whets.c

/**********************************************************/
/* Date: Mon, 10 Mar 1997 07:38:18 -0500                  */
/* From: Roy Longbottom <Roy_Longbottom@compuserve.com>   */
/* Subject: WHET02.txt                                    */
/* To: "Alfred A. Aburto Jr." <aburto@cts.com>            */
/**********************************************************/

/*
 *     C/C++ Whetstone Benchmark Single or Double Precision
 *
 *     Original concept        Brian Wichmann NPL      1960's
 *     Original author         Harold Curnow  CCTA     1972
 *     Self timing versions    Roy Longbottom CCTA     1978/87
 *     Optimisation control    Bangor University       1987/90
 *     C/C++ Version           Roy Longbottom          1996
 *     Compatibility & timers  Al Aburto               1996
 *
 ************************************************************
 *
 *              Official version approved by:
 *
 *         Harold Curnow  100421.1615@compuserve.com
 *
 *      Happy 25th birthday Whetstone, 21 November 1997
 *
 ************************************************************
 *
 *     The program normally runs for about 100 seconds
 *     (adjustable in main - variable duration). This time
 *     is necessary because of poor PC clock resolution.
 *     The original concept included such things as a given
 *     number of subroutine calls and divides which may be
 *     changed by optimisation. For comparison purposes the
 *     compiler and level of optimisation should be identified.
 *
 ************************************************************
 *
 *     The original benchmark had a single variable I which
 *     controlled the running time. Constants with values up
 *     to 899 were multiplied by I to control the number
 *     passes for each loop. It was found that large values
 *     of I could overflow index registers so an extra outer
 *     loop with a second variable J was added.
 *
 *     Self timing versions were produced during the early
 *     days. The 1978 changes supplied timings of individual
 *     loops and these were used later to produce MFLOPS and
 *     MOPS ratings.
 *
 *     1987 changes converted the benchmark to Fortran 77
 *     standards and removed redundant IF statements and
 *     loops to leave the 8 active loops N1 to N8. Procedure
 *     P3 was changed to use global variables to avoid over-
 *     optimisation with the first two statements changed from
 *     X1=X and Y1=Y to X=Y and Y=Z. A self time calibrating
 *     version for PCs was also produced, the facility being
 *     incorporated in this version.
 *
 *     This version has changes to avoid worse than expected
 *     speed ratings, due to underflow, and facilities to show
 *     that consistent numeric output is produced with varying
 *     optimisation levels or versions in different languages.
 *
 *     Some of the procedures produce ever decreasing numbers.
 *     To avoid problems, variables T and T1 have been changed
 *     from 0.499975 and 0.50025 to 0.49999975 and 0.50000025.
 *
 *     Each section now has its own double loop. Inner loops
 *     are run 100 times the loop constants. Calibration
 *     determines the number of outer loop passes. The
 *     numeric results produced in the main output are for
 *     one pass on the outer loop. As underflow problems were
 *     still likely on a processor 100 times faster than a 100
 *     MHZ Pentium, three sections have T=1.0-T inserted in the
 *     outer loop to avoid the problem. The two loops avoid
 *     index register overflows.
 *
 *     The first section is run ten times longer than required
 *     for accuracy in calculating MFLOPS. This time is divided
 *     by ten for inclusion in the MWIPS calculations.
 *
 *     This version has facilities for typing in details of the
 *     particular run. This information is appended to file
 *     whets.res along with the results. The input section can
 *     be avoided using a command line parameter N (for example
 *     Whets.exe N).
 *
 *     Roy Longbottom  101323.2241@compuserve.com
 *
 ************************************************************
 *
 *     Whetstone benchmark results are available in whets.tbl
 *     from ftp.nosc.mil/pub/aburto. The results include
 *     further details of the benchmarks.
 *
 ************************************************************
 *
 *     Source code is available in C/C++, Fortran, Basic and
 *     Visual Basic in the same format as this version. Pre-
 *     compiled versions for PCs are also available via C++.
 *     These comprise optimised and non-optimised versions
 *     for DOS, Windows and NT.
 *
 *     This version compiles and runs correctly either as a
 *     C or CPP program with a WATCOM and Borland compiler.
 *
 ************************************************************
 *
 * Example of initial calibration display (Pentium 100 MHz)
 *
 * Single Precision C/C++ Whetstone Benchmark
 *
 * Calibrate
 *      0.17 Seconds          1   Passes (x 100)
 *      0.77 Seconds          5   Passes (x 100)
 *      3.70 Seconds         25   Passes (x 100)
 *
 * Use 676  passes (x 100)
 *
 * 676 passes are used for an approximate duration of 100
 * seconds, providing an initial estimate of a speed rating
 * of 67.6 MWIPS.
 *
 * This is followed by the table of results as below. Input
 * statements are then supplied to type in the run details.
 *
 ************************************************************
 *
 * Examples of results from file whets.res
 *
 * Whetstone Single  Precision Benchmark in C/C++
 *
 * Month run         4/1996
 * PC model          Escom
 * CPU               Pentium
 * Clock MHz         100
 * Cache             256K
 * H/W Options       Neptune chipset
 * OS/DOS            Windows 95
 * Compiler          Watcom C/C++ 10.5  Win386
 * Options           No optimisation
 * Run by            Roy Longbottom
 * From              UK
 * Mail              101323.2241@compuserve.com
 *
 * Loop content                 Result            MFLOPS     MOPS   Seconds
 *
 * N1 floating point    -1.12475025653839100      19.971              0.274
 * N2 floating point    -1.12274754047393800      11.822              3.240
 * N3 if then else       1.00000000000000000               11.659     2.530
 * N4 fixed point       12.00000000000000000               13.962     6.430
 * N5 sin,cos etc.       0.49904659390449520                2.097    11.310
 * N6 floating point     0.99999988079071040       3.360             45.750
 * N7 assignments        3.00000000000000000                2.415    21.810
 * N8 exp,sqrt etc.      0.75110864639282230                1.206     8.790
 *
 * MWIPS                                          28.462            100.134
 *
 * Whetstone Single  Precision Benchmark in C/C++
 *
 * Compiler          Watcom C/C++ 10.5  Win386
 * Options           -otexan -zp4 -om -fp5 -5r
 *
 * Loop content                 Result            MFLOPS     MOPS   Seconds
 *
 * N1 floating point    -1.12475025653839100      26.751              0.478
 * N2 floating point    -1.12274754047393800      17.148              5.220
 * N3 if then else       1.00000000000000000               19.922     3.460
 * N4 fixed point       12.00000000000000000               15.978    13.130
 * N5 sin,cos etc.       0.49904659390449520                2.663    20.810
 * N6 floating point     0.99999988079071040      10.077             35.650
 * N7 assignments        3.00000000000000000               22.877     5.380
 * N8 exp,sqrt etc.      0.75110864639282230                1.513    16.370
 *
 * MWIPS                                          66.270            100.498
 *
 *
 * Whetstone Double  Precision Benchmark in C/C++
 *
 * Compiler          Watcom C/C++ 10.5 Win32NT
 * Options           -otexan -zp4 -om -fp5 -5r
 *
 * Loop content                 Result           MFLOPS      MOPS   Seconds
 *
 * N1 floating point    -1.12398255667391900     26.548               0.486
 * N2 floating point    -1.12187079889284400     16.542               5.460
 * N3 if then else       1.00000000000000000               19.647     3.540
 * N4 fixed point       12.00000000000000000               15.680    13.500
 * N5 sin,cos etc.       0.49902937281515140                3.019    18.520
 * N6 floating point     0.99999987890802820      9.977              36.330
 * N7 assignments        3.00000000000000000               22.620     5.490
 * N8 exp,sqrt etc.      0.75100163018457870                1.493    16.740
 *
 * MWIPS                                         67.156             100.066
 *
 *  Note different numeric results to single precision. Slight variations
 *  are normal with different compilers and sometimes optimisation levels.
 *
 *
 *             Example Single Precision Optimised Results
 *
 *     MWIPS   MFLOPS  MFLOPS  MFLOPS  COS     EXP     FIXPT    IF    EQUAL
 * PC            1       2       3     MOPS    MOPS    MOPS    MOPS    MOPS
 *
 * P3  5.68    0.928   0.884   0.673   0.461   0.275   2.36    2.16   0.638
 * P4  16.4    5.09    4.03    2.66    0.526   0.342   6.36    6.00    5.28
 * P5  66.3    26.8    17.1    10.1    2.66    1.51    16.0    19.9    22.9
 * P6  161     50.3    45.2    31.5    4.46    2.77    102     20.6    119
 *
 *            Example Single Precision Non-optimised Results
 *
 * P3  3.07    0.860   0.815   0.328   0.355   0.160   1.70    1.32   0.264
 * P4  10.0    4.68    3.51    1.27    0.482   0.298   5.73    5.20    1.18
 * P5  28.5    20.0    11.8    3.36    2.10    1.21    14.0    11.7    2.42
 * P6  81.7    47.5    37.8    10.9    3.91    2.43    51.2    42.8    7.85
 *
 *        Summary results as in whets.tbl at ftp.nosc.mil/pub/aburto
 *
 *           MFLOPS   = Geometric Mean of three MFLOPS loops
 *           VAX MIPS = 5 * Geometric Mean of last three items above
 *
 *                                                                     VAX
 * PC System  CPU/Options               Cache   MHz   MWIPS   MFLOPS  MIPS
 *
 * P3 Clone   AM80386DX with 387        128K    40    5.68    0.820   7.40
 * P4 Escom   80486DX2 CIS chipset      128K    66    16.4    3.79    29.3
 * P5 Escom   Pentium Neptune chipset   256K   100    66.3    16.7    96.9
 * P6 Dell    PentiumPro 440FX PCIset   256K   200    161     41.5    315
 *
 * P3 Clone   AM80386DX with 387        128K    40    3.07    0.613   4.20
 * P4 Escom   80486DX2 CIS chipset      128K    66    10.0    2.75    16.4
 * P5 Escom   Pentium Neptune chipset   256K   100    28.5    9.26    36.6
 * P6 Dell    PentiumPro 440FX PCIset   256K   200    81.7    26.9    129
 *
 **************************************************************************
 *
 *                       Running Instructions
 *
 *      1.  In order to compile successfully, include timer option as
 *          indicated below.
 *      2.  If pre-compiled codes are to be distributed, compile with the
 *          -DPRECOMP option or uncomment #define PRECOMP at PRECOMPILE
 *          below. Also insert compiler name and optimisation details
 *          at #define precompiler and #define preoptions.
 *      3.  Compile and run for single precision results. Include run
 *          time parameter N to bipass typing in hardware details etc.
 *      4.  Compile with -DDP option or uncomment #define DP at PRECISION
 *          below and run for double precision results.
 *      5.  Run with maximum and no optimisation (minimum debug)
 *      6.  Notify Roy Longbottom of other necessary changes
 *      7.  Send results file whets.res to Roy Longbottom - with one
 *          sample of each run and system details fully completed
 *
 *      Roy Longbottom  101323.2241@compuserve.com    6 November 1996
 *
 **************************************************************************
 */

 #include <math.h>       /* for sin, exp etc.           */
 #include <stdio.h>      /* standard I/O                */
 #include <string.h>     /* for strcpy - 3 occurrences  */
 #include <stdlib.h>     /* for exit   - 1 occurrence   */
 #include <float.h>

/***************************************************************/
/* Timer options. You MUST uncomment one of the options below  */
/* or compile, for example, with the '-DUNIX' option.          */
/***************************************************************/
/* #define Amiga       */
/* #define UNIX        */
/* #define UNIX_Old    */
/* #define VMS         */
/* #define BORLAND_C   */
/* #define MSC         */
/* #define MAC         */
/* #define IPSC        */
/* #define FORTRAN_SEC */
/* #define GTODay      */
/* #define CTimer      */
/* #define UXPM        */
/* #define MAC_TMgr    */
/* #define PARIX       */
/* #define POSIX       */
/* #define WIN32       */
/* #define POSIX1      */
/***********************/

/*PRECISION PRECISION PRECISION PRECISION PRECISION PRECISION PRECISION*/

/* #define DP */

 #ifdef DP
    #define SPDP double
    #define Precision "Double"
 #else
    #define SPDP float
    #define Precision "Single"
 #endif


/*PRECOMPILE  PRECOMPILE  PRECOMPILE  PRECOMPILE  PRECOMPILE  PRECOMPILE*/

/* #define PRECOMP */

 #ifdef PRECOMP
    #define precompiler "INSERT COMPILER NAME HERE"
    #define preoptions  "INSERT OPTIMISATION OPTIONS HERE"
 #endif


void whetstones(long xtra, long x100, int calibrate);
void pa(SPDP e[4], SPDP t, SPDP t2);
void po(SPDP e1[4], long j, long k, long l);
void p3(SPDP *x, SPDP *y, SPDP *z, SPDP t, SPDP t1, SPDP t2);
void pout(char title[22], float ops, int type, SPDP checknum,
          SPDP time, int calibrate, int section);


static SPDP loop_time[9];
static SPDP loop_mops[9];
static SPDP loop_mflops[9];
static SPDP TimeUsed;
static SPDP mwips;
static char headings[9][18];
static SPDP Check;
static SPDP results[9];

main(int argc, char *argv[])
{
    int count = 10, calibrate = 1;
    long xtra = 1;
    int section;
    long x100 = 100;
    int duration = 100;
    FILE *outfile;
    char compiler[80] = " ", options[256] = " ", general[10][80] = {" "};
    char *endit = " ";
    char *getinput = "Yes";

    printf("\n");
    printf("##########################################\n");
    printf("%s Precision C/C++ Whetstone Benchmark\n\n", Precision);


    if (argc > 1)
    {
        switch (argv[1][0])
        {
        case 'N':
            getinput = "No";
            break;
        case 'n':
            getinput = "No";
            break;
        }
    }
    if (getinput == "No")
    {
        printf ("No run time input data\n\n");
    }

    outfile = fopen("whets.res", "a+");
    if (outfile == NULL)
    {
        printf ("Cannot open results file \n\n");
        printf("Press RETURN to exit\n");
        gets(endit);
        exit (0);
    }

    printf("Calibrate\n");
    do
    {
        TimeUsed=0;

        whetstones(xtra, x100, calibrate);

        printf("%11.2f Seconds %10.0lf   Passes (x 100)\n",
               TimeUsed, (SPDP)(xtra));
        calibrate++;
        count--;

        if (TimeUsed > 2.0)
        {
            count = 0;
        }
        else
        {
            xtra = xtra * 5;
        }
    }

    while (count > 0);

    if (TimeUsed > 0)
        xtra = (long)((SPDP)(duration * xtra) / TimeUsed);
    if (xtra < 1)
        xtra = 1;

    calibrate = 0;

    printf("\nUse %d  passes (x 100)\n", xtra);

    printf("\n          %s Precision C/C++ Whetstone Benchmark", Precision);

   #ifdef PRECOMP
    printf("\n          Compiler  %s", precompiler);
    printf("\n          Options   %s\n", preoptions);
   #else
    printf("\n");
   #endif

    printf("\nLoop content                  Result              MFLOPS "
           "     MOPS   Seconds\n\n");

    TimeUsed=0;
    whetstones(xtra, x100, calibrate);

    printf("\nMWIPS            ");
    if (TimeUsed>0)
    {
        mwips=(float)(xtra) * (float)(x100) / (10 * TimeUsed);
    }
    else
    {
        mwips = 0;
    }

    printf("%39.3f%19.3f\n\n", mwips, TimeUsed);

    if (Check == 0)
        printf("Wrong answer  ");



    /************************************************************************/
    /*             Type details of hardware, software etc.                  */
    /************************************************************************/

    if (getinput == "Yes")
    {
        printf ("Enter the following which will be added with results to file WHETS.RES\n");
        printf ("When submitting a number of results you need only provide details once\n");
        printf ("but a cross reference such as an abbreviated CPU type would be useful.\n");
        printf ("You can kill (exit or close) the program now and no data will be added.\n\n");

        printf ("Date:       ");
        gets(general[0]);

        printf ("Computer:   ");
        gets(general[1]);

        printf ("CPU chip:   ");
        gets(general[2]);

        printf ("Clock MHz:  ");
        gets(general[3]);

        printf ("Cache size: ");
        gets(general[4]);

        printf ("H/W options:");
        gets(general[5]);

        printf ("OS version: ");
        gets(general[6]);

     #ifdef PRECOMP
        strcpy (compiler, precompiler);
        strcpy (options, preoptions);
     #else
        printf ("Compiler:   ");
        gets(compiler);

        printf ("Options:    ");
        gets(options);
     #endif

        printf ("Your name:  ");
        gets(general[7]);

        printf ("From:       ");
        gets(general[8]);

        printf ("Email:      ");
        gets(general[9]);
    }
    else
    {
     #ifdef PRECOMP
        strcpy (compiler, precompiler);
        strcpy (options, preoptions);
     #endif
    }

    /************************************************************************/
    /*               Add results to output file whets.res                   */
    /************************************************************************/
    fprintf (outfile, "\n");
    fprintf (outfile, "##############################################\n");
    fprintf (outfile, "Whetstone %s  Precision Benchmark in C/C++\n\n", Precision);
    fprintf (outfile, "Date         %s\n", general[0]);
    fprintf (outfile, "Model        %s\n", general[1]);
    fprintf (outfile, "CPU          %s\n", general[2]);
    fprintf (outfile, "Clock MHz    %s\n", general[3]);
    fprintf (outfile, "Cache        %s\n", general[4]);
    fprintf (outfile, "H/W options  %s\n", general[5]);
    fprintf (outfile, "OS           %s\n", general[6]);
    fprintf (outfile, "Compiler     %s\n", compiler);
    fprintf (outfile, "Options      %s\n", options);
    fprintf (outfile, "Run by       %s\n", general[7]);
    fprintf (outfile, "From         %s\n", general[8]);
    fprintf (outfile, "Email        %s\n", general[9]);
    fprintf (outfile, "\n");

    fprintf (outfile, "Loop content                   Result"
             "              MFLOPS      MOPS   Seconds\n\n");

    for (section=1; section<9; section++)
    {
        fprintf (outfile, "%s  %24.17f   ", headings[section],
                 results[section]);
        if (loop_mops[section] == 99999)
        {
            fprintf (outfile, "  %9.3f           %9.3f\n",
                     loop_mflops[section], loop_time[section]);
        }
        else
        {
            fprintf (outfile, "            %9.3f %9.3f\n",
                     loop_mops[section], loop_time[section], results[section]);
        }
    }

    fprintf (outfile, "\nMWIPS             ");
    fprintf (outfile, "%39.3f%20.3f\n\n", mwips, TimeUsed);
    fprintf (outfile, "Results  to  load  to  spreadsheet             ");
    fprintf (outfile, "     MWIPS   Mflops1   Mflops2   Mflops3   Cosmops"
             "   Expmops  Fixpmops    Ifmops    Eqmops\n");
    fprintf (outfile, "Results  to  load  to  spreadsheet             ");

    fprintf (outfile, " %9.3f %9.3f %9.3f", mwips, loop_mflops[1],
             loop_mflops[2]);
    fprintf (outfile, " %9.3f %9.3f %9.3f", loop_mflops[6],
             loop_mops[5], loop_mops[8]);
    fprintf (outfile, " %9.3f %9.3f %9.3f\n\n", loop_mops[4],
             loop_mops[3], loop_mops[7]);

    fclose (outfile);

    printf ("\n");
    printf ("A new results file will have been created in the same directory as the\n");
    printf (".EXE files if one did not already exist. If you made a mistake on input, \n");
    printf ("you can use a text editor to correct it, delete the results or copy \n");
    printf ("them to a different file name. If you intend to run multiple tests you\n");
    printf ("you may wish to rename WHETS.RES with a more informative title.\n\n");
    printf ("Please submit feedback and results files to aburto@nosc.mil or to\n");
    printf ("Roy_Longbottom@compuserve.com\n\n");


}

void whetstones(long xtra, long x100, int calibrate)
{

    long n1, n2, n3, n4, n5, n6, n7, n8, i, ix, n1mult;
    SPDP x, y, z;
    long j, k, l;
    SPDP e1[4], timea, timeb, dtime();

    SPDP t =  0.49999975;
    SPDP t0 = t;
    SPDP t1 = 0.50000025;
    SPDP t2 = 2.0;

    Check=0.0;

    n1 = 12*x100;
    n2 = 14*x100;
    n3 = 345*x100;
    n4 = 210*x100;
    n5 = 32*x100;
    n6 = 899*x100;
    n7 = 616*x100;
    n8 = 93*x100;
    n1mult = 10;

    /* Section 1, Array elements */

    e1[0] = 1.0;
    e1[1] = -1.0;
    e1[2] = -1.0;
    e1[3] = -1.0;
    timea = dtime();
    {
        for (ix=0; ix<xtra; ix++)
        {
            for(i=0; i<n1*n1mult; i++)
            {
                e1[0] = (e1[0] + e1[1] + e1[2] - e1[3]) * t;
                e1[1] = (e1[0] + e1[1] - e1[2] + e1[3]) * t;
                e1[2] = (e1[0] - e1[1] + e1[2] + e1[3]) * t;
                e1[3] = (-e1[0] + e1[1] + e1[2] + e1[3]) * t;
            }
            t = 1.0 - t;
        }
        t =  t0;
    }
    timeb = (dtime()-timea)/(SPDP)(n1mult);
    pout("N1 floating point\0", (float)(n1*16)*(float)(xtra),
         1, e1[3], timeb, calibrate, 1);

    /* Section 2, Array as parameter */

    timea = dtime();
    {
        for (ix=0; ix<xtra; ix++)
        {
            for(i=0; i<n2; i++)
            {
                pa(e1, t, t2);
            }
            t = 1.0 - t;
        }
        t =  t0;
    }
    timeb = dtime()-timea;
    pout("N2 floating point\0", (float)(n2*96)*(float)(xtra),
         1, e1[3], timeb, calibrate, 2);

    /* Section 3, Conditional jumps */
    j = 1;
    timea = dtime();
    {
        for (ix=0; ix<xtra; ix++)
        {
            for(i=0; i<n3; i++)
            {
                if(j==1)
                    j = 2;
                else j = 3;
                if(j>2)
                    j = 0;
                else j = 1;
                if(j<1)
                    j = 1;
                else j = 0;
            }
        }
    }
    timeb = dtime()-timea;
    pout("N3 if then else  \0", (float)(n3*3)*(float)(xtra),
         2, (SPDP)(j), timeb, calibrate, 3);

    /* Section 4, Integer arithmetic */
    j = 1;
    k = 2;
    l = 3;
    timea = dtime();
    {
        for (ix=0; ix<xtra; ix++)
        {
            for(i=0; i<n4; i++)
            {
                j = j *(k-j)*(l-k);
                k = l * k - (l-j) * k;
                l = (l-k) * (k+j);
                e1[l-2] = j + k + l;
                e1[k-2] = j * k * l;
            }
        }
    }
    timeb = dtime()-timea;
    x = e1[0]+e1[1];
    pout("N4 fixed point   \0", (float)(n4*15)*(float)(xtra),
         2, x, timeb, calibrate, 4);

    /* Section 5, Trig functions */
    x = 0.5;
    y = 0.5;
    timea = dtime();
    {
        for (ix=0; ix<xtra; ix++)
        {
            for(i=1; i<n5; i++)
            {
                x = t*atan(t2*sin(x)*cos(x)/(cos(x+y)+cos(x-y)-1.0));
                y = t*atan(t2*sin(y)*cos(y)/(cos(x+y)+cos(x-y)-1.0));
            }
            t = 1.0 - t;
        }
        t = t0;
    }
    timeb = dtime()-timea;
    pout("N5 sin,cos etc.  \0", (float)(n5*26)*(float)(xtra),
         2, y, timeb, calibrate, 5);

    /* Section 6, Procedure calls */
    x = 1.0;
    y = 1.0;
    z = 1.0;
    timea = dtime();
    {
        for (ix=0; ix<xtra; ix++)
        {
            for(i=0; i<n6; i++)
            {
                p3(&x, &y, &z, t, t1, t2);
            }
        }
    }
    timeb = dtime()-timea;
    pout("N6 floating point\0", (float)(n6*6)*(float)(xtra),
         1, z, timeb, calibrate, 6);

    /* Section 7, Array refrences */
    j = 0;
    k = 1;
    l = 2;
    e1[0] = 1.0;
    e1[1] = 2.0;
    e1[2] = 3.0;
    timea = dtime();
    {
        for (ix=0; ix<xtra; ix++)
        {
            for(i=0; i<n7; i++)
            {
                po(e1, j, k, l);
            }
        }
    }
    timeb = dtime()-timea;
    pout("N7 assignments   \0", (float)(n7*3)*(float)(xtra),
         2, e1[2], timeb, calibrate, 7);

    /* Section 8, Standard functions */
    x = 0.75;
    timea = dtime();
    {
        for (ix=0; ix<xtra; ix++)
        {
            for(i=0; i<n8; i++)
            {
                x = sqrt(exp(log(x)/t1));
            }
        }
    }
    timeb = dtime()-timea;
    pout("N8 exp,sqrt etc. \0", (float)(n8*4)*(float)(xtra),
         2, x, timeb, calibrate, 8);

    return;
}


void pa(SPDP e[4], SPDP t, SPDP t2)
{
    long j;
    for(j=0; j<6; j++)
    {
        e[0] = (e[0]+e[1]+e[2]-e[3])*t;
        e[1] = (e[0]+e[1]-e[2]+e[3])*t;
        e[2] = (e[0]-e[1]+e[2]+e[3])*t;
        e[3] = (-e[0]+e[1]+e[2]+e[3])/t2;
    }

    return;
}

void po(SPDP e1[4], long j, long k, long l)
{
    e1[j] = e1[k];
    e1[k] = e1[l];
    e1[l] = e1[j];
    return;
}

void p3(SPDP *x, SPDP *y, SPDP *z, SPDP t, SPDP t1, SPDP t2)
{
    *x = *y;
    *y = *z;
    *x = t * (*x + *y);
    *y = t1 * (*x + *y);
    *z = (*x + *y)/t2;
    return;
}


void pout(char title[18], float ops, int type, SPDP checknum,
          SPDP time, int calibrate, int section)
{
    SPDP mops, mflops;

    Check = Check + checknum;
    loop_time[section] = time;
    strcpy (headings[section], title);
    TimeUsed =  TimeUsed + time;
    if (calibrate == 1)

    {
        results[section] = checknum;
    }
    if (calibrate == 0)
    {
        printf("%s %24.17f    ", headings[section], results[section]);

        if (type == 1)
        {
            if (time>0)
            {
                mflops = ops/(1000000L*time);
            }
            else
            {
                mflops = 0;
            }
            loop_mops[section] = 99999;
            loop_mflops[section] = mflops;
            printf(" %9.3f          %9.3f\n",
                   loop_mflops[section], loop_time[section]);
        }
        else
        {
            if (time>0)
            {
                mops = ops/(1000000L*time);
            }
            else
            {
                mops = 0;
            }
            loop_mops[section] = mops;
            loop_mflops[section] = 0;
            printf("           %9.3f%9.3f\n",
                   loop_mops[section], loop_time[section]);
        }
    }

    return;
}


/*****************************************************/
/* Various timer routines.                           */
/* Al Aburto, aburto@nosc.mil, 18 Feb 1997           */
/*                                                   */
/* t = dtime() outputs the current time in seconds.  */
/* Use CAUTION as some of these routines will mess   */
/* up when timing across the hour mark!!!            */
/*                                                   */
/* For timing I use the 'user' time whenever         */
/* possible. Using 'user+sys' time is a separate     */
/* issue.                                            */
/*                                                   */
/* Example Usage:                                    */
/* [timer options added here]                        */
/* main()                                            */
/* {                                                 */
/*  double starttime,benchtime,dtime();              */
/*                                                   */
/*  starttime = dtime();                             */
/*  [routine to time]                                */
/*  benchtime = dtime() - starttime;                 */
/* }                                                 */
/*                                                   */
/* [timer code below added here]                     */
/*****************************************************/

/*********************************/
/* Timer code.                   */
/*********************************/
/*******************/
/*  Amiga dtime()  */
/*******************/
#ifdef Amiga
#include <ctype.h>
#define HZ 50

SPDP dtime()
{
    SPDP q;

    struct tt
    {
        long days;
        long minutes;
        long ticks;
    } tt;

    DateStamp(&tt);

    q = ((SPDP)(tt.ticks + (tt.minutes * 60L * 50L))) / (SPDP)HZ;

    return q;
}
#endif

/*****************************************************/
/*  UNIX dtime(). This is the preferred UNIX timer.  */
/*  Provided by: Markku Kolkka, mk59200@cc.tut.fi    */
/*  HP-UX Addition by: Bo Thide', bt@irfu.se         */
/*****************************************************/
#ifdef UNIX
#include <sys/time.h>
#include <sys/resource.h>

#ifdef hpux
#include <sys/syscall.h>
#define getrusage(a, b) syscall(SYS_getrusage, a, b)
#endif

struct rusage rusage;

SPDP dtime()
{
    SPDP q;

    getrusage(RUSAGE_SELF, &rusage);

    q = (SPDP)(rusage.ru_utime.tv_sec);
    q = q + (SPDP)(rusage.ru_utime.tv_usec) * 1.0e-06;

    return q;
}
#endif

/***************************************************/
/*  UNIX_Old dtime(). This is the old UNIX timer.  */
/*  Use only if absolutely necessary as HZ may be  */
/*  ill defined on your system.                    */
/***************************************************/
#ifdef UNIX_Old
#include <sys/types.h>
#include <sys/times.h>
#include <sys/param.h>

#ifndef HZ
#define HZ 60
#endif

struct tms tms;

SPDP dtime()
{
    SPDP q;

    times(&tms);

    q = (SPDP)(tms.tms_utime) / (SPDP)HZ;

    return q;
}
#endif

/*********************************************************/
/*  VMS dtime() for VMS systems.                         */
/*  Provided by: RAMO@uvphys.phys.UVic.CA                */
/*  Some people have run into problems with this timer.  */
/*********************************************************/
#ifdef VMS
#include time

#ifndef HZ
#define HZ 100
#endif

struct tbuffer_t
{
    int proc_user_time;
    int proc_system_time;
    int child_user_time;
    int child_system_time;
};
struct tbuffer_t tms;

SPDP dtime()
{
    SPDP q;

    times(&tms);

    q = (SPDP)(tms.proc_user_time) / (SPDP)HZ;

    return q;
}
#endif

/******************************/
/*  BORLAND C dtime() for DOS */
/******************************/
#ifdef BORLAND_C
#include <ctype.h>
#include <dos.h>
#include <time.h>

#define HZ 100
struct time tnow;

SPDP dtime()
{
    SPDP q;

    gettime(&tnow);

    q = 60.0 * (SPDP)(tnow.ti_min);
    q = q + (SPDP)(tnow.ti_sec);
    q = q + (SPDP)(tnow.ti_hund)/(SPDP)HZ;

    return q;
}
#endif

/***************************************/
/*  Microsoft C (MSC) dtime() for DOS  */
/*  Also suitable for Watcom C/C++ and */
/*  some other PC compilers            */
/***************************************/
#ifdef MSC
#include <time.h>
#include <ctype.h>

#define HZ CLOCKS_PER_SEC
clock_t tnow;

SPDP dtime()
{
    SPDP q;

    tnow = clock();
    q = (SPDP)tnow / (SPDP)HZ;
    return q;
}
#endif

/*************************************/
/*  Macintosh (MAC) Think C dtime()  */
/*************************************/
#ifdef MAC
#include <time.h>

#define HZ 60

SPDP dtime()
{
    SPDP q;

    q = (SPDP)clock() / (SPDP)HZ;

    return q;
}
#endif

/************************************************************/
/*  iPSC/860 (IPSC) dtime() for i860.                       */
/*  Provided by: Dan Yergeau, yergeau@gloworm.Stanford.EDU  */
/************************************************************/
#ifdef IPSC
extern double dclock();

SPDP dtime()
{
    SPDP q;

    q = dclock();

    return q;
}
#endif

/**************************************************/
/*  FORTRAN dtime() for Cray type systems.        */
/*  This is the preferred timer for Cray systems. */
/**************************************************/
#ifdef FORTRAN_SEC

fortran double second();

SPDP dtime()
{
    SPDP q;

    second(&q);

    return q;
}
#endif

/***********************************************************/
/*  UNICOS C dtime() for Cray UNICOS systems.  Don't use   */
/*  unless absolutely necessary as returned time includes  */
/*  'user+system' time.  Provided by: R. Mike Dority,      */
/*  dority@craysea.cray.com                                */
/***********************************************************/
#ifdef CTimer
#include <time.h>

SPDP dtime()
{
    SPDP q;
    clock_t   clock(void);

    q = (SPDP)clock() / (SPDP)CLOCKS_PER_SEC;

    return q;
}
#endif

/********************************************/
/* Another UNIX timer using gettimeofday(). */
/* However, getrusage() is preferred.       */
/********************************************/
#ifdef GTODay
#include <sys/time.h>

struct timeval tnow;

SPDP dtime()
{
    SPDP q;

    gettimeofday(&tnow, NULL);
    q = (SPDP)tnow.tv_sec + (SPDP)tnow.tv_usec * 1.0e-6;

    return q;
}
#endif

/*****************************************************/
/*  Fujitsu UXP/M timer.                             */
/*  Provided by: Mathew Lim, ANUSF, M.Lim@anu.edu.au */
/*****************************************************/
#ifdef UXPM
#include <sys/types.h>
#include <sys/timesu.h>
struct tmsu rusage;

SPDP dtime()
{
    SPDP q;

    timesu(&rusage);

    q = (SPDP)(rusage.tms_utime) * 1.0e-06;

    return q;
}
#endif

/**********************************************/
/*    Macintosh (MAC_TMgr) Think C dtime()    */
/*   requires Think C Language Extensions or  */
/*    #include <MacHeaders> in the prefix     */
/*  provided by Francis H Schiffer 3rd (fhs)  */
/*         skipschiffer@genie.geis.com        */
/**********************************************/
#ifdef MAC_TMgr
#include <Timer.h>
#include <stdlib.h>

static TMTask mgrTimer;
static Boolean mgrInited = false;
static SPDP mgrClock;

#define RMV_TIMER RmvTime( (QElemPtr)&mgrTimer )
#define MAX_TIME  1800000000L
/* MAX_TIME limits time between calls to */
/* dtime( ) to no more than 30 minutes   */
/* this limitation could be removed by   */
/* creating a completion routine to sum  */
/* 30 minute segments (fhs 1994 feb 9)   */

static void Remove_timer( )
{
    RMV_TIMER;
    mgrInited = false;
}

SPDP dtime( )
{
    if( mgrInited )
    {
        RMV_TIMER;
        mgrClock += (MAX_TIME + mgrTimer.tmCount)*1.0e-6;
    }
    else {
        if( _atexit( &Remove_timer ) == 0 )
            mgrInited = true;
        mgrClock = 0.0;
    }
    if( mgrInited )
    {
        mgrTimer.tmAddr = NULL;
        mgrTimer.tmCount = 0;
        mgrTimer.tmWakeUp = 0;
        mgrTimer.tmReserved = 0;
        InsTime( (QElemPtr)&mgrTimer );
        PrimeTime( (QElemPtr)&mgrTimer, -MAX_TIME );
    }
    return( mgrClock );
}
#endif

/***********************************************************/
/*  Parsytec GCel timer.                                   */
/*  Provided by: Georg Wambach, gw@informatik.uni-koeln.de */
/***********************************************************/
#ifdef PARIX
#include <sys/time.h>

SPDP dtime()
{
    SPDP q;

    q = (SPDP) (TimeNowHigh()) / (SPDP) CLK_TCK_HIGH;

    return q;
}
#endif

/************************************************/
/*  Sun Solaris POSIX dtime() routine           */
/*  Provided by: Case Larsen, CTLarsen.lbl.gov  */
/************************************************/
#ifdef POSIX
#include <sys/time.h>
#include <sys/resource.h>
#include <sys/rusage.h>

#ifdef __hpux
#include <sys/syscall.h>
#endif

struct rusage rusage;

SPDP dtime()
{
    SPDP q;

    getrusage(RUSAGE_SELF, &rusage);

    q = (SPDP)(rusage.ru_utime.tv_sec);
    q = q + (SPDP)(rusage.ru_utime.tv_nsec) * 1.0e-09;

    return q;
}
#endif


/****************************************************/
/*  Windows NT (32 bit) dtime() routine             */
/*  Provided by: Piers Haken, piersh@microsoft.com  */
/****************************************************/
#ifdef WIN32
#include <windows.h>

SPDP dtime(void)
{
    SPDP q;

    q = (SPDP)GetTickCount() * 1.0e-03;

    return q;
}
#endif

/*****************************************************/
/* Time according to POSIX.1  -  <J.Pelan@qub.ac.uk> */
/* Ref: "POSIX Programmer's Guide"  O'Reilly & Assoc.*/
/*****************************************************/
#ifdef POSIX1
#define _POSIX_SOURCE 1
#include <unistd.h>
#include <limits.h>
#include <sys/times.h>

struct tms tms;

SPDP dtime()
{
    SPDP q;
    times(&tms);
    q = (SPDP)tms.tms_utime / (SPDP)CLK_TCK;
    return q;
}
#endif