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The IEEE Floating Point Standard and Its Users |
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While it is beyond the scope of this book to go into the details of the IEEE standard, the standard represents a significant contribution to improved accuracy of representation, completeness, and operational power. (For example, the IEEE standard supports four rounding modesround to nearest, truncate, round positive, and round negative, in contrast to most machines with either no or one single rounding option.) The standard introduced the notion of denormalized numbersa technique to preserve the accuracy and integrity of very small numbers, rather than set them to zero as done in other machines. The standard defines and supports square root, data conversion operations, and other operations which are not always found in floating-point operational repertoire. As a necessary consequence, the IEEE standard is somewhat difficult to implement. It is complex, and requires designers to add extra hardware to complete the full formation of resultant products, etc. |
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There are some ironies in all this. The IEEE standard is used with almost all microprocessor architectures, including the R/M (Intel x86) and all of the L/S architectures (the RISC microprocessors). Use of the IEEE standard with the RISC processors is particularly interesting. The IEEE standard at first glance appears to be the antithesis of the principles incorporated in the RISC machine design philosophy. It is complex and time-consuming, in both design time and execution time. It is exactly what the RISC machine philosophy was developed to overcome. Yet because it is a standard, few designers have even noted the philosophic inconsistency or irony in it all. It represents the adoption of two conflicting design styles or fashions. |
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There is yet another irony. The IEEE standard, with its extensive rounding support and support for data integrity, is most valuable in large-scale scientific computations which may go on for hours on the largest and most sophisticated of computers. The standard is least valuable in smaller workstation-type applications whose execution time rarely exceeds several minutes. Yet the supercomputer designers, such as Cray Corporation, use a very crude floating-point format supporting a minimum accuracy (minimum rounding flexibility) philosophy in the interest of speed. Most large scientific computations are carried out on supercomputers like the Cray by users who seem to prefer the reduced floating-point capability with perhaps reduced accuracy if providing high speed. Yet those workstation users who have access to the fully featured floating-point standard rarely have applications that really exercise its facilities. |
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