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Today's Topics:
1. Determinant refinement (Richard Crandall)
----------------------------------------------------------------------
Message: 1
Date: Fri, 2 Nov 2007 12:57:43 -0700
From: Richard Crandall <email@hidden>
Subject: [apple scitech] Determinant refinement
To: email@hidden
Message-ID: <email@hidden>
Content-Type: text/plain; charset=US-ASCII; format=flowed
Daniel Farrell:
If you want to try Martin Costabel's variant for 4x4 det, as:
======================================
det = G(0,1,2,3) + G(0,2,1,3) + G(0,3,1,2) +
G(1,2,0,3) + G(1,3,0,2) + G(2,3,0,1);
double
G(int j, int k, int m, int n) {
return(
( a[j][0] * a[k][1] - a[k][0] * a[j][1] ) *
( a[m][2] * a[n][3] - a[n][2] * a[m][3] )
);
}
======================================
then observe that function overhead could be reduced by unrolling
the whole thing, instead of calling G six times...or in-lining G,
something such.
It would be good to know if the F- or G- scheme gives you the speed
you want, for there are yet more speedups possible...it all becomes,
as is typical, a tradeoff between research time and execution time,
i.e. quality-of-life vs. quality-of-machine-life!
Richard Crandall
Advanced Computation Group
------------------------------
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End of Scitech Digest, Vol 4, Issue 168
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