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A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86 Floating-Point Division Algorithm (1996)
| Venue: | IEEE Transactions on Computers |
| Citations: | 38 - 11 self |
BibTeX
@ARTICLE{Moore96amechanically,
author = {J Strother Moore and Tom Lynch and Matt Kaufmann},
title = {A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86 Floating-Point Division Algorithm},
journal = {IEEE Transactions on Computers},
year = {1996},
volume = {47}
}
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Abstract
We describe a mechanically checked proof of the correctness of the kernel of the floating point division algorithm used on the AMD5K 86 microprocessor. The kernel is a non-restoring division algorithm that computes the floating point quotient of two double extended precision floating point numbers, p and d (d 6= 0), with respect to a rounding mode, mode. The algorithm is defined in terms of floating point addition and multiplication. First, two NewtonRaphson iterations are used to compute a floating point approximation of the reciprocal of d. The result is used to compute four floating point quotient digits in the 24,,17 format (24 bits of precision and 17 bit exponents) which are then summed using appropriate rounding modes. We prove that if p and d are 64,,15 (possibly denormal) floating point numbers, d 6= 0 and mode specifies one of six rounding procedures and a desired precision 0 ! n 64, then the output of the algorithm is p=d rounded according to mode. We prove that every int...
Keyphrases
amd5k86 floating-point division algorithm mechanically checked proof point number point addition newtonraphson iteration appropriate rounding mode checked proof floating point approximation non-restoring division algorithm point division algorithm bit exponent point quotient rounding mode point quotient digit desired precision
