Closed p15-git-acc closed 3 years ago
See https://github.com/fredrik-johansson/arb/issues/360.
For positive real nu and z, the cutoff criterion appears to be affine and not depend on nu. I didn't check other values of nu or z.
Evaluating besselk(2.0, 57.9668555791947111700112064539202300037282162) for various precisions:
besselk(2.0, 57.9668555791947111700112064539202300037282162)
Before:
100 [1.136872868128306888443825590e-26 +/- 2.95e-54] 110 [1.136872868128306888443825589950e-26 +/- 4.01e-57] 120 [+/- 1.19e-9] 130 [+/- 1.17e-12] 140 [+/- 1.18e-15] 150 [+/- 1.15e-18] 160 [+/- 1.14e-21] 170 [+/- 1.13e-24] 180 [1e-26 +/- 2.46e-27] 190 [1.137e-26 +/- 2.36e-30] 200 [1.136873e-26 +/- 2.39e-33] 210 [1.136872868e-26 +/- 2.35e-36] 220 [1.136872868128e-26 +/- 4.11e-39] 230 [1.136872868128307e-26 +/- 2.14e-42] 240 [1.136872868128306888e-26 +/- 5.46e-45] 250 [1.136872868128306888444e-26 +/- 2.75e-48]
After:
100 [1.136872868128306888443825590e-26 +/- 2.95e-54] 110 [1.136872868128306888443825589950e-26 +/- 4.01e-57] 120 [1.136872868128306888443825589950094e-26 +/- 6.98e-60] 130 [1.1368728681283068884438255899500943247e-26 +/- 6.98e-64] 140 [1.136872868128306888443825589950094324651e-26 +/- 1.13e-66] 150 [1.1368728681283068884438255899500943246509356e-26 +/- 6.42e-70] 160 [1.136872868128306888443825589950094324650935557e-26 +/- 5.01e-72] 170 [1.136872868128306888443825589950094324650935557413e-26 +/- 3.10e-75] 180 [1.13687286812830688844382558995009432465093555741322e-26 +/- 5.56e-77] 190 [1.13687286812830688844382558995009432465093555741322e-26 +/- 5.48e-77] 200 [1.13687286812830688844382558995009432465093555741322e-26 +/- 5.48e-77] 210 [1.13687286812830688844382558995009432465093555741322e-26 +/- 5.48e-77] 220 [1.13687286812830688844382558995009432465093555741322e-26 +/- 5.48e-77] 230 [1.13687286812830688844382558995009432465093555741322e-26 +/- 5.48e-77] 240 [1.13687286812830688844382558995009432465093555741322e-26 +/- 5.48e-77] 250 [1.13687286812830688844382558995009432465093555741322e-26 +/- 5.48e-77]
The threshold does depend on nu, and the data I was using to determine the threshold for this PR didn't use big enough nu.
See https://github.com/fredrik-johansson/arb/issues/360.
For positive real nu and z, the cutoff criterion appears to be affine and not depend on nu. I didn't check other values of nu or z.
Evaluating
besselk(2.0, 57.9668555791947111700112064539202300037282162)
for various precisions:Before:
After: