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Some math/flonum functions have much larger error than expected

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#38 2 comentarios 0 reacciones 0 asignados Ver en GitHub

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Evaluación

Dificultad
5/5
Tiempo estimado
Más de una semana
Aptitud para principiantes
25/100
Tipo de issue
Error
Claridad
Bastante claro
Estado de actividad
Estancado
Área
backend

Línea de trabajo

Start with the fl2+, fl2-, fl2exp, flexp/error, and fl2expm1 cases shown in the issue, comparing their outputs with the cited bf results. Done means the reported error is brought into line with the documented ulp bounds and the examples no longer reproduce the large discrepancies.

Escrito por el modelo de indexación a partir del texto del issue.

Descripción

Random testing (see #35) discovered a number of cases where functions such as fl2+ and fl2- have substantial error (32 ulps) and functions such as fl2exp, flexp/error, and fl2expm1 have very large error (4e15 ulps, for example).

The documentation says (quoting a few different places):

For arithmetic, error is less than 8 ulps. For fl2exp and fl2expm1, error is less than 3 ulps. For flexp/error and flexpm1/error, the largest observed error is 3 ulps.

Here are some examples:

(fl2+ -6.999886226206346e+45 5.792628225761353e+29 6.9274150349997e+45 5.2105937810748895e+29)                 => -7.247119120664389267701608263587e+43
(bf+ (bf -6999886226206345021638066463653546405883019264) (bf 6927415034999701128961050381017604717751042048)) => -7.247119120664389267701608263594e+43
(fl+ -6.999886226206346e+45 6.9274150349997e+45)                                                               => -7.247119120664499299921676626019e+43
error is 32.0 ulps (relative 9.70989202827024208564e-31, absolute 7.0368744177664e+13) with precision 500                                                   
error when just using floats is 111.10414941005564 ulps (relative 1.5182891054545697262e-14, absolute 1.10032220068362431535e+30) with precision 500        
                                                                                                                                                                                                                                                                                                                      
(fl2- -6.307625868783824e-189 -7.650829856531877e-206 -6.221347182541859e-189 3.486864837367133e-205)               => -8.627868624196532783073584510346e-191
(bf- (bf "-6.307625868783823708767532620142220868851e-189") (bf "-6.221347182541858380936796775038726932571e-189")) => -8.627868624196532783073584510349e-191                                                                                                                                                           
(fl- -6.307625868783824e-189 -6.221347182541859e-189)                                                               => -8.627868624196490263595354307142e-191                                                                                                                                                           
error is 12.0 ulps (relative 3.84769743523996817173e-31, absolute 3.3197427976908391985e-221) with precision 128                                    
error when just using floats is 34.12753813992254 ulps (relative 4.92815550192302754348e-15, absolute 4.25194782302032044546e-205) with precision 128
 
(flexp/error -247.29245235328085)                         => 4.001773708963990941924920379399e-108
(bfexp (bf #e-247.2924523532808507297886535525321960449)) => 4.001773708963991419271664949602e-108
(flexp -247.29245235328085)                               => 4.001773708963991129369240222464e-108
error is 2842247977943596.5 ulps (relative 1.19283792459564869331e-16, absolute 4.77346744570203899599e-124) with precision 128
error when just using floats is 0.383283456465281 ulps (relative 7.24434827680924324972e-17, absolute 2.8990242472713825709e-124) with precision 128

(fl2exp 249.9020736185187 6.819710735232684e-15)         => 3.39696903982644185464484379844e+108
(bfexp (bf #e249.9020736185187058693838948394391650218)) => 3.396969039826441449441493860216e+108
(flexp 249.9020736185187)                                => 3.396969039826418533426604116558e+108
error is 3499404429155425.5 ulps (relative 1.19283792459564860048e-16, absolute 4.05203349938224559331e+92) with precision 128
error when just using floats is 43.944085525744526 ulps (relative 6.7460181771084045627e-15, absolute 2.29160148897436568801e+94) with precision 128

(fl2expm1 253.6199382443308 1.0330029387260226e-14)      => 1.398748649286222641619642494376e+110
(bfexpm1 (bf #e253.61993824433080713605470606162883303)) => 1.398748649286222474771598909821e+110
(flexpm1 253.6199382443308)                              => 1.39874864928620803800496605084e+110
error is 4502899460887364.0 ulps (relative 1.19283792459564859339e-16, absolute 1.66848043584554436406e+94) with precision 128
error when just using floats is 86.51298429857945 ulps (relative 1.03212014826438060794e-14, absolute 1.44367666328589814078e+96) with precision 128

These examples are taken from the samth/fltest program, which can reproduce them with the above output.

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