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opnsense-src/lib/msun/src
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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
..
catrig.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
catrigf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
catrigl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_acos.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_acosf.c Improve accuracy of asinf(3) and acosf(3) 2024-08-29 21:44:48 +02:00
e_acosh.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_acoshf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_acoshl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_acosl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_asin.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_asinf.c Improve accuracy of asinf(3) and acosf(3) 2024-08-29 21:44:48 +02:00
e_asinl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_atan2.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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e_gamma_r.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_gammaf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_gammaf_r.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_hypot.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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e_jnf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_lgamma.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_lgamma_r.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_lgammaf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_lgammaf_r.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_lgammal.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_log.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_log2.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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e_log10.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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e_logf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_pow.c pow,powf(3),__ieee754_rem_pio2(f): Avoid negative integer left shift UB 2024-04-23 14:04:07 -06:00
e_powf.c pow,powf(3),__ieee754_rem_pio2(f): Avoid negative integer left shift UB 2024-04-23 14:04:07 -06:00
e_rem_pio2.c libmsun: remove duplicates after cdefs.h added inline to __always_inline 2024-06-25 10:40:14 -07:00
e_rem_pio2f.c libmsun: remove duplicates after cdefs.h added inline to __always_inline 2024-06-25 10:40:14 -07:00
e_remainder.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_remainderf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_remainderl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_scalb.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_scalbf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_sinh.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_sinhf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_sinhl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_sqrt.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
e_sqrtf.c Purge more stray embedded $FreeBSD$ strings 2023-09-25 07:54:56 -07:00
e_sqrtl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
fenv-softfloat.h Remove $FreeBSD$: two-line .h pattern 2023-08-16 11:54:16 -06:00
k_cos.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_cosf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_cospi.h [LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] 2021-10-26 02:50:20 +03:00
k_exp.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_expf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_log.h lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_logf.h lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_rem_pio2.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_sin.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_sincos.h lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_sincosf.h lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_sincosl.h lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_sinf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_sinpi.h [LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] 2021-10-26 02:50:20 +03:00
k_tan.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
k_tanf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
math.h math.h: Remove support for old gcc versions 2024-06-20 20:41:09 -06:00
math_private.h msun: Fix typo in comment 2024-08-21 14:59:07 +08:00
s_asinh.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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s_cos.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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s_cosl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_cospi.c Fixes for bugs in sinpi/cospi/tanpi 2023-08-03 07:27:58 +03:00
s_cospif.c Fixes for bugs in sinpi/cospi/tanpi 2023-08-03 07:27:58 +03:00
s_cpow.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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s_erff.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_exp2.c msun: Fix math error in comment explaining y reduction 2024-04-12 16:15:04 -06:00
s_exp2f.c msun: Fix math error in comment explaining y reduction 2024-04-12 16:15:04 -06:00
s_expm1.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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s_fma.c libm: fma: correct zero sign with small inputs 2024-07-28 17:37:45 -04:00
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s_fmal.c libm: fma: correct zero sign with small inputs 2024-07-28 17:37:45 -04:00
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s_isfinite.c Remove $FreeBSD$: two-line .h pattern 2023-08-16 11:54:16 -06:00
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s_llrint.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
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s_lrintl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_lround.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_lroundf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_lroundl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_modf.c lib: Remove ancient SCCS tags. 2023-11-26 22:23:28 -07:00
s_modff.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_modfl.c Remove $FreeBSD$: two-line .h pattern 2023-08-16 11:54:16 -06:00
s_nan.c Remove $FreeBSD$: two-line .h pattern 2023-08-16 11:54:16 -06:00
s_nearbyint.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_nextafter.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_nextafterf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_nextafterl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_nexttoward.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_nexttowardf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_remquo.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_remquof.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_remquol.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_rint.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_rintf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_rintl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_round.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_roundf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_roundl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_scalbln.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_scalbn.c msun: Add copyright notices 2021-10-22 22:00:54 -06:00
s_scalbnf.c msun: Add copyright notices 2021-10-22 22:00:54 -06:00
s_scalbnl.c msun: Add copyright notices 2021-10-22 22:00:54 -06:00
s_signbit.c Remove $FreeBSD$: two-line .h pattern 2023-08-16 11:54:16 -06:00
s_signgam.c
s_significand.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_significandf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_sin.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_sincos.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_sincosf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_sincosl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_sinf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_sinl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_sinpi.c Fixes for bugs in sinpi/cospi/tanpi 2023-08-03 07:27:58 +03:00
s_sinpif.c Fixes for bugs in sinpi/cospi/tanpi 2023-08-03 07:27:58 +03:00
s_tan.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_tanf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_tanh.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_tanhf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_tanhl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_tanl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_tanpi.c Fixes for bugs in sinpi/cospi/tanpi 2023-08-03 07:27:58 +03:00
s_tanpif.c Fixes for bugs in sinpi/cospi/tanpi 2023-08-03 07:27:58 +03:00
s_tgammaf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_trunc.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_truncf.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
s_truncl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
w_cabs.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
w_cabsf.c Purge more stray embedded $FreeBSD$ strings 2023-09-25 07:54:56 -07:00
w_cabsl.c lib/msun: Cleanup after $FreeBSD$ removal 2024-01-28 17:00:23 +02:00
w_drem.c msun: Rewrite function definitions with identifier lists 2022-07-12 13:17:47 +08:00
w_dremf.c Remove $FreeBSD$: one-line .c comment pattern 2023-08-16 11:54:29 -06:00