EngineeringComputer EngineeringComputer ScienceCompilersComputer ArchitectureFault ToleranceError DetectionHardware Fault ToleranceArithmetic Circuit EvaluationBit FailureCompiler SupportDivision AlgorithmsFloating-point ArithmeticFloating-point Unit DesignLookup Table Design
The initial release of the Pentium processor has a flaw in its radix-4 SRT division implementation. It is widely-known that five entries were missing in the lookup table, yielding reduced-precision quotients occasionally. In this paper, we use mathematical techniques to analyze the divisors that can possibly cause failures. In particular, we show that Bits 5 through 10 (where Bit 0 is the MSB) of such divisors must be all ones. This result is useful in compiler-level software patches for systems with unreplaced chips; and we believe that the techniques used here are applicable in analyzing SRT division as well as other hardware algorithms for floating-point arithmetic.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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High-Speed Arithmetic in Binary Computers
O. L. Macsorley · Proceedings of the IRE · 1961 · 622 citations