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Summary: Genome-wide association studies are widely used to investigate the genetic basis of diseases and traits, but they pose many computational challenges. We developed gdsfmt and SNPRelate (R packages for multi-core symmetric multiprocessing computer architectures) to accelerate two key computations on SNP data: principal component analysis (PCA) and relatedness analysis using identity-by-descent measures. The kernels of our algorithms are written in C/C++ and highly optimized. Benchmarks show the uniprocessor implementations of PCA and identity-by-descent are ∼8–50 times faster than the implementations provided in the popular EIGENSTRAT (v3.0) and PLINK (v1.07) programs, respectively, and can be sped up to 30–300-fold by using eight cores. SNPRelate can analyse tens of thousands of samples with millions of SNPs. For example, our package was used to perform PCA …