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Date:      Fri, 6 Dec 2013 22:46:02 -0800
From:      Steve Kargl <sgk@troutmask.apl.washington.edu>
To:        Bruce Evans <brde@optusnet.com.au>
Cc:        freebsd-numerics@FreeBSD.org, Filipe Maia <filipe.c.maia@gmail.com>
Subject:   Re: dead code in lgamma_r[f]?
Message-ID:  <20131207064602.GA76042@troutmask.apl.washington.edu>
In-Reply-To: <20131206114426.I1329@besplex.bde.org>
References:  <20131205173700.GA64575@troutmask.apl.washington.edu> <20131205182324.GA65135@troutmask.apl.washington.edu> <CAN5hRiV6N1arc4RDv=9JbRiXp-J9o3WzAbeZSOpAxks2ZeG+_w@mail.gmail.com> <20131205195225.GA65732@troutmask.apl.washington.edu> <20131206102724.W1033@besplex.bde.org> <20131206114426.I1329@besplex.bde.org>

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On Fri, Dec 06, 2013 at 12:55:16PM +1100, Bruce Evans wrote:
> On Fri, 6 Dec 2013, Bruce Evans wrote:
> 
> > On Thu, 5 Dec 2013, Steve Kargl wrote:
> > ...
> >> If we again look at the code from __ieee754_lgamma_r(), we see
> >> that sin_pi() is called if ix < 0x43300000, so by the time we
> >> arrive at the 'if(ix<0x43300000)' statement we already know that
> >> the condition is true.
> >
> > No, only for negative integers.  hx<0 classifies negative values, and
> > then ix>=0x43300000 classifies numbers that are so large negative that
> > they must be integers, and the result is a sort of pole error.  We
> > are just filtering out this case, perhaps as an optimization.
> 
> Oops, sin_pi() is only called for negative integers, so your change
> seems to be correct.  Just add a comment about the limited domain
> of sin_pi() (it already has one saying that "x is assumed negative".
> 

I wish to retract my earlier statement that after 2 additional
years of reading fdlibm code that it was easier to work with.
I spent the better part of Friday giving myself a headache trying
to understand the algorithm for lgamma_r().  The code for x in
the interval (0,2) does not match any comment in lgamma_r().

I also think, but can't prove yet, that like erff() the 
polynomial and rational approximations in lgammaf_r() have
too many terms.

-- 
Steve



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