Intel® Pentium® Processor
Statistical Analysis of Floating Point Flaw: Intel White Paper - Section 7

Section 7: Conclusions
The thorough and detailed characterization of the flaw and the subsequent investigations of its impact on applications through elaborate surveys, analyses and empirical observation lead us to the following conclusions:

  1. The significance of the flaw depends upon (a) the rate of use of specific FP instructions in the Pentium® processor, (b) the data fed to them, (c) the way in which the results of these instructions are propagated into further computation in the application; and (d) the way in which the final results of the application are interpreted.
  2. The flaw is of no significance in the commercial PC market where the vast majority of Intel processors are installed. Failure rates introduced by this flaw are swamped by rates due to existing hard and soft failure mechanisms in PC systems. The average PC user is likely to encounter a failure once in 27,000 years due to this flaw, indicating that it is practically impossible for such a user to encounter a problem in the useful lifetime of the product.
  3. The flaw is of no significance for integer workstation applications, since they do not use the Floating Point Unit.
  4. The flaw is of no significance for Server applications.
  5. The flaw is of no significance in the majority of the financial world, where PC users run spreadsheets with little divide content. For these users the flaw has no effect.
  6. The flaw is of potential significance for a small minority of users in the financial world. These users are primarily involved in running highly numerical applications involving intensive recalculations such as path-dependent derivatives valuations and those valuations involving simulations. Depending on the circumstances, these users should employ either an updated Pentium processor without the flaw or a software workaround.
  7. A small fraction of PCs are installed for use as engineering/scientific workstations. Although there may be an occasional occurrence of a reduced precision divide, our extensive experiments with a range of engineering problems covering CAD, structural analysis, computational fluid dynamics and circuit simulation indicate that meaningful inaccuracies in the end-result will only be seen once in about 1,000 years. Technical users running other applications requiring unusual precision and employing millions of divides per day should employ either an updated Pentium processor without the flaw or a software workaround.
Our overall conclusion is that the flaw in the floating point unit of the Pentium processor is of no concern to the vast majority of users. A few users of applications in the scientific/engineering and financial engineering fields may need to employ either an updated processor without the flaw or a software workaround.

This applies to:

FDIV Replacement Program

Solution ID: CS-013017
Last Modified: 11-Dec-2014
Date Created: 08-Jul-2004
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