Many programming languages provides mechanism lo guarantee the error ranges of exact numbers and intervals. However, when they are integrated with unreliable approximated numbers, we cannot rely on the error-ranges anymore. Such unreliable error-ranges may cause serious errors in programs, and especially in safety critical systems they cost us huge amount of money and'or threaten human's life. Hence, in this paper, we propose a novel number system to safely perform arithmetic operations with guaranteed error ranges. In the number system, exact numbers are separated from approximated numbers, and approximated numbers with strictly guaranteed error-ranges are again separated from unwarranted numbers such as floating-point numbers. A three-valued logic is also shipped with our number system to appropriately deal with uncertainties due to approximations. A prototype implementation of our number system in Python is demonstrated. With this module, we can more reliably execute operations on numbers and make judgments on the conditions involving numbers.
|Number of pages
|Computer Systems Science and Engineering
|Published - 2018 Nov
Bibliographical notePublisher Copyright:
© 2018 CRL Publishing. All rights reserved.
- Approximated number system
- Exact bounds
- Formal methods
- Three-valued logic
ASJC Scopus subject areas
- Control and Systems Engineering
- Theoretical Computer Science
- General Computer Science