QLM benchmark (R. Krivec)

                            Updated 01/03/19


This is a small memory benchmark. The QLM algorithm iterates a numerical
integral using the trapezoidal rule. On "saturn", most of the CPU time (over
90 percent) is spent evaluating the intrinsic function "exp". The remaninder
is a mixture of floating point and integer arithmetic.

Qlmmd is a nice small-memory Fortran program of a "general" arithmetic type.
Its drawback is that it mostly computes the intrinsic "exp".

Note that "saturn" R8000 is the only processor with 4-way floating point
pipeline. Athlon and Alphas have 2-way floating point pipelines. Comparing
saturn to newer Alphas (GS160 etc.) shows a two-fold relative efficiency for
Alphas as compared with R8000. This probably means that on saturn, only 2
pipes can be used by "exp"; also, this explains the 30% efficiency on
saturn.



       Table I.  QLM program (qlmmd) for two values of n. T is
       the theoretical MFLOPS rating. X is the expected CPU time
       if the machine had the same efficiency as "saturn" (first
       entry). RE is the relative efficiency with respect to 
       "saturn", i.e., the ratio of the expected (X) and actual 
       CPU time. The actual (absolute) floating point efficiency 
       on "saturn" is slightly over 30 percent.
       ---------------------------------------------------------
       Processor           CPU time (sec)
                          n=2001  n=10001    T        X     RE
       ---------------------------------------------------------
             1              2         3      4        5     6
       ---------------------------------------------------------
       saturn 90 MHz       14.4      292    360     (292) (1)
       
       helium               5.4      133    800      131   0.98 
       urartu              33.8      838    300      350   0.42
       urnammu            ~33       ~770    350      300   0.39
       
       dexter pgf77 3.1    17.0      427    400      263   0.62
       dexter g77 2.95.2   25.7      628    400      263   0.42
       
       athlon pgif77 3.2    3.7       91    800      131   1.4
       
       Alpha Linux fort     1.8       46   1334       79   1.7
       GS160 f77            1.7       41   1462       72   1.8
       ES40 f77             1.5       37   1666       63   1.7
       ---------------------------------------------------------


Some processor data:

saturn: SGI Power Challenge R8000            (90 MHz)
OSF1 helium.fiz.huji.ac.il V4.0 878 alpha    (400 MHz)
Linux urartu 2.0.35 i686 unknown             (Pentium II 300 MHz)
IRIX urnammu 6.3 12161207 IP32               (R10000 175 MHz)
dexter linux                                 (PII / 400 MHz)
AMD athlon                                   (800 MHz)
Alpha Linux                                  (667 MHz)
GS160, Tru64 32GB (4 x 8 GB)                 (731 MHz, 4MB L2(?))
ES40, Tru64                                  (833 MHz)


R. Krivec  01/03/19.