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Performance Benchmarks

This document details the performance metrics for dreid-kernel. All benchmarks were conducted using the Criterion.rs framework to ensure statistical significance.

Executive Summary

The DREIDING force field kernel achieves extreme throughput by leveraging zero-cost abstractions and compiler optimizations.

  • Fastest Kernel: Cosine Linear Angle (~1.5 Billion Combined Ops/sec).
  • Most Common Kernel: Lennard-Jones vdW (~840 Million Combined Ops/sec).
  • Complex Kernel: Buckingham vdW (~140 Million Combined Ops/sec).
  • Optimization: The compute() function (Energy + Force) is typically faster than the sum of their disparate calls due to shared intermediate calculations (e.g., $r^{-6}$ reuse).

Detailed Results

Legend:

  • Energy: Time to compute potential energy only ($E$).
  • Force: Time to compute the force/derivative factor only (e.g., $-\frac{1}{r}\frac{dE}{dr}$ or $\frac{dE}{dq}$).
  • Combined: Time to compute both simultaneously. This utilizes shared sub-expressions (instruction-level optimization).
  • Throughput: Based on the Combined calculation time.

Non-Bonded Interactions

Potential Variant Energy (ns) Force (ns) Combined (ns) Throughput (MOps/s)
Lennard-Jones 12-6 0.94 0.97 1.19 840
Coulomb Electrostatic 2.08 2.07 2.18 458
Buckingham Exp-6 5.31 6.42 7.08 141
Hydrogen Bond 12-10 (n=4) 1.51 2.09 2.19 456

Note: Lennard-Jones combined calculation is extremely efficient, costing only ~0.25ns more than computing force alone.

Bonded Interactions

Group Potential Energy (ns) Force (ns) Combined (ns) Throughput (MOps/s)
Stretch Harmonic 1.23 2.15 2.20 454
Stretch Morse 4.61 5.92 6.25 160
Angle Cosine Harmonic 0.56 0.55 0.70 1,428
Angle Cosine Linear 0.54 0.39 0.67 1,494
Angle Theta Harmonic 5.02 5.84 6.14 162
Torsion Cosine (n=1) 1.63 1.60 2.03 492
Torsion Cosine (n=3) 2.13 2.18 2.55 392
Torsion Cosine (n=6) 3.22 3.47 3.81 262
Inversion Planar 0.49 0.51 0.62 1,612
Inversion Umbrella 0.57 0.55 0.71 1,408

Test Environment

  • CPU: Intel® Core™ i7-13620H (Raptor Lake)
    • 10 Cores (6P + 4E), 16 Threads
    • Max Turbo Frequency: 4.90 GHz
    • Instruction Set: AVX2, FMA3
  • OS: Linux (Arch Linux, Kernel 6.12.63-1)
  • Date: January 2026

Analysis

  1. Shared Instruction Optimization: In almost all cases, Combined < Energy + Force. For example, in Lennard-Jones, computing both ($1.19,\text{ns}$) is nearly as fast as computing just the force ($0.97,\text{ns}$). This confirms that the compiler and CPU are effectively reusing the expensive $r^{-6}$ and $r^{-12}$ terms.
  2. Cosine vs Theta: We observe a 10x speedup when using the CosineHarmonic form ($\cos\theta - \cos\theta_0$) instead of the ThetaHarmonic form ($\theta - \theta_0$), due to the avoidance of the acos instruction.
  3. Branchless Piecewise Function: The Buckingham kernel uses energy reflection at the potential maximum ($r = r_{max}$) to handle the unphysical divergence at $r \to 0$. This is implemented as a branchless piecewise function: computing both the standard Buckingham energy and the reflected energy ($2E_{max} - E$), then selecting via arithmetic masking. This avoids expensive branch mispredictions and maintains consistent throughput suitable for SIMD vectorization.