IEEE754Standard

IEEE 754, formally the IEEE Standard for Floating-Point Arithmetic, is a technical standard for floating-point computation used by modern computers and programming languages. It defines formats for representing real numbers, rules for performing floating-point operations, and conventions for rounding, exceptions, and special values. The standard governs binary formats, including binary32 (single precision) and binary64 (double precision), as well as binary128 (quadruple precision) in its more recent revisions. It also defines decimal formats such as decimal32, decimal64, and decimal128, intended for accurate decimal arithmetic and financial calculations. Subnormal (denormal) numbers, zero, infinities, and NaNs are specified, with quiet NaNs and signaling NaNs distinguished to support error signaling.

The core operations covered include addition, subtraction, multiplication, division, and square root, along with conversion between formats and between decimal and binary representations. The standard specifies four rounding modes: round to nearest (ties to even), toward zero, toward positive infinity, and toward negative infinity. It also defines a set of floating-point exceptions (inexact, underflow, overflow, divide-by-zero, invalid operation) and the corresponding status flags, which may be raised or trapped according to the implementation.

IEEE 754 also provides requirements for hardware and software implementations to ensure consistent results across platforms, and it supports facilities for testing conformance. The standard has influenced language specifications and compiler implementations, enabling portable numerical software and predictable numerical behavior. It has been adopted widely in CPUs, GPUs, and embedded processors, and remains the reference for the semantics of floating-point arithmetic.