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 Operation with decimal result Preferred Exponent of Result min, max, minmag, maxmag Exponent of lesser or greater operand; if operands are numerically equal, return either value (?) [From MFC, using subtraction as a guide, return smaller exponent if the results are numerically equal? -JDD] Table 5: Preferred Exponents of Decimal Arithmetic Operations [Table entries marked with a question mark do not, at the time of this writing, have clear known precedents from prior decimal work. -JDD] If a member of the result’s cohort does not include an element with the preferred exponent, the element with the exponent closest to the preferred exponent is used. Except for some cases near the overflow threshold, the closest exponent in a cohort will be the least exponent larger than the preferred exponent. [From MFC, this statement is not correct; at least not for divide; e.g. ¼. Whether the exponent range of the cohort is greater than or less than the preferred exponent may depend on the operation. -JDD] (A cohort cannot have two members with exponents equally close to the preferred exponent. For example, if elements of the cohort had exponents (preferred-1) and (preferred+1), a member of the cohort would have the preferred exponent too since the exponent range of a cohort is a set of contiguous integers.) Note that, depending on the representation of zero, for finite x, 0 + x can result in a different member of x's cohort being returned. [Some examples would be very helpful in this section; e.g. divide with lots more result digits (1/32), multiply or add with a carry out, etc. -JDD] [The cohorts of nonfinite values need further discussion and defined if they are to be integrated into table 5. -JDD] 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 54
DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20 [It would be humane for the this section, or an appendix, to provide some guidance on the preferred exponents for standard math library functions, x y , log10, etc. -JDD] 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 55
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DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

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