floating point inconsistency

[Andrew Haley]

On 02/17/2010 02:30 PM, Vincent Lefevre wrote:
> On 2010-02-16 09:14:58 +0100, Christoph Groth wrote:
>> I am aware of the limited precision of floating point calculations.
>> However, I assumed that on the processors in question these calculations
>> are done according to IEEE standards, i.e. the results of are defined
>> unambiguously.
> 
> Note that the old IEEE 754-1985 standard didn't consider elementary
> functions such as sin and cos (only +, -, *, / and square root).
> The current IEEE 754-2008 standard recommends that (some) elementary
> functions be correctly rounded, but that's only a recommendation.

Aha, Vincent Lefèvre from Lyon!  Thanks for posting.

What is the current state of libraries for correctly rounded
functions?  The main paper I see on making this faster dates from
November 1998, although there is [2], not online.  Are we in a
position where we can use something faster than the IBM Accurate
Mathematical Library?

Thanks,
Andrew.

[1] V. Lefevre, J.M. Muller and A. Tisserand, Toward Correctly Rounded Transcendentals,   IEEE Transactions on Computers, Vol. 47 No 11, Nov. 1998. http://perso.ens-lyon.fr/jean-michel.muller/Nov98.pdf
[2] C. Daramy, D. Defour, F. de Dinechin and J.M. Muller, CR-LIBM: a correctly rounded elementary function library, SPIE 48th Annual Meeting International Symposium on Optical Science and Technology, San Diego, USA, Aug 3-8, 2003.