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From: "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu>
Newsgroups: comp.lang.c,comp.arch
Subject: Re: Radians Or Degrees?
Date: Wed, 20 Mar 2024 17:02:57 -0000 (UTC)
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On Wed, 20 Mar 2024 18:21:47 +0200, Michael S wrote:

> On Wed, 20 Mar 2024 09:54:36 -0400
> Stefan Monnier <monnier@iro.umontreal.ca> wrote:
> 
>> >>>> There are groups who have shown that exactly rounded
>> >>>> trancendental functions are in fact achievable with maybe 3X
>> >>>> reduced performance.  
>> >> That much?  I had the impression it was significantly cheaper.  
>> > The J. M. Muller book indicates about 2× to 2.5×  
>> 
>> The [Rlibm](https://people.cs.rutgers.edu/~sn349/rlibm/) project
>> claims to get much better performance (basically, in the same
>> ballpark as not-correctly-rounded implementations).
>> 
> 
> I had only read the 1st page.
> It sounds like they are not particularly interested in IEEE binary64
> which appears to be the major point of interest of math libs of
> conventional languages.
> 

I skimmed their logf(x) implementation.  Their technique will
fall a part for binary64 (and other higher precisions).  With
logf(x), they combine an argument step with table look-up and
a 5th-order polynomial approximation.  The polynomial is computed
in double precision, and provides the correct rounding.  For
binary64, the polynomial would require many more terms and 
double-double or binary128 evaluation.  

-- 
steve