DeepAI AI Chat
Log In Sign Up

Fast evaluation of some p-adic transcendental functions

06/17/2021
by   Xavier Caruso, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

10/20/2021

Rapid computation of special values of Dirichlet L-functions

We consider computing the Riemann zeta function ζ(s) and Dirichlet L-fun...
07/06/2022

Computing elementary functions using multi-prime argument reduction

We describe an algorithm for arbitrary-precision computation of the elem...
12/15/2020

Fast Computation of the N-th Term of a q-Holonomic Sequence and Applications

In 1977, Strassen invented a famous baby-step/giant-step algorithm that ...
06/24/2022

Elementary analytic functions in VTC^0

It is known that rational approximations of elementary analytic function...
04/08/2021

RLIBM-32: High Performance Correctly Rounded Math Libraries for 32-bit Floating Point Representations

This paper proposes a set of techniques to develop correctly rounded mat...
04/10/2020

A Simple Method for Computing Some Pseudo-Elliptic Integrals in Terms of Elementary Functions

We introduce a method for computing some pseudo-elliptic integrals in te...
03/03/2022

Certified Newton schemes for the evaluation of low-genus theta functions

Theta functions and theta constants in low genus, especially genus 1 and...