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From: Stephen Montgomery-Smith <stephen@missouri.edu>
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To: Bruce Evans <brde@optusnet.com.au>
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Cc: freebsd-numerics@freebsd.org
Subject: Re: Complex arg-trig functions
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On 08/15/12 12:13, Bruce Evans wrote:
> On Tue, 14 Aug 2012, Stephen Montgomery-Smith wrote:
>
>> I was looking through the code e_acosh.c, and it made me realize I
>> could get a small fraction more ULP in catrig.c by making the
>> replacements:
>>
>> 216c216
>> <             *rx = log1p(Am1 + sqrt(Am1*(A+1)));
>> ---
>>>             *rx = log1p(Am1 + sqrt(2*Am1 + Am1*Am1));
>> 282c282
>> <             *sqrt_A2my2 = sqrt(Amy*(A+y));
>> ---
>>>             *sqrt_A2my2 = sqrt(2*y*Amy + Amy*Amy);
>>
>> I'm not quite sure if the second replacement makes much difference,
>> but the first replacement seemed quite effective.
>
> This seems to be slightly worse.  In my tests, it makes little difference
> to the peak error, but unimproves the number of correctly rounded cases
> quite often.

I ran some all night tests, and I came to the same conclusion, except 
for the peak error.  I'll revert it back.