On 5/29/22 12:59 AM, Steven D'Aprano wrote:
tan() produces an output that is grossly nonlinear (indeed wildly non-monotonic).
Why is that? The mathematical function tan is monotonically increasing in the range [0, π/2). Shouldn't tan() be the same?
I am considering tan() *near* π/2 ... not just "less than" π/2. See the graph: https://av8n.com/computer/img48/trig-function-accuracy.png cot() is well behaved in this whole neighborhood but tan() is singular. To anticipate the obvious follow-up question: Why am I considering the whole neighborhood? That's because when dealing with roundoff errors, one should prepare for *both* possibilities: some things will get rounded down while other things will get rounded up. In our case, the IEEE double representation of π/2 gets rounded down ... but the representation of π gets rounded up. tan(pi/2) 1.63312e+16 cot(pi) -8.16562e+15 Tangential remark: This is why you should test for infinity using isinf(x) rather than checking for bitwise equality x==inf. That's because tanpi(0.5) could be +inf or it could just as well be -inf. Specifically: (inf == -inf) is false but isinf(-inf) is true. _______________________________________________ gnumeric-list mailing list gnumeric-list@gnome.org https://mail.gnome.org/mailman/listinfo/gnumeric-list
