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It Takes Six Ones To Reach a Flaw

Published: 19 July 1995 Publication History

Abstract

The intial 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.

Cited By

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  • (2022)Formalization of Double-Word Arithmetic, and Comments on “Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic”ACM Transactions on Mathematical Software10.1145/348451448:1(1-24)Online publication date: 16-Feb-2022
  • (2006)An iterative division algorithm for FPGAsProceedings of the 2006 ACM/SIGDA 14th international symposium on Field programmable gate arrays10.1145/1117201.1117213(83-89)Online publication date: 22-Feb-2006
  • (2005)Digit Selection for SRT Division and Square RootIEEE Transactions on Computers10.1109/TC.2005.4754:3(294-303)Online publication date: 1-Mar-2005

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    cover image Guide Proceedings
    ARITH '95: Proceedings of the 12th Symposium on Computer Arithmetic
    July 1995
    ISBN:0818670894

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    IEEE Computer Society

    United States

    Publication History

    Published: 19 July 1995

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    • (2022)Formalization of Double-Word Arithmetic, and Comments on “Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic”ACM Transactions on Mathematical Software10.1145/348451448:1(1-24)Online publication date: 16-Feb-2022
    • (2006)An iterative division algorithm for FPGAsProceedings of the 2006 ACM/SIGDA 14th international symposium on Field programmable gate arrays10.1145/1117201.1117213(83-89)Online publication date: 22-Feb-2006
    • (2005)Digit Selection for SRT Division and Square RootIEEE Transactions on Computers10.1109/TC.2005.4754:3(294-303)Online publication date: 1-Mar-2005

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