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Date: Fri, 15 Mar 2019 12:24:51 +1100 (AEDT)
From: Damian McGuckin <damianm@....com.au>
To: musl@...ts.openwall.com
Subject: Re: atanhf(x) Slight Accuracy Improvements

On Wed, 13 Mar 2019, Damian McGuckin wrote:

> By tweaking some algebra, this can be made more accurate. A comparison 
> of the more accurate version and the original is noted below.
>
> 	 ATANF ... FROM ... TO WORST ERROR % > EPS/2 MEAN ERROR
> 	 --------------------------------------------------------------
> 	 Accurate:0.00000..0.17000 1.00023*EPS 0.76907% 0.01967*EPS
> 	 Accurate:0.17000..0.55000 0.99151*EPS 5.52206% 0.21620*EPS

Sorted for the crucial segment.

More algebraic rearrangement and that 1.00023*EPS drops to 0.6667*EPS.

I will work on the second segment.

Regards - Damian

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