  Unsourced multiple access abstracts grantless simultaneous communication of a
large number of devices (messages) each of which transmits (is transmitted)
infrequently. It provides a model for machine-to-machine communication in the
Internet of Things (IoT), including the special case of radio-frequency
identification (RFID), as well as neighbor discovery in ad hoc wireless
networks. This paper presents a fast algorithm for unsourced multiple access
that scales to $2^{100}$ devices (arbitrary $100$ bit messages). The primary
building block is multiuser detection of binary chirps which are simply
codewords in the second order Reed Muller code. The chirp detection algorithm
originally presented by Howard et al. is enhanced and integrated into a peeling
decoder designed for a patching and slotting framework. In terms of both energy
per bit and number of transmitted messages, the proposed algorithm is within a
factor of $2$ of state of the art approaches. A significant advantage of our
algorithm is its computational efficiency. We prove that the worst-case
complexity of the basic chirp reconstruction algorithm is
$\mathcal{O}[nK(\log_2 n + K)]$, where $n$ is the codeword length and $K$ is
the number of active users, and we report computing times for our algorithm.
Our performance and computing time results represent a benchmark against which
other practical algorithms can be measured.
