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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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