One thing that really did it for me was programming something where you would normally use floats (audio/DSP) on a platform where floats were abysmally slow. This forced me to explore Fixed-Point options which in turn forced me to explore what the differences to floats are.
Fixed point gave rise to the old programmers meme 'if you need floating point you don't understand your problem'. It's of course partially in jest but there is a grain of truth in it as well.
It is quite old, attributable to VonNeumann and Goldstine in 1947. Later Goldstine joked that if rescaling for every step was easy enough for Johnny it ought to be easy for everyone else.
The gag here being that perhaps that isn’t the best dividing line for programming talent.
It gets WORSE. Here's a quote from “The Birth of a Computer” in BYTE Magazine, February 1985, an interview with J.H. Wilkinson, noted numerical slouch, on the Manchester machines ca 1949 (p. 178):
>They were fixed point, but one of the earliest things that I did (at Turing’s request) was to program a set of subroutines for doing floating-point arithmetic.
So we ought to scale to better ourselves with self-study, meanwhile one of the first errands TURING send WILKINSON on was to rid themselves of this duty. ;)
It's interesting how many of these things we take for granted.
I'm working (and have been for a while) on something that requires both ridiculous precision and speed on a relatively puny power budget and it's been a really nice trip down memory lane regarding optimization. I discovered fixed point pretty early in my programming career when doing 3D graphics on the 6502. I never imagined that that knowledge would come in handy more than almost five decades later, but here we are.
