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Not much chance of us seeing an improvements in Fourier transform implementations, then.



And yet we still do, and it's interesting why we do.

Most software, we optimize to make it more legible to the compiler.

But some software—software we don't trust ourselves to optimize without changing its meaning—we leave alone, and then instead we optimize the compiler specifically to compile that kind of software into better object code.

This is what happens with maths code (usually in FORTRAN) and the FORTRAN compilers that work on them. We don't improve the Fourier-transform implementation; we just teach the compiler how to take the "textbook" implementation we've got, and do ever-fancier things to it.

Of course, one could also improve the Fourier transform's design—but that requires a mathematician, not a software engineer. Nobody's going to come up with an algorithm with entirely-better time/space complexities just by noodling around in an editor with the existing one. They've got to start from scratch with new maths, derive new theorems, write a textbook implementation of that, and then contribute it to the codebase. And then we'll start a new cycle of getting the compiler to optimize that textbook code.


Back in 2008 (?), I was in aerospace. The big thing at that time was to become a "systems integrator" instead of a manufacturer. Obviously, while sound on the surface, the OEMs still are manufacturers today. With a higher degree of integration of third party systems, e.g. radar an so on.

Today, the same logic can be applied to all the Xaas business models out there. SaaS, PaaS, algorythms, it seems that there could be two extremes. On the one end you have companies developing the services, on the other you have businesses excelling at combining these services.


Depends is it better for NAG to do that research or for us to do it?

Our funding was to do xxx research and not go off and build a better Fourier transform in this case.

Though I do regret that we couldn't get funding to do Vision /ML on one project in the 80's truly cutting edge stuff




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