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  2. Quadruple-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Quadruple-precision...

    The Siemens 7.700 and 7.500 series mainframes and their successors support the same floating-point formats and instructions as the IBM System/360 and System/370. 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 ...

  3. IEEE 754 - Wikipedia

    en.wikipedia.org/wiki/IEEE_754

    The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and ...

  4. Machine epsilon - Wikipedia

    en.wikipedia.org/wiki/Machine_epsilon

    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.

  5. List of arbitrary-precision arithmetic software - Wikipedia

    en.wikipedia.org/wiki/List_of_arbitrary...

    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.

  6. Single-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Single-precision_floating...

    A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...

  7. Subnormal number - Wikipedia

    en.wikipedia.org/wiki/Subnormal_number

    In a subnormal number, since the exponent is the least that it can be, zero is the leading significant digit (0.m 1 m 2 m 3...m p−2 m p−1), allowing the representation of numbers closer to zero than the smallest normal number. A floating-point number may be recognized as subnormal whenever its exponent has the least possible value.

  8. Double-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Double-precision_floating...

    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.

  9. Half-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Half-precision_floating...

    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]