Quote:
Originally Posted by otherguy
They aren't using a single polynomial, they're using a 5th order poly and 7th order poly, then averaging the two.
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What do you get when you add two polynomials together? They could have gotten the same result with a single polynomial:
If P is a 7th degree poly, and R is a 5th degree poly, then Q = a*P+b*R is a 7th degree polynomial ("a" and "b" are constants).
I was trying to point out that it is not immediately obvious that a piecewise linear function "would significantly cut down on the number of computations needed to return a result" compared to a single polynomial. I inferred, based on the context, that you intended the word "computations" to imply "processing speed" and include not just arithmetic but conditional logic and branching as well.
By the way, if you use two nx1 arrays instead of one nx2 array it saves cycles computing the indices. And if you pre-sort your [x[],y[]] points so they are in increasing order by x[], you can save a few cycles in your table lookup logic by eliminating one of the tests. Assuming x[0,1,..n] and y[0,1,...n] are tables of X and Y data values, and [x[n],y[n]] is a sentinel point to assure the function always returns a value:
for (i=1,i<=n,i++) if (ax<x[i]) return y[i]+(ax-x[i])/(x[i-1]-x[i])*(y[i-1]-y[i]);
Depending on the compiler, it might save a few more cycles to use pointer arithmetic to scan the x[] table.