C PROGRAM MFLOPS(TAPE6=OUTPUT) C LATEST FILE MODIFICATION DATE: 22 Dec 86 C**************************************************************************** C MEASURES CPU PERFORMANCE RANGE OF THE COMPUTER/COMPILER/COMPUTATION COMPLEX C**************************************************************************** C * C L. L. N. L. F O R T R A N K E R N E L S: M F L O P S * C * C These kernels measure Fortran numerical computation rates for a * C spectrum of CPU-limited computational structures. Mathematical * C through-put is measured in units of millions of floating-point * C operations executed per second, called Megaflops/sec. * C * C This program measures a realistic CPU performance range for the * C Fortran programming system on a given day. The CPU performance * C rates depend strongly on the maturity of the Fortran compiler's * C ability to translate Fortran code into efficient machine code. * C * C [ The CPU hardware capability apart from compiler maturity (or * C availability), could be measured (or simulated) by programming the * C kernels in assembly or machine code directly. These measurements * C can also serve as a framework for tracking the maturation of the * C Fortran compiler during system development.] * C * C While this test evaluates the performance of a broad sampling of * C Fortran computations, it is not an application program and hence * C it is not a benchmark per se. The performance of benchmarks and * C even workloads, if CPU limited, could be roughly estimated by * C choosing appropriate weights and loop limits for each kernel (see * C Block Data). * C * C Use of this program is granted with the request that a copy of the * C results be sent to the author at the address shown below, to be * C added to our studies of computer performance. The timing results * C will be held as proprietary data if so marked. In return, you * C will receive a copy of our latest report. * C * C * C F.H. McMahon L-35 * C Lawrence Livermore National Laboratory * C P.0. Box 808 * C Livermore, CA * C 94550 * C * C * C (C) Copyright 1983 the Regents of the * C University of California. All Rights Reserved. * C * C This work was produced under the sponsorship of * C the U.S. Department of Energy. The Government * C retains certain rights therein. * C * C**************************************************************************** C C C C C C C C DIRECTIONS C C 1. We REQUIRE one run of the Fortran kernels as is, that is, with C no reprogramming. Standard product compiler directives may be C used for optimization as these do not constitute reprogramming. C C In addition, the vendor may, if so desired, reprogram the kernels to C demonstrate high performance hardware features. Kernels 13,14,23 C are partially vectorisable and kernels 15,16,24 are vectorisable if C re-written. Kernels 5,11,17,19,20 are implicit computations that C must not be explicitly vectorised using compiler directives to C ignore dependencies. In any case, compiler listings of the codes C actually used should be returned along with the timing results. C C 2. For vector processors, we REQUIRE an ALL scalar-compilation run C to measure the basic scalar performance range of the processor. C C 3. On computers where default single precision is REAL*4 we REQUIRE C an additional run with all mantissas.ge.47 i.e. declare all real C variables REAL*8 using one of the following declarations in each routine: C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C C 4. Installation includes verifying or changing the following: C C First : the I/O output device number= IOU assignment in MAIN. C Second: the definition of function SECOND for CPU time only, and C the value of TIC:= minimum cpu clock time(sec) in SIZES. C Third : the definition of function MOD2N in KERNEL C Fourth: the system names Komput, Kontrl, and Kompil in REPORT C Fifth : after checkout set Nruns=7 in SIZES for Standard Benchmark Test C C 5. Each kernel's computation is check-summed for easy validation. C Verify correct processing using the checksums in subroutine REPORT C which were computed setting Loop= 10*Loop in subroutine SIZES. C Your checksums should compare to the precision used, within round-off. C C 6. Verify CPU Time measurements from function SECOND by comparing the clock C calibration printout of total CPU time with system or real-time measures. C The accuracy of SECOND is also tested using the test routine VERIFY. C C 7. On computers with Virtual Storage Systems assure a working-set space C larger than the entire program so that page faults are negligible, C because we must measure the CPU-limited computation rates. C IT IS ALSO NECESSARY to run this test stand-alone, i.e. NO timesharing. C In VS Systems a series of runs are needed to show stable CPU timings. C C 8. On parallel computer systems which compile vectors or Multi-tasking C at the Do-loop level (Micro-tasking) parallelisation of the first C DO (on L) in each kernel must be prevented by using a compiler directive C or by setting Loop= 1. This outermost DO Loop is merely repitition C used to increase timing accuracy and could distort the computation C sample if parallelisation is based on this artificial iteration level. C C 9. On computers with Cache memories and high resolution CPU clocks we C may ask for an addtional run setting repitition Loop= 1 in SIZES, C to show un-initialized as well as encached execution rates. C Increase the size of array CACHE(in subr. VALUES) from 8192 to cache size C**************************************************************************** C C C c C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C/ PARAMETER( nk= 47, nl= 3, nr= 8 ) c COMMON /ALPHA/ mk,ik,ml,il,Nruns,jr, NPFS(8,3,47) DIMENSION FLOPS(141), TR(141), RATES(141), ID(141) DIMENSION LSPAN(141), WG(141), OSUM (141), TERR(141) REAL SECOND c c t= SECOND(0.0) iou= 6 OPEN (UNIT=6, FILE='FLOP.OUT', STATUS='NEW') cLLNL call Q8EBM cLLNL call PFM( 0, iou) c c Verify Sufficient Loop Size Versus Cpu Clock Accuracy CALL VERIFY( iou) c c Define control limits: Nruns(runs), Loop(time), tic, CALL SIZES(-1) c c c Run test Nruns times Cpu-limited; I/O is deferred: DO 1 k= 1,Nruns jr= k c Run test using one of 3 sets of DO-Loop spans: c Set iou Negative to supress all I/O during Cpu timing. DO 1 j= 1,ml il= j tock= TICK( -iou) c CALL KERNEL 1 continue c c c c Report timing errors, Mflops statistics: DO 2 j= 1,ml il= j CALL RESULT( iou,FLOPS,TR,RATES,LSPAN,WG,OSUM,TERR,ID) c CALL REPORT( iou, mk,mk,FLOPS,TR,RATES,LSPAN,WG,OSUM,ID) 2 continue c CALL REPORT( iou,3*mk,mk,FLOPS,TR,RATES,LSPAN,WG,OSUM,ID) c c t= SECOND(0.0) - t WRITE( iou,9) t 9 FORMAT( 1H1,//,26H CHECK CLOCK CALIBRATION: ,/, . 18H Total cpu Time = ,e14.5, 5H Sec. ) STOP c c c c c c c c c c c Subroutine timing of all-scalar execution on CRAY-1: c c Subroutine Time(%) c c KERNEL 43.46% c SUPPLY 21.82% c VERIFY 13.12% c STATS 8.83% c SQRT 1.84% c SORDID 1.21% c VALUES .74% c SUMO .47% c SIGNAL .34% c IQRANF .26% c STATW .17% c END c*********************************************** BLOCK DATA C*********************************************** C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION SUMS C C l1 := param-dimension governs the size of most 1-d arrays C l2 := param-dimension governs the size of most 2-d arrays C C ISPAN := Array of limits for DO loop control in the kernels C IPASS := Array of limits for multiple pass execution of each kernel C FLOPN := Array of floating-point operation counts for one pass thru kernel C WT := Array of weights to average kernel execution rates. C SKALE := Array of scale factors for SIGNAL data generator. C BIAS := Array of scale factors for SIGNAL data generator. C C MUL := Array of multipliers * FLOPN for each pass C WTP := Array of multipliers * WT for each pass C FR := Array of vectorisation fractions in REPORT C SUMW := Array of quartile weights in REPORT C IQ := Array of workload weights in REPORT C SUMS := Array of Verified Checksums of Kernels results: Nruns= 1 and 7. C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= l13/2, l213= l13+l13h, l813= 8*l13 ) C/ PARAMETER( l14=2048, l16= 75, l416= 4*l16 , l21= 25 ) C C/ PARAMETER( l1= 27, l2= 15, l1d= 2*1001 ) C/ PARAMETER( l13= 8, l13h= 8/2, l213= 8+4, l813= 8*8 ) C/ PARAMETER( l14= 16, l16= 15, l416= 4*15 , l21= 15) C C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= 64/2, l213= 64+32, l813= 8*64 ) C/ PARAMETER( l14= 2048, l16= 75, l416= 4*75 , l21= 25) C C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C/ PARAMETER( m1= 1001-1, m2= 101-1, m7= 1001-6 ) C COMMON /SPACES/ ion,j5,k2,k3,Loop,m,kr,it,n13h,ibuf, 1 n,n1,n2,n13,n213,n813,n14,n16,n416,n21,nt1,nt2 C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C COMMON /PROOF/ SUMS(24,3,2) C **************************************************************** C DATA ( ISPAN(i,1), i= 1,47) / : 1001, 101, 1001, 1001, 1001, 64, 995, 100, : 101, 101, 1001, 1000, 64, 1001, 101, 75, : 101, 100, 101, 1000, 101, 101, 100, 1001, 23*0/ C C* : l1, l2, l1, l1, l1, l13, m7, m2, C* : l2, l2, l1, m1, l13, l1, l2, l16, C* : l2, m2, l2, m1, l21, l2, m2, l1, 23*0/ C DATA ( ISPAN(i,2), i= 1,47) / : 101, 101, 101, 101, 101, 32, 101, 100, : 101, 101, 101, 100, 32, 101, 101, 40, : 101, 100, 101, 100, 50, 101, 100, 101, 23*0/ C DATA ( ISPAN(i,3), i= 1,47) / : 27, 15, 27, 27, 27, 8, 21, 14, : 15, 15, 27, 26, 8, 27, 15, 15, : 15, 14, 15, 26, 20, 15, 14, 27, 23*0/ C DATA ( IPASS(i,1), i= 1,47) / : 7, 67, 9, 14, 10, 3, 4, 10, 36, 34, 11, 12, : 36, 2, 1, 25, 35, 2, 39, 1, 1, 11, 8, 5, 23*0/ C DATA ( IPASS(i,2), i= 1,47) / : 40, 40, 53, 70, 55, 7, 22, 6, 21, 19, 64, 68, : 41, 10, 1, 27, 20, 1, 23, 8, 1, 7, 5, 31, 23*0/ C DATA ( IPASS(i,3), i= 1,47) / : 28, 46, 37, 38, 40, 21, 20, 9, 26, 25, 46, 48, : 31, 8, 1, 14, 26, 2, 28, 7, 1, 8, 7, 23, 23*0/ C DATA ( MUL(i), i= 1,3) / 1, 2, 8 / DATA ( WTP(i), i= 1,3) / 1.0, 2.0, 1.0 / c c The following flop-counts (FLOPN) are required for scalar or serial c execution. The scalar version defines the NECESSARY computation c generally, in the absence of proof to the contrary. The vector c or parallel executions are only credited with executing the same c necessary computation. If the parallel methods do more computation c than is necessary then the extra flops are not counted as through-put. c DATA ( FLOPN(i), i= 1,47) : /5., 4., 2., 2., 2., 2., 16., 36., 17., 9., 1., 1., : 7., 11., 33., 7., 9., 44., 6., 26., 2., 17., 11., 1., 23*0.0/ C DATA ( WT(i), i= 1,47) / : 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, : 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, : 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 23*0.0/ C C DATA ( SKALE(i), i= 1,47) / & 0.100D0, 0.100D0, 0.100D0, 0.100D0, 0.100D0, 0.100D0, & 0.100D0, 0.100D0, 0.100D0, 0.100D0, 0.100D0, 0.100D0, & 0.100D0, 0.100D0, 0.100D0, 0.100D0, 0.100D0, 0.100D0, & 0.100D0, 0.100D0, 0.100D0, 0.100D0, 0.100D0, 0.100D0, & 23*0.000D0 / C c : 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, c : 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, c : 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 23*0.0/ C DATA ( BIAS(i), i= 1,47) / : 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, : 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, : 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 23*0.0/ C DATA ( FR(i), i= 1,9) / : 0.0, 0.2, 0.4, 0.6, 0.7, 0.8, 0.9, 0.95, 1.0/ C DATA ( SUMW(i), i= 1,7) / : 1.0, 0.95, 0.9, 0.8, 0.7, 0.6, 0.5/ C DATA ( IQ(i), i= 1,7) / : 1, 2, 1, 2, 1, 2, 1/ C DATA START /0.0/, NPF/0/, ibuf/0/ C DATA ( SUMS(i,1,1), i= 1,24 ) / &.5114652693224705D+05,.5150345372943066D+03,.1000742883066623D+02, &.5999250595474070D+00,.4548871642388544D+04,.5229095383954675D+13, &.6104251075163778D+05,.1501268005627157D+06,.1189443609975085D+06, &.7310369784325972D+05,.3342910984950433D+08,.2907141428639174D-04, &.4057110454105263D+10,.2982036205992255D+10,.3943816690352311D+05, &.2832600000000000D+05,.1114641772903091D+04,.5165625410757306D+05, &.5421816960150398D+03,.3040644339317275D+08,.8289464835786202D+07, &.2938604376567099D+03,.3549834542446150D+05,.5000000000000000D+03/ c DATA ( SUMS(i,2,1), i= 1,24 ) / &.5253344778938000D+03,.5150345372943066D+03,.1009741436579188D+01, &.5999250595474070D+00,.4589031939602131D+02,.2693280957416549D+16, &.6345586315772524D+03,.1501268005627157D+06,.1189443609975085D+06, &.7310369784325972D+05,.3433560531581074D+05,.7127569144561925D-05, &.2325318944820836D+10,.3045676741897511D+08,.3943816690352311D+05, &.3244100000000000D+05,.1114641772903091D+04,.5165625410757306D+05, &.5421816960150398D+03,.3126205178811007D+05,.3986531136462291D+07, &.2938604376567099D+03,.3549894609776936D+05,.5000000000000000D+02/ c DATA ( SUMS(i,3,1), i= 1,24 ) / &.3855104502494983D+02,.1199847611437483D+02,.2699309089321296D+00, &.5999250595474070D+00,.3182615248448271D+01,.8303480073326955D+12, &.2845720217638848D+02,.2960543667877649D+04,.2623968460874419D+04, &.1651291227698377D+04,.6551162198437113D+03,.1943435981776804D-05, &.4755211251524563D+09,.2547733008933910D+07,.1108997288135066D+04, &.2577600000000000D+05,.2947368618590713D+02,.9700646212341513D+03, &.1268230698051747D+02,.5987713249471801D+03,.2516870081042209D+07, &.6109968728264795D+01,.4850340602751675D+03,.1300000000000000D+02/ c DATA ( SUMS(i,1,2), i= 1,7 ) / &.2982036205992255D+10,.6118901630090488D+10,.9103526877478772D+10, &.1215176334476067D+11,.1519764492169999D+11,.1820312504465359D+11, &.2116750694993432D+11/ c DATA ( SUMS(i,2,2), i= 1,7 ) / &.3045676741897511D+08,.5718526521576222D+08,.8885029941358330D+08, &.1174925822726987D+09,.1501582054695641D+09,.1819691693283694D+09, &.2130649341195080D+09/ c DATA ( SUMS(i,3,2), i= 1,7 ) / &.2547733008933910D+07,.5131714230651644D+07,.7946120246231201D+07, &.1008019578807808D+08,.1269997234773526D+08,.1504905863862026D+08, &.1721399839433381D+08/ END C C*********************************************** SUBROUTINE INDEX C*********************************************** C C MODULE PURPOSE C ------ ----------------------------------------------- C IQRANF computes a vector of pseudo-random indices C C KERNEL executes 24 samples of Fortran computation C C PFM optional call to system hardware performance monitor C C REPORT prints timing results C C RESULT computes execution rates into pushdown store C C SECOND cumulative CPU time for task in seconds (MKS units) C C SENSIT sensitivity analysis of harmonic mean to 49 workloads C C SIGNAL generates a set of floating-point numbers near 1.0 C C SIMD sensitivity analysis of harmonic mean to SISD/SIMD model C C SIZES test and set the loop controls before each kernel test C C SORDID simple sort C C SPACE sets memory pointers for array variables. optional. C C STATS calculates unweighted statistics C C STATW calculates weighted statistics C C SUMO check-sum with ordinal dependency C C SUPPLY initializes common blocks containing type real arrays. C C TALLY computes average and minimum Cpu timings and variances. C C TDIGIT counts lead digits followed by trailing zeroes C C TEST times, tests, and initializes each kernel test C C TICK measures timing overhead of subroutine test C C TILE computes m-tile value and corresponding index C C VALID compresses valid timing results C C VALUES initializes special values C C VERIFY verifies sufficient Loop size versus cpu clock accuracy C ------ ----------------------------------------------- C C C C c c ------------ -------- -------- -------- -------- -------- -------- c ENTRY LEVELS: 1 2 3 4 5 6 c ------------ -------- -------- -------- -------- -------- -------- c MAIN. SECOND c VERIFY SECOND c SIZES c STATS SQRT c TDIGIT ALOG10 c SIZES c c TICK TEST SECOND c SIZES c SUMO c VALUES SUPPLY SIGNAL c IQRANF MOD c VALID c STATS SQRT c IQRANF MOD c c KERNEL SPACE c SQRT c EXP c TEST SECOND c SIZES c SUMO c VALUES SUPPLY SIGNAL c IQRANF MOD c RESULT TALLY SIZES c PAGE c STATS SQRT c ALOG10 c c REPORT VALID c MOD c STATW SORDID c TILE c SQRT c ALOG10 c PAGE c SENSIT VALID c SORDID c PAGE c STATW SORDID c TILE c SIMD VALID c STATW SORDID c TILE C STOP C C C C C C C C C C C C C c ------ ---- ------ ----- ------------------------------------ c BASE TYPE CLASS NAME GLOSSARY c ------ ---- ------ ----- ------------------------------------ c SPACE0 R Array BIAS - scale factors for SIGNAL data generator c SPACE0 R Array CSUM - checksums of KERNEL result arrays c BETA R Array CSUMS - sets of CSUM for all test runs c BETA R Array DOS - sets of TOTAL flops for all test runs c SPACE0 R Array FLOPN - flop counts for one execution pass c BETA R Array FOPN - sets of FLOPN for all test runs c SPACE0 R Array FR - vectorisation fractions; abscissa for REPOR c SPACES I scalar ibuf - flag enables one call to SIGNAL c ALPHA I scalar ik - current number of executing kernel c ALPHA I scalar il - selects one of three sets of loop spans c SPACES I scalar ion - logical I/O unit number for output c SPACEI I Array IPASS - Loop control limits for multiple-pass loops c SPACE0 I Array IQ - set of workload weights for REPORT c SPACEI I Array ISPAN - loop control limits for each kernel c SPACES I scalar it - flags timing call to TEST from TICK c SPACES I scalar j5 - datum in kernel 16 c ALPHA I scalar jr - current test run number (1 thru 7) c SPACES I scalar k2 - counter in kernel 16 c SPACES I scalar k3 - counter in kernel 16 c SPACES I scalar kr - a copy of mk c SPACES I scalar Loop - current multiple-pass loop limit in KERNEL c SPACES I scalar m - temp integer datum c ALPHA I scalar mk - number of kernels to evaluate .LE.24 c ALPHA I scalar ml - maximum value of il= 3 c SPACEI I Array MUL - multipliers * IPASS defines Loop c SPACES I scalar n - current DO loop limit in KERNEL c SPACES I scalar n1 - dimension of most 1-D arrays c SPACES I scalar n13 - dimension used in kernel 13 c SPACES I scalar n13h - dimension used in kernel 13 c SPACES I scalar n14 - dimension used in kernel 14 c SPACES I scalar n16 - dimension used in kernel 16 c SPACES I scalar n2 - dimension of most 2-D arrays c SPACES I scalar n21 - dimension used in kernel 21 c SPACES I scalar n213 - dimension used in kernel 21 c SPACES I scalar n416 - dimension used in kernel 16 c SPACES I scalar n813 - dimension used in kernel 13 c SPACE0 I scalar npf - temp integer datum c ALPHA I Array NPFS - sets of NPFS1 for all test runs c SPACE0 I Array NPFS1 - number of page-faults for each kernel c ALPHA I scalar Nruns - number of complete test runs c SPACES I scalar nt1 - total size of common -SPACE1- words c SPACES I scalar nt2 - total size of common -SPACE2- words c BETA R Array SEE - (i,1,jr,il) sets of TEST overhead times c BETA R Array SEE - (i,2,jr,il) sets of csums of SPACE1 c BETA R Array SEE - (i,3,jr,il) sets of csums of SPACE2 c SPACE0 R Array SKALE - scale factors for SIGNAL data generator c SPACE0 R scalar start - temp start time of each kernel c PROOF R Array SUMS - sets of verified checksums for all test run c SPACE0 R Array SUMW - set of quartile weights for REPORT c SPACE0 R Array TERR1 - overhead-time errors for each kernel c BETA R Array TERRS - sets of TERR1 for all runs c BETA R scalar tic - minimum cpu clock time= resolution c SPACE0 R scalar ticks - average overhead time in TEST linkage c SPACE0 R Array TIME - net execution times for all kernels c BETA R Array TIMES - sets of TIME for all test runs c SPACE0 R Array TOTAL - total flops computed by each kernel c SPACE0 R Array WS - unused c SPACE0 R Array WT - weights for each kernel sample c SPACEI R Array WTP - weights for the 3 span-varying passes c SPACE0 R Array WW - unused C C c --------- ----------------------------------------------------------------- c COMMON Usage c --------- ----------------------------------------------------------------- C C /ALPHA / C VERIFY TICK TALLY SIZES RESULT REPORT KERNEL C MAIN. C /BASE1 / C SUPPLY C /BASE2 / C SUPPLY C /BASER / C SUPPLY C /BETA / C TICK TALLY SIZES RESULT REPORT KERNEL C /PROOF / C RESULT BLOCKDATA C /SPACE0/ C VALUES TICK TEST TALLY SUPPLY SIZES RESULT C REPORT KERNEL BLOCKDATA C /SPACE1/ C VERIFY VALUES TICK TEST SUPPLY SPACE KERNEL C /SPACE2/ C VERIFY VALUES TICK TEST SUPPLY SPACE KERNEL C /SPACE3/ C VALUES C /SPACEI/ C VERIFY VALUES TICK TEST SIZES RESULT REPORT C KERNEL BLOCKDATA C /SPACER/ C VALUES TICK TEST SUPPLY SIZES KERNEL C /SPACES/ C VERIFY VALUES TICK TEST SUPPLY SIZES KERNEL C BLOCKDATA c --------- ----------------------------------------------------------------- RETURN END C C C*************************************** SUBROUTINE IQRANF( M, Mmin,Mmax, n) C*********************************************************************** C * c IQRANF - computes a vector of psuedo-random indices * c in the domain (Mmin,Mmax) * C * C M - result array , psuedo-random positive integers * C Mmin - input integer, lower bound for random integers * C Mmax - input integer, upper bound for random integers * C n - input integer, number of results in M. * C * C M(i)= Mmin + INT( (Mmax-Mmin) * RANF(0)) * C * c CALL IQRANF( IX, 1,1001, 30) should produce in IX: * c 3 674 435 415 389 54 44 790 900 282 * c 177 971 728 851 687 604 815 971 155 112 * c 877 814 779 192 619 894 544 404 496 505 ... * C * C*********************************************************************** C cANSI IMPLICIT DOUBLE PRECISION (A-H,K,O-Z) cIBM IMPLICIT REAL*8 (A-H,K,O-Z) DOUBLE PRECISION dq, dp, per, dk, spin, span C dimension M(n) save k IF( n.LE.0 ) RETURN inset= Mmin span= Mmax - Mmin c spin= 16807.00D0 c per= 2147483647.00D0 spin= 16807 per= 2147483647 realn= n scale= 1.0000100 q= scale*(span/realn) C dk= k DO 1 i= 1,n dp= dk*spin c dk= DMOD( dp, per) dk= dp -INT( dp/per)*per dq= dk*span M(i)= inset + ( dq/ per) IF( M(i).LT.Mmin .OR. M(i).GT.Mmax ) M(i)= inset + i*q 1 continue k= dk C C ciC double precision k, ip, iq, id ci inset= Mmin ci ispan= Mmax - Mmin ci ispin= 16807 ci id= 2147483647 ci q= (REAL(ispan)/REAL(n))*1.00001 ciC ci DO 2 i= 1,n ci ip= k*ispin ci k= MOD( ip, id) ci iq= k*ispan ci M(i)= inset + ( iq/ id) ci IF( M(i).LT.Mmin .OR. M(i).GT.Mmax ) M(i)= inset + i*q ci 2 continue C RETURN DATA k /256/ END C*********************************************** SUBROUTINE KERNEL C*********************************************************************** C * C KERNEL executes 24 samples of Fortran computation * C * C*********************************************************************** C * C L. L. N. L. F O R T R A N K E R N E L S: M F L O P S * C * C These kernels measure Fortran numerical computation * C rates for a spectrum of cpu-limited computational * C structures or benchmarks. Mathematical through-put * C is measured in units of millions of floating-point * C operations executed per second, called Megaflops/sec. * C * C Fonzi's Law: There is not now and there never will be a language * C in which it is the least bit difficult to write * C bad programs. * C F.H.MCMAHON 1972 * C*********************************************************************** C C l1 := param-dimension governs the size of most 1-d arrays C l2 := param-dimension governs the size of most 2-d arrays C C Loop := multiple pass control to execute kernel long enough to time. C n := DO loop control for each kernel. Controls are set in subr. SIZES C C ****************************************************************** C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= l13/2, l213= l13+l13h, l813= 8*l13 ) C/ PARAMETER( l14=2048, l16= 75, l416= 4*l16 , l21= 25 ) C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C C C/ PARAMETER( nk= 47, nl= 3, nr= 8 ) C COMMON /ALPHA/ mk,ik,ml,il,Nruns,jr, NPFS(8,3,47) COMMON /BETA / tic, TIMES(8,3,47), SEE(5,3,8,3), 1 TERRS(8,3,47), CSUMS(8,3,47), 2 FOPN(8,3,47), DOS(8,3,47) C COMMON /SPACES/ ion,j5,k2,k3,Loop,m,kr,it,n13h,ibuf, 1 n,n1,n2,n13,n213,n813,n14,n16,n416,n21,nt1,nt2 C COMMON /SPACER/ A11,A12,A13,A21,A22,A23,A31,A32,A33, 2 AR,BR,C0,CR,DI,DK, 3 DM22,DM23,DM24,DM25,DM26,DM27,DM28,DN,E3,E6,EXPMAX,FLX, 4 Q,QA,R,RI,S,SCALE,SIG,STB5,T,XNC,XNEI,XNM C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C C/ INTEGER E,F,ZONE C/ COMMON /ISPACE/ E(l213), F(l213), C/ 1 IX(l1), IR(l1), ZONE(l416) C/C C/ COMMON /SPACE1/ U(l1), V(l1), W(l1), C/ 1 X(l1), Y(l1), Z(l1), G(l1), C/ 2 DU1(l2), DU2(l2), DU3(l2), GRD(l1), DEX(l1), C/ 3 XI(l1), EX(l1), EX1(l1), DEX1(l1), C/ 4 VX(l14), XX(l14), RX(l14), RH(l14), C/ 5 VSP(l2), VSTP(l2), VXNE(l2), VXND(l2), C/ 6 VE3(l2), VLR(l2), VLIN(l2), B5(l2), C/ 7 PLAN(l416), D(l416), SA(l2), SB(l2) C/C C/ COMMON /SPACE2/ P(4,l813), PX(l21,l2), CX(l21,l2), C/ 1 VY(l2,l21), VH(l2,7), VF(l2,7), VG(l2,7), VS(l2,7), C/ 2 ZA(l2,7) , ZP(l2,7), ZQ(l2,7), ZR(l2,7), ZM(l2,7), C/ 3 ZB(l2,7) , ZU(l2,7), ZV(l2,7), ZZ(l2,7), C/ 4 B(l13,l13), C(l13,l13), H(l13,l13), C/ 5 U1(5,l2,2), U2(5,l2,2), U3(5,l2,2) C C ****************************************************************** C C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= 64/2, l213= 64+32, l813= 8*64 ) C/ PARAMETER( l14= 2048, l16= 75, l416= 4*75 , l21= 25) C C care C INTEGER E,F,ZONE COMMON /ISPACE/ E(96), F(96), 1 IX(1001), IR(1001), ZONE(300) C COMMON /SPACE1/ U(1001), V(1001), W(1001), 1 X(1001), Y(1001), Z(1001), G(1001), 2 DU1(101), DU2(101), DU3(101), GRD(1001), DEX(1001), 3 XI(1001), EX(1001), EX1(1001), DEX1(1001), 4 VX(1001), XX(1001), RX(1001), RH(2048), 5 VSP(101), VSTP(101), VXNE(101), VXND(101), 6 VE3(101), VLR(101), VLIN(101), B5(101), 7 PLAN(300), D(300), SA(101), SB(101) C COMMON /SPACE2/ P(4,512), PX(25,101), CX(25,101), 1 VY(101,25), VH(101,7), VF(101,7), VG(101,7), VS(101,7), 2 ZA(101,7) , ZP(101,7), ZQ(101,7), ZR(101,7), ZM(101,7), 3 ZB(101,7) , ZU(101,7), ZV(101,7), ZZ(101,7), 4 B(64,64), C(64,64), H(64,64), 5 U1(5,101,2), U2(5,101,2), U3(5,101,2) C C ****************************************************************** C DIMENSION XZ(2001), ZX(2001) EQUIVALENCE ( XZ(1), X(1)), ( ZX(1), Z(1)) C C C// DIMENSION E(96), F(96), U(1001), V(1001), W(1001), C// 1 X(1001), Y(1001), Z(1001), G(1001), C// 2 DU1(101), DU2(101), DU3(101), GRD(1001), DEX(1001), C// 3 IX(1001), XI(1001), EX(1001), EX1(1001), DEX1(1001), C// 4 VX(1001), XX(1001), IR(1001), RX(1001), RH(2048), C// 5 VSP(101), VSTP(101), VXNE(101), VXND(101), C// 6 VE3(101), VLR(101), VLIN(101), B5(101), C// 7 PLAN(300), ZONE(300), D(300), SA(101), SB(101) C//C C// DIMENSION P(4,512), PX(25,101), CX(25,101), C// 1 VY(101,25), VH(101,7), VF(101,7), VG(101,7), VS(101,7), C// 2 ZA(101,7) , ZP(101,7), ZQ(101,7), ZR(101,7), ZM(101,7), C// 3 ZB(101,7) , ZU(101,7), ZV(101,7), ZZ(101,7), C// 4 B(64,64), C(64,64), H(64,64), C// 5 U1(5,101,2), U2(5,101,2), U3(5,101,2) C//C C//C ****************************************************************** C//C C// COMMON /POINT/ ME,MF,MU,MV,MW,MX,MY,MZ,MG,MDU1,MDU2,MDU3,MGRD, C// 1 MDEX,MIX,MXI,MEX,MEX1,MDEX1,MVX,MXX,MIR,MRX,MRH,MVSP,MVSTP, C// 2 MVXNE,MVXND,MVE3,MVLR,MVLIN,MB5,MPLAN,MZONE,MD,MSA,MSB, C// 3 MP,MPX,MCX,MVY,MVH,MVF,MVG,MVS,MZA,MZP,MZQ,MZR,MZM,MZB,MZU, C// 4 MZV,MZZ,MB,MC,MH,MU1,MU2,MU3 C//C C// POINTER (ME,E), (MF,F), (MU,U), (MV,V), (MW,W), C// 1 (MX,X), (MY,Y), (MZ,Z), (MG,G), C// 2 (MDU1,DU1),(MDU2,DU2),(MDU3,DU3),(MGRD,GRD),(MDEX,DEX), C// 3 (MIX,IX), (MXI,XI), (MEX,EX), (MEX1,EX1), (MDEX1,DEX1), C// 4 (MVX,VX), (MXX,XX), (MIR,IR), (MRX,RX), (MRH,RH), C// 5 (MVSP,VSP), (MVSTP,VSTP), (MVXNE,VXNE), (MVXND,VXND), C// 6 (MVE3,VE3), (MVLR,VLR), (MVLIN,VLIN), (MB5,B5), C// 7 (MPLAN,PLAN), (MZONE,ZONE), (MD,D), (MSA,SA), (MSB,SB) C//C C// POINTER (MP,P), (MPX,PX), (MCX,CX), C// 1 (MVY,VY), (MVH,VH), (MVF,VF), (MVG,VG), (MVS,VS), C// 2 (MZA,ZA), (MZP,ZP), (MZQ,ZQ), (MZR,ZR), (MZM,ZM), C// 3 (MZB,ZB), (MZU,ZU), (MZV,ZV), (MZZ,ZZ), C// 4 (MB,B), (MC,C), (MH,H), C// 5 (MU1,U1), (MU2,U2), (MU3,U3) C.. COMMON DUMMY(2000) C.. LOC(X) =.LOC.X C.. IQ8QDSP = 64*LOC(DUMMY) C C ****************************************************************** C C STANDARD PRODUCT COMPILER DIRECTIVES MAY BE USED FOR OPTIMIZATION C CDIR$ VECTOR CLLL. OPTIMIZE LEVEL i CLLL. OPTION INTEGER (7) CLLL. OPTION ASSERT (NO HAZARD) CLLL. OPTION NODYNEQV C C ****************************************************************** C BINARY MACHINES MAY USE THE AND(P,Q) FUNCTION IF AVAILABLE C IN PLACE OF THE FOLLOWING CONGRUENCE FUNCTION (SEE KERNEL 13, 14) C CLLL. INTEGER AND, OR, XOR CLLL. AND(j,k) = j.INT.k AND(j,k) = j.AND.k C AND(j,k) = IAND(j,k) C MOD2N(i,j)= MOD(i,j) +j/2 -ISIGN(j/2,i) MOD2N(i,j)= AND(i,j-1) MOD2P(i,j)= AND(i-1,j-1) + 1 C i is Congruent to MOD2N(i,j) mod(j) C ****************************************************************** C C MAX(x,y)= AMAX1(x,y) or DMAX1(x,y) C MIN(x,y)= AMIN1(x,y) or DMIN1(x,y) C C CALL SPACE C cLLNL call PFM( 0, ion) CALL TEST(0) C C****************************************************************************** C*** KERNEL 1 HYDRO FRAGMENT C****************************************************************************** C DO 1 L = 1,Loop DO 1 k = 1,n 1 X(k)= Q + Y(k)*(R*ZX(k+10) + T*ZX(k+11)) C C................... CALL TEST(1) C C****************************************************************************** C*** KERNEL 2 ICCG EXCERPT (INCOMPLETE CHOLESKY - CONJUGATE GRADIENT) C****************************************************************************** C DO 200 L= 1,Loop II= n IPNTP= 0 222 IPNT= IPNTP IPNTP= IPNTP+II II= II/2 i= IPNTP CDIR$ IVDEP C DO 2 k= IPNT+2,IPNTP,2 i= i+1 2 X(i)= X(k) - V(k)*X(k-1) - V(k+1)*X(k+1) IF( II.GT.1) GO TO 222 200 CONTINUE C C................... CALL TEST(2) C C****************************************************************************** C*** KERNEL 3 INNER PRODUCT C****************************************************************************** C DO 3 L= 1,Loop Q= 0.000D0 DO 3 k= 1,n 3 Q= Q + Z(k)*X(k) C C................... CALL TEST(3) C C C C****************************************************************************** C*** KERNEL 4 BANDED LINEAR EQUATIONS C****************************************************************************** C m= (1001-7)/2 DO 444 L= 1,Loop DO 444 k= 7,1001,m lw= k-6 temp= X(k-1) CDIR$ IVDEP DO 4 j= 5,n,5 temp = temp - XZ(lw)*Y(j) 4 lw= lw+1 X(k-1)= Y(5)*temp 444 CONTINUE C C................... CALL TEST(4) C C****************************************************************************** C*** KERNEL 5 TRI-DIAGONAL ELIMINATION, BELOW DIAGONAL C****************************************************************************** C DO 5 L = 1,Loop CDIR$ NOVECTOR DO 5 i = 2,n 5 X(i)= Z(i)*(Y(i) - X(i-1)) CDIR$ VECTOR C C................... CALL TEST(5) C C****************************************************************************** C*** KERNEL 6 GENERAL LINEAR RECURRENCE EQUATIONS C****************************************************************************** C DO 6 L= 1,Loop DO 6 i= 2,n C W(i)= 0.0100D0 use only if overflow occurs DO 6 k= 1,i-1 W(i)= W(i) + B(i,k) * W(i-k) 6 CONTINUE C C................... CALL TEST(6) C C****************************************************************************** C*** KERNEL 7 EQUATION OF STATE FRAGMENT C****************************************************************************** C DO 7 L= 1,Loop DO 7 k= 1,n X(k)= U(k ) + R*( Z(k ) + R*Y(k )) + . T*( U(k+3) + R*( U(k+2) + R*U(k+1)) + . T*( U(k+6) + R*( U(k+5) + R*U(k+4)))) 7 CONTINUE C C................... CALL TEST(7) C C C****************************************************************************** C*** KERNEL 8 A.D.I. INTEGRATION C****************************************************************************** C DO 8 L = 1,Loop nl1 = 1 nl2 = 2 fw= 2.000D0 DO 8 kx = 2,3 CDIR$ IVDEP DO 8 ky = 2,n DU1(ky)=U1(kx,ky+1,nl1) - U1(kx,ky-1,nl1) DU2(ky)=U2(kx,ky+1,nl1) - U2(kx,ky-1,nl1) DU3(ky)=U3(kx,ky+1,nl1) - U3(kx,ky-1,nl1) U1(kx,ky,nl2)=U1(kx,ky,nl1) +A11*DU1(ky) +A12*DU2(ky) +A13*DU3(ky) . + SIG*(U1(kx+1,ky,nl1) -fw*U1(kx,ky,nl1) +U1(kx-1,ky,nl1)) U2(kx,ky,nl2)=U2(kx,ky,nl1) +A21*DU1(ky) +A22*DU2(ky) +A23*DU3(ky) . + SIG*(U2(kx+1,ky,nl1) -fw*U2(kx,ky,nl1) +U2(kx-1,ky,nl1)) U3(kx,ky,nl2)=U3(kx,ky,nl1) +A31*DU1(ky) +A32*DU2(ky) +A33*DU3(ky) . + SIG*(U3(kx+1,ky,nl1) -fw*U3(kx,ky,nl1) +U3(kx-1,ky,nl1)) 8 CONTINUE C C................... CALL TEST(8) C C****************************************************************************** C*** KERNEL 9 INTEGRATE PREDICTORS C****************************************************************************** C DO 9 L = 1,Loop DO 9 i = 1,n PX( 1,i)= DM28*PX(13,i) + DM27*PX(12,i) + DM26*PX(11,i) + . DM25*PX(10,i) + DM24*PX( 9,i) + DM23*PX( 8,i) + . DM22*PX( 7,i) + C0*(PX( 5,i) + PX( 6,i))+ PX( 3,i) 9 CONTINUE C C................... CALL TEST(9) C C****************************************************************************** C*** KERNEL 10 DIFFERENCE PREDICTORS C****************************************************************************** C DO 10 L= 1,Loop DO 10 i= 1,n AR = CX(5,i) BR = AR - PX(5,i) PX(5,i) = AR CR = BR - PX(6,i) PX(6,i) = BR AR = CR - PX(7,i) PX(7,i) = CR BR = AR - PX(8,i) PX(8,i) = AR CR = BR - PX(9,i) PX(9,i) = BR AR = CR - PX(10,i) PX(10,i)= CR BR = AR - PX(11,i) PX(11,i)= AR CR = BR - PX(12,i) PX(12,i)= BR PX(14,i)= CR - PX(13,i) PX(13,i)= CR 10 CONTINUE C C................... CALL TEST(10) C C****************************************************************************** C*** KERNEL 11 FIRST SUM. PARTIAL SUMS. C****************************************************************************** C fw= 1.000D-25 DO 11 L = 1,Loop C Y(1)= Y(1) + L*fw use only if optimization eliminates L-loop. X(1)= Y(1) CDIR$ NOVECTOR DO 11 k = 2,n 11 X(k)= X(k-1) + Y(k) CDIR$ VECTOR C C................... CALL TEST(11) C C****************************************************************************** C*** KERNEL 12 FIRST DIFF. C****************************************************************************** C fw= 1.000D-25 DO 12 L = 1,Loop C Y(1)= Y(1) + L*fw use only if optimization eliminates L-loop. DO 12 k = 1,n 12 X(k)= Y(k+1) - Y(k) C C................... CALL TEST(12) C C****************************************************************************** C*** KERNEL 13 2-D PIC Particle In Cell C****************************************************************************** C fw= 1.000D0 DO 13 L= 1,Loop DO 13 ip= 1,n i1= P(1,ip) j1= P(2,ip) i1= 1 + MOD2N(i1,64) j1= 1 + MOD2N(j1,64) P(3,ip)= P(3,ip) + B(i1,j1) P(4,ip)= P(4,ip) + C(i1,j1) P(1,ip)= P(1,ip) + P(3,ip) P(2,ip)= P(2,ip) + P(4,ip) i2= P(1,ip) j2= P(2,ip) i2= MOD2N(i2,64) j2= MOD2N(j2,64) P(1,ip)= P(1,ip) + Y(i2+32) P(2,ip)= P(2,ip) + Z(j2+32) i2= i2 + E(i2+32) j2= j2 + F(j2+32) H(i2,j2)= H(i2,j2) + fw 13 CONTINUE C C................... CALL TEST(13) C C****************************************************************************** C*** KERNEL 14 1-D PIC Particle In Cell C****************************************************************************** C C fw= 1.000D0 DO 14 L= 1,Loop DO 141 k= 1,n VX(k)= 0.0 XX(k)= 0.0 IX(k)= INT( GRD(k)) XI(k)= REAL( IX(k)) EX1(k)= EX ( IX(k)) DEX1(k)= DEX ( IX(k)) 141 CONTINUE C DO 142 k= 1,n VX(k)= VX(k) + EX1(k) + (XX(k) - XI(k))*DEX1(k) XX(k)= XX(k) + VX(k) + FLX IR(k)= XX(k) RX(k)= XX(k) - IR(k) IR(k)= MOD2N( IR(k),2048) + 1 XX(k)= RX(k) + IR(k) 142 CONTINUE C DO 14 k= 1,n RH(IR(k) )= RH(IR(k) ) + fw - RX(k) RH(IR(k)+1)= RH(IR(k)+1) + RX(k) 14 CONTINUE C C................... CALL TEST(14) C C C C C C C C C C C C C C C C C C C C****************************************************************************** C*** KERNEL 15 CASUAL FORTRAN. DEVELOPMENT VERSION. C****************************************************************************** C C C CASUAL ORDERING OF SCALAR OPERATIONS IS TYPICAL PRACTICE. C THIS EXAMPLE DEMONSTRATES THE NON-TRIVIAL TRANSFORMATION C REQUIRED TO MAP INTO AN EFFICIENT MACHINE IMPLEMENTATION. C DO 45 L = 1,Loop NG= 7 NZ= n AR= 0.05300D0 BR= 0.07300D0 15 DO 45 j = 2,NG DO 45 k = 2,NZ IF( j-NG) 31,30,30 30 VY(k,j)= 0.0 GO TO 45 31 IF( VH(k,j+1) -VH(k,j)) 33,33,32 32 T= AR GO TO 34 33 T= BR 34 IF( VF(k,j) -VF(k-1,j)) 35,36,36 35 R= MAX( VH(k-1,j), VH(k-1,j+1)) S= VF(k-1,j) GO TO 37 36 R= MAX( VH(k,j), VH(k,j+1)) S= VF(k,j) 37 VY(k,j)= SQRT( VG(k,j)**2 +R*R)*T/S 38 IF( k-NZ) 40,39,39 39 VS(k,j)= 0.0 GO TO 45 40 IF( VF(k,j) -VF(k,j-1)) 41,42,42 41 R= MAX( VG(k,j-1), VG(k+1,j-1)) S= VF(k,j-1) T= BR GO TO 43 42 R= MAX( VG(k,j), VG(k+1,j)) S= VF(k,j) T= AR 43 VS(k,j)= SQRT( VH(k,j)**2 +R*R)*T/S 45 CONTINUE C C................... CALL TEST(15) C C C C C C C C C C C C C C C****************************************************************************** C*** KERNEL 16 MONTE CARLO SEARCH LOOP C****************************************************************************** C II= n/3 LB= II+II k2= 0 k3= 0 C DO 485 L= 1,Loop m= 1 405 i1= m 410 j2= (n+n)*(m-1)+1 DO 470 k= 1,n k2= k2+1 j4= j2+k+k j5= ZONE(j4) IF( j5-n ) 420,475,450 415 IF( j5-n+II ) 430,425,425 420 IF( j5-n+LB ) 435,415,415 425 IF( PLAN(j5)-R) 445,480,440 430 IF( PLAN(j5)-S) 445,480,440 435 IF( PLAN(j5)-T) 445,480,440 440 IF( ZONE(j4-1)) 455,485,470 445 IF( ZONE(j4-1)) 470,485,455 450 k3= k3+1 IF( D(j5)-(D(j5-1)*(T-D(j5-2))**2+(S-D(j5-3))**2 . +(R-D(j5-4))**2)) 445,480,440 455 m= m+1 IF( m-ZONE(1) ) 465,465,460 460 m= 1 465 IF( i1-m) 410,480,410 470 CONTINUE 475 CONTINUE 480 CONTINUE 485 CONTINUE C C................... CALL TEST(16) C C****************************************************************************** C*** KERNEL 17 IMPLICIT, CONDITIONAL COMPUTATION C****************************************************************************** C C C RECURSIVE-DOUBLING VECTOR TECHNIQUES CAN NOT BE USED C BECAUSE CONDITIONAL OPERATIONS APPLY TO EACH ELEMENT. C dw= 5.0000D0/3.0000D0 fw= 1.0000D0/3.0000D0 tw= 1.0300D0/3.0700D0 DO 62 L= 1,Loop i= n j= 1 INK= -1 SCALE= dw XNM= fw E6= tw GO TO 61 C STEP MODEL 60 E6= XNM*VSP(i)+VSTP(i) VXNE(i)= E6 XNM= E6 VE3(i)= E6 i= i+INK IF( i.EQ.j) GO TO 62 61 E3= XNM*VLR(i) +VLIN(i) XNEI= VXNE(i) VXND(i)= E6 XNC= SCALE*E3 C SELECT MODEL IF( XNM .GT.XNC) GO TO 60 IF( XNEI.GT.XNC) GO TO 60 C LINEAR MODEL VE3(i)= E3 E6= E3+E3-XNM VXNE(i)= E3+E3-XNEI XNM= E6 i= i+INK IF( i.NE.j) GO TO 61 62 CONTINUE C C................... CALL TEST(17) C C****************************************************************************** C*** KERNEL 18 2-D EXPLICIT HYDRODYNAMICS FRAGMENT C****************************************************************************** C DO 75 L= 1,Loop T= 0.003700D0 S= 0.004100D0 KN= 6 JN= n DO 70 k= 2,KN DO 70 j= 2,JN ZA(j,k)= (ZP(j-1,k+1)+ZQ(j-1,k+1)-ZP(j-1,k)-ZQ(j-1,k)) . *(ZR(j,k)+ZR(j-1,k))/(ZM(j-1,k)+ZM(j-1,k+1)) ZB(j,k)= (ZP(j-1,k)+ZQ(j-1,k)-ZP(j,k)-ZQ(j,k)) . *(ZR(j,k)+ZR(j,k-1))/(ZM(j,k)+ZM(j-1,k)) 70 CONTINUE C DO 72 k= 2,KN DO 72 j= 2,JN ZU(j,k)= ZU(j,k)+S*(ZA(j,k)*(ZZ(j,k)-ZZ(j+1,k)) . -ZA(j-1,k) *(ZZ(j,k)-ZZ(j-1,k)) . -ZB(j,k) *(ZZ(j,k)-ZZ(j,k-1)) . +ZB(j,k+1) *(ZZ(j,k)-ZZ(j,k+1))) ZV(j,k)= ZV(j,k)+S*(ZA(j,k)*(ZR(j,k)-ZR(j+1,k)) . -ZA(j-1,k) *(ZR(j,k)-ZR(j-1,k)) . -ZB(j,k) *(ZR(j,k)-ZR(j,k-1)) . +ZB(j,k+1) *(ZR(j,k)-ZR(j,k+1))) 72 CONTINUE C DO 75 k= 2,KN DO 75 j= 2,JN ZR(j,k)= ZR(j,k)+T*ZU(j,k) ZZ(j,k)= ZZ(j,k)+T*ZV(j,k) 75 CONTINUE C C................... CALL TEST(18) C C****************************************************************************** C*** KERNEL 19 GENERAL LINEAR RECURRENCE EQUATIONS C****************************************************************************** C C IF( JR.GT.1 ) GO TO 192 C KB5I= 0 DO 194 L= 1,Loop DO 191 k= 1,n B5(k+KB5I)= SA(k) +STB5*SB(k) STB5= B5(k+KB5I) -STB5 191 CONTINUE C GO TO 194 C 192 DO 193 i= 1,n k= n-i+1 B5(k+KB5I)= SA(k) +STB5*SB(k) STB5= B5(k+KB5I) -STB5 193 CONTINUE 194 CONTINUE C C................... CALL TEST(19) C C****************************************************************************** C*** KERNEL 20 DISCRETE ORDINATES TRANSPORT: CONDITIONAL RECURRENCE ON XX. C****************************************************************************** C dw= 0.200D0 DO 20 L= 1,Loop DO 20 k= 1,n DI= Y(k)-G(k)/( XX(k)+DK) DN= dw IF( DI.NE.0.0) DN= MAX( S,MIN( Z(k)/DI, T)) X(k)= ((W(k)+V(k)*DN)* XX(k)+U(k))/(VX(k)+V(k)*DN) XX(k+1)= (X(k)- XX(k))*DN+ XX(k) 20 CONTINUE C C................... CALL TEST(20) C C****************************************************************************** C*** KERNEL 21 MATRIX*MATRIX PRODUCT C****************************************************************************** C DO 21 L= 1,Loop DO 21 k= 1,25 DO 21 i= 1,25 DO 21 j= 1,n PX(i,j)= PX(i,j) +VY(i,k) * CX(k,j) 21 CONTINUE C C................... CALL TEST(21) C C C C C C C C****************************************************************************** C*** KERNEL 22 PLANCKIAN DISTRIBUTION C****************************************************************************** C C C EXPMAX= 234.500D0 EXPMAX= 20.0000D0 fw= 1.00000D0 U(n)= 0.99000D0*EXPMAX*V(n) DO 22 L= 1,Loop DO 22 k= 1,n CARE IF( U(k) .LT. EXPMAX*V(k)) THEN Y(k)= U(k)/V(k) CARE ELSE CARE Y(k)= EXPMAX CARE ENDIF W(k)= X(k)/( EXP( Y(k)) -fw) 22 CONTINUE C................... CALL TEST(22) C C****************************************************************************** C*** KERNEL 23 2-D IMPLICIT HYDRODYNAMICS FRAGMENT C****************************************************************************** C fw= 0.17500D0 DO 23 L= 1,Loop DO 23 j= 2,6 DO 23 k= 2,n QA= ZA(k,j+1)*ZR(k,j) +ZA(k,j-1)*ZB(k,j) + . ZA(k+1,j)*ZU(k,j) +ZA(k-1,j)*ZV(k,j) +ZZ(k,j) 23 ZA(k,j)= ZA(k,j) +fw*(QA -ZA(k,j)) C C................... CALL TEST(23) C C****************************************************************************** C*** KERNEL 24 FIND LOCATION OF FIRST MINIMUM IN ARRAY C****************************************************************************** C C X( n/2)= -1.000D+50 X( n/2)= -1.000D+10 DO 24 L= 1,Loop m= 1 DO 24 k= 2,n IF( X(k).LT.X(m)) m= k 24 CONTINUE C C m= imin1( n,x,1) 35 nanosec./element STACKLIBE/CRAY C................... CALL TEST(24) C C****************************************************************************** C C IF( jr .LT. 1) jr= 1 IF( jr .GT. 8) jr= 8-1 IF( il .LT. 1) il= 1 IF( il .GT. 3) il= 3 C DO 999 k= 1,mk TIMES(jr,il,k)= TIME (k) TERRS(jr,il,k)= TERR1(k) NPFS (jr,il,k)= NPFS1(k) CSUMS(jr,il,k)= CSUM (k) DOS (jr,il,k)= TOTAL(k) FOPN (jr,il,k)= FLOPN(k) 999 continue C RETURN END C C*********************************************** SUBROUTINE PAGE( iou) C*********************************************** WRITE(iou,1) 1 FORMAT(1H1) c 1 FORMAT(1H ) RETURN END C*********************************************** SUBROUTINE REPORT( iou, ntk,nek,FLOPS,TR,RATES,LSPAN,WG,OSUM,ID) C*********************************************************************** C * C REPORT - Prints Statistical Evaluation Of Fortran Kernel Timings* C * C iou - Logical Output Device Number * C ntk - Total number of Kernels to Edit in Report * C nek - Number of Effective Kernels in each set to Edit * C FLOPS - Array: Number of Flops executed by each kernel * C TR - Array: Time of execution of each kernel(microsecs) * C RATES - Array: Rate of execution of each kernel(megaflops/sec)* C LSPAN - Array: Span of inner DO loop in each kernel * C WG - Array: Weight assigned to each kernel for statistics * C OSUM - Array: Checksums of the results of each kernel * C * C*********************************************************************** C C C REFERENCE C C F.H.McMahon, The Livermore Fortran Kernels: A Computer C Test Of The Numerical Performance Range, Lawrence C Livermore National Laboratory, Livermore, California, C UCRL-53745, October 1986. C C C C C NOTICE C C "This report was prepared as an account C of work sponsored by the United States C Government. Neither the United States C nor the United States Department of C Energy, nor any of their employees, nor C any of their contractors, subcontractors, C or their employees, makes any warranty, C express or implied, or assumes any legal C liability or responsibility for the C accuracy, completeness or usefulness of C any information, apparatus, product or C process disclosed, or represents that its C use would not infringe privateiy-owned C rights." C C Reference to a company or product name C does not impiy approval or recommendation C of the product by the University of C California or the U.S. Department of C Energy to the exclusion of others that C may be suitable. C C C Work performed under the auspices of the C U.S. Department of Energy by the Lawrence C Livermore Laboratory under contract C number W-7405-ENG-48. C C*********************************************************************** C C C I: FORTRAN CPU PERFORMANCE ANALYSIS F.H.McMahon C C c These kernels measure Fortran numerical computation rates for a c spectrum of CPU-limited computational structures or benchmarks. c The kernels benchmark contains extracts or kernels from more c than a score CPU-limited scientific application programs. These c kernels are The most important CPU time components from The c application programs. This benchmark may be easily extended c with important new kernels leaving performance statistics intact. c c The time required to convert, debug, execute and time many, c entire, large programs on new machines each having a new c implementation of Fortran, or several implementations or c dialects rapidly becomes excessive. Almost all The conversion c costs are in segments of The programs which are irrelevant for c evaluation of The CPU, e.g., I/O, Fortran variations, memory c allocation, overlays, job control, etc. all of these c complexities are reduced to a single, small benchmark which uses c a minimum of I/O and a single level of storage. further, the c computation in the kernels is the most stable part of the c Fortran language. c c The kernels benchmark is sufficient to determine a range of CPU c performance for many different computational structures in a c single computer run. Since The range in performance is usually c large the mean has a secondary significance. To estimate the c performance of a particular, CPU-limited application program c select the case(s) which are most similar to the application as c most relevent to the estimate. The performance ratio of a c kernel on two different machines or compiled by two different c compilers on the same machine will approximate the ratio of c through-puts for an application which is very similar in c structure. c c This set of kernels was chosen to measure lower and upper bounds c for scalar Fortran computation rates. The upper bound on scalar c rates serves as a base to evaluate the effectiveness of vector c computation. The kind of Fortran which has the highest MIP c rates is pure arithmetic in DO-loops where complete local code c optimization by a Fortran compiler is possible. All other kinds c of Fortran operations execute at much lower MIP rates on c multiple register machines (these ops may not be necessary). c c Through-put is measured in units of floating-point operations c executed per micro-second; called results per micro-second or c mega-flops. The Mflop is a measure of the NECESSARY results in c a scientific application program regardless of the number or c kind of operations or processing. The ratio of Mflops for two c different machines will approximate the ratio of through-puts c for the majority of compute-limited scientific applications on c the two machines. The kernels measure performance scale c factors. c C C c c ----------------------------------------------------------------------------- c II: A CPU Performance Metric For Computational Physics: Mega-Flops/sec. c ----------------------------------------------------------------------------- c F.H. McMahon c c A: Floating-Point Instructions: The Necessary Mathematics c c Computational physics applies systems of PDEs from Mathematical physics to c simulate the evolution of physical systems. The mathematical methods depend c on real valued functions and the algorithms are programmed, almost c exclusively, in Fortran Floating-point computer operations (Flops). These c floating-point operations are, unquestionably, the NECESSARY computer c operations on ANY computer and the total number is INVARIANT. Thus a c meaningful computation rate can always be measured by counting the total c number of Flops and dividing by the total execution time of a program. c c B: Procedural Machine Instructions: Artifices Of An Archetecture c c All of the non-arithmetic instructions in a machine program are artifices of c a particular hardware architecture, i.e. machine dependant, as well as the c result of a particular compiler's imperfect coding techniques. How many of c these procedural machine instructions are strictly necessary can only be c determined by further, tedious analysis which is ALWAYS machine dependant. A c famous example of software masking hardware capabilities is the PASCAL c compiler written by n.Wirth which used only 50% of the command set to c generate machine programs for the CDC-7600. c c Unless the next generation computer design is constrained for some reason, to c closely resemble its obsolete predecessor, the instruction mix used in c current machines is not necessarily relevent. Furthermore, the instruction c mix is not a definitive characterization of the intrinsic physics or the c mathematical algorithms. c c 1. Primary Memory Access Instructions c c The number of memory instructions that are necessary for a given algorithm c depends strongly on the number and kind of CPU registers and is a highly c machine dependent number. Operating registers, scratch-pad memories, vector c buffers, short-stop and feed-back paths in the cpu are examples of hardware c artifices which reduce the number of primary memory operations. Compilers c and other coders must make intelligent use of these particular cpu resources c to minimize memory operations and this is generally not the case, as is well c known. c c 2. Branching Instructions c c Branching instructions are the slowest and most expensive procedural c instructions and are very often unecessary. Here the source programmer has c primary responsibility to minimize branching in the program by avoiding IF c statements whenever possible by using MAX, MIN, or merge functions like c CSMG. Careful logical reduction and placement of IF tests is required to c minimize the execution of branching operations. Compilers can do very little c to change or optimize the branch graph specified in the source program. c c On vector computers ALL IF tests over mesh or array (state) variables can be c eliminated. Conditional computation can be vectorized by direct construction c using explicit sub-set mappings. Vector relationals replace the IF clauses. c Then sparse, one-to-one mappings called vector Compress/Decompress and c one-to-many mappings called vector Gather/Scatter are necessary and c sufficient to compose sub-vector operands for simple vector operations. c c C CIII: FORTRAN PROGRAMMING SYSTEM MATURITY c c Hardware performance gains depend criticaly on compiler c maturity. These kernels measure the joint performance of c hardware and Fortran compiler software and may easily be used c for a comparative analysis of all the available compilers or c options on a given machine. For a new or proposed machine where c no compiler is available the performance may be estimated by c simulating a reasonable compilation. An example of simulation c rationale is given below. c c Fortran compilers for new types of machines require a lengthy c development cycle to achive an effective level of machine c utilization. A fully mature compiler may not be completed in c the first years of a new machine. Indeed, maturity is not a c stationary state but evolves with advances in program c optimization techniques. Some of these techniques depend on c special facilities in the new machines and serious development c and implementation cannot start much earlier than development of c the new machine. Assumptions on the maturity of available c Fortran compilers are crucial to the evaluation of Fortran c performance and thus, compiler characteristics should be c explicit parameters of the performance analysis. c C C A: OPTIMIZATION CRITERIA FOR SIMULATING A MODERATELY MATURE COMPILER c c The coding is deliberately simplified to the level of complexity c of a moderately mature compiler, i.e. a proper compiler for c processors with segmented cpu design circa 1975. The coding is c deliberately not lossless, ideal assembly language since this c technique may outperform Fortran by more than a factor of two c and may over estimate typical Fortran performance. c c 0. reduction of redundant operations in the source text. c c 1. all scalar values are defined in registers over the c scope of loops. c c 2. all scripted input variables are loaded into registers c at the begining of loops. c c 3. code optimization techniques include: c c 3.1 effective address computation for subscripted c variables which are a function of the loop variable c is optimized by: c 3.1.1 reduction to recursive address functions. c 3.1.2 indicial address and increment as well as c current index are register values. c 3.2 moderate scheduling of instructions. c not pert scheduling level, hence not best ordering. c 3.3 loop controls are defined in registers. c specific, minimum loop branch tests. c 3.4 pre-loading operands for the next loop iteration c was not allowed. all operations in a loop have c the same phase, i.e. are the same iteration. c c 4. memory bank conflicts were ignored. c c 5. branch ratios on if conditionals are equal, then c averaged for two cases. c C C B: OPTIMIZATION CRITERIA FOR A MATURE COMPILER INCLUDE: c c 0. minimization of effective address computation c especially in loops. c c 1. optimal register allocation; ranked by usage. c c 2. critical path(pert) time schedule for each block of c instructions on machines with segmented function units. c c 3. global program optimization, viz IBM Fortran-H. implies c reduction of redundant operations in object code string. c important reductions for programs using dynamic addressing c and dynamically dimensioned arrays. c c 4. decomposition of iterative scalar Fortran into parallel c vector or array operations where these exist as parallel c machine operations. c c 5. recomposition of scalar Fortran loops that cannot be c decomposed as in (4.) into multi-phase loops. the goal c is to eliminate serial fetch delays by forward-fetching c of scalar operands, i.e. memory references in a loop are c for operands in the next iteration. c c c C C: EXTENSIONS TO THE SET OF KERNELS C c The kernels benchmarks were extended from 14 to 20 kernels in c 1976 , largely as a result of our experiences in vectorizing old c applications. They are intended to compensate for the c oversimplicity of some of the original kernels which are mostly c elementary matrix operations and thus, to help represent the c Fortran workload more accurately. The new kernels have c significant improvements: c c 1. more complete excerpts of real applications. c c 2. high complexity computation to test the claims c made for Fortran compiler code optimization. c c 3. original, amateur Fortran coding to test the claims c made for automatic vectorizers of olde Fortran. c c As a matter of policy kernels should be updated, without prior c notice or further justification, whenever new algorithms are c percieved in important applications. The primitive kernels c should be retained for comparisons and scaling over long c periods. c C C c c c c c c C C IV: PERFORMANCE MEASUREMENTS c c c c c Through-put is measured in units of millions of floating-point c operations executed per second, called mflops. c c c Artificially long computer runs do not have to be contrived for c timing on machines where a cpu clock may be read in job mode. c Statistics on the accuracy of the timing method should be c measured. c c Net mflops is meaningful only if real run time of each kernel c is adjusted such that it weights the total time in proportion c to the actual usage of that catagory of computation in the c total workload. c C C c c c 1. Assignment Of Weights To Floating-Point Operations c c Weights are assigned to different kinds of floating-point c operations to normalize their hardware execution time to c addition time so that the flop rates computed for various c Fortran Kernels will be commensurable. c C +,-,* 1 C /,SQRT 4 C EXP,SIN,ETC. 8 C IF(X.REL.Y) 1 c c c Each Kernel flop-count is the weighted number of flops required for c serial execution. The scalar version defines the NECESSARY computation c generally, in the absence of proof to the contrary. The vector c or parallel executions are only credited with executing the same c necessary computation. If the parallel methods do more computation c than is necessary then the extra flops are not counted as through-put. c c c c c C C c c c c c c c c C C C C 2. SAMPLE OUTPUT: CDC-7600/FTN-4.4 C C C KERNEL FLOPS TIME MFLOPS C 1 500 94.4 5.30 C 2 300 45.3 6.62 C 3 100 21.9 4.57 C 4 300 109.3 2.75 C 5 100 25.6 3.91 C 6 100 27.8 3.60 C 7 640 88.2 7.25 C 8 1440 249.0 5.78 C 9 680 123.2 5.52 C 10 360 102.8 3.50 C 11 49 34.8 1.41 C 12 49 18.3 2.68 C 13 224 107.7 2.08 C 14 3300 809.3 4.08 C 15 3960 1769.5 2.24 C 16 530 320.3 1.65 C 17 405 92.2 4.39 C 18 6600 1121.5 5.88 C 19 540 105.8 5.11 C 20 1300 266.0 4.89 C 21 1250 370.9 3.37 c 22 1700 601.9 2.82 c 23 1650 362.4 4.55 c 24 200 171.7 1.16 C C C AVERAGE RATE = 3.96 MEGA-FLOPS/SEC. C C MEDIAN RATE = 4.08 MEGA-FLOPS/SEC. C C HARMONIC MEAN = 3.15 MEGA-FLOPS/SEC. C C STANDARD DEV. = 1.61 MEGA-FLOPS/SEC. C C C F.H.MCMAHON 1972 c c c c c c c c c c c c c c C SAMPLE OUTPUT FROM SUBROUTINe REPORT: (CRAY-XMP4/CFT Compiler) C C c aus c c c c c c C C The following output was produced on CRAY-XMP4 in a C fully loaded, multi-processing, multi-programming system: C c c c c C C VERIFY ADEQUATE Loop SIZE VERSUS CPU CLOCK ACCURACY C ----- ------- ------- ------- -------- C EXTRA MAXIMUM DIGITAL DYNAMIC RELATIVE C Loop CPUTIME CLOCK CLOCK TIMING C SIZE SECONDS ERROR ERROR ERROR C ----- ------- ------- ------- -------- C 1 5.0000e-06 10.00% 17.63% 14.26% C 2 7.0000e-06 7.14% 6.93% 4.79% C 4 1.6000e-05 3.12% 6.56% 7.59% C 8 2.8000e-05 1.79% 2.90% 2.35% C 16 6.1000e-05 0.82% 6.72% 4.50% C 32 1.1700e-04 0.43% 4.21% 4.62% C 64 2.2700e-04 0.22% 3.13% 2.41% C 128 4.4900e-04 0.11% 3.14% 0.96% C 256 8.8900e-04 0.06% 2.06% 2.50% C 512 1.7740e-03 0.03% 1.92% 1.59% C 1024 3.4780e-03 0.01% 0.70% 1.63% C 1360 Current Run: Loop= 10.000*Loop C 2048 7.0050e-03 0.01% 0.74% 1.28% C 4096 1.3823e-02 0.00% 1.35% 0.78% C ----- ------- ------- ------- -------- C C Approximate Serial Job Time= 2.5e+01 Sec. ( Nruns= 7 RUNS) C c c c c c c c c c c c c c c c c c c 1 c c c c c CPU CLOCK OVERHEAD (t err): c c RUN AVERAGE STANDEV MINIMUM MAXIMUM c TICK 1 4.666667e-06 4.714045e-07 4.000000e-06 5.000000e-06 c TICK 2 4.733333e-06 4.422166e-07 4.000000e-06 5.000000e-06 c TICK 3 5.000000e-06 1.932305e-14 5.000000e-06 5.000000e-06 c TICK 4 4.800000e-06 4.000000e-07 4.000000e-06 5.000000e-06 c TICK 5 4.733333e-06 4.422166e-07 4.000000e-06 5.000000e-06 c TICK 6 4.866667e-06 3.399346e-07 4.000000e-06 5.000000e-06 c TICK 7 5.066667e-06 5.734884e-07 4.000000e-06 7.000000e-06 c DATA 7 9.998664e-02 5.433188e-07 9.998564e-02 9.998765e-02 c DATA 7 9.998599e-02 9.174211e-07 9.998434e-02 9.998765e-02 c TICK 7 4.838095e-06 1.373543e-07 4.666667e-06 5.066667e-06 c c c c c THE EXPERIMENTAL TIMING ERRORS FOR ALL 7 RUNS c -- --------- --------- --------- ----- ----- --- c k T min T avg T max T err t err P-F c -- --------- --------- --------- ----- ----- --- c 1 2.3125e-03 2.3215e-03 2.3375e-03 0.34% 0.19% 0 c 2 1.0258e-02 1.0344e-02 1.0427e-02 0.58% 0.04% 0 c 3 1.4115e-03 1.4585e-03 1.4987e-03 2.24% 0.30% 0 c 4 4.0003e-03 4.0989e-03 4.1958e-03 1.70% 0.11% 0 c 5 3.3954e-02 3.4047e-02 3.4153e-02 0.25% 0.01% 0 c 6 1.0215e-02 1.0350e-02 1.0475e-02 0.85% 0.04% 0 c 7 3.7788e-03 3.7967e-03 3.8267e-03 0.44% 0.12% 0 c 8 6.8435e-03 6.9755e-03 7.1138e-03 1.07% 0.06% 0 c 9 4.4287e-03 4.5215e-03 4.5795e-03 0.99% 0.10% 0 c 10 5.2315e-03 5.3632e-03 5.4845e-03 1.49% 0.08% 0 c 11 1.3358e-02 1.3369e-02 1.3376e-02 0.04% 0.03% 0 c 12 1.9138e-03 2.0810e-03 2.2345e-03 4.38% 0.21% 0 c 13 3.7553e-02 3.7656e-02 3.7814e-02 0.25% 0.01% 0 c 14 1.8911e-02 1.9014e-02 1.9120e-02 0.37% 0.02% 0 c 15 3.5405e-02 3.5446e-02 3.5505e-02 0.09% 0.01% 0 c 16 3.9233e-02 3.9362e-02 3.9782e-02 0.45% 0.01% 0 c 17 3.4725e-02 3.4837e-02 3.4940e-02 0.22% 0.01% 0 c 18 4.0667e-03 4.0942e-03 4.1595e-03 0.72% 0.11% 0 c 19 3.3786e-02 3.4032e-02 3.4180e-02 0.35% 0.01% 0 c 20 2.2068e-02 2.2096e-02 2.2120e-02 0.08% 0.02% 0 c 21 1.9691e-02 2.0053e-02 2.0386e-02 1.27% 0.02% 0 c 22 2.8807e-03 2.8906e-03 2.8965e-03 0.22% 0.15% 0 c 23 3.3050e-02 3.3136e-02 3.3235e-02 0.19% 0.01% 0 c 24 3.1530e-02 3.1588e-02 3.1646e-02 0.13% 0.01% 0 c -- --------- --------- --------- ----- ----- --- c c NET CPU TIMING VARIANCE (T err); A few % is ok: c c AVERAGE STANDEV MINIMUM MAXIMUM c Terr 0.78% 0.94% 0.04% 4.38% c c c c 1 c ******************************************** c THE LIVERMORE FORTRAN KERNELS: M F L O P S c ******************************************** c c Computer : CRAY-XMP-1 of 4 procs c System : CTSS 10e fully loaded c Compiler : CFT 1.14e Auto vector c c Mean DO Span = 471 c c When the computer performance range is very large c the net Mflops rate of many Fortran programs and c workloads will be in the sub-range between the equi- c weighted harmonic and arithmetic means depending c on the degree of code parallelism and optimization. c More accurate estimates of cpu workload rates depend c on assigning appropriate weights for each kernel. c c c c KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT CHECK-SUMS OK c ------ ----- -------- --------- ---- ------ ---------- -- c 1 3.5035e+05 2.3215e+03 150.9181 1001 1.00 3.580256885257e+05 15 c 2 2.5996e+05 1.0344e+04 25.1321 101 1.00 3.605241761060e+03 14 c 3 1.8018e+05 1.4585e+03 123.5415 1001 1.00 7.005200181467e+01 14 c 4 1.6800e+05 4.0989e+03 40.9867 1001 1.00 4.199475416832e+00 15 c 5 2.0000e+05 3.4047e+04 5.8743 1001 1.00 3.184210149672e+04 14 c 6 1.1904e+05 1.0350e+04 11.5011 64 1.00 3.660366768768e+13 13 c 7 6.3680e+05 3.7967e+03 167.7227 995 1.00 4.272975752615e+05 14 c 8 7.1280e+05 6.9755e+03 102.1869 100 1.00 1.050887603939e+06 14 c 9 6.1812e+05 4.5215e+03 136.7081 101 1.00 8.326105269826e+05 15 c 10 3.0906e+05 5.3632e+03 57.6264 101 1.00 5.117258849028e+05 15 c 11 1.1000e+05 1.3369e+04 8.2278 1001 1.00 2.340037689466e+08 9 c 12 1.1988e+05 2.0810e+03 57.6061 1000 1.00 2.034999000047e-04 9 c 13 1.6128e+05 3.7656e+04 4.2830 64 1.00 2.839977317873e+10 12 c 14 2.2022e+05 1.9014e+04 11.5819 1001 1.00 2.116750694993e+10 14 c 15 1.6500e+05 3.5446e+04 4.6550 101 1.00 2.760671683247e+05 15 c 16 1.3250e+05 3.9362e+04 3.3662 75 1.00 1.982820000000e+05 16 c 17 3.1815e+05 3.4837e+04 9.1325 101 1.00 7.802492410322e+03 14 c 18 4.3560e+05 4.0942e+03 106.3952 100 1.00 3.615937787530e+05 14 c 19 2.3634e+05 3.4032e+04 6.9447 101 1.00 3.795271872105e+03 14 c 20 2.6000e+05 2.2096e+04 11.7666 1000 1.00 2.128451037522e+08 12 c 21 1.2625e+06 2.0053e+04 62.9576 101 1.00 5.802625385051e+07 13 c 22 1.8887e+05 2.8906e+03 65.3394 101 1.00 2.057023063597e+03 15 c 23 4.3560e+05 3.3136e+04 13.1456 100 1.00 2.484884179713e+05 14 c 24 5.0000e+04 3.1588e+04 1.5829 1001 1.00 3.500000000000e+03 16 c ------ ----- -------- --------- ---- ------ ---------- -- c MFLOPS Range : 332 c c Maximum Rate = 167.7227 Mega-Flops/Sec. c Average Rate = 49.5493 Mega-Flops/Sec. c Geometric Mean = 22.9138 Mega-Flops/Sec. c Median Rate = 19.1321 Mega-Flops/Sec. c Harmonic Mean = 9.8602 Mega-Flops/Sec. c Minimum Rate = 1.5829 Mega-Flops/Sec. c c Standard Dev. = 52.3398 Mega-Flops/Sec. c Median Dev. = 37.8255 Mega-Flops/Sec. c c c c c c c SENSITIVITY ANALYSIS c c c The sensitivity of the harmonic mean rate (Mflops) c to various weightings is shown in the table below. c Seven work distributions are generated by assigning c two distinct weights to ranked kernels by quartiles. c Forty nine possible cpu workloads are then evaluated c using seven sets of values for the total weights: c c c ------ ------ ------ ------ ------ ------ ------ c 1st QT: O O O O O X X c 2nd QT: O O O X X X O c 3rd QT: O X X X O O O c 4th QT: X X O O O O O c ------ ------ ------ ------ ------ ------ ------ c Total c Weights Net Mflops: c X O c ---- ---- c c 1.00 0.00 3.55 5.32 10.61 17.25 46.12 67.69 127.17 c c 0.95 0.05 3.71 5.57 10.56 16.05 37.04 42.67 70.92 c c 0.90 0.10 3.88 5.86 10.51 15.00 30.95 31.15 49.17 c c 0.80 0.20 4.28 6.52 10.40 13.27 23.29 20.23 30.48 c c 0.70 0.30 4.77 7.35 10.30 11.90 18.67 14.98 22.08 c c 0.60 0.40 5.39 8.42 10.20 10.78 15.57 11.89 17.31 c c 0.50 0.50 6.19 9.86 10.10 9.86 13.36 9.86 14.24 c ---- ---- c ------ ------ ------ ------ ------ ------ ------ c c c c c c c SENSITIVITY OF NET MFLOPS RATE TO USE OF OPTIMAL FORTRAN CODE(SISD/SIMD MODEL c c 5.31 6.57 8.61 12.50 16.13 22.76 38.60 59.23 127.17 c c 0.00 0.20 0.40 0.60 0.70 0.80 0.90 0.95 1.00 c Fraction Of Operations Run At Optimal Fortran Rates c c c c c c c c c c c CPU CLOCK OVERHEAD (t err): c c RUN AVERAGE STANDEV MINIMUM MAXIMUM c TICK 1 4.733333e-06 4.422166e-07 4.000000e-06 5.000000e-06 c TICK 2 4.866667e-06 3.399346e-07 4.000000e-06 5.000000e-06 c TICK 3 4.800000e-06 4.000000e-07 4.000000e-06 5.000000e-06 c TICK 4 4.733333e-06 4.422166e-07 4.000000e-06 5.000000e-06 c TICK 5 4.800000e-06 4.000000e-07 4.000000e-06 5.000000e-06 c TICK 6 4.866667e-06 3.399346e-07 4.000000e-06 5.000000e-06 c TICK 7 4.866667e-06 4.988876e-07 4.000000e-06 6.000000e-06 c DATA 7 9.998664e-02 5.433188e-07 9.998564e-02 9.998765e-02 c DATA 7 9.998599e-02 9.174211e-07 9.998434e-02 9.998765e-02 c TICK 7 4.809524e-06 5.553288e-08 4.733333e-06 4.866667e-06 c c c c c THE EXPERIMENTAL TIMING ERRORS FOR ALL 7 RUNS c -- --------- --------- --------- ----- ----- --- c k T min T avg T max T err t err P-F c -- --------- --------- --------- ----- ----- --- c 1 3.6396e-03 3.7041e-03 3.7478e-03 0.86% 0.12% 0 c 2 1.2313e-02 1.2445e-02 1.2518e-02 0.58% 0.03% 0 c 3 6.0748e-03 6.1361e-03 6.1847e-03 0.82% 0.07% 0 c 4 2.0149e-02 2.0526e-02 2.0930e-02 1.12% 0.02% 0 c 5 3.7970e-02 3.8241e-02 3.8436e-02 0.34% 0.01% 0 c 6 1.9979e-02 2.0156e-02 2.0372e-02 0.64% 0.02% 0 c 7 4.8317e-03 4.9201e-03 5.0215e-03 1.21% 0.09% 0 c 8 8.2217e-03 8.4281e-03 8.5418e-03 1.15% 0.05% 0 c 9 5.2438e-03 5.3005e-03 5.3525e-03 0.87% 0.08% 0 c 10 5.7437e-03 6.0877e-03 6.4375e-03 3.70% 0.07% 0 c 11 2.0656e-02 2.0681e-02 2.0727e-02 0.11% 0.02% 0 c 12 3.4358e-03 3.5171e-03 3.7247e-03 2.81% 0.12% 0 c 13 4.2846e-02 4.3043e-02 4.3223e-02 0.26% 0.01% 0 c 14 1.9670e-02 1.9733e-02 1.9833e-02 0.28% 0.02% 0 c 15 7.0843e-02 7.0946e-02 7.1094e-02 0.11% 0.01% 0 c 16 4.5160e-02 4.5291e-02 4.5388e-02 0.17% 0.01% 0 c 17 3.9607e-02 3.9716e-02 3.9859e-02 0.25% 0.01% 0 c 18 4.0446e-03 4.0740e-03 4.1098e-03 0.48% 0.11% 0 c 19 4.0040e-02 4.0279e-02 4.0477e-02 0.30% 0.01% 0 c 20 3.5444e-02 3.5467e-02 3.5490e-02 0.04% 0.01% 0 c 21 2.7746e-02 2.8205e-02 2.8780e-02 1.34% 0.02% 0 c 22 3.6666e-03 3.6830e-03 3.6978e-03 0.27% 0.12% 0 c 23 4.1323e-02 4.1499e-02 4.1603e-02 0.22% 0.01% 0 c 24 3.9596e-02 3.9644e-02 3.9715e-02 0.11% 0.01% 0 c -- --------- --------- --------- ----- ----- --- c c NET CPU TIMING VARIANCE (T err); A few % is ok: c c AVERAGE STANDEV MINIMUM MAXIMUM c Terr 0.75% 0.86% 0.04% 3.70% c c c c c c 1 c ******************************************** c THE LIVERMORE FORTRAN KERNELS: M F L O P S c ******************************************** c c Computer : CRAY-XMP-1 of 4 procs c System : CTSS 10e fully loaded c Compiler : CFT 1.14e Auto vector c c Mean DO Span = 90 c c When the computer performance range is very large c the net Mflops rate of many Fortran programs and c workloads will be in the sub-range between the equi- c weighted harmonic and arithmetic means depending c on the degree of code parallelism and optimization. c More accurate estimates of cpu workload rates depend c on assigning appropriate weights for each kernel. c c c c KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT CHECK-SUMS OK c ------ ----- -------- --------- ---- ------ ---------- -- c 1 4.0400e+05 3.7041e+03 109.0679 101 2.00 3.677341345257e+03 14 c 2 3.1040e+05 1.2445e+04 24.9427 101 2.00 3.605241761060e+03 14 c 3 2.1412e+05 6.1361e+03 34.8950 101 2.00 7.068190056054e+00 14 c 4 1.6800e+05 2.0526e+04 8.1848 101 2.00 4.199475416832e+00 15 c 5 2.2000e+05 3.8241e+04 5.7530 101 2.00 3.212322357721e+02 14 c 6 1.3440e+05 2.0156e+04 6.6679 32 2.00 1.885296670192e+16 12 c 7 7.1104e+05 4.9201e+03 144.5170 101 2.00 4.441910421041e+03 14 c 8 8.5536e+05 8.4281e+03 101.4889 100 2.00 1.050887603939e+06 14 c 9 7.2114e+05 5.3005e+03 136.0502 101 2.00 8.326105269825e+05 15 c 10 3.4542e+05 6.0877e+03 56.7408 101 2.00 5.117258849028e+05 14 c 11 1.2800e+05 2.0681e+04 6.1893 101 2.00 2.403492372107e+05 8 c 12 1.3464e+05 3.5171e+03 38.2814 100 2.00 4.989298401193e-05 9 c 13 1.8368e+05 4.3043e+04 4.2673 32 2.00 1.627723261374e+10 12 c 14 2.2220e+05 1.9733e+04 11.2604 101 2.00 2.130649341195e+08 14 c 15 3.3000e+05 7.0946e+04 4.6514 101 2.00 2.760671683247e+05 15 c 16 1.5120e+05 4.5291e+04 3.3384 40 2.00 2.270870000000e+05 16 c 17 3.6360e+05 3.9716e+04 9.1550 101 2.00 7.802492410321e+03 14 c 18 4.3560e+05 4.0740e+03 106.9227 100 2.00 3.615937787530e+05 14 c 19 2.7876e+05 4.0279e+04 6.9208 101 2.00 3.795271872105e+03 14 c 20 4.1600e+05 3.5467e+04 11.7292 100 2.00 2.188343625168e+05 14 c 21 1.2500e+06 2.8205e+04 44.3180 50 2.00 2.790571795524e+07 13 c 22 2.4038e+05 3.6830e+03 65.2680 101 2.00 2.057023063597e+03 15 c 23 5.4450e+05 4.1499e+04 13.1207 100 2.00 2.484926226843e+05 14 c 24 6.2000e+04 3.9644e+04 1.5639 101 2.00 3.500000000000e+02 16 c ------ ----- -------- --------- ---- ------ ---------- -- c MFLOPS Range : 331 c c Maximum Rate = 144.5170 Mega-Flops/Sec. c Average Rate = 39.8039 Mega-Flops/Sec. c Geometric Mean = 18.5628 Mega-Flops/Sec. c Median Rate = 12.4307 Mega-Flops/Sec. c Harmonic Mean = 8.9125 Mega-Flops/Sec. c Minimum Rate = 1.5639 Mega-Flops/Sec. c c Standard Dev. = 44.9777 Mega-Flops/Sec. c Median Dev. = 31.1973 Mega-Flops/Sec. c c c c c c c SENSITIVITY ANALYSIS c c c The sensitivity of the harmonic mean rate (Mflops) c to various weightings is shown in the table below. c Seven work distributions are generated by assigning c two distinct weights to ranked kernels by quartiles. c Forty nine possible cpu workloads are then evaluated c using seven sets of values for the total weights: c c c ------ ------ ------ ------ ------ ------ ------ c 1st QT: O O O O O X X c 2nd QT: O O O X X X O c 3rd QT: O X X X O O O c 4th QT: X X O O O O O c ------ ------ ------ ------ ------ ------ ------ c Total c Weights Net Mflops: c X O c ---- ---- c c 1.00 0.00 3.48 4.95 8.57 13.17 28.40 44.57 103.51 c c 0.95 0.05 3.63 5.18 8.59 12.57 24.79 31.83 60.62 c c 0.90 0.10 3.79 5.43 8.62 12.02 21.99 24.76 42.86 c c 0.80 0.20 4.16 6.02 8.66 11.06 17.94 17.14 27.02 c c 0.70 0.30 4.60 6.75 8.71 10.24 15.15 13.11 19.73 c c 0.60 0.40 5.16 7.68 8.75 9.53 13.11 10.61 15.54 c c 0.50 0.50 5.86 8.91 8.80 8.91 11.56 8.91 12.82 c ---- ---- c ------ ------ ------ ------ ------ ------ ------ c c c c c c c SENSITIVITY OF NET MFLOPS RATE TO USE OF OPTIMAL FORTRAN CODE(SISD/SIMD MODEL c c 4.95 6.11 7.99 11.54 14.84 20.77 34.60 51.86 103.51 c c 0.00 0.20 0.40 0.60 0.70 0.80 0.90 0.95 1.00 c Fraction Of Operations Run At Optimal Fortran Rates c c c c c c c c c c c c CPU CLOCK OVERHEAD (t err): c c RUN AVERAGE STANDEV MINIMUM MAXIMUM c TICK 1 4.933333e-06 2.494438e-07 4.000000e-06 5.000000e-06 c TICK 2 4.933333e-06 4.422166e-07 4.000000e-06 6.000000e-06 c TICK 3 4.800000e-06 4.000000e-07 4.000000e-06 5.000000e-06 c TICK 4 4.800000e-06 5.416026e-07 4.000000e-06 6.000000e-06 c TICK 5 4.800000e-06 4.000000e-07 4.000000e-06 5.000000e-06 c TICK 6 4.933333e-06 2.494438e-07 4.000000e-06 5.000000e-06 c TICK 7 4.800000e-06 4.000000e-07 4.000000e-06 5.000000e-06 c DATA 7 9.998664e-02 5.433188e-07 9.998564e-02 9.998765e-02 c DATA 7 9.998599e-02 9.174211e-07 9.998434e-02 9.998765e-02 c TICK 7 4.857143e-06 6.598289e-08 4.800000e-06 4.933333e-06 c c c c c THE EXPERIMENTAL TIMING ERRORS FOR ALL 7 RUNS c -- --------- --------- --------- ----- ----- --- c k T min T avg T max T err t err P-F c -- --------- --------- --------- ----- ----- --- c 1 4.9255e-03 4.9673e-03 5.0215e-03 0.62% 0.09% 0 c 2 2.5391e-02 2.5497e-02 2.5668e-02 0.43% 0.02% 0 c 3 1.2076e-02 1.2181e-02 1.2255e-02 0.44% 0.04% 0 c 4 4.1387e-02 4.1650e-02 4.1767e-02 0.30% 0.01% 0 c 5 3.0290e-02 3.0553e-02 3.0731e-02 0.42% 0.01% 0 c 6 4.8437e-02 4.8809e-02 4.9144e-02 0.42% 0.01% 0 c 7 5.5685e-03 5.5897e-03 5.6178e-03 0.32% 0.08% 0 c 8 1.0261e-02 1.0418e-02 1.0573e-02 0.97% 0.04% 0 c 9 7.0038e-03 7.0966e-03 7.1828e-03 0.98% 0.06% 0 c 10 7.7975e-03 7.9491e-03 8.0408e-03 0.94% 0.05% 0 c 11 2.5637e-02 2.5858e-02 2.6006e-02 0.41% 0.02% 0 c 12 5.5238e-03 5.5703e-03 5.6385e-03 0.61% 0.08% 0 c 13 3.3584e-02 3.3680e-02 3.3751e-02 0.14% 0.01% 0 c 14 1.8261e-02 1.8469e-02 1.8586e-02 0.52% 0.02% 0 c 15 3.9167e-02 3.9268e-02 3.9397e-02 0.20% 0.01% 0 c 16 3.4676e-02 3.4778e-02 3.4840e-02 0.14% 0.01% 0 c 17 3.1477e-02 3.1622e-02 3.1756e-02 0.26% 0.01% 0 c 18 8.7125e-03 8.7759e-03 8.8358e-03 0.46% 0.05% 0 c 19 3.2181e-02 3.2335e-02 3.2427e-02 0.27% 0.01% 0 c 20 3.2594e-02 3.2634e-02 3.2668e-02 0.06% 0.01% 0 c 21 8.8811e-02 8.9406e-02 8.9884e-02 0.43% 0.00% 0 c 22 3.9238e-03 3.9380e-03 3.9808e-03 0.46% 0.11% 0 c 23 3.3196e-02 3.3461e-02 3.3900e-02 0.62% 0.01% 0 c 24 3.1468e-02 3.1525e-02 3.1665e-02 0.21% 0.01% 0 c -- --------- --------- --------- ----- ----- --- c c NET CPU TIMING VARIANCE (T err); A few % is ok: c c AVERAGE STANDEV MINIMUM MAXIMUM c Terr 0.44% 0.25% 0.06% 0.98% c c c c c c 1 c ******************************************** c THE LIVERMORE FORTRAN KERNELS: M F L O P S c ******************************************** c c Computer : CRAY-XMP-1 of 4 procs c System : CTSS 10e fully loaded c Compiler : CFT 1.14e Auto vector c c Mean DO Span = 19 c c When the computer performance range is very large c the net Mflops rate of many Fortran programs and c workloads will be in the sub-range between the equi- c weighted harmonic and arithmetic means depending c on the degree of code parallelism and optimization. c More accurate estimates of cpu workload rates depend c on assigning appropriate weights for each kernel. c c c c KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT CHECK-SUMS OK c ------ ----- -------- --------- ---- ------ ---------- -- c 1 3.0240e+05 4.9673e+03 60.8783 27 1.00 2.698573151746e+02 14 c 2 1.6192e+05 2.5497e+04 6.3506 15 1.00 8.398933280062e+01 15 c 3 1.5984e+05 1.2181e+04 13.1216 27 1.00 1.889516362525e+00 14 c 4 9.1200e+04 4.1650e+04 2.1897 27 1.00 4.199475416832e+00 15 c 5 1.6640e+05 3.0553e+04 5.4464 27 1.00 2.227830673914e+01 15 c 6 8.0640e+04 4.8809e+04 1.6522 8 1.00 5.812436051329e+12 11 c 7 5.3760e+05 5.5897e+03 96.1767 21 1.00 1.992004152347e+02 14 c 8 6.7392e+05 1.0418e+04 64.6898 14 1.00 2.072380567514e+04 15 c 9 5.3040e+05 7.0966e+03 74.7403 15 1.00 1.836777922612e+04 15 c 10 2.7000e+05 7.9491e+03 33.9659 15 1.00 1.155903859389e+04 15 c 11 9.5680e+04 2.5858e+04 3.7002 27 1.00 4.585813538906e+03 7 c 12 9.6000e+04 5.5703e+03 17.2343 26 1.00 1.360405187244e-05 10 c 13 1.3888e+05 3.3680e+04 4.1235 8 1.00 3.328647876067e+09 12 c 14 1.9008e+05 1.8469e+04 10.2921 27 1.00 1.721399839433e+07 14 c 15 1.8480e+05 3.9268e+04 4.7061 15 1.00 7.762981016945e+03 14 c 16 1.2320e+05 3.4778e+04 3.5425 15 1.00 1.804320000000e+05 16 c 17 2.8080e+05 3.1622e+04 8.8799 15 1.00 2.063158033013e+02 14 c 18 4.5760e+05 8.7759e+03 52.1431 14 1.00 6.790452348639e+03 14 c 19 2.0160e+05 3.2335e+04 6.2347 15 1.00 8.877614886362e+01 14 c 20 3.7856e+05 3.2634e+04 11.6002 26 1.00 4.191399274630e+03 14 c 21 2.0000e+06 8.9406e+04 22.3698 20 1.00 1.761809056730e+07 12 c 22 1.6320e+05 3.9380e+03 41.4424 15 1.00 4.276978109785e+01 15 c 23 4.0040e+05 3.3461e+04 11.9660 14 1.00 3.395238421926e+03 15 c 24 4.7840e+04 3.1525e+04 1.5175 27 1.00 9.100000000000e+01 16 c ------ ----- -------- --------- ---- ------ ---------- -- c MFLOPS Range : 330 c c Maximum Rate = 96.1767 Mega-Flops/Sec. c Average Rate = 23.2902 Mega-Flops/Sec. c Geometric Mean = 11.6641 Mega-Flops/Sec. c Median Rate = 10.9402 Mega-Flops/Sec. c Harmonic Mean = 6.1274 Mega-Flops/Sec. c Minimum Rate = 1.5786 Mega-Flops/Sec. c c Standard Dev. = 26.5479 Mega-Flops/Sec. c Median Dev. = 10.7695 Mega-Flops/Sec. c c c c c c c SENSITIVITY ANALYSIS c c c The sensitivity of the harmonic mean rate (Mflops) c to various weightings is shown in the table below. c Seven work distributions are generated by assigning c two distinct weights to ranked kernels by quartiles. c Forty nine possible cpu workloads are then evaluated c using seven sets of values for the total weights: c c c ------ ------ ------ ------ ------ ------ ------ c 1st QT: O O O O O X X c 2nd QT: O O O X X X O c 3rd QT: O X X X O O O c 4th QT: X X O O O O O c ------ ------ ------ ------ ------ ------ ------ c Total c Weights Net Mflops: c X O c ---- ---- c c 1.00 0.00 2.38 3.49 6.50 9.22 15.87 25.15 60.62 c c 0.95 0.05 2.49 3.65 6.47 8.77 14.35 19.19 38.06 c c 0.90 0.10 2.60 3.82 6.44 8.37 13.09 15.52 27.73 c c 0.80 0.20 2.85 4.21 6.39 7.67 11.14 11.22 17.98 c c 0.70 0.30 3.16 4.70 6.34 7.08 9.70 8.79 13.30 c c 0.60 0.40 3.54 5.32 6.29 6.57 8.59 7.22 10.56 c c 0.50 0.50 4.02 6.13 6.25 6.13 7.70 6.13 8.75 c ---- ---- c ------ ------ ------ ------ ------ ------ ------ c c c c c c c SENSITIVITY OF NET MFLOPS RATE TO USE OF OPTIMAL FORTRAN CODE(SISD/SIMD MODEL c c 3.49 4.30 5.60 8.03 10.25 14.18 22.98 33.33 60.62 c c 0.00 0.20 0.40 0.60 0.70 0.80 0.90 0.95 1.00 c Fraction Of Operations Run At Optimal Fortran Rates c c c c c c c 1 c ******************************************** c THE LIVERMORE FORTRAN KERNELS: M F L O P S c ******************************************** c c Computer : CRAY-XMP-1 of 4 procs c System : CTSS 10e fully loaded c Compiler : CFT 1.14e Auto vector c c Mean DO Span = 167 c c When the computer performance range is very large c the net Mflops rate of many Fortran programs and c workloads will be in the sub-range between the equi- c weighted harmonic and arithmetic means depending c on the degree of code parallelism and optimization. c More accurate estimates of cpu workload rates depend c on assigning appropriate weights for each kernel. c c c c KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT CHECK-SUMS OK c ------ ----- -------- --------- ---- ------ ---------- -- c 1 3.0240e+05 4.9673e+03 60.8783 27 1.00 2.698573151746e+02 14 c 2 1.6192e+05 2.5497e+04 6.3506 15 1.00 8.398933280062e+01 15 c 3 1.5984e+05 1.2181e+04 13.1216 27 1.00 1.889516362525e+00 14 c 4 9.1200e+04 4.1650e+04 2.1897 27 1.00 4.199475416832e+00 15 c 5 1.6640e+05 3.0553e+04 5.4464 27 1.00 2.227830673914e+01 15 c 6 8.0640e+04 4.8809e+04 1.6522 8 1.00 5.812436051329e+12 11 c 7 5.3760e+05 5.5897e+03 96.1767 21 1.00 1.992004152347e+02 14 c 8 6.7392e+05 1.0418e+04 64.6898 14 1.00 2.072380567514e+04 15 c 9 5.3040e+05 7.0966e+03 74.7403 15 1.00 1.836777922612e+04 15 c 10 2.7000e+05 7.9491e+03 33.9659 15 1.00 1.155903859389e+04 15 c 11 9.5680e+04 2.5858e+04 3.7002 27 1.00 4.585813538906e+03 7 c 12 9.6000e+04 5.5703e+03 17.2343 26 1.00 1.360405187244e-05 10 c 13 1.3888e+05 3.3680e+04 4.1235 8 1.00 3.328647876067e+09 12 c 14 1.9008e+05 1.8469e+04 10.2921 27 1.00 1.721399839433e+07 14 c 15 1.8480e+05 3.9268e+04 4.7061 15 1.00 7.762981016945e+03 14 c 16 1.2320e+05 3.4778e+04 3.5425 15 1.00 1.804320000000e+05 16 c 17 2.8080e+05 3.1622e+04 8.8799 15 1.00 2.063158033013e+02 14 c 18 4.5760e+05 8.7759e+03 52.1431 14 1.00 6.790452348639e+03 14 c 19 2.0160e+05 3.2335e+04 6.2347 15 1.00 8.877614886362e+01 14 c 20 3.7856e+05 3.2634e+04 11.6002 26 1.00 4.191399274630e+03 14 c 21 2.0000e+06 8.9406e+04 22.3698 20 1.00 1.761809056730e+07 12 c 22 1.6320e+05 3.9380e+03 41.4424 15 1.00 4.276978109785e+01 15 c 23 4.0040e+05 3.3461e+04 11.9660 14 1.00 3.395238421926e+03 15 c 24 4.7840e+04 3.1525e+04 1.5175 27 1.00 9.100000000000e+01 16 c 1 4.0400e+05 3.7041e+03 109.0679 101 2.00 3.677341345257e+03 14 c 2 3.1040e+05 1.2445e+04 24.9427 101 2.00 3.605241761060e+03 14 c 3 2.1412e+05 6.1361e+03 34.8950 101 2.00 7.068190056054e+00 14 c 4 1.6800e+05 2.0526e+04 8.1848 101 2.00 4.199475416832e+00 15 c 5 2.2000e+05 3.8241e+04 5.7530 101 2.00 3.212322357721e+02 14 c 6 1.3440e+05 2.0156e+04 6.6679 32 2.00 1.885296670192e+16 12 c 7 7.1104e+05 4.9201e+03 144.5170 101 2.00 4.441910421041e+03 14 c 8 8.5536e+05 8.4281e+03 101.4889 100 2.00 1.050887603939e+06 14 c 9 7.2114e+05 5.3005e+03 136.0502 101 2.00 8.326105269825e+05 15 c 10 3.4542e+05 6.0877e+03 56.7408 101 2.00 5.117258849028e+05 14 c 11 1.2800e+05 2.0681e+04 6.1893 101 2.00 2.403492372107e+05 8 c 12 1.3464e+05 3.5171e+03 38.2814 100 2.00 4.989298401193e-05 9 c 13 1.8368e+05 4.3043e+04 4.2673 32 2.00 1.627723261374e+10 12 c 14 2.2220e+05 1.9733e+04 11.2604 101 2.00 2.130649341195e+08 14 c 15 3.3000e+05 7.0946e+04 4.6514 101 2.00 2.760671683247e+05 15 c 16 1.5120e+05 4.5291e+04 3.3384 40 2.00 2.270870000000e+05 16 c 17 3.6360e+05 3.9716e+04 9.1550 101 2.00 7.802492410321e+03 14 c 18 4.3560e+05 4.0740e+03 106.9227 100 2.00 3.615937787530e+05 14 c 19 2.7876e+05 4.0279e+04 6.9208 101 2.00 3.795271872105e+03 14 c 20 4.1600e+05 3.5467e+04 11.7292 100 2.00 2.188343625168e+05 14 c 21 1.2500e+06 2.8205e+04 44.3180 50 2.00 2.790571795524e+07 13 c 22 2.4038e+05 3.6830e+03 65.2680 101 2.00 2.057023063597e+03 15 c 23 5.4450e+05 4.1499e+04 13.1207 100 2.00 2.484926226843e+05 14 c 24 6.2000e+04 3.9644e+04 1.5639 101 2.00 3.500000000000e+02 16 c 1 3.5035e+05 2.3215e+03 150.9181 1001 1.00 3.580256885257e+05 15 c 2 2.5996e+05 1.0344e+04 25.1321 101 1.00 3.605241761060e+03 14 c 3 1.8018e+05 1.4585e+03 123.5415 1001 1.00 7.005200181467e+01 14 c 4 1.6800e+05 4.0989e+03 40.9867 1001 1.00 4.199475416832e+00 15 c 5 2.0000e+05 3.4047e+04 5.8743 1001 1.00 3.184210149672e+04 14 c 6 1.1904e+05 1.0350e+04 11.5011 64 1.00 3.660366768768e+13 13 c 7 6.3680e+05 3.7967e+03 167.7227 995 1.00 4.272975752615e+05 14 c 8 7.1280e+05 6.9755e+03 102.1869 100 1.00 1.050887603939e+06 14 c 9 6.1812e+05 4.5215e+03 136.7081 101 1.00 8.326105269826e+05 15 c 10 3.0906e+05 5.3632e+03 57.6264 101 1.00 5.117258849028e+05 15 c 11 1.1000e+05 1.3369e+04 8.2278 1001 1.00 2.340037689466e+08 9 c 12 1.1988e+05 2.0810e+03 57.6061 1000 1.00 2.034999000047e-04 9 c 13 1.6128e+05 3.7656e+04 4.2830 64 1.00 2.839977317873e+10 12 c 14 2.2022e+05 1.9014e+04 11.5819 1001 1.00 2.116750694993e+10 14 c 15 1.6500e+05 3.5446e+04 4.6550 101 1.00 2.760671683247e+05 15 c 16 1.3250e+05 3.9362e+04 3.3662 75 1.00 1.982820000000e+05 16 c 17 3.1815e+05 3.4837e+04 9.1325 101 1.00 7.802492410322e+03 14 c 18 4.3560e+05 4.0942e+03 106.3952 100 1.00 3.615937787530e+05 14 c 19 2.3634e+05 3.4032e+04 6.9447 101 1.00 3.795271872105e+03 14 c 20 2.6000e+05 2.2096e+04 11.7666 1000 1.00 2.128451037522e+08 12 c 21 1.2625e+06 2.0053e+04 62.9576 101 1.00 5.802625385051e+07 13 c 22 1.8887e+05 2.8906e+03 65.3394 101 1.00 2.057023063597e+03 15 c 23 4.3560e+05 3.3136e+04 13.1456 100 1.00 2.484884179713e+05 14 c 24 5.0000e+04 3.1588e+04 1.5829 1001 1.00 3.500000000000e+03 16 c ------ ----- -------- --------- ---- ------ ---------- -- c MFLOPS Range : 993 c c Maximum Rate = 167.7227 Mega-Flops/Sec. c Average Rate = 38.1118 Mega-Flops/Sec. c Geometric Mean = 17.0512 Mega-Flops/Sec. c Median Rate = 11.7660 Mega-Flops/Sec. c Harmonic Mean = 8.1796 Mega-Flops/Sec. c Minimum Rate = 1.5175 Mega-Flops/Sec. c c Standard Dev. = 44.2901 Mega-Flops/Sec. c Median Dev. = 40.1770 Mega-Flops/Sec. c c c c c c c c c c c c c c c c c TOP QUARTILE: BEST ARCHITECTURE/APPLICATION MATCH c c c c KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT SUM c ------ ----- -------- --------- ---- ------ --- c 7 6.3680e+05 3.7967e+03 167.7227 995 1.00 c 1 3.5035e+05 2.3215e+03 150.9181 1001 1.00 c 7 7.1104e+05 4.9201e+03 144.5170 101 2.00 c 9 6.1812e+05 4.5215e+03 136.7081 101 1.00 c 9 7.2114e+05 5.3005e+03 136.0502 101 2.00 c 3 1.8018e+05 1.4585e+03 123.5415 1001 1.00 c 1 4.0400e+05 3.7041e+03 109.0679 101 2.00 c 18 4.3560e+05 4.0740e+03 106.9227 100 2.00 c 18 4.3560e+05 4.0942e+03 106.3952 100 1.00 c 8 7.1280e+05 6.9755e+03 102.1869 100 1.00 c 8 8.5536e+05 8.4281e+03 101.4889 100 2.00 c 7 5.3760e+05 5.5897e+03 96.1767 21 1.00 c 9 5.3040e+05 7.0966e+03 74.7403 15 1.00 c 22 1.8887e+05 2.8906e+03 65.3394 101 1.00 c 22 2.4038e+05 3.6830e+03 65.2680 101 2.00 c 8 6.7392e+05 1.0418e+04 64.6898 14 1.00 c 21 1.2625e+06 2.0053e+04 62.9576 101 1.00 c 1 3.0240e+05 4.9673e+03 60.8783 27 1.00 c ------ ----- -------- --------- ---- ------ --- c FRAC. WEIGHTS = 0.2500 c AVERAGE RATE = 105.7868 Mega-Flops/Sec. c HARMONIC MEAN = 96.0137 Mega-Flops/Sec. c STANDARD DEV. = 31.3357 Mega-Flops/Sec. c c c c KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT SUM c ------ ----- -------- --------- ---- ------ --- c 10 3.0906e+05 5.3632e+03 57.6264 101 1.00 c 12 1.1988e+05 2.0810e+03 57.6061 1000 1.00 c 10 3.4542e+05 6.0877e+03 56.7408 101 2.00 c 18 4.5760e+05 8.7759e+03 52.1431 14 1.00 c 21 1.2500e+06 2.8205e+04 44.3180 50 2.00 c 22 1.6320e+05 3.9380e+03 41.4424 15 1.00 c 4 1.6800e+05 4.0989e+03 40.9867 1001 1.00 c 12 1.3464e+05 3.5171e+03 38.2814 100 2.00 c 3 2.1412e+05 6.1361e+03 34.8950 101 2.00 c 10 2.7000e+05 7.9491e+03 33.9659 15 1.00 c 2 2.5996e+05 1.0344e+04 25.1321 101 1.00 c 2 3.1040e+05 1.2445e+04 24.9427 101 2.00 c 21 2.0000e+06 8.9406e+04 22.3698 20 1.00 c 12 9.6000e+04 5.5703e+03 17.2343 26 1.00 c 23 4.3560e+05 3.3136e+04 13.1456 100 1.00 c 3 1.5984e+05 1.2181e+04 13.1216 27 1.00 c 23 5.4450e+05 4.1499e+04 13.1207 100 2.00 c 23 4.0040e+05 3.3461e+04 11.9660 14 1.00 c 20 2.6000e+05 2.2096e+04 11.7666 1000 1.00 c 20 4.1600e+05 3.5467e+04 11.7292 100 2.00 c 20 3.7856e+05 3.2634e+04 11.6002 26 1.00 c 14 2.2022e+05 1.9014e+04 11.5819 1001 1.00 c 6 1.1904e+05 1.0350e+04 11.5011 64 1.00 c 14 2.2220e+05 1.9733e+04 11.2604 101 2.00 c 14 1.9008e+05 1.8469e+04 10.2921 27 1.00 c 17 3.6360e+05 3.9716e+04 9.1550 101 2.00 c 17 3.1815e+05 3.4837e+04 9.1325 101 1.00 c 17 2.8080e+05 3.1622e+04 8.8799 15 1.00 c 11 1.1000e+05 1.3369e+04 8.2278 1001 1.00 c 4 1.6800e+05 2.0526e+04 8.1848 101 2.00 c 19 2.3634e+05 3.4032e+04 6.9447 101 1.00 c 19 2.7876e+05 4.0279e+04 6.9208 101 2.00 c 6 1.3440e+05 2.0156e+04 6.6679 32 2.00 c 2 1.6192e+05 2.5497e+04 6.3506 15 1.00 c 19 2.0160e+05 3.2335e+04 6.2347 15 1.00 c 11 1.2800e+05 2.0681e+04 6.1893 101 2.00 c ------ ----- -------- --------- ---- ------ --- c FRAC. WEIGHTS = 0.5104 c AVERAGE RATE = 21.1033 Mega-Flops/Sec. c HARMONIC MEAN = 12.5546 Mega-Flops/Sec. c STANDARD DEV. = 16.5497 Mega-Flops/Sec. c c c c KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT SUM c ------ ----- -------- --------- ---- ------ --- c 5 2.0000e+05 3.4047e+04 5.8743 1001 1.00 c 5 2.2000e+05 3.8241e+04 5.7530 101 2.00 c 5 1.6640e+05 3.0553e+04 5.4464 27 1.00 c 15 1.8480e+05 3.9268e+04 4.7061 15 1.00 c 15 1.6500e+05 3.5446e+04 4.6550 101 1.00 c 15 3.3000e+05 7.0946e+04 4.6514 101 2.00 c 13 1.6128e+05 3.7656e+04 4.2830 64 1.00 c 13 1.8368e+05 4.3043e+04 4.2673 32 2.00 c 13 1.3888e+05 3.3680e+04 4.1235 8 1.00 c 11 9.5680e+04 2.5858e+04 3.7002 27 1.00 c 16 1.2320e+05 3.4778e+04 3.5425 15 1.00 c 16 1.3250e+05 3.9362e+04 3.3662 75 1.00 c 16 1.5120e+05 4.5291e+04 3.3384 40 2.00 c 4 9.1200e+04 4.1650e+04 2.1897 27 1.00 c 6 8.0640e+04 4.8809e+04 1.6522 8 1.00 c 24 5.0000e+04 3.1588e+04 1.5829 1001 1.00 c 24 6.2000e+04 3.9644e+04 1.5639 101 2.00 c 24 4.7840e+04 3.1525e+04 1.5175 27 1.00 c ------ ----- -------- --------- ---- ------ --- c FRAC. WEIGHTS = 0.2396 c AVERAGE RATE = 3.7299 Mega-Flops/Sec. c HARMONIC MEAN = 3.0328 Mega-Flops/Sec. c STANDARD DEV. = 1.4192 Mega-Flops/Sec. c c c c c c c c c c c c c c c c 1 c c SENSITIVITY ANALYSIS c c c The sensitivity of the harmonic mean rate (Mflops) c to various weightings is shown in the table below. c Seven work distributions are generated by assigning c two distinct weights to ranked kernels by quartiles. c Forty nine possible cpu workloads are then evaluated c using seven sets of values for the total weights: c c c ------ ------ ------ ------ ------ ------ ------ c 1st QT: O O O O O X X c 2nd QT: O O O X X X O c 3rd QT: O X X X O O O c 4th QT: X X O O O O O c ------ ------ ------ ------ ------ ------ ------ c Total c Weights Net Mflops: c X O c ---- ---- c c 1.00 0.00 2.99 4.43 8.54 12.72 24.95 39.41 93.75 c c 0.95 0.05 3.12 4.63 8.50 12.00 21.84 28.25 54.56 c c 0.90 0.10 3.26 4.86 8.45 11.36 19.42 22.02 38.47 c c 0.80 0.20 3.59 5.38 8.37 10.27 15.90 15.27 24.20 c c 0.70 0.30 3.98 6.04 8.30 9.36 13.46 11.69 17.65 c c 0.60 0.40 4.48 6.87 8.22 8.61 11.67 9.47 13.90 c c 0.50 0.50 5.12 7.96 8.14 7.96 10.30 7.96 11.46 c ---- ---- c ------ ------ ------ ------ ------ ------ ------ c c c c c SENSITIVITY OF NET MFLOPS RATE TO USE OF OPTIMAL FORTRAN CODE(SISD/SIMD MODEL c c 4.55 5.62 7.34 10.61 13.64 19.11 31.87 47.86 96.01 c c 0.00 0.20 0.40 0.60 0.70 0.80 0.90 0.95 1.00 c Fraction Of Operations Run At Optimal Fortran Rates c c c c c c c c c c c c Quadruple precision checksums computed by Dr. D.S. Lindsey, NAS: c c CUMULATIVE CHECKSUMS: RUN= 1 c c K VL= 471 90 19 c 1 .5114652693224705102Q+05 .5253344778938000681Q+03 .3855104502494983491Q+02 c 2 .5150345372943066022Q+03 .5150345372943066022Q+03 .1199847611437483513Q+02 c 3 .1000742883066623145Q+02 .1009741436579188086Q+01 .2699309089321296439Q+00 c 4 .5999250595474070357Q+00 .5999250595474070357Q+00 .5999250595474070357Q+00 c 5 .4548871642388544199Q+04 .4589031939602131581Q+02 .3182615248448271678Q+01 c 6 .5229095383954675635Q+13 .2693280957416549457Q+16 .8303480073326955433Q+12 c 7 .6104251075163778121Q+05 .6345586315772524401Q+03 .2845720217638848365Q+02 c 8 .1501268005627157186Q+06 .1501268005627157186Q+06 .2960543667877649943Q+04 c 9 .1189443609975085966Q+06 .1189443609975085966Q+06 .2623968460874419268Q+04 c 10 .7310369784325972183Q+05 .7310369784325972183Q+05 .1651291227698377392Q+04 c 11 .3342910984950433340Q+08 .3433560531581074341Q+05 .6551162198437113656Q+03 c 12 .2907141428639174056Q-04 .7127569144561925151Q-05 .1943435981776804808Q-05 c 13 .4057110454105263471Q+10 .2325318944820836005Q+10 .4755211251524563699Q+09 c 14 .2982036205992255154Q+10 .3045676741897511424Q+08 .2547733008933910800Q+07 c 15 .3943816690352311804Q+05 .3943816690352311804Q+05 .1108997288135066584Q+04 c 16 .2832600000000000000Q+05 .3244100000000000000Q+05 .2577600000000000000Q+05 c 17 .1114641772903091760Q+04 .1114641772903091760Q+04 .2947368618590713935Q+02 c 18 .5165625410757306606Q+05 .5165625410757306606Q+05 .9700646212341513210Q+03 c 19 .5421816960150398899Q+03 .5421816960150398899Q+03 .1268230698051747067Q+02 c 20 .3040644339317275409Q+08 .3126205178811007613Q+05 .5987713249471801461Q+03 c 21 .8289464835786202431Q+07 .3986531136462291709Q+07 .2516870081042209239Q+07 c 22 .2938604376567099667Q+03 .2938604376567099667Q+03 .6109968728264795136Q+01 c 23 .3549834542446150511Q+05 .3549894609776936556Q+05 .4850340602751675804Q+03 c 24 .5000000000000000000Q+03 .5000000000000000000Q+02 .1300000000000000000Q+02 c c c CUMULATIVE CHECKSUMS: RUN= 2 c c K VL= 471 90 19 c 1 .1022930538644941020Q+06 .1050668955787600136Q+04 .7710209004989966983Q+02 c 2 .1030069074588613204Q+04 .1030069074588613204Q+04 .2399695222874967026Q+02 c 3 .2001485766133246290Q+02 .2019482873158376173Q+01 .5398618178642592878Q+00 c 4 .1199850119094814071Q+01 .1199850119094814071Q+01 .1199850119094814071Q+01 c 5 .9097743284777088398Q+04 .9178063879204263162Q+02 .6365230496896543357Q+01 c 6 .1045819076790935127Q+14 .5386561914833098914Q+16 .1660696014665391086Q+13 c 7 .1220850215032755624Q+06 .1269117263154504880Q+04 .5691440435277696731Q+02 c 8 .3002536011254314373Q+06 .3002536011254314373Q+06 .5921087335755299887Q+04 c 9 .2378887219950171932Q+06 .2378887219950171932Q+06 .5247936921748838536Q+04 c 10 .1462073956865194436Q+06 .1462073956865194436Q+06 .3302582455396754785Q+04 c 11 .6685821969900866681Q+08 .6867121063162148682Q+05 .1310232439687422731Q+04 c 12 .5814282857278348113Q-04 .1425513828912385030Q-04 .3886871963553609616Q-05 c 13 .8114220908210526943Q+10 .4650637889641672010Q+10 .9510422503049127399Q+09 c 14 .6118901630090488734Q+10 .5718526521576222224Q+08 .5131714230651644153Q+07 c 15 .7887633380704623608Q+05 .7887633380704623608Q+05 .2217994576270133168Q+04 c 16 .5665200000000000000Q+05 .6488200000000000000Q+05 .5155200000000000000Q+05 c 17 .2229283545806183520Q+04 .2229283545806183520Q+04 .5894737237181427870Q+02 c 18 .1033125082151461321Q+06 .1033125082151461321Q+06 .1940129242468302642Q+04 c 19 .1084363392030079779Q+04 .1084363392030079779Q+04 .2536461396103494135Q+02 c 20 .6081288678634550819Q+08 .6252410357622015226Q+05 .1197542649894360292Q+04 c 21 .1657892967157240486Q+08 .7973062272924583418Q+07 .5033740162084418479Q+07 c 22 .5877208753134199335Q+03 .5877208753134199335Q+03 .1221993745652959027Q+02 c 23 .7099669084892301023Q+05 .7099789219553873113Q+05 .9700681205503351609Q+03 c 24 .1000000000000000000Q+04 .1000000000000000000Q+03 .2600000000000000000Q+02 c c c CUMULATIVE CHECKSUMS: RUN= 3 c c K VL= 471 90 19 c 1 .1534395807967411530Q+06 .1576003433681400204Q+04 .1156531350748495047Q+03 c 2 .1545103611882919806Q+04 .1545103611882919806Q+04 .3599542834312450539Q+02 c 3 .3002228649199869435Q+02 .3029224309737564260Q+01 .8097927267963889317Q+00 c 4 .1799775178642221107Q+01 .1799775178642221107Q+01 .1799775178642221107Q+01 c 5 .1364661492716563259Q+05 .1376709581880639474Q+03 .9547845745344815036Q+01 c 6 .1568728615186402690Q+14 .8079842872249648371Q+16 .2491044021998086629Q+13 c 7 .1831275322549133436Q+06 .1903675894731757320Q+04 .8537160652916545097Q+02 c 8 .4503804016881471560Q+06 .4503804016881471560Q+06 .8881631003632949831Q+04 c 9 .3568330829925257898Q+06 .3568330829925257898Q+06 .7871905382623257805Q+04 c 10 .2193110935297791654Q+06 .2193110935297791654Q+06 .4953873683095132178Q+04 c 11 .1002873295485130002Q+09 .1030068159474322302Q+06 .1965348659531134097Q+04 c 12 .8721424285917522169Q-04 .2138270743368577545Q-04 .5830307945330414425Q-05 c 13 .1217133136231579041Q+11 .6975956834462508016Q+10 .1426563375457369109Q+10 c 14 .9103526877478772509Q+10 .8885029941358330359Q+08 .7946120246231201651Q+07 c 15 .1183145007105693541Q+06 .1183145007105693541Q+06 .3326991864405199752Q+04 c 16 .8497800000000000000Q+05 .9732300000000000000Q+05 .7732800000000000000Q+05 c 17 .3343925318709275281Q+04 .3343925318709275281Q+04 .8842105855772141805Q+02 c 18 .1549687623227191981Q+06 .1549687623227191981Q+06 .2910193863702453963Q+04 c 19 .1626545088045119669Q+04 .1626545088045119669Q+04 .3804692094155241203Q+02 c 20 .9121933017951826228Q+08 .9378615536433022839Q+05 .1796313974841540438Q+04 c 21 .2486839450735860729Q+08 .1195959340938687512Q+08 .7550610243126627718Q+07 c 22 .8815813129701299003Q+03 .8815813129701299003Q+03 .1832990618479438540Q+02 c 23 .1064950362733845153Q+06 .1064968382933080966Q+06 .1455102180825502741Q+04 c 24 .1500000000000000000Q+04 .1500000000000000000Q+03 .3900000000000000000Q+02 c c c CUMULATIVE CHECKSUMS: RUN= 4 c c K VL= 471 90 19 c 1 .2045861077289882040Q+06 .2101337911575200272Q+04 .1542041800997993396Q+03 c 2 .2060138149177226409Q+04 .2060138149177226409Q+04 .4799390445749934052Q+02 c 3 .4002971532266492580Q+02 .4038965746316752347Q+01 .1079723635728518575Q+01 c 4 .2399700238189628143Q+01 .2399700238189628143Q+01 .2399700238189628143Q+01 c 5 .1819548656955417679Q+05 .1835612775840852632Q+03 .1273046099379308671Q+02 c 6 .2091638153581870254Q+14 .1077312382966619782Q+17 .3321392029330782173Q+13 c 7 .2441700430065511248Q+06 .2538234526309009760Q+04 .1138288087055539346Q+03 c 8 .6005072022508628747Q+06 .6005072022508628747Q+06 .1184217467151059977Q+05 c 9 .4757774439900343865Q+06 .4757774439900343865Q+06 .1049587384349767707Q+05 c 10 .2924147913730388873Q+06 .2924147913730388873Q+06 .6605164910793509571Q+04 c 11 .1337164393980173336Q+09 .1373424212632429736Q+06 .2620464879374845462Q+04 c 12 .1162856571455669622Q-03 .2851027657824770060Q-04 .7773743927107219233Q-05 c 13 .1622844181642105388Q+11 .9301275779283344021Q+10 .1902084500609825479Q+10 c 14 .1215176334476067437Q+11 .1174925822726987451Q+09 .1008019578807808401Q+08 c 15 .1577526676140924721Q+06 .1577526676140924721Q+06 .4435989152540266336Q+04 c 16 .1133040000000000000Q+06 .1297640000000000000Q+06 .1031040000000000000Q+06 c 17 .4458567091612367041Q+04 .4458567091612367041Q+04 .1178947447436285574Q+03 c 18 .2066250164302922642Q+06 .2066250164302922642Q+06 .3880258484936605284Q+04 c 19 .2168726784060159559Q+04 .2168726784060159559Q+04 .5072922792206988271Q+02 c 20 .1216257735726910163Q+09 .1250482071524403045Q+06 .2395085299788720584Q+04 c 21 .3315785934314480972Q+08 .1594612454584916683Q+08 .1006748032416883695Q+08 c 22 .1175441750626839867Q+04 .1175441750626839867Q+04 .2443987491305918054Q+02 c 23 .1419933816978460204Q+06 .1419957843910774622Q+06 .1940136241100670321Q+04 c 24 .2000000000000000000Q+04 .2000000000000000000Q+03 .5200000000000000000Q+02 c c c c c CUMULATIVE CHECKSUMS: RUN= 5 c c K VL= 471 90 19 c 1 .2557326346612352551Q+06 .2626672389469000340Q+04 .1927552251247491745Q+03 c 2 .2575172686471533011Q+04 .2575172686471533011Q+04 .5999238057187417565Q+02 c 3 .5003714415333115725Q+02 .5048707182895940434Q+01 .1349654544660648219Q+01 c 4 .2999625297737035178Q+01 .2999625297737035178Q+01 .2999625297737035178Q+01 c 5 .2274435821194272099Q+05 .2294515969801065790Q+03 .1591307624224135839Q+02 c 6 .2614547691977337817Q+14 .1346640478708274728Q+17 .4151740036663477716Q+13 c 7 .3052125537581889060Q+06 .3172793157886262200Q+04 .1422860108819424182Q+03 c 8 .7506340028135785934Q+06 .7506340028135785934Q+06 .1480271833938824971Q+05 c 9 .5947218049875429831Q+06 .5947218049875429831Q+06 .1311984230437209634Q+05 c 10 .3655184892162986091Q+06 .3655184892162986091Q+06 .8256456138491886963Q+04 c 11 .1671455492475216670Q+09 .1716780265790537170Q+06 .3275581099218556828Q+04 c 12 .1453570714319587028Q-03 .3563784572280962575Q-04 .9717179908884024042Q-05 c 13 .2028555227052631735Q+11 .1162659472410418002Q+11 .2377605625762281849Q+10 c 14 .1519764492169999253Q+11 .1501582054695641385Q+09 .1269997234773526700Q+08 c 15 .1971908345176155902Q+06 .1971908345176155902Q+06 .5544986440675332920Q+04 c 16 .1416300000000000000Q+06 .1622050000000000000Q+06 .1288800000000000000Q+06 c 17 .5573208864515458802Q+04 .5573208864515458802Q+04 .1473684309295356967Q+03 c 18 .2582812705378653303Q+06 .2582812705378653303Q+06 .4850323106170756605Q+04 c 19 .2710908480075199449Q+04 .2710908480075199449Q+04 .6341153490258735339Q+02 c 20 .1520322169658637704Q+09 .1563102589405503806Q+06 .2993856624735900730Q+04 c 21 .4144732417893101215Q+08 .1993265568231145854Q+08 .1258435040521104619Q+08 c 22 .1469302188283549833Q+04 .1469302188283549833Q+04 .3054984364132397568Q+02 c 23 .1774917271223075255Q+06 .1774947304888468278Q+06 .2425170301375837902Q+04 c 24 .2500000000000000000Q+04 .2500000000000000000Q+03 .6500000000000000000Q+02 c c c CUMULATIVE CHECKSUMS: RUN= 6 c c K VL= 471 90 19 c 1 .3068791615934823061Q+06 .3152006867362800409Q+04 .2313062701496990095Q+03 c 2 .3090207223765839613Q+04 .3090207223765839613Q+04 .7199085668624901078Q+02 c 3 .6004457298399738870Q+02 .6058448619475128521Q+01 .1619585453592777863Q+01 c 4 .3599550357284442214Q+01 .3599550357284442214Q+01 .3599550357284442214Q+01 c 5 .2729322985433126519Q+05 .2753419163761278948Q+03 .1909569149068963007Q+02 c 6 .3137457230372805381Q+14 .1615968574449929674Q+17 .4982088043996173259Q+13 c 7 .3662550645098266873Q+06 .3807351789463514640Q+04 .1707432130583309019Q+03 c 8 .9007608033762943120Q+06 .9007608033762943120Q+06 .1776326200726589966Q+05 c 9 .7136661659850515797Q+06 .7136661659850515797Q+06 .1574381076524651561Q+05 c 10 .4386221870595583309Q+06 .4386221870595583309Q+06 .9907747366190264356Q+04 c 11 .2005746590970260004Q+09 .2060136318948644604Q+06 .3930697319062268194Q+04 c 12 .1744284857183504433Q-03 .4276541486737155090Q-04 .1166061589066082885Q-04 c 13 .2434266272463158082Q+11 .1395191366892501603Q+11 .2853126750914738219Q+10 c 14 .1820312504465359131Q+11 .1819691693283694618Q+09 .1504905863862026021Q+08 c 15 .2366290014211387082Q+06 .2366290014211387082Q+06 .6653983728810399504Q+04 c 16 .1699560000000000000Q+06 .1946460000000000000Q+06 .1546560000000000000Q+06 c 17 .6687850637418550562Q+04 .6687850637418550562Q+04 .1768421171154428361Q+03 c 18 .3099375246454383963Q+06 .3099375246454383963Q+06 .5820387727404907926Q+04 c 19 .3253090176090239339Q+04 .3253090176090239339Q+04 .7609384188310482407Q+02 c 20 .1824386603590365245Q+09 .1875723107286604567Q+06 .3592627949683080876Q+04 c 21 .4973678901471721458Q+08 .2391918681877375025Q+08 .1510122048625325543Q+08 c 22 .1763162625940259800Q+04 .1763162625940259800Q+04 .3665981236958877081Q+02 c 23 .2129900725467690306Q+06 .2129936765866161933Q+06 .2910204361651005482Q+04 c 24 .3000000000000000000Q+04 .3000000000000000000Q+03 .7800000000000000000Q+02 c c c c CUMULATIVE CHECKSUMS: RUN= 7 c c K VL= 471 90 19 c 1 .3580256885257293571Q+06 .3677341345256600477Q+04 .2698573151746488444Q+03 c 2 .3605241761060146215Q+04 .3605241761060146215Q+04 .8398933280062384591Q+02 c 3 .7005200181466362015Q+02 .7068190056054316608Q+01 .1889516362524907507Q+01 c 4 .4199475416831849250Q+01 .4199475416831849250Q+01 .4199475416831849250Q+01 c 5 .3184210149671980939Q+05 .3212322357721492106Q+03 .2227830673913790175Q+02 c 6 .3660366768768272944Q+14 .1885296670191584620Q+17 .5812436051328868803Q+13 c 7 .4272975752614644685Q+06 .4441910421040767080Q+04 .1992004152347193856Q+03 c 8 .1050887603939010030Q+07 .1050887603939010030Q+07 .2072380567514354960Q+05 c 9 .8326105269825601763Q+06 .8326105269825601763Q+06 .1836777922612093487Q+05 c 10 .5117258849028180528Q+06 .5117258849028180528Q+06 .1155903859388864174Q+05 c 11 .2340037689465303338Q+09 .2403492372106752038Q+06 .4585813538905979559Q+04 c 12 .2034999000047421839Q-03 .4989298401193347605Q-04 .1360405187243763365Q-04 c 13 .2839977317873684430Q+11 .1627723261374585203Q+11 .3328647876067194589Q+10 c 14 .2116750694993432503Q+11 .2130649341195080691Q+09 .1721399839433381833Q+08 c 15 .2760671683246618263Q+06 .2760671683246618263Q+06 .7762981016945466088Q+04 c 16 .1982820000000000000Q+06 .2270870000000000000Q+06 .1804320000000000000Q+06 c 17 .7802492410321642323Q+04 .7802492410321642323Q+04 .2063158033013499754Q+03 c 18 .3615937787530114624Q+06 .3615937787530114624Q+06 .6790452348639059247Q+04 c 19 .3795271872105279229Q+04 .3795271872105279229Q+04 .8877614886362229475Q+02 c 20 .2128451037522092786Q+09 .2188343625167705329Q+06 .4191399274630261022Q+04 c 21 .5802625385050341702Q+08 .2790571795523604196Q+08 .1761809056729546467Q+08 c 22 .2057023063596969767Q+04 .2057023063596969767Q+04 .4276978109785356595Q+02 c 23 .2484884179712305358Q+06 .2484926226843855589Q+06 .3395238421926173063Q+04 c 24 .3500000000000000000Q+04 .3500000000000000000Q+03 .9100000000000000000Q+02 c c c c c c c CHECK CLOCK CALIBRATION: c Total cpu Time = 1.62376e+01 Sec. c C F.H.MCMAHON 1986 C********************************************************************** c c C C C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION sum C C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C/ PARAMETER( nk= 47, nl= 3, nr= 8 ) C COMMON /ALPHA/ mk,ik,ml,il,Nruns,jr, NPFS(8,3,47) COMMON /BETA / tic, TIMES(8,3,47), SEE(5,3,8,3), 1 TERRS(8,3,47), CSUMS(8,3,47), 2 FOPN(8,3,47), DOS(8,3,47) C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C DIMENSION FLOPS(141), TR(141), RATES(141) DIMENSION LSPAN(141), WG(141), OSUM (141), ID(141) DIMENSION HM(12), N1(10), N2(10), LVL(10) DIMENSION LQ(5), STAT1(20), STAT2(20) DIMENSION IN(141), CSUM1(141) DIMENSION MAP1(141), MAP2(141), IN2(141), VL1(141) DIMENSION MAP(141), VL(141), WL(141), TV(141), TV1(141), TV2(141) DIMENSION FLOPS1(141), RT1(141), ISPAN1(141), WT1(141) DIMENSION FLOPS2(141), RT2(141), ISPAN2(141), WT2(141) SAVE Komput, Kontrl, Kompil C C The Fortran-77 Character variables Komput, Kontrl, Kompil, Tag are C used in Format statements 7007, 7057, 7008, 7341, 7342, 7343, 7344 C CHARACTER Komput*24, Kontrl*24, Kompil*24 f77 C MODI(i,M)= (MOD(i,M) + M*( 1 - MIN(1,MOD(i,M)))) C DATA Komput /'VAX-11/780 w/FPA '/ c DATA Komput /'VAX-11/780 wo/FPA '/ c DATA Komput /'CRAY-1 '/ f77 c DATA Komput /'CRAY-XMP '/ f77 c DATA Komput / 8HCRAY-XMP/ f66 c DATA Komput / 8HCRAY-1 / f66 C DATA Kontrl /'VMS 4.5 '/ c DATA Kontrl /'UNIX 4.2 '/ c DATA Kontrl /'CTSS 10e fully loaded '/ f77 c DATA Kontrl / 8HCTSS 10e/ f66 C DATA Kompil /'VAX/Fortran-77 V4.0 '/ c DATA Kompil /' 4.2bsd UNIX F77 '/ c DATA Kompil /'LCC CC 1.05 '/ f77 c DATA Kompil /'CFT 1.14 '/ f77 c DATA Kompil /'CIVIC 30i '/ f77 c DATA Kompil / 8HCFT-1.14/ f66 c DATA Kompil / 8HCIVIC30i/ f66 C C IF( iou.LT.0) RETURN C fuzz= 1.0e-9 DO 1000 k= 1,ntk VL(k)= LSPAN(k) 1000 CONTINUE C bl= 1.0D-5 bu= 1.0D+4 CALL VALID( TV,MAP,neff, bl, RATES, bu, ntk) C C Compress valid data sets mapping on MAP. C nd= 0 DO 1 k= 1,neff MAP1(k)= MODI( MAP(k),nek) FLOPS1(k)= FLOPS( MAP(k)) RT1(k)= TR( MAP(k)) VL1(k)= VL( MAP(k)) ISPAN1(k)= LSPAN( MAP(k)) WT1(k)= WG( MAP(k)) TV1(k)= RATES( MAP(k)) CSUM1(k)= OSUM( MAP(k)) nd= ID( MAP(k)) + nd 1 continue C CALL STATW( STAT1,TV,IN, VL1,WT1,neff) LV= STAT1(1) C CALL STATW( STAT1,TV,IN, TV1,WT1,neff) twt= STAT1(6) C WRITE ( iou,7001) WRITE ( iou,7001) WRITE ( iou,7001) WRITE ( iou,7001) WRITE ( iou,7001) WRITE ( iou,7001) CALL PAGE( iou) WRITE ( iou,7002) WRITE ( iou,7003) WRITE ( iou,7002) WRITE ( iou,7007) Komput WRITE ( iou,7057) Kontrl WRITE ( iou,7008) Kompil WRITE ( iou,7009) LV WRITE ( iou,7061) WRITE ( iou,7062) WRITE ( iou,7063) WRITE ( iou,7064) WRITE ( iou,7065) WRITE ( iou,7066) WRITE ( iou,7067) WRITE ( iou,7001) WRITE ( iou,7004) WRITE ( iou,7005) WRITE ( iou,7011) (MAP1(k), FLOPS1(k), RT1(k), TV1(k), . ISPAN1(k), WT1(k), CSUM1(k), ID(k), k=1,neff) WRITE ( iou,7005) C WRITE ( iou,7022) nd WRITE ( iou,7041) STAT1( 4) WRITE ( iou,7033) STAT1( 1) WRITE ( iou,7043) STAT1(10) WRITE ( iou,7030) STAT1( 7) WRITE ( iou,7055) STAT1( 5) WRITE ( iou,7042) STAT1( 3) WRITE ( iou,7001) WRITE ( iou,7044) STAT1( 2) WRITE ( iou,7031) STAT1( 9) C 7001 FORMAT(/) 7002 FORMAT( 45H ******************************************** ) 7003 FORMAT( 45H THE LIVERMORE FORTRAN KERNELS: M F L O P S ) 7004 FORMAT(/,53H KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT CH, X19HECK-SUMS OK ) 7005 FORMAT( 53H ------ ----- -------- --------- ---- ------ --, X19H---------------- -- ) 7007 FORMAT(/,9X,16H Computer : ,A ) f77 7057 FORMAT( 9X,16H System : ,A ) f77 7008 FORMAT( 9X,16H Compiler : ,A ) f77 c7007 FORMAT(/,9X,16H Computer : ,A8) f66 c7057 FORMAT( 9X,16H System : ,A8) f66 c7008 FORMAT( 9X,16H Compiler : ,A8) f66 7009 FORMAT(/,9X,16HMean DO Span = ,I5,/) 7011 FORMAT(1X,i2,E11.4,E11.4,F12.4,1X,I4,1X,F6.2,E20.12,1X,I2) 7012 FORMAT(1X,i2,E11.4,E11.4,F12.4,1X,I4,1X,F6.2) 7022 FORMAT( 9X,16HMFLOPS Range : ,43X,I4) 7041 FORMAT(/,9X,16HMaximum Rate = ,F12.4,16H Mega-Flops/Sec. ) 7033 FORMAT( 9X,16HAverage Rate = ,F12.4,16H Mega-Flops/Sec. ) 7043 FORMAT( 9X,16HGeometric Mean = ,F12.4,16H Mega-Flops/Sec. ) 7030 FORMAT( 9X,16HMedian Rate = ,F12.4,16H Mega-Flops/Sec. ) 7055 FORMAT( 9X,16HHarmonic Mean = ,F12.4,16H Mega-Flops/Sec. ) 7042 FORMAT( 9X,16HMinimum Rate = ,F12.4,16H Mega-Flops/Sec. ) 7044 FORMAT( 9X,16HStandard Dev. = ,F12.4,16H Mega-Flops/Sec. ) 7031 FORMAT( 9X,16HMedian Dev. = ,F12.4,16H Mega-Flops/Sec. ) 7053 FORMAT(/,9X,16HFrac. Weights = ,F12.4) 7104 FORMAT(/,50H KERNEL FLOPS MICROSEC MFLOP/SEC SPAN WEIGHT ) 7105 FORMAT( 50H ------ ----- -------- --------- ---- ------ ) C 7061 FORMAT(9X,52HWhen the computer performance range is very large ) 7062 FORMAT(9X,52Hthe net Mflops rate of many Fortran programs and ) 7063 FORMAT(9X,52Hworkloads will be in the sub-range between the equi-) 7064 FORMAT(9X,52Hweighted harmonic and arithmetic means depending ) 7065 FORMAT(9X,52Hon the degree of code parallelism and optimization. ) 7066 FORMAT(9X,52HMore accurate estimates of cpu workload rates depend) 7067 FORMAT(9X,52Hon assigning appropriate weights for each kernel. ) C IF( ntk .NE. nek ) THEN C CALL PAGE( iou) WRITE ( iou,7070) 7070 FORMAT(//,50H TOP QUARTILE: BEST ARCHITECTURE/APPLICATION MATCH ) C C Compute compression index-list MAP1: Non-zero weights. C bl= 1.0D-6 bu= 1.0D+6 CALL VALID( TV,MAP1,meff, bl, WT1, bu, neff) C C Re-order data sets mapping on IN (descending order of MFlops). C DO 2 k= 1,meff i= IN( MAP1(k)) FLOPS2(k)= FLOPS1(i) RT2(k)= RT1(i) ISPAN2(k)= ISPAN1(i) WT2(k)= WT1(i) TV2(k)= TV1(i) MAP2(k)= MODI( MAP(i),nek) 2 continue C nq= meff/4 lo= meff -4*nq LQ(1)= nq LQ(2)= nq + nq + lo LQ(3)= nq i2= 0 C DO 5 j= 1,3 i1= i2 + 1 i2= i2 + LQ(j) ll= i2 - i1 + 1 CALL STATW( STAT2,TV,IN2, TV2(i1),WT2(i1),ll) frac= STAT2(6)/( twt +fuzz) WL(j)= STAT2(5) C WRITE ( iou,7001) WRITE ( iou,7104) WRITE ( iou,7105) WRITE ( iou,7012) ( MAP2(k), FLOPS2(k), RT2(k), TV2(k), . ISPAN2(k), WT2(k), k=i1,i2 ) WRITE ( iou,7105) C WRITE ( iou,7053) frac WRITE ( iou,7033) STAT2(1) WRITE ( iou,7055) STAT2(5) WRITE ( iou,7044) STAT2(2) 5 continue ENDIF C C C Sensitivity analysis of harmonic mean rate to 49 workloads C CALL SENSIT( iou,RATES,WG,IQ,SUMW, MAP,TV,TV1,TV2,RT1, ntk) C C C Sensitivity analysis of harmonic mean rate to SISD/SIMD model C CALL SIMD( HM, iou,RATES,WG,FR,9, MAP,TV,TV1,TV2, ntk) C C IF( ntk .NE. nek ) THEN CALL PAGE( iou) mrl= Nruns IF( Nruns.gt.8) mrl= 8 C DO 8 k= 1,mk DO 8 j= 1,ml sum= 0. DO 8 i= 1,mrl sum= sum + CSUMS(i,j,k) CSUMS(i,j,k)= sum 8 continue C DO 10 i= 1,mrl IF( (i.NE.1).AND.(i.NE.mrl)) GO TO 10 WRITE( iou,76) i WRITE( iou,77) ( LVL(j), j= 1,3 ) 76 FORMAT( //,29h Cumulative Checksums: RUN=,i5) 77 FORMAT( /,10h k VL=,i5,3i19) C DO 9 k= 1,mk WRITE( iou,78) k, ( CSUMS(i,j,k), j= 1,3) 78 FORMAT( 1x,i2,4e19.12) 9 continue 10 continue C ENDIF LVL(il)= LV RETURN C END C********************************************** SUBROUTINE RESULT( iou,FLOPS,TR,RATES,LSPAN,WG,OSUM,TERR,ID) C*********************************************************************** C * C RESULT - Computes timing Results into pushdown store. * C * C iou - Input IO unit number for print output * C FLOPS - Out.Ary Number of Flops executed by each kernel * C TR - Out.Ary Time of execution of each kernel(microsecs) * C RATES - Out.Ary Rate of execution of each kernel(megaflops/sec)* C LSPAN - Out.Ary Span of inner DO loop in each kernel * C WG - Out.Ary Weight assigned to each kernel for statistics * C OSUM - Out.Ary Checksums of the results of each kernel * C * C*********************************************************************** C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION SUMS, cs C C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C/ PARAMETER( nk= 47, nl= 3, nr= 8 ) C COMMON /ALPHA/ mk,ik,ml,il,Nruns,jr, NPFS(8,3,47) COMMON /BETA / tic, TIMES(8,3,47), SEE(5,3,8,3), 1 TERRS(8,3,47), CSUMS(8,3,47), 2 FOPN(8,3,47), DOS(8,3,47) C DIMENSION FLOPS(141), TR(141), RATES(141), ID(141) DIMENSION LSPAN(141), WG(141), OSUM (141), TERR(141) C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C COMMON /PROOF/ SUMS(24,3,2) C C C CALL TALLY( iou, 1 ) C C Push Result Arrays Down before entering new resul limit= 141 - mk j = 141 DO 1001 k = limit,1,-1 FLOPS(j)= FLOPS(k) TR(j)= TR(k) RATES(j)= RATES(k) LSPAN(j)= LSPAN(k) WG(j)= WG(k) OSUM(j)= OSUM(k) TERR(j)= TERR(k) ID(j)= ID(k) j = j - 1 1001 CONTINUE C C CALCULATE MFLOPS FOR EACH KERNEL tmin= 5.0*tic DO 1010 k = 1,mk FLOPS(k)= FLOPN(k)*TOTAL(k) TR(k)= TIME(k) * 1.0e+6 RATES(k)= 0.0 IF( TR(k).NE. 0.0) RATES(k)= FLOPS(k)/TR(k) IF( WT(k).LE. 0.0) RATES(k)= 0.0 IF( TIME(k).LE.tmin) RATES(k)= 0.0 LSPAN(k)= ISPAN(k,il) WG(k)= WT(k)*WTP(il) OSUM(k)= CSUM(k) TERR(k)= TERR1(k) c c compute relative error and digits of precision in CSUM c cs= REAL( Nruns) * SUMS(k,il,1) IF( k .EQ. 14 ) cs= SUMS( Nruns,il,2) re= ABS( CSUM(k)) IF( cs.NE. 0.0 ) re= ABS( (CSUM(k) - cs)/cs) IF((re.GT. 0.0 ) .AND. (re.LT. 1.0)) THEN ID(k)= INT( ABS( ALOG10( re)) + 0.9999999 ) ELSE ID(k)= 16 ENDIF IF( re.GE. 1.0 ) ID(k)= 0 IF( ID(k).GT. 16 ) ID(k)= 16 1010 CONTINUE C RETURN C END C C C********************************************** function SECOND( OLDSEC) C*********************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) REAL SECOND C C SECOND= Cumulative CPU time for job in seconds. MKS unit is seconds. C Clock resolution should be less than 2% of Kernel 12 run-time. C ONLY CPU time should be measured, NO system or I/O time included. C In VM systems, page-fault time must be avoided (Direction 4). C SECOND accuracy may be tested by calling the test program VERIFY. C C If your system provides a timing routine that satisfies C the definition above; then simply delete this function. C C Else this function must be programmed using some C timing routine available in your system. C Timing routines with CPU clock resolution are always sufficient. C Timing routines with microsec. resolution are usually sufficient. C C Timing routines with much less resolution may require the use C of multiple-pass loops around each kernel to make the run time C at least 50 times the tick-period of the timing routine. C To reduce timing errors you can increase the value of Loop C in subroutine SIZES. C C If no CPU timer is available, then you can time each kernel by C the wall clock using the PAUSE statement at the end of subr. VALUES. C C Function TICK measures the overhead time for a call to SECOND. C An independent calibration of the running time of at least C one kernel may be wise. See Subroutine VERIFY. C C C The following statement is deliberately incomplete: C c SECOND= sdef C C****************************************************************************** C C The following statements were used on the DEC VAX/780 VMS 3.0 . C Enable page-fault tallys in TEST by un-commenting LIB$STAT_TIMER calls. C Also set: Loop= 10*Loop in Subroutine SIZES to run kernels long enough. C DATA INITIA /123/ IF( INITIA.EQ.123 ) THEN INITIA= 1 NSTAT = LIB$INIT_TIMER() ELSE NSTAT = LIB$STAT_TIMER(2,ISEC) SECOND= REAL(ISEC)*0.01 - OLDSEC ENDIF C C* OR less accurately: C* REAL SECNDS C* SECOND= SECNDS( OLDSEC) C C****************************************************************************** C C The following statements were used on UNIX 4.2bsd systems, e.g. SUN C Also set: Loop= 10*Loop in Subroutine SIZES to run kernels long enough. C C* DIMENSION XTIME(2) unix C* REAL*4 XTIME unix C* XT= ETIME( XTIME) unix C* SECOND= XTIME(1) - OLDSEC unix C C****************************************************************************** C C The following statements were used on the DEC PDP-11/23 RT-11 system. C Also set: Loop=100*Loop in Subroutine SIZES to run kernels long enough. C C* DIMENSION JT(2) C* CALL GTIM(JT) C* TIME1 = JT(1) C* TIME2 = JT(2) C* TIME = TIME1 * 65768. + TIME2 C* SECOND=TIME/60. - OLDSEC C C****************************************************************************** C C The following statements were used on the Hewlett-Packard HP 9000 C Also set: Loop= 10*Loop in Subroutine SIZES to run kernels long enough. C C* INTEGER*4 ITIME(4) C* CALL TIMES( ITIME(4)) C* TIMEX= ITIME(1) + ITIME(2) + ITIME(3) + ITIME(4) C* SECOND= TIMEX/60. - OLDSEC C C****************************************************************************** C C The following statement was used on the IBM 3090 MVS C c CALL TOD( itime) c xtime = ( DFLOAT( itime)/64.0) * 1.0D-6 c SECOND= xtime - oldsec C C C****************************************************************************** C C FOR THE GOULD 32/87 WITH MPX 3.2 (et seq. gratis D.Lindsey) C C INTEGER*4 NSEC, NCLICK C REAL*8 CPUTIM C C CALL M:CLOCK (NSEC, NCLICK) C CPUTIM = FLOAT(NSEC) C SECOND = CPUTIM + FLOAT(NCLICK)/60. C C****************************************************************************** C C FOR THE HP 1000 RUNNING FORTRAN 77. C note that since the hp operating system has no facility for C returning cpu time, this routine only measures elapsed time. C therefore, the tests must be run stand-alone. C C REAL*8 TOTIME C INTEGER*2 TIMEA(5) C C CALL EXEC (11, TIMEA) C TOTIME = DBLE (TIMEA(1))/100. C TOTIME = TOTIME + DBLE (TIMEA(2)) C TOTIME = TOTIME + DBLE (TIMEA(3)) * 60. C SECOND = TOTIME + DBLE (TIMEA(4)) * 3600. C C****************************************************************************** C C FOR THE IBM PC. C note that the pc's operating system has no facility for C returning cpu time; this routine only measures elapsed time. C also, the pc does not have real*8. Remove all references to real*8 C C IMPLICIT INTEGER*4 (I-N) C LOGICAL FIRST C DATA FIRST /.TRUE./ C C CALL GETTIM (IYEAR, IMONTH, IDAY, IHOUR, IMIN, ISEC, IFRACT) C C ifract is integer fractions of a second C in units of 1/32,768 seconds C C IF (.NOT. FIRST) GO TO 10 C FIRST = .FALSE. C C LASTHR = IHOUR C BASETM = 0. C10 CONTINUE C C because of limited precision, do not include the time of day C in hours in the total time. but correct for an hour change. C C IF (LASTHR .EQ. IHOUR) GO TO 20 C BASETM = BASETM + 3600. C LASTHR = IHOUR C C20 TOTIME = FLOAT(IMIN) * 60 C . + FLOAT(ISEC) C . + FLOAT(IFRACT)/32768. C SECOND = TOTIM + BASETM C C****************************************************************************** C C FOR THE PR1ME SYSTEM UNDER PRIMOS C C REAL*8 CPUTIM C INTEGER*2 TIMERS (28) C C CALL TMDAT (TIMERS) C SECOND = DBLE (TIMERS(7)) C .+ DBLE(TIMERS(8)) / DBLE(TIMERS(11)) C C C C****************************************************************************** C C FOR IBM M V S (Calls following MVSTIM assembly code) C C the microsecond clock accessed by the routine MVSTIM counts down C from about 2 billion (2**31). so when it gets below 1 minute, C reset it to prevent underflow. C C a call to MVSTIM with an argument of 0 resets the clock; C any other argument causes the counted-down clock to be returned. C C IMPLICIT REAL*8 (T) C LOGICAL FIRST C DATA FIRST /.TRUE./ C C IF (.NOT. FIRST) GO TO 5 C L = 0 C CALL MVSTIM (L) C FIRST = .FALSE. C TBASE = L C TBASE = TBASE/1.D6 C5 CONTINUE C C always get current time (even if first entry) C C CALL MVSTIM (L) C TEMP = L C TEMP = TEMP/1.D6 C SECOND = TBASE - TEMP C IF (L .GT. 60000000) RETURN C C here we reset the counter if less than one minute left. C C L = 0 C CALL MVSTIM (L) C TNEW = L C TNEW = TNEW/1.D6 C TBASE = TBASE + TNEW - TEMP C RETURN C END C C for MVS systems, remove these 2 cards, move all the following C assembler code 1 space left (to remove column 1 stuff), and assembl CMVSTIM CSECT C PRINT GEN C USING *,12 C******************************************************************** C* STANDARD SUBROUTINE LINKAGE FROM FORTRAN PROGRAM C* GPR 1: ARGUMENT LIST ADDRESS FROM CALLER C* GPR 13: CALLER'S SAVEAREA ADDRESS C* GPR 14: ADDRESS IN CALLER FOR RETURN C* GPR 15: ENTRY ADDRESS OF THIS SUBPROGRAM C******************************************************************** C* REGISTER USAGE IN THIS PROGRAM... C* GPR 0: RETURN OF ELAPSED MICROSECONDS TO FORTRAN C* GPR 1: ARGUMENT LIST ADDRESS FROM CALLER C/C* GPR 2: ADDRESS OF PARAMETER PASSED FROM FORTRAN C* GPR 3: WORK REGISTER C* GPR 4: WORK REGISTER C* GPR 5: WORK REGISTER C* GPR 6: NOT USED C* GPR 7: NOT USED C* GPR 8: NOT USED C* GPR 9: NOT USED C* GPR 10: NOT USED C* GPR 11: NOT USED C* GPR 12: BASE REGISTER FOR THIS PROGRAM C* GPR 13: NOT USED C* GPR 14: NOT USED C* GPR 15: RETURN CODE TO FORTRAN IN CASE OF ERROR IN PROCESSING C******************************************************************** C******************************************************************** C* REGISTER EQUATES C******************************************************************** CR0 EQU 0 CR1 EQU 1 CR2 EQU 2 CR3 EQU 3 CR4 EQU 4 CR5 EQU 5 CR6 EQU 6 CR7 EQU 7 CR8 EQU 8 CR9 EQU 9 CR10 EQU 10 CR11 EQU 11 CR12 EQU 12 CR13 EQU 13 CR14 EQU 14 CR15 EQU 15 C*********************************************************************** C* END REGISTER EQUATES * C*********************************************************************** C* BEGIN BODY OF PROGRAM CODE * C*********************************************************************** C STM R14,R12,12(R13) STORE CALLING PGM'S GPRS C LR R12,R15 OUR ENTRY POINT INTO BASE REG C LA R15,SAVEAREA THIS PGM'S SAVEAREA ADDR IN 15 C ST R13,4(R15) SAVE CALLER'S SAVEAREA ADDR C ST R15,8(R13) SAVE OUR SAVEAREA ADDR IN CALLER C LR R13,R15 CURRENT SAVEAREA ADDR IN 13 C L R2,0(R1) ADDRESS OF PASSED VARIABLE C SR R3,R3 ZERO OUT R3 C C R3,0(R2) IS SUBROUTINE INVOKED WITH 0? C BE SETIT YES, SET INTERVAL TIMER CGETIT DS 0H NO, GET INTERVAL TIMER VALUE C TTIMER ,MIC,TVAL2 GET TIME INTO TVAL2 C L R4,TVAL2 LOAD, GET READY FOR SHIFT C L R5,TVAL2+4 LOAD, GET READY FOR SHIFT C LA R3,X'0C' LOAD 12 TO REG 3 C SRDL R4,0(R3) SHIFT RIGHT 12 BITS C ST R5,0(R2) SAVE ELAPSED TIME FOR CALLER C B GETOUT OUR WORK HERE IS DONE KEMOSABE CSETIT DS 0H HERE IS WHERE WE SET THE I.T. C L R4,HOURS1 PART 1 OF TIME VAL TO R3 C ST R4,TVAL SET TVAL PART 1 C L R5,HOURS2 PART 2 OF TIME VAL TO R3 C ST R5,TVAL+4 SET TVAL PART 2 C LA R3,X'0C' LOAD 12 TO REG 3 C SRDL R4,0(R3) SHIFT RIGHT 12 BITS C ST R5,0(R2) SAVE START TIME FOR CALLER C STIMER TASK,MICVL=TVAL SET TIMER BASED IN MICROSECS C SR R0,R0 RETURN DUMMY VALUE ON SET C*********************************************************************** C* END OF PROGRAM * C*********************************************************************** CGETOUT DS 0H C L R13,4(R13) LOAD CALLER'S SAVEAREA ADDR TO 13 C L R14,12(R13) LOAD RETURN ADDR OF CALLER TO 14 C LM R1,R12,24(R13) RESTORE CALLER'S REGISTERS C* (BUT DON'T RELOAD R0) C SR R15,R15 SET RETURN CODE TO FORTRAN C BR R14 RETURN TO CALLER C*********************************************************************** C* DATA AREAS REQUIRED FOR OPERATION * C*********************************************************************** CALGN0 DS 0D DOUBLEWORD ALIGNMENT REQUIRED CTVAL DC D'0' TIMER VALUE CTVAL2 DC D'0' TIMER VALUE 2 - ("NEW" VALUE) CHOURS1 DC X'000007FF' CHOURS2 DC X'FFFFF000' CSAVEAREA DS 18F 18 WORD REGISTER SAVE AREA C END C C C C C****************************************************************************** C C FOR IBM VM SYSTEMS (Calls following VMTIME assembly code) C C IMPLICIT INTEGER*4 (I-N) C REAL*8 CPUTIM C INTEGER*4 VSEC, VUSEC C C CALL VMTIME (VSEC, VUSEC) C C SECOND = VSEC + VUSEC/1.D6 C C RETURN C END C C********************************************************************** C* * C* this program is a fortran callable routine that returns a * C* result of the diagnose x'c' instruction. * C* * C* FORTRAN CALL: CALL VMTIME(VSEC, VUSEC) * C* * C* where: * C* vsec the virtual cpu time, the seconds portion (i*4) * C* vusec the virtual cpu time, the micro-second portion * C* * C********************************************************************** C CVMTIME START 0 CBEGIN SAVE (14,12) C BALR 3,0 C USING *,3 C ST 13,SAVE+4 C LA 13,SAVE C C LM 4,5,0(1) LOAD THE FORTRAN PLIST INTO REGS C C LA 2,PTIMER C C DIAG 2,0,X'C' C C L 6,VCPU C L 7,VCPU+4 C D 6,=F'1000000' SEPARATE SEC AND USEC C ST 7,0(4) STORE THE SECOND PORTION C ST 6,0(5) STORE THE MICROSECOND PORTION C C C L 13,SAVE+4 C RETURN (14,12),RC=0 C C CPTIMER DS 0D CDATE DS D CURRENT DATE CTIME DS D CURRENT TIME CVCPU DS D VIRTUAL CPU TIME CTCPU DS D TOTAL CPUTIME CSAVE DS 18F C C LTORG C END RETURN END c c c C C*********************************************************************** SUBROUTINE SENSIT( iou, RATES,WG,IQ,SUMW, MAP,TV,TV1,TV2,TV3,n) C*********************************************************************** C * C SENSIT - Sensitivity Of Harmonic Mean Rate(Mflops) 49 Workloads * C * C iou - input scalar, i/o unit number * C RATES - input array , execution rates (Mflops) * C WG - input array , weights paired with RATES * C IQ - input array , 1 or 2 quartiles specifier * C SUMW - input array , workload fractions. * C * C MAP,TV,TV1,TV2,TV3 - output temporary arrays * C n - input scalar, number of rates, etc. * C * C*********************************************************************** C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C c In DIMENSION RATES(n), WG(n), IQ(7), SUMW(7) c Temp DIMENSION MAP(n), TV(n), TV1(n), TV2(n), TV3(n) DIMENSION NR1(10), NR2(10), STAT2(20) c DIMENSION TAG(4) f66 CHARACTER*8 TAG(4) f77 C DATA ( TAG(i), i= 1,4) . /'1st QT: ', '2nd QT: ', '3rd QT: ', '4th QT: '/ f77 c ./8H1st QT: , 8H2nd QT: , 8H3rd QT: , 8H4th QT: / f66 C C Compress valid data sets RATES, mapping on MAP. bl= 1.0D-5 bu= 1.0D+5 CALL VALID( TV1,MAP,neff, bl, RATES, bu, n) DO 1 k= 1,neff TV3(k)= WG( MAP(k)) 1 continue C Compress valid data sets WG, mapping on MAP. CALL VALID( TV3,MAP,meff, bl, TV3, bu, neff) DO 3 k= 1,meff TV(k)=TV1( MAP(k)) 3 continue C C Sort selected rates into descending order CALL SORDID( MAP,TV2, TV,meff,2) C C CALL PAGE( iou) WRITE ( iou,7001) C 7001 FORMAT(/) 7301 FORMAT(9X,31H SENSITIVITY ANALYSIS ) 7302 FORMAT(9X,52HThe sensitivity of the harmonic mean rate (Mflops) ) 7303 FORMAT(9X,52Hto various weightings is shown in the table below. ) 7304 FORMAT(9X,52HSeven work distributions are generated by assigning ) 7305 FORMAT(9X,52Htwo distinct weights to ranked kernels by quartiles.) 7306 FORMAT(9X,52HForty nine possible cpu workloads are then evaluated) 7307 FORMAT(9X,52Husing seven sets of values for the total weights: ) 7341 FORMAT(3X,A ,6X,43HO O O O O X X) f77 7342 FORMAT(3X,A ,6X,43HO O O X X X O) f77 7343 FORMAT(3X,A ,6X,43HO X X X O O O) f77 7344 FORMAT(3X,A ,6X,43HX X O O O O O) f77 c7341 FORMAT(3X,A7,6X,43HO O O O O X X) f66 c7342 FORMAT(3X,A7,6X,43HO O O X X X O) f66 c7343 FORMAT(3X,A7,6X,43HO X X X O O O) f66 c7344 FORMAT(3X,A7,6X,43HX X O O O O O) f66 7346 FORMAT(13X, 48H------ ------ ------ ------ ------ ------ ------) 7348 FORMAT(3X,5HTotal,/,3X,7HWeights,20X,11HNet Mflops:,/,4X,6HX O) 7349 FORMAT(2X,9H---- ---- ) 7220 FORMAT(/,1X,2F5.2,1X,7F7.2) C WRITE ( iou,7001) WRITE ( iou,7001) WRITE ( iou,7301) WRITE ( iou,7001) WRITE ( iou,7302) WRITE ( iou,7303) WRITE ( iou,7304) WRITE ( iou,7305) WRITE ( iou,7306) WRITE ( iou,7307) WRITE ( iou,7001) WRITE ( iou,7346) WRITE ( iou,7341) TAG(1) WRITE ( iou,7342) TAG(2) WRITE ( iou,7343) TAG(3) WRITE ( iou,7344) TAG(4) WRITE ( iou,7346) WRITE ( iou,7348) WRITE ( iou,7349) C IF( meff .LE. 0 ) RETURN fuzz= 1.0e-9 r= meff mq= (meff+3)/4 q= mq j= 1 DO 21 i= 8,2,-2 NR1(i )= j NR1(i+1)= j NR2(i )= j + mq + mq - 1 NR2(i+1)= j + mq - 1 j= j + mq 21 continue C DO 29 j= 1,7 sumo= 1.0 - SUMW(j) DO 27 i= 1,7 p= IQ(i)*q xt= SUMW(j)/(p + fuzz) ot= sumo /(r - p + fuzz) DO 23 k= 1,meff TV3(k)= ot 23 continue k1= NR1(i+2) k2= NR2(i+2) DO 25 k= k1,k2 TV3(k)= xt 25 continue CALL STATW( STAT2,TV,MAP, TV2,TV3,meff) TV1(i)= STAT2(5) 27 continue WRITE ( iou,7220) SUMW(j), sumo, ( TV1(k), k=1,7) 29 continue C WRITE ( iou,7349) WRITE ( iou,7346) C C RETURN C END C*********************************************** SUBROUTINE SIGNAL( V, SCALE,BIAS, n) C*********************************************** C C SIGNAL GENERATES VERY FRIENDLY FLOATING-POINT NUMBERS NEAR 1.0 C WHEN SCALE= 1.0 AND BIAS= 0. C C V - result array, floating-point test data C SCALE - input scalar, scales magnitude of results C BIAS - input scalar, offsets magnitude of results C n - input integer, number of results in V. C C*********************************************** cANSI DOUBLE PRECISION V, SCALE, BIAS cIBM REAL*8 V, SCALE, BIAS c DOUBLE PRECISION SCALED,BIASED,FUZZ,BUZZ,FIZZ,ONE cIBM REAL*16 SCALED,BIASED,FUZZ,BUZZ,FIZZ,ONE C DIMENSION V(n) C SCALED= SCALE BIASED= BIAS C SCALED= 10.00D0 SCALED= 1.00D0/SCALED BIASED= 0.00D0 C C FUZZ= 1.234500D-9 FUZZ= 1.234500D-3 BUZZ= 1.000D0 + FUZZ FIZZ= 1.100D0 * FUZZ ONE= 1.000D0 C DO 1 k= 1,n BUZZ= (ONE - FUZZ)*BUZZ +FUZZ FUZZ= -FUZZ c V(k)=((BUZZ- FIZZ) -BIASED)*SCALED V(k)= (BUZZ- FIZZ)*SCALED 1 CONTINUE C RETURN END C C C*********************************************************************** SUBROUTINE SIMD( HM, iou,RATES,WG,FR,m, MAP,TV1,TV2,TV3,n) C*********************************************************************** C * C SIMD - Sensitivity Of Harmonic Mean Rate(Mflops) SISD/SIMD Model* C * C iou - input scalar, i/o unit number * C RATES - input array , execution rates (Mflops) * C WG - input array , weights paired with RATES * C FR - input array , fractions of flops executed SIMD * C m - input scalar, number of fractions * C * C MAP,TV,TV1,TV2,TV3 - output temporary arrays * C n - input scalar, number of rates, etc. * C * C*********************************************************************** C C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C c SENSITIVITY OF NET MFLOPS RATE TO USE OF OPTIMAL FORTRAN CODE(SISD/SIMD MODEL c Out DIMENSION HM(m) c In DIMENSION FR(m), RATES(n), WG(n) c Temp DIMENSION MAP(n), TV1(n), TV2(n), TV3(n), STAT2(20) C Compress valid data sets RATES, mapping on MAP. bl= 1.0D-5 bu= 1.0D+5 CALL VALID( TV1,MAP,neff, bl, RATES, bu, n) DO 1 k= 1,neff TV3(k)= WG( MAP(k)) 1 continue C Compress valid data sets WG, mapping on MAP. CALL VALID( TV3,MAP,meff, bl, TV3, bu, neff) DO 3 k= 1,meff TV2(k)= TV1( MAP(k)) 3 continue C Sort RATES,WT into descending order. CALL STATW( STAT2,TV1,MAP, TV2, TV3, meff) med= meff + 1 - INT(STAT2(8)) lh= meff + 1 - med DO 5 k= 1,meff TV2(k)= TV3( MAP(k)) 5 continue C Estimate vector rate= HMean of top LFK quartile. nq= meff/4 CALL STATW( STAT2,TV3,MAP, TV1,TV2,nq) vmf= STAT2(5) C Estimate scalar rate= HMean of lowest two LFK quartiles. CALL STATW( STAT2,TV3,MAP, TV1(med),TV2(med),lh) smf= STAT2(5) fuzz= 1.0e-9 g= 1.0 - smf/( vmf + fuzz) HM(1)= smf DO 7 k= 2,m HM(k)= smf/( 1.0 - FR(k)*g + fuzz) 7 continue C IF( iou .GT. 0) THEN C WRITE ( iou,7001) WRITE ( iou,7001) WRITE ( iou,7001) WRITE ( iou,7101) WRITE ( iou,7102) ( HM(k), k= 1,9) WRITE ( iou,7102) ( FR(k), k= 1,9) WRITE ( iou,7103) WRITE ( iou,7001) 7001 FORMAT(/) 7101 FORMAT(' SENSITIVITY OF NET MFLOPS RATE TO USE OF OPTIMAL FORTRAN 1CODE(SISD/SIMD MODEL)' ) 7102 FORMAT(/,1X,5F7.2,4F8.2) 7103 FORMAT(3x,52H Fraction Of Operations Run At Optimal Fortran Rates) C ENDIF C RETURN C END C C C*********************************************** SUBROUTINE SIZES(i) C*********************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C C SIZES test and set the loop controls before each kernel test C C i := kernel number C C mk := number of kernels to test C Nruns:= number of timed runs of complete test. C tic := cpu clock resolution or minimum time in seconds. C Loop := multiple pass control to execute kernel long enough to time. C n := DO loop control for each kernel. C ****************************************************************** C C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= l13/2, l213= l13+l13h, l813= 8*l13 ) C/ PARAMETER( l14=2048, l16= 75, l416= 4*l16 , l21= 25 ) C C/ PARAMETER( l1= 27, l2= 15, l1d= 2*1001 ) C/ PARAMETER( l13= 8, l13h= 8/2, l213= 8+4, l813= 8*8 ) C/ PARAMETER( l14= 16, l16= 15, l416= 4*15 , l21= 15) C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= 64/2, l213= 64+32, l813= 8*64 ) C/ PARAMETER( l14= 2048, l16= 75, l416= 4*75 , l21= 25) C C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C C/ PARAMETER( NNI= 2*l1 +2*l213 +l416 ) C/ PARAMETER( NN1= 16*l1 +13*l2 +2*l416 + l14 ) C/ PARAMETER( NN2= 4*l813 + 3*l21*l2 +121*l2 +3*l13*l13 ) C/ PARAMETER( Nl1= 19*l1, Nl2= 131*l2 +3*l21*l2 ) C/ PARAMETER( Nl13= 3*l13*l13 +34*l13 +32) C C/ PARAMETER( nk= 47, nl= 3, nr= 8 ) C COMMON /ALPHA/ mk,ik,ml,il,Nruns,jr, NPFS(8,3,47) COMMON /BETA / tic, TIMES(8,3,47), SEE(5,3,8,3), 1 TERRS(8,3,47), CSUMS(8,3,47), 2 FOPN(8,3,47), DOS(8,3,47) C C COMMON /SPACES/ ion,j5,k2,k3,Loop,m,kr,it,n13h,ibuf, 1 n,n1,n2,n13,n213,n813,n14,n16,n416,n21,nt1,nt2 C COMMON /SPACER/ A11,A12,A13,A21,A22,A23,A31,A32,A33, 2 AR,BR,C0,CR,DI,DK, 3 DM22,DM23,DM24,DM25,DM26,DM27,DM28,DN,E3,E6,EXPMAX,FLX, 4 Q,QA,R,RI,S,SCALE,SIG,STB5,T,XNC,XNEI,XNM C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C C ****************************************************************** C C C nif= 0 C c Set mk .LE. 47 number of kernels to test. c mk= 14 mk= 24 ml= 3 c Set Nruns .LT. 8 number of timed runs of KERNEL test c Set Nruns= 1 to REDUCE RUN TIME for debug runs. Nruns= 1 c Set Nruns= 7 for Standard BENCHMARK Test. c Nruns= 7 IF( Nruns.GT. 7) Nruns= 7 c Set tic to the minimum Cpu clock resolution time(Sec.) c tic= 1./60. tic= 1.0e-6 C IF( i.EQ.-1) RETURN C C C Domain tests follow to detect overstoring of controls for array opns. C nif= 1 iup= 999000 IF( iup.LT.65000 ) iup= 65000 IF( i.LT.0 .OR. (i-1).GT. 24) GO TO 911 IF( n.LT.0 .OR. n.GT. 1001) GO TO 911 IF(Loop.LT.0 .OR. Loop.GT.iup) GO TO 911 C nif= 2 IF( il.LT.1 .OR. il.GT.3 ) GO TO 911 n= ISPAN(i,il) Loop = IPASS(i,il) * MUL(il) C c C If clock resolution test fails, you must increase Loop= 40*Loop etc. C Standard Checksums in REPORT were obtained with Loop= 10*Loop. C Verify correct execution using these checksums then, if timing C errors are too large, increase the value of Loop: c C Loop= 100*Loop Loop= 10*Loop c Computers with high resolution clocks tic= O(microsec.) should use Loop= 1 C C Loop= 1 C IF( Loop.LT. 1) Loop= 1 nif= 3 IF( n.LT.0 .OR. n.GT. 1001) GO TO 911 IF(Loop.LT.0 .OR. Loop.GT.iup) GO TO 911 n1 = 1001 n2 = 101 n13 = 64 n13h= 32 n213= 96 n813= 512 n14 = 2048 n16 = 75 n416= 300 n21 = 25 C nt1= 16*1001 +13*101 +2*300 + 2048 nt2= 4*512 + 3*25*101 +121*101 +3*64*64 C RETURN C C 911 io= ABS( ion) IF( io.LE.0 .OR. io.GT.100 ) io=6 WRITE( io,913) i, nif, n, Loop, il 913 FORMAT(1H1,///,37H FATAL OVERSTORE/ DATA LOSS. TEST= ,6I6) STOP C END C*********************************************** SUBROUTINE SORDID( i,W, V,n,KIND) C*********************************************** C QUICK AND DIRTY PORTABLE SORT. C C i - RESULT INDEX-LIST. MAPS V TO SORTED W. C W - RESULT ARRAY, SORTED V. C C V - INPUT ARRAY SORTED IN PLACE. C n - INPUT NUMBER OF ELEMENTS IN V C KIND - SORT ORDER: = 1 ASCENDING MAGNITUDE C = 2 DESCENDING MAGNITUDE C C*********************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C DIMENSION i(n), W(n), V(n) C DO 1 k= 1,n W(k)= V(k) 1 i(k)= k C IF( KIND.EQ.2) GO TO 4 C DO 3 j= 1,n-1 m= j DO 2 k= j+1,n IF( W(k).LT.W(m)) m= k 2 CONTINUE X= W(j) k= i(j) W(j)= W(m) i(j)= i(m) W(m)= X i(m)= k 3 CONTINUE RETURN C C 4 DO 6 j= 1,n-1 m= j DO 5 k= j+1,n IF( W(k).GT.W(m)) m= k 5 CONTINUE X= W(j) k= i(j) W(j)= W(m) i(j)= i(m) W(m)= X i(m)= k 6 CONTINUE RETURN END C C*********************************************** SUBROUTINE SPACE C*********************************************** C C SPACE sets memory pointers for array variables. optional. C C Subroutine Space dynamically allocates physical memory space C for the array variables in KERNEL by setting pointer values. C The POINTER declaration has been defined in the IBM PL1 language C and defined as a Fortran extension in Livermore and CRAY compilers. C C In general, large FORTRAN simulation programs use a memory C manager to dynamically allocate arrays to conserve high speed C physical memory and thus avoid slow disk references (page faults). C C It is sufficient for our purposes to trivially set the values C of pointers to the location of static arrays used in common. C The efficiency of pointered (indirect) computation should be measured C if available. C C*********************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= 64/2, l213= 64+32, l813= 8*64 ) C/ PARAMETER( l14= 2048, l16= 75, l416= 4*75 , l21= 25) C INTEGER E,F,ZONE COMMON /ISPACE/ E(96), F(96), 1 IX(1001), IR(1001), ZONE(300) C COMMON /SPACE1/ U(1001), V(1001), W(1001), 1 X(1001), Y(1001), Z(1001), G(1001), 2 DU1(101), DU2(101), DU3(101), GRD(1001), DEX(1001), 3 XI(1001), EX(1001), EX1(1001), DEX1(1001), 4 VX(1001), XX(1001), RX(1001), RH(2048), 5 VSP(101), VSTP(101), VXNE(101), VXND(101), 6 VE3(101), VLR(101), VLIN(101), B5(101), 7 PLAN(300), D(300), SA(101), SB(101) C COMMON /SPACE2/ P(4,512), PX(25,101), CX(25,101), 1 VY(101,25), VH(101,7), VF(101,7), VG(101,7), VS(101,7), 2 ZA(101,7) , ZP(101,7), ZQ(101,7), ZR(101,7), ZM(101,7), 3 ZB(101,7) , ZU(101,7), ZV(101,7), ZZ(101,7), 4 B(64,64), C(64,64), H(64,64), 5 U1(5,101,2), U2(5,101,2), U3(5,101,2) C C ****************************************************************** C C// COMMON /POINT/ ME,MF,MU,MV,MW,MX,MY,MZ,MG,MDU1,MDU2,MDU3,MGRD, C// 1 MDEX,MIX,MXI,MEX,MEX1,MDEX1,MVX,MXX,MIR,MRX,MRH,MVSP,MVSTP, C// 2 MVXNE,MVXND,MVE3,MVLR,MVLIN,MB5,MPLAN,MZONE,MD,MSA,MSB, C// 3 MP,MPX,MCX,MVY,MVH,MVF,MVG,MVS,MZA,MZP,MZQ,MZR,MZM,MZB,MZU, C// 4 MZV,MZZ,MB,MC,MH,MU1,MU2,MU3 C//C C//CLLL. LOC(X) =.LOC.X C//C C// ME = LOC( E ) C// MF = LOC( F ) C// MU = LOC( U ) C// MV = LOC( V ) C// MW = LOC( W ) C// MX = LOC( X ) C// MY = LOC( Y ) C// MZ = LOC( Z ) C// MG = LOC( G ) C// MDU1 = LOC( DU1 ) C// MDU2 = LOC( DU2 ) C// MDU3 = LOC( DU3 ) C// MGRD = LOC( GRD ) C// MDEX = LOC( DEX ) C// MIX = LOC( IX ) C// MXI = LOC( XI ) C// MEX = LOC( EX ) C// MEX1 = LOC( EX1 ) C// MDEX1 = LOC( DEX1 ) C// MVX = LOC( VX ) C// MXX = LOC( XX ) C// MIR = LOC( IR ) C// MRX = LOC( RX ) C// MRH = LOC( RH ) C// MVSP = LOC( VSP ) C// MVSTP = LOC( VSTP ) C// MVXNE = LOC( VXNE ) C// MVXND = LOC( VXND ) C// MVE3 = LOC( VE3 ) C// MVLR = LOC( VLR ) C// MVLIN = LOC( VLIN ) C// MB5 = LOC( B5 ) C// MPLAN = LOC( PLAN ) C// MZONE = LOC( ZONE ) C// MD = LOC( D ) C// MSA = LOC( SA ) C// MSB = LOC( SB ) C// MP = LOC( P ) C// MPX = LOC( PX ) C// MCX = LOC( CX ) C// MVY = LOC( VY ) C// MVH = LOC( VH ) C// MVF = LOC( VF ) C// MVG = LOC( VG ) C// MVS = LOC( VS ) C// MZA = LOC( ZA ) C// MZP = LOC( ZP ) C// MZQ = LOC( ZQ ) C// MZR = LOC( ZR ) C// MZM = LOC( ZM ) C// MZB = LOC( ZB ) C// MZU = LOC( ZU ) C// MZV = LOC( ZV ) C// MZZ = LOC( ZZ ) C// MB = LOC( B ) C// MC = LOC( C ) C// MH = LOC( H ) C// MU1 = LOC( U1 ) C// MU2 = LOC( U2 ) C// MU3 = LOC( U3 ) C RETURN END C*********************************************** SUBROUTINE STATS( STAT, X,n) C*********************************************** C C UNWEIGHTED STATISTICS: MEAN, STADEV, MIN, MAX, HARMONIC MEAN. C C STAT(1)= THE MEAN OF X. C STAT(2)= THE STANDARD DEVIATION OF THE MEAN OF X. C STAT(3)= THE MINIMUM OF X. C STAT(4)= THE MAXIMUM OF X. C STAT(5)= THE HARMONIC MEAN C X IS THE ARRAY OF INPUT VALUES. C n IS THE NUMBER OF INPUT VALUES IN X. C C*********************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C DIMENSION X(n), STAT(9) cLLL. OPTIMIZE LEVEL G C C DO 10 k= 1,9 10 STAT(k)= 0.0 C IF(n.LE.0) RETURN C CALCULATE MEAN OF X. S= 0.0 DO 1 k= 1,n 1 S= S + X(k) A= S/n STAT(1)= A C CALCULATE STANDARD DEVIATION OF X. D= 0.0 DO 2 k= 1,n 2 D= D + (X(k)-A)**2 D= D/n STAT(2)= SQRT(D) C CALCULATE MINIMUM OF X. U= X(1) DO 3 k= 2,n 3 U= MIN(U,X(k)) STAT(3)= U C CALCULATE MAXIMUM OF X. V= X(1) DO 4 k= 2,n 4 V= MAX(V,X(k)) STAT(4)= V C CALCULATE HARMONIC MEAN OF X. H= 0.0 DO 5 k= 1,n IF( X(k).NE.0.0) H= H + 1.0/X(k) 5 CONTINUE IF( H.NE.0.0) H= REAL(n)/H STAT(5)= H C RETURN END C*********************************************** SUBROUTINE STATW( STAT,OX,IX, X,W,n) C*********************************************** C C WEIGHTED STATISTICS: MEAN, STADEV, MIN, MAX, HARMONIC MEAN, MEDIAN. C C STAT( 1)= THE MEAN OF X. C STAT( 2)= THE STANDARD DEVIATION OF THE MEAN OF X. C STAT( 3)= THE MINIMUM OF X. C STAT( 4)= THE MAXIMUM OF X. C STAT( 5)= THE HARMONIC MEAN C STAT( 6)= THE TOTAL WEIGHT. C STAT( 7)= THE MEDIAN. C STAT( 8)= THE MEDIAN INDEX, ASCENDING. C STAT( 9)= THE ROBUST MEDIAN ABSOLUTE DEVIATION. C STAT(10)= THE GEOMETRIC MEAN C STAT(11)= THE MOMENTAL SKEWNESS C STAT(12)= THE KURTOSIS C STAT(13)= THE LOWER QUARTILE BOUND Q1/Q2 VALUE C STAT(14)= THE UPPER QUARTILE BOUND Q3/Q4 VALUE C C OX IS THE ARRAY OF ORDERED (DECENDING) Xs. C IX IS THE ARRAY OF INDEX LIST MAPS X TO OX. C C X IS THE ARRAY OF INPUT VALUES. C W IS THE ARRAY OF INPUT WEIGHTS. C n IS THE NUMBER OF INPUT VALUES IN X. C C*********************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) C DIMENSION STAT(14), OX(n), IX(n), X(n), W(n) cLLL. OPTIMIZE LEVEL G C C DO 50 k= 1,14 50 STAT(k)= 0.0 C IF( n.LE.0 ) RETURN C IF( n.EQ.1 ) THEN STAT( 1)= X(1) STAT( 3)= X(1) STAT( 4)= X(1) STAT( 5)= X(1) STAT( 6)= W(1) STAT( 7)= X(1) STAT( 8)= 1.0 STAT(10)= X(1) RETURN ENDIF C C C CALCULATE MEAN OF X. A= 0.0 S= 0.0 T= 0.0 C DO 1 k= 1,n S= S + W(k)*X(k) 1 T= T + W(k) IF( T.NE.0.0) A= S/T STAT(1)= A C CALCULATE STANDARD DEVIATION OF X. D= 0.0 E= 0.0 F= 0.0 Q= 0.0 U= 0.0 C DO 2 k= 1,n B= W(k) *( X(k) -A)**2 D= D + B E= E + B*( X(k) -A) 2 F= F + B*( X(k) -A)**2 IF( T.NE.0.0) Q= 1.0/T D= D*Q E= E*Q F= F*Q IF( D.GE.0.0) U= SQRT(D) STAT(2)= U C CALCULATE MINIMUM OF X. U= X(1) DO 3 k= 2,n 3 U= MIN(U,X(k)) STAT(3)= U C CALCULATE MAXIMUM OF X. V= X(1) DO 4 k= 2,n 4 V= MAX(V,X(k)) STAT(4)= V C CALCULATE HARMONIC MEAN OF X. H= 0.0 DO 5 k= 1,n IF( X(k).NE.0.0) H= H + W(k)/X(k) 5 CONTINUE IF( H.NE.0.0) H= T/H STAT(5)= H STAT(6)= T C CALCULATE WEIGHTED MEDIAN CALL SORDID( IX, OX, X, n, 1) C ew= 0.0 DO 7 k= 2,n IF( W(1) .NE. W(k)) GO TO 75 7 continue ew= 1.0 75 continue C qt= 0.500D0 CALL TILE( STAT( 7), STAT(8), OX,IX,W,ew,T, qt,n) C qt= 0.250D0 CALL TILE( STAT(13), stin13, OX,IX,W,ew,T, qt,n) C qt= 0.750D0 CALL TILE( STAT(14), stin14, OX,IX,W,ew,T, qt,n) C C C CALCULATE ROBUST MEDIAN ABSOLUTE DEVIATION (MAD) DO 90 k= 1,n 90 OX(k)= ABS( X(k) - STAT(7)) C CALL SORDID( IX, OX, OX, n, 1) C qt= 0.700D0 CALL TILE( STAT( 9), stin09, OX,IX,W,ew,T, qt,n) C C CALCULATE GEOMETRIC MEAN R= 0.0 DO 10 k= 1,n IF( X(k).LE. 0.) GO TO 10 R= R + W(k) *ALOG10( X(k)) 10 CONTINUE U= R*Q G= 10.0 IF( U.LT. 0.) G= 0.1 POWTEN= 50.0 IF( ABS(U) .GT. POWTEN) U= SIGN( POWTEN, U) STAT(10)= G** ABS(U) C C CALCULATE MOMENTAL SKEWNESS G= 0.0 DXD= D*D IF( DXD.NE.0.0) G= 1.0/(DXD) STAT(11)= 0.5*E*G*STAT(2) C C CALCULATE KURTOSIS STAT(12)= 0.5*( F*G -3.0) C C CALCULATE DESCENDING ORDERED X. CALL SORDID( IX, OX, X, n, 2) C RETURN END C C*********************************************** FUNCTION SUMO( V,n) C*********************************************** C C CHECK-SUM WITH ORDINAL DEPENDENCY. C C V - input array, floating-point numbers C n - input integer, number of elements in V. C C*********************************************** cANSI DOUBLE PRECISION SUMO, V cIBM REAL*8 SUMO, V c DOUBLE PRECISION S cIBM REAL*16 S C DIMENSION V(1) S= 0.00D0 C DO 1 k= 1,n 1 S= S + REAL(k)*V(k) SUMO = S RETURN END C C*********************************************** SUBROUTINE SUPPLY(i) C*********************************************** C C SUPPLY initializes common blocks containing type real arrays. C C i := kernel number C C**************************************************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= 64/2, l213= 64+32, l813= 8*64 ) C/ PARAMETER( l14= 2048, l16= 75, l416= 4*75 , l21= 25) C C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C/C C/C/ PARAMETER( NN0= 39 ) C/C/ PARAMETER( NNI= 2*l1 +2*l213 +l416 ) C/C/ PARAMETER( NN1= 16*l1 +13*l2 +2*l416 + l14 ) C/C/ PARAMETER( NN2= 4*512 + 3*25*101 +121*101 +3*64*64 ) C COMMON /SPACES/ ion,j5,k2,k3,Loop,m,kr,it,n13h,ibuf, 1 n,n1,n2,n13,n213,n813,n14,n16,n416,n21,nt1,nt2 C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C C/ COMMON /SPACE1/ U(NN1) C/ COMMON /SPACE2/ P(NN2) C/ COMMON /SPACER/ A11(NN0) C/C COMMON /SPACE1/ U(19977) COMMON /SPACE2/ P(34132) COMMON /SPACER/ A11(39) C C C*********************************************************************** C Method 1: Least space and most cpu time (D.P. SIGNAL arith) C*********************************************************************** C Csmall IP1= i+1 Csmall nt0= 39 CsmallC Csmall CALL SIGNAL( U, SKALE(IP1), BIAS(IP1), nt1) Csmall CALL SIGNAL( P, SKALE(IP1), BIAS(IP1), nt2) Csmall CALL SIGNAL(A11, SKALE(IP1), BIAS(IP1), nt0) Csmall RETURN C C*********************************************************************** C Method 2: Double space and least cpu time C*********************************************************************** C COMMON /BASE1/ BUFU(19977) COMMON /BASE2/ BUFP(34132) COMMON /BASER/ BUFA(39) C IP1= i+1 nt0= 39 C Execute SIGNAL calls only once; re-use generated data. ibuf= ibuf+1 IF( ibuf.EQ. 1) THEN CALL SIGNAL( BUFU, SKALE(IP1), BIAS(IP1), nt1) CALL SIGNAL( BUFP, SKALE(IP1), BIAS(IP1), nt2) CALL SIGNAL( BUFA, SKALE(IP1), BIAS(IP1), nt0) ENDIF C DO 1 k= 1,nt0 1 A11(k)= BUFA(k) DO 2 k= 1,nt1 2 U(k)= BUFU(k) DO 3 k= 1,nt2 3 P(k)= BUFP(k) C RETURN END C C*********************************************************************** SUBROUTINE TALLY( iou, mode ) C*********************************************************************** C * C TALLY computes average and minimum Cpu timings and variances.* C * C iou - i/o unit number * C * C mode - = 1 selects average run time: Preferred mode. * C = 2 selects minimum run time: Less accurate mode* C * C*********************************************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION cs C C/ PARAMETER( nk= 47, nl= 3, nr= 8 ) C COMMON /ALPHA/ mk,ik,ml,il,Nruns,jr, NPFS(8,3,47) COMMON /BETA / tic, TIMES(8,3,47), SEE(5,3,8,3), 1 TERRS(8,3,47), CSUMS(8,3,47), 2 FOPN(8,3,47), DOS(8,3,47) C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C DIMENSION S1(12), S2(12), S3(12), S4(12) DIMENSION T1(47), T4(47) C CALL SIZES(-1) C m= 1 IF( mode .EQ. 2 ) m= 3 C IF( jr .LT. 1) jr= 1 IF( jr .GE. 8) jr= 8-1 IF( Nruns .LT. 1) Nruns= 1 IF( Nruns .GE. 8) Nruns= 8-1 IF( il .LT. 1) il= 1 IF( il .GT. 3) il= 3 IF( mk .LT. 1) mk= 1 IF( mk .GT. 24) mk= 24 C CALL PAGE(iou) WRITE( iou, 99) WRITE( iou,100) C DO 2 j= 1,Nruns WRITE( iou,102) j, ( SEE(k,1,j,il), k= 1,4) T1(j)= SEE(1,1,j,il) i= 0 IF( (SEE(3,2,j,il).LT. 0.01) .OR. (SEE(4,2,j,il).GT. 1.0)) i= i+1 IF( (SEE(3,3,j,il).LT. 0.01) .OR. (SEE(4,3,j,il).GT. 1.0)) i= i+1 IF( i.GT.0 ) THEN WRITE( iou,131) j, il ENDIF IF( ( j.EQ.Nruns ) .OR. ( i.GT.0 )) THEN WRITE( iou,104) j, ( SEE(k,2,j,il), k= 1,4) WRITE( iou,104) j, ( SEE(k,3,j,il), k= 1,4) ENDIF 2 continue C CALL STATS( S1, T1, Nruns) WRITE( iou,102) Nruns, ( S1(k), k= 1,4) C C C WRITE( iou,120) Nruns WRITE( iou,122) WRITE( iou,121) WRITE( iou,122) C DO 8 k= 1,mk npft= 0 cs= 0.0 C DO 4 j= 1,Nruns npft= npft + NPFS(j,il,k) cs= cs + CSUMS(j,il,k) 4 continue C CALL STATS( S2, TIMES(1,il,k), Nruns) TIME(k)= S2(m) CSUM(k)= cs TERR1(k)= 100.0*( S2(2)/( S2(1) + 1.0e-9)) T4(k)= TERR1(k) C C C If this clock resolution test fails, you must increase Loop (Subr. SIZES) C CALL STATS( S3, TERRS(1,il,k), Nruns) IF( S3(1) .GT. 15.0) THEN WRITE( iou,113) k ENDIF C WRITE( iou,123) k, S2(3), S2(1), S2(4), TERR1(k), S3(1), npft TERR1(k)= MAX( TERR1(k), S3(1)) CALL STATS( S1, DOS(1,il,k), Nruns) TOTAL(k)= S1(1) IF( (S1(1).LE.0.) .OR. (ABS(S1(3)-S1(4)).GT.1.0E-5)) THEN WRITE( iou,131) il, k, ( S1(k4), k4= 1,4) ENDIF CALL STATS( S4, FOPN(1,il,k), Nruns) FLOPN(k)= S4(1) IF( (S4(1).LE.0.) .OR. (ABS(S4(3)-S4(4)).GT.1.0E-5)) THEN WRITE( iou,131) il, k, ( S4(k4), k4= 1,4) ENDIF 8 continue C WRITE( iou,122) CALL STATS( S4, T4, mk) WRITE( iou,124) WRITE( iou,133) WRITE( iou,125) ( S4(k), k= 1,4) C RETURN C 99 FORMAT(//,29H CPU CLOCK OVERHEAD (t err): ) 100 FORMAT(/,6X,3HRUN,8X,7HAVERAGE,8X,7HSTANDEV,8X,7HMINIMUM,8X, 1 7HMAXIMUM ) 102 FORMAT(1X,5HTICK ,I3,4E15.6) 104 FORMAT(1X,5HDATA ,I3,4E15.6) 113 FORMAT(/,1X,I2,45H POOR CPU CLOCK RESOLUTION; NEED LONGER RUN. ) 120 FORMAT(//,39H THE EXPERIMENTAL TIMING ERRORS FOR ALL,I3,5H RUNS) 121 FORMAT(55H k T min T avg T max T err tick P-F) 122 FORMAT(55H -- --------- --------- --------- ----- ----- ---) 123 FORMAT(1X,I2,3E11.4,F6.2,1H%,F6.2,1H%,1X,I5) 124 FORMAT(//,50H NET CPU TIMING VARIANCE (T err); A few % is ok: ) 125 FORMAT(4X,5H Terr,4(F14.2,1H%)) 131 FORMAT(1X,25H** ERROR: INVALID DATA** ,2I6,4E14.6) 133 FORMAT(/,17X,7HAVERAGE,8X,7HSTANDEV,8X,7HMINIMUM,8X,7HMAXIMUM ) END C C*********************************************** SUBROUTINE TDIGIT( derr, nzd, s ) C*********************************************************************** C * C TDIGIT - Count Lead Digits Followed By Trailing Zeroes. * C * C derr - Result, Digital Error in percent. * C nzd - Result, Number Of Lead Digits * C s - Input , A Floated Integer * C * C*********************************************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C frac(z)= (ABS(z) - REAL(INT(ABS(z)))) C n= 14 x= ABS(s) fuzz= 1.0e-6 derr= 100. nzd= 0 IF( x.EQ. 0.0) RETURN C Normalize x y= ALOG10(x) v= REAL( 10**( ABS( INT(y)) + 1 )) IF( (y.GE. 0.0) .AND. (v.NE. 0.0)) v= 10./v x= x*v C Multiply x Until Trailing Digits= Fuzz DO 1 k= 1,n IF( ((1.-frac(x)).LE.fuzz) .OR. (frac(x).LE.fuzz)) GO TO 2 x= 10.*x 1 continue C 2 IF( x.NE. 0.0) derr= 50./x IF( x.NE. 0.0) nzd= INT( ALOG10( ABS( 9.99999*x ))) C RETURN END C C*********************************************** SUBROUTINE TEST(i) C*********************************************** C C TIME, TEST, AND INITIALIZE THE EXECUTION OF KERNEL i. C C****************************************************************************** C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C C SIZES test and set the loop controls before each kernel test C C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= l13/2, l213= l13+l13h, l813= 8*l13 ) C/ PARAMETER( l14=2048, l16= 75, l416= 4*l16 , l21= 25 ) C C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C COMMON /SPACES/ ion,j5,k2,k3,Loop,m,kr,it,n13h,ibuf, 1 n,n1,n2,n13,n213,n813,n14,n16,n416,n21,nt1,nt2 C COMMON /SPACER/ A11,A12,A13,A21,A22,A23,A31,A32,A33, 2 AR,BR,C0,CR,DI,DK, 3 DM22,DM23,DM24,DM25,DM26,DM27,DM28,DN,E3,E6,EXPMAX,FLX, 4 Q,QA,R,RI,S,SCALE,SIG,STB5,T,XNC,XNEI,XNM C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C INTEGER E,F,ZONE COMMON /ISPACE/ E(96), F(96), 1 IX(1001), IR(1001), ZONE(300) C COMMON /SPACE1/ U(1001), V(1001), W(1001), 1 X(1001), Y(1001), Z(1001), G(1001), 2 DU1(101), DU2(101), DU3(101), GRD(1001), DEX(1001), 3 XI(1001), EX(1001), EX1(1001), DEX1(1001), 4 VX(1001), XX(1001), RX(1001), RH(2048), 5 VSP(101), VSTP(101), VXNE(101), VXND(101), 6 VE3(101), VLR(101), VLIN(101), B5(101), 7 PLAN(300), D(300), SA(101), SB(101) C C COMMON /SPACE2/ P(4,512), PX(25,101), CX(25,101), 1 VY(101,25), VH(101,7), VF(101,7), VG(101,7), VS(101,7), 2 ZA(101,7) , ZP(101,7), ZQ(101,7), ZR(101,7), ZM(101,7), 3 ZB(101,7) , ZU(101,7), ZV(101,7), ZZ(101,7), 4 B(64,64), C(64,64), H(64,64), 5 U1(5,101,2), U2(5,101,2), U3(5,101,2) C C REAL SECOND C C****************************************************************************** C t= second(0) := cumulative cpu time for task in seconds. C TEMPUS= SECOND(0.0) - START C cLLNL call ENDPFM C$C 5 get number of page faults (optional) C$ KSTAT= LIB$STAT_TIMER(5,KPF) C$ NPF = KPF - IPF NN= n NP= Loop Loop= 0 ik= i IF( i.LT.0 .OR. i.GT.kr ) GO TO 200 IF( i.EQ.0 ) GO TO 100 CALL SIZES(i) C Net Time= Timing - Overhead Time TIME(i)= TEMPUS - ticks IF( it.EQ.23456) GO TO 200 C GO TO( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, . 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, . 21, 22, 23, 24, 25 ), i C C C C****************************************************************************** C 1 CSUM (1) = SUMO ( X, n) TOTAL(1) = NP*NN GO TO 100 C C****************************************************************************** C 2 CSUM (2) = SUMO ( X, n) TOTAL(2) = NP*(NN-4) GO TO 100 C C****************************************************************************** C 3 CSUM (3) = Q TOTAL(3) = NP*NN GO TO 100 C C****************************************************************************** C 4 MM= (1001-7)/2 DO 400 k = 7,1001,MM 400 V(k)= X(k) CSUM (4) = SUMO ( V, 3) TOTAL(4) = NP*(((NN-5)/5)+1)*3 GO TO 100 C C****************************************************************************** C 5 CSUM (5) = SUMO ( X(2), n-1) TOTAL(5) = NP*(NN-1) GO TO 100 C C****************************************************************************** C 6 CSUM (6) = SUMO ( W, n) TOTAL(6) = NP*NN*((NN-1)/2) GO TO 100 C C****************************************************************************** C 7 CSUM (7) = SUMO ( X, n) TOTAL(7) = NP*NN GO TO 100 C C****************************************************************************** C 8 CSUM (8) = SUMO ( U1,5*n*2) + SUMO ( U2,5*n*2) + SUMO ( U3,5*n*2) TOTAL(8) = NP*(NN-1)*2 GO TO 100 C C****************************************************************************** C 9 CSUM (9) = SUMO ( PX, 15*n) TOTAL(9) = NP*NN GO TO 100 C C****************************************************************************** C 10 CSUM (10) = SUMO ( PX, 15*n) TOTAL(10) = NP*NN GO TO 100 C C****************************************************************************** C 11 CSUM (11) = SUMO ( X(2), n-1) TOTAL(11) = NP*(NN-1) GO TO 100 C C****************************************************************************** C 12 CSUM (12) = SUMO ( X, n-1) TOTAL(12) = NP*NN GO TO 100 C C****************************************************************************** C 13 CSUM (13) = SUMO ( P, 8*n) + SUMO ( H, 8*n) TOTAL(13) = NP*NN GO TO 100 C C****************************************************************************** C 14 CSUM (14) = SUMO ( VX,n) + SUMO ( XX,n) + SUMO ( RH,67) TOTAL(14) = NP*NN GO TO 100 C C****************************************************************************** C 15 CSUM (15) = SUMO ( VY, n*7) + SUMO ( VS, n*7) TOTAL(15) = NP*(NN-1)*5 GO TO 100 C C****************************************************************************** C 16 CSUM (16) = REAL( k3+k2+j5+m) FLOPN(16) = k2+k2+10*k3 TOTAL(16) = 1. GO TO 100 C C****************************************************************************** C 17 CSUM (17) = SUMO ( VXNE, n) + SUMO ( VXND, n) + XNM TOTAL(17) = NP*NN GO TO 100 C C****************************************************************************** C 18 CSUM (18) = SUMO ( ZR, n*7) + SUMO ( ZZ, n*7) TOTAL(18) = NP*(NN-1)*5 GO TO 100 C C****************************************************************************** C 19 CSUM (19) = SUMO ( B5, n) + STB5 TOTAL(19) = NP*NN GO TO 100 C C****************************************************************************** C 20 CSUM (20) = SUMO ( XX(2), n) TOTAL(20) = NP*NN GO TO 100 C C****************************************************************************** C 21 CSUM (21) = SUMO ( PX, 25*n) TOTAL(21) = NP*25*25*NN GO TO 100 C C****************************************************************************** C 22 CSUM (22) = SUMO ( W, n) TOTAL(22) = NP*NN GO TO 100 C C****************************************************************************** C 23 CSUM (23) = SUMO ( ZA, n*7) TOTAL(23) = NP*(NN-1)*5 GO TO 100 C C****************************************************************************** C 24 CSUM (24) = REAL(m) TOTAL(24) = NP*(NN-1) GO TO 100 C C****************************************************************************** C 25 CONTINUE GO TO 100 C C****************************************************************************** C 100 CONTINUE C CALL SIZES (i+1) C it = 23456 IF( it.EQ.23456) GO TO 120 IF( i.EQ.0 ) GO TO 120 TERR0= 100.0 IF( TEMPUS.NE. 0.0) TERR0= TERR0*(ticks/TEMPUS) TERR1(i)= TERR0 NPFS1(i)= NPF IF( ion .LE. 0 ) GO TO 120 C C If this clock resolution test fails, you must increase Loop (Subr. SIZES) C IF( TERR0 .LT. 15.0) GO TO 114 WRITE( ion,113) I 113 FORMAT(/,1X,I2,45H INACCURATE TIMING OR ERROR. NEED LONGER RUN ) C 114 WRITE ( ion,115) i, TEMPUS, TERR0, NPF 115 FORMAT( 2X,i2,9H Done T= ,E11.4,8H T err= ,F8.2,1H% , 1 I8,13H Page-Faults ) C 120 CALL VALUES(i) CALL SIZES (i+1) C C The following pause can be used for stop-watch timing of each kernel. C You may have to increase the iteration count Loop in Subr. SIZES. C C/ pause 200 CONTINUE C IF( jr .LT. 1) jr= 1 IF( jr .GE. 8) jr= 8-1 IF( Nruns .LT. 1) Nruns= 1 IF( Nruns .GE. 8) Nruns= 8-1 IF( il .LT. 1) il= 1 IF( il .GT. 3) il= 3 IF( mk .LT. 1) mk= 1 IF( mk .GT. 24) mk= 24 C C C$C 5 get number of page faults (optional) C$ NSTAT= LIB$STAT_TIMER(5,IPF) cLLNL call PFM( 0, ion) C ik= i+1 START= SECOND(0.0) RETURN C C$ DATA IPF/0/, KPF/0/ END C C*********************************************** FUNCTION TICK( iou ) C*********************************************** C C TICK measures timing overhead of subroutine test C C iou - Logical Output Device Number * C C*********************************************** C cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= l13/2, l213= l13+l13h, l813= 8*l13 ) C/ PARAMETER( l14=2048, l16= 75, l416= 4*l16 , l21= 25 ) C C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C C/ PARAMETER( nk= 47, nl= 3, nr= 8 ) C COMMON /ALPHA/ mk,ik,ml,il,Nruns,jr, NPFS(8,3,47) COMMON /BETA / tic, TIMES(8,3,47), SEE(5,3,8,3), 1 TERRS(8,3,47), CSUMS(8,3,47), 2 FOPN(8,3,47), DOS(8,3,47) C C COMMON /SPACES/ ion,j5,k2,k3,Loop,m,kr,it,n13h,ibuf, 1 n,n1,n2,n13,n213,n813,n14,n16,n416,n21,nt1,nt2 C COMMON /SPACER/ A11,A12,A13,A21,A22,A23,A31,A32,A33, 2 AR,BR,C0,CR,DI,DK, 3 DM22,DM23,DM24,DM25,DM26,DM27,DM28,DN,E3,E6,EXPMAX,FLX, 4 Q,QA,R,RI,S,SCALE,SIG,STB5,T,XNC,XNEI,XNM C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C INTEGER E,F,ZONE COMMON /ISPACE/ E(96), F(96), 1 IX(1001), IR(1001), ZONE(300) C COMMON /SPACE1/ U(1001), V(1001), W(1001), 1 X(1001), Y(1001), Z(1001), G(1001), 2 DU1(101), DU2(101), DU3(101), GRD(1001), DEX(1001), 3 XI(1001), EX(1001), EX1(1001), DEX1(1001), 4 VX(1001), XX(1001), RX(1001), RH(2048), 5 VSP(101), VSTP(101), VXNE(101), VXND(101), 6 VE3(101), VLR(101), VLIN(101), B5(101), 7 PLAN(300), D(300), SA(101), SB(101) C COMMON /SPACE2/ P(4,512), PX(25,101), CX(25,101), 1 VY(101,25), VH(101,7), VF(101,7), VG(101,7), VS(101,7), 2 ZA(101,7) , ZP(101,7), ZQ(101,7), ZR(101,7), ZM(101,7), 3 ZB(101,7) , ZU(101,7), ZV(101,7), ZZ(101,7), 4 B(64,64), C(64,64), H(64,64), 5 U1(5,101,2), U2(5,101,2), U3(5,101,2) C C C DIMENSION TSEC(16), MAP(47) C ion= iou kr = mk n = 0 Loop = 0 k2 = 0 k3 = 0 it = 23456 m = 0 ticks= 0.0 C C CALL TEST(0) CALL TEST(1) CALL TEST(2) CALL TEST(3) CALL TEST(4) CALL TEST(5) CALL TEST(6) CALL TEST(7) CALL TEST(8) it = 0 C DO 10 k= 1,8 10 TSEC(k)= TIME(k) C bl= 0.00D0 bu= 10.00D0 CALL VALID( TIME,MAP,neff, bl, TSEC, bu, 8) CALL STATS( SEE(1,1,jr,il), TIME, neff) c ticks= MAX( tic, SEE(1,1,jr,il)) ticks= SEE(1,1,jr,il) TICK= ticks C DO 20 k= 1,47 TIME(k)= 0.0 CSUM(k)= 0.0 20 CONTINUE C CALL STATS( SEE(1,2,jr,il), U, nt1) CALL STATS( SEE(1,3,jr,il), P, nt2) C mmin= 1 mmax= 1001 CALL IQRANF( IX, mmin, mmax, 1001) c C IF( iou.LE.0) GO TO 73 WRITE( iou, 99) WRITE( iou,100) WRITE( iou,102) ( SEE(k,1,jr,il), k= 1,4) WRITE( iou,104) ( SEE(k,2,jr,il), k= 1,4) WRITE( iou,104) ( SEE(k,3,jr,il), k= 1,4) C 73 RETURN C 99 FORMAT(//,17H CLOCK OVERHEAD: ) 100 FORMAT(/,14X,7HAVERAGE,8X,7HSTANDEV,8X,7HMINIMUM,8X,7HMAXIMUM ) 102 FORMAT(/,1X,5H TICK,4E15.6) 104 FORMAT(/,1X,5H DATA,4E15.6) END C C*********************************************** SUBROUTINE TILE( sm, si, OX,IX,W,ew,T,tiles,n) C*********************************************** C C TILE computes m-tile value and corresponding index C C sm - RESULT VALUE IS m-TILE VALUE C si - RESULT VALUE IS CORRESPONDING INDEX.r IN W C C OX - INPUT ARRAY OF ORDERED (DECENDING) Xs. C IX - INPUT ARRAY OF INDEX LIST MAPS X TO OX. C W - INPUT ARRAY OF INPUT WEIGHTS. C ew - INPUT VALUE FLAGS EQUAL WEIGHTS= 1.0; ELSE 0.0 C T - INPUT VALUE IS SUM OF WEIGHTS C tiles - INPUT VALUE IS FRACTION OF RANGE, E.G. 0.25 C n - INPUT NUMBER OF INPUT VALUES IN X. C C*********************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C DIMENSION OX(n), IX(n), W(n) C C thresh= tiles*T + 0.50*ew*W(1) R= 0.0 DO 70 k= 1,n S= R R= R + W( IX(k)) IF( R .GT. thresh ) GO TO 7 70 CONTINUE k= n 7 z= 0.0 y= 0.0 IF( k.GT.1 ) y = OX(k-1) IF( R.NE.S ) z = ( thresh - S)/( R - S) sm= y + z * ( OX(k) - y) si= REAL(k-1) + z C RETURN END C C*********************************************** SUBROUTINE VALID( VX,MAP,L, BL,X,BU,n ) C*********************************************** C C Compress valid data sets; form compression list. C C C VX - ARRAY OF RESULT COMPRESSED Xs. C MAP - ARRAY OF RESULT COMPRESSION INDICES C L - RESULT COMPRESSED LENGTH OF VX, MAP C - C BL - INPUT LOWER BOUND FOR VX C X - ARRAY OF INPUT VALUES. C BU - INPUT UPPER BOUND FOR VX C n - NUMBER OF INPUT VALUES IN X. C C*********************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C DIMENSION VX(n), MAP(n), X(n) CLLL. OPTIMIZE LEVEL G C m= 0 DO 1 k= 1,n IF( X(k).LE. BL .OR. X(k).GE. BU ) GO TO 1 m= m + 1 MAP(m)= k VX(m)= X(k) 1 CONTINUE C L= m RETURN END C C*********************************************** SUBROUTINE VALUES(i) C*********************************************** C C VALUES initializes special values C C i := kernel number C C**************************************************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION DS, DW C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= 64/2, l213= 64+32, l813= 8*64 ) C/ PARAMETER( l14= 2048, l16= 75, l416= 4*75 , l21= 25) C C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C COMMON /SPACES/ ion,j5,k2,k3,Loop,m,kr,it,n13h,ibuf, 1 n,n1,n2,n13,n213,n813,n14,n16,n416,n21,nt1,nt2 C COMMON /SPACER/ A11,A12,A13,A21,A22,A23,A31,A32,A33, 2 AR,BR,C0,CR,DI,DK, 3 DM22,DM23,DM24,DM25,DM26,DM27,DM28,DN,E3,E6,EXPMAX,FLX, 4 Q,QA,R,RI,S,SCALE,SIG,STB5,T,XNC,XNEI,XNM C COMMON /SPACE0/ TIME(47), CSUM(47), WW(47), WT(47), ticks, 1 FR(9), TERR1(47), SUMW(7), START, 2 SKALE(47), BIAS(47), WS(95), TOTAL(47), FLOPN(47), 3 IQ(7), NPF, NPFS1(47) C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C INTEGER E,F,ZONE COMMON /ISPACE/ E(96), F(96), 1 IX(1001), IR(1001), ZONE(300) C COMMON /SPACE1/ U(1001), V(1001), W(1001), 1 X(1001), Y(1001), Z(1001), G(1001), 2 DU1(101), DU2(101), DU3(101), GRD(1001), DEX(1001), 3 XI(1001), EX(1001), EX1(1001), DEX1(1001), 4 VX(1001), XX(1001), RX(1001), RH(2048), 5 VSP(101), VSTP(101), VXNE(101), VXND(101), 6 VE3(101), VLR(101), VLIN(101), B5(101), 7 PLAN(300), D(300), SA(101), SB(101) C COMMON /SPACE2/ P(4,512), PX(25,101), CX(25,101), 1 VY(101,25), VH(101,7), VF(101,7), VG(101,7), VS(101,7), 2 ZA(101,7) , ZP(101,7), ZQ(101,7), ZR(101,7), ZM(101,7), 3 ZB(101,7) , ZU(101,7), ZV(101,7), ZZ(101,7), 4 B(64,64), C(64,64), H(64,64), 5 U1(5,101,2), U2(5,101,2), U3(5,101,2) C COMMON /SPACE3/ CACHE(8192) C C ****************************************************************** C IP1= i+1 C CALL SUPPLY( i) C 13 IF( IP1.NE.13 ) GO TO 14 DS= 1.000D0 DW= 0.500D0 DO 205 j= 1,4 DO 205 k= 1,512 P(j,k) = DS DS= DS + DW 205 CONTINUE C DO 210 j= 1,96 E(j) = 1 F(j) = 1 210 CONTINUE C 14 IF( IP1.NE.14) GO TO 16 C mmin= 1 mmax= 1001 CALL IQRANF( IX, mmin, mmax, 1001) c DW= -100.000D0 DO 215 J= 1,1001 DEX(J) = DW*DEX(J) GRD(J) = IX(J) 215 CONTINUE FLX= 0.00100D0 C 16 IF( IP1.NE.16 ) GO TO 73 CONDITIONS: MC= 2 lr= n II= lr/3 LB= II+II FW= 1.000D-4 D(1)= 1.0198048642876400D0 DO 400 k= 2,300 400 D(k)= D(k-1) + FW/D(k-1) R= D(lr) FW= 1.000D0 DO 403 L= 1,MC m= (lr+lr)*(L-1) DO 401 j= 1,2 DO 401 k= 1,lr m= m+1 S= REAL(k) PLAN(m)= R*((S + FW)/S) 401 ZONE(m)= k+k 403 CONTINUE k= lr+lr+1 ZONE(k)= lr S= D(lr-1) T= D(lr-2) C 73 CONTINUE c Clear the scalar Cache-memory with never used data-set. c fw= 1.000D0 c CALL SIGNAL( CACHE, fw, 0.0, 8192) c CACHE(1 )= 0.0 CACHE(5 )= 0.0 DO 520 k= 9,8192,8 CACHE(k )= CACHE(k-4) + 0.1 CACHE(k+4)= CACHE(k ) + 0.1 520 CONTINUE C RETURN END C C*********************************************** SUBROUTINE VERIFY( iou) C*********************************************************************** C * C VERIFY auxiliary test routine to check-out function SECOND * C and to verify that sufficiently long Loop sizes are * C defined in Subr. SIZES for accurate CPU timing. * C * C iou - Logical Output Device Number * C * C*********************************************************************** cANSI IMPLICIT DOUBLE PRECISION (A-H,O-Z) cIBM IMPLICIT REAL*8 (A-H,O-Z) C C C/ PARAMETER( l1= 1001, l2= 101, l1d= 2*1001 ) C/ PARAMETER( l13= 64, l13h= 64/2, l213= 64+32, l813= 8*64 ) C/ PARAMETER( l14= 2048, l16= 75, l416= 4*75 , l21= 25) C/ PARAMETER( kn= 47, kn2= 95, np= 3, ls= 3*47, krs= 24) C C COMMON /SPACE1/ U(1001), V(1001), W(1001), 1 X(1001), Y(1001), Z(1001), G(1001), 2 DU1(101), DU2(101), DU3(101), GRD(1001), DEX(1001), 3 XI(1001), EX(1001), EX1(1001), DEX1(1001), 4 VX(1001), XX(1001), RX(1001), RH(2048), 5 VSP(101), VSTP(101), VXNE(101), VXND(101), 6 VE3(101), VLR(101), VLIN(101), B5(101), 7 PLAN(300), D(300), SA(101), SB(101) C COMMON /SPACE2/ P(4,512), PX(25,101), CX(25,101), 1 VY(101,25), VH(101,7), VF(101,7), VG(101,7), VS(101,7), 2 ZA(101,7) , ZP(101,7), ZQ(101,7), ZR(101,7), ZM(101,7), 3 ZB(101,7) , ZU(101,7), ZV(101,7), ZZ(101,7), 4 B(64,64), C(64,64), H(64,64), 5 U1(5,101,2), U2(5,101,2), U3(5,101,2) C COMMON /ALPHA/ mk,ik,ml,il,Nruns,jr, NPFS(8,3,47) C COMMON /SPACES/ ion,j5,k2,k3,Loop,m,kr,it,n13h,ibuf, 1 n,n1,n2,n13,n213,n813,n14,n16,n416,n21,nt1,nt2 C COMMON /SPACEI/ WTP(3), MUL(3), ISPAN(47,3), IPASS(47,3) C C DIMENSION TIM(20), TUM(20), TAV(20), TER(20), TMX(20) DIMENSION LEN(20), SIG(20) C C C C C C C C C C C C C C**************************************************************************** C VERIFY ADEQUATE Loop SIZE VERSUS CPU CLOCK ACCURACY C**************************************************************************** C C VERIFY produced the following output on CRAY-XMP4 in a C fully loaded, multi-processing, multi-programming system: C C C VERIFY ADEQUATE Loop SIZE VERSUS CPU CLOCK ACCURACY C ----- ------- ------- ------- -------- C EXTRA MAXIMUM DIGITAL DYNAMIC RELATIVE C Loop CPUTIME CLOCK CLOCK TIMING C SIZE SECONDS ERROR ERROR ERROR C ----- ------- ------- ------- -------- C 1 5.0000e-06 10.00% 17.63% 14.26% C 2 7.0000e-06 7.14% 6.93% 4.79% C 4 1.6000e-05 3.12% 6.56% 7.59% C 8 2.8000e-05 1.79% 2.90% 2.35% C 16 6.1000e-05 0.82% 6.72% 4.50% C 32 1.1700e-04 0.43% 4.21% 4.62% C 64 2.2700e-04 0.22% 3.13% 2.41% C 128 4.4900e-04 0.11% 3.14% 0.96% C 256 8.8900e-04 0.06% 2.06% 2.50% C 512 1.7740e-03 0.03% 1.92% 1.59% C 1024 3.4780e-03 0.01% 0.70% 1.63% C 1360 Current Run: Loop= 10.000*Loop C 2048 7.0050e-03 0.01% 0.74% 1.28% C 4096 1.3823e-02 0.00% 1.35% 0.78% C ----- ------- ------- ------- -------- C C Approximate Serial Job Time= 2.5e+01 Sec. ( Nruns= 7 RUNS) C C**************************************************************************** c c DO 1 k = 1,101 X(k)= 0.0 1 CX(1,k)= 0.0 C t0= SECOND(0.0) to= SECOND(0.0) - t0 C il= 2 CALL SIZES(12) C loops= IPASS(12,il)*MUL(il) scale= REAL(Loop)/( REAL(loops) - 1.0e-6) WRITE( iou,45) WRITE( iou,49) WRITE( iou,46) WRITE( iou,47) WRITE( iou,48) WRITE( iou,49) 45 FORMAT(8X,51HVERIFY ADEQUATE Loop SIZE VERSUS CPU CLOCK ACCURACY) 46 FORMAT(8X,'EXTRA MAXIMUM DIGITAL DYNAMIC RELATIVE') 47 FORMAT(8X,'Loop CPUTIME CLOCK CLOCK TIMING ') 48 FORMAT(8X,'SIZE SECONDS ERROR ERROR ERROR ') 49 FORMAT(8X,'----- ------- ------- ------- --------') C C C**************************************************************************** C Test Cpu Clock Timing Errors As A Function Of Loop Size(lo) C**************************************************************************** C m= 0 lo= 1 DO 59 i= 1,18 mj= Nruns+1 DO 53 j= 1,mj n= 101-1 t0= SECOND(0.0) c Time Kernel 12 DO 12 L = 1,lo DO 12 k = 1,n 12 X(k)= Y(k+1) - Y(k) c TIM(j)= SECOND(0.0) - t0 - to 53 continue c Compute Dynamic Clock Error c CALL STATS( TUM, TIM, mj) rterr= 100.0*( TUM(2)/( TUM(1) +1.0E-9)) IF( TUM(1).LE. 0.0) rterr= 100.0 c c Compute Digital Clock Error c CALL TDIGIT( SIG(i), nzd, TUM(4)) C TAV(i)= TUM(1) TMX(i)= TUM(4) TER(i)= rterr LEN(i)= lo lo= lo + lo IF( (i.GT.13) .AND. (rterr.LT. 4.0)) GO TO 60 nn= i 59 continue C C C**************************************************************************** C Test Timing Error By Comparing Time Of Each Run With Longest Run C**************************************************************************** C 60 m= 0 tnn= ( TAV(nn+1) + 2.0* TAV(nn))* 0.5 fuzz= 1.0e-9 IF( tnn.LT.fuzz) tnn= fuzz DO 69 i= 1,nn rterr= TER(i) lo= LEN(i) c Compute Relative Clock Error c rt= 0. IF( LEN(i).GE. 0) rt= LEN(nn+1)/LEN(i) rperr= 100. IF( tnn.GT. fuzz) rperr= 100.*(ABS( tnn - rt* TAV(i)) /tnn) WRITE( iou,64) lo, TMX(i), SIG(i),rterr, rperr 64 FORMAT(6X,I7,E12.4,F11.2,1H%,F10.2,1H%,F10.2,1H%) c c Find Loop Size Used in Subr. SIZES c IF( (Loop.GE.lo) .AND. (Loop.LE.2*lo)) THEN m= lo WRITE( iou,66) Loop, scale IF( rterr .GT. 10.0) THEN WRITE( iou, 67) WRITE( iou, 68) ENDIF 66 FORMAT(7X,i6,14X,21HCurrent Run: Loop=, f9.3,5H*Loop ) 67 FORMAT(34X,44HINACCURATE TIMING OR ERROR. NEED LONGER RUN ) 68 FORMAT(34X,44HINCREASE: Loop OR Nruns IN SUBR. SIZES ) ENDIF C 69 continue IF( m.LE.0 ) THEN WRITE( iou,66) Loop, scale ENDIF WRITE( iou,49) C C C**************************************************************************** C Estimate Approximate Job Time By Scaling Time For Kernel 11 C**************************************************************************** C c Time Kernel 11. Calibrate with static timing of machine code lo= LEN(nn) t0= SECOND(0.0) DO 51 L = 1,lo PX(1,1)= CX(1,1) + REAL(L)*1.0e-6 PX(1,2)= CX(1,2) CDIR$ NOVECTOR DO 51 k = 3,101 51 PX(1,k)= PX(1,k-1) + PX(1,k-2) c TIM(nn)= SECOND(0.0) - t0 - to tx=(TIM(nn)/( 101*LEN(nn) +1.0e-9)) su= tx/3.2E-7 estime= su*( 2.387 + Nruns*( 0.1616*scale + 1.534)) WRITE( iou,70) estime, Nruns 70 FORMAT(/,9X,28HApproximate Serial Job Time= ,E10.1,5H Sec., 1 4X,8H( Nruns=,i2,6H RUNS),/) C RETURN C C**************************************************************************** C C C EXTRA CLOCK CALIBRATION TEST C C Timing For A Very Long Run Versus External Clock Time. C C C VERIFY is an auxiliary test that is not needed to execute MFLOPS. C This optional routine may be called to verify the accuracy of C the function SECOND programmed above to time CPU execution. C C In most cases, the calibration timing in the main program MFLOPS C will be sufficient, if the total CPU time measured by SECOND agrees C well with the CPU time charged by the operating system for several, C stand-alone computer runs. Stable timings should be demonstrated. C C The method used below times Kernel 11 using SECOND and then C scales this timing up to predict the time for a very long run C of Kernel 11. This long run is also timed using SECOND and C should be long enough to time independently using external, wall-clock C timings and/or CPU charge time measured by the operating system. C Function SECOND is verified by a close agreement of the C predicted total CPU time, the total CPU time measured by SECOND, C and the CPU time measured by the operating system. C To increase CPU run time simply increase the value of MORE. The C total CPU time is then nearly equal to the CPU time for loop DO 99. C C C Print output from VERIFY on processor: CRAY-1S/CFT 1.11 C C SECOND time for 1 loops= 4.524000e-07 Sec. C C Predict time for 10000000 loops= 4.524000e+00 Sec. C C SECOND time for 10000000 loops= 4.527072e+00 Sec. C C C Print output from VERIFY on processor: CRAY-1S/CIVIC 130k C C SECOND time for 1 loops= 3.620000e-07 Sec. C C Predict time for 10000000 loops= 3.620000e+00 Sec. C C SECOND time for 10000000 loops= 3.622626e+00 Sec. C C The results of this test on both processors demonstrate a C consistant error of three in the fourth significant digit. C More important these SECOND measurements agree with external timings. C Consistant timing accuracy of two significant digits may be adequate. C C The time for one execution pass can also be compared with a C timing analysis of the machine code for Kernel 11 for additional C verification of the accuracy of function SECOND. C Verification of CPU time measurements in Virtual Memory systems may C require this degree of circumspection. C C**************************************************************************** C cd MORE= 1000 cd loop= 100 cd m= loop*MORE cd n= 101 cd nloop= loop*(n-1) cd mnloop= m*(n-1) cd r= 1.0/float(nloop) cd t0= SECOND(0.0) C cd t0= SECOND(0.0) cd DO 11 L = 1,loop C PX(1,1)= CX(1,1) + L*1.0e-25 use only if optimization distributes L-loo cd PX(1,1)= CX(1,1) cd DO 11 k = 2,n cd 11 PX(1,k)= PX(1,k-1) + CX(1,k) cd tl= SECOND(0.0) - t0 - to C cd i= 1 cd t1= tl*r cd tp= tl*float(MORE) cd WRITE( iou,15) i, t1 cd 15 FORMAT(/,18H SECOND time for ,I10,8H loops= ,E14.6,5H Sec.) cd WRITE( iou,16) mnloop, tp cd 16 FORMAT(/,18H Predict time for ,I10,8H loops= ,E14.6,5H Sec.) C C**************************************************************************** C C The following loop should be set-up to run long enough for C an accurate, independent CPU job timing which should be nearly C equal to the total time predicted above (in WRITE-16) if the C timing measured by SECOND is valid. C**************************************************************************** C cd t0= SECOND(0.0) cd DO 99 L = 1,m C PX(1,1)= CX(1,1) + L*1.0e-25 use only if optimization distributes L-loo cd PX(1,1)= CX(1,1) cd DO 99 k = 2,n cd 99 PX(1,k)= PX(1,k-1) + CX(1,k) cd tm= SECOND(0.0) - t0 - to C cd WRITE( iou,15) mnloop, tm cd STOP END