Assignment 4 Vanilla Code in assign4 folder

Signed-off-by: Gaurav Kukreja <mailme.gaurav@gmail.com>

assign4/Makefile

+# Intel compiler
+CC =  icc
+CFLAGS = -g
+
+MPICC = mpicc
+
+all: heat
+
+heat : heat.o input.o misc.o timing.o relax_gauss.o relax_jacobi.o
+	$(CC) $(CFLAGS) -o $@ $+ -lm 
+
+%.o : %.c %.h
+	$(CC) $(CFLAGS) -c -o $@ $<
+
+clean:
+	rm -f *.o heat *~ *.ppm
+
+remake : clean all

assign4/heat.c

+/*
+ * heat.h
+ *
+ * Iterative solver for heat distribution
+ */
+
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include "input.h"
+#include "heat.h"
+#include "timing.h"
+
+
+void usage( char *s )
+{
+    fprintf(stderr, 
+	    "Usage: %s <input file> [result file]\n\n", s);
+}
+
+
+int main( int argc, char *argv[] )
+{
+    unsigned iter;
+    FILE *infile, *resfile;
+    char *resfilename;
+
+	double *tmp;
+
+    // algorithmic parameters
+    algoparam_t param;
+    int np;
+
+    double runtime, flop;
+    double residual;
+
+    // check arguments
+    if( argc < 2 )
+    {
+	usage( argv[0] );
+	return 1;
+    }
+
+    // check input file
+    if( !(infile=fopen(argv[1], "r"))  ) 
+    {
+	fprintf(stderr, 
+		"\nError: Cannot open \"%s\" for reading.\n\n", argv[1]);
+      
+	usage(argv[0]);
+	return 1;
+    }
+  
+
+    // check result file
+    resfilename= (argc>=3) ? argv[2]:"heat.ppm";
+
+    if( !(resfile=fopen(resfilename, "w")) )
+    {
+	fprintf(stderr, 
+		"\nError: Cannot open \"%s\" for writing.\n\n", 
+		resfilename);
+      
+	usage(argv[0]);
+	return 1;
+    }
+
+    // check input
+    if( !read_input(infile, &param) )
+    {
+	fprintf(stderr, "\nError: Error parsing input file.\n\n");
+      
+	usage(argv[0]);
+	return 1;
+    }
+
+    print_params(&param);
+
+    // set the visualization resolution
+    param.visres = param.max_res;
+
+    param.u     = 0;
+    param.uhelp = 0;
+    param.uvis  = 0;
+
+    param.act_res = param.initial_res;
+
+    // loop over different resolutions
+    while(1) {
+
+	// free allocated memory of previous experiment
+	if (param.u != 0)
+	    finalize(&param);
+
+	if( !initialize(&param) )
+	{
+	    fprintf(stderr, "Error in Jacobi initialization.\n\n");
+
+	    usage(argv[0]);
+	}
+
+	fprintf(stderr, "Resolution: %5u\r", param.act_res);
+
+	// full size (param.act_res are only the inner points)
+	np = param.act_res + 2;
+    
+	// starting time
+	runtime = wtime();
+	residual = 999999999;
+
+	iter = 0;
+	while(1) {
+
+	    switch( param.algorithm ) {
+
+		case 0: // JACOBI
+      
+		    residual = relax_jacobi_return_residual(param.u, param.uhelp, np, np);
+			tmp = param.u;
+			param.u = param.uhelp;
+			param.uhelp = tmp;
+		    break;
+
+		case 1: // GAUSS
+
+		    relax_gauss(param.u, np, np);
+		    residual = residual_gauss( param.u, param.uhelp, np, np);
+		    break;
+	    }
+	    
+	    iter++;
+
+	    // solution good enough ?
+	    if (residual < 0.000005) break;
+
+	    // max. iteration reached ? (no limit with maxiter=0)
+	    if (param.maxiter>0 && iter>=param.maxiter) break;
+	    
+	    if (iter % 100 == 0)
+		fprintf(stderr, "residual %f, %d iterations\n", residual, iter);
+	}
+
+	// Flop count after <i> iterations
+	flop = iter * 11.0 * param.act_res * param.act_res;
+	// stopping time
+	runtime = wtime() - runtime;
+
+	fprintf(stderr, "Resolution: %5u, ", param.act_res);
+	fprintf(stderr, "Time: %04.3f ", runtime);
+	fprintf(stderr, "(%3.3f GFlop => %6.2f MFlop/s, ", 
+		flop/1000000000.0,
+		flop/runtime/1000000);
+	fprintf(stderr, "residual %f, %d iterations)\n", residual, iter);
+
+	// for plot...
+	printf("%5d %f\n", param.act_res, flop/runtime/1000000);
+
+	if (param.act_res + param.res_step_size > param.max_res) break;
+	param.act_res += param.res_step_size;
+    }
+
+    coarsen( param.u, np, np,
+	     param.uvis, param.visres+2, param.visres+2 );
+  
+    write_image( resfile, param.uvis,  
+		 param.visres+2, 
+		 param.visres+2 );
+
+    finalize( &param );
+
+    return 0;
+}

assign4/heat.h

+/*
+ * heat.h
+ *
+ * Global definitions for the iterative solver
+ */
+
+#ifndef JACOBI_H_INCLUDED
+#define JACOBI_H_INCLUDED
+
+#include <stdio.h>
+
+// configuration
+
+typedef struct
+{
+    float posx;
+    float posy;
+    float range;
+    float temp;
+}
+heatsrc_t;
+
+typedef struct
+{
+    unsigned maxiter;       // maximum number of iterations
+    unsigned act_res;
+    unsigned max_res;       // spatial resolution
+    unsigned initial_res;
+    unsigned res_step_size;
+    int algorithm;          // 0=>Jacobi, 1=>Gauss
+
+    unsigned visres;        // visualization resolution
+  
+    double *u, *uhelp;
+    double *uvis;
+
+    unsigned   numsrcs;     // number of heat sources
+    heatsrc_t *heatsrcs;
+}
+algoparam_t;
+
+
+// function declarations
+
+// misc.c
+int initialize( algoparam_t *param );
+int finalize( algoparam_t *param );
+void write_image( FILE * f, double *u,
+		  unsigned sizex, unsigned sizey );
+int coarsen(double *uold, unsigned oldx, unsigned oldy ,
+	    double *unew, unsigned newx, unsigned newy );
+
+// Gauss-Seidel: relax_gauss.c
+double residual_gauss( double *u, double *utmp,
+		       unsigned sizex, unsigned sizey );
+void relax_gauss( double *u, 
+		  unsigned sizex, unsigned sizey  );
+
+// Jacobi: relax_jacobi.c
+#if 0
+double residual_jacobi( double *u,
+			unsigned sizex, unsigned sizey );
+#endif
+double relax_jacobi_return_residual( double *u, double *utmp,
+		   unsigned sizex, unsigned sizey ); 
+
+
+#endif // JACOBI_H_INCLUDED

assign4/input.c

+//
+// input.c
+// 
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include "input.h"
+
+#define BUFSIZE 100
+
+int read_input( FILE *infile, algoparam_t *param )
+{
+  int i, n;
+  char buf[BUFSIZE];
+
+  fgets(buf, BUFSIZE, infile);
+  n = sscanf( buf, "%u", &(param->maxiter) );
+  if( n!=1 )
+    return 0;
+
+  fgets(buf, BUFSIZE, infile);
+  n = sscanf( buf, "%u", &(param->initial_res) );
+  if( n!=1 )
+    return 0;
+
+  fgets(buf, BUFSIZE, infile);
+  n = sscanf( buf, "%u", &(param->max_res) );
+  if( n!=1 )
+    return 0;
+
+  fgets(buf, BUFSIZE, infile);
+  n = sscanf( buf, "%u", &(param->res_step_size) );
+  if( n!=1 )
+    return 0;
+
+
+  fgets(buf, BUFSIZE, infile);
+  n = sscanf(buf, "%d", &(param->algorithm) );
+  if( n!=1 )
+    return 0;
+
+  fgets(buf, BUFSIZE, infile);
+  n = sscanf(buf, "%u", &(param->numsrcs) );
+  if( n!=1 )
+    return 0;
+
+  (param->heatsrcs) = 
+    (heatsrc_t*) malloc( sizeof(heatsrc_t) * (param->numsrcs) );
+  
+  for( i=0; i<param->numsrcs; i++ )
+    {
+      fgets(buf, BUFSIZE, infile);
+      n = sscanf( buf, "%f %f %f %f",
+		  &(param->heatsrcs[i].posx),
+		  &(param->heatsrcs[i].posy),
+		  &(param->heatsrcs[i].range),
+		  &(param->heatsrcs[i].temp) );
+
+      if( n!=4 )
+	return 0;
+    }
+
+  return 1;
+}
+
+
+void print_params( algoparam_t *param )
+{
+  int i;
+
+  fprintf(stderr, "Resolutions       : (%u, %u, ... %u)\n",
+	  param->initial_res,
+	  param->initial_res + param->res_step_size,
+	  param->max_res);
+  fprintf(stderr, "Iterations        : %u\n", param->maxiter);
+  fprintf(stderr, "Algorithm         : %d (%s)\n",
+	  param->algorithm,
+	  (param->algorithm == 0) ? "Jacobi":"Gauss-Jacobi" );
+  fprintf(stderr, "Num. Heat sources : %u\n", param->numsrcs);
+
+  for( i=0; i<param->numsrcs; i++ )
+    {
+      fprintf(stderr, "  %2d: (%2.2f, %2.2f) %2.2f %2.2f \n",
+	     i+1,
+	     param->heatsrcs[i].posx,
+	     param->heatsrcs[i].posy,
+	     param->heatsrcs[i].range,
+	     param->heatsrcs[i].temp );
+    }
+}

assign4/input.h

+//
+// input.h
+//
+
+#ifndef INPUT_H_INCLUDED
+#define INPUT_H_INCLUDED
+
+#include <stdio.h>
+
+#include "heat.h"
+
+int read_input( FILE *infile, algoparam_t *param );
+void print_params( algoparam_t *param );
+
+
+#endif // INPUT_H_INCLUDED

assign4/misc.c

+/*
+ * misc.c
+ *
+ * Helper functions for
+ * - initialization
+ * - finalization,
+ * - writing out a picture
+ */
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <math.h>
+#include <float.h>
+
+#include "heat.h"
+
+/*
+ * Initialize the iterative solver
+ * - allocate memory for matrices
+ * - set boundary conditions according to configuration
+ */
+int initialize( algoparam_t *param )
+{
+    int i, j;
+    double dist;
+
+    // total number of points (including border)
+    const int np = param->act_res + 2;
+  
+    //
+    // allocate memory
+    //
+    (param->u)     = (double*)calloc( sizeof(double),np*np );
+    (param->uhelp) = (double*)calloc( sizeof(double),np*np );
+    (param->uvis)  = (double*)calloc( sizeof(double),
+				      (param->visres+2) *
+				      (param->visres+2) );
+  
+
+    if( !(param->u) || !(param->uhelp) || !(param->uvis) )
+    {
+	fprintf(stderr, "Error: Cannot allocate memory\n");
+	return 0;
+    }
+
+    for( i=0; i<param->numsrcs; i++ )
+    {
+	/* top row */
+	for( j=0; j<np; j++ )
+	{
+	    dist = sqrt( pow((double)j/(double)(np-1) - 
+			     param->heatsrcs[i].posx, 2)+
+			 pow(param->heatsrcs[i].posy, 2));
+	  
+	    if( dist <= param->heatsrcs[i].range )
+	    {
+		(param->u)[j] +=
+		    (param->heatsrcs[i].range-dist) /
+		    param->heatsrcs[i].range *
+		    param->heatsrcs[i].temp;
+		(param->uhelp)[j] = (param->u)[j];
+	    }
+	}
+      
+	/* bottom row */
+	for( j=0; j<np; j++ )
+	{
+	    dist = sqrt( pow((double)j/(double)(np-1) - 
+			     param->heatsrcs[i].posx, 2)+
+			 pow(1-param->heatsrcs[i].posy, 2));
+	  
+	    if( dist <= param->heatsrcs[i].range )
+	    {
+		(param->u)[(np-1)*np+j]+=
+		    (param->heatsrcs[i].range-dist) / 
+		    param->heatsrcs[i].range * 
+		    param->heatsrcs[i].temp;
+		(param->uhelp)[(np-1)*np+j] = (param->u)[(np-1)*np+j];
+	    }
+	}
+      
+	/* leftmost column */
+	for( j=1; j<np-1; j++ )
+	{
+	    dist = sqrt( pow(param->heatsrcs[i].posx, 2)+
+			 pow((double)j/(double)(np-1) - 
+			     param->heatsrcs[i].posy, 2)); 
+	  
+	    if( dist <= param->heatsrcs[i].range )
+	    {
+		(param->u)[ j*np ]+=
+		    (param->heatsrcs[i].range-dist) / 
+		    param->heatsrcs[i].range *
+		    param->heatsrcs[i].temp;
+		(param->uhelp)[ j*np ] = (param->u)[ j*np ];
+	    }
+	}
+      
+	/* rightmost column */
+	for( j=1; j<np-1; j++ )
+	{
+	    dist = sqrt( pow(1-param->heatsrcs[i].posx, 2)+
+			 pow((double)j/(double)(np-1) - 
+			     param->heatsrcs[i].posy, 2)); 
+	  
+	    if( dist <= param->heatsrcs[i].range )
+	    {
+		(param->u)[ j*np+(np-1) ]+=
+		    (param->heatsrcs[i].range-dist) /
+		    param->heatsrcs[i].range *
+		    param->heatsrcs[i].temp;
+		(param->uhelp)[ j*np+(np-1) ] = (param->u)[ j*np+(np-1) ];
+	    }
+	}
+    }
+
+    return 1;
+}
+
+/*
+ * free used memory
+ */
+int finalize( algoparam_t *param )
+{
+    if( param->u ) {
+	free(param->u);
+	param->u = 0;
+    }
+
+    if( param->uhelp ) {
+	free(param->uhelp);
+	param->uhelp = 0;
+    }
+
+    if( param->uvis ) {
+	free(param->uvis);
+	param->uvis = 0;
+    }
+
+    return 1;
+}
+
+
+/*
+ * write the given temperature u matrix to rgb values
+ * and write the resulting image to file f
+ */
+void write_image( FILE * f, double *u,
+		  unsigned sizex, unsigned sizey ) 
+{
+    // RGB table
+    unsigned char r[1024], g[1024], b[1024];
+    int i, j, k;
+  
+    double min, max;
+
+    j=1023;
+
+    // prepare RGB table
+    for( i=0; i<256; i++ )
+    {
+	r[j]=255; g[j]=i; b[j]=0;
+	j--;
+    }
+    for( i=0; i<256; i++ )
+    {
+	r[j]=255-i; g[j]=255; b[j]=0;
+	j--;
+    }
+    for( i=0; i<256; i++ )
+    {
+	r[j]=0; g[j]=255; b[j]=i;
+	j--;
+    }
+    for( i=0; i<256; i++ )
+    {
+	r[j]=0; g[j]=255-i; b[j]=255;
+	j--;
+    }
+
+    min=DBL_MAX;
+    max=-DBL_MAX;
+
+    // find minimum and maximum 
+    for( i=0; i<sizey; i++ )
+    {
+	for( j=0; j<sizex; j++ )
+	{
+	    if( u[i*sizex+j]>max )
+		max=u[i*sizex+j];
+	    if( u[i*sizex+j]<min )
+		min=u[i*sizex+j];
+	}
+    }
+  
+
+    fprintf(f, "P3\n");
+    fprintf(f, "%u %u\n", sizex, sizey);
+    fprintf(f, "%u\n", 255);
+
+    for( i=0; i<sizey; i++ )
+    {
+	for( j=0; j<sizex; j++ )
+	{
+	    k=(int)(1024.0*(u[i*sizex+j]-min)/(max-min));
+	    fprintf(f, "%d %d %d  ", r[k], g[k], b[k]);
+	}
+	fprintf(f, "\n");
+    }
+}
+
+
+int coarsen( double *uold, unsigned oldx, unsigned oldy ,
+	     double *unew, unsigned newx, unsigned newy )
+{
+    int i, j;
+
+    int stepx;
+    int stepy;
+    int stopx = newx;
+    int stopy = newy;
+
+    if (oldx>newx)
+	stepx=oldx/newx;
+    else {
+	stepx=1;
+	stopx=oldx;
+    }
+    if (oldy>newy)
+	stepy=oldy/newy;
+    else {
+	stepy=1;
+	stopy=oldy;
+    }
+
+    // NOTE: this only takes the top-left corner,
+    // and doesnt' do any real coarsening 
+    for( i=0; i<stopy-1; i++ )
+    {
+	for( j=0; j<stopx-1; j++ )
+        {
+	    unew[i*newx+j]=uold[i*oldx*stepy+j*stepx];
+        }
+    }
+
+  return 1;
+}
+

assign4/pfmon2cg

+#!/usr/bin/perl
+#
+# pfmon2cg, version 0.02
+# Converter for pfmon output to Cachegrind profile format
+#
+# 4/2007, Josef Weidendorfer
+#
+
+#
+# Read in pfmon data, e.g. written from the command
+#
+#  pfmon --with-header --smpl-outfile=pfmon.out \
+#        -e l2_misses --short-smpl-periods=100000 -- <command>
+#  (sampling points every 100000 L2 Misses)
+#
+# This gives a list of sampled instruction addresses ($ipps)
+ 
+while(<>) {
+	if (/^#/) {
+		if (/command line\s*:\s*(.*)$/) { $command = $1; }
+		if (/PMD\d+: (.*?)\s*(,|=)/) { $events .= "$1 "; }
+		next; 
+	}
+	if (/^entry/) {
+		($iip) = ($entry =~ /IIP:(\S+)/);
+		if ($iip ne "") { $iips .= "$iip\n"; }
+		$entry = "";
+	}
+	chomp;
+	$entry .= $_;
+}
+($iip) = ($entry =~ /IIP:(\S+)/);
+if ($iip ne "") { $iips .= "$iip\n"; }
+
+($pid) = ($entry =~ /PID:(\S+)/);
+
+open OUT, ">.p2cg";
+print OUT $iips;
+close OUT;
+
+
+# Let addr2line convert the instruction addresses into
+# source code references (needs debug info)
+#
+# This creates hashes with event sums
+
+# Strip command line arguments
+$onlycommand = $command;
+$onlycommand =~ s/\s.*//;
+
+$cmd = "addr2line -f -e $onlycommand < .p2cg";
+#print "#Run Cmd $cmd\n";
+open ATOL, "$cmd < .p2cg|";
+while(<ATOL>) {
+	chomp;
+	$func = $_;
+	$fileline = <ATOL>;
+	chomp $fileline;
+	($file,$line) = ($fileline =~ /(.*?):(.*)/);
+	#print "Func $func, file $file, line $line\n";
+
+	if ($file{$func} eq "") {
+		push @funcs, $func;
+		$file{$func} = $file;
+	}
+	if ($count{$func,$line} eq "") {
+		$tmp = $lines->{$func};
+		$tmp = [] unless defined $tmp;
+		push @$tmp, $line;
+		$lines->{$func} = $tmp;
+	}
+	$count{$func,$line}++;
+	$totals++;
+}
+close ATOL;
+
+#
+# Dump out Cachegrind format
+#
+
+# First header info...
+print "version: 1\n";
+print "creator: pf2mon 0.02\n";
+print "pid: $pid\n";
+print "cmd: $command\n\n";
+
+print "positions: line\n";
+print "events: $events\n";
+print "summary: $totals\n\n";
+
+
+# Now profiling data.
+# 
+# We only support static linked binaries for now, so all code
+# is in the binary
+print "ob=$onlycommand\n";
+
+foreach $f (@funcs) {
+	print "\nfl=$file{$f}\n";
+	print "fn=$f\n";
+	$tmp = $lines->{$f};
+	foreach $l (@$tmp) {
+		print "$l $count{$f,$l}\n";
+	}
+}
+

assign4/relax_gauss.c

+/*
+ * relax_gauss.c
+ *
+ * Gauss-Seidel Relaxation
+ *
+ */
+
+#include "heat.h"
+
+/*
+ * Residual (length of error vector)
+ * between current solution and next after a Gauss-Seidel step
+ *
+ * Temporary array utmp needed to not change current solution
+ *
+ * Flop count in inner body is 7
+ */
+
+double residual_gauss( double *u, double *utmp,
+		       unsigned sizex, unsigned sizey )
+{
+    unsigned i, j;
+    double unew, diff, sum=0.0;
+
+    // first row (boundary condition) into utmp
+    for( j=1; j<sizex-1; j++ )
+	utmp[0*sizex + j] = u[0*sizex + j];
+    // first column (boundary condition) into utmp
+    for( i=1; i<sizey-1; i++ )
+	utmp[i*sizex + 0] = u[i*sizex + 0];
+
+    for( i=1; i<sizey-1; i++ )
+    {
+	for( j=1; j<sizex-1; j++ )
+	{
+	    unew = 0.25 * (utmp[ i*sizex     + (j-1) ]+  // new left
+			   u   [ i*sizex     + (j+1) ]+  // right  
+			   utmp[ (i-1)*sizex + j     ]+  // new top
+			   u   [ (i+1)*sizex + j     ]); // bottom
+
+	    diff = unew - u[i*sizex + j];
+	    sum += diff * diff; 
+
+	    utmp[i*sizex + j] = unew;
+	}
+    }
+
+    return sum;
+}
+
+
+/*
+ * One Gauss-Seidel iteration step
+ *
+ * Flop count in inner body is 4
+ */
+void relax_gauss( double *u, 
+		  unsigned sizex, unsigned sizey )
+{
+    unsigned i, j;
+  
+
+    for( i=1; i<sizey-1; i++ )
+    {
+	for( j=1; j<sizex-1; j++ )
+	{
+	    u[i*sizex+j]= 0.25 * (u[ i*sizex     + (j-1) ]+
+				  u[ i*sizex     + (j+1) ]+
+				  u[ (i-1)*sizex + j     ]+
+				  u[ (i+1)*sizex + j     ]);
+	}
+    }
+}

assign4/relax_jacobi.c

+/*
+ * relax_jacobi.c
+ *
+ * Jacobi Relaxation
+ *
+ */
+
+#include "heat.h"
+
+#if 0
+/*
+ * Residual (length of error vector)
+ * between current solution and next after a Jacobi step
+ */
+double residual_jacobi( double *u, 
+			unsigned sizex, unsigned sizey )
+{
+    unsigned i, j;
+    double unew, diff, sum=0.0;
+
+    for( i=1; i<sizey-1; i++ )
+    {
+	for( j=1; j<sizex-1; j++ )
+        {
+	    unew = 0.25 * (u[ i*sizex     + (j-1) ]+  // left
+			   u[ i*sizex     + (j+1) ]+  // right
+			   u[ (i-1)*sizex + j     ]+  // top
+			   u[ (i+1)*sizex + j     ]); // bottom
+
+	    diff = unew - u[i*sizex + j];
+	    sum += diff * diff; 
+	}
+    }
+
+    return sum;
+}
+#endif
+
+/*
+ * One Jacobi iteration step
+ */
+double relax_jacobi_return_residual( double *u, double *utmp,
+		unsigned sizex, unsigned sizey )
+{
+	int i, j;
+	double unew, diff, sum=0.0;
+
+	for( i=1; i<sizey-1; i++ )
+	{
+		for( j=1; j<sizex-1; j++ )
+		{
+			{
+				utmp[i*sizex + j]= 0.25 * (u[ i*sizex+j -1 ]+  // left
+						u[ i*sizex+j +1 ]+  // right
+						u[ (i-1)*sizex + j ]+  // top
+						u[ (i+1)*sizex + j ]); // bottom
+
+				diff = utmp[i*sizex + j] - u[i*sizex +j];
+				sum += diff * diff;
+			}
+		}
+	}
+	return sum;
+}

assign4/test.dat

+50     # iterations
+100    # initial resolution
+2900   # max resolution (spatial resolution)
+200    # resolution step size
+0      # Algorithm 0=Jacobi 1=Gauss 
+2                     # number of heat sources
+0.0  0.0  1.0  1.0    # (x,y), size temperature
+1.0  1.0  1.0  0.5 

assign4/test2.dat

+0      # iterations
+100    # initial resolution
+100    # max resolution (spatial resolution)
+200    # resolution step size
+1      # Algorithm 0=Jacobi 1=Gauss 
+2                     # number of heat sources
+0.0  0.0  1.0  1.0    # (x,y), size temperature
+1.0  1.0  1.0  0.5 

assign4/timing.c

+//
+// timing.c 
+// 
+
+
+#include <sys/time.h>
+#include "timing.h"
+
+
+double wtime()
+{
+  struct timeval tv;
+  gettimeofday(&tv, 0);
+
+  return tv.tv_sec+1e-6*tv.tv_usec;
+}
+

assign4/timing.h

+//
+// timing.h
+//
+
+#ifndef TIMING_H_INCLUDED
+#define TIMING_H_INCLUDED
+
+double wtime();
+
+#endif // TIMING_H_IINCLUDED