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33c82f11c2
This uses a better rational approximation to improve the accuracy of
both functions. For exhaustive testing of asinf(3) 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
Similarly, for exhaustive testing of asinf(3) in the interval, the
current libm gives:
% ./tlibm acos -fPED -x -1 -X -0x1p-12f
Interval tested for acosf: [-1,-0.000244141]
ulp <= 0.5: 97.008% 97651921 | 97.008% 97651921
0.5 < ulp < 0.6: 2.441% 2457242 | 99.450% 100109163
0.6 < ulp < 0.7: 0.472% 475503 | 99.922% 100584666
0.7 < ulp < 0.8: 0.071% 71309 | 99.993% 100655975
0.8 < ulp < 0.9: 0.007% 7319 | 100.000% 100663294
0.9 < ulp < 1.0: 0.000% 2 | 100.000% 100663296
Max ulp: 0.914007 at -5.01484931e-01
% ./tlibm acos -fPED -x 0x1p-12f -X 1
Interval tested for acosf: [0.000244141,1]
ulp <= 0.5: 97.317% 97962530 | 97.317% 97962530
0.5 < ulp < 0.6: 2.340% 2355182 | 99.657% 100317712
0.6 < ulp < 0.7: 0.314% 316134 | 99.971% 100633846
0.7 < ulp < 0.8: 0.029% 29450 | 100.000% 100663296
Max ulp: 0.796035 at 4.99814630e-01
With the new rational approximation, exhaustive testing yields:
% ./tlibm acos -fPED -x -1 -X -0x1p-12f
Interval tested for acosf: [-1,-0.000244141]
ulp <= 0.5: 97.010% 97653245 | 97.010% 97653245
0.5 < ulp < 0.6: 2.442% 2458373 | 99.452% 100111618
0.6 < ulp < 0.7: 0.473% 476012 | 99.925% 100587630
0.7 < ulp < 0.8: 0.068% 68603 | 99.993% 100656233
0.8 < ulp < 0.9: 0.007% 7063 | 100.000% 100663296
Max ulp: 0.896189 at -5.04511118e-01
% ./tlibm acos -fPED -x 0x1p-12f -X 1
Interval tested for acosf: [0.000244141,1]
ulp <= 0.5: 97.650% 98298175 | 97.650% 98298175
0.5 < ulp < 0.6: 2.028% 2041709 | 99.679% 100339884
0.6 < ulp < 0.7: 0.292% 293555 | 99.970% 100633439
0.7 < ulp < 0.8: 0.030% 29857 | 100.000% 100663296
Max ulp: 0.775875 at 4.91849005e-01
PR: 281001
MFC after: 1 week
(cherry picked from commit 41e016289f77deb88b0ef1ec3f7b2ab3515ac7c8)
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| .. | ||
| aarch64 | ||
| amd64 | ||
| arm | ||
| bsdsrc | ||
| i387 | ||
| ld80 | ||
| ld128 | ||
| man | ||
| powerpc | ||
| riscv | ||
| src | ||
| tests | ||
| x86 | ||
| Makefile | ||
| Makefile.depend | ||
| Symbol.map | ||