DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

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DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20 • The reserved value 2 w − 1 to encode ±∞ and NaNs. [Should comment on, or reference to, a discussion of NaN encoding issues such as • What does the sign bit of a NaN mean? • What does the significand of a NaN mean? These issues are largely elided from sections 6.2 and 6.3. -JDD] The value v is inferred from the constituent fields thus: 1. If E = 2 w –1 and T ≠ 0, then v is NaN regardless of S. If d 1 , the most significant bit of T, is 0, then the NaN is signaling; otherwise the NaN is quiet. 2. If E = 2 w –1 and T= 0 , then v = (–1) S ∞ 3. If 1
DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20 3.3. Basic Decimal Format Encodings Unlike basic binary floating-point formats, a representable numerical value may have multiple representations in a basic decimal format; the set of all the distinct representations of the name numerical value form that value’s cohort. For example, in terms of the parameters in section 3.1, the values {e+1-p = 0, m = 100}, {e+1-p = 1, m = 10}, and {e+1-p = 2, m = 1} are three distinct and distinguishable representations from the cohort of one hundred. Consequently, unlike basic binary formats, basic decimal formats do not require values to have a normalized representation. While numerically equal, different members of a cohort can be distinguished by the decimal-specific operations discussed in section 5.11. The cohorts of different values may have different numbers of elements. If a nonzero value has v decimal digits from its most significant nonzero digit to its least significant nonzero digit, the value’s cohort will have at most (p-v)+1 elements where p is the number of digits of precision in the format. For example, a 1-digit value can have up to p different representations while a p-digit value only has one representation. (A v digit value may have fewer than (p-v)+1 elements in its cohort if the value is near the extremes of the format’s exponent range.) Zero has a much larger cohort; +0 and -0 have a representation for each exponent. For decimal arithmetic, besides specifying a numerical result, the arithmetic operands also specify which member of the cohort to return; see section 5.12 for a discussion of this determination. Traditional decimal applications make use of the additional exponent encoding information cohorts allow. Copyright © 2003 by the Institute of Electrical and Electronics Engineers, Inc. This document is an unapproved draft of a proposed IEEE-SA Standard - USE AT YOUR OWN RISK. See statement on page 1. Page 23
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