#!SP2 ##16 Thin node system at University of Southampton, UK, June 1995 ##IBM 390 Power2 nodes, 62.5MHz, 128MByte Memory, 2*2GByte SCSI Disk ##Compiler version : xlc 1.3.0.19 ##Operating system : AIX 3.2.5 #Benchmarker was Dr Simeon Warner ================================================= === === === GENESIS / PARKBENCH Parallel Benchmarks === === === === POLY2 === === === === Program: Out-cache (r-hat f-half) === === Version: Standard Fortran 77 === === Author: Roger Hockney === === Update: November 1993; Release: 1.0 === === === ================================================= POLYNOMIAL BENCHMARK FOR FHALF ------------------------------ (DOUBLE PRECISION) This benchmark determines the severity of memory bottlenecks by varying the amount of arithmetic per memory reference which is called the computational intensity of the loop. The performance for long loop (vector) lengths, RINF, is represented as : RINF = RHAT/(1 + FHALF/F) where RHAT = peak Mflop/s rate of arithmetic pipeline approached as F goes to infinity and F = computational intensity = ratio floating operations/memory references FHALF = F required to obtain RINF=RHAT/2 The loop executed is polynomial evaluation by Horners rule, F varies as the order increases from 1 to 10 Roger Hockney, August 1989 -------------------------------------------------------------- POLYNOMIALS : A(I)=S0+B(I)*(S1+B(I)*(S2+B(I)*S3)) ICASE= 1 NCASE= 1 NMAX=100000 NTIMES= 1 NPROCS= 1 COMPUTATIONAL INTENSITY = flop per mem ref 1.000000000 ------------------------------------------ Floating operations per iteration = 2 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 1.015E-03 .000000 .000 0.000E+00 .00 19.705444 1.015E-03 1 20000 1.985E-03 20.618429 463.316 9.266E+02 .00 20.151602 4.494E-05 1 30000 2.986E-03 20.294203 246.361 4.927E+02 2.45 20.094078 2.428E-05 1 40000 3.899E-03 20.718752 600.178 1.200E+03 5.00 20.518196 5.794E-05 1 50000 4.879E-03 20.741804 623.099 1.246E+03 3.59 20.495512 6.008E-05 1 60000 5.892E-03 20.600130 459.466 9.189E+02 3.50 20.366879 4.461E-05 1 70000 6.791E-03 20.713982 609.388 1.219E+03 3.47 20.615896 5.884E-05 1 80000 7.655E-03 20.945711 951.818 1.904E+03 5.36 20.901630 9.088E-05 1 90000 8.681E-03 20.950788 960.126 1.920E+03 4.46 20.734798 9.166E-05 1 100000 9.649E-03 20.937386 936.057 1.872E+03 3.82 20.727453 8.941E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 2.000000000 ------------------------------------------ Floating operations per iteration = 4 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 1.015E-03 .000000 .000 0.000E+00 .00 39.410889 1.015E-03 1 20000 2.027E-03 39.522301 28.269 1.131E+02 .00 39.466515 2.861E-06 1 30000 2.933E-03 41.711025 768.227 3.073E+03 8.54 40.915051 7.367E-05 1 40000 3.895E-03 41.900093 847.257 3.389E+03 5.66 41.076580 8.088E-05 1 50000 5.047E-03 40.272243 37.326 1.493E+02 11.50 39.626850 3.707E-06 1 60000 5.835E-03 41.028828 476.385 1.906E+03 10.99 41.131550 4.644E-05 1 70000 6.786E-03 41.415913 732.463 2.930E+03 9.41 41.262215 7.074E-05 1 80000 7.710E-03 41.729671 965.288 3.861E+03 8.33 41.504005 9.253E-05 1 90000 8.778E-03 41.560253 826.038 3.304E+03 7.11 41.011173 7.950E-05 1 100000 9.648E-03 41.692852 945.659 3.783E+03 6.32 41.459518 9.073E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 3.000000000 ------------------------------------------ Floating operations per iteration = 6 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 1.044E-03 .000000 .000 0.000E+00 .00 57.475903 1.044E-03 1 20000 2.041E-03 60.183727 471.123 2.827E+03 .00 58.798656 4.697E-05 1 30000 3.015E-03 60.878918 630.581 3.783E+03 1.78 59.700672 6.215E-05 1 40000 4.058E-03 59.903648 353.482 2.121E+03 3.79 59.144119 3.541E-05 1 50000 5.015E-03 60.244236 469.203 2.815E+03 3.17 59.818932 4.673E-05 1 60000 6.057E-03 59.946564 351.593 2.110E+03 2.89 59.435131 3.519E-05 1 70000 6.997E-03 60.233112 480.742 2.884E+03 2.91 60.025818 4.789E-05 1 80000 7.895E-03 60.853859 794.869 4.769E+03 4.82 60.798027 7.837E-05 1 90000 8.950E-03 60.862480 799.703 4.798E+03 4.01 60.335228 7.884E-05 1 100000 9.966E-03 60.764954 739.667 4.438E+03 3.49 60.203880 7.304E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 4.000000000 ------------------------------------------ Floating operations per iteration = 8 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 1.131E-03 .000000 .000 0.000E+00 .00 70.737709 1.131E-03 1 20000 2.283E-03 69.442123 -183.154 -1.465E+03 .00 70.083923 -2.110E-05 1 30000 3.309E-03 73.459435 577.600 4.621E+03 8.98 72.529213 6.290E-05 1 40000 4.396E-03 73.927170 687.399 5.499E+03 6.02 72.792107 7.439E-05 1 50000 5.545E-03 73.119263 461.321 3.691E+03 5.25 72.138351 5.047E-05 1 60000 6.636E-03 72.918823 396.093 3.169E+03 4.10 72.331177 4.346E-05 1 70000 7.665E-03 73.336441 551.082 4.409E+03 3.90 73.060135 6.012E-05 1 80000 8.816E-03 73.174416 483.585 3.869E+03 3.30 72.595253 5.287E-05 1 90000 9.913E-03 73.082642 441.173 3.529E+03 2.82 72.632133 4.829E-05 1 100000 1.115E-02 72.524796 157.927 1.263E+03 4.27 71.754234 1.742E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 5.000000000 ------------------------------------------ Floating operations per iteration = 10 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 1.776E-03 .000000 .000 0.000E+00 .00 56.306938 1.776E-03 1 20000 3.088E-03 76.218513 3536.255 3.536E+04 .00 64.766899 4.640E-04 1 30000 4.539E-03 72.381104 2686.916 2.687E+04 7.22 66.091927 3.712E-04 1 40000 6.103E-03 69.290688 1860.586 1.861E+04 10.32 65.542404 2.685E-04 1 50000 7.605E-03 68.152969 1501.645 1.502E+04 8.66 65.746597 2.203E-04 1 60000 9.074E-03 67.824150 1381.826 1.382E+04 6.80 66.124054 2.037E-04 1 70000 1.092E-02 65.910973 590.636 5.906E+03 11.39 64.079201 8.961E-05 1 80000 1.213E-02 66.246773 746.485 7.465E+03 9.81 65.925499 1.127E-04 1 90000 1.365E-02 66.385612 817.911 8.179E+03 8.27 65.929749 1.232E-04 1 100000 1.619E-02 64.051620 -499.976 -5.000E+03 17.22 61.754955 -7.806E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 6.000000000 ------------------------------------------ Floating operations per iteration = 12 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 1.823E-03 .000000 .000 0.000E+00 .00 65.823120 1.823E-03 1 20000 3.669E-03 65.006973 -123.991 -1.488E+03 .00 65.412498 -2.289E-05 1 30000 5.477E-03 65.681389 13.049 1.566E+02 1.63 65.728561 2.384E-06 1 40000 7.286E-03 65.944717 79.921 9.591E+02 1.40 65.879120 1.454E-05 1 50000 9.166E-03 65.564171 -35.953 -4.314E+02 1.91 65.460144 -6.580E-06 1 60000 1.090E-02 65.950279 101.244 1.215E+03 2.43 66.054924 1.842E-05 1 70000 1.270E-02 66.184952 196.495 2.358E+03 2.34 66.167397 3.563E-05 1 80000 1.451E-02 66.284103 241.730 2.901E+03 2.01 66.170891 4.376E-05 1 90000 1.635E-02 66.243355 221.092 2.653E+03 1.70 66.039032 4.005E-05 1 100000 1.817E-02 66.207420 201.084 2.413E+03 1.47 66.031662 3.645E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 7.000000000 ------------------------------------------ Floating operations per iteration = 14 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 2.142E-03 .000000 .000 0.000E+00 .00 65.360924 2.142E-03 1 20000 4.318E-03 64.336868 -156.677 -2.193E+03 .00 64.844856 -3.409E-05 1 30000 6.400E-03 65.756165 134.005 1.876E+03 3.46 65.623886 2.853E-05 1 40000 8.582E-03 65.414803 46.787 6.550E+02 2.53 65.253792 1.001E-05 1 50000 1.072E-02 65.383484 37.189 5.207E+02 1.82 65.322388 7.963E-06 1 60000 1.284E-02 65.436882 56.277 7.879E+02 1.41 65.405212 1.204E-05 1 70000 1.502E-02 65.326515 11.205 1.569E+02 1.28 65.237480 2.401E-06 1 80000 1.730E-02 64.930084 -170.918 -2.393E+03 2.66 64.724686 -3.685E-05 1 90000 1.927E-02 65.126892 -70.398 -9.856E+02 2.62 65.383568 -1.513E-05 1 100000 2.151E-02 65.082939 -95.098 -1.331E+03 2.25 65.092125 -2.046E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 8.000000000 ------------------------------------------ Floating operations per iteration = 16 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 2.414E-03 .000000 .000 0.000E+00 .00 66.280357 2.414E-03 1 20000 4.815E-03 66.639061 54.118 8.659E+02 .00 66.459229 1.299E-05 1 30000 7.261E-03 66.019539 -70.339 -1.125E+03 1.46 66.106255 -1.705E-05 1 40000 9.667E-03 66.101479 -49.742 -7.959E+02 .99 66.204346 -1.204E-05 1 50000 1.206E-02 66.274467 2.469 3.950E+01 1.03 66.340637 5.960E-07 1 60000 1.452E-02 66.160034 -37.824 -6.052E+02 .96 66.138283 -9.147E-06 1 70000 1.700E-02 65.910469 -138.272 -2.212E+03 1.59 65.863113 -3.357E-05 1 80000 1.931E-02 66.079903 -61.507 -9.841E+02 1.67 66.279953 -1.489E-05 1 90000 2.186E-02 65.927338 -138.327 -2.213E+03 1.72 65.870857 -3.357E-05 1 100000 2.412E-02 66.100670 -42.288 -6.766E+02 1.93 66.338013 -1.024E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 9.000000000 ------------------------------------------ Floating operations per iteration = 18 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 2.745E-03 .000000 .000 0.000E+00 .00 65.575851 2.745E-03 1 20000 5.534E-03 64.533264 -158.989 -2.862E+03 .00 65.050385 -4.435E-05 1 30000 8.262E-03 65.252785 -12.100 -2.178E+02 1.75 65.360123 -3.338E-06 1 40000 1.099E-02 65.514389 54.669 9.840E+02 1.46 65.490517 1.502E-05 1 50000 1.373E-02 65.626007 88.837 1.599E+03 1.15 65.554207 2.437E-05 1 60000 1.768E-02 61.772503 -1286.493 -2.316E+04 19.10 61.089512 -3.749E-04 1 70000 1.925E-02 63.578442 -544.496 -9.801E+03 19.67 65.454422 -1.542E-04 1 80000 2.222E-02 64.095490 -304.950 -5.489E+03 16.29 64.803650 -8.564E-05 1 90000 2.490E-02 64.539841 -75.976 -1.368E+03 14.04 65.062531 -2.119E-05 1 100000 2.744E-02 65.089249 235.507 4.239E+03 12.74 65.604904 6.513E-05 1 COMPUTATIONAL INTENSITY = flop per mem ref 10.00000000 ------------------------------------------ Floating operations per iteration = 20 Memory references per iteration = 2 LOOP LOOP RINF N1/2 S1/2 ERROR R-AVERAGE T0 NTIM LENGTH SECS MFLOP/S VEC.LEN FLOP % MFLOP/S SECS repeat 10000 3.064E-03 .000000 .000 0.000E+00 .00 65.275917 3.064E-03 1 20000 6.007E-03 67.954208 410.303 8.206E+03 .00 66.588142 1.208E-04 1 30000 9.049E-03 66.833511 183.644 3.673E+03 2.57 66.306122 5.496E-05 1 40000 1.205E-02 66.666206 141.461 2.829E+03 1.77 66.389862 4.244E-05 1 50000 1.509E-02 66.468643 81.772 1.635E+03 1.51 66.281670 2.460E-05 1 60000 1.808E-02 66.466454 81.003 1.620E+03 1.15 66.375633 2.437E-05 1 70000 2.109E-02 66.468109 81.669 1.633E+03 .92 66.391830 2.457E-05 1 80000 2.408E-02 66.494484 93.606 1.872E+03 .77 66.439812 2.815E-05 1 90000 2.712E-02 66.460602 76.574 1.531E+03 .68 66.369064 2.304E-05 1 100000 3.012E-02 66.453400 72.591 1.452E+03 .58 66.396561 2.185E-05 1 CALCULATION OF FHALF -------------------- F RINF RHAT FHALF ERROR f/m Mflop/s Mflop/s flop/mref % 1.0 20.937386 .000000 .0000 .00 2.0 41.692852 4798.545898 228.1855 .00 3.0 60.764954 1242.923584 58.1168 .57 4.0 72.524796 424.142090 18.7342 2.61 5.0 64.051620 147.525574 5.2118 8.18 6.0 66.207420 112.767303 3.4341 7.87 7.0 65.082939 95.438980 2.4966 7.26 8.0 66.100670 87.732292 2.0528 6.52 9.0 65.089249 81.849396 1.6916 5.86 10.0 66.453400 79.150215 1.5149 5.27 LAST VALUES : RHAT = 79.150215 Mflop/s FHALF = 1.5149 flop/mref TOTAL EXECUTION TIME IS 2.0659179688E+00 SECONDS.