Energy Minimization Using Multiple Supply Voltages

We present a dynamic programming technique for solving the multiple supply voltage scheduling problem in both non-pipelined and functionally pipelined data-paths. The scheduling problem refers to the assignment of a supply voltage level (selected from a fixed and known number of voltage levels) to each operation in a data flow graph so as to minimize the average energy consumption for given computation time or throughput constraints or both. The energy model is accurate and accounts for the input pattern dependencies, re-convergent fanout induced dependencies, and the energy cost of level shifters. Experimental results show that using four supply voltage levels on a number of standard benchmarks, an average energy saving of 43.74% (with a computation time constraint of 1.5 times the critical path delay) can be obtained compared to using a single supply voltage level. The published version of this work appears in [ChPe96b].

The summary and contributions of this work are as follows.

• We presented a dynamic programming approach for assigning voltage levels to the modules in non-pipelined and functionally pipelined data-paths
• Although one can reduce the energy consumption by using a single lowered supply voltage on the circuit and use pipelining or parallelism on whole or part of the circuit to recover performance when the computation time constraint is violated. The area overhead can be very large
• When multiple voltages are used, one can instead lower the supply voltages of operations which are not on the critical path while keeping the supply voltages of operations on the critical path at a maximum. The computation time constraint for non-pipelined data-path will be thus achieved with lower area overhead
• We discover the absolute lower bound on the number of modules for a multi-frame operation in a functionally pipelined data-path is necessary to maintain the throughput. This lower bound is then used in the revolving schedule for scheduling the multi-frame operation in a functionally pipelined data-path.