Method and hardware for computing reciprocal square root and...

Details Method and hardware for computing reciprocal square root and... Method and hardware for computing reciprocal square root and...

2007-09-04

2007-09-04

Mai, Tan V. (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

10160966

ABSTRACT:
A reciprocal square root for a radix ofxis calculated when S[j] represents the partial result obtained afterjiterations of calculation, W[j], a residual, and P[j], the product of an operand X and the S[j]. Firstly, appropriate values are set to the initial values S[0], W[0], and P[0]. Secondly,niterations of calculations from j=0 to n−1 are performed. One calculation includes selecting a reciprocal square root digit qj+1from the digit set {−a, . . . , −1, 0, 1, . . . , a}, and calculating a recurrence equation of the S[j], i.e., S[j+1]:=S[j]+qj+1r−j−1, a recurrence equation of the W[j], i.e., W[j+1]:=rW[j]−(2P[j]+Xqj+1r−j−1)qj+1, and a recurrence equation of the P[j], i.e., P[j+1]:=P[j]+Xqj+1r−j−1.

REFERENCES:
patent: 5253215 (1993-10-01), Lindsley
patent: 5307302 (1994-04-01), Nakano
patent: 6163791 (2000-12-01), Schmookler et al.
patent: 6175907 (2001-01-01), Elliott et al.
patent: 2001/0010051 (2001-07-01), Oberman et al.
Lang, T., and E. Antelo, “Correctly Rounded Reciprocal Square-Root by Digit Recurrence and Radix-4 Implementation,”Proceedings of 15thIEEE Symposium on Computer Arithmetic, Vail, Colorado, Jun. 11-13, 2001, pp. 83-93.

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