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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--Kj7319i9nmIyA2yE Content-Type: text/plain; charset=us-ascii Content-Disposition: inline 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 --Kj7319i9nmIyA2yE Content-Type: application/pdf Content-Disposition: attachment; filename="Ng.pdf" Content-Transfer-Encoding: base64 JVBERi0xLjQKJcfsj6IKMTcgMCBvYmoKPDwvTGVuZ3RoIDE4IDAgUi9GaWx0ZXIgL0ZsYXRl RGVjb2RlPj4Kc3RyZWFtCniczV1ZsyVHcebRccN/wG/HL6aPrdOqfSGCByQkGIxAy2A5QtbD aGakEdKMtYyA+ffOrKruyqrOOt1Hc2WAAA59u2vJPb/MKn17ErNUJ4H/Xn48fn735ocynr74 /k6cfgP/+eLu27swa/xXeoH+fvz89NZDeF+Jk7Rz0EGdHn5+J9Pf5EkKN4eTF3qO8Pz53SfT r84XORttQ5g+PCs1exXj9JvzRcxRK+Xj9KeznoWW3k3vnS/w03sRpnfwBamiCXr6A/7WUSpl pofnC3w026CmD+k7v8ZZ4J1oyHhvn9UshRUaPxOzClpIPT04i9l4q2FBf8QJlQ4xTYIDuyin d/GpjjE4+sKH8IKMsHw1/RbGNdY4TeaiO3onj2VUWHdv5NHds3tX0kTYhDRz8EJNH+FHNtrp F+nVIJX3nz783Z1UsEtzgoXO0Z0ePgHyw1xhtiLE6X/PcoZ5jCW/nuBK4Rtvp5dpTCXhrxel NVAi1mfPgGbBS6X99BQ/SUNOv09UNU7IMD2CNxSsA8jzPW7EGKNwUHjZ4DvTW2fpZwlknb7E UQMQehkel54FCsgSg28EyoWTMyHL0n/CB9qHYKcZB7awS+QysssqmJk8/cPZztoZJ6cvcD9q 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