Partial Evaluation

Partial evaluation is the technique of evaluating those parts of a program that can be evaluated at compile time, rather than waiting for execution time.

For example, the rotation of a point in homogeneous coordinates by an angle θ around the x axis is accomplished by multiplying by the matrix:

lccr 1 0 0 0
0 cos θ - sin θ 0
0 sin θ cos θ 0
0 0 0 1

Many of the cycles consumed in the matrix multiply would be wasted because they would be trivial computations ( e.g., multiplying by 1 or adding 0).

By unrolling the loops of matrix multiply, substituting the values from the coefficient matrix, and performing partial evaluation on the result, a specialized version of the matrix multiply can be obtained. This version saves many operations:

Version:	Load	Store	Add/Sub	Mul	Total
General	128	16	48	64	256
Specialized	24	16	8	16	64