Date: Mon, 28 May 2018 15:18:19 -0700 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: Adhemerval Zanella <adhemerval.zanella@linaro.org> Cc: Konstantin Belousov <kib@freebsd.org>, freebsd-hackers@freebsd.org, emaste@freebsd.org Subject: Re: Code with apache-2 on /usr/src Message-ID: <20180528221819.GA77894@troutmask.apl.washington.edu> In-Reply-To: <b79b4bc0-c584-1888-3207-9a7b640989fc@linaro.org> References: <b38baac0-f326-5d46-5afe-0981af61538f@linaro.org> <20180528190444.GE3789@kib.kiev.ua> <f9f10762-651d-d2f2-c46f-6960b9a69705@linaro.org> <20180528193506.GA76705@troutmask.apl.washington.edu> <1c09023e-9bf5-d23a-dedc-1c4f4706bbde@linaro.org> <20180528202117.GA77184@troutmask.apl.washington.edu> <72101038-9e89-3f23-ab67-1c97b2a89803@linaro.org> <20180528210907.GA77475@troutmask.apl.washington.edu> <b79b4bc0-c584-1888-3207-9a7b640989fc@linaro.org>
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On Mon, May 28, 2018 at 06:12:13PM -0300, Adhemerval Zanella wrote: > > >> And is having a different algorithm for single and double prevision > >> a blocker for a future patch proposal? > > > > No. Given the comment in sinf.c that max ULP is 0.56072, I do note that > > the current implementation of sinf in lib/msun is more accurate (for > > interesting values of x). I also looked at single/s_sincosf.c. It is > > rather dubious to have 80+ digit numerical constants for a float, which > > at most has 9 relevant digits. > > > > Also keep in mind my initial idea is to propose patches only to expf, powf, > logf, expf2, and log2f. OK, so I peeked at expf. Comment claims max ulp of 0.502. Exhaustive testing for normal numbers in relevent range for the current implementation of expf(x) shows Interval tested: [-18,88.72] ULP: 0.90951, x = -5.19804668e+00f, /* 0xc0a65666 */ flt = 5.52735012e-03f, /* 0x3bb51ec6 */ dbl = 5.5273505437686398e-03, /* 0x3f76a3d8, 0xdd1aae8e */ But, then one looks at implementation details. msun's current implementation is written in terms of single precision; while the routine you're suggesting is written in terms of double_t. So, achieving 0.502 ULP is due to having 53-bits in intermediate results. It appears that the algorithm of the suggested code cannot easily be generalized to double and long double without implementing a multiple-precision routines. Note, years ago, I submitted implementations for expf, exp, ld80/expl, ld128/expl, logf, log, ld80/logl, and ld128/logl based on papers by PTP Tang [1,2]. My versions for single and double precision were not adopted even though these had better accuracy. Either Bruce Evans improved or with Bruce's help I improved the ld80 and ld128 routines, which were added to msun. I know Bruce fixed minor issues with the single and double precision routines, but he has not submitted patches. 1. PTP Tang, "Table-driven implementation of the exponential function in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 15, 144-157 (1989). 2. PTP Tang, "Table-driven implementation of the logarithm function in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 16, 378-400 (1990). -- Steve
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