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Direct Search Algorithm for Clock Skew Compensation Immune to Floating-Point Precision Loss

Kyeong Soo Kim

TL;DR

This work tackles clock skew compensation under resource-constrained hardware where floating-point precision loss can impair accuracy. It introduces direct search, an incremental-error algorithm that operates with integer arithmetic and does not rely on initial-value bounds, defined by $j = argmin_{k\ge 0} |k - iD/A|$ with $k$ initialized as $floor(fp(iD/A) + 0.5)$. The method unifies the $D/A<1$ and $D/A>1$ cases and employs a small, finite-step update to obtain the skew-compensated clock, thereby avoiding floating-point divisions entirely. Numerical results demonstrate zero compensation error and substantially fewer iterations than prior extended Bresenham-based approaches, proving robustness to FP precision differences and practical for sensor-network time synchronization. Overall, the direct search approach offers a practically impactful solution for clock skew compensation immune to floating-point precision loss in digital communication systems.

Abstract

We have been investigating clock skew compensation immune to floating-point precision loss by taking into account the discrete nature of clocks in digital communication systems; extending Bresenham's line drawing algorithm, we constructed an incremental error algorithm using only integer addition/subtraction and comparison. Still, bounding the initial value of the clock remains a challenge, which determines the initial condition of the algorithm and thereby its number of iterations. In this letter, we propose a new incremental error algorithm for clock skew compensation, called direct search, which no longer relies on the bounds on the initial value of the clock. The numerical examples demonstrate that the proposed algorithm can significantly reduce the number of iterations in comparison to the prior work while eliminating the effect of floating-point precision loss on clock skew compensation.

Direct Search Algorithm for Clock Skew Compensation Immune to Floating-Point Precision Loss

TL;DR

This work tackles clock skew compensation under resource-constrained hardware where floating-point precision loss can impair accuracy. It introduces direct search, an incremental-error algorithm that operates with integer arithmetic and does not rely on initial-value bounds, defined by with initialized as . The method unifies the and cases and employs a small, finite-step update to obtain the skew-compensated clock, thereby avoiding floating-point divisions entirely. Numerical results demonstrate zero compensation error and substantially fewer iterations than prior extended Bresenham-based approaches, proving robustness to FP precision differences and practical for sensor-network time synchronization. Overall, the direct search approach offers a practically impactful solution for clock skew compensation immune to floating-point precision loss in digital communication systems.

Abstract

We have been investigating clock skew compensation immune to floating-point precision loss by taking into account the discrete nature of clocks in digital communication systems; extending Bresenham's line drawing algorithm, we constructed an incremental error algorithm using only integer addition/subtraction and comparison. Still, bounding the initial value of the clock remains a challenge, which determines the initial condition of the algorithm and thereby its number of iterations. In this letter, we propose a new incremental error algorithm for clock skew compensation, called direct search, which no longer relies on the bounds on the initial value of the clock. The numerical examples demonstrate that the proposed algorithm can significantly reduce the number of iterations in comparison to the prior work while eliminating the effect of floating-point precision loss on clock skew compensation.

Paper Structure

This paper contains 5 sections, 3 theorems, 24 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Review of Clock Skew Compensation Based on the Extended Bresenham's Algorithm
  3. Direct Search Algorithm
  4. Numerical Examples
  5. Conclusions

Key Result

Theorem 1

Given a hardware clock $i$, we can obtain its skew-compensated clock $j$ as follows: Case 1.$\frac{D}{A}{<}1$: The skew-compensated clock $j$ satisfies Unless $i\frac{D}{A}$ is an integer, there are two values satisfying eq:csc-scc_bounds. Because we cannot know the exact value of $i\frac{D}{A}$ due to limited floating-point precision, however, we extend eq:csc-scc_bounds to include the effect of

Figures (3)

  • Figure 1: Clock skew compensation based on the extended Bresenham's algorithm Kim:22-1Kang:23 for the case of $\frac{D}{A}{<}1$.
  • Figure 2: Clock skew compensation based on the direct search algorithm.
  • Figure 3: Comparison of the recursive steps between the direct search algorithm (in blue) and the extended Bresenham's algorithm Kim:22-1Kang:23 (in red).

Theorems & Definitions (4)

  • Theorem 1: Clock Skew Compensation Based on the Extended Bresenham's Algorithm Kim:22-1Kang:23
  • Definition 1
  • Lemma 1
  • Theorem 2: Clock Skew Compensation Based on Direct Search