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ILM was searching for an image format that could handle a wide dynamic range, but without the hard drive and memory cost of single or double precision floating point. [5] The hardware-accelerated programmable shading group led by John Airey at SGI (Silicon Graphics) used the s10e5 data type in 1997 as part of the 'bali' design effort.
The Java virtual machine's set of primitive data types consists of: [12] byte, short, int, long, char (integer types with a variety of ranges) float and double, floating-point numbers with single and double precisions; boolean, a Boolean type with logical values true and false; returnAddress, a value referring to an executable memory address ...
This alternative definition is significantly more widespread: machine epsilon is the difference between 1 and the next larger floating point number.This definition is used in language constants in Ada, C, C++, Fortran, MATLAB, Mathematica, Octave, Pascal, Python and Rust etc., and defined in textbooks like «Numerical Recipes» by Press et al.
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.
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.
The range of a double-double remains essentially the same as the double-precision format because the exponent has still 11 bits, [4] significantly lower than the 15-bit exponent of IEEE quadruple precision (a range of 1.8 × 10 308 for double-double versus 1.2 × 10 4932 for binary128).
The significand (or mantissa) of an IEEE floating-point number is the part of a floating-point number that represents the significant digits. For a positive normalised number, it can be represented as m 0 . m 1 m 2 m 3 ... m p −2 m p −1 (where m represents a significant digit, and p is the precision) with non-zero m 0 .
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.