Abstractdspsr is a high-performance, open-source, object-oriented, digital signal processing software library and application suite for use in radio pulsar astronomy. Written primarily in C++, the library implements an extensive range of modular algorithms that can optionally exploit both multiple-core processors and general-purpose graphics processing units. After over a decade of research and development, dspsr is now stable and in widespread use in the community. This paper presents a detailed description of its functionality, justification of major design decisions, analysis of phase-coherent dispersion removal algorithms, and demonstration of performance on some contemporary microprocessor architectures.