flops profiling

Conventional algorithm analysis treats basic operations as equally costly, ignoring substantial disparities in execution time, energy consumption, carbon emissions, and monetary cost across modern processor architectures. Method: We propose a multidimensional weighted operation complexity model that unifies computational cost, energy usage, carbon footprint, and financial expense—enabling architecture-aware, sustainability-oriented algorithm evaluation. Our approach integrates instruction-level fine-grained cost modeling, automated source-code analysis, and empirical measurement tooling, supporting user-defined weight configurations for diverse optimization objectives. Contribution/Results: Experiments demonstrate strong correlation with ground-truth measurements (Spearman ρ > 0.9) and significantly higher prediction accuracy for runtime and energy than baseline methods—including Big-O, ICE, and EVM gas metrics. The model establishes a novel, interpretable, cross-architectural paradigm for algorithmic efficiency assessment in green computing and resource-constrained environments.

This study systematically evaluates the performance overhead of generic mechanisms in modern programming languages for scientific and symbolic computation, identifying key contributing factors. By extending the SciGMark 1.5 benchmark suite, the authors introduce, for the first time, generic performance analysis to symbolic tasks such as finite-field linear algebra, FFT, and Gröbner basis computation. Generic and specialized implementations are compared across Rust, Java, Go, TypeScript, C++, and Julia. The findings reveal that generic overhead is primarily governed by when type resolution occurs and how numeric values are represented: compile-time monomorphization closely matches specialized performance, whereas type erasure or object-based generics incur significant costs. Runtime specialization can also achieve efficient steady-state execution under specific conditions. This work provides empirical foundations for designing high-performance generic systems.

A critical gap exists between the design of floating-point (FP) tools and real-world usage patterns in statically typed languages, due to the lack of large-scale empirical evidence on actual FP practices. Method: We conducted the first large-scale, empirical study of FP usage across 12,000+ open-source GitHub projects. Our methodology combined keyword-based filtering, syntactic parsing, random sampling, intrinsic property filtering, and static analysis to construct the first unbiased, reproducible FP code corpus. Contribution/Results: We find that FP operations are pervasive yet highly concentrated in specific idioms; mainstream FP benchmarks (e.g., FPBench, ROSE) exhibit significant distributional biases—diverging markedly from real code in operator frequency, precision requirements, and contextual complexity. This work provides foundational empirical evidence and a rigorously curated dataset to guide the design, evaluation, and optimization of FP analysis, verification, and compilation tools.

Scientific computing programs rely on aggressive floating-point optimizations—such as fused multiply-add (FMA)—to improve performance, yet must rigorously preserve numerical correctness. Method: This work presents the first formal verification of FMA optimization at the LLVM IR level within the Rocq theorem prover, built upon the Verified LLVM framework. It formally models IEEE 754-compliant floating-point semantics in LLVM IR, enables path-sensitive, precise preservation reasoning, and designs a scalable verification architecture to accommodate more complex program structures and optimization patterns. Contribution/Results: The approach proves semantic equivalence for FMA replacements of arithmetic expressions of the form $a imes b + c$ within basic blocks. Experimental validation confirms the mathematical correctness of FMA substitution, establishing the first end-to-end, IR-level formal verification of floating-point optimizations for trustworthy high-performance compilers.

This work addresses the challenge of statically quantifying rounding errors in floating-point computations. We introduce Λnum, a functional language that—uniquely—integrates sensitivity analysis with graded monads within a linear type system, enabling fully automatic, sound static inference of upper bounds on rounding errors in numerical programs. Λnum natively models IEEE 754 rounding semantics and supports extensions to nondeterministic and stochastic rounding. By rigorously connecting denotational and operational semantics, we establish, for the first time at the type level, soundness guarantees for inferred error bounds. Our prototype implementation demonstrates effectiveness across multiple classical numerical algorithms: it achieves error-bound precision comparable to state-of-the-art tools while significantly accelerating inference speed.

This study addresses a critical gap in quantum software research: the absence of a systematic auditing mechanism for empirically grounded comparative claims, which has led to a pervasive “instantiation gap” characterized by insufficient evidentiary support. To bridge this gap, the authors propose CLAIMSTAB-QC, the first source-bound auditing framework tailored to empirical comparisons in quantum software. By integrating claim modeling, audit scope delimitation, evidence boundary identification, and directional classification, the framework enables precise validation of comparative assertions against original source materials. An evaluation across 455 claims from 119 papers reveals that only eight claims possessed sufficient matched evidence for direct auditing; among these, two were confirmed, four lacked adequate support, and two were contradicted—highlighting substantial deficiencies in the empirical rigor of current quantum software studies.

This study addresses the lack of cross-platform evaluation methods for quantum computing that jointly account for computational fidelity and cost, a gap that hinders optimal hardware selection under heterogeneous cloud pricing models. The authors introduce, for the first time, a “Quantum Fidelity per Cost” (QFC) metric that integrates Kullback–Leibler divergence, sampling overhead, and actual platform fees. They empirically evaluate 14 quantum processors across AWS, IBM, IQM, and OQC using this metric. Their findings reveal that incorporating cost substantially alters rankings based solely on fidelity; QFC remains stable under reweighting, and its scaling behavior is governed primarily by billing models rather than hardware characteristics. Furthermore, QFC dynamically adapts to device availability and price changes, offering users a practical, cost-aware decision framework for quantum hardware selection.

This study addresses the substantial time and energy costs associated with high-precision scientific computing. The authors propose a strategy that integrates mixed-precision computation with computer arithmetic optimizations to significantly improve energy efficiency while rigorously preserving numerical accuracy. Experimental evaluation on two representative scientific computing benchmarks—ReactorSimulator and LULESH—demonstrates the effectiveness of the approach: on ReactorSimulator, both execution time and energy consumption are reduced by 30%, while on LULESH, execution time decreases by 30% and energy usage drops by 25%. These results validate the method’s practicality and efficacy for enabling high-fidelity, energy-efficient simulations in scientific computing.

This study addresses the limited scope of traditional high-performance computing (HPC) evaluations, which typically focus solely on performance and energy consumption while overlooking the comprehensive environmental costs of operational configurations. The authors propose the first job-level unified accounting framework that integrates both operational and full life-cycle (embodied) carbon and water footprints. Leveraging life-cycle assessment methodologies, real-time runtime monitoring, and hardware manufacturing emission data, the framework enables fine-grained quantification of environmental impacts. The analysis reveals that increasing thread count generally reduces total environmental footprints, albeit with diminishing marginal returns; while carbon footprints are predominantly driven by operational phases, water footprints are largely dominated by embodied impacts. By jointly incorporating both footprint types at the job granularity, this work establishes a novel paradigm for assessing HPC sustainability.

This work addresses the lack of compiler integration and configurable-precision floating-point support in existing SRAM-based in-memory computing systems, as conventional IEEE 754 floating-point units incur substantial area and power overheads. Within the OpenACM framework, the study presents the first compiler-integrated, precision-configurable floating-point multiplier. It begins by establishing an IEEE 754-compliant baseline design and then introduces a mantissa-segmentation-based approximate multiplication strategy that significantly reduces hardware costs without adding latency. Post-layout results demonstrate a 69% reduction in logic area and a 72% decrease in power consumption, while maintaining negligible accuracy loss on image processing and ResNet-18 inference tasks, thereby validating the approach’s efficiency and practicality.