@Thomas Klemm -> CORDIC Article

[Paul Dale]

(06-02-2014 11:20 PM)pito Wrote:  Maybe it depends on how you calculate the trig functions - do you iterate Taylor against an epsilon smaller than set precision? I did it that way with decNumber (long time back though) and afaik the results were precise to the last digit.

Yes, this is what is used for SIN, COS. I will change this in the 43S, naïve Taylor series expansions aren't ideal for fixed precision results.

It won't necessarily be precise to the last digit however. Consider COS(PI/2-ULP). The Taylor series for COS(x) starts 1 - x^2/2 + ... The import thing is the leading 1. Since COS(PI/2-ULP) is very very close to zero, the Taylor expansion is subtracting almost 1 from 1 which causes quite a number of lost digits. This can be mitigated of course but you have to realise it is happening.

- Pauli