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A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86 FloatingPoint Division Algorithm
 IEEE Transactions on Computers
, 1996
"... 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 nonrestoring division algorithm that computes the floating point quotient of two double extended precision floating point numbers, ..."
Abstract

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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 nonrestoring 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...