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 8.3. Trapped Underflow When an underflow trap has been implemented and is enabled, underflow shall be signaled when tininess is detected regardless of loss of accuracy. Trapped underflows on all operations except conversion shall deliver to the trap handler the result obtained by multiplying the infinitely precise result by b a and then rounding. The bias-adjust a is determined by the format's exponent bias from Table 1b: (3/2)(bias+1) - thus 192 in the binary32 format. The bias-adjust a is 192 in the single, 1536 in the double, 24576 in the quad § Q, and 3 × b n– 2 in the extended format, where n is the number of bits in the exponent field. [FOOTNOTE 8: Note that a system whose underlying hardware always traps on underflow, producing a rounded, bias-adjusted result, shall indicate whether such a result is rounded up in magnitude in order that the correctly subnormal denormalized §2 result may be produced in system software when the user underflow trap is disabled.] Trapped underflows on conversion shall be handled analogously to the handling of overflows on conversion. A trapped underflowed result Z of a conversion or scaling operation, intended for a binary floating-point destination, might not round to a normal number in the destination format, even after multiplying by the bias-adjust b a . But for some integral value n > α , Z × b n would round to a normal number z in the destination format, 1
DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20 SECTION 1. Scope 1.1. Implementation Objectives 1.2 Inclusions 1.3. Exclusions 2. Definitions 3. Formats Contents 3.1. Sets of Representable Numerical Values 3.2. Basic Binary Format Encodings 3.3 Basic Decimal Format Encodings 3.4 Extended Formats 3.1. Sets of Values 3.2. Basic Formats 3.3. Extended Formats 3.4. Combinations of Formats 4. Rounding 4.1. Round to Nearest 4.2. Directed Roundings 4.3. Rounding Precision 5. Operations 5.1. Arithmetic 5.2. Square Root 5.3. Floating-Point Format Conversions 5.4. Conversion Between Floating-Point and Integer Formats 5.5. Round Floating-Point Number to Integer Value 5.6. Conversion between binary or decimal internal formats and external decimal formats Binary Decimal Conversion 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 69
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DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

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