Matrix Computations in Basic on a Microcomputer

We consider the efficient implementation of matrix computations in interpreted Basic on a microcomputer. Linear equations routines SGEFA and SGESL from the LINPACK library of Fortran programs are translated into Basic and run on four microcomputers: the Commodore 64, the Amstrad CPC 464, the BBC Microcomputer, and the BBC with a Z-80 second processor. The computational cost of the routines is found to be dominated by subscripting calculations rather than by floating point arithmetic. For the BBC Microcomputer and the Commodore 64, the BLAS routines which constitute the inner loops of SGEFA and SGESL are coded in assembly language; speed increases of factors 2.8 (BBC) and 5.3 (Commodore 64) accrue, and the improved execution times are comparable to ones which have been quoted for the more powerful and expensive IBM PC running under a Fortran compiler. The computational cost of the routines using coded BLAS is found to be dominated by floating point arithmetic, subscripting calculations and other overheads having been reduced to a negligible level, and it is concluded that these hybrid Basic/assembly language routines extract near optimum performance from their host machines. Our findings are shown to be applicable to any matrix routine whose computational cost can be measured in "flops"