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Binade

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Interval of binary floating-point numbers with a common sign and exponent
An axis with tick marks for each floating-point number between 0 and 1 with 3 bits of precision and minimum exponent −5, with an underbrace labelled +1.xy × 2^(−2) to highlight the ticks for numbers from 1/4, inclusive, to 1/2, exclusive.
The binade of exponent −2 in the floating-point numbers with 3 bits of precision and minimum exponent −5

In software engineering and numerical analysis, a binade is a set of numbers in a binary floating-point format that all have the same sign and exponent. In other words, a binade is the interval [ 2 e , 2 e + 1 ) {\displaystyle [2^{e},2^{e+1})} ( − 2 e + 1 , − 2 e ] {\displaystyle (-2^{e+1},-2^{e}]} for some integer value  e {\displaystyle e} , that is, the set of real numbers or floating-point numbers x {\displaystyle x} of the same sign such that 2 e ≤ | x | < 2 e + 1 {\displaystyle 2^{e}\leq |x|<2^{e+1}} .

Some authors use the convention of the closed interval [ 2 e , 2 e + 1 ] {\displaystyle } instead of a half-open interval, sometimes using both conventions in a single paper. Some authors additionally treat each of various special quantities such as NaN, infinities, and zeroes as its own binade, or similarly for the exceptional interval ( 0 , 2 e m i n ) {\displaystyle (0,2^{\mathrm {emin} })} of subnormal numbers.

See also

References

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  3. Benet, Luis; Ferranti, Luca; Revol, Nathalie (2023). "A framework to test interval arithmetic libraries and their IEEE 1788-2015 compliance". Concurrency and Computation: Practice and Experience. 36: e7856. arXiv:2307.06953. doi:10.1002/cpe.7856. ISSN 1532-0626.
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  5. Hanrot, Guillaume; Lefèvre, Vincent; Stehlé, Damien; Zimmermann, Paul (2007). "Worst Cases of a Periodic Function for Large Arguments". 18th IEEE Symposium on Computer Arithmetic. ARITH 2007. pp. 133–140. doi:10.1109/ARITH.2007.37. ISSN 1063-6889.
  6. Thomas, David B. (2015). "A general-purpose method for faithfully rounded floating-point function approximation in FPGAs". 22nd IEEE Symposium on Computer Arithmetic. ARITH 2015. pp. 42–49. doi:10.1109/ARITH.2015.27. ISSN 1063-6889.
  7. Agrawal, Ankur; Mueller, Sylvia M.; Fleischer, Bruce M.; Choi, Jungwook; Wang, Naigang; Sun, Xiao; Gopalakrishnan, Kailash (2019). "DLFloat: A 16-b Floating Point format designed for Deep Learning Training and Inference". 26th IEEE Symposium on Computer Arithmetic. ARITH 2019. pp. 92–95. doi:10.1109/ARITH.2019.00023. ISSN 1063-6889.
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