A parallel-prefix broadcast for a parallel-prefix operation on a parallel computer includes: configuring, on each node, a parallel-prefix contribution buffer for storing the node's parallel-prefix contribution; configuring, on each node, a parallel-prefix results buffer for storing results of a operation, the results buffer having a position for each node that corresponds to node's rank; and repeatedly for each position in the results buffer: processing in parallel by each node, including: determining, by the node, whether the current position in the results buffer is to include the node's contribution, if the current position is not to include the contribution, contributing the identity element, and if the current position is to include the contribution, contributing the contribution, performing, by each node, the operation using the contributed identity elements and the contributed contributions, yielding a result from the operation, and storing, by each node, the result in the position in the results buffer.