Existing built-in self test (BIST) strategies require the use of specialized test pattern generation hardware which introduces signicant area overhead and performance degradation. In this paper, we propose a novel method for implementing test pattern generators based on adders widely available in data-path architectures and digital signal processing circuits. Test patterns are generated by continuously accumulating a constant value and their quality is evaluated in terms of the pseudo-exhaustive state coverage on subspaces of contiguous bits. This new test generation scheme, along with the recently introduced accumulator-based compaction scheme facilitates a BIST strategy for high performance datapath architectures that uses the functionality of existing hardware, is entirely integrated with the circuit under test, and results in at-speed testing with no performance degradation and area overhead.