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Manuscript Title: A new version of the multi-dimensional integration and event generation package BASES/SPRING.
Authors: S. Kawabata
Program title: BASES/SPRING V5.1
Catalogue identifier: AAFW_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 88(1995)309
Programming language: Fortran.
Computer: HP750.
Operating system: UNIX, OSIV/F4 MSP.
RAM: 392K words
Word size: 32
Peripherals: disc.
Keywords: Particle physics, Elementary, Event simulation, Multi-dimensional, Integration, Monte carlo simulation, Event generation and, Four momentum vector, Generation.
Classification: 11.2.

Nature of problem:
The previous version of the numerical integration and event generation package BASES/SPRING has been useful to obtain total cross sections and to generate events of elementary processes in high energy physics. It is applicable to processes with up to ten independent variables. In order to study, for example, e+e- physics at much higher energies, we often need more than ten independent variables to describe processes of our interest. As far as the numerical integration by BASES is concerned, it is easy to extend the dimension of integral. However, the event generation requires a huge memory space with the previous generation algorithm of SPRING.

Solution method:
BASES/SPRING is suited for the integration and generation of a very singular function. The number of those independent variables which give the function a singular behaviour is usually small. Then, if we divide the subspace spanned by these singular variables into hypercubes, the number of hypercubes becomes not too large. Applying the previous BASES/SPRING algorithm only to this subspace and handling the other variables as additional integral variables, we could extend the dimension of integral and event generation up to 50 variables.

Running time:
The running time is essentially determined by the complexity of the function program which gives the differential cross section of an elementary process. If we take the process e+e- -> nu nu gamma as an example, the two dimensional integration and the generation of 10000 events require 4.4 seconds in total on a FACOM M780 computer.