A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86 Floating-Point Division Algorithm

A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86 Floating-Point Division Algorithm (1996)

by J Strother Moore , Tom Lynch , Matt Kaufmann

Venue:	IEEE Transactions on Computers
Citations:	28 - 11 self

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Datum	Value	Source
TITLE	A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86 Floating-Point Division Algorithm	user correction - Legacy Corrections
AUTHOR NAME	J Strother Moore	SVM HeaderParse 0.1
AUTHOR NAME	Tom Lynch	SVM HeaderParse 0.1
AUTHOR NAME	Matt Kaufmann	SVM HeaderParse 0.1
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...	user correction - Legacy Corrections
YEAR	1996	user correction - Legacy Corrections
VENUE	IEEE Transactions on Computers	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
VOLUME	47	INFERENCE
CITATIONS	15 found	ParsCit 1.0