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.

#### How do we make sure that the undeferring is done?

If we left the FACE nx,ny,nz,orig_area members unchanged, then it would be hard to find all the users. We could just rename them, but it is easier to place them in a struct and have a function called to get a pointer to the struct, and have the function do the undeferral. This is a standard data hiding technique, implemented here in C. Now all the places that need to be changed are compilation errors.

Why put the structs into a separate vector?

If we coded this as MRIS has a vector of FACE which has one FaceNormCacheEntry member, then the loop that sets deferred = true would bring in one fno per cache line fetch. Since there are about 100,000 faces, this would bring in about 100,000 cache lines. If instead we code this as MRIS has a vector of then the same loop will bring in about 3 fno per cache line, which will run about three times faster.

It would be even faster if we separated the deferred flags from the nx,ny,nz,orig_area then the loop would go even faster - 64 fno per cache line - but every other use of them would require 2 cache line fetches. I did not measure to see whether this would be faster, because the loop was no longer important.