An Improved Integer Modular Multiplicative Inverse (modulo 2^w)

04/09/2022
by   Jeffrey Hurchalla, et al.
0

This paper presents an algorithm for the integer multiplicative inverse (mod 2^w) which completes in the fewest cycles known for modern microprocessors, when using the native bit width w for the modulus 2^w. The algorithm is a modification of a method by Dumas, and for computers it slightly increases generality and efficiency. A proof is given, and the algorithm is shown to be closely related to the better known Newton's method algorithm for the inverse. Simple direct formulas, which are needed by this algorithm and by Newton's method, are reviewed and proven for the integer inverse modulo 2^k with k = 1, 2, 3, 4, or 5, providing the first proof of the preferred formula with k=4 or 5.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/17/2018

Improving the accuracy of the fast inverse square root algorithm

We present improved algorithms for fast calculation of the inverse squar...
research
04/04/2023

Efficient Generic Quotients Using Exact Arithmetic

The usual formulation of efficient division uses Newton iteration to com...
research
07/13/2020

Inverse Cubic Iteration

There are thousands of papers on rootfinding for nonlinear scalar equati...
research
07/17/2020

A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón's method in the plane

A direct reconstruction algorithm based on Calderón's linearization meth...
research
01/23/2020

Canonical form of modular hyperbolas with an application to integer factorization

For a composite n and an odd c with c not dividing n, the number of solu...
research
07/25/2019

Improved Girth Approximation and Roundtrip Spanners

In this paper we provide improved algorithms for approximating the girth...
research
02/05/2019

Faster Remainder by Direct Computation: Applications to Compilers and Software Libraries

On common processors, integer multiplication is many times faster than i...

Please sign up or login with your details

Forgot password? Click here to reset