We start of with a range reduction to [0, pi/4] (presumably this would be [0, 1/8] in cycles), and then the polynomial happens.
If cycles really were that better, why isn't this implemented as starting with a conversion to cycles, then removal of the interval part, and then a division by 8, followed by whatever the appropriate polynomial/rational function is?
> adding or subtracting Pi or its submultiples cannot be done exactly.
I was also assuming that we've been talking about floating point this whole time.
I was assuming that as part of the table stakes of the conversation.
Let's look at something basic and traditional like Cephes: https://github.com/jeremybarnes/cephes/blob/master/cmath/sin...
We start of with a range reduction to [0, pi/4] (presumably this would be [0, 1/8] in cycles), and then the polynomial happens.
If cycles really were that better, why isn't this implemented as starting with a conversion to cycles, then removal of the interval part, and then a division by 8, followed by whatever the appropriate polynomial/rational function is?
> adding or subtracting Pi or its submultiples cannot be done exactly.
I was also assuming that we've been talking about floating point this whole time.