added common random-number generation and timer utilities

darcs-hash:20070824163515-c8de0-a83acc3d0d58d0e818fa27585dcefbc0c6a578b4.gz

Makefile.am

@@ -3,11 +3,11 @@ lib_LTLIBRARIES = libnlopt.la
 
 ACLOCAL_AMFLAGS=-I ./m4
 
-SUBDIRS=lbfgs subplex direct stogo api . test
+SUBDIRS= util lbfgs subplex direct stogo api . test
 EXTRA_DIST=COPYRIGHT autogen.sh nlopt.pc.in m4
 
 libnlopt_la_SOURCES = 
-libnlopt_la_LIBADD = lbfgs/liblbfgs.la subplex/libsubplex.la direct/libdirect.la stogo/libstogo.la api/libapi.la
+libnlopt_la_LIBADD = lbfgs/liblbfgs.la subplex/libsubplex.la direct/libdirect.la stogo/libstogo.la api/libapi.la util/libutil.la
 
 libnlopt_la_LDFLAGS = -no-undefined -version-info @SHARED_VERSION_INFO@
 

api/Makefile.am

-AM_CPPFLAGS = -I$(top_srcdir)/direct -I$(top_srcdir)/stogo -I$(top_srcdir)/lbfgs -I$(top_srcdir)/subplex
+AM_CPPFLAGS = -I$(top_srcdir)/direct -I$(top_srcdir)/stogo -I$(top_srcdir)/lbfgs -I$(top_srcdir)/subplex -I$(top_srcdir)/util
 
 include_HEADERS = nlopt.h
 noinst_LTLIBRARIES = libapi.la

api/nlopt.c

@@ -2,6 +2,7 @@
 #include <math.h>
 
 #include "nlopt.h"
+#include "nlopt-util.h"
 #include "config.h"
 
 static const char nlopt_algorithm_names[NLOPT_NUM_ALGORITHMS][128] = {
@@ -18,6 +19,16 @@ const char *nlopt_algorithm_name(nlopt_algorithm a)
      return nlopt_algorithm_names[a];
 }
 
+static int nlopt_srand_called = 0;
+void nlopt_srand(unsigned long seed) {
+     nlopt_srand_called = 1;
+     nlopt_init_genrand(seed);
+}
+
+void nlopt_srand_time() {
+     nlopt_srand(nlopt_time_seed());
+}
+
 static int my_isinf(double x) {
      return x == HUGE_VAL
 #ifdef HAVE_ISINF
@@ -89,6 +100,10 @@ nlopt_result nlopt_minimize(
      d.lb = lb;
      d.ub = ub;
 
+     /* make sure rand generator is inited */
+     if (!nlopt_srand_called)
+	  nlopt_srand_time(); /* default is non-deterministic */
+
      /* check bound constraints */
      for (i = 0; i < n; ++i)
 	  if (lb[i] > ub[i] || x[i] < lb[i] || x[i] > ub[i])

api/nlopt.h

@@ -48,6 +48,9 @@ extern nlopt_result nlopt_minimize(
      double xtol_rel, const double *xtol_abs,
      int maxeval, double maxtime);
 
+extern void nlopt_srand(unsigned long seed);
+extern void nlopt_srand_time(void);
+
 #ifdef __cplusplus
 }  /* extern "C" */
 #endif /* __cplusplus */

api/nlopt_minimize.3

@@ -167,12 +167,14 @@ NaN is specified by the macro NAN in math.h (for ANSI C99).
 .SH ALGORITHMS
 The 
 .I algorithm
-parameter can take on any of the following values:
+parameter specifies the optimization algorithm (for more detail on
+these, see the README files in the source-code subdirectories), and
+can take on any of the following values:
 .TP 
 .B NLOPT_GLOBAL_DIRECT
 Perform a global derivative-free optimization using the DIRECT search
-algorithm by Jones et al.  See direct/README.  Supports arbitrary
-nonlinear constraints as described above.
+algorithm by Jones et al.  Supports arbitrary nonlinear constraints as
+described above.
 .TP 
 .B NLOPT_GLOBAL_DIRECT_L
 Perform a global derivative-free optimization using the DIRECT-L
@@ -194,6 +196,12 @@ works (both for simple bound constraints via
 and
 .I ub
 as well as nonlinear constraints as described above).
+.TP 
+.B NLOPT_GLOBAL_STOGO
+Global optimization using the StoGO algorithm by Madsen et al.  StoGO
+exploits gradient information (which must be supplied by the
+objective) for its local searches, and performs the global search by a
+stochastic branch-and-bound technique.  This stochastic
 .SH RETURN VALUE
 The value returned is one of the following enumerated constants.
 (Positive return values indicate successful termination, while negative

configure.ac

@@ -22,13 +22,21 @@ AC_PROG_LIBTOOL
 dnl Checks for typedefs, structures, and compiler characteristics.
 AC_HEADER_STDC
 AC_HEADER_TIME
-AC_CHECK_HEADERS([unistd.h getopt.h])
+AC_CHECK_HEADERS([unistd.h getopt.h stdint.h])
 AC_C_CONST
 AC_C_INLINE
 
+dnl find 32-bit unsigned integer type for random-number generator
+AC_CHECK_SIZEOF(unsigned int)
+AC_CHECK_SIZEOF(unsigned long)
+AC_CHECK_TYPES(uint32_t, [], [], [$ac_includes_default
+#ifdef HAVE_STDINT_H
+#  include <stdint.h>
+#endif])
+
 dnl Checks for libraries and functions
 AC_CHECK_LIB(m, sin)
-AC_CHECK_FUNCS([BSDgettimeofday gettimeofday])
+AC_CHECK_FUNCS([BSDgettimeofday gettimeofday time])
 
 AC_MSG_CHECKING([for isnan])
 AC_TRY_LINK([#include <math.h>
@@ -79,6 +87,7 @@ AC_CONFIG_FILES([
    Makefile
    nlopt.pc
    api/Makefile
+   util/Makefile
    direct/Makefile
    stogo/Makefile
    lbfgs/Makefile

stogo/Makefile.am

+AM_CPPFLAGS = -I$(top_srcdir)/util
+
 noinst_LTLIBRARIES = libstogo.la
 libstogo_la_SOURCES = global.cc linalg.cc local.cc stogo.cc tools.cc	\
 global.h linalg.h local.h stogo_config.h stogo.h tools.h

stogo/global.cc

@@ -19,9 +19,10 @@
 #include "stogo_config.h"
 #include "global.h"
 #include "local.h"
+#include "nlopt-util.h"
 
 // Timer stuff
-time_t   StartTime;
+double   StartTime;
 
 double MacEpsilon ;
 int FC=0, GC=0 ;
@@ -93,8 +94,7 @@ void Global::FillRandom(RTBox SampleBox, RTBox box) {
   tmpTrial.objval=DBL_MAX;
   for (int i=1 ; i<=rnd_pnts ; i++) {
     for (int dir=0 ; dir<dim ; dir++)
-      tmpTrial.xvals(dir) =
-	box.lb(dir)+(box.ub(dir)-box.lb(dir))*(double(rand())/RAND_MAX) ;
+      tmpTrial.xvals(dir) = nlopt_urand(box.lb(dir), box.ub(dir));
     SampleBox.AddTrial(tmpTrial) ;
   }
 }
@@ -196,7 +196,7 @@ void Global::Search(int axis, RCRVector x_av){
   }
 
   // Initialize timer
-  time(&StartTime);
+  StartTime = nlopt_seconds();
 
   // Clear priority_queues
   while (!Garbage.empty())
@@ -275,8 +275,7 @@ void Global::Search(int axis, RCRVector x_av){
 /************* Various utility functions ****************/
 double Global::GetTime()
 {
- time_t ctime; time(&ctime);
- return difftime(ctime,StartTime);
+  return nlopt_seconds() - StartTime;
 }
 
 bool Global::InTime()

test/Makefile.am

-AM_CPPFLAGS = -I$(top_srcdir)/api
+AM_CPPFLAGS = -I$(top_srcdir)/api -I$(top_srcdir)/util
 
 noinst_PROGRAMS = testopt
 

test/testopt.cpp

@@ -10,39 +10,43 @@
 #ifdef HAVE_GETOPT_H
 #  include <getopt.h>
 #endif
-#if TIME_WITH_SYS_TIME
-# include <sys/time.h>
-# include <time.h>
-#else
-# if HAVE_SYS_TIME_H
-#  include <sys/time.h>
-# else
-#  include <time.h>
-# endif
-#endif
 
 #include "nlopt.h"
+#include "nlopt-util.h"
 #include "testfuncs.h"
 
-static double urand(double a, double b)
-{
-  return a + (rand() * (b - a) / RAND_MAX);
-}
-
 static nlopt_algorithm algorithm = NLOPT_GLOBAL_DIRECT;
 static double ftol_rel = 0, ftol_abs = 0, xtol_rel = 0;
 static int maxeval = 1000;
 static double maxtime = 0.0;
 
+static void listalgs(FILE *f)
+{
+  int i;
+  fprintf(f, "Available algorithms:\n");
+  for (i = 0; i < NLOPT_NUM_ALGORITHMS; ++i)
+    fprintf(f, "  %2d: %s\n", i, nlopt_algorithm_name((nlopt_algorithm) i));
+}
+
+static void listfuncs(FILE *f)
+{
+  int i;
+  fprintf(f, "Available objective functions:\n");
+  for (i = 0; i < NTESTFUNCS; ++i)
+    fprintf(f, "  %2d: %s (%d dims)\n", i, testfuncs[i].name, testfuncs[i].n);
+}
+
 static int test_function(int ifunc)
 {
   testfunc func;
   int i;
   double *x, fmin, f0;
   nlopt_result ret;
+  double start = nlopt_seconds();
   
   if (ifunc < 0 || ifunc >= NTESTFUNCS) {
     fprintf(stderr, "testopt: invalid function %d\n", ifunc);
+    listfuncs(stderr);
     return 0;
   }
   func = testfuncs[ifunc];
@@ -61,7 +65,7 @@ static int test_function(int ifunc)
 	 func.name, func.n, nlopt_algorithm_name(algorithm));
   printf("Starting guess x = [");
   for (i = 0; i < func.n; ++i)
-    printf(" %g", x[i] = urand(func.lb[i], func.ub[i]));
+    printf(" %g", x[i] = nlopt_urand(func.lb[i], func.ub[i]));
   printf("]\n");
   f0 = func.f(func.n, x, x + func.n, func.f_data);
   printf("Starting function value = %g\n", f0);
@@ -85,6 +89,7 @@ static int test_function(int ifunc)
 		       x, &fmin,
 		       HUGE_VAL, ftol_rel, ftol_abs, xtol_rel, NULL,
 		       maxeval, maxtime);
+  printf("finished after %g seconds.\n", nlopt_seconds() - start);
   printf("return code %d from nlopt_minimize\n", ret);
   if (ret < 0) {
     fprintf(stderr, "testopt: error in nlopt_minimize\n");
@@ -110,6 +115,7 @@ static void usage(FILE *f)
   fprintf(f, "Usage: testopt [OPTIONS]\n"
 	  "Options:\n"
 	  "     -h : print this help\n"
+	  "     -L : list available algorithms and objective functions\n"
 	  "     -v : verbose mode\n"
 	  " -r <s> : use random seed <s> for starting guesses\n"
 	  " -a <n> : use optimization algorithm <n>\n"
@@ -122,17 +128,21 @@ int main(int argc, char **argv)
 {
   int c;
   
-  srand((unsigned) time(NULL));
+  nlopt_srand_time();
   testfuncs_verbose = 0;
   
   if (argc <= 1)
     usage(stdout);
   
-  while ((c = getopt(argc, argv, "hvra:o:e:")) != -1)
+  while ((c = getopt(argc, argv, "hLvra:o:e:")) != -1)
     switch (c) {
     case 'h':
       usage(stdout);
       return EXIT_SUCCESS;
+    case 'L':
+      listalgs(stdout);
+      listfuncs(stdout);
+      return EXIT_SUCCESS;
     case 'v':
       testfuncs_verbose = 1;
       break;
@@ -143,6 +153,7 @@ int main(int argc, char **argv)
       c = atoi(optarg);
       if (c < 0 || c >= NLOPT_NUM_ALGORITHMS) {
 	fprintf(stderr, "testopt: invalid algorithm %d\n", c);
+	listalgs(stderr);
 	return EXIT_FAILURE;
       }
       algorithm = (nlopt_algorithm) c;

util/Makefile.am

+noinst_LTLIBRARIES = libutil.la
+libutil_la_SOURCES = mt19937ar.c timer.c nlopt-util.h

util/mt19937ar.c

+/* 
+   A C-program for MT19937, with initialization improved 2002/1/26.
+   Coded by Takuji Nishimura and Makoto Matsumoto.
+
+   Before using, initialize the state by using init_genrand(seed)  
+   or init_by_array(init_key, key_length).
+
+   Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
+   All rights reserved.                          
+
+   Modified 2007 by Steven G. Johnson for use with NLopt (to avoid
+   namespace pollution, use uint32_t instead of unsigned long,
+   and add the urand function).
+
+   Redistribution and use in source and binary forms, with or without
+   modification, are permitted provided that the following conditions
+   are met:
+
+     1. Redistributions of source code must retain the above copyright
+        notice, this list of conditions and the following disclaimer.
+
+     2. Redistributions in binary form must reproduce the above copyright
+        notice, this list of conditions and the following disclaimer in the
+        documentation and/or other materials provided with the distribution.
+
+     3. The names of its contributors may not be used to endorse or promote 
+        products derived from this software without specific prior written 
+        permission.
+
+   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+   A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+   CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+   Any feedback is very welcome.
+   http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
+   email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
+*/
+
+#include "nlopt-util.h"
+#include "config.h"
+
+#if defined(HAVE_STDINT_H)
+#  include <stdint.h>
+#endif
+
+#ifndef HAVE_UINT32_T
+#  if SIZEOF_UNSIGNED_LONG == 4
+      typedef unsigned long uint32_t;
+#  elif SIZEOF_UNSIGNED_INT == 4
+      typedef unsigned int uint32_t;
+#  else
+#    error No 32-bit unsigned integer type
+#  endif
+#endif
+
+/* Period parameters */  
+#define N 624
+#define M 397
+#define MATRIX_A 0x9908b0dfUL   /* constant vector a */
+#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
+#define LOWER_MASK 0x7fffffffUL /* least significant r bits */
+
+static uint32_t mt[N]; /* the array for the state vector  */
+static int mti=N+1; /* mti==N+1 means mt[N] is not initialized */
+
+/* initializes mt[N] with a seed */
+void nlopt_init_genrand(unsigned long s)
+{
+    mt[0]= s & 0xffffffffUL;
+    for (mti=1; mti<N; mti++) {
+        mt[mti] = 
+	    (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti); 
+        /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
+        /* In the previous versions, MSBs of the seed affect   */
+        /* only MSBs of the array mt[].                        */
+        /* 2002/01/09 modified by Makoto Matsumoto             */
+        mt[mti] &= 0xffffffffUL;
+        /* for >32 bit machines */
+    }
+}
+
+/* generates a random number on [0,0xffffffff]-interval */
+static uint32_t nlopt_genrand_int32(void)
+{
+    uint32_t y;
+    static uint32_t mag01[2]={0x0UL, MATRIX_A};
+    /* mag01[x] = x * MATRIX_A  for x=0,1 */
+
+    if (mti >= N) { /* generate N words at one time */
+        int kk;
+
+        if (mti == N+1)   /* if init_genrand() has not been called, */
+	    nlopt_init_genrand(5489UL); /* a default initial seed is used */
+
+        for (kk=0;kk<N-M;kk++) {
+            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
+            mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1UL];
+        }
+        for (;kk<N-1;kk++) {
+            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
+            mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
+        }
+        y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
+        mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];
+
+        mti = 0;
+    }
+  
+    y = mt[mti++];
+
+    /* Tempering */
+    y ^= (y >> 11);
+    y ^= (y << 7) & 0x9d2c5680UL;
+    y ^= (y << 15) & 0xefc60000UL;
+    y ^= (y >> 18);
+
+    return y;
+}
+
+#if 0 /* not used in NLopt */
+
+/* initialize by an array with array-length */
+/* init_key is the array for initializing keys */
+/* key_length is its length */
+/* slight change for C++, 2004/2/26 */
+static void nlopt_init_by_array(uint32_t init_key[], int key_length)
+{
+    int i, j, k;
+    nlopt_init_genrand(19650218UL);
+    i=1; j=0;
+    k = (N>key_length ? N : key_length);
+    for (; k; k--) {
+        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL))
+          + init_key[j] + j; /* non linear */
+        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
+        i++; j++;
+        if (i>=N) { mt[0] = mt[N-1]; i=1; }
+        if (j>=key_length) j=0;
+    }
+    for (k=N-1; k; k--) {
+        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
+          - i; /* non linear */
+        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
+        i++;
+        if (i>=N) { mt[0] = mt[N-1]; i=1; }
+    }
+
+    mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */ 
+}
+
+/* generates a random number on [0,0x7fffffff]-interval */
+static long nlopt_genrand_int31(void)
+{
+    return (long)(nlopt_genrand_int32()>>1);
+}
+
+/* generates a random number on [0,1]-real-interval */
+static double nlopt_genrand_real1(void)
+{
+    return nlopt_genrand_int32()*(1.0/4294967295.0); 
+    /* divided by 2^32-1 */ 
+}
+
+/* generates a random number on [0,1)-real-interval */
+static double nlopt_genrand_real2(void)
+{
+    return nlopt_genrand_int32()*(1.0/4294967296.0); 
+    /* divided by 2^32 */
+}
+
+/* generates a random number on (0,1)-real-interval */
+static double nlopt_genrand_real3(void)
+{
+    return (((double)nlopt_genrand_int32()) + 0.5)*(1.0/4294967296.0); 
+    /* divided by 2^32 */
+}
+
+#endif
+
+/* generates a random number on [0,1) with 53-bit resolution*/
+static double nlopt_genrand_res53(void) 
+{ 
+    uint32_t a=nlopt_genrand_int32()>>5, b=nlopt_genrand_int32()>>6; 
+    return(a*67108864.0+b)*(1.0/9007199254740992.0); 
+} 
+/* These real versions are due to Isaku Wada, 2002/01/09 added */
+
+/* generate uniform random number in [a,b) with 53-bit resolution,
+   added by SGJ */
+double nlopt_urand(double a, double b)
+{
+     return(a + (b - a) * nlopt_genrand_res53());
+}
+
+#if 0
+#include <stdio.h>
+int main(void)
+{
+    int i;
+    uint32_t init[4]={0x123, 0x234, 0x345, 0x456}, length=4;
+    init_by_array(init, length);
+    printf("1000 outputs of nlopt_genrand_int32()\n");
+    for (i=0; i<1000; i++) {
+      printf("%10lu ", nlopt_genrand_int32());
+      if (i%5==4) printf("\n");
+    }
+    printf("\n1000 outputs of genrand_real2()\n");
+    for (i=0; i<1000; i++) {
+      printf("%10.8f ", genrand_real2());
+      if (i%5==4) printf("\n");
+    }
+    return 0;
+}
+#endif

util/nlopt-util.h

+#ifndef NLOPT_UTIL_H
+#define NLOPT_UTIL_H
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif /* __cplusplus */
+
+/* seconds timer */
+extern double nlopt_seconds(void);
+extern unsigned long nlopt_time_seed(void);
+
+/* pseudorandom number generation by Mersenne twister algorithm */
+extern void nlopt_init_genrand(unsigned long s);
+extern double nlopt_urand(double a, double b);
+
+#ifdef __cplusplus
+}  /* extern "C" */
+#endif /* __cplusplus */
+
+#endif

util/timer.c

+#include "nlopt-util.h"
+#include "config.h"
+
+#if TIME_WITH_SYS_TIME
+# include <sys/time.h>
+# include <time.h>
+#else
+# if HAVE_SYS_TIME_H
+#  include <sys/time.h>
+# else
+#  include <time.h>
+# endif
+#endif
+
+#if defined(_WIN32) || defined(__WIN32__)
+#  include <windows.h>    
+#endif
+
+/* return time in seconds since some arbitrary point in the past */
+double nlopt_seconds(void)
+{
+     static int start_inited = 0; /* whether start time has been initialized */
+#if defined(HAVE_GETTIMEOFDAY)
+     static struct timeval start;
+     struct timeval tv;
+     if (!start_inited) {
+	  start_inited = 1;
+	  gettimeofday(&start, NULL);
+     }
+     gettimeofday(&tv, NULL);
+     return (tv.tv_sec - start.tv_sec) + 1.e-6 * (tv.tv_usec - start.tv_sec);
+#elif defined(HAVE_TIME)
+     return time(NULL);
+#elif defined(_WIN32) || defined(__WIN32__)
+     static ULONGLONG start;
+     FILETIME ft;
+     if (!start_inited) {
+	  start_inited = 1;
+	  GetSystemTimeAsFileTime(&ft);
+	  start = (((ULONGLONG) ft.dwHighDateTime) << 32) + ft.dwLowDateTime;
+     }
+     GetSystemTimeAsFileTime(&ft);
+     return 100e-9 * (((((ULONGLONG) ft.dwHighDateTime) << 32) + ft.dwLowDateTime) - start);
+#else
+     /* use clock() as a fallback... this is somewhat annoying
+	because clock() may wrap around with a fairly short period */
+     static clock_t start;
+     if (!start_inited) {
+	  start_inited = 1;
+	  start = clock();
+     }
+     return (clock() - start) * 1.0 / CLOCKS_PER_SEC;
+#endif
+}
+
+/* number based on time for use as random seed */
+unsigned long nlopt_time_seed(void)
+{
+#if defined(HAVE_GETTIMEOFDAY)
+     struct timeval tv;
+     gettimeofday(&tv, NULL);
+     return (tv.tv_sec ^ tv.tv_usec);
+#elif defined(HAVE_TIME)
+     return time(NULL);
+#elif defined(_WIN32) || defined(__WIN32__)
+     FILETIME ft;
+     GetSystemTimeAsFileTime(&ft);
+     return ft.dwHighDateTime ^ ft.dwLowDateTime;
+#else
+     return clock();
+#endif
+}