Commits on Apr 29, 2024

1. Improve perf of Legendre polynomial calculations …

   The current code for calculating associated Legengre polynomials in
   G4LegendrePolynomial has two issues:
   
   1. It is a recursive solution to a recurrence whose time grows
      exponentially without a cache/memoization.
   
   2. The code can take a user-provided cache, but the user must be careful
      to supply a fresh cache for for each value of x or wrong results will
      be generated (silently).
   
   This commit rewrites the G4LegendrePolynomial::EvalAssocLegendrePoly
   routine to address both of these issues:
   
   1. It iteratively walks up from P[m,m,x] to P[l,m,x] in O(l-m) time.
   
   2. It eliminates use of the cache entirely. A new signature without the
      cache has been introduced, and any call made with a cache falls
      through to this new one. The cache-bearing call has been retained
      in case any external callers rely on it.
   
   3. There do not appear to be any references to this method in the Geant4
      codebase itself that pass a non-null cache. The few references that
      do exist are in G4PolarizationTransition; these have been rewritten
      to use the cache-free call.
   
   4. The list of special cases for small l and m values has been slightly
      expended (to negative m) and restructured as a case statement,
      primarily to improve readability. These have been retained since they
      appear to offer a modest performance benefit for these small cases.
   
   This new method appears to perform better (often substantially better)
   than the old one over all tested parameters, even when a proper cache
   was used. It uses the same recurrence as the old method, and results
   seem identical.

   

   isaackunen committed Apr 29, 2024
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