Date: Sat, 4 Dec 2021 20:40:56 +0100 From: Hans Petter Selasky <hps@selasky.org> To: Steve Kargl <sgk@troutmask.apl.washington.edu>, freebsd-hackers@freebsd.org, freebsd-current@freebsd.org Subject: Re: What to do about tgammal? Message-ID: <46162af1-b63f-be10-ebdf-cd328dcfb6e2@selasky.org> In-Reply-To: <20211204185352.GA20452@troutmask.apl.washington.edu> References: <20211204185352.GA20452@troutmask.apl.washington.edu>
next in thread | previous in thread | raw e-mail | index | archive | help
On 12/4/21 19:53, Steve Kargl wrote: > What to do about tgammal? > > A long time ago (2013-09-06), theraven@ committed a kludge that mapped > several missing long double math functions to double math functions > (e.g., tanhl(x) was mapped to tanh(x)). Over the next few years, I > (along with bde and das reviews) provided Intel 80-bit (ld80) and IEEE > 128-bit (ld128) implementations for some of these functions; namely, > coshl(x), sinhl(x), tanhl(x), erfl(x), erfcl(x), and lgamma(x). The > last remaining function is tgammal(x). If one links a program that uses > tgammal(x) with libm, one sees > > /usr/local/bin/ld: fcn_list.o: in function `build_fcn_list': > fcn_list.c:(.text+0x7c4): warning: tgammal has lower than advertised > precision > > The warning is actually misleading. Not only does tgammal(x) have a > *MUCH* lower precision, it has a reduced domain. That is, tgammal(x) > produces +inf for x > 172 whereas tgammal(x) should produce a finite > result for values of x up to 1755 (or so). On amd64-*-freebsd, > testing 1000000 in the below intervals demonstrates pathetic accuracy. > > Current implmentation via imprecise.c > > Interval | Max ULP > -------------------+------------ > [6,171] | 1340542.2 > [1.0662,6] | 14293.3 > [1.01e-17,1.0661] | 3116.1 > [-1.9999,-1.0001] | 15330369.3 > -------------------+------------ > > Well, I finally have gotten around to removing theraven@'s last kludge > for FreeBSD on systems that support ld80. This is done with a straight > forward modification of the msun/bsdsrc code. The limitation on > domain is removed and the accuracy substantially improved. > > Interval | Max ULP > -------------------+---------- > [6,1755] | 8.457 > [1.0662,6] | 11.710 > [1.01e-17,1.0661] | 11.689 > [-1.9999,-1.0001] | 11.871 > -------------------+---------- > > My modifications leverage the fact that tgamma(x) (ie., double function) > uses extend arithmetic to do the computations (approximately 85 bits of > precision). To get the Max ULP below 1 (the desired upper limit), a few > minimax polynomials need to be determined and the mystery around a few > magic numbers need to be unraveled. > > Extending what I have done to an ld128 implementation requires much > more effort than I have time and energy to pursue. Someone with > interest in floating point math on ld128 system can provide an > implementation. > > So, is anyone interested in seeing a massive patch? > Hi, Do you need a implementation of tgamma() which is 100% correct, or a so-called speed-hack version of tgamma() which is almost correct? I've looked a bit into libm in FreeBSD and I see some functions are implemented so that they execute quickly, instead of producing exact results. Is this true? --HPS
Want to link to this message? Use this URL: <https://mail-archive.FreeBSD.org/cgi/mid.cgi?46162af1-b63f-be10-ebdf-cd328dcfb6e2>