Modified Givens Transformation

We look at how both logical restructuring and improvements available from successive versions of Fortran allow us to reduce the complexity (measured by a number of the com-monly used software metrics) of the Level 1 BLAS code used to compute the modified Givens transformation. With these reductions in complexity we claim that we have improved both the maintainability and clarity of the code; in addition, we report a fix to a minor problem with the original code. The performance of two commercial Fortran restructuring tools is also reported. 1 In t roduct ion The Level 1 BLAS [LHKK79], originally published in Fortran 66 [ANS66], implemented a number of common vector operations and were designed to be used as building blocks for linear algebra software. Hopkins [Hop96] used knot counts [WHH79] and path counts [Nej88] to identify routines from the Level 1 BLAS which might benefit from code restructuring Two sets of routines, *NRM2, used to compute the Euclidean orm of a vector and *ROTMG, for computing the modified Givens transformation, were identified as having Extremely high metric values given their relatively low number of executable statements. The restructuring ofthe *NRM2 routines, along with a dramatic decrease in the metric values, was reported by Hopkins [Hop96]; the *ROTMG routines are considered here. Following a brief description of the software metrics used to compare versions of the *ROTMG routines, we present a fiowgraph of the published code and look at how two Fortran code restruc-turing tools fared on this original source. We then compare the metric values obtained for the original and automatically restructured code with hand-coded Fortran 66 and Fortran 77 versions. Section 5 looks at how the metric values may be reduced further by using Fortran 90 and we show how the use of some of the new facilities available in Fortran 90 may be used to improve these routines further. Finally we look briefly at the testing of the new routine and report a fix to a minor problem in the original code. 2 Mod i f ied G ivens Rotat ion Mat r ix The input values to *ROTMG, dl, d2, Xl and Yl, define a two-vector [al, a2] T in the partitioned form as a2 0 d ~ Y