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Every mainstream processor vendor provides an optimized BLAS implementation for its CPU, as BLAS is a fundamental math library in scientific computing. The Loongson 3A CPU is a general-purpose 64-bit MIPS64 quad-core processor, developed by the Institute of Computing Technology, Chinese Academy of Sciences. To date, there has not been a sufficiently optimized BLAS on the Loongson 3A CPU. The purpose of this research is to optimize level 3 BLAS performance on the Loongson 3A CPU. We analyzed the Loongson 3A architecture and built a performance model to highlight the key point, L1 data cache misses, which is different from level 3 BLAS optimization on the mainstream x86 CPU. Therefore, we employed a variety of methods to avoid L1 cache misses in single thread optimization, including cache and register blocking, the Loongson 3A 128-bit memory accessing extension instructions, software prefetching, and single precision floating-point SIMD instructions. Furthermore, we improved parallel performance by reducing bank conflicts among multiple threads in the shared L2 cache. We created an open source BLAS project, OpenBLAS, to demonstrate the performance improvement on the Loongson 3A quad-core processor.