Compile-time const (and constexpr) vs constant-memory constants (layouts; physics parameters?)

[valassi]

I dump here a few observations I made while analysing AOS/SOA/ASA memory layouuts is issue #16. Th ebottom line is that there is a (small) performance penalty in using constant memory for variables that could instead be taken as compile time constants.

In that context, I want to compare a few different layouts (eg ASA with 1, 2, 4.. events per "page"). Initially my code was only allowing some parameters to be defined at compile time, so every different test needed a rebuild. I then thought of allowing runtime choices of these parameters.

This is implemented here for instance: 576ba40. In this version both the random and momenta lyaouts (neppM and neppR) are ready to be received as command line options (not done fully yet). For neppR, this is passed around in function signatures. For neppM, this wwould have been too complex an dI pass it around in device constant memory.

Anyway, the point is that then I compared, for the same choice neppM=32, the difference between the compile time and constant memory constants. It is clear that there is a performance penalty, even if small. This is at the level of 5%, eg throughput goes down from 6.0E8 to 5.0E8 (all these numbers have the usual large spread due to VM load). I compared with ncu the profiles, and this is quite interesting. I would say that the problem is not an extra load on memory (constant memory is fast), but rather the fact that there are extra arithmetic operations which somehow can be avoided if the constants are known at compile time.

This is the overview

One of the most interesting plots is the instruction statistics. Here it is clear that the constant memory version needs many more IMAD (integer multiply and add) operations. I believe these are the runtime calculation of the momenta indices, which comehoe can otherwise be avoided if the constants are know at compile time

Also interesting to know that 2 more registers are used, but this has impact on occupancy

Conclusion: if possible, it is best to use compile-time constants rather than constant memory. The difference is small, but it's probably worth it to avoid the penalty unless necessary.

• For my ASA studies, I will consider several options. One, keep compile time constants and rebuild for every test. Two, use constant memory and accept the penalty, only for the purpose of comparing options (but then again, I would not be comparing final codes which have these hardcoded at compile time...). Three, ugly and cumbersome, use template for all possible options I want to study, but then it means having much larger executables (embed all possible values of int in functions), more complex makefiles (all templated functions muct be compiled in the same unit as the main, probably), and a more polluted code with templates everywhere. I will probably stay with option one and clean up around that.
• For physics parameters, one may eventually think of hardcoding them rather that reading them from a file into constant memory. All code is auto-generated anyway, so this is entirely feasible. One should study if it makes any difference in performance.

[valassi]

For completeness, I did the same study on the other parameter neppR fo rthe random number array layout. The relevant function is now rambo get final momenta, not sigmakin. I use the same neppR=32, but in one case it is constant at compile time, in another it is passed dynamically (via function signatures). I get he same results as before: there is a sall penalty from using dynamic parameters. I do not observe this as a change in rambo throughput (but thats because the copy backl to host is even heavier). I do see however again a reduction in SM and memory usage, and in increase in IMAD. The number of registers is unchanged (I am not using constant memory here).

Overview

IMAD increase

Note also (same as in the previous case, but I did not add the plot) that there is a higher number of stalled for no instructions.

The difference is again a single line change here
2d0eb1e

Conclusions:

• For ASA layouts neppR and neppM, I will move back to compile-time constants. I will remove all other code I had tested to make this more dynamic, and I will investigate options with header changes and rebuilds...

[valassi]

En passant, using compile time constants allows the use of casts to multidimensional arrays, which may make the code more readable.
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The performance is the same

[valassi]

Discussion with Stefan and Olivier. Should check again the effect of having masses/couplings in constant memory instead of compile time constants. Chek again that we save 4 registers. Is this because some are 0? (And are there couplings that are not purely real or purely imaginary?)

[valassi]

I have just changed the title to mention constexpr. I realised that I am using const in amny places in the code where constexpr would be possible. Not sure if this could also give some speedups, but I dump this idea also in this same basket...

[valassi]

As discussed in PR #306, constexpr is a fundamental ingredient of any strategy to use hardcoded parameters. I am merging a PR with a first implmentation of this, but precisely some constexpr issues in complex will need to be fixed (#307)

[valassi]

The option to use compile time constants for physics parameters is now fully functional (HRDCOD=1), for instance thorugh MR #306. I would close the older issue #23 where the initial studies were done, for issue cleanup, but I would keep #39 still open for further studies. It is still not completely clear to me when/if one option is sfatsre than the other. In reweighting in any case we need HRDCOD=0, rather than HRDCOD=1. Closing #23 and leaving #39 open.