FD gauge

[stloufra]

Implementation of FD gauge according to Fortran.

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Minor error of Fortran vs CudaCPP.

For instance for mu- mu+ > vm vm~ t t~ h for same set of momenta:
F: Matrix element = 5.9713719090142515E-015
C: Matrix element = 5.9713722257490237E-15 with O3
C: Matrix element = 5.9713719875208053E-15 with O0

So I debug for ihel=0 and everything is bitwise same until FFV1_1. This function is identical with unitary gauge.

Error on first computed amplitude is:
F: (4.09608603589097649E-012,-2.09848757006381190E-012)
C: (4.09608603589098296E-12, -2.09848757006381594e-12)

So the abs error is 10E-27 and relative error is 10E-15 so order of machine epsilon. I therefore asume that it is simply the error introduced by rounding and different order of evaluation of the operations.

Cross-section for 10000 events
For 14 TeV:
F: Cross-section : 2.627e-06 +- 5.864e-09 pb
C: Cross-section : 2.627e-06 +- 5.892e-09 pb

For 100 TeV:
F: Cross-section : 0.0005703 +- 3.926e-06 pb
C: Cross-section : 0.0005714 +- 3.911e-06 pb

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Validity of result checked on CUDA, CPNONE, AVX2, SSE4.

[stloufra]

To be noted - The FDgauge is supported only by MadGraph5_aMC@NLO v3.7.1 or higher. Probably should be asserted somewhere.