ex0: theory document

.gitignore

@@ -54,5 +54,4 @@ dkms.conf
 
 *.zip
 *.pdf
-*.bmp
+*.png
-!main*

exercise0/Makefile

@@ -1,17 +1,13 @@
-build: main.c bitmap.c
+build:
-	gcc main.c bitmap.c -o main -O2
+	gcc main.c bitmap.c -o main -O3
 
-run: build
+run:
+	make build
 	./main
 
-show: run
+show:
+	make run
 	feh after.bmp
 
-convert: run
+convert:
 	magick after.bmp after.png # for showing image in pdf
-
-zip: before.bmp main.pdf Makefile main.c bitmap.h bitmap.c
-	zip handin.zip before.bmp main.pdf Makefile main.c bitmap.h bitmap.c
-
-unzip: handin.zip
-	unzip handin.zip -d handin

exercise1/.gitignore

@@ -1,3 +0,0 @@
-data
-images
-*.mp4

exercise1/Makefile

@@ -1,19 +0,0 @@
-CFLAGS+= -std=c99 -O2 -Wall -Wextra
-LDLIBS+= -lm
-TARGETS=wave_1d
-IMAGES=$(shell find data -type f | sed s/\\.dat/.png/g | sed s/data/images/g )
-.PHONY: all clean dirs plot movie
-all: dirs ${TARGETS}
-dirs:
-	mkdir -p data images
-plot: ${IMAGES}
-images/%.png: data/%.dat
-	./plot_image.sh $<
-movie: ${IMAGES}
-	ffmpeg -y -an -i images/%5d.png -vcodec libx264 -pix_fmt yuv420p -profile:v baseline -level 3 -r 12 wave.mp4
-clean:
-	-rm -fr ${TARGETS} data images wave.mp4
-zip: theory.pdf Makefile wave_1d.c
-	zip handin.zip theory.pdf Makefile wave_1d.c
-unzip: handin.zip
-	unzip handin.zip -d handin

exercise1/README.md

@@ -1,4 +0,0 @@
-* make       : builds the executable 'wave_1d'
-* ./wave\_1d : fills the 'data/' directory with stored time steps
-* make plot  : converts saved time steps to png files under 'images/', using gnuplot. Runs faster if launched with e.g. 4 threads (make -j4 plot).
-* make movie : converts collection of png files under 'images' into an mp4 movie file

exercise1/plot_image.sh

@@ -1,10 +0,0 @@
-#! /usr/bin/env bash
-SIZE=1024
-DATAFILE=$1
-IMAGEFILE=`echo $1 | sed s/dat$/png/ | sed s/data/images/`
-cat <<END_OF_SCRIPT | gnuplot -
-set term png
-set output "$IMAGEFILE"
-set yrange[-1:1]
-plot "$DATAFILE" binary array=${SIZE} format='%double' with lines
-END_OF_SCRIPT

exercise1/theory.typ

@@ -1,70 +0,0 @@
-#import "@preview/cetz:0.3.2";
-#import "@preview/cetz-plot:0.1.1": plot
-#import "@preview/physica:0.9.4": *
-#import "@preview/plotsy-3d:0.1.0": plot-3d-parametric-surface
-#import "@preview/fletcher:0.5.4" as fletcher: diagram, edge, node
-
-#set page(paper: "a4", margin: (x: 2.6cm, y: 2.8cm), numbering: "1 : 1")
-#set par(justify: true, leading: 0.52em)
-
-#let FONT_SIZE = 18pt;
-#set text(font: "FreeSerif", size: FONT_SIZE, lang: "us")
-#show math.equation: set text(font: "Euler Math", size: (FONT_SIZE * 1.0), lang: "en")
-
-#set heading(numbering: none)
-#show heading.where(level: 1): it => {
-  rect(inset: FONT_SIZE / 2)[#it]
-}
-
-// Dracula palette
-#let bg = rgb("#282a36")
-#let fg = rgb("#f8f8f2")
-#let sec = rgb("#44475a")
-
-
-#align(center)[
-  #text(size: FONT_SIZE * 2, weight: "bold")[#underline[exercise 0]]
-]
-
-these are my solutions to exercise set 1 of TDT4200.
-
-this document was created using
-#link("https://typst.app/")[#text(blue.darken(5%))[typst]].
-
-#v(42pt)
-
-#outline(title: none)
-
-#v(42pt)
-
-= macros
-
-macros define programmer-friendly syntax that is preprocessed at compile time,
-thus incurring no performance penality. they constitute a fundamental part in
-meta programming (see lisp). excessive use of macros may obfuscate semantics,
-but can often be used to make the code clearer to read. in this case, it helps
-simplify the indexing of the buffers for easier to read calculations.
-
-= boundary conditions
-
-the boundary condition could be changed from reflection to wrapping around. this
-can be achieved by setting the left boundary to be the right-most point, and the
-right boundary to be the left-most point.
-
-= no memory
-
-if you don't allocate memory in T1, the buffers will be unallocated and you will
-get indexing errors as you try to access the buffers using the predefined
-macros.
-
-basically, you segfault.
-
-= `float const *a` vs `float *const b`
-
-- `float const *a` is a constant pointer to some memory address, assigned to the
-  constant name `a`. since `a` is constant, it cannot be reassigned.
-- `float *const b` is a pointer to some constant value, assigned to the
-  variable `b`. since `b` points to a constant, the dereferenced value cannot be
-  changed.
-
-these are not the same.

exercise1/wave_1d.c

@@ -1,120 +0,0 @@
-#define _XOPEN_SOURCE 600
-#include <math.h>
-#include <stdint.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-// Option to change numerical precision.
-typedef int64_t int_t;
-typedef double real_t;
-
-// Simulation parameters: size, step count, and how often to save the state.
-const int_t
-    N = 1024,
-    max_iteration = 4000,
-    snapshot_freq = 10;
-
-// Wave equation parameters, time step is derived from the space step.
-const real_t
-    c = 1.0,
-    dx = 1.0;
-real_t
-    dt;
-
-// Buffers for three time steps, indexed with 2 ghost points for the boundary.
-real_t
-    *buffers[3] = { NULL, NULL, NULL };
-
-#define U_prv(i) buffers[0][(i) + 1]
-#define U(i) buffers[1][(i) + 1]
-#define U_nxt(i) buffers[2][(i) + 1]
-
-// Save the present time step in a numbered file under 'data/'.
-void domain_save(int_t step) {
-  char filename[256];
-  sprintf(filename, "data/%.5ld.dat", step);
-  FILE *out = fopen(filename, "wb");
-  fwrite(&U(0), sizeof(real_t), N, out);
-  fclose(out);
-}
-
-// TASK: T1
-// Set up our three buffers, fill two with an initial cosine wave,
-// and set the time step.
-void domain_initialize(void) {
-  // allocate memory
-  for (int i = 0; i < 3; i++)
-    buffers[i] = malloc((N + 2) * sizeof(real_t));
-
-  // apply initial condition
-  real_t x = 0.0f;
-  for (int i = 0; i < N; i++) {
-    U_prv(i) = cos(2 * M_PI * x);
-    U(i) = U_prv(i);
-    U_nxt(i) = 0.0f;
-    x += (real_t)dx / (real_t)N;
-  }
-
-  // set the time-step dt according to CFL
-  dt = dx / c;
-}
-
-// TASK T2:
-// Return the memory to the OS.
-void domain_finalize(void) {
-  for (int i = 0; i < 3; i++) {
-    free(buffers[i]);
-    buffers[i] = NULL;
-  }
-}
-
-// TASK: T3
-// Rotate the time step buffers.
-void rotate_buffers(void) {
-  real_t *temp = buffers[0];
-  buffers[0] = buffers[1];
-  buffers[1] = buffers[2];
-  buffers[2] = temp;
-}
-
-// TASK: T4
-// Derive step t+1 from steps t and t-1.
-void time_step(void) {
-  for (int i = 0; i < N; i++) {
-    U_nxt(i) = -U_prv(i) + 2 * U(i) + dt * dt * c * c / (dx * dx) * (U(i - 1) + U(i + 1) - 2 * U(i));
-  }
-}
-
-// TASK: T5
-// Neumann (reflective) boundary condition.
-void boundary(void) {
-  U_prv(-1) = U_prv(1);
-  U(-1) = U(1);
-  U_nxt(-1) = U_nxt(1);
-  U_prv(N) = U_prv(N - 2);
-  U(N) = U(N - 2);
-  U_nxt(N) = U_nxt(N - 2);
-}
-
-// TASK: T6
-// Main time integration.
-void simulate(void) {
-  int_t iteration = 0;
-  while (iteration < max_iteration) {
-    boundary();
-    time_step();
-    rotate_buffers();
-    domain_save(iteration / snapshot_freq);
-    iteration++;
-  }
-}
-
-int main(void) {
-  domain_initialize();
-
-  simulate();
-
-  domain_finalize();
-  exit(EXIT_SUCCESS);
-}

exercise2/.gitignore

@@ -1 +0,0 @@
-out/

exercise2/Makefile

@@ -1,33 +0,0 @@
-CC      := gcc
-CFLAGS  := -Wall -Wextra -std=c17
-SRC     := mandel_mpi.c
-TARGET  := $(SRC:.c=)
-OUTDIR  := out
-OUT     := $(OUTDIR)/$(TARGET)
-ARGS    := 1
-NBENCH  := 1
-NPROC   := 3
-
-.PHONY: all clean run parallel
-
-all: clean parallel show
-
-$(OUT): $(SRC)
-	$(CC) $(CFLAGS) -o $(OUT) $<
-
-run: $(OUT)
-	cd $(OUTDIR) && ./$(TARGET) $(ARGS)
-
-clean:
-	rm -rf $(OUTDIR)/*
-
-time: $(OUT)
-	python3 bench.py './$(OUT) 0' $(NBENCH)
-
-parallel: $(SRC)
-	mpicc -o $(OUT) $(SRC)
-	cd $(OUTDIR) && mpirun -np $(NPROC) $(TARGET) $(ARGS)
-
-show: $(OUTDIR)/mandel.bmp
-	feh $<
-

exercise2/bench.py

@@ -1,24 +0,0 @@
-#!/usr/bin/env python3
-
-from statistics import mean
-from subprocess import DEVNULL, run
-from sys import argv, exit
-from time import perf_counter
-
-
-def benchmark(cmd, N=10):
-    times = []
-    for _ in range(N):
-        start = perf_counter()
-        run(cmd, shell=True, stdout=DEVNULL, stderr=DEVNULL)
-        times.append(perf_counter() - start)
-    return mean(times)
-
-
-if __name__ == "__main__":
-    if len(argv) < 2:
-        print("usage: python3 bench.py 'cmd' [N]")
-        exit(1)
-    cmd = argv[1]
-    N = int(argv[2]) if len(argv) > 2 else 10
-    print(f"{benchmark(cmd, N):.4f}")

exercise2/mandel_cpu.c

@@ -1,100 +0,0 @@
-#include <stdio.h>
-#include <stdlib.h>
-#include <math.h>
-
-#define XSIZE 2560
-#define YSIZE 2048
-
-#define MAXITER 255
-
-double xleft=-2.01;
-double xright=1;
-double yupper,ylower;
-double ycenter=1e-6;
-double step;
-
-int pixel[XSIZE*YSIZE];
-
-#define PIXEL(i,j) ((i)+(j)*XSIZE)
-
-typedef struct {
-	double real,imag;
-} complex_t;
-
-void calculate() {
-	for(int i=0;i<XSIZE;i++) {
-		for(int j=0;j<YSIZE;j++) {
-			/* Calculate the number of iterations until divergence for each pixel.
-			   If divergence never happens, return MAXITER */
-			complex_t c,z,temp;
-			int iter=0;
-			c.real = (xleft + step*i);
-			c.imag = (ylower + step*j);
-			z = c;
-			while(z.real*z.real + z.imag*z.imag < 4) {
-				temp.real = z.real*z.real - z.imag*z.imag + c.real;
-				temp.imag = 2*z.real*z.imag + c.imag;
-				z = temp;
-				if(++iter==MAXITER) break;
-			}
-			pixel[PIXEL(i,j)]=iter;
-		}
-	}
-}
-
-typedef unsigned char uchar;
-
-/* save 24-bits bmp file, buffer must be in bmp format: upside-down */
-void savebmp(char *name,uchar *buffer,int x,int y) {
-	FILE *f=fopen(name,"wb");
-	if(!f) {
-		printf("Error writing image to disk.\n");
-		return;
-	}
-	unsigned int size=x*y*3+54;
-	uchar header[54]={'B','M',size&255,(size>>8)&255,(size>>16)&255,size>>24,0,
-		0,0,0,54,0,0,0,40,0,0,0,x&255,x>>8,0,0,y&255,y>>8,0,0,1,0,24,0,0,0,0,0,0,
-		0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
-	fwrite(header,1,54,f);
-	fwrite(buffer,1,XSIZE*YSIZE*3,f);
-	fclose(f);
-}
-
-/* given iteration number, set a colour */
-void fancycolour(uchar *p,int iter) {
-	if(iter==MAXITER);
-	else if(iter<8) { p[0]=128+iter*16; p[1]=p[2]=0; }
-	else if(iter<24) { p[0]=255; p[1]=p[2]=(iter-8)*16; }
-	else if(iter<160) { p[0]=p[1]=255-(iter-24)*2; p[2]=255; }
-	else { p[0]=p[1]=(iter-160)*2; p[2]=255-(iter-160)*2; }
-}
-
-int main(int argc,char **argv) {
-	if(argc==1) {
-		puts("Usage: MANDEL n");
-		puts("n decides whether image should be written to disk (1=yes, 0=no)");
-		return 0;
-	}
-	/* Calculate the range in the y-axis such that we preserve the
-	   aspect ratio */
-	step=(xright-xleft)/XSIZE;
-	yupper=ycenter+(step*YSIZE)/2;
-	ylower=ycenter-(step*YSIZE)/2;
-
-	calculate();
-
-	if(strtol(argv[1],NULL,10)!=0) {
-		/* create nice image from iteration counts. take care to create it upside
-		   down (bmp format) */
-		unsigned char *buffer=calloc(XSIZE*YSIZE*3,1);
-		for(int i=0;i<XSIZE;i++) {
-			for(int j=0;j<YSIZE;j++) {
-				int p=((YSIZE-j-1)*XSIZE+i)*3;
-				fancycolour(buffer+p,pixel[PIXEL(i,j)]);
-			}
-		}
-		/* write image to disk */
-		savebmp("mandel2.bmp",buffer,XSIZE,YSIZE);
-	}
-	return 0;
-}

exercise2/mandel_mpi.c

@@ -1,158 +0,0 @@
-#include <math.h>
-#include <mpi.h>
-#include <stdbool.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#define XSIZE 2560
-#define YSIZE 2048
-
-#define MAXITER 255
-
-double xleft = -2.01;
-double xright = 1;
-double yupper, ylower;
-double ycenter = 1e-6;
-double step;
-
-int pixel[XSIZE * YSIZE];
-
-#define PIXEL(i, j) ((i) + (j) * XSIZE)
-
-typedef struct {
-  double real, imag;
-} complex_t;
-
-int rank, size;
-bool save = false;
-
-void calculate() {
-  for (int i = 0; i < XSIZE; i++) {
-    for (int j = 0; j < YSIZE; j++) {
-      /* Calculate the number of iterations until divergence for each pixel.
-         If divergence never happens, return MAXITER */
-      complex_t c, z, temp;
-      int iter = 0;
-      c.real = (xleft + step * i);
-      c.imag = (ylower + step * j);
-      z = c;
-      while (z.real * z.real + z.imag * z.imag < 4) {
-        temp.real = z.real * z.real - z.imag * z.imag + c.real;
-        temp.imag = 2 * z.real * z.imag + c.imag;
-        z = temp;
-        if (++iter == MAXITER)
-          break;
-      }
-      pixel[PIXEL(i, j)] = iter;
-    }
-  }
-}
-
-typedef unsigned char uchar;
-
-/* save 24-bits bmp file, buffer must be in bmp format: upside-down */
-void savebmp(char *name, uchar *buffer, int x, int y) {
-  FILE *f = fopen(name, "wb");
-  if (!f) {
-    printf("Error writing image to disk.\n");
-    return;
-  }
-  unsigned int size = x * y * 3 + 54;
-  uchar header[54] = { 'B', 'M', size & 255, (size >> 8) & 255, (size >> 16) & 255, size >> 24, 0,
-                       0, 0, 0, 54, 0, 0, 0, 40, 0, 0, 0, x & 255, x >> 8, 0, 0, y & 255, y >> 8, 0, 0, 1, 0, 24, 0, 0, 0, 0, 0, 0,
-                       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
-  fwrite(header, 1, 54, f);
-  fwrite(buffer, 1, XSIZE * YSIZE * 3, f);
-  fclose(f);
-}
-
-/* given iteration number, set a colour */
-void fancycolour(uchar *p, int iter) {
-  if (iter == MAXITER)
-    ;
-  else if (iter < 8) {
-    p[0] = 128 + iter * 16;
-    p[1] = p[2] = 0;
-  } else if (iter < 24) {
-    p[0] = 255;
-    p[1] = p[2] = (iter - 8) * 16;
-  } else if (iter < 160) {
-    p[0] = p[1] = 255 - (iter - 24) * 2;
-    p[2] = 255;
-  } else {
-    p[0] = p[1] = (iter - 160) * 2;
-    p[2] = 255 - (iter - 160) * 2;
-  }
-}
-
-int main(int argc, char **argv) {
-  if (argc <= 1) {
-    printf("usage: mandel_mpi [y/n]\n");
-    printf("y/n denotes if you want to save the resulting\n");
-    printf("calculations to mandel.bmp or not.\n");
-    return 1;
-  } else {
-    char arg = argv[1][0];
-    save = arg == 'y' || arg == '1';
-  }
-  MPI_Init(&argc, &argv);
-  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
-  MPI_Comm_size(MPI_COMM_WORLD, &size);
-
-#undef YSIZE
-#define YSIZE (2048 / size)
-
-  step = (xright - xleft) / XSIZE;
-  double old_yupper = ycenter + (step * YSIZE * size) / 2;
-  double old_ylower = ycenter - (step * YSIZE * size) / 2;
-  double delta = (old_yupper - old_ylower) / size;
-
-  ylower = old_ylower + rank * delta;
-  yupper = old_ylower + (rank + 1) * delta;
-  ycenter = (ylower + yupper) / 2;
-
-  calculate();
-
-  printf("after calculate %d\n", rank);
-
-  const int bufsize = XSIZE * YSIZE * 3;
-  unsigned char *buffer = calloc(bufsize, 1);
-  for (int i = 0; i < XSIZE; i++) {
-    for (int j = 0; j < YSIZE; j++) {
-      int p = ((YSIZE - j - 1) * XSIZE + i) * 3;
-      fancycolour(buffer + p, pixel[PIXEL(i, j)]);
-    }
-  }
-
-  printf("after buffer %d\n", rank);
-
-  if (rank != 0)
-    MPI_Send(buffer, bufsize, MPI_UNSIGNED_CHAR, 0, 0, MPI_COMM_WORLD);
-
-  printf("hello again from %d\n", rank);
-
-  // use process 0 as central process: gather calulations and output image
-  if (rank == 0) {
-    unsigned char *total = calloc(bufsize, size);
-    memcpy(total + (size - 1) * bufsize, buffer, bufsize);
-    printf("after memcpy 0\n");
-
-    for (int i = 1; i < size; i++) {
-      MPI_Recv(total + (size - 1 - i) * bufsize, bufsize, // write reverse order
-               MPI_UNSIGNED_CHAR, i, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
-      printf("after direct receive %d\n", i);
-    }
-    printf("after loop\n");
-
-#undef YSIZE
-#define YSIZE 2048
-
-    if (save)
-      savebmp("mandel.bmp", total, XSIZE, YSIZE);
-    printf("after save %d\n", save);
-  }
-
-  MPI_Finalize();
-  return 0;
-}

flake.nix

@@ -16,17 +16,8 @@
         buildInputs = with pkgs; [
           gcc
           gnumake
-          imagemagick_light
-          typst
-          typstyle
-          zip
-          unzip
-          feh
-          # exercise 1: 1D wave equation plotting utils
-          gnuplot
-          ffmpeg
           mpi
-          python3
+          feh
         ];
         shellHook = ''
           echo welcome!