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]

How can we test it gets the right answers?

When checking code is enabled, the normal[fno] is computed from the inputs twice - once when it is deferred, and again when it is undeferred. It is checked that these two values are the same.