Fwd: Re: cos(1.0d97) with GCL, Clozure, and Julia
- Subject: Fwd: Re: cos(1.0d97) with GCL, Clozure, and Julia
- From: Raymond Toy
- Date: Thu, 10 May 2012 19:27:16 -0700
On 5/10/12 5:21 PM, Richard Fateman wrote:
> Julia (etc.) presumably make an error in the representation of the
> original input.
> Intel (etc) know how to do the range reduction, I think.
>
> e.g. see
> http://www.researchgate.net/publication/3798381_New_algorithms_for_improved_transcendental_functions_on_IA-64
Indeed. If you follow that reference you can get the actual paper at
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.27.2080&rep=rep1&type=pdf.
In brief the ia-64 architecture uses about 190 bits of pi/2, so that
arguments up to 2^63 can be reduced to full precision. I'm pretty sure
the old ia-32 arch only had 66 bits of pi.
Doesn't help, of course, if you want numbers like 1d97. :-)
Ray