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Conversely, precision can be lost when converting representations from integer to floating-point, since a floating-point type may be unable to exactly represent all possible values of some integer type. For example, float might be an IEEE 754 single precision type, which cannot represent the integer 16777217 exactly, while a 32-bit integer type ...
Before the widespread adoption of IEEE 754-1985, the representation and properties of floating-point data types depended on the computer manufacturer and computer model, and upon decisions made by programming-language designers. E.g., GW-BASIC's single-precision data type was the 32-bit MBF floating-point format.
IBM mainframes support IBM's own hexadecimal floating point format and IEEE 754-2008 decimal floating point in addition to the IEEE 754 binary format. The Cray T90 series had an IEEE version, but the SV1 still uses Cray floating-point format. [citation needed] The standard provides for many closely related formats, differing in only a few details.
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;
In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied. Languages that support a rational data type usually allow the construction of such a value from two integers, instead of a base-2 floating-point number, due to the loss of exactness the latter would cause.
Besides integers, floating-point numbers, and Booleans, other built-in types include: The void type and null pointer type nullptr_t in C++11 and C23; Characters and strings (see below) Tuple in Standard ML, Python, Scala, Swift, Elixir; List in Common Lisp, Python, Scheme, Haskell; Fixed-point number with a variety of precisions and a ...
To approximate the greater range and precision of real numbers, we have to abandon signed integers and fixed-point numbers and go to a "floating-point" format. In the decimal system, we are familiar with floating-point numbers of the form (scientific notation): 1.1030402 × 10 5 = 1.1030402 × 100000 = 110304.02. or, more compactly: 1.1030402E5
^ The current default format is binary. ^ The "classic" format is plain text, and an XML format is also supported. ^ Theoretically possible due to abstraction, but no implementation is included. ^ The primary format is binary, but text and JSON formats are available. [8] [9]