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Some computer languages have implementations of decimal floating-point arithmetic, including PL/I, .NET, [3] emacs with calc, and Python's decimal module. [4] In 1987, the IEEE released IEEE 854, a standard for computing with decimal floating point, which lacked a specification for how floating-point data should be encoded for interchange with ...
Some programming languages (or compilers for them) provide a built-in (primitive) or library decimal data type to represent non-repeating decimal fractions like 0.3 and −1.17 without rounding, and to do arithmetic on them. Examples are the decimal.Decimal or num7.Num type of Python, and analogous types provided by other languages.
The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.
The standard defines five basic formats that are named for their numeric base and the number of bits used in their interchange encoding. There are three binary floating-point basic formats (encoded with 32, 64 or 128 bits) and two decimal floating-point basic formats (encoded with 64 or 128 bits).
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A minifloat is usually described using a tuple of four numbers, (S, E, M, B): S is the length of the sign field. It is usually either 0 or 1. E is the length of the exponent field.
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).
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