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QR decomposition is used prevalently in wireless communication. In thispaper, we express the Givens-rotation-based QR decomposition algorithm on aspatial architecture using T2S (Temporal To Spatial), a high-productivityspatial programming methodology for expressing high-performance spatialdesigns. There are interesting challenges: the loop iteration space is notrectangular, and it is not obvious how the imperative algorithm can beexpressed in a functional notation, the starting point of T2S. Using QRdecomposition as an example, this paper elucidates some general principle, andde-mystifies high-performance spatial programming. The paper also serves as atutorial of spatial programming for programmers who are not mathematicians, notexpert programmers, and not experts on spatial architectures, but still hope tointuitively identify a high-performance design and map to spatial architecturesefficiently.

Productively Expressing High-performance Spatial Designs of Givens Rotation-based QR Decomposition Algorithm