On a general note, instructions like division and square root are roughly equal to trig functions in cycle count on modern CPUs. So, replacing one with the other will not confer much benefit, as evidenced from the results. They're all typically implemented using LUTs, and it's hard to beat the performance of an optimized LUT, which is basically a multiplexer connected to some dedicated memory cells in hardware.
For a little toy ray tracer, it is pretty measly. But for a larger corporation (with a professional project) a 4% speed improvement can mean MASSIVE cost savings.
Some of these tiny improvements can also have a cascading effect. Imagining finding a +4%, a +2% somewhere else, +3% in neighboring code, and a bunch of +1%s here and there. Eventually you'll have built up something that is 15-20% faster. Down the road you'll come across those optimizations which can yield the big results too (e.g. the +25%).
If you're alluding to gcc vs fbstring's performance (circa 15:43), then the performance improvement is not because fbstring is faster/simpler, but due to a foundational gcc design decision to always use the heap for string variables. Also, at around 16:40, the speaker concedes that gcc's simpler size() implementation runs significantly faster (3x faster at 0.3 ns) when the test conditions are different.
People have gotten PhDs for smaller optimizations. I know. I've worked with them.
> instructions like division and square root are roughly equal to trig functions in cycle count on modern CPUs.
What's the x86-64 opcode for arcsin?
x86-64 had instructions for the exponential and logarithmic functions in Xeon Phi, but those instructions have been removed in Skylake Server and the later Intel or AMD CPUs with AVX-512 support.
However, instructions for trigonometric functions have no longer been added after Intel 80387, and those of 8087 and 80387 are deprecated.
Not required. ATAN and SQRTS(S|D) are sufficient, the half-angle approach in the article is the recommended way.
> People have gotten PhDs for smaller optimizations. I know. I've worked with them.
I understand the can, not sure about the should. Not trying to be snarky, we just seem to be producing PhDs with the slimmest of justifications. The bar needs to be higher.
I couldn't disagree more. Sure, making a 4% faster asin isn't going to change the world, but if it makes all callers a teensy bit faster, multiplied by the number of callers using it, then it adds up. Imagine the savings for a hyperscaler if they managed to made a more common instruction 4% faster.
I've spent the past few months improving the performance of some work thing by ~8% and the fun I've been having reminds me of the nineties, when I tried to squeeze every last % of performance out of the 3D graphics engine that I wrote as a hobby.