Date: Wed, 17 May 2017 18:42:26 -0700 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: Bruce Evans <brde@optusnet.com.au> Cc: freebsd-numerics@freebsd.org Subject: Re: Implementation of half-cycle trignometric functions Message-ID: <20170518014226.GA63819@troutmask.apl.washington.edu> In-Reply-To: <20170518072636.E951@besplex.bde.org> References: <20170409220809.GA25076@troutmask.apl.washington.edu> <20170427231411.GA11346@troutmask.apl.washington.edu> <20170428175851.A1386@besplex.bde.org> <20170516224618.GA40855@troutmask.apl.washington.edu> <20170517094848.A52247@besplex.bde.org> <20170517180927.GA54431@troutmask.apl.washington.edu> <20170518072636.E951@besplex.bde.org>
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On Thu, May 18, 2017 at 09:25:58AM +1000, Bruce Evans wrote: > On Wed, 17 May 2017, Steve Kargl wrote: > > > On Wed, May 17, 2017 at 12:49:45PM +1000, Bruce Evans wrote: > >> On Tue, 16 May 2017, Steve Kargl wrote: > >> > >>> Index: lib/msun/ld128/s_cospil.c > >>> ... > >>> +static const long double > >>> +pihi = 3.14159265358979322702026593105983920e+00L, > >>> +pilo = 1.14423774522196636802434264184180742e-17L; > >> > >> These are not in normal format, and are hard to read. I can't see if > >> pihi has the correct number of zero bits for exact multiplication. > > > > I don't have access to an ld128 system with suitable > > facilities to allow me to spit out the hex representation. > > flame is still in the freebsd cluster, but is almost unusable because > its files are an old copy of actual home directories on freefall. Yes, I know flame is still available. I deleted all infrastructure I had on freefall over 2 years agos. Need at a minimum GMP and MPFR. > Utilities for printing hex and FP in good formats are remarkably rare. > pari/gp supports many special math types but can only input or output > ordinarly numbers in decimal. I use my library routines to print hex > and special FP formats for it. sh, printf(1) and awk(1) are limited > by native tyoes and have many other defects. I wrote my own utility with the catchy name hex. > > As such, I've added a comment > > > > /* > > * pi_hi contains the leading 56 bits of a 169 bit approximation for pi. > > */ > > Why 56? 53 + 56 = 109. This is ld128. static const long double pi_hi = 3.14159265358979322702026593105983920e+00L, pi_lo = 1.14423774522196636802434264184180742e-17L; pi_hi has 113/2 = 56 bits. pi_lo has 113 bit. 56 + 113 = 169 > > >> These don't have the normal spelling. fdlibm never uses pihi or pio2hi, > >> or pi_hi. It often uses pio2_hi and other pio2_*. My s_sinpi.c uses > >> pi_hi. I've changed my spelling. > > My improvements to lgamma()'s sin_pi*() are buggy. I forgot the original > target of avoiding inexact better: I'll need to wait until the weekend to study your improved sin_pi. -- Steve 20170425 https://www.youtube.com/watch?v=VWUpyCsUKR4 20161221 https://www.youtube.com/watch?v=IbCHE-hONow
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