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The Julia package QRecoupling evaluates classical and quantum recoupling coefficients, such as Clebsch-Gordan coefficients and $3j$ and $6j$ symbols, and user-defined sums of factorial products, with numerical, exact and symbolic targets. One compact factorial rule covers classical and deformed evaluations, while its cyclotomic exponents reveal common factors and determine which terms contribute at unitary levels. Adaptive arithmetic resolves strongly cancelling sums, while exact tests in quantum integers distinguish algebraic zeros from small nonzero values without a computer-algebra system. At spin cutoff 500, classical $3j$ and $6j$ symbols are evaluated about 7 and 15 times faster than with WIGXJPF. For the tested quantum deformations, relative errors remain below $4\times10^{-14}$ through spin cutoff 400. Recurrences compute fusion matrices with 401 channels about 100 times faster than loops over their entries. The resulting coefficients support recoupling identities, changes of coupling basis and tensor-network calculations.

Datacenter GPUs increasingly favour low-precision floating-point formats, offering higher throughput than FP64. Double-word (DW) arithmetic represents numbers as unevaluated sums of two floating-point values, providing higher accuracy. We present the first error analysis of complex DW multiplication and division. Both operations reduce to sums of two DW products, combined using one of three DW addition algorithms: accurate, sloppy, or Madd. Normalising DW products ensures nonoverlapping components, but omitting this step reduces the number of arithmetic operations. We bound the resulting overlap and prove that Madd retains a relative error bound of $3u^2+O(u^3)$ for overlapping inputs, where $u$ is the unit roundoff. For all variants, we establish relative error bounds of the form $(ακ+β)u^2+O(u^3)$, where $κ$ is the condition number of the sum of products. Our analysis shows that the less expensive sloppy addition suffices. We implement these variants in CompleXDW, an open-source C++ library for CPUs and GPUs. In the high-energy physics code MadGraph7, FP32-based DW arithmetic achieves up to 2.9x and 2.1x higher throughput than FP64 on NVIDIA L40S and AMD Radeon Pro W7900 GPUs, respectively, while losing approximately 1.4 correct significant digits.

The sparse identification of nonlinear dynamics (SINDy) recovers interpretable governing equations from time-series data by sparse regression over a library of candidate functions. As data sets, candidate libraries and the number of repeated fits grow, the cost of SINDy becomes dominated by the evaluation of the library matrix and its least-squares problems. We present an open-source Python implementation of SINDy in which a single set of loop-based kernels is just-in-time compiled with Numba and executed on a shared-memory multicore node by four interchangeable back ends: Numba prange, OpenMP directives through PyOMP, Python threads that release the global interpreter lock, and multiprocessing with shared memory. The normal equations are accumulated in one cache-blocked pass over the data, with an automatic fallback to a tall-skinny QR reduction for ill-conditioned problems. Two decompositions are studied on the Lorenz and Rössler systems: an ensemble (task-parallel) workload of 960 independent identifications and a library (data-parallel) workload of one trajectory with $2\times10^7$ samples and a fifth-order library of 56 candidate terms. All back ends recover the exact sparsity pattern in every identification, with coefficient errors identical to PySINDy. On a dual-socket Intel Xeon E5-2650 v4 node of the University of Houston-Downtown HPC cluster (24 cores, 48 hardware threads), the compiled serial code is 4.3-5.6x faster than PySINDy, the parallel back ends reach speed-ups of 14.8-20.3 on 24 cores (parallel efficiency 0.61-0.84), and the overall time to solution is reduced by up to 117x with respect to PySINDy. We analyse the differences between the back ends, the effect of the two sockets and of hyper-threading, and give practical recommendations.