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Date: Wed, 6 Dec 2017 12:17:40 +1100 (AEDT)
From: Damian McGuckin <damianm@....com.au>
To: musl@...ts.openwall.com
Subject: Re: remquo - underlying logic


While my exploration with floating point numbers was less than stellar,
I did notice that when

 	ex - ey < p (where p is the digits in the significant)

you can use the

 	fma

routine to compute some appropriately rounded/truncated version of the 
quotient for both remquo and fmod. And this appears to not loose any 
precision for the obvious reasons.

>From my limited testing, the speed gain for this extremely limited range 
of exponent difference is huge over the standard routine in MUSL. I will 
do some more testing and report in detail but it seems to be orders of 
magnitude.

Somebody might want to comment on that sort of approach.

In 99% of the floating point work I do, the calculations involve physical 
stresses and strains and loads and such within digital models. They differ 
in exponent range between 10^6 through to 10^12 unless I have screwed up 
in my model. This is a lot less than 2^52 for a double and mostly is still 
under the 2^23 for a float which is just above 10^6. So, in my sort of 
calculations, the speed gain can be quite significant.  The burden of the 
extra branch seems to be trivial, even for the cases where the FMA is not 
used.

Regards - Damian

Pacific Engineering Systems International, 277-279 Broadway, Glebe NSW 2037
Ph:+61-2-8571-0847 .. Fx:+61-2-9692-9623 | unsolicited email not wanted here
Views & opinions here are mine and not those of any past or present employer

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