IEEE754Standards

IEEE 754, the IEEE Standard for Floating-Point Arithmetic, specifies the representation, rounding, and operation rules for floating-point numbers used in computer systems. First published in 1985 and updated in subsequent revisions, including a major 2008 revision and a 2019 edition, the standard aims to provide portable and predictable numerical results across hardware and software.

The standard defines both binary and decimal floating-point formats. Common binary formats include binary32 (single precision), binary64 (double precision), and binary128 (quadruple precision). Decimal formats include decimal32, decimal64, and decimal128. Each floating-point value comprises a sign bit, an exponent field, and a significand (fraction). Normal numbers have an implicit leading 1 in binary formats; subnormal numbers use an exponent of zero and do not have that leading bit, enabling gradual underflow. Special values include +infinity, -infinity, and NaN (not-a-number); zeros come in both +0 and -0 forms. Exponent encoding uses a biased representation, with specific patterns reserved for infinities and NaNs.

Rounding modes are defined, including round to nearest, ties to even; round toward zero; round toward +infinity; and round toward −infinity. The standard specifies arithmetic operations (addition, subtraction, multiplication, division, and square root), conversions between formats, and conversions to and from decimal representations. It also covers exceptional conditions such as overflow, underflow, inexact results, invalid operations, and division by zero, with optional support for fused multiply-add.

IEEE 754 is widely adopted in CPUs, GPUs, and numerical libraries to ensure consistent results across platforms. Compliance is verified by conformance tests, and the standard continues to evolve to address advances in hardware and decimal arithmetic requirements.