Comparison-based sorting has a proven lower bound: Ω(n log n) comparisons are necessary to sort n elements. Every comparison-based algorithm — quicksort, mergesort, heapsort — lives above this floor. The bound comes from information theory: n! possible orderings require log₂(n!) ≈ n log n bits to distinguish.
Non-comparison sorts escape by exploiting the structure of the keys. Radix sort processes digits. Counting sort uses key values as indices. These achieve O(wn) time, where w is the word size — linear in n for fixed w. The tradeoff is that they need specific knowledge of the key representation.
Bsort takes a different path. Derived from binary quicksort, it partitions elements by examining individual bits, working from the most significant bit downward. At each level, elements are split into two groups based on a single bit, then recursively sorted within each group. The recursion depth is bounded by the word size w, giving O(wn) time. The auxiliary space is O(w) — just a stack of recursion frames.
The algorithm handles signed integers, unsigned integers, and floating-point numbers, accommodating the IEEE 754 representation's sign-magnitude encoding (where the bit-level ordering doesn't match the numerical ordering without preprocessing). The preprocessing — flipping the appropriate bits so that bit-level comparison agrees with numerical comparison — is O(n) and doesn't change the asymptotic complexity.
For small word sizes (8-bit, 16-bit), bsort is competitive with highly optimized library sorts (C++ std::sort, Rust's sort_unstable). For 64-bit data, the word-size factor w = 64 makes it less competitive against comparison sorts whose n log n scaling is gentler for moderate n.
The structural distinction from radix sort: radix processes fixed-width digits from least significant to most significant (LSD radix) or partitions by most significant first (MSD radix). Bsort processes single bits, which is the finest granularity of MSD radix sort. The simplicity is the point — one bit, one partition, no digit extraction.