We introduce the Collatz-Weyl Generators, a family of uniform pseudorandom number generators (PRNGs) which are based on generalized Collatz mappings, derived from the Collatz conjecture and Weyl sequences. The high-quality statistical properties of our generators is demonstrated by the fact that they pass stringent randomness tests used by the research and standardization community. The proposed Collatz-Weyl Generators have a number of important properties, including solid mathematical foundations, enablement of high throughput and low latency implementation, small code and/or ASIC size, enablement of producing multiple independent streams and potential of support of cryptographic applications.

翻译：我们提出了Collatz-Weyl随机数生成器，这是一类基于广义Collatz映射的一致伪随机数生成器（PRNG），其源于Collatz猜想与Weyl序列。该生成器的高质量统计特性通过其能够通过研究界与标准化领域使用的严格随机性检验而得到验证。所提出的Collatz-Weyl生成器具有若干重要性质，包括坚实的数学基础、支持高吞吐量与低延迟实现、代码和/或专用集成电路规模小、支持生成多个独立数据流，并具备支持加密应用的潜力。