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Swift introduced half-precision floating point numbers in Swift 5.3 with the Float16 type. [20] OpenCL also supports half-precision floating point numbers with the half datatype on IEEE 754-2008 half-precision storage format. [21] As of 2024, Rust is currently working on adding a new f16 type for IEEE half-precision 16-bit floats. [22]
An IEEE 754 format is a "set of representations of numerical values and symbols". A format may also include how the set is encoded. [9] A floating-point format is specified by a base (also called radix) b, which is either 2 (binary) or 10 (decimal) in IEEE 754; a precision p;
Additionally, they are frequently encountered as a pedagogical tool in computer-science courses to demonstrate the properties and structures of floating-point arithmetic and IEEE 754 numbers. Minifloats with 16 bits are half-precision numbers (opposed to single and double precision). There are also minifloats with 8 bits or even fewer. [2]
Bfloat16 is designed to maintain the number range from the 32-bit IEEE 754 single-precision floating-point format (binary32), while reducing the precision from 24 bits to 8 bits. This means that the precision is between two and three decimal digits, and bfloat16 can represent finite values up to about 3.4 × 10 38.
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.
The octuple-precision binary floating-point exponent is encoded using an offset binary representation, with the zero offset being 262143; also known as exponent bias in the IEEE 754 standard. E min = −262142
Microsoft provides a dynamic link library for 16-bit Visual Basic containing functions to convert between MBF data and IEEE 754. This library wraps the MBF conversion functions in the 16-bit Visual C(++) CRT. These conversion functions will round an IEEE double-precision number like ¾ ⋅ 2 −128 to zero rather than to 2 −128.
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.