Date: Sat, 22 Sep 2012 19:08:10 -0500 From: Stephen Montgomery-Smith <stephen@missouri.edu> To: freebsd-numerics@freebsd.org Subject: Re: Complex arg-trig functions Message-ID: <505E52EA.7090102@missouri.edu> In-Reply-To: <505E3AE6.2010006@missouri.edu> References: <5017111E.6060003@missouri.edu> <20120917022614.R2943@besplex.bde.org> <50562213.9020400@missouri.edu> <20120917060116.G3825@besplex.bde.org> <50563C57.60806@missouri.edu> <20120918012459.V5094@besplex.bde.org> <5057A932.3000603@missouri.edu> <5057F24B.7020605@missouri.edu> <20120918162105.U991@besplex.bde.org> <20120918232850.N2144@besplex.bde.org> <20120919010613.T2493@besplex.bde.org> <505BD9B4.8020801@missouri.edu> <20120921172402.W945@besplex.bde.org> <20120921212525.W1732@besplex.bde.org> <505C7490.90600@missouri.edu> <20120922042112.E3044@besplex.bde.org> <505CBF14.70908@missouri.edu> <505CC11A.5030502@missouri.edu> <20120922081607.F3613@besplex.bde.org> <20120922091625.Y3828@besplex.b! de.org> <505D1037.8010202@missouri.edu> <20120922142349.X4599@besplex.bde.org> <20120923044814.S1465@besplex.bde.org> <505E2575.6030302@missouri.edu> <505E27CE.3060107@missouri.edu> <20120923073807.K2059@besplex.bde.org> <505E3AE6.2010006@missouri.edu>
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On 09/22/2012 05:25 PM, Stephen Montgomery-Smith wrote: > On 09/22/2012 04:47 PM, Bruce Evans wrote: >> On Sat, 22 Sep 2012, Stephen Montgomery-Smith wrote: >> >>> 2. In my accuracy tests for casin(h), I have never seen the double or >>> long double have an error greater than 4 ULP. But for the float case >>> I have seen 4.15 ULP. >> >> I haven't seen any larger than 3.4. What is the worst case you found? >> Errors found for float precision tend to be because the density of bad >> cases is higher so it is easier to test more of them accidentally. I >> did do some non-random testing for all float cases in narrow strips >> about x or y = 0 or 1, but not for all combinations of this with all >> functions. > > Here are some examples for float. In all these outputs: > The first entry is the "count". > The second entry is the function. > The third and fourth entries are the real and imaginary part of the > error in ULP. > The fifth and sixth entries are the real and imaginary part of the input. > The seventh and eighth and ninth and tenth entries are the real part and > imaginary part of the answers from the float/double respectively > (printed to few enough decimal places that you cannot tell they are > different.) > > 2365614 acos 3.75621 0.86681 1.0338860750198364258 > -0.090228326618671417236 0.246582 0.361712 0.246582 0.361712 > 3087248 acos 3.56538 0.1165 2.3730618953704833984 0.26976472139358520508 > 0.124496 -1.51821 0.124496 -1.51821 > 5973027 asinh 3.61544 0.513 0.10977014899253845215 > 0.48254761099815368652 0.124712 0.499309 0.124712 0.499309 > 6558511 acosh 3.57286 0.419525 -0.29658588767051696777 > -0.11975207924842834473 0.124975 -1.8695 0.124975 -1.8695 > 9998127 acos 3.51324 1.09793 1.0892471075057983398 > -0.12541522085666656494 0.247452 0.491951 0.247452 0.491951 > 14879751 asinh 3.5643 1.83067 -0.11303693056106567383 > 0.4351412653923034668 -0.124994 0.446448 -0.124994 0.446448 > 19510082 asin 3.61922 0.0103899 0.46096378564834594727 > -0.01612871512770652771 0.478995 -0.0181731 0.478995 -0.0181731 > > I can send more examples on request. I'm not seeing a real pattern here. Here is an error of about 4.15 ULP 171886645 acosh 0.504775 4.15104 1.0684067010879516602 -0.049668960273265838623 0.389377 -0.124716 0.389377 -0.124716
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