[phkahler]

>> Ummm, actually it did. The Taylor-series of sine and cosine is the simplest when they work with radians. Euler's formula (e^ix = cosx + isinx) is the simplest when working with radians.

That's nice, but as the article points out most implementations of trig functions on computers don't use things like Taylor series.

Another terrific use of turns is in calculating angle differences, where you take a difference and just use the fractional part of the result. No bother with wrap around at some arbitrary 2*pi value. Since it wraps at integer values we simply discard the integer part. This can even be for free when using fixed-point math.

[topaz0]

That's an obfuscation from the blog post. If you read further down in the code that is mentioned, the actual computation of sin is done by a polynomial expansion in x (radians), not y (turns). The purpose of y is mainly in case x is more than pi, and if so, what the corresponding angle in [0,pi/4) is.

[jacobolus]

You can if you want make a polynomial in turns. The CPU isn’t going to care one way or the other.

Implementations which are accurate in terms of turns even for values close to half a turn can be useful for avoiding numerical issues that sometimes pop up because π is not exactly expressible as a floating point number. These functions usually names like sinpi, cospi, etc. It would be nice if they were provided more often in standard libraries.

[bee_rider]

Based on the article, CUDA has a sinpi instruction (or whatever they call them in CUDA-land). Does anyone know -- is sinpi commonly provided in the CPU assembly extension ecosystem (avx & friends)? Light googling showed me some APIs that had implementations, but I didn't dig in enough to see if they are directly implemented in assembly (this seems like the sort of info a wizard here would know about, and probably whether these types of instructions tend to be well-implemented...).