On-Line Schemes For Computing Rotation Angles For SVDS

Two floating-point radix-2 schemes using on-line arithmetic for implementing the direct two-angle method for SVDs are presented. The first scheme is an on-line variant of the cosine/sine approach and is the fastest of the schemes considered: it performs the 2x2 SVD step in about 2n clock cycles. However, it requires a relatively large number of modules; this number is reduced when some modules are reused, resulting in a time of 3n clock cycles. The number of modules of this on-line version is still larger than that of the conventional one, but this is compensated by the smaller number of bit-slices per module and by the digit-serial communication among modules. The corresponding speed-up ratios are of 5 and 3 with respect to a conventional arithmetic implementation. The second scheme uses an on-line CORDIC approach and performs the 2x2 SVD in about 7n clock cycles and is advantageous because it is more time-area efficient. It results in a speed-up of about 2.5 with respect to the conventional CORDIC implementation.

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