We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linear complexity with respect to the target precision and most of them are based on an adaptation to the-adic setting of the binary splitting and bit-burst strategies.

中文翻译：

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一些 p-adic 超越函数的快速求值

我们设计了用于计算许多 p-adic 基本和特殊函数值的算法，包括对数、指数、多对数和超几何函数。我们所有的算法都具有相对于目标精度的准线性复杂度，其中大多数算法都基于对二进制分裂和比特突发策略的进阶设置的适应。