Date: Mon, 24 Apr 2017 16:27:43 -0700 From: Steve Kargl <sgk@troutmask.apl.washington.edu> To: freebsd-numerics@freebsd.org Cc: freebsd-standards@freebsd.org Subject: Re: Implementation of half-cycle trignometric functions Message-ID: <20170424232743.GA54621@troutmask.apl.washington.edu> In-Reply-To: <20170413171248.GA86780@troutmask.apl.washington.edu> References: <20170409220809.GA25076@troutmask.apl.washington.edu> <20170413171248.GA86780@troutmask.apl.washington.edu>
next in thread | previous in thread | raw e-mail | index | archive | help
On Thu, Apr 13, 2017 at 10:12:48AM -0700, Steve Kargl wrote:
> On Sun, Apr 09, 2017 at 03:08:09PM -0700, Steve Kargl wrote:
> > Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle
> > trignometric functions cospi, sinpi, and tanpi. The attached
> > patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited
> > testing on the cospi and sinpi reveal a max ULP less than 0.89;
> > while tanpi is more problematic with a max ULP less than 2.01
> > in the interval [0,0.5]. The algorithms used in these functions
> > are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c.
> >
> > Note 1. ISO/IEC TS 18661-4 says these funstions are guarded by
> > a predefine macro. I have no idea or interest in what clang and
> > gcc do with regards to this macro. I've put the functions behind
> > __BSD_VISIBLE.
> >
> > Note 2. I no longer have access to a system with ld128 and
> > adequate support to compile and test the ld128 implementations
> > of these functions. Given the almost complete lack of input from
> > others on improvements to libm, I doubt that anyone cares. If
> > someone does care, the ld128 files contain a number of FIXME comments,
> > and in particular, while the polynomial coefficients are given
> > I did not update the polynomial algorithms to properly use the
> > coefficients.
> >
> > The code is attached the bug reportr.
> >
> > https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=218514
> >
>
> While everyone is busy reviewing and testing the patch available
> in bugzilla, I suspect some may be wondering about the inverse
> half-cycle trignometric functions. I have worked out an algorithm
> for asinpi[fl] and have a working implemenation of asinpif(x).
> It will take a couple of weeks (due to limited available time)
> before I can submit asinpi[fl], acospi[fl], and atanpi[fl], but
> work is in progress.
>
I have what appears to be working versions of asinpi[fl]. It
was suggested elsewhere that using an Estrin's method to
sum the polynomial approximations instead of Horner's method
may allow modern CPUs to better schedule generated code.
I have implemented an Estrin's-like method for sinpi[l]
and cospi[l], and indeed the generated code is faster on
my Intel core2 duo with only a slight degradation in the
observed max ULP. I'll post new versions to bugzilla in
the near future.
--
Steve
20161221 https://www.youtube.com/watch?v=IbCHE-hONow
Want to link to this message? Use this URL: <https://mail-archive.FreeBSD.org/cgi/mid.cgi?20170424232743.GA54621>