A variety of techniques have been used.
Deferring calculations until needed
mris_fix_topology has a hot loop, which does unnecessary calculations of the face normals
mrisComputeOptimalRetessellation and mrisComputeRandomRetessellation have a similar structure
_:_: it loops over a set of patches, or iterates on one patch. For each patch it calls
_:_:_: mrisDefectPatchFitness, which calls
_:_:_:_: mrisComputeDefectLogLikelihood, which calls
_:_:_:_:_: mrisComputeDefectMRILogUnlikelihood, which
_:_:_:_:_:_: does an expensive computation all the face normals for ALL the faces
_:_:_:_:_:_: does two other expensive steps, which only use a few of the face normals
To simplify, the original code does this
_: loop
_:_: for all fno normal[fno] = f (inputs)
_:_: for a few fno use normal[fno]
_: end loop
_: change some inputs
_: use some normal[fno]
Since only a few of the face normals are used, it is a waste of time to calculate all of them every time around the loop!
This is replaced by code that does
_: loop
_:_: for all fno: normal[fno].deferred = true
_:_: for a few fno: use normal[fno], computing it from f (inputs) if is deferred, and changing it to being no-longer deferred
_: end loop
_: compute any remaining deferred normal[fno] before their inputs can change
_: change some inputs
_: use some normal[fno]