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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.
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.
Converting a double-precision binary floating-point number to a decimal string is a common operation, but an algorithm producing results that are both accurate and minimal did not appear in print until 1990, with Steele and White's Dragon4. Some of the improvements since then include:
Quadruple-precision floating-point format; Octuple-precision floating-point format; Of these, octuple-precision format is rarely used. The single- and double-precision formats are most widely used and supported on nearly all platforms. The use of half-precision format has been increasing especially in the field of machine learning since many ...
The VAX processor implemented non-IEEE quadruple-precision floating point as its "H Floating-point" format. It had one sign bit, a 15-bit exponent and 112-fraction bits, however the layout in memory was significantly different from IEEE quadruple precision and the exponent bias also differed.
Exact numbers also include rationals, so (/ 3 4) produces 3/4. Arbitrary precision floating point numbers are included in the standard library math/bigfloat module. Raku: Rakudo supports Int and FatRat data types that promote to arbitrary-precision integers and rationals. Rexx: variants including Open Object Rexx and NetRexx
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.
It was designed to support a 32-bit "single precision" format and a 64-bit "double-precision" format for encoding and interchanging floating-point numbers. The extended format was designed not to store data at higher precision, but rather to allow for the computation of temporary double results more reliably and accurately by minimising ...