IBM Power4TM processor uses series apprmimation to calculate divide and square root. We formally verified that the algorithms with a series of rigorous error hound analysis using the ACLZ theorem prover. In order to carry out the verification, we need to show that the error of the Chebyshev series used in the square root algorithm is suitably bounded. This was performed by analyzing the Chebyshev series using Taylor series. In general, Taylor series has less accuracy than Chebyshev series, however, we used ACLZ’s mwo extensions and computed hints to automatically generate Taylor serious approximation for small segments, and proved that the approximation error in each of these segments is smaller than the requirement.
By: Jun Sawada
Published in: RC22444 in 2002
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