Markus Püschel, Franz Franchetti and Yevgen Voronenko (in Encyclopedia of Parallel Computing, Eds. David Padua, pp. 1920-1933, Springer 2011)
Comment: The abstract below is the definition used in the encyclopedia
Preprint (362 KB)
Published paper (link to publisher)

Spiral is a program generation system (software that generates other software) for linear transforms and an increasing list of other mathematical functions. The goal of Spiral is to automate the development and porting of performance libraries. Linear transforms include the discrete Fourier transform (DFT), discrete cosine transforms, convolution, and the discrete wavelet transform. The input to Spiral consists of a high-level mathematical algorithm specification and selected architectural and microarchitectural parameters. The output is performance-optimized code in a high-level language such as C, possibly augmented with vector intrinsics and threading instructions.

Learn the current Spiral system, SPL compiler: Translating math into code, SIMD vectorization, SPIRAL program generation system for transforms, Spiral overview paper, Discrete/fast Fourier transform, Tutorial, General size libraries, Parallel processing