Abstract
We study arithmetic properties of a new tree-based canonical number representation, recursively run-length compressed natural numbers, defined by applying recursively a run-length encoding of their binary digits.
We design arithmetic operations with recursively run-length compressed natural numbers that work a block of digits at a time and are limited only by the representation complexity of their operands, rather than their bitsizes.
As a result, operations on very large numbers exhibiting a regular structure become tractable.
In addition, we ensure that the average complexity of our operations is still within constant factors of the usual arithmetic operations on binary numbers.
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Tarau, P. (2014). The Arithmetic of Recursively Run-Length Compressed Natural Numbers. In: Ciobanu, G., Méry, D. (eds) Theoretical Aspects of Computing – ICTAC 2014. ICTAC 2014. Lecture Notes in Computer Science, vol 8687. Springer, Cham. https://doi.org/10.1007/978-3-319-10882-7_24
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DOI: https://doi.org/10.1007/978-3-319-10882-7_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10881-0
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