Steve Kargl 41e016289f Improve accuracy of asinf(3) and acosf(3) ... 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		2024-08-29 21:44:48 +02:00
..
aarch64	Remove residual blank line at start of Makefile	2024-07-15 16:43:39 -06:00
amd64	Remove residual blank line at start of Makefile	2024-07-15 16:43:39 -06:00
arm	Remove residual blank line at start of Makefile	2024-07-15 16:43:39 -06:00
bsdsrc	lib/msun: Cleanup after $FreeBSD$ removal	2024-01-28 17:00:23 +02:00
i387	Remove residual blank line at start of Makefile	2024-07-15 16:43:39 -06:00
ld80	msun/ld80/e_powl.c: make powl() thread-safe by making static variables thread-local	2024-08-07 11:46:48 +03:00
ld128	libmsun: remove duplicates after cdefs.h added inline to __always_inline	2024-06-25 10:40:14 -07:00
man	erf.3: Add a STANDARDS section	2024-06-23 12:50:47 +02:00
powerpc	Remove residual blank line at start of Makefile	2024-07-15 16:43:39 -06:00
riscv	Remove residual blank line at start of Makefile	2024-07-15 16:43:39 -06:00
src	Improve accuracy of asinf(3) and acosf(3)	2024-08-29 21:44:48 +02:00
tests	Remove residual blank line at start of Makefile	2024-07-15 16:43:39 -06:00
x86
Makefile	lib/msun: Fix tgammal(3) on IEEE 128-bit platforms	2024-03-18 09:48:43 +00:00
Makefile.depend
Symbol.map