Spiral (www.spiral.net) is a program and hardware design generation system for linear transforms such as the discrete Fourier transform, discrete cosine transforms, filters, and others. For a user-selected transform, Spiral autonomously generates different algorithms, represented in a declarative form as mathematical formulas, and their implementations to find the best match to the given target platform. Besides the search, Spiral performs deterministic optimizations on the formula level, effectively restructuring the code in ways unpractical at the code or design level.<br/><br/>In this talk, we give a short overview on Spiral. We explain then how Spiral generates efficient programs for parallel platforms including vector architectures, shared and distributed memory platforms, and GPUs; as well as hardware designs (Verilog) and automatically partitioned software/hardware implementations. As all optimizations in Spiral, parallelization and partitioning are performed on a high abstraction level of algorithm representation, using rewriting systems. We also discuss how Spiral is currently extended beyond its original problem domain, using coding algorithms (Viterbi decoding and JPEG 2000 encoding) and image formation synthetic aperture radar, SAR) as examples.