IEEE Floating Point

IEEE Floating Point

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). Many hardware floating point units use the IEEE 754 standard. The current version, IEEE 754-2008 published in August 2008, includes nearly all of the original IEEE 754-1985 standard and the IEEE Standard for Radix-Independent Floating-Point Arithmetic (IEEE 854-1987). The international standard ISO/IEC/IEEE 60559:2011 (with identical content to IEEE 754) has been approved for adoption through JTC1/SC 25 under the ISO/IEEE PSDO Agreement and published.

The standard defines

• arithmetic formats: sets of binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinities, and special "not a number" values (NaNs)
• interchange formats: encodings (bit strings) that may be used to exchange floating-point data in an efficient and compact form
• rounding rules: properties to be satisfied when rounding numbers during arithmetic and conversions
• operations: arithmetic and other operations on arithmetic formats
• exception handling: indications of exceptional conditions (such as division by zero, overflow, etc.)

The standard also includes extensive recommendations for advanced exception handling, additional operations (such as trigonometric functions), expression evaluation, and for achieving reproducible results.

The standard is derived from and replaces IEEE 754-1985, the previous version, following a seven-year revision process, chaired by Dan Zuras and edited by Mike Cowlishaw. The binary formats in the original standard are included in the new standard along with three new basic formats (one binary and two decimal). To conform to the current standard, an implementation must implement at least one of the basic formats as both an arithmetic format and an interchange format.