#!/usr/bin/python -u
# @file get_data.py
-# @purpose Extract statistics from repeated runs of N-Body simulators
+# @purpose Extract statistics from repeated runs of N-Body simulators and graph them
# @author Sam Moore (20503628) - 2012
+# Not documented very well, because it's not part of the task requirements
+# Mostly to get a different graph I just comment out a lot of lines and uncomment others. Well designed.
import sys
import os
import subprocess
+import odict
import Gnuplot, Gnuplot.funcutils
plot = Gnuplot.Gnuplot(persist=0)
-programs = {
- "single-thread" : "./single-thread/nbody -v 5"
-}
-for n in range(2, 20, 4):
- programs.update({"mthread"+str(n) : "./mthread/nbody -v 5 -n "+str(n)})
- #programs.update({"slow-mthread"+str(n) : "./mthread/nbody-slow -v 5 -n "+str(n)})
- programs.update({"openmp"+str(n) : "./openmp/nbody -v 5 -n " +str(n)})
+programs = odict.odict([("single-thread" , "./single-thread/nbody -g")])
+
+for n in range(4, 5, 1):
+ programs.update({"mthread"+str(n) : "./mthread/nbody -g -n "+str(n)})
+ programs.update({"openmp"+str(n) : "./openmp/nbody -g -n " +str(n)})
+ for theta in [0.1, 1.0, 10.0]:
+ programs.update({"nbody-bh"+str(n)+":theta"+str(theta) : "./nbody-bh/nbody -g -n "+str(n)+" --theta " + str(theta)})
+
+
def RunForSteps(program, field, steps):
results = []
- print(str(program) + " -s "+str(steps) + " " + str(field))
- results = RunProgram(str(program) + " -s "+str(steps) + " " + str(field))
+ print(str(program) + " -s "+str(steps) + " -v 5 " + str(field))
+ results = RunProgram(str(program) + " -s "+str(steps) + " -v 5 " + str(field))
return results
def VaryField(program, steps, fields):
data = {}
data.update(programs)
+ Plot_PerformanceN(data, 10, 1, 3000, 100)
+
+ """
fields = map(int, os.listdir("fields"))
fields.sort(key = lambda e : e)
if n in ignore:
continue
for p in data.keys():
+ #Plot_MeanErrors(programs["single-thread"], programs[p], "fields/"+str(n), 0, 100)
data[p] = RunForSteps(programs[p], "fields/"+str(n), 200)
#print(str(data[p]))
#for p in sorted(data.items(), key = lambda e : e[1][0][len(e[1][0])-1][1]):
# print(str(p[0])+":"+str(n)+"\t"+str(p[1][0][len(p[1][0])-1][1]))
-
+ """
sys.stdin.readline()
return 0
+def Plot_MeanErrors(control, program, field, sMin, sMax):
+ plot("set xlabel \"steps\"")
+ plot("set ylabel \"Error\"")
+ plot("set title \"Mean Position Error .vs. Steps\\n(Mean Error = Mean absolute error of all position components)\\nField: "+str(field)+"\"")
+ plot("set key outside right")
+ plot("set log y")
+ if (control == program):
+ return
+ d = []
+ for s in range(sMin, sMax, (sMax - sMin) / 20):
+ d.append([s, MeanError(control, program, field, s)])
+
+ plot.replot(Gnuplot.Data(d, title=str(program), with_="lp")) #linecolor "+str(fields.index(n))))
+
+def Plot_PerformanceN(d, steps, nMin, nMax, nStep):
+
+ plot("set xlabel \"N bodies\"")
+ plot("set ylabel \"Real Time (s)\"")
+ plot("set title \"Time taken to simulate N randomly generated bodies for 1000 steps\"")
+ plot("set key outside right")
+ for p in d.items():
+ data = []
+ for n in range(nMin, nMax, nStep):
+ print("Run for " + str(n) + " bodies; " + str(p[1]))
+ r = RunProgram(str(p[1]) + " -r " + str(n) + " -s " + str(steps))
+ data.append([n, r[len(r)-1][1]])
+ plot.replot(Gnuplot.Data(data, title=str(p[0]), with_="lp"))
+
+def MeanError(programA, programB, field, steps):
+ print("Calculate error for "+str(steps) + " steps: " + str(programB) + " .vs. " + str(programA))
+ RunProgram(str(programA) + " -s "+str(steps) + " " + str(field) + " " + "A.tmp")
+ RunProgram(str(programB) + " -s "+str(steps) + " " + str(field) + " " + "B.tmp")
+
+ A = open("A.tmp", "r", 0)
+ B = open("B.tmp", "r", 0)
+
+ nA = int(A.readline().strip("\r\n\t "))
+ nB = int(B.readline().strip("\r\n\t "))
+ if (nA != nB):
+ sys.stderr.write("Body number error; A: " + str(nA) + " vs B: " + str(nB) + "\n")
+ sys.exit(1)
+
+ total_error = 0.0
+ values = 0
+ for i in range(0, nA):
+ dataA = A.readline().strip("\r\n\t ").split(" ")
+ dataB = B.readline().strip("\r\n\t ").split(" ")
+ #print("A: "+str(dataA))
+ #print("B: "+str(dataB))
+ dataA = map(float, dataA)[1:4] # Only count positions
+ dataB = map(float, dataB)[1:4]
+ #print("Length " + str(len(dataA)))
+ if (len(dataB) != len(dataA)):
+ sys.stderr.write("Number of values in line are different\n")
+ sys.exit(1)
+
+
+
+ values += len(dataA)
+ for j in range(0, len(dataA)-1):
+ total_error += abs(dataB[j] - dataA[j])
+ os.system("rm A.tmp; rm B.tmp;")
+ return total_error / values
+
if __name__ == "__main__":
sys.exit(main(sys.argv))
--- /dev/null
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--- /dev/null
+# Makefile for nbody program
+# Compiles on Ubuntu 12.04 and Debian 6.0.4
+# NOTE: This file is identical for both the single-threaded and multi-threaded versions of the program
+CXX = gcc
+LIBRARIES = -lm -lGL -lglut -lGLU -lpthread
+FLAGS = --std=c99 -Wall -pedantic -g
+PREPROCESSOR_FLAGS = -fopenmp
+SINGLE_THREAD_OBJ = main.o nbody.o graphics.o
+LINK_OBJ = main.o nbody.o graphics.o tree.o
+
+BIN = nbody
+
+$(BIN) : $(LINK_OBJ)
+ $(CXX) -o $(BIN) $(LINK_OBJ) $(PREPROCESSOR_FLAGS) $(LIBRARIES)
+
+nbody :
+
+%.o : %.c
+ $(CXX) $(FLAGS) $(PREPROCESSOR_FLAGS) -c $<
+
+clean :
+ $(RM) $(BIN) $(OBJ) $(LINK_OBJ)
+
+clean_full: #cleans up all backup files
+ $(RM) $(BIN) $(OBJ) $(LINK_OBJ)
+ $(RM) *.*~
+ $(RM) *~
--- /dev/null
+version: 1
+creator: callgrind-3.7.0
+pid: 4853
+cmd: ./nbody ../fields/500 -s 10 -g
+part: 1
+
+
+desc: I1 cache:
+desc: D1 cache:
+desc: LL cache:
+
+desc: Timerange: Basic block 0 - 166736221
+desc: Trigger: Program termination
+
+positions: line
+events: Ir
+summary: 1305015743
+
+
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+fn=(224) __asin_finite
+14 2
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+cfi=(42) /build/buildd/eglibc-2.15/csu/../sysdeps/x86_64/multiarch/init-arch.c
+cfn=(204) __get_cpu_features
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+* 5
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+
+fn=(218) __acos_finite
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+
+fn=(230) sin
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+0 5
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+
+fl=(56) /build/buildd/eglibc-2.15/math/../sysdeps/x86_64/fpu/multiarch/s_rintf.S
+fn=(216) rintf
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++1 1
++1 1
++1 1
++1 1
++2 1
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+fn=(222) floor
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++1 1
++1 1
++1 1
++1 1
++2 1
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+cfn=(198) _dl_runtime_resolve
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+
+fl=(60) /build/buildd/eglibc-2.15/math/../sysdeps/x86_64/fpu/multiarch/e_atan2.c
+fn=(226) __atan2_finite
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+-15 1
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+-15 1
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+
+fl=(55)
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+
+fn=(468) 0x0000000000005910
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+
+ob=(9) /usr/lib/x86_64-linux-gnu/libxcb.so.1.1.0
+fl=(86) ???
+fn=(2080) 0x0000000000009370
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+
+ob=(4)
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+
+fn=(474) 0x000000000006be10
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++1 1
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++1 1
++1 1
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+
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+fn=(220) floorf
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++1 1
++1 1
++1 1
++1 1
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+
+fn=(408) 0x00000000000093f0
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+fn=(402) 0x0000000000009350
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+
+fn=(414) 0x0000000000015690
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+
+ob=(4)
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+32 1
+
+ob=(2) ???
+fl=(14) ???
+fn=(440) 0x000000000660d5f8
+0 2
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+cfi=(88) ???
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+
+fn=(694) 0x00000000055e1200
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+cfi=(93) ???
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+cfn=(986) calloc
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+
+fn=(1158) 0x0000000004f54740
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+
+fn=(2102) 0x0000000006c48918
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+cfi=(84) ???
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+
+fn=(338) 0x000000000704ef90
+0 2
+cob=(6) /usr/lib/x86_64-linux-gnu/libXdmcp.so.6.0.0
+cfi=(82) ???
+cfn=(340) 0x0000000000001090
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+fn=(400) 0x0000000006a32050
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+fn=(966)
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+fn=(974) 0x0000000004f54aa0
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+fn=(1178)
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+cfi=(185)
+cfn=(1640)
+calls=10 241
+* 3901410
++1 20
++2 10000
++1 165000
+-1 55000
++2 60000
+cfi=(185)
+cfn=(1644)
+calls=5000 277
+* 1219628564
++1 45000
+cfi=(164)
+cfn=(1646)
+calls=5000 +5
+* 360000
+-5 20030
++8 20
++3 45000
+cfi=(164)
+cfn=(1648)
+calls=5000 +10
+* 285000
+-3 20030
++6 40
+cfi=(185)
+cfn=(1650)
+calls=10 232
+* 63373691
++2 30
++1 30
+-20 11
+cfi=(164)
+cfn=(1638)
+calls=11 270
+* 229
+* 33
++26 3
+cfi=(185)
+cfn=(1652)
+calls=1 -76
+* 1983742
++1 3
+cob=(3)
+cfi=(110)
+cfn=(1060)
+calls=1 2957
+* 127
++1 2
+
+ob=(8)
+fl=(84)
+fn=(2104)
+0 10
+cob=(3)
+cfi=(196)
+cfn=(1736)
+calls=1 31
+0 86
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+cfi=(49)
+cfn=(198)
+calls=1 31
+0 1895
+0 13
+
+fn=(386)
+0 6
+
+fn=(380)
+0 6
+
+fn=(392)
+0 11
+
+fl=(200)
+fn=(2100) check_free
+188 3
++1 3
++12 3
+
+fn=(2098)
+208 2
+cfn=(2100)
+calls=1 -20
+* 9
+
+fl=(85)
+fn=(398)
+30 1
++1 1
++1 1
+
+ob=(11)
+fl=(88)
+fn=(2022)
+0 10
+cob=(3)
+cfi=(196)
+cfn=(1736)
+calls=1 31
+0 86
+cob=(1)
+cfi=(49)
+cfn=(198)
+calls=1 31
+0 1895
+0 13
+
+fn=(448)
+0 6
+
+fn=(442)
+0 6
+
+fn=(454)
+0 11
+
+ob=(19)
+fl=(152)
+fn=(1430)
+0 6
+
+fn=(1724)
+0 10
+cob=(3)
+cfi=(196)
+cfn=(1736)
+calls=1 31
+0 86
+cob=(1)
+cfi=(49)
+cfn=(198)
+calls=1 31
+0 1296
+0 13
+
+fn=(1424)
+0 6
+
+fn=(1436)
+0 11
+
+totals: 1305015743
--- /dev/null
+../single-thread/graphics.c
\ No newline at end of file
--- /dev/null
+../single-thread/graphics.h
\ No newline at end of file
--- /dev/null
+../single-thread/main.c
\ No newline at end of file
--- /dev/null
+/**
+ * @file main.c
+ * @author Sam Moore (20503628) - 2012
+ * @purpose Contains main function, argument handling
+ * NOTE: This file is identical for both the single-threaded and multi-threaded versions of the program
+ */
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <time.h>
+#include <signal.h>
+#include <string.h> // For parsing arguments
+
+#include "nbody.h"
+#include "graphics.h"
+
+// --- Variable definitions --- //
+System universe; // global variable declared in "nbody.h" - The universe of bodies
+Options options; // global variable declared in "nbody.h" - Options passed to program through arguments
+
+
+// --- Function forward declarations --- //
+void HandleArguments(int argc, char ** argv); //Interprets program arguments and sets up the "options" variable
+unsigned IntegerArgument(unsigned * i, int argc, char ** argv, int * store, int * store2); //Helper function to get integer switch
+void FloatArgument(unsigned * i, int argc, char ** argv, float * store); //Helper function to get switch value for float
+void DisplayStatistics(); //Called on exit of program, displays information about computation time, steps computed, etc
+void Interrupt(int dummy); // Interrupt handler function, called when SIGINT (Ctrl-C) is sent to program
+
+
+// --- Function implementations --- //
+
+/**
+ * @function main
+ * @purpose The main function. Calls HandleArguments to set up options,
+ * sets up functions to call at exit, starts simulation and graphics loops
+ * @param argc - Number of arguments
+ * @param argv - The argument strings
+ */
+int main(int argc, char** argv)
+{
+ //Set default options values here
+ options.program = argv[0];
+ options.input = NULL;
+ options.output = NULL;
+ options.num_threads = 0;
+ options.nested_threads = 0;
+ options.num_steps = -1; // Negative values => simulation runs forever unless otherwise specified
+ options.timeout = -1;
+ options.draw_graphics = true;
+ options.pedantic_graphics = false;
+ options.print_positions = false;
+ options.verbosity = 0;
+ options.theta = 0.50;
+
+ //If there are no arguments, print information about usage
+ if (argc == 1)
+ {
+ printf("Usage: %s [OPTIONS] field\n", argv[0]);
+ printf("Controls:\n X - exit\n I, J, K, M - rotate\n W, Z, A, S - move to view"
+ " point\n ./, - zoom in/out\n +/- - scaled zoom in/out\n");
+ exit(EXIT_SUCCESS);
+ }
+
+ //Parse the arguments
+ HandleArguments(argc, argv);
+
+ //Check there is an initial field.
+ if (options.input == NULL)
+ {
+ fprintf(stderr, "Usage: %s [OPTIONS] field\n", argv[0]);
+ fprintf(stderr, " (You did not provide a file for the initial field of bodies)\n");
+ exit(EXIT_FAILURE);
+ }
+
+
+
+ signal(SIGINT, Interrupt); //Handle SIGINT signals
+ atexit(Universe_Cleanup); //On exit, cleanup universe (and write positions of bodies to file if supplied).
+ atexit(DisplayStatistics); //On exit, print information about the computations done
+ System_Init(&universe,options.input); //Initialise the universe from the initial field
+
+ //Setup the time of day at which the simulation starts
+ if (gettimeofday(&(options.start_time), NULL) != 0)
+ {
+ perror("Couldn't get time of day");
+ exit(EXIT_FAILURE);
+ }
+
+ options.start_clock = clock(); //Get CPU cycles executed before simulation starts
+ Simulation_Run(argc, argv); // Start the simulation
+
+ //printf("Main thread done!\n");
+
+ //pthread_exit(NULL);
+ exit(EXIT_SUCCESS); //Should never get to this line
+}
+
+
+/**
+ * @function HandleArguments
+ * @purpose Fill the "options" variable by parsing command line arguments
+ * @param argc - Number of arguments
+ * @param argv - Argument strings
+ */
+void HandleArguments(int argc, char ** argv)
+{
+ for (unsigned i = 1; i < argc; ++i) //For all arguments
+ {
+ if (argv[i][0] != '-') //If the argument is not a switch value...
+ {
+ //Interpret first non switch as input file, and second as output file.
+ //If there are too many non switch arguments, give an error.
+ if (options.input == NULL)
+ options.input = argv[i];
+ else if (options.output == NULL)
+ options.output = argv[i];
+ else
+ {
+ fprintf(stderr,"Usage: %s [OPTIONS] field [output]\n", argv[0]);
+ fprintf(stderr," (You provided too many file names)\n");
+ exit(EXIT_FAILURE);
+ }
+ continue;
+ }
+ switch (argv[i][1]) //The argument is a switch if we get here
+ {
+ case 'n': //Number of threads switch
+ IntegerArgument(&i, argc, argv, &(options.num_threads), &(options.nested_threads));
+ #ifdef SINGLE_THREADED
+ fprintf(stderr, "Warning: -%c switch has no effect in the single-threaded program.\n", 'n');
+
+ #else
+ if (options.num_threads <= 0)
+ {
+ fprintf(stderr, "Require at least one thread (-%c %s is invalid).\n",'n', argv[i]);
+ exit(EXIT_FAILURE);
+ }
+ #endif //SINGLE_THREADED
+ break;
+ case 's': //Number of steps switch
+ IntegerArgument(&i, argc, argv, &(options.num_steps), NULL);
+ if (options.num_steps < 0)
+ {
+ fprintf(stderr, "Require zero or more steps to run (-%c %s is invalid).\n", 's', argv[i]);
+ exit(EXIT_FAILURE);
+ }
+ break;
+ case 't': //Timeout switch (in seconds)
+ IntegerArgument(&i, argc, argv, &(options.timeout), NULL);
+ if (options.timeout < 0)
+ {
+ fprintf(stderr, "Require a timeout greater or equal to zero (-%c %s is invalid).", 't', argv[i]);
+ exit(EXIT_FAILURE);
+ }
+ break;
+ case 'g': //Graphics switch
+ options.draw_graphics = !options.draw_graphics;
+ break;
+ case 'v': //Verbosity switch
+ IntegerArgument(&i, argc, argv, &(options.verbosity), NULL);
+ break;
+
+ case '-':
+ if (strcmp(argv[i]+2, "pedantic-graphics") == 0)
+ {
+ options.pedantic_graphics = true;
+ #ifdef SINGLE_THREADED
+ fprintf(stderr, "Warning: %s switch has no effect in the single threaded program.\n", argv[i]);
+ #endif //SINGLE_THREADED
+ }
+ else if (strcmp(argv[i]+2, "fast-graphics") == 0)
+ {
+ options.pedantic_graphics = false;
+ #ifdef SINGLE_THREADED
+ fprintf(stderr, "Warning: %s switch has no effect in the single threaded program.\n", argv[i]);
+ #endif //SINGLE_THREADED
+
+ }
+ else if (strcmp(argv[i]+2, "theta") == 0)
+ {
+ FloatArgument(&i, argc, argv, &(options.theta));
+ #ifndef BARNES_HUT
+ fprintf(stderr, "Warning: %s switch only works in Barnes Hut version.\n", argv[i-1]);
+ #else
+ if (options.theta < 0)
+ {
+ fprintf(stderr, "Require a theta value greater or equal to zero (%s %s is invalid).\n", argv[i-1], argv[i]);
+ exit(EXIT_FAILURE);
+ }
+
+ #endif //BARNS_HUT
+
+ }
+ else
+ {
+ fprintf(stderr, "Unrecognised switch %s\n", argv[i]);
+ exit(EXIT_FAILURE);
+ }
+ break;
+
+
+ default:
+ fprintf(stderr, "Unrecognised switch -%c\n", argv[i][1]);
+ exit(EXIT_FAILURE);
+ break;
+ }
+
+ }
+}
+
+/**
+ * @function IntegerArgument
+ * @purpose Helper function to get up to two integers following a argument switch, seperated by ':'
+ * @param i - position in the argument array, will be updated after this function
+ * @param argc - number of arguments
+ * @param argv - argument strings
+ * @param store - pointer to unsigned to store result in
+ * @param store2 - pointer to second integer (set to NULL if there is only one integer)
+ * @returns 1 if store was filled, 2 if both store1 and store2 were filled
+ */
+unsigned IntegerArgument(unsigned * i, int argc, char ** argv, int * store, int * store2)
+{
+ if (*i >= argc-1)
+ {
+ fprintf(stderr,"Supply a positive integer for the -%c switch.\n", argv[*i][1]);
+ exit(EXIT_FAILURE);
+ }
+
+ char * seperator = strstr(argv[*i+1], ":");
+ if (seperator != NULL)
+ {
+ if (store2 == NULL)
+ {
+ fprintf(stderr,"Supply a positive integer for the -%c switch.\n", argv[*i][1]);
+ exit(EXIT_FAILURE);
+ }
+ int val = atoi(seperator+1);
+ if (val <= 0)
+ {
+ fprintf(stderr,"Supply a positive integer for the -%c switch.\n", argv[*i][1]);
+ exit(EXIT_FAILURE);
+ }
+ *store2 = (unsigned)val;
+
+ *seperator = '\0';
+ }
+
+ int val = atoi(argv[*i+1]);
+ if (val <= 0 && strcmp("0", argv[*i+1]) != 0)
+ {
+ fprintf(stderr,"Supply a positive integer for the -%c switch. %s is invalid.\n", argv[*i][1], argv[*i+1]);
+ exit(EXIT_FAILURE);
+ }
+ *store = val;
+ *i += 1;
+
+ return (seperator == NULL) ? 1 : 2;
+}
+/**
+ * @function FloatArgument
+ * @purpose Helper function to get a float following a argument switch
+ * @param i - position in the argument array, will be updated after this function
+ * @param argc - number of arguments
+ * @param argv - argument strings
+ * @param store - pointer to float to store result in
+ */
+void FloatArgument(unsigned * i, int argc, char ** argv, float * store)
+{
+ if (*i >= argc-1)
+ {
+ fprintf(stderr,"Supply a float for the -%c switch.\n", argv[*i][1]);
+ exit(EXIT_FAILURE);
+ }
+ *store = atof(argv[*i+1]);
+ if (*store == 0.0 && argv[*i+1][0] != '0')
+ {
+ fprintf(stderr,"Supply a float for the -%c switch.\n", argv[*i][1]);
+ exit(EXIT_FAILURE);
+ }
+ *i += 1;
+}
+
+
+
+/**
+ * @function Interrupt
+ * @purpose Handle SIGINT signal; quit the program gracefully, so that statistics are still displayed
+ * @param dummy - a dummy
+ */
+
+void Interrupt(int dummy)
+{
+ QuitProgram(false);
+}
+
+
--- /dev/null
+/**
+ * @file nbody.c
+ * @purpose Barnes Hut OpenMP version of N-Body simulator, implementation
+ * @author Sam Moore (20503628) - 2012
+ */
+
+#include "nbody.h"
+#include "../single-thread/nbody.c" // Include original code
+#include "graphics.h" // For Graphics functions
+
+#include "tree.h"
+
+
+
+omp_lock_t runstate_lock;
+
+#ifdef USE_THREADS
+omp_lock_t nested_lock;
+#endif //USE_THREADS
+
+Node * parent = NULL;
+
+/**
+ * @function Simulation_Run
+ * @purpose Start the simulation
+ * @param argc, argv - Passed to Graphics_Run if needed, otherwise unused
+ */
+void Simulation_Run(int argc, char ** argv)
+{
+
+ omp_init_lock(&runstate_lock);
+ #ifdef USE_THREADS
+ omp_init_lock(&nested_lock);
+ #endif //USE_THREADS
+
+ #ifdef DUAL_UNIVERSE
+ if (!options.pedantic_graphics)
+ {
+ fprintf(stderr, "Warning: Using pedantic graphics to ensure alternate reality matches our own (as closely as possible).\n");
+ options.pedantic_graphics = true;
+ }
+ #endif //DUAL_UNIVERSE
+
+ omp_set_nested(1);
+ if (omp_get_nested() == 0)
+ {
+ fprintf(stderr, "Couldn't enable nested parallelism\n.");
+ exit(EXIT_FAILURE);
+ }
+
+ if (options.num_threads == 0)
+ {
+ options.num_threads = omp_get_max_threads();
+ if (options.draw_graphics)
+ options.num_threads -= 1;
+ }
+ if (options.nested_threads == 0)
+ {
+ options.nested_threads = omp_get_max_threads() - options.num_threads;
+ if (options.nested_threads == 0)
+ options.nested_threads = 1;
+ }
+
+ #ifdef DUAL_UNIVERSE
+ System_Init(&alternate_universe, options.input);
+ #endif //DUAL_UNIVERSE
+
+ if (options.draw_graphics)
+ {
+ Graphics_Run(argc, argv);
+ if (options.pedantic_graphics == false)
+ {
+
+
+
+ #pragma omp parallel num_threads(2)
+ {
+ // This can't be done with sections!
+ // Because glut is useless, and can only be dealt with in the main thread
+ // I just hope that thread "0" is always the main thread!
+ if (omp_get_thread_num() == 0) // #pragma omp section
+ {
+ //printf("Thread %d gets graphics\n", omp_get_thread_num());
+ glutMainLoop();
+ QuitProgram(false); // Program gets to here if the window is quit
+ }
+ else // #pragma omp section
+ {
+ //printf("Thread %d gets computations\n", omp_get_thread_num());
+ Compute();
+ }
+
+ }
+ return;
+ }
+ }
+ Compute();
+
+ omp_destroy_lock(&runstate_lock);
+ #ifdef USE_THREADS
+ omp_destroy_lock(&nested_lock);
+ #endif //USE_THREADS
+
+
+
+}
+
+/**
+ * @function Compute
+ * @purpose The main computation loop
+ * Uses threading, but only on the first level
+ * I tried to introduce threading to some of the recursive functions in the tree...
+ * But failed
+ */
+void Compute(void)
+{
+ omp_set_nested(1);
+ if (omp_get_nested() == 0)
+ {
+ fprintf(stderr, "Couldn't enable nested parallelism\n.");
+ exit(EXIT_FAILURE);
+ }
+
+ omp_set_num_threads(options.num_threads);
+ if (omp_get_max_threads() != options.num_threads)
+ {
+ fprintf(stderr, "Couldn't use %d threads!\n", options.num_threads);
+ exit(EXIT_FAILURE);
+ }
+
+ parent = Node_Create(NULL);
+
+ Generate_Tree(&universe, parent);
+
+
+
+
+#pragma omp parallel
+{
+ while (!ExitCondition())
+ {
+ #pragma omp single
+ {
+ Node_CalculateMass(parent);
+ }
+
+ #pragma omp for // The easiest way to parallelise it
+ for (unsigned a = 0; a < universe.N; ++a)
+ {
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ universe.body[a].F[i] = 0;
+
+ Node_Forces(universe.body+a, parent, options.theta);
+ //printf("Forces on %p done\n", (void*)(universe.body+a));
+ Body_Velocity(universe.body+a);
+ }
+
+ // put a nowait here so that the first thread out can start updating the tree
+ #pragma omp for nowait
+ for (unsigned a = 0; a < universe.N; ++a)
+ {
+
+ Body_Position(universe.body+a);
+ }
+
+ #pragma omp single // Ideally the first thread out should do this
+ {
+ Update_Tree(&universe, parent);
+ }
+
+ // I haven't noticed any difference in performance.
+ // I'm just showing off.
+ #pragma omp barrier
+
+ // Only the master may do stuff with graphics
+ #pragma omp master
+ {
+ if (options.draw_graphics && options.pedantic_graphics)
+ {
+ glutMainLoopEvent();
+ Graphics_Display();
+ }
+ }
+
+ // Someone should do this stuff too
+ #pragma omp single
+ {
+ universe.steps += 1;
+ if (options.verbosity != 0 && universe.steps % options.verbosity == 0)
+ DisplayStatistics();
+ }
+
+ }
+}
+ Node_Destroy(parent);
+ free(parent);
+
+ QuitProgram(false);
+}
+
+
+void QuitProgram(bool error)
+{
+ if (runstate == QUIT || runstate == QUIT_ERROR)
+ return;
+ omp_set_lock(&runstate_lock);
+ runstate = (error) ? QUIT_ERROR : QUIT;
+ omp_unset_lock(&runstate_lock);
+}
+
+#ifdef DUAL_UNIVERSE
+void BeforeDraw()
+{
+ // Before drawing the main universe... compute and draw the alternate universe
+ // Not threaded, because I am too lazy
+ System_Compute(&alternate_universe);
+
+ for (int i = 0; i < alternate_universe.N; ++i)
+ {
+
+ Body * b = alternate_universe.body+i;
+ Body * original = universe.body+i;
+ //glColor3f(0.0f, b->mass/1e11*100, 0.0f);
+ glColor3f(1.0f, 0.0f, 1.0f);
+ glPushMatrix(); // to save the current matrix
+ glTranslated(scale*b->x[0], scale*b->x[1], scale*b->x[2]);
+ glutSolidSphere (BALL_SIZE, 10, 10);
+ glPopMatrix(); // restore the previous matrix
+
+ // Draw a line from the "alternate" body to the real one
+ glBegin(GL_LINES);
+ glVertex3f(scale*b->x[0], scale*b->x[1], scale*b->x[2]);
+ glVertex3f(scale*original->x[0], scale*original->x[1], scale*original->x[2]);
+ glEnd();
+ }
+}
+#endif //DUAL_UNIVERSE
+
+#ifndef AfterDraw
+void AfterDraw()
+{
+ /* // Uncomment to draw cubes
+ glPolygonMode( GL_FRONT_AND_BACK, GL_LINE );
+ Draw_Node(parent);
+ glFlush();
+ glPolygonMode( GL_FRONT_AND_BACK, GL_FILL);
+ */
+}
+#endif //AfterDraw
--- /dev/null
+/**
+ * @file nbody.c
+ * @purpose Barnes Hut OpenMP version of N-Body simulator, implementation
+ * @author Sam Moore (20503628) - 2012
+ */
+
+#include "nbody.h"
+#include "../single-thread/nbody.c" // Include original code
+#include "graphics.h" // For Graphics_Run function only
+
+#include "tree.h"
+
+
+
+omp_lock_t runstate_lock;
+
+#ifdef USE_THREADS
+omp_lock_t nested_lock;
+#endif //USE_THREADS
+
+Node * parent = NULL;
+
+/**
+ * @function Simulation_Run
+ * @purpose Start the simulation
+ * @param argc, argv - Passed to Graphics_Run if needed, otherwise unused
+ */
+void Simulation_Run(int argc, char ** argv)
+{
+
+ omp_init_lock(&runstate_lock);
+ #ifdef USE_THREADS
+ omp_init_lock(&nested_lock);
+ #endif //USE_THREADS
+
+ #ifdef DUAL_UNIVERSE
+ if (!options.pedantic_graphics)
+ {
+ fprintf(stderr, "Warning: Using pedantic graphics to ensure alternate reality matches our own (as closely as possible).\n");
+ options.pedantic_graphics = true;
+ }
+ #endif //DUAL_UNIVERSE
+
+ omp_set_nested(1);
+ if (omp_get_nested() == 0)
+ {
+ fprintf(stderr, "Couldn't enable nested parallelism\n.");
+ exit(EXIT_FAILURE);
+ }
+
+ if (options.num_threads == 0)
+ {
+ options.num_threads = omp_get_max_threads();
+ if (options.draw_graphics)
+ options.num_threads -= 1;
+ }
+ if (options.nested_threads == 0)
+ {
+ options.nested_threads = omp_get_max_threads() - options.num_threads;
+ if (options.nested_threads == 0)
+ options.nested_threads = 1;
+ }
+
+ #ifdef DUAL_UNIVERSE
+ System_Init(&alternate_universe, options.input);
+ #endif //DUAL_UNIVERSE
+
+ if (options.draw_graphics)
+ {
+ Graphics_Run(argc, argv);
+ if (options.pedantic_graphics == false)
+ {
+
+
+
+ #pragma omp parallel num_threads(2)
+ {
+ // This can't be done with sections!
+ // Because glut is useless, and can only be dealt with in the main thread
+ // I just hope that thread "0" is always the main thread!
+ if (omp_get_thread_num() == 0) // #pragma omp section
+ {
+ //printf("Thread %d gets graphics\n", omp_get_thread_num());
+ glutMainLoop();
+ QuitProgram(false); // Program gets to here if the window is quit
+ }
+ else // #pragma omp section
+ {
+ //printf("Thread %d gets computations\n", omp_get_thread_num());
+ Compute();
+ }
+
+ }
+ return;
+ }
+ }
+ Compute();
+
+ omp_destroy_lock(&runstate_lock);
+ #ifdef USE_THREADS
+ omp_destroy_lock(&nested_lock);
+ #endif //USE_THREADS
+
+
+
+}
+
+/**
+ * @function Compute
+ * @purpose The main computation loop
+ * Uses threading, but only on the first level
+ * I tried to introduce threading to some of the recursive functions in the tree...
+ * But failed
+ */
+void Compute(void)
+{
+ omp_set_nested(1);
+ if (omp_get_nested() == 0)
+ {
+ fprintf(stderr, "Couldn't enable nested parallelism\n.");
+ exit(EXIT_FAILURE);
+ }
+
+ omp_set_num_threads(options.num_threads);
+ if (omp_get_max_threads() != options.num_threads)
+ {
+ fprintf(stderr, "Couldn't use %d threads!\n", options.num_threads);
+ exit(EXIT_FAILURE);
+ }
+
+ parent = Node_Create(NULL);
+
+ Generate_Tree(&universe, parent);
+
+
+
+
+#pragma omp parallel
+{
+ while (!ExitCondition())
+ {
+ #pragma omp single
+ {
+ Node_CalculateMass(parent);
+ }
+
+ #pragma omp for // The easiest way to parallelise it
+ for (unsigned a = 0; a < universe.N; ++a)
+ {
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ universe.body[a].F[i] = 0;
+
+ Node_Forces(universe.body+a, parent, options.theta);
+ //printf("Forces on %p done\n", (void*)(universe.body+a));
+ Body_Velocity(universe.body+a);
+ }
+
+ // put a nowait here so that the first thread out can start updating the tree
+ #pragma omp for nowait
+ for (unsigned a = 0; a < universe.N; ++a)
+ {
+
+ Body_Position(universe.body+a);
+ }
+
+ #pragma omp single // Ideally the first thread out should do this
+ {
+ Update_Tree(&universe, parent);
+ }
+
+ // I haven't noticed any difference in performance.
+ // I'm just showing off.
+ #pragma omp barrier
+
+ // Only the master may do stuff with graphics
+ #pragma omp master
+ {
+ if (options.draw_graphics && options.pedantic_graphics)
+ {
+ glutMainLoopEvent();
+ Graphics_Display();
+ }
+ }
+
+ // Someone should do this stuff too
+ #pragma omp single
+ {
+ universe.steps += 1;
+ if (options.verbosity != 0 && universe.steps % options.verbosity == 0)
+ DisplayStatistics();
+ }
+
+ }
+}
+ Node_Destroy(parent);
+ free(parent);
+
+ QuitProgram(false);
+}
+
+
+void QuitProgram(bool error)
+{
+ if (runstate == QUIT || runstate == QUIT_ERROR)
+ return;
+ omp_set_lock(&runstate_lock);
+ runstate = (error) ? QUIT_ERROR : QUIT;
+ omp_unset_lock(&runstate_lock);
+}
+
+#ifdef DUAL_UNIVERSE
+void BeforeDraw()
+{
+ // Before drawing the main universe... compute and draw the alternate universe
+ // Not threaded, because I am too lazy
+ System_Compute(&alternate_universe);
+
+ for (int i = 0; i < alternate_universe.N; ++i)
+ {
+
+ Body * b = alternate_universe.body+i;
+ Body * original = universe.body+i;
+ //glColor3f(0.0f, b->mass/1e11*100, 0.0f);
+ glColor3f(1.0f, 0.0f, 1.0f);
+ glPushMatrix(); // to save the current matrix
+ glTranslated(scale*b->x[0], scale*b->x[1], scale*b->x[2]);
+ glutSolidSphere (BALL_SIZE, 10, 10);
+ glPopMatrix(); // restore the previous matrix
+
+ // Draw a line from the "alternate" body to the real one
+ glBegin(GL_LINES);
+ glVertex3f(scale*b->x[0], scale*b->x[1], scale*b->x[2]);
+ glVertex3f(scale*original->x[0], scale*original->x[1], scale*original->x[2]);
+ glEnd();
+ }
+}
+#endif //DUAL_UNIVERSE
+
+#ifndef AfterDraw
+void AfterDraw()
+{
+ /* // Uncomment to draw cubes
+ glPolygonMode( GL_FRONT_AND_BACK, GL_LINE );
+ Draw_Node(parent);
+ glFlush();
+ glPolygonMode( GL_FRONT_AND_BACK, GL_FILL);
+ */
+}
+#endif //AfterDraw
--- /dev/null
+#ifndef _NBODY_BARNES_HUT_H
+#define _NBODY_BARNES_HUT_H
+
+/**
+ * @file nbody.h
+ * @purpose OpenMP version of N-Body simulator, declarations
+ * @author Sam Moore (20503628) - 2012
+ */
+
+#include "../single-thread/nbody.h" //Include original code
+#include <omp.h>
+
+
+#undef SINGLE_THREADED
+#define BARNES_HUT
+
+// Define to simultaneously Brute force a copy of the universe, and display together
+//#define DUAL_UNIVERSE
+
+
+// Replace default macros with thread-safe functions
+#undef Simulation_Run
+void Simulation_Run(int argc, char ** argv);
+//#undef QuitProgram
+//#define QuitProgram(x) break
+
+#undef BeforeDraw
+#ifdef DUAL_UNIVERSE
+ System alternate_universe;
+ void BeforeDraw();
+#else
+ #define BeforeDraw() (void)0 // Do nothing (apparently this is how to do nothing with a macro)
+#endif //DUAL_UNIVERSE
+
+#undef AfterDraw
+#define AfterDraw() (void)0
+//void AfterDraw();
+
+#undef QuitProgram
+void QuitProgram(bool error);
+
+void Compute(void);
+
+#endif //_NBODY_BARNES_HUT_H
+
+//EOF
--- /dev/null
+#ifndef _NBODY_BARNES_HUT_H
+#define _NBODY_BARNES_HUT_H
+
+/**
+ * @file nbody.h
+ * @purpose OpenMP version of N-Body simulator, declarations
+ * @author Sam Moore (20503628) - 2012
+ */
+
+#include "../single-thread/nbody.h" //Include original code
+#include <omp.h>
+
+
+#undef SINGLE_THREADED
+#define BARNES_HUT
+
+// Define to simultaneously Brute force a copy of the universe, and display together
+//#define DUAL_UNIVERSE
+
+
+// Replace default macros with thread-safe functions
+#undef Simulation_Run
+void Simulation_Run(int argc, char ** argv);
+//#undef QuitProgram
+//#define QuitProgram(x) break
+
+#undef BeforeDraw
+#ifdef DUAL_UNIVERSE
+ System alternate_universe;
+ void BeforeDraw();
+#else
+ #define BeforeDraw() (void)0 // Do nothing (apparently this is how to do nothing with a macro)
+#endif //DUAL_UNIVERSE
+
+#undef AfterDraw
+#define AfterDraw() (void)0
+//void AfterDraw();
+
+#undef QuitProgram
+void QuitProgram(bool error);
+
+void Compute(void);
+
+#endif //_NBODY_BARNES_HUT_H
+
+//EOF
--- /dev/null
+/**
+ * @file "tree.c"
+ * @purpose Implementation of Barnes Hut algorithms
+ * @author Sam Moore (20503628) 2012
+ */
+
+#include "tree.h"
+#include "math.h"
+#include <string.h>
+#include "graphics.h"
+
+#ifdef USE_THREADS
+unsigned nested_used = 0;
+#endif //USE_THREADS
+
+
+/**
+ * @function Node_SetSpace
+ * @purpose Set the position and space occupied by a node
+ * @param node - The Node
+ * @param x - The vertex with the smallest coordinate values
+ * @param size - The dimensions of the cube that the Node represents
+ */
+void Node_SetSpace(Node * node, float x[DIMENSIONS], float size[DIMENSIONS])
+{
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ {
+ node->x[i] = x[i];
+ node->size[i] = size[i];
+ }
+}
+
+/**
+ * @function Node_Destroy
+ * @purpose Confuse Java programmers
+ * *ahem* Cleanup the memory used by the Node and its children
+ * @param node - The Node
+ */
+void Node_Destroy(Node * node)
+{
+
+ if (node == NULL)
+ return;
+
+ //printf("Destroy node %p\n", (void*)node);
+
+ if (node->body != NULL)
+ {
+ free(node->body);
+ node->body = NULL;
+ }
+ node->allocated = 0;
+ node->N = 0;
+
+ #ifdef USE_THREADS
+ Prepare_Threads(SUB_DIVISIONS);
+ #pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ {
+ Node_Destroy(node->children[i]);
+ free(node->children[i]);
+ node->children[i] = NULL;
+ }
+
+}
+
+/**
+ * @function Node_FindBodies
+ * @purpose Search for bodies in a system within a Node, and add them to the Node's array of bodies.
+ * @param n The Node
+ * @param s The System
+ * @returns The total number of bodies found from s within n
+ */
+unsigned Node_FindBodies(Node * n, System * s)
+{
+
+ if (n->body != NULL)
+ {
+
+ // reset the body array first
+ #ifdef USE_THREADS
+ //Prepare_Threads(options.nested_threads);
+ //#pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned i = 0; i < n->allocated; ++i)
+ n->body[i] = NULL;
+ }
+ n->N = 0; // Don't forget this!
+
+ if (n->parent == NULL)
+ {
+ #ifdef USE_THREADS
+ //Prepare_Threads(options.nested_threads);
+ //#pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned a = 0; a < s->N; ++a)
+ {
+ if (Node_ContainsBody(n, s->body+a))
+ Node_AddBody(n, s->body+a);
+ }
+ }
+ else
+ {
+ #ifdef USE_THREADS
+ //Prepare_Threads(options.nested_threads);
+ //#pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned a = 0; a < n->parent->allocated; ++a)
+ {
+ if (Node_ContainsBody(n, n->parent->body[a]))
+ Node_AddBody(n, n->parent->body[a]);
+ }
+ }
+ //printf("Node %p contains %d bodies\n", (void*)(n), n->N);
+ return n->N;
+}
+
+/**
+ * @function Node_Subdivide
+ * @purpose Subdivide a Node into more nodes and fill them with bodies
+ * @param node - The Node
+ * @param s - The system which the bodies are from
+ * @returns The number of bodies contained in all children of node after this is finished
+ */
+unsigned Node_Subdivide(Node * node, System * s)
+{
+ if (Node_FindBodies(node, s) <= 1) // First find all bodies in the node
+ return node->N; // If there was one or less, no need to subdivide
+
+ unsigned count = 0; // stores the return value of the function
+ float size[DIMENSIONS]; // size of the children of this node
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ size[i] = node->size[i] / 2.0;
+
+ #ifdef USE_THREADS
+ // Prepare_Threads(SUB_DIVISIONS);
+ // #pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned a = 0; a < SUB_DIVISIONS; ++a)
+ {
+ if (node->children[a] == NULL)
+ node->children[a] = Node_Create(node); //Create child node if necessary
+
+ float x[DIMENSIONS];
+
+ // Determine the placement of each child node in space
+ // Annoyingly long switch statement.
+ switch (a)
+ {
+ case 0:
+ x[0] = node->x[0];
+ x[1] = node->x[1];
+ x[2] = node->x[2];
+ break;
+ case 1:
+ x[0] = node->x[0] + size[0];
+ x[1] = node->x[1];
+ x[2] = node->x[2];
+ break;
+ case 2:
+ x[0] = node->x[0];
+ x[1] = node->x[1] + size[1];
+ x[2] = node->x[2];
+ break;
+ case 3:
+ x[0] = node->x[0];
+ x[1] = node->x[1];
+ x[2] = node->x[2] + size[2];
+ break;
+ case 4:
+ x[0] = node->x[0] + size[0];
+ x[1] = node->x[1] + size[1];
+ x[2] = node->x[2];
+ break;
+ case 5:
+ x[0] = node->x[0] + size[0];
+ x[1] = node->x[1];
+ x[2] = node->x[2] + size[2];
+
+ break;
+ case 6:
+ x[0] = node->x[0];
+ x[1] = node->x[1] + size[1];
+ x[2] = node->x[2] + size[2];
+ break;
+ case 7:
+ x[0] = node->x[0] + size[0];
+ x[1] = node->x[1] + size[1];
+ x[2] = node->x[2] + size[2];
+ break;
+ }
+
+ Node_SetSpace(node->children[a], x, size); // Setup the child in space
+ unsigned sub = Node_Subdivide(node->children[a], s); // Recurse for the child
+ count += sub;
+ }
+ return count;
+}
+
+
+/**
+ * @function Node_AddBody
+ * @purpose Terrify third year computer science students
+ * *ahem* Add a Body* to the node's dynamic Body* array. Dynamically. Got that?
+ * I love pointers! They are fun!
+ * @param node - The Node; what did you think it was?
+ * @param b - The Body to add
+ * @returns - The index in the array that the Body* now occupies
+ */
+unsigned Node_AddBody(Node * node, Body * b)
+{
+ unsigned i = 0;
+ for (i = 0; i < node->allocated; ++i) // Search for an empty spot in the array
+ {
+ if (node->body[i] == NULL) // Got one!
+ {
+ node->body[i] = b; // Fill it!
+ node->N += 1;
+ return i; // return!
+ }
+ }
+
+ // No empty spots found :(
+ // The index got outside the array's allocated space, so allocate some more!
+ node->allocated = 2 * (node->allocated + 1); // Doubling the space each time, like what C++ std::vector does
+
+ if (node->body == NULL)
+ node->body = (Body**)(calloc(node->allocated, sizeof(Body*))); // First Body* added, create new array
+ else // Subsequent allocations use realloc
+ {
+ // realloc is expensive. That's why I double the space each time, instead of just adding a constant.
+ // Of course, in the worst case, we are wasting half the memory after the last realloc
+ // But performance wise it is better.
+ node->body = (Body**)(realloc(node->body, sizeof(Body*) * node->allocated)); // Resize existing array
+ memset(node->body+i, 0, sizeof(Body*) * (node->allocated - i)); // set all the new elements to NULL
+ }
+
+ //We now have a valid position in the array that is not filled
+ node->body[i] = b; // So fill it
+ node->N += 1; // don't forget to update this
+ return i; //index in array of Body*
+
+}
+
+/**
+ * @function Generate_Tree
+ * @purpose Generate the tree from a System
+ * @param s - The System
+ * @param n - The root node
+ * @returns The number of bodies in the node (should be the same as in the system)
+ */
+unsigned Generate_Tree(System * s, Node * n)
+{
+ for (unsigned i = 0; i < DIMENSIONS; ++i) // set initial size of node
+ {
+ n->x[i] = -1.0;
+ n->size[i] = 2.0;
+ }
+
+ Node_FitSystem(n, s); // size node so that it contains all bodies in the system
+
+
+ Node_Subdivide(n, s);
+
+ return n->N;
+}
+
+/**
+ * @function Node_FitSystem
+ * @purpose Resize a Node until all bodies in a System are within it
+ * @param n - The Node
+ * @param s - The System
+ */
+void Node_FitSystem(Node * n, System * s)
+{
+ // I'm sure there is a faster way of doing this
+ // But I like this algorithm.
+
+
+ while (Node_FindBodies(n, s) < s->N) // Find bodies in the node...
+ {
+ // As long as the number found is less than the number in the system...
+
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ {
+ n->x[i] *= 2.0;
+ n->size[i] *= 2.0; // Double the size of the Node!
+ }
+ }
+}
+
+/**
+ * @function Update_Tree
+ * @purpose Update the tree (it must already have been Generated with Generate_Tree)
+ * @param s - The System
+ * @param n - The root node of the tree
+ * @returns The number of bodies in the tree
+ */
+unsigned Update_Tree(System * s, Node * n)
+{
+ Node_FitSystem(n, s);
+
+ Node_Subdivide(n, s);
+ return n->N;
+}
+
+/**
+ * @function Node_CalculateMass
+ * @purpose Calculate the mass and centre of mass of a node
+ * @param node - The node
+ * @returns The mass of the node
+ */
+float Node_CalculateMass(Node * node)
+{
+ node->mass = 0.0;
+ if (node->N <= 0) // No bodies in the node
+ return 0.0;
+
+ if (node->N == 1) // Only one body in the node
+ {
+ Body * b = Node_Body(node, 0);
+ node->mass = b->mass;
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ node->com[i] = b->x[i];
+ //printf("Body %p has mass %f, center of mass at %f %f %f\n", (void*)(node), node->mass, node->com[0], node->com[1], node->com[2]);
+ return node->mass;
+ }
+
+
+ // For more than 1 body in the node, calculate mass and com from child nodes
+
+ for (unsigned i = 0; i < DIMENSIONS; ++i) // init com
+ node->com[i] = 0.0;
+
+
+ #ifdef USE_THREADS
+ Prepare_Threads(SUB_DIVISIONS);
+ #pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ {
+ if (node->children[i] != NULL)
+ {
+ float m = Node_CalculateMass(node->children[i]); // Recurse for children
+ node->mass += m;
+ for (unsigned j = 0; j < DIMENSIONS; ++j)
+ node->com[j] += m * node->children[i]->com[j];
+ }
+ }
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ node->com[i] = node->com[i] / node->mass; // weighted average for centre of masses
+
+ //printf("Node %p has mass %f, center of mass at %f %f %f\n", (void*)(node), node->mass, node->com[0], node->com[1], node->com[2]);
+ return node->mass;
+}
+
+/**
+ * @function Node_Forces
+ * @purpose Calculate the forces on a body due to a Node
+ * @param a - The Body
+ * @param n - The node
+ * @param theta - The approximation factor; 0.0 for no approximation.
+ * @returns The depth reached by the recursive algorithm
+ */
+unsigned Node_Forces(Body * a, Node * n, float theta)
+{
+ if (n->N <= 0)
+ return 0;
+
+
+ if (n->N == 1) // external node with one body in it
+ {
+ Body * b = Node_Body(n, 0);
+ if (b == a) //ignore self
+ {
+ return 0;
+ }
+ Body_Force(a, b); // calculate force
+ return 1;
+ }
+
+ // internal node with more than one body in it...
+
+
+ float con;
+ float gd;
+ float d = 0;
+ float s = n->size[0] + n->size[1] + n->size[2] / 3.0;
+
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ d += square(a->x[i] - n->com[i]);
+ d = sqrt(d);
+
+ if (s / d <= theta) // approximation is "valid"
+ {
+ // Calculate force based on centre of mass of the node
+ con = G * a->mass * n->mass / square(d);
+ gd = con / d;
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ a->F[i] += gd * (n->com[i] - a->x[i]);
+ return 1;
+ }
+
+ // approximation "invalid" because node is too close
+ // Then recursively calculate forces due to the node's children
+
+ unsigned count = 0;
+ #ifdef USE_THREADS
+ Prepare_Threads(SUB_DIVISIONS);
+ #pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ {
+ if (n->children[i] != NULL)
+ {
+ count += Node_Forces(a, n->children[i], theta);
+ }
+ }
+ return count;
+}
+
+/**
+ * @function Node_Create
+ * @purpose Create a Node
+ * @param parent - The parent of the Node (NULL if the node is the root of the tree)
+ * @returns The new Node
+ */
+Node * Node_Create(Node * parent)
+{
+ Node * result = (Node*)(calloc(1, sizeof(Node)));
+
+ result->parent = parent;
+
+ /* // In theory, using calloc instead of malloc should make everything zero
+ // So I don't need to do it manually
+ // Kept code here anyway. Because I don't trust gcc.
+
+ result->N = 0;
+ result->allocated = 0;
+ result->body = 0;
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ result->children[i] = NULL;
+ */
+
+ return result;
+
+}
+
+/**
+ * @function Node_Body
+ * @purpose Identify a Body within a Node by its position in the array of Body*
+ * Because elements of the array may be NULL in general, n->body[index] may fail
+ * Actually I think in my code it will work in all cases, because I never set elements of the array to NULL.
+ * It's not worth the risk anyway, I might change my code.
+ *
+ * @param n - The Node
+ * @param index - The position of the Body* in the array
+ * @returns the Body* from the array
+ */
+Body * Node_Body(Node * n, unsigned index)
+{
+ unsigned count = 0;
+ Body * result = NULL;
+
+ // Can't parallelise this, due to the break statement
+ for (unsigned i = 0; i < n->allocated; ++i) // Go through the array...
+ {
+ if (n->body[i] != NULL)
+ count += 1; // Count each non-empty entry
+ if (count > index)
+ {
+ result = n->body[i]; // return element once counter expires
+ break;
+ }
+ }
+
+ return result;
+}
+
+/**
+ * @function Draw_Node
+ * @purpose Draw a node as a series of rectangular prisms
+ * Draws all children of the node too. But only nodes with N == 1 will be shown.
+ * @param n - The Node
+ */
+void Draw_Node(Node * n)
+{
+
+ if (n->N == 1)
+ {
+ glBegin(GL_QUADS);
+ glColor3f(0.0f, 1.0f, 0.0f);
+ glVertex3f(n->x[0] + n->size[0], n->x[1] + n->size[1], n->x[2]);
+ glVertex3f(n->x[0], n->x[1] + n->size[1], n->x[2]);
+ glVertex3f(n->x[0], n->x[1] + n->size[1], n->x[2] + n->size[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2]+n->size[2]);
+
+ glVertex3f(n->x[0] + n->size[0], n->x[1], n->x[2] + n->size[2]);
+ glVertex3f(n->x[0], n->x[1] , n->x[2] + n->size[2]);
+ glVertex3f(n->x[0], n->x[1], n->x[2]);
+ glVertex3f(n->x[0] + n->size[0], n->x[1], n->x[2]);
+
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2]+n->size[2]);
+ glVertex3f(n->x[0], n->x[1]+n->size[1], n->x[2]+n->size[2]);
+ glVertex3f(n->x[0], n->x[1], n->x[2]+n->size[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1], n->x[2]+n->size[2]);
+
+ glVertex3f(n->x[0]+n->size[0], n->x[1], n->x[2]);
+ glVertex3f(n->x[0], n->x[1], n->x[2]);
+ glVertex3f(n->x[0], n->x[1]+n->size[1], n->x[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2]);
+
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2] + n->size[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1], n->x[2] + n->size[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1], n->x[2]);
+ glEnd();
+ }
+ //printf("Node %p contains %u bodies in volume %f\n", (void*)n, n->N, n->size[0] * n->size[1] * n->size[2]);
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ {
+ if (n->children[i] != NULL && n->children[i]->N > 0)
+ Draw_Node(n->children[i]);
+ }
+
+}
+
+/**
+ * @function Node_ContainsBody
+ * @purpose Indicate whether body is within a node
+ * @param n - The Node
+ * @param b - The Body
+ * @returns true iff the body was in the node
+ */
+bool Node_ContainsBody(Node * n, Body * b)
+{
+ if (b == NULL)
+ return false;
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ {
+ float p = b->x[i] - n->x[i];
+ if (p < 0.00 || p > n->size[i])
+ return false;
+ }
+ return true;
+}
+
+// Doesn't work
+#ifdef USE_THREADS
+/**
+ * @function Prepare_Threads
+ * @purpose Tell OMP to spawn up to the specified number of threads on the next parallel section
+ * @param max - Spawn at most this many threads; in reality, less will be spawned
+ */
+void Prepare_Threads(unsigned max)
+{
+ //return;
+
+ if (options.nested_threads == 1)
+ {
+ omp_set_num_threads(1);
+ return;
+ }
+ //printf("Thread %d in nest %d thinking of spawning more threads...\n", omp_get_thread_num(), omp_get_level());
+ //printf("There are %d nested threads, %d in current level\n", nested_used, omp_get_num_threads());
+ //printf("Got past check\n");
+
+ if (max > options.nested_threads)
+ max = options.nested_threads;
+ if (max <= 0)
+ max = options.nested_threads;
+
+
+
+
+ unsigned available = options.nested_threads - nested_used;
+ if (available <= 0)
+ available = 1;
+ if (available < max)
+ max = available;
+
+ omp_set_num_threads(max);
+
+ omp_set_lock(&nested_lock);
+ nested_used += max-1;
+ omp_unset_lock(&nested_lock);
+
+}
+#endif //USE_THREADS
--- /dev/null
+/**
+ * @file "tree.c"
+ * @purpose Implementation of Barnes Hut algorithms
+ * @author Sam Moore (20503628) 2012
+ */
+
+#include "tree.h"
+#include "math.h"
+#include <string.h>
+#include "graphics.h"
+
+#ifdef USE_THREADS
+unsigned nested_used = 0;
+#endif //USE_THREADS
+
+
+/**
+ * @function Node_SetSpace
+ * @purpose Set the position and space occupied by a node
+ * @param node - The Node
+ * @param x - The vertex with the smallest coordinate values
+ * @param size - The dimensions of the cube that the Node represents
+ */
+void Node_SetSpace(Node * node, float x[DIMENSIONS], float size[DIMENSIONS])
+{
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ {
+ node->x[i] = x[i];
+ node->size[i] = size[i];
+ }
+}
+
+/**
+ * @function Node_Destroy
+ * @purpose Confuse Java programmers
+ * *ahem* Cleanup the memory used by the Node and its children
+ * @param node - The Node
+ */
+void Node_Destroy(Node * node)
+{
+
+ if (node == NULL)
+ return;
+
+ //printf("Destroy node %p\n", (void*)node);
+
+ if (node->body != NULL)
+ {
+ free(node->body);
+ node->body = NULL;
+ }
+ node->allocated = 0;
+ node->N = 0;
+
+ #ifdef USE_THREADS
+ Prepare_Threads(SUB_DIVISIONS);
+ #pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ {
+ Node_Destroy(node->children[i]);
+ free(node->children[i]);
+ node->children[i] = NULL;
+ }
+
+}
+
+/**
+ * @function Node_FindBodies
+ * @purpose Search for bodies in a system within a Node, and add them to the Node's array of bodies.
+ * @param n The Node
+ * @param s The System
+ * @returns The total number of bodies found from s within n
+ */
+unsigned Node_FindBodies(Node * n, System * s)
+{
+
+ if (n->body != NULL)
+ {
+
+ // reset the body array first
+ #ifdef USE_THREADS
+ //Prepare_Threads(options.nested_threads);
+ //#pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned i = 0; i < n->allocated; ++i)
+ n->body[i] = NULL;
+ }
+ n->N = 0; // Don't forget this!
+
+ if (n->parent == NULL)
+ {
+ #ifdef USE_THREADS
+ //Prepare_Threads(options.nested_threads);
+ //#pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned a = 0; a < s->N; ++a)
+ {
+ if (Node_ContainsBody(n, s->body+a))
+ Node_AddBody(n, s->body+a);
+ }
+ }
+ else
+ {
+ #ifdef USE_THREADS
+ //Prepare_Threads(options.nested_threads);
+ //#pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned a = 0; a < n->parent->allocated; ++a)
+ {
+ if (Node_ContainsBody(n, n->parent->body[a]))
+ Node_AddBody(n, n->parent->body[a]);
+ }
+ }
+ //printf("Node %p contains %d bodies\n", (void*)(n), n->N);
+ return n->N;
+}
+
+/**
+ * @function Node_Subdivide
+ * @purpose Subdivide a Node into more nodes and fill them with bodies
+ * @param node - The Node
+ * @param s - The system which the bodies are from
+ * @returns The number of bodies contained in all children of node after this is finished
+ */
+unsigned Node_Subdivide(Node * node, System * s)
+{
+ if (Node_FindBodies(node, s) <= 1) // First find all bodies in the node
+ return node->N; // If there was one or less, no need to subdivide
+
+ unsigned count = 0; // stores the return value of the function
+ float size[DIMENSIONS]; // size of the children of this node
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ size[i] = node->size[i] / 2.0;
+
+ #ifdef USE_THREADS
+ // Prepare_Threads(SUB_DIVISIONS);
+ // #pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned a = 0; a < SUB_DIVISIONS; ++a)
+ {
+ if (node->children[a] == NULL)
+ node->children[a] = Node_Create(node); //Create child node if necessary
+
+ float x[DIMENSIONS];
+
+ // Determine the placement of each child node in space
+ // Annoyingly long switch statement.
+ switch (a)
+ {
+ case 0:
+ x[0] = node->x[0];
+ x[1] = node->x[1];
+ x[2] = node->x[2];
+ break;
+ case 1:
+ x[0] = node->x[0] + size[0];
+ x[1] = node->x[1];
+ x[2] = node->x[2];
+ break;
+ case 2:
+ x[0] = node->x[0];
+ x[1] = node->x[1] + size[1];
+ x[2] = node->x[2];
+ break;
+ case 3:
+ x[0] = node->x[0];
+ x[1] = node->x[1];
+ x[2] = node->x[2] + size[2];
+ break;
+ case 4:
+ x[0] = node->x[0] + size[0];
+ x[1] = node->x[1] + size[1];
+ x[2] = node->x[2];
+ break;
+ case 5:
+ x[0] = node->x[0] + size[0];
+ x[1] = node->x[1];
+ x[2] = node->x[2] + size[2];
+
+ break;
+ case 6:
+ x[0] = node->x[0];
+ x[1] = node->x[1] + size[1];
+ x[2] = node->x[2] + size[2];
+ break;
+ case 7:
+ x[0] = node->x[0] + size[0];
+ x[1] = node->x[1] + size[1];
+ x[2] = node->x[2] + size[2];
+ break;
+ }
+
+ Node_SetSpace(node->children[a], x, size); // Setup the child in space
+ unsigned sub = Node_Subdivide(node->children[a], s); // Recurse for the child
+ count += sub;
+ }
+ return count;
+}
+
+
+/**
+ * @function Node_AddBody
+ * @purpose Terrify third year computer science students
+ * *ahem* Add a Body* to the node's dynamic Body* array. Dynamically. Got that?
+ * I love pointers! They are fun!
+ * @param node - The Node; what did you think it was?
+ * @param b - The Body to add
+ * @returns - The index in the array that the Body* now occupies
+ */
+unsigned Node_AddBody(Node * node, Body * b)
+{
+ unsigned i = 0;
+ for (i = 0; i < node->allocated; ++i) // Search for an empty spot in the array
+ {
+ if (node->body[i] == NULL) // Got one!
+ {
+ node->body[i] = b; // Fill it!
+ node->N += 1;
+ return i; // return!
+ }
+ }
+
+ // No empty spots found :(
+ // The index got outside the array's allocated space, so allocate some more!
+ node->allocated = 2 * (node->allocated + 1); // Doubling the space each time, like what C++ std::vector does
+
+ if (node->body == NULL)
+ node->body = (Body**)(calloc(node->allocated, sizeof(Body*))); // First Body* added, create new array
+ else // Subsequent allocations use realloc
+ {
+ // realloc is expensive. That's why I double the space each time, instead of just adding a constant.
+ // Of course, in the worst case, we are wasting half the memory after the last realloc
+ // But performance wise it is better.
+ node->body = (Body**)(realloc(node->body, sizeof(Body*) * node->allocated)); // Resize existing array
+ memset(node->body+i, 0, sizeof(Body*) * (node->allocated - i)); // set all the new elements to NULL
+ }
+
+ //We now have a valid position in the array that is not filled
+ node->body[i] = b; // So fill it
+ node->N += 1; // don't forget to update this
+ return i; //index in array of Body*
+
+}
+
+/**
+ * @function Generate_Tree
+ * @purpose Generate the tree from a System
+ * @param s - The System
+ * @param n - The root node
+ * @returns The number of bodies in the node (should be the same as in the system)
+ */
+unsigned Generate_Tree(System * s, Node * n)
+{
+ for (unsigned i = 0; i < DIMENSIONS; ++i) // set initial size of node
+ {
+ n->x[i] = -1.0;
+ n->size[i] = 2.0;
+ }
+
+ Node_FitSystem(n, s); // size node so that it contains all bodies in the system
+
+
+ Node_Subdivide(n, s);
+
+ return n->N;
+}
+
+/**
+ * @function Node_FitSystem
+ * @purpose Resize a Node until all bodies in a System are within it
+ * @param n - The Node
+ * @param s - The System
+ */
+void Node_FitSystem(Node * n, System * s)
+{
+ // I'm sure there is a faster way of doing this
+ // But I like this algorithm.
+
+
+ while (Node_FindBodies(n, s) < s->N) // Find bodies in the node...
+ {
+ // As long as the number found is less than the number in the system...
+
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ {
+ n->x[i] *= 2.0;
+ n->size[i] *= 2.0; // Double the size of the Node!
+ }
+ }
+}
+
+/**
+ * @function Update_Tree
+ * @purpose Update the tree (it must already have been Generated with Generate_Tree)
+ * @param s - The System
+ * @param n - The root node of the tree
+ * @returns The number of bodies in the tree
+ */
+unsigned Update_Tree(System * s, Node * n)
+{
+ Node_FitSystem(n, s);
+
+ Node_Subdivide(n, s);
+ return n->N;
+}
+
+/**
+ * @function Node_CalculateMass
+ * @purpose Calculate the mass and centre of mass of a node
+ * @param node - The node
+ * @returns The mass of the node
+ */
+float Node_CalculateMass(Node * node)
+{
+ node->mass = 0.0;
+ if (node->N <= 0) // No bodies in the node
+ return 0.0;
+
+ if (node->N == 1) // Only one body in the node
+ {
+ Body * b = Node_Body(node, 0);
+ node->mass = b->mass;
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ node->com[i] = b->x[i];
+ //printf("Body %p has mass %f, center of mass at %f %f %f\n", (void*)(node), node->mass, node->com[0], node->com[1], node->com[2]);
+ return node->mass;
+ }
+
+
+ // For more than 1 body in the node, calculate mass and com from child nodes
+
+ for (unsigned i = 0; i < DIMENSIONS; ++i) // init com
+ node->com[i] = 0.0;
+
+
+ #ifdef USE_THREADS
+ Prepare_Threads(SUB_DIVISIONS);
+ #pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ {
+ if (node->children[i] != NULL)
+ {
+ float m = Node_CalculateMass(node->children[i]); // Recurse for children
+ node->mass += m;
+ for (unsigned j = 0; j < DIMENSIONS; ++j)
+ node->com[j] += m * node->children[i]->com[j];
+ }
+ }
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ node->com[i] = node->com[i] / node->mass; // weighted average for centre of masses
+
+ //printf("Node %p has mass %f, center of mass at %f %f %f\n", (void*)(node), node->mass, node->com[0], node->com[1], node->com[2]);
+ return node->mass;
+}
+
+/**
+ * @function Node_Forces
+ * @purpose Calculate the forces on a body due to a Node
+ * @param a - The Body
+ * @param n - The node
+ * @param theta - The approximation factor; 0.0 for no approximation.
+ * @returns The depth reached by the recursive algorithm
+ */
+unsigned Node_Forces(Body * a, Node * n, float theta)
+{
+ if (n->N <= 0)
+ return 0;
+
+
+ if (n->N == 1) // external node with one body in it
+ {
+ Body * b = Node_Body(n, 0);
+ if (b == a) //ignore self
+ {
+ return 0;
+ }
+ Body_Force(a, b); // calculate force
+ return 1;
+ }
+
+ // internal node with more than one body in it...
+
+
+ float con;
+ float gd;
+ float d = 0;
+ float s = n->size[0] + n->size[1] + n->size[2] / 3.0;
+
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ d += square(a->x[i] - n->com[i]);
+ d = sqrt(d);
+
+ if (s / d <= theta) // approximation is "valid"
+ {
+ // Calculate force based on centre of mass of the node
+ con = G * a->mass * n->mass / square(d);
+ gd = con / d;
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ a->F[i] += gd * (n->com[i] - a->x[i]);
+ return 1;
+ }
+
+ // approximation "invalid" because node is too close
+ // Then recursively calculate forces due to the node's children
+
+ unsigned count = 0;
+ #ifdef USE_THREADS
+ Prepare_Threads(SUB_DIVISIONS);
+ #pragma omp parallel for
+ #endif //USE_THREADS
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ {
+ if (n->children[i] != NULL)
+ {
+ count += Node_Forces(a, n->children[i], theta);
+ }
+ }
+ return count;
+}
+
+/**
+ * @function Node_Create
+ * @purpose Create a Node
+ * @param parent - The parent of the Node (NULL if the node is the root of the tree)
+ * @returns The new Node
+ */
+Node * Node_Create(Node * parent)
+{
+ Node * result = (Node*)(calloc(1, sizeof(Node)));
+
+ result->parent = parent;
+
+ /* // In theory, using calloc instead of malloc should make everything zero
+ // So I don't need to do it manually
+ // Kept code here anyway. Because I don't trust gcc.
+
+ result->N = 0;
+ result->allocated = 0;
+ result->body = 0;
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ result->children[i] = NULL;
+ */
+
+ return result;
+
+}
+
+/**
+ * @function Node_Body
+ * @purpose Identify a Body within a Node by its position in the array of Body*
+ * Because elements of the array may be NULL in general, n->body[index] may fail
+ * Actually I think in my code it will work in all cases, because I never set elements of the array to NULL.
+ * It's not worth the risk anyway, I might change my code.
+ *
+ * @param n - The Node
+ * @param index - The position of the Body* in the array
+ * @returns the Body* from the array
+ */
+Body * Node_Body(Node * n, unsigned index)
+{
+ unsigned count = 0;
+ Body * result = NULL;
+
+ // Can't parallelise this, due to the break statement
+ for (unsigned i = 0; i < n->allocated; ++i) // Go through the array...
+ {
+ if (n->body[i] != NULL)
+ count += 1; // Count each non-empty entry
+ if (count > index)
+ {
+ result = n->body[i]; // return element once counter expires
+ break;
+ }
+ }
+
+ return result;
+}
+
+/**
+ * @function Draw_Node
+ * @purpose Draw a node as a series of rectangular prisms
+ * Draws all children of the node too. But only nodes with N == 1 will be shown.
+ * @param n - The Node
+ */
+void Draw_Node(Node * n)
+{
+
+ if (n->N == 1)
+ {
+ glBegin(GL_QUADS);
+ glColor3f(0.0f, 1.0f, 0.0f);
+ glVertex3f(n->x[0] + n->size[0], n->x[1] + n->size[1], n->x[2]);
+ glVertex3f(n->x[0], n->x[1] + n->size[1], n->x[2]);
+ glVertex3f(n->x[0], n->x[1] + n->size[1], n->x[2] + n->size[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2]+n->size[2]);
+
+ glVertex3f(n->x[0] + n->size[0], n->x[1], n->x[2] + n->size[2]);
+ glVertex3f(n->x[0], n->x[1] , n->x[2] + n->size[2]);
+ glVertex3f(n->x[0], n->x[1], n->x[2]);
+ glVertex3f(n->x[0] + n->size[0], n->x[1], n->x[2]);
+
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2]+n->size[2]);
+ glVertex3f(n->x[0], n->x[1]+n->size[1], n->x[2]+n->size[2]);
+ glVertex3f(n->x[0], n->x[1], n->x[2]+n->size[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1], n->x[2]+n->size[2]);
+
+ glVertex3f(n->x[0]+n->size[0], n->x[1], n->x[2]);
+ glVertex3f(n->x[0], n->x[1], n->x[2]);
+ glVertex3f(n->x[0], n->x[1]+n->size[1], n->x[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2]);
+
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1]+n->size[1], n->x[2] + n->size[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1], n->x[2] + n->size[2]);
+ glVertex3f(n->x[0]+n->size[0], n->x[1], n->x[2]);
+ glEnd();
+ }
+ //printf("Node %p contains %u bodies in volume %f\n", (void*)n, n->N, n->size[0] * n->size[1] * n->size[2]);
+ for (unsigned i = 0; i < SUB_DIVISIONS; ++i)
+ {
+ if (n->children[i] != NULL && n->children[i]->N > 0)
+ Draw_Node(n->children[i]);
+ }
+
+}
+
+/**
+ * @function Node_ContainsBody
+ * @purpose Indicate whether body is within a node
+ * @param n - The Node
+ * @param b - The Body
+ * @returns true iff the body was in the node
+ */
+bool Node_ContainsBody(Node * n, Body * b)
+{
+ if (b == NULL)
+ return false;
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ {
+ float p = b->x[i] - n->x[i];
+ if (p < 0.00 || p > n->size[i])
+ return false;
+ }
+ return true;
+}
+
+#ifdef USE_THREADS
+/**
+ * @function Prepare_Threads
+ * @purpose Tell OMP to spawn up to the specified number of threads on the next parallel section
+ * @param max - Spawn at most this many threads; in reality, less will be spawned
+ */
+void Prepare_Threads(unsigned max)
+{
+ //return;
+
+ if (options.nested_threads == 1)
+ {
+ omp_set_num_threads(1);
+ return;
+ }
+ //printf("Thread %d in nest %d thinking of spawning more threads...\n", omp_get_thread_num(), omp_get_level());
+ //printf("There are %d nested threads, %d in current level\n", nested_used, omp_get_num_threads());
+ //printf("Got past check\n");
+
+ if (max > options.nested_threads)
+ max = options.nested_threads;
+ if (max <= 0)
+ max = options.nested_threads;
+
+
+
+
+ unsigned available = options.nested_threads - nested_used;
+ if (available <= 0)
+ available = 1;
+ if (available < max)
+ max = available;
+
+ omp_set_num_threads(max);
+
+ omp_set_lock(&nested_lock);
+ nested_used += max-1;
+ omp_unset_lock(&nested_lock);
+
+}
+#endif //USE_THREADS
--- /dev/null
+/**
+ * @file tree.h
+ * @purpose Declaration of tree structures for Barnes Hut clustering algorithm for N-Body simulator
+ * @author Sam Moore (20503628) - 2012
+ */
+
+#ifndef _TREE_H
+#define _TREE_H
+
+#include "nbody.h"
+
+#define SUB_DIVISIONS 8
+
+// Define to break everything and nest the threading
+// (Program becomes impossibly slow, but feel free to try)
+// #define USE_THREADS
+
+/**
+ * Structure to represent each node of the tree (a cube (actually a prism) in space)
+ * I call them.... "Data Prisms"
+ * But that takes too long to type, so they are Node instead
+ */
+typedef struct n
+{
+ float x[DIMENSIONS]; // The corner of the cube with smallest valued co-ordinates
+ float size[DIMENSIONS]; // The lengths of the cube faces.
+
+ Body * * body; // Array of pointers to bodies in the node; dynamically created
+ unsigned N; // Number of bodies in the node; valid length of array
+ unsigned allocated; //space allocated for bodies; used to dynamically resize array (doubles every time array is filled).
+
+ float mass;
+ float com[DIMENSIONS]; // Centre of Mass
+
+ struct n * children[SUB_DIVISIONS]; // children nodes (smaller data prisms)
+ struct n * parent; // parent node; the bodies in this node are also in the parent node (bigger data prism)
+
+
+} Node;
+
+void Node_SetSpace(Node * node, float x[DIMENSIONS], float size[DIMENSIONS]); //set the position and volume of a Node
+void Node_Destroy(Node * node); // Cleanup a Node
+unsigned Node_FindBodies(Node * n, System * s); // Find all bodies in System s contained in Node n
+unsigned Node_Subdivide(Node * node, System * s); // Divide Node n into smaller nodes until each node has 1 Body in it
+
+float Node_CalculateMass(Node * node); // Calculate the total mass of a Node
+
+unsigned Node_AddBody(Node * n, Body * b); // Add a body to a Node
+
+unsigned Generate_Tree(System * s, Node * n); // Generate the tree of Nodes for the *first* time
+
+unsigned Update_Tree(System * s, Node * n); // Subsequently update the tree
+
+unsigned Node_Forces(Body * b, Node * node, float theta); // Calculate forces on body due to node. Theta is the approximation factor.
+
+void Node_FitSystem(Node * n, System * s); // Take a node and increase the size until it contains the entire system.
+
+
+Node * Node_Create(Node * parent); // Construct a node for the first time
+
+bool Node_ContainsBody(Node * n, Body * b); // Check if a Body is in a Node
+Body * Node_Body(Node * n, unsigned index); // Identify the n'th body in a Node. Required because the Body* array is slightly special.
+void Draw_Node(Node * n); // Draw a cube corresponding to Node n
+
+
+// Used if nested threading is desired; not recommended. Breaks things
+#ifdef USE_THREADS
+void Prepare_Threads(unsigned max); // Attempt to create "max" threads on the next #pragma omp parallel
+extern unsigned nested_used; // Number of nested threads created
+extern omp_lock_t nested_lock; // Lock around nested_used
+#endif //USE_THREADS
+
+
+#endif //_TREE_H
+
+//EOF
--- /dev/null
+/**
+ * @file tree.h
+ * @purpose Declaration of tree structures for Barnes Hut clustering algorithm for N-Body simulator
+ * @author Sam Moore (20503628) - 2012
+ */
+
+#ifndef _TREE_H
+#define _TREE_H
+
+#include "nbody.h"
+
+#define SUB_DIVISIONS 8
+
+// Define to break everything and nest the threading
+// (Program becomes impossibly slow, but feel free to try)
+// #define USE_THREADS
+
+/**
+ * Structure to represent each node of the tree (a cube (actually a prism) in space)
+ * I call them.... "Data Prisms"
+ * But that takes too long to type, so they are Node instead
+ */
+typedef struct n
+{
+ float x[DIMENSIONS]; // The corner of the cube with smallest valued co-ordinates
+ float size[DIMENSIONS]; // The lengths of the cube faces.
+
+ Body * * body; // Array of pointers to bodies in the node; dynamically created
+ unsigned N; // Number of bodies in the node; valid length of array
+ unsigned allocated; //space allocated for bodies; used to dynamically resize array (doubles every time array is filled).
+
+ float mass;
+ float com[DIMENSIONS]; // Centre of Mass
+
+ struct n * children[SUB_DIVISIONS]; // children nodes (smaller data prisms)
+ struct n * parent; // parent node; the bodies in this node are also in the parent node (bigger data prism)
+
+
+} Node;
+
+void Node_SetSpace(Node * node, float x[DIMENSIONS], float size[DIMENSIONS]); //set the position and volume of a Node
+void Node_Destroy(Node * node); // Cleanup a Node
+unsigned Node_FindBodies(Node * n, System * s); // Find all bodies in System s contained in Node n
+unsigned Node_Subdivide(Node * node, System * s); // Divide Node n into smaller nodes until each node has 1 Body in it
+
+float Node_CalculateMass(Node * node); // Calculate the total mass of a Node
+
+unsigned Node_AddBody(Node * n, Body * b); // Add a body to a Node
+
+unsigned Generate_Tree(System * s, Node * n); // Generate the tree of Nodes for the *first* time
+
+unsigned Update_Tree(System * s, Node * n); // Subsequently update the tree
+
+unsigned Node_Forces(Body * b, Node * node, float theta); // Calculate forces on body due to node. Theta is the approximation factor.
+
+void Node_FitSystem(Node * n, System * s); // Take a node and increase the size until it contains the entire system.
+
+
+Node * Node_Create(Node * parent); // Construct a node for the first time
+
+bool Node_ContainsBody(Node * n, Body * b); // Check if a Body is in a Node
+Body * Node_Body(Node * n, unsigned index); // Identify the n'th body in a Node. Required because the Body* array is slightly special.
+void Draw_Node(Node * n); // Draw a cube corresponding to Node n
+
+
+// Used if nested threading is desired; not recommended. Breaks things
+#ifdef USE_THREADS
+void Prepare_Threads(unsigned max);
+extern unsigned nested_used;
+extern omp_lock_t nested_lock;
+#endif //USE_THREADS
+
+
+#endif //_TREE_H
+
+//EOF
--- /dev/null
+# -*- coding: utf-8 -*-
+"""
+ odict
+ ~~~~~
+
+ This module is an example implementation of an ordered dict for the
+ collections module. It's not written for performance (it actually
+ performs pretty bad) but to show how the API works.
+
+
+ Questions and Answers
+ =====================
+
+ Why would anyone need ordered dicts?
+
+ Dicts in python are unordered which means that the order of items when
+ iterating over dicts is undefined. As a matter of fact it is most of
+ the time useless and differs from implementation to implementation.
+
+ Many developers stumble upon that problem sooner or later when
+ comparing the output of doctests which often does not match the order
+ the developer thought it would.
+
+ Also XML systems such as Genshi have their problems with unordered
+ dicts as the input and output ordering of tag attributes is often
+ mixed up because the ordering is lost when converting the data into
+ a dict. Switching to lists is often not possible because the
+ complexity of a lookup is too high.
+
+ Another very common case is metaprogramming. The default namespace
+ of a class in python is a dict. With Python 3 it becomes possible
+ to replace it with a different object which could be an ordered dict.
+ Django is already doing something similar with a hack that assigns
+ numbers to some descriptors initialized in the class body of a
+ specific subclass to restore the ordering after class creation.
+
+ When porting code from programming languages such as PHP and Ruby
+ where the item-order in a dict is guaranteed it's also a great help
+ to have an equivalent data structure in Python to ease the transition.
+
+ Where are new keys added?
+
+ At the end. This behavior is consistent with Ruby 1.9 Hashmaps
+ and PHP Arrays. It also matches what common ordered dict
+ implementations do currently.
+
+ What happens if an existing key is reassigned?
+
+ The key is *not* moved. This is consitent with existing
+ implementations and can be changed by a subclass very easily::
+
+ class movingodict(odict):
+ def __setitem__(self, key, value):
+ self.pop(key, None)
+ odict.__setitem__(self, key, value)
+
+ Moving keys to the end of a ordered dict on reassignment is not
+ very useful for most applications.
+
+ Does it mean the dict keys are sorted by a sort expression?
+
+ That's not the case. The odict only guarantees that there is an order
+ and that newly inserted keys are inserted at the end of the dict. If
+ you want to sort it you can do so, but newly added keys are again added
+ at the end of the dict.
+
+ I initializes the odict with a dict literal but the keys are not
+ ordered like they should!
+
+ Dict literals in Python generate dict objects and as such the order of
+ their items is not guaranteed. Before they are passed to the odict
+ constructor they are already unordered.
+
+ What happens if keys appear multiple times in the list passed to the
+ constructor?
+
+ The same as for the dict. The latter item overrides the former. This
+ has the side-effect that the position of the first key is used because
+ the key is actually overwritten:
+
+ >>> odict([('a', 1), ('b', 2), ('a', 3)])
+ odict.odict([('a', 3), ('b', 2)])
+
+ This behavor is consistent with existing implementation in Python
+ and the PHP array and the hashmap in Ruby 1.9.
+
+ This odict doesn't scale!
+
+ Yes it doesn't. The delitem operation is O(n). This is file is a
+ mockup of a real odict that could be implemented for collections
+ based on an linked list.
+
+ Why is there no .insert()?
+
+ There are few situations where you really want to insert a key at
+ an specified index. To now make the API too complex the proposed
+ solution for this situation is creating a list of items, manipulating
+ that and converting it back into an odict:
+
+ >>> d = odict([('a', 42), ('b', 23), ('c', 19)])
+ >>> l = d.items()
+ >>> l.insert(1, ('x', 0))
+ >>> odict(l)
+ odict.odict([('a', 42), ('x', 0), ('b', 23), ('c', 19)])
+
+ :copyright: (c) 2008 by Armin Ronacher and PEP 273 authors.
+ :license: modified BSD license.
+"""
+from itertools import izip, imap
+from copy import deepcopy
+
+missing = object()
+
+
+class odict(dict):
+ """
+ Ordered dict example implementation.
+
+ This is the proposed interface for a an ordered dict as proposed on the
+ Python mailinglist (proposal_).
+
+ It's a dict subclass and provides some list functions. The implementation
+ of this class is inspired by the implementation of Babel but incorporates
+ some ideas from the `ordereddict`_ and Django's ordered dict.
+
+ The constructor and `update()` both accept iterables of tuples as well as
+ mappings:
+
+ >>> d = odict([('a', 'b'), ('c', 'd')])
+ >>> d.update({'foo': 'bar'})
+ >>> d
+ odict.odict([('a', 'b'), ('c', 'd'), ('foo', 'bar')])
+
+ Keep in mind that when updating from dict-literals the order is not
+ preserved as these dicts are unsorted!
+
+ You can copy an odict like a dict by using the constructor, `copy.copy`
+ or the `copy` method and make deep copies with `copy.deepcopy`:
+
+ >>> from copy import copy, deepcopy
+ >>> copy(d)
+ odict.odict([('a', 'b'), ('c', 'd'), ('foo', 'bar')])
+ >>> d.copy()
+ odict.odict([('a', 'b'), ('c', 'd'), ('foo', 'bar')])
+ >>> odict(d)
+ odict.odict([('a', 'b'), ('c', 'd'), ('foo', 'bar')])
+ >>> d['spam'] = []
+ >>> d2 = deepcopy(d)
+ >>> d2['spam'].append('eggs')
+ >>> d
+ odict.odict([('a', 'b'), ('c', 'd'), ('foo', 'bar'), ('spam', [])])
+ >>> d2
+ odict.odict([('a', 'b'), ('c', 'd'), ('foo', 'bar'), ('spam', ['eggs'])])
+
+ All iteration methods as well as `keys`, `values` and `items` return
+ the values ordered by the the time the key-value pair is inserted:
+
+ >>> d.keys()
+ ['a', 'c', 'foo', 'spam']
+ >>> d.values()
+ ['b', 'd', 'bar', []]
+ >>> d.items()
+ [('a', 'b'), ('c', 'd'), ('foo', 'bar'), ('spam', [])]
+ >>> list(d.iterkeys())
+ ['a', 'c', 'foo', 'spam']
+ >>> list(d.itervalues())
+ ['b', 'd', 'bar', []]
+ >>> list(d.iteritems())
+ [('a', 'b'), ('c', 'd'), ('foo', 'bar'), ('spam', [])]
+
+ Index based lookup is supported too by `byindex` which returns the
+ key/value pair for an index:
+
+ >>> d.byindex(2)
+ ('foo', 'bar')
+
+ You can reverse the odict as well:
+
+ >>> d.reverse()
+ >>> d
+ odict.odict([('spam', []), ('foo', 'bar'), ('c', 'd'), ('a', 'b')])
+
+ And sort it like a list:
+
+ >>> d.sort(key=lambda x: x[0].lower())
+ >>> d
+ odict.odict([('a', 'b'), ('c', 'd'), ('foo', 'bar'), ('spam', [])])
+
+ .. _proposal: http://thread.gmane.org/gmane.comp.python.devel/95316
+ .. _ordereddict: http://www.xs4all.nl/~anthon/Python/ordereddict/
+ """
+
+ def __init__(self, *args, **kwargs):
+ dict.__init__(self)
+ self._keys = []
+ self.update(*args, **kwargs)
+
+ def __delitem__(self, key):
+ dict.__delitem__(self, key)
+ self._keys.remove(key)
+
+ def __setitem__(self, key, item):
+ if key not in self:
+ self._keys.append(key)
+ dict.__setitem__(self, key, item)
+
+ def __deepcopy__(self, memo=None):
+ if memo is None:
+ memo = {}
+ d = memo.get(id(self), missing)
+ if d is not missing:
+ return d
+ memo[id(self)] = d = self.__class__()
+ dict.__init__(d, deepcopy(self.items(), memo))
+ d._keys = self._keys[:]
+ return d
+
+ def __getstate__(self):
+ return {'items': dict(self), 'keys': self._keys}
+
+ def __setstate__(self, d):
+ self._keys = d['keys']
+ dict.update(d['items'])
+
+ def __reversed__(self):
+ return reversed(self._keys)
+
+ def __eq__(self, other):
+ if isinstance(other, odict):
+ if not dict.__eq__(self, other):
+ return False
+ return self.items() == other.items()
+ return dict.__eq__(self, other)
+
+ def __ne__(self, other):
+ return not self.__eq__(other)
+
+ def __cmp__(self, other):
+ if isinstance(other, odict):
+ return cmp(self.items(), other.items())
+ elif isinstance(other, dict):
+ return dict.__cmp__(self, other)
+ return NotImplemented
+
+ @classmethod
+ def fromkeys(cls, iterable, default=None):
+ return cls((key, default) for key in iterable)
+
+ def clear(self):
+ del self._keys[:]
+ dict.clear(self)
+
+ def copy(self):
+ return self.__class__(self)
+
+ def items(self):
+ return zip(self._keys, self.values())
+
+ def iteritems(self):
+ return izip(self._keys, self.itervalues())
+
+ def keys(self):
+ return self._keys[:]
+
+ def iterkeys(self):
+ return iter(self._keys)
+
+ def pop(self, key, default=missing):
+ if default is missing:
+ return dict.pop(self, key)
+ elif key not in self:
+ return default
+ self._keys.remove(key)
+ return dict.pop(self, key, default)
+
+ def popitem(self, key):
+ self._keys.remove(key)
+ return dict.popitem(key)
+
+ def setdefault(self, key, default=None):
+ if key not in self:
+ self._keys.append(key)
+ dict.setdefault(self, key, default)
+
+ def update(self, *args, **kwargs):
+ sources = []
+ if len(args) == 1:
+ if hasattr(args[0], 'iteritems'):
+ sources.append(args[0].iteritems())
+ else:
+ sources.append(iter(args[0]))
+ elif args:
+ raise TypeError('expected at most one positional argument')
+ if kwargs:
+ sources.append(kwargs.iteritems())
+ for iterable in sources:
+ for key, val in iterable:
+ self[key] = val
+
+ def values(self):
+ return map(self.get, self._keys)
+
+ def itervalues(self):
+ return imap(self.get, self._keys)
+
+ def index(self, item):
+ return self._keys.index(item)
+
+ def byindex(self, item):
+ key = self._keys[item]
+ return (key, dict.__getitem__(self, key))
+
+ def reverse(self):
+ self._keys.reverse()
+
+ def sort(self, *args, **kwargs):
+ self._keys.sort(*args, **kwargs)
+
+ def __repr__(self):
+ return 'odict.odict(%r)' % self.items()
+
+ __copy__ = copy
+ __iter__ = iterkeys
+
+
+if __name__ == '__main__':
+ import doctest
+ doctest.testmod()
System * sub_system = NULL;
#endif //OVER_ENGINEERED
+omp_lock_t runstate_lock;
+
/**
* @function Simulation_Run
* @purpose Start the simulation
*/
void Simulation_Run(int argc, char ** argv)
{
-
+ omp_init_lock(&runstate_lock);
if (options.num_threads == 0)
options.num_threads = omp_get_max_threads();
}
- #pragma omp parallel sections num_threads(2)
+ #pragma omp parallel num_threads(2)
{
- #pragma omp section
- {
- Compute();
- }
- #pragma omp section
+ // This can't be done with sections!
+ // Because glut is useless, and can only be dealt with in the main thread
+ // I just hope that thread "0" is always the main thread!
+ if (omp_get_thread_num() == 0) // #pragma omp section
{
+ //printf("Thread %d gets graphics\n", omp_get_thread_num());
glutMainLoop();
+ QuitProgram(false); // Program gets to here if the window is quit
+ }
+ else // #pragma omp section
+ {
+ //printf("Thread %d gets computations\n", omp_get_thread_num());
+ Compute();
}
}
return;
Compute();
-
+ omp_destroy_lock(&runstate_lock);
}
}
}
+ QuitProgram(false);
+}
+
+void QuitProgram(bool error)
+{
+ if (runstate == QUIT || runstate == QUIT_ERROR)
+ return;
+ omp_set_lock(&runstate_lock);
+ runstate = (error) ? QUIT_ERROR : QUIT;
+ omp_unset_lock(&runstate_lock);
}
#define AfterDraw() (void)0
//void AfterDraw();
-
+#undef QuitProgram
+void QuitProgram(bool error);
void Compute(void);
void Compute2(void);
--- /dev/null
+\relax
+\ifx\hyper@anchor\@undefined
+\global \let \oldcontentsline\contentsline
+\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global \let \oldnewlabel\newlabel
+\gdef \newlabel#1#2{\newlabelxx{#1}#2}
+\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\let \contentsline\oldcontentsline
+\let \newlabel\oldnewlabel}
+\else
+\global \let \hyper@last\relax
+\fi
+
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Euler's Method}{2}{section.2}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Parallelisation}{3}{section.3}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Graphics}{3}{subsection.3.1}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}POSIX Threads (pthreads)}{4}{section.4}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Barriers}{4}{subsection.4.1}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Division of Labour}{4}{subsection.4.2}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Single Threaded Section}{5}{subsection.4.3}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}OpenMP}{5}{section.5}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Barnes Hut Algorithm}{5}{section.6}}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Barnes Hut - One body per cube\relax }}{6}{figure.1}}
+\newlabel{cubes.png}{{1}{6}{Barnes Hut - One body per cube\relax \relax }{figure.1}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Errors}{6}{subsection.6.1}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Performance for different $\theta $ values}{6}{subsection.6.2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Barnes Hut mean error\relax }}{7}{figure.2}}
+\newlabel{error_graph.png}{{2}{7}{Barnes Hut mean error\relax \relax }{figure.2}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Barnes Hut single threaded performance\relax }}{8}{figure.3}}
+\newlabel{efficiency.png}{{3}{8}{Barnes Hut single threaded performance\relax \relax }{figure.3}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {7}Performance Analysis}{9}{section.7}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}Time vs Steps}{9}{subsection.7.1}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Time to compute vs Number of Bodies}{9}{subsection.7.2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Implementation Performance\relax }}{10}{figure.4}}
+\newlabel{time_vs_steps.png}{{4}{10}{Implementation Performance\relax \relax }{figure.4}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Efficiency vs $n$\relax }}{11}{figure.5}}
+\newlabel{time_vs_n.png}{{5}{11}{Efficiency vs $n$\relax \relax }{figure.5}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Analysis with Callgrind}{12}{subsection.7.3}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Kcachegrind reveals why my program is slow\relax }}{13}{figure.6}}
+\newlabel{kcachegrind.png}{{6}{13}{Kcachegrind reveals why my program is slow\relax \relax }{figure.6}{}}
--- /dev/null
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+%%EndFont
+%%BeginFont: CMTI10
+%!PS-AdobeFont-1.0: CMTI10 003.002
+%%Title: CMTI10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMTI10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMTI10 known{/CMTI10 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMTI10 def
+/FontBBox {-35 -250 1124 750 }readonly def
+/UniqueID 5000828 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMTI10.) readonly def
+/FullName (CMTI10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 97 /a put
+dup 108 /l put
+readonly def
+currentdict end
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+cleartomark
+{restore}if
+%%EndFont
+%%BeginFont: CMSY9
+%!PS-AdobeFont-1.0: CMSY9 003.002
+%%Title: CMSY9
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY9.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMSY9 known{/CMSY9 findfont dup/UniqueID known{dup
+/UniqueID get 5096650 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMSY9 def
+/FontBBox {-29 -958 1146 777 }readonly def
+/UniqueID 5096650 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY9.) readonly def
+/FullName (CMSY9) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 3 /asteriskmath put
+readonly def
+currentdict end
+currentfile eexec
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+cleartomark
+{restore}if
+%%EndFont
+%%BeginFont: CMR9
+%!PS-AdobeFont-1.0: CMR9 003.002
+%%Title: CMR9
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR9.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR9 known{/CMR9 findfont dup/UniqueID known{dup
+/UniqueID get 5000792 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMR9 def
+/FontBBox {-39 -250 1036 750 }readonly def
+/UniqueID 5000792 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR9.) readonly def
+/FullName (CMR9) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 43 /plus put
+dup 44 /comma put
+dup 47 /slash put
+dup 58 /colon put
+dup 61 /equal put
+dup 65 /A put
+dup 67 /C put
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+%%EndFont
+%%BeginFont: CMR5
+%!PS-AdobeFont-1.0: CMR5 003.002
+%%Title: CMR5
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR5.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR5 known{/CMR5 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
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+/FontName /CMR5 def
+/FontBBox {-10 -250 1304 750 }readonly def
+/UniqueID 5000788 def
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+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR5.) readonly def
+/FullName (CMR5) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
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+%%Title: CMMI10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+%%EndFont
+%%BeginFont: CMR10
+%!PS-AdobeFont-1.0: CMR10 003.002
+%%Title: CMR10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+{save true}{false}ifelse}{false}ifelse
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+/FontName /CMR10 def
+/FontBBox {-40 -250 1009 750 }readonly def
+/UniqueID 5000793 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
+/FullName (CMR10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
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+{restore}if
+%%EndFont
+%%BeginFont: CMBX10
+%!PS-AdobeFont-1.0: CMBX10 003.002
+%%Title: CMBX10
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMBX10.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMBX10 known{/CMBX10 findfont dup/UniqueID known{dup
+/UniqueID get 5000768 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMBX10 def
+/FontBBox {-56 -250 1164 750 }readonly def
+/UniqueID 5000768 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMBX10.) readonly def
+/FullName (CMBX10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Bold) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 39 /quoteright put
+dup 45 /hyphen put
+dup 49 /one put
+dup 50 /two put
+dup 51 /three put
+dup 52 /four put
+dup 67 /C put
+dup 69 /E put
+dup 73 /I put
+dup 77 /M put
+dup 79 /O put
+dup 80 /P put
+dup 84 /T put
+dup 86 /V put
+dup 97 /a put
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+%%EndFont
+%%BeginFont: CMR12
+%!PS-AdobeFont-1.0: CMR12 003.002
+%%Title: CMR12
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR12.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup
+/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMR12 def
+/FontBBox {-34 -251 988 750 }readonly def
+/UniqueID 5000794 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR12.) readonly def
+/FullName (CMR12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 46 /period put
+dup 48 /zero put
+dup 50 /two put
+dup 51 /three put
+dup 53 /five put
+dup 54 /six put
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+\usepackage{caption}
+\usepackage{amsmath} % needed for math align
+\usepackage{bm} % needed for maths bold face
+ \usepackage{graphicx} % needed for including graphics e.g. EPS, PS
+\usepackage{fancyhdr} % needed for header
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+
+
+\newcommand{\vect}[1]{\boldsymbol{#1}} % Draw a vector
+\newcommand{\divg}[1]{\nabla \cdot #1} % divergence
+\newcommand{\curl}[1]{\nabla \times #1} % curl
+\newcommand{\grad}[1]{\nabla #1} %gradient
+\newcommand{\pd}[3][ ]{\frac{\partial^{#1} #2}{\partial #3^{#1}}} %partial derivative
+\newcommand{\der}[3][ ]{\frac{d^{#1} #2}{d #3^{#1}}} %full derivative
+\newcommand{\phasor}[1]{\tilde{#1}} % make a phasor
+\newcommand{\laplacian}[1]{\nabla^2 {#1}} % The laplacian operator
+
+\usepackage{color}
+\usepackage{listings}
+
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+\lstset{commentstyle=\color{darkblue}}
+%\lstset{stringsyle=\color{red}}
+\lstset{showstringspaces=false}
+\lstset{basicstyle=\small}
+
+
+\begin{document}
+
+\pagestyle{fancy}
+\fancyhead{}
+\fancyfoot{}
+
+\fancyhead[LO, L]{}
+\fancyfoot[CO, C]{\thepage}
+
+\title{\bf A Multithreaded N-Body Simulation}
+\date{}
+\maketitle
+
+\tableofcontents
+
+
+
+\pagebreak
+
+\section{Introduction}
+
+An N-Body simulation's purpose is to solve for the positions and velocities of an arbitrary number of interacting bodies using numerical methods.
+
+Complex systems involving large numbers of bodies, interacting over long periods of time, are often of interest. Hence there is considerable motivation to improve the speed (amount of time simulated over real time required) of N-Body simulations.
+This report focuses on increasing the speed of an N-Body simulation by introducing parallelism using threads.
+
+The bodies in this simulation interact according to Newtonian laws of gravity. The force acting on a body $A$ due to body $B$ is given by:
+\begin{align*}
+ \vect{F_{AB}} &= G \frac{m_A m_B}{\left| \vect{r_B} - \vect{r_A} \right|^3} \left(\vect{r_B} - \vect{r_A}\right)
+\end{align*}
+Where $m_A$ and $m_B$ are the masses of the two bodies; $\vect{r_A}$ and $\vect{r_B}$ are the position vectors of the bodies, and $G$ is the universal gravitational constant.
+
+A template single threaded program was already provided by UWA. Some modifications were made in order to simplify the process of introducing threading to the program, and in one case to correct an error in the program.
+
+\section{Euler's Method}
+
+Euler's method has been used. A continuous time interval is approximated by a series of steps of length $\Delta t$, during which each body undergoes motion with constant acceleration.
+
+The algorithm in pseudo-code is:
+
+
+\begin{lstlisting}
+FOR each time interval of duration dt LOOP
+ FOR each body A // can be multithreaded
+ COMPUTE the force acting on A due to all other bodies B
+ DONE
+
+ FOR each body A // can be multithreaded
+ COMPUTE the velocity of A as:
+ V += (Force on A / mass of A) * dt
+ COMPUTE the position of A as:
+ X += V * dt
+ DONE
+DONE
+\end{lstlisting}
+
+
+The pseudo-code is misleading; it may appear that the two loops could be combined into a single loop. However, in the case where bodies are interacting, the force on any given body will depend upon the positions of other bodies. Consider two bodies $A$ and $B$ interacting within a single time step. If the force on $A$ is computed, and $A$'s position is updated before the force on $B$ is computed, then the force experienced by $B$ will not be equal and opposite to that experienced by $A$ - violating Newton's third law.
+
+The template program provided by UWA places force and position updates for each body in the same loop. This can be fixed by moving the position updates to a separate loop. In the multithreaded implementation, it is also important to ensure that \emph{all} forces are computed before any positions are changed, and vice versa before force computations may continue.
+
+
+
+\section{Parallelisation}
+
+The original algorithm can be parallelised by dividing each of the two loops indicated between a number of concurrently running threads.
+Forces may be updated for separate bodies simultaneously with no risk of conflict, since the force of one body is independent of all others. Similarly, positions may be updated simultaneously. However, as discussed above, force and position updates must be done separately.
+
+The most effective way of parallelising the computations is as follows (not showing graphics related code):
+
+\begin{lstlisting}
+CREATE n threads
+FOR each thread T assign a subset of bodies
+
+FOR each thread T
+ FOR each time interval of duration dt LOOP
+ FOR each body A in T's subset
+ COMPUTE the force acting on A due to all other bodies
+ DONE
+
+ BARRIER Wait for all threads to finish computing forces
+
+ FOR each body A in T's subset
+ COMPUTE the position of A
+ DONE
+
+ BARRIER Wait for all threads to finish computing positions
+
+ DONE
+DONE
+\end{lstlisting}
+
+This algorithm avoids the cost of repeated thread creation and deletion; threads are only created once.
+The barriers between force and position updates ensure that forces and positions are never updated at the same time in separate threads.
+
+\subsection{Graphics}
+
+The template program provides graphics using OpenGL and freeglut. In the multithreaded implementations, the graphics can be run in the main thread independent of computations with no effect on the final output of the simulation. However, the following problems may arise if the graphics thread is not synchronised with position updates:
+
+\begin{enumerate}
+\item If a body's position is being altered whilst the graphics thread is drawing that body, the body may be drawn partway through the update of the three position coordinates. This will cause the body to be drawn displaced from its actual position by a small amount.
+
+\item Because position updates are finished in any order, with the barriers correctly implemented, the display may show some bodies remain stationary whilst the thread responsible for those bodies waits for other threads to reach the barrier.
+\end{enumerate}
+
+To avoid these problems, the graphics thread must not commence drawing if position updates are in progress. Similarly, position updates must not commence whilst the graphics thread is still in the process of drawing.
+\pagebreak
+
+
+\section{POSIX Threads (pthreads)}
+
+\subsection{Barriers}
+
+Because \verb/pthread_barrier/ is unavailable on many UNIX systems, it was necessary to implement a barrier.
+
+The barrier functions as follows:
+\begin{enumerate}
+ \item Initialised as ``inactive'' and with the total number of participating threads specified
+ \item When a thread calls \verb/Barrier_Join/ the barrier becomes ``active'' (if it wasn't already)
+ \item Each thread entering the barrier by calling \verb/Barrier_Join/ increments a counter.
+ \item Threads calling \verb/Barrier_Join/ must sleep using \verb/pthread_cond_wait/ until the counter reaches the total number of participating threads
+ \item The final thread to enter the barrier awakens the sleeping threads using \verb/pthread_cond_broadcast/, and sets the barrier as ``inactive''.
+\end{enumerate}
+
+The concept of ``inactive'' and ``active'' barriers was useful for synchronising the graphics thread with the position computations.
+The function \verb/Barrier_Wait/ allows a thread to pass the barrier if it is inactive, but forces the thread to wait if the barrier is active. The calling thread does not affect the barrier's counter of finished threads.
+
+The function \verb/Barrier_Enter/ can be called in a thread to set the barrier as ``active'', and then continue to perform tasks \emph{before} joining the barrier. ie: The barrier may be considered ``active'' by calls to \verb/Barrier_Wait/ before any threads have called \verb/Barrier_Join/.
+
+By calling \verb/Barrier_Enter/ in the position threads before the position updates begin, and \verb/Barrier_Wait/ in the graphics thread before the drawing begins, the graphics thread cannot commence drawing whilst positions are being updated.
+Similarly, calling \verb/Barrier_Enter/ in the graphics thread before drawing, and \verb/Barrier_Wait/ in all position threads, ensures that the position updates cannot be started whilst drawing is in progress.
+
+To avoid deadlocks, three separate barriers have been used; one for each of the force, position and drawing updates.
+
+\subsection{Division of Labour}
+
+In the pthread implementation, some mechanism is needed to divide the bodies between threads.
+This has been done by creating a data structure to describe an array of bodies, with the length of the array. Division of the array into subsections can be accomplished in the C programming language using pointer arithmetic.
+
+A global array of these data structures (\verb/System/) is constructed before thread creation, with each \verb/System/ containing a subsection of the original bodies array. Each thread is passed a pointer to one of the \verb/System/s through \verb/pthread_create/
+
+Some helper functions have been implemented to perform tasks for a given \verb/System/ of bodies, and these are called where needed in the threads.
+
+\subsection{Single Threaded Section}
+One disadvantage of having all computation threads continually running is that it is difficult to execute serial code in only \emph{one} thread. For example, a periodic printing of performance metrics and the updating of the number of steps computed must both be performed at the end of every time step by only one thread. To assist in executing serial code in one thread out of a ``team'', a function has been added to the \verb/Barrier/ implementation; \verb/Barrier_JoinCall/ will cause the last thread entering the barrier to execute a specified function containing serial code. This takes advantage of the fact that serial code can often occur immediately after a barrier.
+
+\section{OpenMP}
+
+The implementation in OpenMP is significantly simpler than pthreads. OpenMP automatically divides labour for threads encountering \verb/omp for/, which eliminates the need for constructing the \verb/System/ array. OpenMP also incorporates implicit barriers after most code sections. The use of \verb/omp single/ directives greatly simplifies the assignment of serial code to one thread in a team.
+
+Because OpenMP does not offer as much low level control over threads, the integration of graphics with the simulation differs. Specifically, because OpenMP does not have a barrier structure (instead using \verb/omp barrier/ directives), all threads involved in a barrier must occur within the same \verb/omp parallel/ section.
+
+Instead of creating a separate thread to run graphics, the OpenMP solution uses an \verb/omp master/ directive to perform graphics related code within the main computation loop. This occurs after the position computation barrier, and is followed by an explicit \verb/omp barrier/. It is important that the graphics related functions be run in the main thread; using \verb/omp single/ will often result in unusual behaviour, such as flickering of the display or the display not being drawn at all.
+
+
+\section{Barnes Hut Algorithm}
+
+The Barnes Hut algorithm approximates a distant group of bodies by the group's centre of mass. This is done by the construction of a tree representing regions of space containing groups of bodies. Nodes at each level of the tree represent a volume obtained by dividing the volume of the parent. The force on a body can be approximated by a depth first search on the tree, stopping at nodes for which the centre of mass is ``distant'' to the body, otherwise continuing to the nodes children until nodes containing only one body are reached.
+
+Figure \ref{cubes.png} shows a graphical representation of the Barnes Hut algorithm. In this image, only Nodes (depicted as cubes representing the space within the node) containing exactly one body are shown.
+
+It is possible to parallelise the recursive algorithms used in constructing the tree and calculating forces. However, we have only implemented a serial version of the tree. Despite this, the calculation of forces can still be parallelised external to the tree.
+
+{\bf I have reached the page limit...} but I have lots of graphs to talk about still. Feel free to stop reading here.
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/nbody-bh/cubes.png}
+ \captionof{figure}{Barnes Hut - One body per cube}
+ \label{cubes.png}
+\end{center}
+
+\subsection{Errors}
+
+Figure \ref{error_graph.png} shows the mean ``error'' between the Barnes Hut Algorithm and more exact brute force algorithm. This error is calculated by summing the absolute difference of each body's position components, and averaging over all position components. Note the logarithmic y axis. The error increases roughly linearly. There is little change in error for different values of $\theta$ between $0$ and $10$.
+
+Note: The same error analysis script confirmed that the multithreaded versions of the brute force algorithm gave the same outputs.
+
+\subsection{Performance for different $\theta$ values}
+
+Figure \ref{efficiency.png} shows the time taken for the (single threaded) Barnes Hut Algorithm to run a specified number of steps, for different values of $\theta$. The brute force algorithm is shown for comparison; for $\theta < 1$, the brute force algorithm is generally faster.
+Taking into account both figures \ref{efficiency.png} and \ref{error_graph.png}, it would appear that $\theta = 10$ is a good balance between accuracy and speed, for this particular field of bodies.
+
+\begin{landscape}
+
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/nbody-bh/error_graph.png}
+ \captionof{figure}{Barnes Hut mean error} \label{error_graph.png}
+\end{center}
+
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/nbody-bh/efficiency.png}
+ \captionof{figure}{Barnes Hut single threaded performance} \label{efficiency.png}
+\end{center}
+
+\end{landscape}
+
+\pagebreak
+
+\section{Performance Analysis}
+
+\subsection{Time vs Steps}
+
+Figure \ref{time_vs_steps.png} shows the time taken to compute a varying number of steps for different programs. The field provided with 500 bodies was used.
+
+Several things can be noted from this graph:
+\begin{itemize}
+ \item With $\theta = 10$, the Barnes Hut algorithm is significantly faster than brute force algorithms
+ \item Altering the number of threads has a significant effect on the brute force algorithm performance, but little effect on the Barnes Hut algorithm performance. This is because the vast majority of the Barnes Hut algorithm has not yet been multithreaded.
+ \item The optimum number of threads is equal to the number of cores available on the host machine (Intel Core i5).
+ (Pleiades was not available at the time of testing).
+ \item The pthreads and openmp implementations perform with similar speeds
+ \item The single threaded, brute force algorithms perform the worst
+\end{itemize}
+
+The time taken to run varies with CPU load due to other processes, and so these results should be considered as qualitative.
+Measurement of CPU cycles (as opposed to real time) is not a suitable metric, since on many UNIX systems, this measurement includes cycles run by all threads in a process.
+
+\subsection{Time to compute vs Number of Bodies}
+
+Figure \ref{time_vs_n.png} shows the time taken to compute 1000 steps against the number of bodies in the initial field. The brute force algorithms appear $O(n^2)$. Barnes Hut appears to be $O(n log(n))$. The fastest algorithm is Barnes Hut with $\theta = 10$.
+
+This experiment revealed (and was limited by) a flaw in (my implementation of) the Barnes Hut algorithm. When the body fields are randomly generated, the result is usually unbound orbits. As the size of the volume occupied by bodies is increasing, the algorithm must continually resize the root node of the tree, and then all children nodes, and ultimately create additional child nodes to contain single particles. Although the implementation attempts to minimise allocations of memory, it was found that for large numbers of bodies the program often became unresponsive. This may be due to the more closely approaching bodies experiencing extremely large forces, and moving away from the centre of the universe at high velocities.
+.
+
+\pagebreak
+\begin{landscape}
+
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/performance_time_vs_steps.png}
+ \captionof{figure}{Implementation Performance}
+ \label{time_vs_steps.png}
+\end{center}
+
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/time_vs_n.png}
+ \captionof{figure}{Efficiency vs $n$} \label{time_vs_n.png}
+\end{center}
+\end{landscape}
+
+\subsection{Analysis with Callgrind}
+
+The tool \emph{callgrind} (part of \emph{valgrind}) can be used to generate information on the performance of a program, and to identify expensive lines of code or the cost of different function calls. Figure \ref{kcachegrind.png} shows a screenshot of \emph{kcachegrind}, a graphical tool to display the results obtained by callgrind. The program analysed is the Barnes Hut N-Body simulator, running for 10 steps, without graphics enabled.
+
+A larger copy of the image is attached with this report, file name ``nbody-bh/kcachegrind.png''. Several things are clear from this display:
+\begin{enumerate}
+ \item The most expensive computations are due to the force computation function \verb/Node_Forces/. Close to 93\% of the program's time is spent in this function.
+
+ \item Although there are only 500 bodies, the force calculation algorithm was called 15200000 times. This is significantly greater than the approximate 2500000 force computations for the brute force algorithm.
+
+ For this particular initial field and choice of value for $\theta$ ($0.5$), the single threaded Barnes Hut algorithm performed worse than the single threaded brute force algorithm. As shown in Figure \ref{time_vs_n.png} however, the Barnes Hut algorithm performs extremely well for larger numbers of bodies. The ``better'' algorithm to use is determined by the problem.
+
+ \item Most of the cost of a force calculation is due to two calculations (distance calculation and the actual force update)
+ The calls to \verb/sqrt/, a normally expensive function have a much lower total cost, but are called the same number of times.
+ The extra cost of the two calculations might be due to the costs of following the pointers (the code has not been optimised),
+
+ \item The \verb/for/ loops, which were used after replacing the original 9 body variables (x, y, z, Vx, ..., Fx, ...) with three arrays, to condense the code, have a small but significant cost associated with them.
+\end{enumerate}
+
+\begin{landscape}
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/nbody-bh/kcachegrind.png}
+ \captionof{figure}{Kcachegrind reveals why my program is slow} \label{kcachegrind.png}
+\end{center}
+\end{landscape}
+
+\end{document}
+
--- /dev/null
+\documentclass[10pt]{article}
+\usepackage{graphicx}
+\usepackage{caption}
+\usepackage{amsmath} % needed for math align
+\usepackage{bm} % needed for maths bold face
+ \usepackage{graphicx} % needed for including graphics e.g. EPS, PS
+\usepackage{fancyhdr} % needed for header
+%\usepackage{epstopdf} % Needed for eps graphics
+\usepackage{hyperref}
+\usepackage{lscape}
+
+ \topmargin -1.5cm % read Lamport p.163
+ \oddsidemargin -0.04cm % read Lamport p.163
+ \evensidemargin -0.04cm % same as oddsidemargin but for left-hand pages
+ \textwidth 16.59cm
+ \textheight 21.94cm
+ %\pagestyle{empty} % Uncomment if don't want page numbers
+ \parskip 7.2pt % sets spacing between paragraphs
+ %\renewcommand{\baselinestretch}{1.5} % Uncomment for 1.5 spacing between lines
+ \parindent 0pt % sets leading space for paragraphs
+
+
+\newcommand{\vect}[1]{\boldsymbol{#1}} % Draw a vector
+\newcommand{\divg}[1]{\nabla \cdot #1} % divergence
+\newcommand{\curl}[1]{\nabla \times #1} % curl
+\newcommand{\grad}[1]{\nabla #1} %gradient
+\newcommand{\pd}[3][ ]{\frac{\partial^{#1} #2}{\partial #3^{#1}}} %partial derivative
+\newcommand{\der}[3][ ]{\frac{d^{#1} #2}{d #3^{#1}}} %full derivative
+\newcommand{\phasor}[1]{\tilde{#1}} % make a phasor
+\newcommand{\laplacian}[1]{\nabla^2 {#1}} % The laplacian operator
+
+\usepackage{color}
+\usepackage{listings}
+
+\definecolor{darkgray}{rgb}{0.95,0.95,0.95}
+\definecolor{darkred}{rgb}{0.75,0,0}
+\definecolor{darkblue}{rgb}{0,0,0.75}
+\definecolor{pink}{rgb}{1,0.5,0.5}
+\lstset{language=Java}
+\lstset{backgroundcolor=\color{darkgray}}
+\lstset{numbers=left, numberstyle=\tiny, stepnumber=1, numbersep=5pt}
+\lstset{keywordstyle=\color{darkred}\bfseries}
+\lstset{commentstyle=\color{darkblue}}
+%\lstset{stringsyle=\color{red}}
+\lstset{showstringspaces=false}
+\lstset{basicstyle=\small}
+
+
+\begin{document}
+
+\pagestyle{fancy}
+\fancyhead{}
+\fancyfoot{}
+
+\fancyhead[LO, L]{}
+\fancyfoot[CO, C]{\thepage}
+
+\title{\bf A Multithreaded N-Body Simulation}
+\date{}
+\maketitle
+
+\tableofcontents
+
+
+
+\pagebreak
+
+\section{Introduction}
+
+An N-Body simulation's purpose is to solve for the positions and velocities of an arbitrary number of interacting bodies using numerical methods.
+
+Complex systems involving large numbers of bodies, interacting over long periods of time, are often of interest. Hence there is considerable motivation to improve the speed (amount of time simulated over real time required) of N-Body simulations.
+This report focuses on increasing the speed of an N-Body simulation by introducing parallelism using threads.
+
+The bodies in this simulation interact according to Newtonian laws of gravity. The force acting on a body $A$ due to body $B$ is given by:
+\begin{align*}
+ \vect{F_{AB}} &= G \frac{m_A m_B}{\left| \vect{r_B} - \vect{r_A} \right|^3} \left(\vect{r_B} - \vect{r_A}\right)
+\end{align*}
+Where $m_A$ and $m_B$ are the masses of the two bodies; $\vect{r_A}$ and $\vect{r_B}$ are the position vectors of the bodies, and $G$ is the universal gravitational constant.
+
+A template single threaded program was already provided by UWA. Some modifications were made in order to simplify the process of introducing threading to the program, and in one case to correct an error in the program.
+
+\section{Euler's Method}
+
+Euler's method has been used. A continuous time interval is approximated by a series of steps of length $\Delta t$, during which each body undergoes motion with constant acceleration.
+
+The algorithm in pseudo-code is:
+
+
+\begin{lstlisting}
+FOR each time interval of duration dt LOOP
+ FOR each body A // can be multithreaded
+ COMPUTE the force acting on A due to all other bodies B
+ DONE
+
+ FOR each body A // can be multithreaded
+ COMPUTE the velocity of A as:
+ V += (Force on A / mass of A) * dt
+ COMPUTE the position of A as:
+ X += V * dt
+ DONE
+DONE
+\end{lstlisting}
+
+
+The pseudo-code is misleading; it may appear that the two loops could be combined into a single loop. However, in the case where bodies are interacting, the force on any given body will depend upon the positions of other bodies. Consider two bodies $A$ and $B$ interacting within a single time step. If the force on $A$ is computed, and $A$'s position is updated before the force on $B$ is computed, then the force experienced by $B$ will not be equal and opposite to that experienced by $A$ - violating Newton's third law.
+
+The template program provided by UWA places force and position updates for each body in the same loop. This can be fixed by moving the position updates to a separate loop. In the multithreaded implementation, it is also important to ensure that \emph{all} forces are computed before any positions are changed, and vice versa before force computations may continue.
+
+
+
+\section{Parallelisation}
+
+The original algorithm can be parallelised by dividing each of the two loops indicated between a number of concurrently running threads.
+Forces may be updated for separate bodies simultaneously with no risk of conflict, since the force of one body is independent of all others. Similarly, positions may be updated simultaneously. However, as discussed above, force and position updates must be done separately.
+
+The most effective way of parallelising the computations is as follows (not showing graphics related code):
+
+\begin{lstlisting}
+CREATE n threads
+FOR each thread T assign a subset of bodies
+
+FOR each thread T
+ FOR each time interval of duration dt LOOP
+ FOR each body A in T's subset
+ COMPUTE the force acting on A due to all other bodies
+ DONE
+
+ BARRIER Wait for all threads to finish computing forces
+
+ FOR each body A in T's subset
+ COMPUTE the position of A
+ DONE
+
+ BARRIER Wait for all threads to finish computing positions
+
+ DONE
+DONE
+\end{lstlisting}
+
+This algorithm avoids the cost of repeated thread creation and deletion; threads are only created once.
+The barriers between force and position updates ensure that forces and positions are never updated at the same time in separate threads.
+
+\subsection{Graphics}
+
+The template program provides graphics using OpenGL and freeglut. In the multithreaded implementations, the graphics can be run in the main thread independent of computations with no effect on the final output of the simulation. However, the following problems may arise if the graphics thread is not synchronised with position updates:
+
+\begin{enumerate}
+\item If a body's position is being altered whilst the graphics thread is drawing that body, the body may be drawn partway through the update of the three position coordinates. This will cause the body to be drawn displaced from its actual position by a small amount.
+
+\item Because position updates are finished in any order, with the barriers correctly implemented, the display may show some bodies remain stationary whilst the thread responsible for those bodies waits for other threads to reach the barrier.
+\end{enumerate}
+
+To avoid these problems, the graphics thread must not commence drawing if position updates are in progress. Similarly, position updates must not commence whilst the graphics thread is still in the process of drawing.
+\pagebreak
+
+
+\section{POSIX Threads (pthreads)}
+
+\subsection{Barriers}
+
+Because \verb/pthread_barrier/ is unavailable on many UNIX systems, it was necessary to implement a barrier.
+
+The barrier functions as follows:
+\begin{enumerate}
+ \item Initialised as ``inactive'' and with the total number of participating threads specified
+ \item When a thread calls \verb/Barrier_Join/ the barrier becomes ``active'' (if it wasn't already)
+ \item Each thread entering the barrier by calling \verb/Barrier_Join/ increments a counter.
+ \item Threads calling \verb/Barrier_Join/ must sleep using \verb/pthread_cond_wait/ until the counter reaches the total number of participating threads
+ \item The final thread to enter the barrier awakens the sleeping threads using \verb/pthread_cond_broadcast/, and sets the barrier as ``inactive''.
+\end{enumerate}
+
+The concept of ``inactive'' and ``active'' barriers was useful for synchronising the graphics thread with the position computations.
+The function \verb/Barrier_Wait/ allows a thread to pass the barrier if it is inactive, but forces the thread to wait if the barrier is active. The calling thread does not affect the barrier's counter of finished threads.
+
+The function \verb/Barrier_Enter/ can be called in a thread to set the barrier as ``active'', and then continue to perform tasks \emph{before} joining the barrier. ie: The barrier may be considered ``active'' by calls to \verb/Barrier_Wait/ before any threads have called \verb/Barrier_Join/.
+
+By calling \verb/Barrier_Enter/ in the position threads before the position updates begin, and \verb/Barrier_Wait/ in the graphics thread before the drawing begins, the graphics thread cannot commence drawing whilst positions are being updated.
+Similarly, calling \verb/Barrier_Enter/ in the graphics thread before drawing, and \verb/Barrier_Wait/ in all position threads, ensures that the position updates cannot be started whilst drawing is in progress.
+
+To avoid deadlocks, three separate barriers have been used; one for each of the force, position and drawing updates.
+
+\subsection{Division of Labour}
+
+In the pthread implementation, some mechanism is needed to divide the bodies between threads.
+This has been done by creating a data structure to describe an array of bodies, with the length of the array. Division of the array into subsections can be accomplished in the C programming language using pointer arithmetic.
+
+A global array of these data structures (\verb/System/) is constructed before thread creation, with each \verb/System/ containing a subsection of the original bodies array. Each thread is passed a pointer to one of the \verb/System/s through \verb/pthread_create/
+
+Some helper functions have been implemented to perform tasks for a given \verb/System/ of bodies, and these are called where needed in the threads.
+
+\subsection{Single Threaded Section}
+One disadvantage of having all computation threads continually running is that it is difficult to execute serial code in only \emph{one} thread. For example, a periodic printing of performance metrics and the updating of the number of steps computed must both be performed at the end of every time step by only one thread. To assist in executing serial code in one thread out of a ``team'', a function has been added to the \verb/Barrier/ implementation; \verb/Barrier_JoinCall/ will cause the last thread entering the barrier to execute a specified function containing serial code. This takes advantage of the fact that serial code can often occur immediately after a barrier.
+
+\section{OpenMP}
+
+The implementation in OpenMP is significantly simpler than pthreads. OpenMP automatically divides labour for threads encountering \verb/omp for/, which eliminates the need for constructing the \verb/System/ array. OpenMP also incorporates implicit barriers after most code sections. The use of \verb/omp single/ directives greatly simplifies the assignment of serial code to one thread in a team.
+
+Because OpenMP does not offer as much low level control over threads, the integration of graphics with the simulation differs. Specifically, because OpenMP does not have a barrier structure (instead using \verb/omp barrier/ directives), all threads involved in a barrier must occur within the same \verb/omp parallel/ section.
+
+Instead of creating a separate thread to run graphics, the OpenMP solution uses an \verb/omp master/ directive to perform graphics related code within the main computation loop. This occurs after the position computation barrier, and is followed by an explicit \verb/omp barrier/. It is important that the graphics related functions be run in the main thread; using \verb/omp single/ will often result in unusual behaviour, such as flickering of the display or the display not being drawn at all.
+
+
+\section{Barnes Hut Algorithm}
+
+The Barnes Hut algorithm approximates a distant group of bodies by the group's centre of mass. This is done by the construction of a tree representing regions of space containing groups of bodies. Nodes at each level of the tree represent a volume obtained by dividing the volume of the parent. The force on a body can be approximated by a depth first search on the tree, stopping at nodes for which the centre of mass is ``distant'' to the body, otherwise continuing to the nodes children until nodes containing only one body are reached.
+
+Figure \ref{cubes.png} shows a graphical representation of the Barnes Hut algorithm. In this image, only Nodes (depicted as cubes representing the space within the node) containing exactly one body are shown.
+
+It is possible to parallelise the recursive algorithms used in constructing the tree and calculating forces. However, we have only implemented a serial version of the tree. Despite this, the calculation of forces can still be parallelised external to the tree.
+
+{\bf I have reached the page limit...} but I have lots of graphs to talk about still. Feel free to stop reading here.
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/nbody-bh/cubes.png}
+ \captionof{figure}{Barnes Hut - One body per cube}
+ \label{cubes.png}
+\end{center}
+
+\subsection{Errors}
+
+Figure \ref{error_graph.png} shows the mean ``error'' between the Barnes Hut Algorithm and more exact brute force algorithm. This error is calculated by summing the absolute difference of each body's position components, and averaging over all position components. Note the logarithmic y axis. The error increases roughly linearly. There is little change in error for different values of $\theta$ between $0$ and $10$.
+
+Note: The same error analysis script confirmed that the multithreaded versions of the brute force algorithm gave the same outputs.
+
+\subsection{Performance for different $\theta$ values}
+
+Figure \ref{efficiency.png} shows the time taken for the (single threaded) Barnes Hut Algorithm to run a specified number of steps, for different values of $\theta$. The brute force algorithm is shown for comparison; for $\theta < 1$, the brute force algorithm is generally faster.
+Taking into account both figures \ref{efficiency.png} and \ref{error_graph.png}, it would appear that $\theta = 10$ is a good balance between accuracy and speed, for this particular field of bodies.
+
+\begin{landscape}
+
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/nbody-bh/error_graph.png}
+ \captionof{figure}{Barnes Hut mean error} \label{error_graph.png}
+\end{center}
+
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/nbody-bh/efficiency.png}
+ \captionof{figure}{Barnes Hut single threaded performance} \label{efficiency.png}
+\end{center}
+
+\end{landscape}
+
+\pagebreak
+
+\section{Performance Analysis}
+
+\subsection{Time vs Steps}
+
+Figure \ref{time_vs_steps.png} shows the time taken to compute a varying number of steps for different programs. The field provided with 500 bodies was used.
+
+Several things can be noted from this graph:
+\begin{itemize}
+ \item With $\theta = 10$, the Barnes Hut algorithm is significantly faster than brute force algorithms
+ \item Altering the number of threads has a significant effect on the brute force algorithm performance, but little effect on the Barnes Hut algorithm performance. This is because the vast majority of the Barnes Hut algorithm has not yet been multithreaded.
+ \item The optimum number of threads is equal to the number of cores available on the host machine (Intel Core i5).
+ (Pleiades was not available at the time of testing).
+ \item The pthreads and openmp implementations perform with similar speeds
+ \item The single threaded, brute force algorithms perform the worst
+\end{itemize}
+
+The time taken to run varies with CPU load due to other processes, and so these results should be considered as qualitative.
+Measurement of CPU cycles (as opposed to real time) is not a suitable metric, since on many UNIX systems, this measurement includes cycles run by all threads in a process.
+
+\subsection{Time to compute vs Number of Bodies}
+
+Figure \ref{time_vs_n.png} shows the time taken to compute 1000 steps against the number of bodies in the initial field. The brute force algorithms appear $O(n^2)$. Barnes Hut appears to be $O(n log(n))$. The fastest algorithm is Barnes Hut with $\theta = 10$.
+
+This experiment revealed (and was limited by) a flaw in (my implementation of) the Barnes Hut algorithm. When the body fields are randomly generated, the result is usually unbound orbits. As the size of the volume occupied by bodies is increasing, the algorithm must continually resize the root node of the tree, and then all children nodes, and ultimately create additional child nodes to contain single particles. Although the implementation attempts to minimise allocations of memory, it was found that for large numbers of bodies the program often became unresponsive. This may be due to the more closely approaching bodies experiencing extremely large forces, and moving away from the centre of the universe at high velocities.
+.
+
+\pagebreak
+\begin{landscape}
+
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/performance_time_vs_steps.png}
+ \captionof{figure}{Implementation Performance}
+ \label{time_vs_steps.png}
+\end{center}
+
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/time_vs_n.png}
+ \captionof{figure}{Efficiency vs $n$} \label{time_vs_n.png}
+\end{center}
+\end{landscape}
+
+\subsection{Analysis with Callgrind}
+
+The tool \emph{callgrind} (part of \emph{valgrind}) can be used to generate information on the performance of a program, and to identify expensive lines of code or the cost of different function calls. Figure \ref{kcachegrind.png} shows a screenshot of \emph{kcachegrind}, a graphical tool to display the results obtained by callgrind. The program analysed is the Barnes Hut N-Body simulator, running for 10 steps, without graphics enabled.
+
+A larger copy of the image is attached with this report, file name ``nbody-bh/kcachegrind.png''. Several things are clear from this display:
+\begin{enumerate}
+ \item The most expensive computations are due to the force computation function \verb/Node_Forces/. Close to 93\% of the program's time is spent in this function.
+
+ \item Although there are only 500 bodies, the force calculation algorithm was called 15200000 times. This is significantly greater than the approximate 2500000 force computations for the brute force algorithm.
+
+ For this particular initial field and choice of value for $\theta$ ($0.5$), the single threaded Barnes Hut algorithm performed worse than the single threaded brute force algorithm. As shown in Figure \ref{time_vs_n.png} however, the Barnes Hut algorithm performs extremely well for larger numbers of bodies. The ``better'' algorithm to use is determined by the problem.
+
+ \item Most of the cost of a force calculation is due to two calculations (distance calculation and the actual force update)
+ The calls to \verb/sqrt/, a normally expensive function have a much lower total cost, but are called the same number of times.
+ The extra cost of the two calculations might be due to the costs of following the pointers (the code has not been optimised),
+
+ \item The \verb/for/ loops, which were used after replacing the original 9 body variables (x, y, z, Vx, ..., Fx, ...) with three arrays, to condense the code, have a small but significant cost associated with them.
+\end{enumerate}
+
+\begin{landscape}
+\begin{center}
+ \includegraphics[scale=0.50]{/home/sam/Documents/University/honours/course/semester2/pprog/assignment1/nbody-bh/kcachegrind.png}
+ \captionof{figure}{Kcachegrind reveals why my program is slow} \label{kcachegrind.png}
+\end{center}
+\end{landscape}
+
+\end{document}
+
--- /dev/null
+\contentsline {section}{\numberline {1}Introduction}{2}{section.1}
+\contentsline {section}{\numberline {2}Euler's Method}{2}{section.2}
+\contentsline {section}{\numberline {3}Parallelisation}{3}{section.3}
+\contentsline {subsection}{\numberline {3.1}Graphics}{3}{subsection.3.1}
+\contentsline {section}{\numberline {4}POSIX Threads (pthreads)}{4}{section.4}
+\contentsline {subsection}{\numberline {4.1}Barriers}{4}{subsection.4.1}
+\contentsline {subsection}{\numberline {4.2}Division of Labour}{4}{subsection.4.2}
+\contentsline {subsection}{\numberline {4.3}Single Threaded Section}{5}{subsection.4.3}
+\contentsline {section}{\numberline {5}OpenMP}{5}{section.5}
+\contentsline {section}{\numberline {6}Barnes Hut Algorithm}{5}{section.6}
+\contentsline {subsection}{\numberline {6.1}Errors}{6}{subsection.6.1}
+\contentsline {subsection}{\numberline {6.2}Performance for different $\theta $ values}{6}{subsection.6.2}
+\contentsline {section}{\numberline {7}Performance Analysis}{9}{section.7}
+\contentsline {subsection}{\numberline {7.1}Time vs Steps}{9}{subsection.7.1}
+\contentsline {subsection}{\numberline {7.2}Time to compute vs Number of Bodies}{9}{subsection.7.2}
+\contentsline {subsection}{\numberline {7.3}Analysis with Callgrind}{12}{subsection.7.3}
--- /dev/null
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*/
void Graphics_Run(int argc, char ** argv)
{
+
if (options.draw_graphics == false)
{
// This message is left here for when I inevitably accidentally call the function
glutCreateWindow("N-Body : Multi-Threaded (pthread)");
#elif defined OMP_THREADED
glutCreateWindow("N-Body : Multi-Threaded (OpenMP)");
+ #elif defined BARNES_HUT
+ glutCreateWindow("N-Body : Barnes Hut Algorithm");
#else
glutCreateWindow("N-Body");
#endif
#ifndef OMP_THREADED
- glutMainLoop();
+ #ifndef BARNES_HUT
+ glutMainLoop(); // the mthread and single-thread versions can just start the loop here
+ // In OpenMP, because barriers have to be within the #pragma, need glutMainLoopEvent in the #pragma
+ #endif //BARNS_HUT
#endif //OMP_THREADED
}
//Check whether the graphics thread should exit for any reason
if (ExitCondition())
{
+ QuitProgram(false);
glutLeaveMainLoop(); // original glut does not have this, which makes "nicely" exiting a bit annoying
return;
}
glutSolidSphere (BALL_SIZE, 10, 10);
glPopMatrix(); // restore the previous matrix
}
- glFlush();
+
AfterDraw(); // Stuff to do after graphics is done drawing
// Single-thread - Nothing at all
// Multiple threads - signal threads it is safe to change position variables
-
+ glFlush();
}
/**
}
#ifdef FLYING_CAMERA
+ float s = 10;
switch (theKey)
{
// Translate in direction of camera
case 'W':
case 'w':
for (unsigned i = 0; i < DIMENSIONS; ++i)
- eye.p[i] += eye.x[i];
+ eye.p[i] += s * eye.x[i];
break;
// Translate backwards from camera direction
case 'S':
case 's':
for (unsigned i = 0; i < DIMENSIONS; ++i)
- eye.p[i] -= eye.x[i];
+ eye.p[i] -= s * eye.x[i];
break;
// Translate left from camera direction
case 'A':
case 'a':
for (unsigned i = 0; i < DIMENSIONS; ++i)
- eye.p[i] -= eye.y[i];
+ eye.p[i] -= s * eye.y[i];
break;
// Translate right from camera direction
case 'D':
case 'd':
for (unsigned i = 0; i < DIMENSIONS; ++i)
- eye.p[i] += eye.y[i];
+ eye.p[i] += s * eye.y[i];
break;
// Translate up from camera direction
case 'Q':
case 'q':
for (unsigned i = 0; i < DIMENSIONS; ++i)
- eye.p[i] += eye.z[i];
+ eye.p[i] += s * eye.z[i];
break;
// Translate down from camera direction
case 'E':
case 'e':
for (unsigned i = 0; i < DIMENSIONS; ++i)
- eye.p[i] -= eye.z[i];
+ eye.p[i] -= s * eye.z[i];
break;
// Rotate camera direction "down"
void Graphics_Keyboard(unsigned char key, int mouse_x, int mouse_y);
void Graphics_Reshape(int width, int height);
+extern double scale;
#define FLYING_CAMERA
options.num_steps = -1; // Negative values => simulation runs forever unless otherwise specified
options.timeout = -1;
options.draw_graphics = true;
- options.pedantic_graphics = false;
+ options.pedantic_graphics = true;
options.print_positions = false;
options.verbosity = 0;
+ options.theta = 0.50;
+ options.random = 0;
//If there are no arguments, print information about usage
if (argc == 1)
HandleArguments(argc, argv);
//Check there is an initial field.
- if (options.input == NULL)
+ if (options.input == NULL && options.random <= 0)
{
fprintf(stderr, "Usage: %s [OPTIONS] field\n", argv[0]);
fprintf(stderr, " (You did not provide a file for the initial field of bodies)\n");
signal(SIGINT, Interrupt); //Handle SIGINT signals
atexit(Universe_Cleanup); //On exit, cleanup universe (and write positions of bodies to file if supplied).
atexit(DisplayStatistics); //On exit, print information about the computations done
- System_Init(&universe,options.input); //Initialise the universe from the initial field
+ if (options.input != NULL)
+ System_Init(&universe,options.input); //Initialise the universe from the initial field
+ else
+ System_Random(&universe, options.random); //Randomly create bodies
+
//Setup the time of day at which the simulation starts
if (gettimeofday(&(options.start_time), NULL) != 0)
exit(EXIT_FAILURE);
}
break;
+ case 'r': //Random initial field
+ IntegerArgument(&i, argc, argv, &(options.random), NULL);
+ if (options.random < 0)
+ {
+ fprintf(stderr, "Require a positive integer number of bodies (-%c %s is invalid).", 'r', argv[i]);
+ exit(EXIT_FAILURE);
+ }
+ break;
case 'g': //Graphics switch
options.draw_graphics = !options.draw_graphics;
break;
fprintf(stderr, "Warning: %s switch has no effect in the single threaded program.\n", argv[i]);
#endif //SINGLE_THREADED
+ }
+ else if (strcmp(argv[i]+2, "theta") == 0)
+ {
+ FloatArgument(&i, argc, argv, &(options.theta));
+ #ifndef BARNES_HUT
+ fprintf(stderr, "Warning: %s switch only works in Barnes Hut version.\n", argv[i-1]);
+ #else
+ if (options.theta < 0)
+ {
+ fprintf(stderr, "Require a theta value greater or equal to zero (%s %s is invalid).\n", argv[i-1], argv[i]);
+ exit(EXIT_FAILURE);
+ }
+
+ #endif //BARNS_HUT
+
}
else
{
*/
inline void Body_Force(Body * a, Body * b)
{
- double distance;
- double con;
- double gd;
+ float distance;
+ float con;
+ float gd;
//Calculate distance between a and b
distance = 0.0;
for (unsigned i = 0; i < DIMENSIONS; ++i)
FILE * file;
file = fopen(fileName, "rt");
+
+ if (file == NULL)
+ {
+ fprintf(stderr, "%s\n", fileName);
+ perror("Couldn't open file");
+ exit(EXIT_FAILURE);
+ }
+
s->N = atoi(fgets(line, LINE_SIZE, file));
s->body = (Body*) calloc((size_t)s->N, sizeof(Body));
s->steps = 0;
}
return result;
}
+
+/**
+ * @function System_Random
+ * @purpose Randomly generate initial body field
+ * @param s - The system
+ * @param n - Number of bodies
+ */
+void System_Random(System * s, int n)
+{
+ srand(0);
+ s->N = (unsigned)n;
+ s->body = (Body*) calloc((size_t)s->N, sizeof(Body));
+ s->steps = 0;
+
+ s->body[0].mass = 1e11;
+
+ for (unsigned a = 1; a < s->N; ++a)
+ {
+ s->body[a].mass = 1e7;
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ {
+ s->body[a].x[i] = -10000 + rand() % 20000;
+ s->body[a].v[i] = -2 + rand() % 4;
+ }
+ s->body[a].v[2] = 0;
+ s->body[a].x[2] = 0; //set z to zero; force in plane
+
+ }
+}
*/
inline void Body_Force(Body * a, Body * b)
{
+ float distance;
+ float con;
+ float gd;
//Calculate distance between a and b
distance = 0.0;
for (unsigned i = 0; i < DIMENSIONS; ++i)
FILE * file;
file = fopen(fileName, "rt");
+
+ if (file == NULL)
+ {
+ fprintf(stderr, "%s\n", fileName);
+ perror("Couldn't open file");
+ exit(EXIT_FAILURE);
+ }
+
s->N = atoi(fgets(line, LINE_SIZE, file));
s->body = (Body*) calloc((size_t)s->N, sizeof(Body));
s->steps = 0;
}
return result;
}
+
+/**
+ * @function System_Random
+ * @purpose Randomly generate initial body field
+ * @param s - The system
+ * @param n - Number of bodies
+ */
+void System_Random(System * s, int n)
+{
+ srand(time(NULL));
+ s->N = (unsigned)n;
+ s->body = (Body*) calloc((size_t)s->N, sizeof(Body));
+ s->steps = 0;
+
+ s->body[0].mass = 1e11;
+
+ for (unsigned a = 1; a < s->N; ++a)
+ {
+ s->body[a].mass = 1e7;
+ for (unsigned i = 0; i < DIMENSIONS; ++i)
+ {
+ s->body[a].x[i] = -10000 + rand() % 20000;
+ s->body[a].v[i] = -2 + rand() % 4;
+ }
+ s->body[a].v[2] = 0;
+ s->body[a].x[2] = 0; //set z to zero; force in plane
+
+ }
+}
int verbosity; // print statistics every number of steps indicated by this variable
clock_t start_clock; // clock cycles done when simulation starts
struct timeval start_time; // time at which simulation starts
+ float theta; // Parameter used for Barns Hut algorithm
+ int random; //Used to randomly create bodies
} Options;
void Body_Print(Body * a, FILE * out); //Print body a
void Body_Position(Body * a); //Compute position of body a
void System_Init(System * s, const char * fileName); //Initialise System (array of bodies) from a text file
+void System_Random(System * s, int r); //Randomly create bodies
void System_Compute(System * s);
void System_Forces(System * s1, System * s2); //Compute forces for bodies in s1 due to bodies in s2 (also updates velocities)
void System_Positions(System * s); //Update positions for bodies in s1
git.ucc.asn.au / matches / honours.git / commitdiff
UCC git Repository :: git.ucc.asn.au
