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Single precision is termed REAL in Fortran; [1] SINGLE-FLOAT in Common Lisp; [2] float in C, C++, C# and Java; [3] Float in Haskell [4] and Swift; [5] and Single in Object Pascal , Visual Basic, and MATLAB. However, float in Python, Ruby, PHP, and OCaml and single in versions of Octave before 3.2 refer to double-precision numbers.
For example, the number 2469/200 is a floating-point number in base ten with five digits: / = = ⏟ ⏟ ⏞ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346.
Go: the standard library package math/big implements arbitrary-precision integers (Int type), rational numbers (Rat type), and floating-point numbers (Float type) Guile: the built-in exact numbers are of arbitrary precision. Example: (expt 10 100) produces the expected (large) result. Exact numbers also include rationals, so (/ 3 4) produces 3/4.
This gives from 33 to 36 significant decimal digits precision. If a decimal string with at most 33 significant digits is converted to the IEEE 754 quadruple-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string.
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.
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]
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.
The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits). The two most commonly used levels of precision for floating-point numbers are single precision and double precision.