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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).
IEEE 754-1985 [1] is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. [2] During its 23 years, it was the most widely used format for floating-point computation.
In the IEEE 754 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 single precision and, more recently, base-10 representations ( decimal floating point ).
The new IEEE 754 (formally IEEE Std 754-2008, the IEEE Standard for Floating-Point Arithmetic) was published by the IEEE Computer Society on 29 August 2008, and is available from the IEEE Xplore website [4] This standard replaces IEEE 754-1985. IEEE 854, the Radix-Independent floating-point standard was withdrawn in December 2008.
The Bfloat16 format requires the same amount of memory (16 bits) as the IEEE 754 half-precision format, but allocates 8 bits to the exponent instead of 5, thus providing the same range as a IEEE 754 single-precision number. The tradeoff is a reduced precision, as the trailing significand field is reduced from 10 to 7 bits.
IEEE 754 specifies additional floating-point types, such as 64-bit base-2 double precision and, more recently, base-10 representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and properties of ...
William Kahan, primary architect of the original IEEE 754 floating-point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format ...
The IEEE 754-2008 standard defines 32-, 64- and 128-bit decimal floating-point representations. Like the binary floating-point formats, the number is divided into a sign, an exponent, and a significand.