1_height); // point against nothing (no length)
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// absolute results
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quantity system_height = glass1_height + glass2_height;
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// delta results
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quantity empty_height_res = glass1_height - fluid_level;
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quantity glass2_height_res = system_height - glass1_height; // could result in an absolute quantity
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assert(glass2_height_res == glass2_height);
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quantity height_diff_res = glass2_height - glass1_height; // but this one should definitely return delta
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// point results
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quantity<point<isq::height[cm], floor_level>> glass1_top = table_top + glass1_height;
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quantity point1 = glass1_top - glass1_height;
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assert(point1 == table_top);
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// quantity point2 = glass1_height - glass1_top; // no sense - does not compile
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```
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## New opportunities
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@ -228,9 +280,9 @@ It worked but was far from being physically pure and pretty.
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## Summary
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We believe that adding absolute quantities will be a major improvement in the library that
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will allow us to more correctly model physical equations making them terser and easier to
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understand at the same time.
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We believe that adding absolute quantities will be a significant improvement in the library
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that will allow us to model physical equations in a terser, more correct, easier to
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write, understand, and maintain way.
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We plan to deliver the features mentioned in this post as a part of **mp-units** V3.
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