Port alpaka phi functions to DataFormats

[VourMa]

This PR addresses the comments from our CMSSW integration PR where people were asking us to port the generic alpaka functions to CMSSW. I copied our LST functions to the package DataFormats/Math, under the interface/alpaka folder, which I thought it would be useful for people to add any additional math functions that have been written in alpaka.

The functions are not exact copies of what we have in

cmssw/RecoTracker/LSTCore/src/alpaka/Hit.h

Lines 10 to 57 in 3950ee4

	template <typename TAcc>
	ALPAKA_FN_HOST_ACC ALPAKA_FN_INLINE float eta(TAcc const& acc, float x, float y, float z) {
	float r3 = alpaka::math::sqrt(acc, x * x + y * y + z * z);
	float rt = alpaka::math::sqrt(acc, x * x + y * y);
	float eta = ((z > 0) - (z < 0)) * alpaka::math::acosh(acc, r3 / rt);
	return eta;
	}
	template <typename TAcc>
	ALPAKA_FN_HOST_ACC ALPAKA_FN_INLINE float phi_mpi_pi(TAcc const& acc, float x) {
	if (alpaka::math::abs(acc, x) <= kPi)
	return x;
	constexpr float o2pi = 1.f / (2.f * kPi);
	float n = alpaka::math::round(acc, x * o2pi);
	return x - n * float(2.f * kPi);
	}
	template <typename TAcc>
	ALPAKA_FN_HOST_ACC ALPAKA_FN_INLINE float phi(TAcc const& acc, float x, float y) {
	return phi_mpi_pi(acc, kPi + alpaka::math::atan2(acc, -y, -x));
	}
	template <typename TAcc>
	ALPAKA_FN_HOST_ACC ALPAKA_FN_INLINE float deltaPhi(TAcc const& acc, float x1, float y1, float x2, float y2) {
	float phi1 = phi(acc, x1, y1);
	float phi2 = phi(acc, x2, y2);
	return phi_mpi_pi(acc, (phi2 - phi1));
	}
	template <typename TAcc>
	ALPAKA_FN_HOST_ACC ALPAKA_FN_INLINE float deltaPhiChange(TAcc const& acc, float x1, float y1, float x2, float y2) {
	return deltaPhi(acc, x1, y1, x2 - x1, y2 - y1);
	}
	ALPAKA_FN_ACC ALPAKA_FN_INLINE float calculate_dPhi(float phi1, float phi2) {
	// Calculate dPhi
	float dPhi = phi1 - phi2;
	// Normalize dPhi to be between -pi and pi
	if (dPhi > kPi) {
	dPhi -= 2 * kPi;
	} else if (dPhi < -kPi) {
	dPhi += 2 * kPi;
	}
	return dPhi;
	}

as I have tried to generalize, optimize and rename things a bit to be more inline with
https://github.com/SegmentLinking/cmssw/blob/master/DataFormats/Math/interface/deltaPhi.h.

Note that I have not ported the eta functions. As far as I checked and tested, it is not used in our code any longer, so it will be deleted in an upcoming PR. Also, calculate_dPhi can be replaced with

cmssw/DataFormats/Math/interface/deltaPhi.h

Line 32 in 3950ee4

constexpr float deltaPhi(float phi1, float phi2) { return reduceRange(phi1 - phi2); }

so it has also not been ported.

I have used the new functions in place of our current ones and things check out, as can be seen in:
https://uaf-10.t2.ucsd.edu/~evourlio/SDL/CMSSWPR142/compare/

Nothing much to test in this PR but feedback is welcome before I move this to cms-sw.

[VourMa]

/run all

[github-actions]

There was a problem while building and running in standalone mode. The logs can be found here.

[github-actions]

The PR was built and ran successfully with CMSSW. Here are some plots.

OOTB All Tracks

The full set of validation and comparison plots can be found here.

[ariostas]

I updated the CI to 15_0_0_pre1, so now the standalone test works again. I'll think of a way to have the CI always pick the latest release.

[VourMa]

/run all

[github-actions]

The PR was built and ran successfully in standalone mode. Here are some of the comparison plots.

The full set of validation and comparison plots can be found here.

Here is a timing comparison:

   Evt    Hits       MD       LS      T3       T5       pLS       pT5      pT3      TC       Reset    Event     Short             Rate
   avg     44.9    392.5    187.3    152.7    146.7    548.4    123.1    232.6    150.5      3.7    1982.4    1389.1+/- 382.8     525.0   explicit[s=4] (target branch)
   avg     44.9    393.7    188.0    151.3    147.7    546.7    121.5    229.3    150.3      3.2    1976.6    1385.0+/- 381.2     524.3   explicit[s=4] (this PR)

[github-actions]

The PR was built and ran successfully with CMSSW. Here are some plots.

OOTB All Tracks

The full set of validation and comparison plots can be found here.

[slava77]

thanks for the updates. I don't have anything to add; perhaps time to make a PR upstream

[ariostas]

I left a few small comments that are pretty pedantic, but I feel like they could be brought up during the review.

[ariostas]

Maybe it should be

Suggested change

	#ifndef DataFormats_Math_alpaka_deltaPhi_h
	#define DataFormats_Math_alpaka_deltaPhi_h
	#ifndef DataFormats_Math_interface_alpaka_deltaPhi_h
	#define DataFormats_Math_interface_alpaka_deltaPhi_h

[ariostas]

Isn't this name too generic? Maybe reducePhiRange would be better

[ariostas]

Since CMSSW now uses C++20 you could use std::numbers::pi_v<T> or std::numbers::inv_pi_v<T>

[VourMa]

I left a few small comments that are pretty pedantic, but I feel like they could be brought up during the review.

I agree with all your comments. However, I made sure that the new file closely follows DataFormats/Math/interface/deltaPhi.h in naming conventions and variables to follow the path of least resistance during review. At this stage, I would propose the PR upstream as is, and you can bring up these points as comments there and I would fully support implementing them (also in the non-alpaka file, if need be) - I can also bring them up if you prefer so.

[ariostas]

Ah okay, that makes sense. Then yeah, it makes more sense to leave it as it is for consistency.