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z{mqN*1sqYYmcLJ&KCw4e+unFx&(lp>r?#JtEQ~++_v6p2&9zKDKbt?Vt2TU*;pAzW zQL<)+X>{mot$(G;+1s-JGw6nYUj1}>QeLl*&~mvcr<1~*_}8ZP3*J~)Z1k_xbx-2* z;{}J$#h+{SE5BhmwQp10*>K%CCKc*i3(VuJH$9|7qM}Ml&XLZw6%k7R>y6=2Z zIAPPoS&c*F8O*NQ*; zMKw|s^3+|@opIe;0GI~uP2ofr3{hWcf7{FrG}5|n*zd*Hs+ufF^ie!HyP_oLM7b9&u9ms5W9*SvE7x=y-O z?bZ53{|$TB?4BE3aqGuM#f|f;I`^cmkpG!cZ}n`m=dAUqe22bGdRM~#=&a*^hNmn4 zyxLvS_jmu(jq<(8&nBD3OnjrCsrPL5>+-eN(*C>>yYg=KnzKKz>Rd{jujTYCb=uy! zppwJa%iOuxE__;7b&daa%GYIo*E!#tzllGquQ4^|>+;Ua<$*Ex zZ>9YEs(wr5-^ax_eztG3s^6;qy;UpDZTU3O(?8$;eeC(%{(G<7QTFZWA*CGKYahCQ zTjKnqwFuPYGT**d?vUc!C#Cmq2WmX%a(u*beQ!~8|61u4zxJ?#gg;Eyc<=q6fir@+ z>xr>j=5Mar*0;+_k00Z+du#IJT;0`^&w4I@3wWcSY4_~f>PMWV5>57N9dp;lL@x+Q zVoiP47`9MiwTkzgCGXCj|KX``Z7JWYT+#J&|I^KNrM`l^U&N6mwsLM3=JuA74d9z#Q&Lw9V>`i7ad)9NA5t2kEw5Ro4F7}+2U~Q5%dzJ=B zR8@pw=OR#B@1m#YEQXkiv%E9}b}m^osX?sEOM@|E$s!N~oL(9<7EPML?FmXasF(wq zJRC##aVe7 zXPI|EXl>TxX_HOvT%1+L-3L~8F+toUZL-PCMTa0N799YGlCi__w4Tcu3)n$H=a#{E zbIFpkA{^j=Vk~x5m0ZBo<#TZsLzJemTLxpslCz*nF0Cs;S5*=e5KF*yB}0^^#uBEB zp58u=uBsvppzOocrLoLlQI`e-1Z%P=k*P*n+43DN` `quantity>`. I initially planned `quantity` to be the same as `quantity>`, -but it turns out that deltas probably should not be the default. It is consistent with how we -write physical expressions on paper, right? Delta symbol (∆) is always "verbose" -in our equations, it would be nice for the C++ code to do the same. So, deltas will always +but it turns out that deltas probably should not be the default. It is consistent with how +we write physical expressions on paper, right? Delta symbol (∆) is always "verbose" +in physical equations, it would be nice for the C++ code to do the same. So, deltas will always need to be explicit. And this brings us to absolute quantities. They should actually be the default we are looking @@ -165,37 +164,90 @@ Affine space arithmetic is well-defined. However, we are adding a new type to th that lands between points and deltas. This is why we must agree on the arithmetic for all possible combinations. -Let's try to define them here, assuming that points and absolute values share -a common origin. - -!!! note - - If points and absolute values do not share a common absolute point origin - the operation should fail to compile. - ### Addition -In case of addition, a more constrained type is preserved (except for adding two points, -which is undefined): +Absolute quantities are deltas against nothing so adding them to a point yields another point. -| Lhs \ Rhs | Point | Absolute | Delta | -|--------------|:----------------------:|:--------:|:--------:| -| **Point** | :material-close-thick: | Point | Point | -| **Absolute** | Point | Absolute | Absolute | -| **Delta** | Point | Absolute | Delta | +Adding a delta to them yields a delta, as a delta may represent only a part of something and +a whole, and a part is not a whole. The delta may also be negative and greater +than the absolute quantity, which may yield a negative value. This is why delta is a good +result here. + +Only adding whole non-negative entities of the system yields a system being expressed as +an entire non-negative entity. This is why adding absolute quantities results in an absolute +quantity. + +| Lhs \ Rhs | Point | Absolute | Delta | +|--------------|:----------------------:|:--------:|:-----:| +| **Point** | :material-close-thick: | Point | Point | +| **Absolute** | Point | Absolute | Delta | +| **Delta** | Point | Delta | Delta | ### Subtraction -Subtraction is more tricky. To verify the logic below, it might be helpful to ask whether -a result may be negative when two arguments are non-negative. If the answer is true, -the result should be a delta quantity. +Similarly, during subtraction, regular affine space arithmetics for deltas apply. +Subtracting an absolute quantity from a point yields a point, and trying to do the opposite +does not make physical sense. -| Lhs \ Rhs | Point | Absolute | Delta | -|--------------|:----------------------:|:--------:|:--------:| -| **Point** | Delta | Point | Point | -| **Absolute** | Delta | Delta | Absolute | -| **Delta** | :material-close-thick: | Delta | Delta | +Subtracting two non-negative absolute quantities may yield a negative value if we subtract +a larger one from the smaller one, so the result should be a delta. A similar result +may be obtained by subtracting a delta from absolute quantity or absolute quantity from a delta. +| Lhs \ Rhs | Point | Absolute | Delta | +|--------------|:----------------------:|:--------:|:-----:| +| **Point** | Delta | Point | Point | +| **Absolute** | :material-close-thick: | Delta | Delta | +| **Delta** | :material-close-thick: | Delta | Delta | + +!!! info + + Based on the above assumptions, one of the lines of the below code can't compile: + + ```cpp + quantity temp1 = 270 * K; + quantity temp2 = point(300); + quantity temp3 = temp2 - temp1; // Point + // quantity temp4 = temp1 - temp2; // Compile-time error + quantity temp5 = temp1 - temp2.absolute(); // Delta + ``` + + +### Motivating example + +Let's consider a room with a table and two glasses filled with fluid on top of it. +Let's also assume that we want to stack one on top of the other and treat them as a system +we observe. + +![Absolute quantities](absolute-quantities.jpeg){ width="500" } + +```cpp +// absolute quantities +quantity glass1_height = 20 * cm; +quantity glass2_height = 15 * cm; + +// delta quantities +quantity[cm]> fluid_level = 16 * cm; + +// point quantities +inline constexpr struct floor_level final : absolute_point_origin floor_level; +quantity> table_top = floor_level + 1 * m; +// quantity> glass1_top(glass1_height); // point against nothing (no length) + +// absolute results +quantity system_height = glass1_height + glass2_height; + +// delta results +quantity empty_height_res = glass1_height - fluid_level; +quantity glass2_height_res = system_height - glass1_height; // could result in an absolute quantity +assert(glass2_height_res == glass2_height); +quantity height_diff_res = glass2_height - glass1_height; // but this one should definitely return delta + +// point results +quantity> glass1_top = table_top + glass1_height; +quantity point1 = glass1_top - glass1_height; +assert(point1 == table_top); +// quantity point2 = glass1_height - glass1_top;      // no sense - does not compile +``` ## New opportunities @@ -228,9 +280,9 @@ It worked but was far from being physically pure and pretty. ## Summary -We believe that adding absolute quantities will be a major improvement in the library that -will allow us to more correctly model physical equations making them terser and easier to -understand at the same time. +We believe that adding absolute quantities will be a significant improvement in the library +that will allow us to model physical equations in a terser, more correct, easier to +write, understand, and maintain way. We plan to deliver the features mentioned in this post as a part of **mp-units** V3.