RECURSUM: Automated Code Generation for Recurrence Relations Exceeds Expert Optimization via LayeredCodegen
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914492834643968 |
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| author | Guerrero, Rubén Darío |
| author_facet | Guerrero, Rubén Darío |
| contents | Automated code generation can systematically exceed expert hand-optimization for recurrence relations-computational primitives ubiquitous in orthogonal polynomials, special functions, numerical integration, and molecular integral evaluation. We present RECURSUM, a Python-based domain-specific language generating optimized C++ for arbitrary recurrence relations via three backends: template metaprogramming for compile-time evaluation, a novel LayeredCodegen backend with architectural optimizations, and runtime loop-based evaluation. The DSL uses einsum-inspired notation to specify recurrences, validity constraints, and base cases in 10-30 lines of Python, generating 650+ lines of production C++.
LayeredCodegen achieves 9.8x speedup over expert hand-written implementations and 1.9x over template metaprogramming for McMurchie-Davidson Hermite coefficients. Architecture analysis reveals three quantifiable effects: (1) zero-copy output parameters eliminate return-by-value overhead (70-80% of speedup), (2) guaranteed function inlining eliminates compiler-refused overhead (15-20%), (3) exact-sized stack buffers achieve 100% cache efficiency vs 27% for MAX-sized arrays (5-10%).
We validate on 24 recurrence types spanning pure mathematics (Legendre, Chebyshev, Hermite, Laguerre polynomials), numerical analysis (Clenshaw, Golub-Welsch), and quantum chemistry (McMurchie-Davidson, Rys quadrature, Boys function). Production benchmarks show speedups propagate to complete algorithms, with generated code matching expert baselines within 3.3%.
RECURSUM demonstrates that systematic code generation serves as the performance ceiling for recurrence algorithms. By eliminating the dual expertise barrier (domain knowledge + C++ metaprogramming), the framework democratizes high-performance scientific computing-establishing a paradigm where automated generation systematically exceeds manual optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18585 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | RECURSUM: Automated Code Generation for Recurrence Relations Exceeds Expert Optimization via LayeredCodegen Guerrero, Rubén Darío Programming Languages Automated code generation can systematically exceed expert hand-optimization for recurrence relations-computational primitives ubiquitous in orthogonal polynomials, special functions, numerical integration, and molecular integral evaluation. We present RECURSUM, a Python-based domain-specific language generating optimized C++ for arbitrary recurrence relations via three backends: template metaprogramming for compile-time evaluation, a novel LayeredCodegen backend with architectural optimizations, and runtime loop-based evaluation. The DSL uses einsum-inspired notation to specify recurrences, validity constraints, and base cases in 10-30 lines of Python, generating 650+ lines of production C++. LayeredCodegen achieves 9.8x speedup over expert hand-written implementations and 1.9x over template metaprogramming for McMurchie-Davidson Hermite coefficients. Architecture analysis reveals three quantifiable effects: (1) zero-copy output parameters eliminate return-by-value overhead (70-80% of speedup), (2) guaranteed function inlining eliminates compiler-refused overhead (15-20%), (3) exact-sized stack buffers achieve 100% cache efficiency vs 27% for MAX-sized arrays (5-10%). We validate on 24 recurrence types spanning pure mathematics (Legendre, Chebyshev, Hermite, Laguerre polynomials), numerical analysis (Clenshaw, Golub-Welsch), and quantum chemistry (McMurchie-Davidson, Rys quadrature, Boys function). Production benchmarks show speedups propagate to complete algorithms, with generated code matching expert baselines within 3.3%. RECURSUM demonstrates that systematic code generation serves as the performance ceiling for recurrence algorithms. By eliminating the dual expertise barrier (domain knowledge + C++ metaprogramming), the framework democratizes high-performance scientific computing-establishing a paradigm where automated generation systematically exceeds manual optimization. |
| title | RECURSUM: Automated Code Generation for Recurrence Relations Exceeds Expert Optimization via LayeredCodegen |
| topic | Programming Languages |
| url | https://arxiv.org/abs/2604.18585 |