Timeline for Whittaker-Shannon interpolation: Accuracy dies with speedup; can it be fixed?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2019 at 6:00 | history | tweeted | twitter.com/StackSciComp/status/1113682787645763584 | ||
| Apr 3, 2019 at 13:01 | vote | accept | user14717 | ||
| Apr 3, 2019 at 4:30 | answer | added | njuffa | timeline score: 14 | |
| Apr 3, 2019 at 3:55 | comment | added | njuffa |
I have repro and I think I have identified the culprit. sin of large arguments polluted by rounding error. Suggest switching sin to sin_pi: return y*sin(pi<Real>()*x)/pi<Real>(); --> return y*boost::math::sin_pi(x)/pi<Real>(); Note: I used my own sinpi from this answer instead of Boost.
|
|
| Apr 2, 2019 at 23:16 | comment | added | user14717 |
The compilation is with g++-8 -O3 -march=native; none of these flags break IEEE compliance. I feel like my reference function has no need for skepticism, esp. since I draw the test values away from it's problematic range as |x| -> 1.
|
|
| Apr 2, 2019 at 20:38 | comment | added | njuffa |
(1) Make sure you are compiling with strictest adherence to IEEE-754 (for my Intel compiler that is /fp:strict for example). (2) Try explicitly using of fma() as extensively as possible (convert divisions to multiplication if need be) to guard against subtractive cancellation when combining products. (3) Be skeptical of your reference function, as it may have numerical issues, too. I would suggest using triple the precision of the actual computation you are trying to implement.
|
|
| Apr 2, 2019 at 19:48 | comment | added | user14717 | I believe (1) is discussed by Higham where he demonstrates it doesn't work; see doi.org/10.1137/0914050, I just tried (2), and it doesn't help. The summation condition number is not large at the abscissas where the unit tests fail (I computed it around to be ~5 at the problem abscissas.) There are abscissas where the condition number is ~3000, at those points, the unit tests pass. | |
| Apr 2, 2019 at 18:20 | comment | added | njuffa | Have you tried (1) Accumulating positive and negative terms separately and subtracting at the end (2) Compensated addition (Kahan summation)? | |
| Apr 2, 2019 at 15:38 | history | edited | user14717 | CC BY-SA 4.0 |
added 941 characters in body
|
| Apr 2, 2019 at 15:00 | history | edited | user14717 | CC BY-SA 4.0 |
deleted 51 characters in body; edited tags
|
| Apr 2, 2019 at 14:38 | history | asked | user14717 | CC BY-SA 4.0 |