Optimized code generation of multiplication-free linear transforms

We present code generation of multiplication-free linear transforms targeted to single-register DSP architectures such as TMS320C2x/C5x. We first present an algorithm to generate optimized code from a DAG representation. We then present techniques that transform a DAG so as to minimize the number of nodes and the accumulator-spills. We then introduce a concept of spill-free DAGs and present an algorithm for synthesizing such DAGs. The results for Walsh-Hadamard, Haar and Slant transforms show 25% to 40% reduction in the cycle count using our techniques.