Formal Verification of Floating-Point Hardware Design by David M. Russinoff

Author:David M. Russinoff
Language: eng
Format: epub
ISBN: 9783319955131
Publisher: Springer International Publishing

Fig. 10.3Comparison constants m k(i, j)

In Chap. 19, we shall prove that the implementation satisfies the invariant (10.15). The proof will also establish the required bounds on the partial roots. The following result will be the basis of the induction. Note that this induction is based on a slightly different scheme from that used for division: each of Lemmas 10.7 and 10.8 derives the conclusion that a set of properties hold for an index j + 1 from the assumption that they hold for j, whereas the proof below requires the explicit assumption that the desired properties hold for all indices between 0 and j.

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