  Wallace has proposed a new class of pseudo-random generators for normal
variates. These generators do not require a stream of uniform pseudo-random
numbers, except for initialisation. The inner loops are essentially
matrix-vector multiplications and are very suitable for implementation on
vector processors or vector/parallel processors such as the Fujitsu VPP300. In
this report we outline Wallace's idea, consider some variations on it, and
describe a vectorised implementation RANN4 which is more than three times
faster than its best competitors (the Polar and Box-Muller methods) on the
Fujitsu VP2200 and VPP300.
