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c: cosine s: sine

c: cosine s: sine. FPGA Based Systolic Array Implementation of QR Transformation Using Givens Rotations by Xiaojun Wang and Miriam Leeser (mel@coe.neu.edu). Givens Rotation Algorithm:. Divide and square root are required. x. c. ×. /. +. y. s. ×. /. c. r 1. ×. r 1. s. +.

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c: cosine s: sine

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  1. c: cosine s: sine FPGA Based Systolic Array Implementation of QR Transformation Using Givens Rotationsby Xiaojun Wang and Miriam Leeser (mel@coe.neu.edu) Givens Rotation Algorithm: • Divide and square root are required

  2. x c × / + y s × / c r1 × r1 s + r2 × s r1 × r2 c ─ × r2 2D Systolic Array Architecturefor QR Implementation x1 x2 x3 xN ……… r1 r1,2 r1,3 r1,N ……… r2 r2,3 r2,N …… …… rN • Diagonal PE: calculate the rotation parameters c and s • Off-diagonal PE: update the matrix elements using rotation parameters

  3. Experimental Results Resources and Speed: XC5VLX220 Latency IEEE Single-precision square matrix • 1D implementation: 1302 cycles • Our 2D implementation: 954 cycles • 2D latency increases linearly with matrix size, scales well for larger matrices

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