Mixed-Precision For Energy Efficient Computations

G\"ul\c{c}in Gedik; Robert Sch\"one; Roman Iakymchuk

arxiv: 2606.27949 · v1 · pith:RYVLTYVVnew · submitted 2026-06-26 · 💻 cs.PF

Mixed-Precision For Energy Efficient Computations

G\"ul\c{c}in Gedik , Robert Sch\"one , Roman Iakymchuk This is my paper

Pith reviewed 2026-06-29 01:58 UTC · model grok-4.3

classification 💻 cs.PF

keywords mixed-precisionenergy efficiencytime-to-solutionreactor simulatorLULESHscientific simulationsfloating-point arithmetic

0 comments

The pith

Mixed-precision cuts time and energy to solution by up to 30 percent in reactor and hydrodynamics simulations while keeping accuracy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines whether mixed-precision arithmetic can lower both the time and energy required for realistic simulations without losing accuracy. It applies the approach to the Reactor Simulator benchmark and obtains 30 percent reductions in both time-to-solution and energy-to-solution. The same strategy on LULESH produces up to 30 percent faster time-to-solution and 25 percent lower energy-to-solution. If the accuracy holds under the chosen checks, the method offers a practical route to more efficient scientific computing on existing hardware.

Core claim

Applying mixed-precision strategies to the Reactor Simulator achieves a 30 percent reduction in both time-to-solution and energy-to-solution without compromising accuracy. The same approach on LULESH delivers up to 30 percent improvement in time-to-solution and 25 percent reduction in energy-to-solution.

What carries the argument

Mixed-precision computing, the selective use of lower floating-point precision in parts of a calculation where it does not affect final accuracy.

If this is right

Reactor simulations can complete with 30 percent less time and energy.
Hydrodynamics codes such as LULESH gain comparable time and energy savings.
Accuracy remains acceptable when the paper's specific error metrics are applied.
Mixed-precision offers an immediate efficiency gain on current hardware without requiring new machines.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same precision-tuning pattern may transfer to other large-scale scientific codes that tolerate comparable local errors.
Hardware designs that make mixed-precision switches cheaper could amplify the reported savings.
Routine use of mixed precision might shift how developers allocate floating-point operations across entire simulation pipelines.

Load-bearing premise

Accuracy is preserved only if the error metrics and test cases chosen for the benchmarks catch every failure mode that matters in real workloads.

What would settle it

A production run of either benchmark under mixed precision that shows a clear accuracy failure missed by the paper's error metrics would disprove the no-compromise result.

Figures

Figures reproduced from arXiv: 2606.27949 by G\"ul\c{c}in Gedik, Robert Sch\"one, Roman Iakymchuk.

read the original abstract

As simulations grow more realistic, the pursuit of higher accuracy results in extended computation times and substantial power consumption. This study explores mixed-precision computing as a promising strategy to address these challenges, leveraging computer arithmetic tools to optimize performance. Using Reactor Simulator and LULESH benchmarks as case studies, we evaluated the potential of mixed-precision strategies to reduce both time-to-solution and energy-to-solution. For Reactor Simulator, we achieved a 30% reduction in both metrics without compromising accuracy. Similarly, for LULESH, results demonstrated up to a 30% improvement in time-to-solution and a 25% reduction in energy-to-solution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper reports 25-30% time and energy savings from mixed precision on two benchmarks but supplies no details on precisions used or accuracy metrics.

read the letter

The main takeaway is that the authors ran mixed-precision versions of Reactor Simulator and LULESH and measured roughly 30% drops in both runtime and energy for the first benchmark, with up to 30% time and 25% energy gains for the second, while stating that accuracy held. Those measured numbers are what the work contributes.

The paper applies an established technique to two known codes and records the resulting time and energy figures. It does a straightforward job of showing that energy can be reduced in these cases when the precision mix is chosen appropriately for the workload.

The soft spots are the missing pieces that make the accuracy claim hard to judge. The abstract never names the floating-point formats combined, the error metric (L2 norm, max deviation, conservation error, or something else), the tolerance threshold, or the test cases used to declare accuracy preserved. Without those, it is not possible to tell whether the savings come at an acceptable cost or whether the metrics simply overlook relevant failure modes. There is also no information on run-to-run variation or how the mixed-precision code was actually written.

The work stays within empirical reporting and does not add new methods or first-principles analysis. The stress-test note about unspecified accuracy criteria is on target given what is shown.

This paper is mainly for people already tuning energy use on these exact benchmarks or similar HPC codes. A reader looking for general guidance on mixed precision or for reproducible methods will not find enough. It shows honest measurement but limited depth.

I would not bring it to reading group. I would not cite it. It does not merit sending out for peer review until the authors add the missing methodological information.

Referee Report

2 major / 0 minor

Summary. The manuscript presents an empirical study on mixed-precision computing strategies to reduce time-to-solution and energy-to-solution in scientific simulations. Using the Reactor Simulator and LULESH benchmarks, it reports a 30% reduction in both metrics for Reactor Simulator without compromising accuracy, and up to 30% improvement in time-to-solution with 25% reduction in energy-to-solution for LULESH.

Significance. If the accuracy preservation and performance claims can be substantiated with full methodological details, the work would provide practical evidence for energy savings in HPC workloads via mixed precision, adding to the literature on sustainable scientific computing. The purely empirical approach, if made reproducible, could serve as a useful case study for benchmark-driven evaluation of arithmetic optimizations.

major comments (2)

[Abstract] Abstract: The central claim that a 30% reduction in time-to-solution and energy-to-solution was achieved for Reactor Simulator 'without compromising accuracy' provides no information on the error metric (e.g., relative L2 norm, max pointwise error, conservation violation), the tolerance threshold applied, or the specific test cases and input configurations used to verify this. This renders the headline result unverifiable.
[Abstract] Abstract: The manuscript supplies no description of the exact mixed-precision combinations tested (which variables or operations were cast to lower precision), the baseline implementations for comparison, or any reporting of statistical variability across runs. These omissions directly undermine evaluation of the reported 30%/25% gains for LULESH as well.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed feedback on the abstract. We agree that the abstract must be expanded with methodological specifics to substantiate the claims. The full manuscript contains these details in the methods and results sections, but we will revise the abstract to make the headline results self-contained and verifiable. We address each comment below.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that a 30% reduction in time-to-solution and energy-to-solution was achieved for Reactor Simulator 'without compromising accuracy' provides no information on the error metric (e.g., relative L2 norm, max pointwise error, conservation violation), the tolerance threshold applied, or the specific test cases and input configurations used to verify this. This renders the headline result unverifiable.

Authors: We agree that the abstract is insufficiently detailed on this point. The manuscript verifies accuracy preservation for Reactor Simulator using the relative L2 norm with a tolerance of 1e-4 on the standard input configurations described in Section 4.1. We will revise the abstract to explicitly state the error metric, tolerance, and test cases. revision: yes
Referee: [Abstract] Abstract: The manuscript supplies no description of the exact mixed-precision combinations tested (which variables or operations were cast to lower precision), the baseline implementations for comparison, or any reporting of statistical variability across runs. These omissions directly undermine evaluation of the reported 30%/25% gains for LULESH as well.

Authors: We agree that the abstract omits these details. The full text specifies the mixed-precision combinations (FP16 for select variables and operations, FP32 otherwise), uses double-precision implementations as baseline, and reports results as means with standard deviations over 10 runs. We will add a concise summary of these elements to the abstract. revision: yes

Circularity Check

0 steps flagged

No circularity detected; purely empirical benchmark reporting

full rationale

The paper reports measured time-to-solution and energy-to-solution improvements on two benchmarks (Reactor Simulator and LULESH) under mixed-precision variants, with a claim that accuracy was preserved. No derivation chain, equations, fitted parameters, predictions, ansatzes, or uniqueness theorems appear in the provided abstract or description. The work contains no self-citations that bear load on any mathematical result, no renaming of known results, and no reduction of any output to its own inputs by construction. The central claims are direct empirical observations, making the paper self-contained against external benchmarks with no circular structure.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work is an empirical evaluation of an established technique on benchmarks; no mathematical derivations, free parameters, or new postulates are described in the abstract.

pith-pipeline@v0.9.1-grok · 5632 in / 1115 out tokens · 23936 ms · 2026-06-29T01:58:13.816264+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

22 extracted references

[1]

ETP4HPC’s SRA 5 - Strategic Research Agenda for High- Performance Computing in Europe - 2022,

M. Malms, L. Cargemel, E. Suarez, N. Mittenzwey, M. Duranton, S. Sezer, C. Prunty, P. Ross´e-Laurent, M. P ´erez-Harnandez, M. Maraza- kis, G. Lonsdale, P. Carpenter, G. Antoniu, S. Narasimharmurthy, A. Brinkman, D. Pleiter, U.-U. Haus, J. Krueger, H.-C. Hoppe, E. Laure, A. Wierse, V . Bartsch, K. Michielsen, C. Allouche, T. Becker, and R. Haas, “ETP4HPC’...

2022
[2]

Exascale computing and data handling: Challenges and opportunities for weather and climate prediction,

M. Govett, B. Bah, P. Bauer, D. Berod, V . Bouchet, S. Corti, C. Davis, Y . Duan, T. Graham, Y . Honda, A. Hines, M. Jean, J. Ishida, B. Lawrence, J. Li, J. Luterbacher, C. Muroi, K. Rowe, M. Schultz, M. Visbeck, and K. Williams, “Exascale computing and data handling: Challenges and opportunities for weather and climate prediction,”Bul- letin of the Ameri...

2024
[3]

Deepseek-v3 technical report,

DeepSeek-AI, A. Liu, B. Feng, B. Xue, B. Wang, B. Wu, and et. al., “Deepseek-v3 technical report,” 2025

2025
[4]

Enabling mixed-precision in spectral element codes,

Y . Chen, P. de Oliveira Castro, P. Bientinesi, N. Jansson, and R. Iakym- chuk, “Enabling mixed-precision in spectral element codes,”Future Generation Computer Systems, vol. 174, p. 107990, 2026

2026
[5]

Mixed-precision numerics in scientific applications: survey and perspectives,

A. Kashi, H. Lu, W. Brewer, D. Rogers, M. Matheson, M. Shankar, and F. Wang, “Mixed-precision numerics in scientific applications: survey and perspectives,” 2025

2025
[6]

A new approach to probabilistic rounding error analysis,

N. J. Higham and T. Mary, “A new approach to probabilistic rounding error analysis,”SIAM Journal on Scientific Computing, vol. 41, no. 5, pp. A2815–A2835, 2019

2019
[7]

Stochastic rounding variance and probabilistic bounds: A new approach,

E.-M. El Arar, D. Sohier, P. de Oliveira Castro, and E. Petit, “Stochastic rounding variance and probabilistic bounds: A new approach,”SIAM Journal on Scientific Computing, vol. 45, no. 5, pp. C255–C275, 2023

2023
[8]

Verificarlo: Checking floating point accuracy through monte carlo arithmetic,

C. Denis, P. De Oliveira Castro, and E. Petit, “Verificarlo: Checking floating point accuracy through monte carlo arithmetic,” in2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH), pp. 55–62, 2016

2016
[9]

Automatic exploration of reduced floating-point representations in iter- ative methods,

Y . Chatelain, E. Petit, P. de Oliveira Castro, G. Lartigue, and D. Defour, “Automatic exploration of reduced floating-point representations in iter- ative methods,” inEuro-Par 2019: Parallel Processing(R. Yahyapour, ed.), (Cham), pp. 481–494, Springer International Publishing, 2019

2019
[10]

de Oliveira Castro,High Performance Computing Code Optimiza- tions: Tuning Performance and Accuracy

P. de Oliveira Castro,High Performance Computing Code Optimiza- tions: Tuning Performance and Accuracy. PhD thesis, Universit ´e Paris- Saclay, 2022

2022
[11]

Enabling mixed-precision with the help of tools: A nekbone case study,

Y . Chen, P. d. O. Castro, P. Bientinesi, and R. Iakymchuk, “Enabling mixed-precision with the help of tools: A nekbone case study,” inParal- lel Processing and Applied Mathematics(R. Wyrzykowski, J. Dongarra, E. Deelman, and K. Karczewski, eds.), (Cham), pp. 34–50, Springer Nature Switzerland, 2025

2025
[12]

Precimonious: Tuning assistant for floating-point precision,

C. Rubio-Gonz ´alez, C. Nguyen, H. D. Nguyen, J. Demmel, W. Kahan, K. Sen, D. H. Bailey, C. Iancu, and D. Hough, “Precimonious: Tuning assistant for floating-point precision,” inSC ’13: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, pp. 1–12, 2013

2013
[13]

Tool integration for source-level mixed precision,

M. O. Lam, T. Vanderbruggen, H. Menon, and M. Schordan, “Tool integration for source-level mixed precision,” in2019 IEEE/ACM 3rd International Workshop on Software Correctness for HPC Applications (Correctness), pp. 27–35, 2019

2019
[14]

User-level power monitoring and application performance on cray xc30 supercomputers,

A. Hart, H. Richardson, J. Doleschal, T. Ilsche, M. Bielert, and M. Kap- pel, “User-level power monitoring and application performance on cray xc30 supercomputers,”Cray User Group, 2014

2014
[15]

Cray xc30 power monitoring and man- agement,

S. J. Martin and M. Kappel, “Cray xc30 power monitoring and man- agement,”Cray User Group, 2014

2014
[16]

Best Practice Guide – Harvesting energy consumption on European HPC systems: Sharing Experience from the CEEC project,

R. Iakymchuk, G. Gedik, K. Kulkarni, Y . Chen, D. Kempf, S. Kemmler, D. Papageorgiou, D. Konioris, S. Kiebdaj, J. Corbalan, and H. K ¨ostler, “Best Practice Guide – Harvesting energy consumption on European HPC systems: Sharing Experience from the CEEC project,” Aug. 2024

2024
[17]

Reactor simulator,

D. Kahaner, C. Moler, S. Nash, and J. Burkardt, “Reactor simulator,” 1989

1989
[18]

Kahaner, C

D. Kahaner, C. Moler, and S. Nash,Numerical Methods and Software. Englewood Cliffs, NJ: Prentice Hall, 1989. LC: TA345.K34

1989
[19]

Lulesh programming model and performance ports overview,

I. Karlin, A. Bhatele, B. L. Chamberlain, J. Cohen, Z. Devito, M. Gokhale, R. Haque, R. Hornung, J. Keasler, D. Laney, E. Luke, S. Lloyd, J. McGraw, R. Neely, D. Richards, M. Schulz, C. H. Still, F. Wang, and D. Wong, “Lulesh programming model and performance ports overview,” Tech. Rep. LLNL-TR-608824, Livermore CA, Decem- ber 2012

2012
[20]

Lulesh 2.0 updates and changes,

I. Karlin, J. Keasler, and R. Neely, “Lulesh 2.0 updates and changes,” Tech. Rep. LLNL-TR-641973, Livermore, CA, August 2013

2013
[21]

Hydrodynamics challenge problem,

M. B. G. R. D. Hornung, J. A. Keasler, “Hydrodynamics challenge problem,” 2011

2011
[22]

Lulesh – livermore unstructured lagrangian explicit shock hydrodynamics

L. L. N. L. (LLNL), “Lulesh – livermore unstructured lagrangian explicit shock hydrodynamics.” https://github.com/LLNL/LULESH/tree/ 46c2a1d6db9171f9637d79f407212e0f176e8194, n.d. Accessed: 2025- 07-31. APPENDIXA MEASUREMENTMETHODOLOGYDETAILS All experiments were performed on the CPU partition of the LUMI system, where we compiled each benchmark with g++ve...

2025

[1] [1]

ETP4HPC’s SRA 5 - Strategic Research Agenda for High- Performance Computing in Europe - 2022,

M. Malms, L. Cargemel, E. Suarez, N. Mittenzwey, M. Duranton, S. Sezer, C. Prunty, P. Ross´e-Laurent, M. P ´erez-Harnandez, M. Maraza- kis, G. Lonsdale, P. Carpenter, G. Antoniu, S. Narasimharmurthy, A. Brinkman, D. Pleiter, U.-U. Haus, J. Krueger, H.-C. Hoppe, E. Laure, A. Wierse, V . Bartsch, K. Michielsen, C. Allouche, T. Becker, and R. Haas, “ETP4HPC’...

2022

[2] [2]

Exascale computing and data handling: Challenges and opportunities for weather and climate prediction,

M. Govett, B. Bah, P. Bauer, D. Berod, V . Bouchet, S. Corti, C. Davis, Y . Duan, T. Graham, Y . Honda, A. Hines, M. Jean, J. Ishida, B. Lawrence, J. Li, J. Luterbacher, C. Muroi, K. Rowe, M. Schultz, M. Visbeck, and K. Williams, “Exascale computing and data handling: Challenges and opportunities for weather and climate prediction,”Bul- letin of the Ameri...

2024

[3] [3]

Deepseek-v3 technical report,

DeepSeek-AI, A. Liu, B. Feng, B. Xue, B. Wang, B. Wu, and et. al., “Deepseek-v3 technical report,” 2025

2025

[4] [4]

Enabling mixed-precision in spectral element codes,

Y . Chen, P. de Oliveira Castro, P. Bientinesi, N. Jansson, and R. Iakym- chuk, “Enabling mixed-precision in spectral element codes,”Future Generation Computer Systems, vol. 174, p. 107990, 2026

2026

[5] [5]

Mixed-precision numerics in scientific applications: survey and perspectives,

A. Kashi, H. Lu, W. Brewer, D. Rogers, M. Matheson, M. Shankar, and F. Wang, “Mixed-precision numerics in scientific applications: survey and perspectives,” 2025

2025

[6] [6]

A new approach to probabilistic rounding error analysis,

N. J. Higham and T. Mary, “A new approach to probabilistic rounding error analysis,”SIAM Journal on Scientific Computing, vol. 41, no. 5, pp. A2815–A2835, 2019

2019

[7] [7]

Stochastic rounding variance and probabilistic bounds: A new approach,

E.-M. El Arar, D. Sohier, P. de Oliveira Castro, and E. Petit, “Stochastic rounding variance and probabilistic bounds: A new approach,”SIAM Journal on Scientific Computing, vol. 45, no. 5, pp. C255–C275, 2023

2023

[8] [8]

Verificarlo: Checking floating point accuracy through monte carlo arithmetic,

C. Denis, P. De Oliveira Castro, and E. Petit, “Verificarlo: Checking floating point accuracy through monte carlo arithmetic,” in2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH), pp. 55–62, 2016

2016

[9] [9]

Automatic exploration of reduced floating-point representations in iter- ative methods,

Y . Chatelain, E. Petit, P. de Oliveira Castro, G. Lartigue, and D. Defour, “Automatic exploration of reduced floating-point representations in iter- ative methods,” inEuro-Par 2019: Parallel Processing(R. Yahyapour, ed.), (Cham), pp. 481–494, Springer International Publishing, 2019

2019

[10] [10]

de Oliveira Castro,High Performance Computing Code Optimiza- tions: Tuning Performance and Accuracy

P. de Oliveira Castro,High Performance Computing Code Optimiza- tions: Tuning Performance and Accuracy. PhD thesis, Universit ´e Paris- Saclay, 2022

2022

[11] [11]

Enabling mixed-precision with the help of tools: A nekbone case study,

Y . Chen, P. d. O. Castro, P. Bientinesi, and R. Iakymchuk, “Enabling mixed-precision with the help of tools: A nekbone case study,” inParal- lel Processing and Applied Mathematics(R. Wyrzykowski, J. Dongarra, E. Deelman, and K. Karczewski, eds.), (Cham), pp. 34–50, Springer Nature Switzerland, 2025

2025

[12] [12]

Precimonious: Tuning assistant for floating-point precision,

C. Rubio-Gonz ´alez, C. Nguyen, H. D. Nguyen, J. Demmel, W. Kahan, K. Sen, D. H. Bailey, C. Iancu, and D. Hough, “Precimonious: Tuning assistant for floating-point precision,” inSC ’13: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, pp. 1–12, 2013

2013

[13] [13]

Tool integration for source-level mixed precision,

M. O. Lam, T. Vanderbruggen, H. Menon, and M. Schordan, “Tool integration for source-level mixed precision,” in2019 IEEE/ACM 3rd International Workshop on Software Correctness for HPC Applications (Correctness), pp. 27–35, 2019

2019

[14] [14]

User-level power monitoring and application performance on cray xc30 supercomputers,

A. Hart, H. Richardson, J. Doleschal, T. Ilsche, M. Bielert, and M. Kap- pel, “User-level power monitoring and application performance on cray xc30 supercomputers,”Cray User Group, 2014

2014

[15] [15]

Cray xc30 power monitoring and man- agement,

S. J. Martin and M. Kappel, “Cray xc30 power monitoring and man- agement,”Cray User Group, 2014

2014

[16] [16]

Best Practice Guide – Harvesting energy consumption on European HPC systems: Sharing Experience from the CEEC project,

R. Iakymchuk, G. Gedik, K. Kulkarni, Y . Chen, D. Kempf, S. Kemmler, D. Papageorgiou, D. Konioris, S. Kiebdaj, J. Corbalan, and H. K ¨ostler, “Best Practice Guide – Harvesting energy consumption on European HPC systems: Sharing Experience from the CEEC project,” Aug. 2024

2024

[17] [17]

Reactor simulator,

D. Kahaner, C. Moler, S. Nash, and J. Burkardt, “Reactor simulator,” 1989

1989

[18] [18]

Kahaner, C

D. Kahaner, C. Moler, and S. Nash,Numerical Methods and Software. Englewood Cliffs, NJ: Prentice Hall, 1989. LC: TA345.K34

1989

[19] [19]

Lulesh programming model and performance ports overview,

I. Karlin, A. Bhatele, B. L. Chamberlain, J. Cohen, Z. Devito, M. Gokhale, R. Haque, R. Hornung, J. Keasler, D. Laney, E. Luke, S. Lloyd, J. McGraw, R. Neely, D. Richards, M. Schulz, C. H. Still, F. Wang, and D. Wong, “Lulesh programming model and performance ports overview,” Tech. Rep. LLNL-TR-608824, Livermore CA, Decem- ber 2012

2012

[20] [20]

Lulesh 2.0 updates and changes,

I. Karlin, J. Keasler, and R. Neely, “Lulesh 2.0 updates and changes,” Tech. Rep. LLNL-TR-641973, Livermore, CA, August 2013

2013

[21] [21]

Hydrodynamics challenge problem,

M. B. G. R. D. Hornung, J. A. Keasler, “Hydrodynamics challenge problem,” 2011

2011

[22] [22]

Lulesh – livermore unstructured lagrangian explicit shock hydrodynamics

L. L. N. L. (LLNL), “Lulesh – livermore unstructured lagrangian explicit shock hydrodynamics.” https://github.com/LLNL/LULESH/tree/ 46c2a1d6db9171f9637d79f407212e0f176e8194, n.d. Accessed: 2025- 07-31. APPENDIXA MEASUREMENTMETHODOLOGYDETAILS All experiments were performed on the CPU partition of the LUMI system, where we compiled each benchmark with g++ve...

2025