https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=281001
Bug ID: 281001
Summary: Improve accuracy of asinf(x)
Product: Base System
Version: CURRENT
Hardware: Any
OS: Any
Status: New
Severity: Affects Only Me
Priority: ---
Component: bin
Assignee: [email protected]
Reporter: [email protected]
Created attachment 253025
--> https://bugs.freebsd.org/bugzilla/attachment.cgi?id=253025&action=edit
patch to lib/msun/src/e_asinf.c
The attached patch improves the accuracy of asinf(x). It contains a better
rational
approximation. For exhaustive testing in the interval, the current libm gives
% ./tlibm asin -fPED -x 0x1p-12f -X 1
Interval tested for asinf: [0.000244141,1]
ulp <= 0.5: 97.916% 98564994 | 97.916% 98564994
0.5 < ulp < 0.6: 2.038% 2051023 | 99.953% 100616017
0.6 < ulp < 0.7: 0.047% 47254 | 100.000% 100663271
0.7 < ulp < 0.8: 0.000% 25 | 100.000% 100663296
Max ulp: 0.729891 at 5.00732839e-01
which isn't too bad given that much of the computation is actually done in
double
floating point.
With the new rational approximation, exhaustive testing yields
% ./tlibm asin -fPED -x 0x1p-12f -X 1
Interval tested for asinf: [0.000244141,1]
ulp <= 0.5: 99.711% 100372643 | 99.711% 100372643
0.5 < ulp < 0.6: 0.288% 290357 | 100.000% 100663000
0.6 < ulp < 0.7: 0.000% 296 | 100.000% 100663296
Max ulp: 0.636344 at 5.09706438e-01
That is, it's better.
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