Drawing Random Floating-point Numbers from an Interval
Article No.: 16, Pages 1 - 24
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The authors have requested minor, non-substantive changes to the VoR and, in accordance with ACM policies, a Corrected Version of Record was published on December 11, 2023. For reference purposes, the VoR may still be accessed via the Supplemental Material section on this citation page.
Abstract
Drawing a floating-point number uniformly at random from an interval [a, b) is usually performed by a location-scale transformation of some floating-point number drawn uniformly from [0, 1). Due to the weak properties of floating-point arithmetic, such a transformation cannot ensure respect of the bounds, uniformity or spatial equidistributivity. We investigate and quantify precisely these shortcomings while reviewing the actual implementations of the method in major programming languages and libraries, and we propose a simple algorithm to avoid these shortcomings without compromising performances.
Supplementary Material
Version of Record for "Drawing Random Floating-point Numbers from an Interval" by Frédéric Goualard, ACM Transactions on Modeling and Computer Simulation, Volume 32, No. 3 (TOMACS 32:3).
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References
[1]
Nelson H. F. Beebe. 2017. The Mathematical-Function Computation Handbook: Programming Using the MathCW Portable Software Library. Springer International Publishing.
[2]
T. J. Dekker. 1971. A floating-point technique for extending the available precision. Numer. Math. 18, 3 (June 1971), 224–242.
[3]
Frédéric Goualard. 2020. Generating random floating-point numbers by dividing integers: A case study. In Proceedings of the International Conference on Computational Science. V. Krzhizhanovskaya (Ed.), Lecture Notes in Computer Science, Vol. 12138. Springer, Amsterdam, The Netherlands, 15–28.
[4]
Nicholas J. Higham. 2002. Accuracy and Stability of Numerical Algorithms (2nd ed.). Society for Industrial and Applied Mathematics, Philadelphia.
[5]
Brad Lee Holian, Ora E. Percus, Tony T. Warnock, and Paula A. Whitlock. 1994. Pseudorandom number generator for massively parallel molecular-dynamics simulations. Phys. Rev. E 50, 2 (August 1994), 1607–1615.
[6]
IEEE. 2019. IEEE Standard for Floating-Point Arithmetic. Technical Report IEEE Std 754-2019 (Revision of IEEE 754-2008). The Institute of Electrical and Electronics Engineers, Inc.
[7]
Daniel Lemire. 2019. Fast random integer generation in an interval. ACM Trans. Model. Comput. Simul. 29, 1, Article 3 (January 2019).
[8]
George Marsaglia and Wai Wan Tsang. 2004. The 64-bit universal RNG. Stat. Probab. Lett. 66, 2 (2004), 183–187.
[9]
Makoto Matsumoto and Takuji Nishimura. 1998. Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8, 1 (January 1998), 3–30.
[10]
Jean-Michel Muller (Ed.). 2010. Handbook of Floating-point Arithmetic. Birkhäuser, Boston.
[11]
Pat H. Sterbenz. 1973. Floating-point Computation. Prentice-Hall, Englewood Cliffs, NJ.
Index Terms
- Drawing Random Floating-point Numbers from an Interval
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Published In
July 2022
119 pages
Publication rights licensed to ACM. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.
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Association for Computing Machinery
New York, NY, United States
Publication History
Published: 11 April 2022
Accepted: 01 December 2021
Revised: 01 November 2021
Received: 01 July 2021
Published in TOMACS Volume 32, Issue 3
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