Re: Faster div or 1/sqrt approximations

Thomas Koenig wrote:

MitchAlsup1 <mitchalsup@aol.com> schrieb:
 

I, personally, have found many Newton-Raphson iterators that converge
faster using 1/SQRT(x) than using the SQRT(x) equivalent.

 I can well believe that.
 It is interesting to see what different architectures offer for
faster reciprocals.
 POWER has fre and fres (double and single version) for approximate
divisin, which are accurate to 1/256.  These operations are quite
fast, 4 to 7 cycles on POWER9, with up to 4 instructions per cycle
so obviously fully pipelined.  With 1/256 accuracy, this could
actually be the original Quake algorithm (or its modification)
with a single Newton step, but this is of course much better in
hardware where exponent handling can be much simplified (and
done only once).

I've taken both a second and third look at InvSqrt() over the last few years, it turns out that the Quake version is far from optimal: With the exact same instructions, just a different set of constants, you can get about 1.5 bits more than quake does, i.e. about 10 bits after that single NR step (which isn't really NR since it modifies both the 1.5 and the 0.5 factors).
Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"