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Date:      Fri, 14 Sep 2012 17:34:08 -0700
From:      Steve Kargl <sgk@troutmask.apl.washington.edu>
To:        Stephen Montgomery-Smith <stephen@missouri.edu>
Cc:        freebsd-numerics@freebsd.org, Bruce Evans <brde@optusnet.com.au>
Subject:   Re: cexp error
Message-ID:  <20120915003408.GA70269@troutmask.apl.washington.edu>
In-Reply-To: <5053CB4F.3030709@missouri.edu>
References:  <5048D00B.8010401@missouri.edu> <504D3CCD.2050006@missouri.edu> <504FF726.9060001@missouri.edu> <20120912191556.F1078@besplex.bde.org> <20120912225847.J1771@besplex.bde.org> <50511B40.3070009@missouri.edu> <20120913204808.T1964@besplex.bde.org> <5052A923.9030806@missouri.edu> <20120914143553.X870@besplex.bde.org> <5053CB4F.3030709@missouri.edu>
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[-- Attachment #1 --]
On Fri, Sep 14, 2012 at 07:26:55PM -0500, Stephen Montgomery-Smith wrote:
> On 09/14/2012 01:05 AM, Bruce Evans wrote:
> 
> >My tests also determined the exact minimum for all multiples up to the
> >thresholds for "large" multiples in e_rem_pio2.c, except for ld128,
> >to verify that there are enough bits in the special approximations for
> >Pi/2 there, except for ld128.  The maximum multiples handled there are
> >2**28*Pi/2, except for ld128 they are 2**45*Pi/2.  2**45 is too many
> >to check exhaustively.
> 
> But presumably one could prove a result to this effect using continued 
> fractions, right?
> 

See attached.  It shows a method for determining the number
of needed bits.

-- 
Steve

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