Binade

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 [2e,2e+1) or (−2e+1,−2e] for some integer value e, that is, the set of real numbers or floating-point numbers x of the same sign such that 2e≤|x|<2e+1.

Some authors use the convention of the closed interval [2e,2e+1] 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 (0,2emin) of subnormal numbers.

References

  1. ↑ Muller, Jean-Michel; Brunie, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge (2018). Handbook of Floating-Point Arithmetic (2nd ed.). Birkhäuser. pp. 418–419. doi:10.1007/978-3-319-76526-6. ISBN 978-3-319-76525-9.
  2. ↑ Lefèvre, Vincent; Muller, Jean-Michel (2001). "Worst cases for correct rounding of the elementary functions in double precision" (PDF). 15th IEEE Symposium on Computer Arithmetic. ARITH 2001. IEEE. pp. 111–118. doi:10.1109/ARITH.2001.930110. ISSN 1063-6889.
  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.
  4. ↑ Coonen, Jerome T. (1981). "Underflow and the Denormalized Numbers". Computer. 14 (3). IEEE: 75–87. doi:10.1109/C-M.1981.220382. ISSN 0018-9162.
  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.