IEEE 754-2008 revision

IEEE 754-2008 was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 floating-point standard, while in 2019 it was updated with a minor revision IEEE 754-2019. The 2008 revision extended the previous standard where it was necessary, added decimal arithmetic and formats, tightened up certain areas of the original standard which were left undefined, and merged in IEEE 854.
In a few cases, where stricter definitions of binary floating-point arithmetic might be performance-incompatible with some existing implementation, they were made optional.

Revision process

The standard had been under revision since 2000, with a target completion date of December 2006. The revision of an IEEE standard broadly follows three phases:
  1. Working group - a committee that creates a draft standard
  2. Ballot - interested parties subscribe to the balloting group and vote on the draft ; comments from the votes are resolved by a Ballot Resolution Committee and changes made have to be recirculated with a new ballot if they are substantive
  3. When all comments are resolved and there are no further changes, the draft is submitted to the IEEE for review, approval, and publication.
On 11 June 2008, it was approved unanimously by the IEEE Revision Committee, and it was formally approved by the IEEE-SA Standards Board on 12 June 2008. It was published on 29 August 2008.

754r Working Group phase

Participation in drafting the standard was open to people with a solid knowledge of floating-point arithmetic. More than 90 people attended at least one of the monthly meetings, which were held in Silicon Valley, and many more participated through the mailing list.
Progress at times was slow, leading the chairman to declare at the 15 September 2005 meeting that "no progress is being made, I am suspending these meetings until further notice on those grounds".
In December 2005, the committee reorganized under new rules with a target completion date of December 2006.
New policies and procedures were adopted in February 2006. In September 2006, a working draft was approved to be sent to the parent sponsoring committee for editing and to be sent to sponsor ballot.

754r Ballot phase

The last version of the draft, version 1.2.5, submitted to the MSC was from 4 October 2006. The MSC accepted the draft on 9 October 2006. The draft has been changed significantly in detail during the balloting process.
The first sponsor ballot took place from 29 November 2006 through 28 December 2006. Of the 84 members of the voting body, 85.7% responded—78.6% voted approval. There were negative votes so there was a recirculation ballot in March 2007; this received an 84% approval. There were sufficient comments from that ballot that a third draft was prepared for second, 15-day, recirculation ballot which started in mid-April 2007. For a technical reason, the ballot process was restarted with the 4th ballot in October 2007; there were also substantial changes in the draft resulting from 650 voters' comments and from requests from the sponsor ; this ballot just failed to reach the required 75% approval. The 5th ballot had a 98.0% response rate with 91.0% approval, with comments leading to relatively small changes. The 6th, 7th, and 8th ballots sustained approval ratings of over 90% with progressively fewer comments on each draft; the 8th was submitted to the IEEE Standards Revision Committee for approval as an IEEE standard.

754r Review and Approval phase

The IEEE Standards Revision Committee considered and unanimously approved the IEEE 754r draft at its June 2008 meeting, and it was approved by the IEEE-SA Standards Board on 12 June 2008. Final editing is complete and the document has now been forwarded to the IEEE Standards Publications Department for publication.

IEEE Std 754-2008 publication

The new IEEE 754 was published by the IEEE Computer Society on 29 August 2008, and is available from the IEEE Xplore website
This standard replaces IEEE 754-1985. IEEE 854, the Radix-Independent floating-point standard was withdrawn in December 2008.

Summary of the revisions

The most obvious enhancements to the standard are the addition of a 16-bit and a 128-bit binary type and three decimal types, some new operations, and many recommended functions. However, there have been significant clarifications in terminology throughout. This summary highlights the main differences in each major clause of the standard.

Clause 1: Overview

The scope has been widened to include decimal formats and arithmetic, and adds extendable formats.

Clause 2: Definitions

Many of the definitions have been rewritten for clarification and consistency. A few terms have been renamed for clarity.

Clause 3: Formats

The description of formats has been made more regular, with a distinction between arithmetic formats and interchange formats. Conformance to the standard is now defined in these terms.
The specification levels of a floating-point format have been enumerated, to clarify the distinction between:
  1. the theoretical real numbers
  2. the entities which can be represented in the format
  3. the particular representations of the entities: sign-exponent-significand, etc.
  4. the bit-pattern used.
The sets of representable entities are then explained in detail, showing that they can be treated with the significand being considered either as a fraction or an integer. The particular sets known as basic formats are defined, and the encodings used for interchange of binary and decimal formats are explained.
The binary interchange formats have the "half precision" and "quad precision" added, together with generalized formulae for some wider formats; the basic formats have 32-bit, 64-bit, and 128-bit encodings.
Three new decimal formats are described, matching the lengths of the 32–128-bit binary formats. These give decimal interchange formats with 7, 16, and 34-digit significands, which may be normalized or unnormalized. For maximum range and precision, the formats merge part of the exponent and significand into a combination field, and compress the remainder of the significand using either a decimal integer encoding encoding or conventional binary integer encoding. The basic formats are the two larger sizes, which have 64-bit and 128-bit encodings. Generalized formulae for some other interchange formats are also specified.
Extended and extendable formats allow for arithmetic at other precisions and ranges.

Clause 4: Attributes and rounding

This clause has been changed to encourage the use of static attributes for controlling floating-point operations, and allow for alternate exception handling, widening of intermediate results, value-changing optimizations, and reproducibility.
The round-to-nearest, ties away from zero rounding attribute has been added.

Clause 5: Operations

This section has numerous clarifications, and several previously recommended operations are now required.
New operations include fused multiply–add, explicit conversions, classification predicates, various min and max functions, a total ordering predicate, and two decimal-specific operations.

Min and max

The min and max operations are defined but leave some leeway for the case where the inputs are equal in value but differ in representation. In particular:
In order to support operations such as windowing in which a NaN input should be quietly replaced with one of the end points, min and max are defined to select a number, x, in preference to a quiet NaN:
These functions are called minNum and maxNum to indicate their preference for a number over a quiet NaN. However, in the presence of a signaling NaN input, a quiet NaN is returned as with the usual operations. After the publication of the standard, it was noticed that these rules make these operations non-associative; for this reason, they have been replaced by new operations in IEEE 754-2019.

Decimal arithmetic

Decimal arithmetic, compatible with that used in Java, C#, PL/I, COBOL, Python, REXX, etc., is also defined in this section. In general, decimal arithmetic follows the same rules as binary arithmetic, with additional rules that define the exponent of a result.

Correctly rounded base conversion

Unlike in 854, 754-2008 requires correctly rounded base conversion between decimal and binary floating point within a range which depends on the format.

Clause 6: Infinity, NaNs, and sign bit

This clause has been revised and clarified, but with no major additions.

Clause 7: Default exception handling

This clause has been revised and considerably clarified, but with no major additions.

Clause 8: Alternate exception handling

This clause has been extended from the previous Clause 8 to allow optional exception handling in various forms, including traps and other models such as try/catch. Traps and other exception mechanisms remain optional, as they were in IEEE 754-1985.

Clause 9: Recommended operations

This clause is new; it recommends fifty operations, including log, power, and trigonometric functions, that language standards should define. These are all optional. The operations include some on dynamic modes for attributes, and also a set of reduction operations.

Clause 10: Expression evaluation

This clause is new; it recommends how language standards should specify the semantics of sequences of operations, and points out the subtleties of literal meanings and optimizations that change the value of a result.

Clause 11: Reproducibility

This clause is new; it recommends that language standards should provide a means to write reproducible programs, and describes what needs to be done to achieve reproducible results.

Annex B: Program debugging support

This annex is new; it provides guidance to debugger developers for features that are desired for supporting the debugging of floating-point code.

Index of operations

This is a new index, which lists all the operations described in the standard.

Discussed but not included

Due to changes in CPU design and development, the 2008 IEEE floating-point standard could be viewed as historical or outdated as the 1985 standard it replaced. There were many outside discussions and items not covered in the standardization process, the items below are the ones that became public knowledge: