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arXiv · 2303.14321

Exact Short Products From Truncated Multipliers

Daniel Lemire
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Abstract

We sometimes need to compute the most significant digits of the product of small integers with a multiplier requiring much storage: e.g., a large integer (e.g., $5^{100}$) or an irrational number ($\pi$). We only need to access the most significant digits of the multiplier-as long as the integers are sufficiently small. We provide an efficient algorithm to compute the range of integers given a truncated multiplier and a desired number of digits.

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Daniel Lemire. 2023-03-25. Exact Short Products From Truncated Multipliers. https://doi.org/10.1093/comjnl%2Fbxad077

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