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A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable computers and calculators. [1] Numerical values are stored as groupings of bits , such as bytes and words.
The bfloat16 (brain floating point) [1] [2] floating-point format is a computer number format occupying 16 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
In computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural networks .
The Q notation is a way to specify the parameters of a binary fixed point number format. For example, in Q notation, the number format denoted by Q8.8 means that the fixed point numbers in this format have 8 bits for the integer part and 8 bits for the fraction part. A number of other notations have been used for the same purpose.
(The term "exception" as used in IEEE 754 is a general term meaning an exceptional condition, which is not necessarily an error, and is a different usage to that typically defined in programming languages such as a C++ or Java, in which an "exception" is an alternative flow of control, closer to what is termed a "trap" in IEEE 754 terminology.)
strictfp, an obsolete keyword in the Java programming language that previously restricted arithmetic to IEEE 754 single and double precision to ensure reproducibility across common hardware platforms (as of Java 17, this behavior is required) Table-maker's dilemma for more about the correct rounding of functions; Standard Apple Numerics Environment
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
Hexadecimal floating point (now called HFP by IBM) is a format for encoding floating-point numbers first introduced on the IBM System/360 computers, and supported on subsequent machines based on that architecture, [1] [2] [3] as well as machines which were intended to be application-compatible with System/360.