High-Performance Embedded Computing

392 Chapter 7 Hardware and Software Co-design

probability at that control step becomes 1 and at any other control step 0. As the

shape of the distribution graph for a function unit changes, force-directed sched-

uling tries to select control steps for the remaining operations, which keeps the

operator distribution balanced.

Force-directed scheduling calculates forces like those exerted by springs to

help balance the utilization of operators. The spring forces are a linear function

of displacement, as given by Hooke’s Law:

, (EQ 7-1)

where x is the displacement and k is the spring constant, which represents the

spring’s stiffness. When computing forces on the operator we are trying to

schedule, we first choose a candidate schedule time for the operator, ...