IEEE 754

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard.

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 (such as trigonometric functions) on arithmetic formats

exception handling: indications of exceptional conditions (such as division by zero, overflow, etc.)

IEEE 754-2008, published in August 2008, includes nearly all of the original IEEE 754-1985 standard, plus the IEEE 854-1987 (Radix-Independent Floating-Point Arithmetic) standard. The current version, IEEE 754-2019, was published in July 2019. It is a minor revision of the previous version, incorporating mainly clarifications, defect fixes and new recommended operations.

History

The need for a floating-point standard arose from chaos in the business and scientific computing industry in the 1960s and 1970s. IBM used a hexadecimal floating-point format with seven bits always used for the exponent regardless of precision. CDC and Cray computers used ones' complement representation, which admits a value of +0 and −0. CDC 60-bit computers did not have full 60-bit adders, so integer arithmetic was limited to 48 bits of precision from the floating-point unit.