26 Mar
2017
26 Mar
'17
3:42 p.m.
asinh(x) ~ x for |x|<C, C some a priori constant. You can't get much nicer than linear (in this case, the identity function). %i25) taylor(asinh(x),x,0,9); 3 5 7 9 x 3 x 5 x 35 x (%o25)/T/ x - -- + ---- - ---- + ----- + . . . 6 40 112 1152 Thus, for alpha=1/asinh(beta) and beta ~ 2^(-46), round(alpha*asinh(beta*x)) = x for integer |x|<2^32. At 11:45 AM 3/26/2017, Warren D Smith wrote:
Another problem: While asinh(x) is nice for large x, it is not so nice for very tiny x. I think that should cause a very bad precision loss in many real computations.