Compression and decompression of numerical data utilizing single instruction, multiple data (SIMD) instructions is described. The numerical data includes integer and floating-point samples. Compression supports three encoding modes: lossless, fixed-rate, and fixed-quality. SIMD instructions for compression operations may include attenuation, derivative calculations, bit packing to form compressed packets, header generation for the packets, and packed array output operations. SIMD instructions for decompression may include packed array input operations, header recovery, decoder control, bit unpacking, integration, and amplification. Compression and decompression may be implemented in a microprocessor, digital signal processor, field-programmable gate array, application-specific integrated circuit, system-on-chip, or graphics processor, using SIMD instructions. Compression and decompression of numerical data can reduce memory, networking, and storage bottlenecks. This abstract does not limit the scope of the invention as described in the claims.