1. A parallel computer that selects algorithms for data communications in a parallel active messaging interface (‘PAMI’) of the parallel computer, the parallel computer comprising a plurality of compute nodes that execute a parallel application, the PAMI comprising data communications endpoints, each endpoint comprising a specification of data communications parameters for a thread of execution on a compute node, including specifications of a client, a context, and a task, the compute nodes and the endpoints coupled for data communications through the PAMI and through data communications resources, the compute nodes comprising computer processors operatively coupled to computer memory having disposed within it computer program instructions that, when executed by the computer processors, cause the parallel computer to function by: associating in the PAMI data communications algorithms and ranges of message sizes so that each algorithm is associated with a separate range of message sizes; receiving in an origin endpoint of the PAMI a data communications instruction, the instruction specifying transmission of a data communications message from the origin endpoint to a target endpoint, the data communications message characterized by a message size; selecting, from among the associated algorithms and ranges, a data communications algorithm in dependence upon the message size, a number of ranges, an upper boundary value and an index identifying a range containing the message size; transmitting, according to the selected data communications algorithm from the origin endpoint to the target endpoint, the data communications message.