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quantum-chemistry

DFT and quantum chemistry

VASP, Quantum ESPRESSO

SystemTechniques · 2Primitives · 17 quantum-chemistry Spherical harmonic transformnumerics · medium: Fast spherical harmonic transforms via FFT in longitude and Legendre in latitudeThermostats barostatsphysics · medium: Temperature and pressure control in MD: Langevin, Nose-Hoover, velocity rescale, Parrinello-RahmanFast Fourier transformnumerics · low: Computes the DFT in O(n log n) by recursively splitting into even and odd halves; the basis of fast convolution and spectral methods.›Gaussian quadraturenumerics · low: Approximate an integral by a weighted sum of n function values at roots of orthogonal polynomials; exact for polynomials up to degree 2n-1.›Verlet / leapfrognumerics · low: Half-kick, drift, half-kick: a second-order, time-reversible, symplectic integrator with one force evaluation per step whose energy error stays bounded for millions of steps.›Periodic boundary conditionsphysics · low: Minimum image convention and wrapping for simulations in periodic boxesCUDA and GPU languageslanguages · low: Programming GPUs: thousands of lockstep threads, bound by memory bandwidth; libraries first, Triton for fused kernels, CUDA C++ for peak speed.›Collective communicationml-training · low: The family of group exchanges (broadcast, reduce, all-gather, reduce-scatter, all-to-all) and the latency-plus-bytes cost model that picks ring, tree or direct algorithms by message size and topology.›Mixed-precision trainingml-training · low: Run matmuls in bf16/fp16/fp8 on tensor cores while keeping master weights, optimizer state and reductions in fp32; about 2x speed, half the activation memory.›Tiled matrix multiplicationml-training · low: Block GEMM into tiles held in shared memory and registers, so each byte loaded from DRAM feeds many FMAs; the core of fast GEMM.›Conjugate gradientnumerics · low: Krylov iteration for symmetric positive definite Ax = b using one matrix-vector product and two dot products per step; converges in about √κ iterations.›L-BFGSnumerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.›LU and Cholesky factorizationnumerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).›Spherical gridsnumerics · low: Lat-lon, cubed-sphere and icosahedral grids for global models; pole and area issuesPRNGs (PCG, xoshiro)numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.›Gpu memory coalescing bankinghardware-os · low: Coalesced global loads, shared memory bank conflicts, L2 and HBM bandwidth on GPUsAdamWml-training · low: Adam's per-parameter adaptive steps with weight decay applied directly to the weights; the default optimizer for transformers and LLM pretraining.›Floating-point errornumerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.›+ 1 more primitives

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