From be818315f63545af24da0bf9ec534843a3499d46 Mon Sep 17 00:00:00 2001
From: KoroLion <korolion31@yandex.ru>
Date: Sun, 26 Apr 2020 16:08:03 +0300
Subject: [PATCH] Initial commit

---
 BMPImage.pas                | 258 ++++++++++++++++++++++++++++++++++++
 build.sh                    |   1 +
 generate.sh                 |   1 +
 gui/constants.pas           |   8 ++
 gui/gui.pas                 | 214 ++++++++++++++++++++++++++++++
 gui/utils.pas               |  34 +++++
 images/generated/.gitignore |   2 +
 images/k.bmp                | Bin 0 -> 252934 bytes
 main.pas                    | 240 +++++++++++++++++++++++++++++++++
 ucomplex.pas                |  71 ++++++++++
 10 files changed, 829 insertions(+)
 create mode 100644 BMPImage.pas
 create mode 100644 build.sh
 create mode 100644 generate.sh
 create mode 100644 gui/constants.pas
 create mode 100644 gui/gui.pas
 create mode 100644 gui/utils.pas
 create mode 100644 images/generated/.gitignore
 create mode 100644 images/k.bmp
 create mode 100644 main.pas
 create mode 100644 ucomplex.pas

diff --git a/BMPImage.pas b/BMPImage.pas
new file mode 100644
index 0000000..850dc62
--- /dev/null
+++ b/BMPImage.pas
@@ -0,0 +1,258 @@
+unit BMPImage;
+
+interface
+
+uses classes;
+
+type
+  TColor = object
+    r: byte;
+    g: byte;
+    b: byte;
+
+    procedure set_color(tr: byte; tg: byte; tb: byte);
+    procedure reset();
+  end;
+
+  TPxData = array of array of TColor;
+
+  TBMPImage = object
+    private
+      width, height: integer;
+
+      function get_padding(): integer;
+    public
+      pixel_data: array of array of TColor;
+
+      constructor init();
+      constructor init(w: integer; h: integer; c: TColor);
+      constructor init(px_data: TPxData);
+      destructor done();
+
+      procedure set_pixel_data(px_data: TPxData);
+      procedure set_width(w: integer);
+      procedure set_height(h: integer);
+
+      function get_width(): integer;
+      function get_height(): integer;
+
+      procedure open(path: string);
+      procedure save(path: string; monochrome: boolean);
+  end;
+
+implementation
+
+procedure TColor.reset();
+begin
+  r := 0;
+  g := 0;
+  b := 0;
+end;
+
+procedure TColor.set_color(tr: byte; tg: byte; tb: byte);
+begin
+  r := tr;
+  g := tg;
+  b := tb;
+end;
+
+procedure TBMPImage.set_pixel_data(px_data: TPxData);
+var
+  i, j: longint;
+begin
+  width := length(px_data);
+  height := length(px_data[0]);
+  setLength(pixel_data, width, height);
+
+  for i := 0 to width - 1 do begin
+    for j := 0 to height - 1 do begin
+      pixel_data[i][j] := px_data[i][j];
+    end;
+  end;
+end;
+
+constructor TBMPImage.init();
+begin
+  setLength(pixel_data, 0, 0);
+  width := 0;
+  height := 0;
+end;
+
+constructor TBMPImage.init(w: integer; h: integer; c: TColor);
+var
+  i, j: integer;
+begin
+  setLength(pixel_data, w, h);
+  width := w;
+  height := h;
+
+  for i := 0 to width - 1 do begin
+    for j := 0 to height - 1 do begin
+      pixel_data[i][j] := c;
+    end;
+  end;
+end;
+
+constructor TBMPImage.init(px_data: TPxData);
+begin
+  set_pixel_data(px_data);
+end;
+
+
+destructor TBMPImage.done();
+begin
+  setLength(pixel_data, 0, 0); // not neccesary
+  width := 0;
+  height := 0;
+end;
+
+function TBMPImage.get_padding(): integer;
+var
+  bytes_per_row, padding: integer;
+begin
+  bytes_per_row := width * 3;
+  padding := 4 - bytes_per_row mod 4;
+  if padding = 4 then padding := 0;
+  get_padding := padding;
+end;
+
+procedure TBMPImage.set_width(w: integer);
+var
+  color: TColor;
+  i, j: integer;
+begin
+  setLength(pixel_data, w, height);
+  if (w > width) then begin
+    for i := width to w - 1 do begin
+      for j := 0 to height - 1 do begin
+        color.set_color(255, 255, 255);
+        pixel_data[i][j] := color;
+      end;
+    end;
+  end;
+  width := w;
+end;
+
+procedure TBMPImage.set_height(h: integer);
+var
+  color: TColor;
+  i, j: integer;
+begin
+  setLength(pixel_data, width, h);
+  if (h > height) then begin
+    for i := 0 to width - 1 do begin
+      for j := height to h - 1 do begin
+        color.set_color(255, 255, 255);
+        pixel_data[i][j] := color;
+      end;
+    end;
+  end;
+  height := h;
+end;
+
+function TBMPImage.get_width(): integer;
+begin
+  get_width := width;
+end;
+
+function TBMPImage.get_height(): integer;
+begin
+  get_height := height;
+end;
+
+procedure TBMPImage.open(path: string);
+var
+  instream: TFileStream;
+  px_data_offset, i, j, k, padding: integer;
+  color: TColor;
+begin
+  instream := TFileStream.Create(path, fmOpenRead);
+
+  instream.position := 10;
+  px_data_offset := instream.readword();
+
+  instream.position := 18;
+  width := instream.readword();
+  instream.position := 22;
+  height := instream.readword();
+
+  setLength(pixel_data, width, height); // indexes begins with zero
+
+  padding := get_padding();
+
+  instream.position := px_data_offset;
+  k := 1;
+  for i := height - 1 downto 0 do begin
+    for j := 0 to width - 1 do begin
+      color.b := instream.readbyte();
+      color.g := instream.readbyte();
+      color.r := instream.readbyte();
+
+      pixel_data[j][i] := color;
+
+      inc(k);
+    end;
+    instream.position := instream.position + padding;
+  end;
+end;
+
+procedure TBMPImage.save(path: string; monochrome: boolean);
+var
+  ostream: TFileStream;
+  padding, i, j, cs: integer;
+  color: TColor;
+  buf: array[1..1000000] of byte;
+  k, size: longint;
+begin
+  ostream := TFileStream.Create(path, fmCreate + fmOpenWrite);
+
+  ostream.writeword(19778); // "BM" - format specifier
+
+  ostream.position := 10;
+  ostream.WriteDWord(54); // pixel data offset is bytes (54)
+  ostream.WriteDWord(40); // second header size in bytes (40, 14 - first header)
+  ostream.WriteDWord(width);
+  ostream.WriteDWord(height);
+  ostream.position := 26;
+  ostream.writeword(1); // must be one
+  // bits per pixel
+  if (monochrome) then ostream.writeword(1) else ostream.writeword(24);
+
+  padding := get_padding();
+  ostream.position := 54;
+
+  size := width * 3 + padding;
+  for k := 1 to size do begin // we need zero bytes to fill padding
+    buf[k] := 0;
+  end;
+
+  if (monochrome) then begin
+    {color := pixel_data[j][i];
+    cs := color.r + color.g + color.b;
+    if (cs > 425) then begin
+      cs := 255;
+    end else begin
+      cs := 0;
+    end;
+    ostream.writebyte(cs);
+    ostream.writebyte(cs);
+    ostream.writebyte(cs);}
+  end else begin
+    for i := height - 1 downto 0 do begin
+      k := 1;
+      for j := 0 to width - 1 do begin
+        color := pixel_data[j][i];
+
+        buf[k + 0] := color.b;
+        buf[k + 1] := color.g;
+        buf[k + 2] := color.r;
+
+        k := k + 3;
+      end;
+      ostream.writebuffer(buf, size);
+    end;
+  end;
+end;
+
+begin
+end.
diff --git a/build.sh b/build.sh
new file mode 100644
index 0000000..a9b2d4c
--- /dev/null
+++ b/build.sh
@@ -0,0 +1 @@
+fpc gui.pas -Fu/usr/local/Cellar/fpc/3.0.4_1/lib/fpc/3.0.4/units/x86_64-darwin/fv
diff --git a/generate.sh b/generate.sh
new file mode 100644
index 0000000..c4116aa
--- /dev/null
+++ b/generate.sh
@@ -0,0 +1 @@
+./main 13 -100 1800
diff --git a/gui/constants.pas b/gui/constants.pas
new file mode 100644
index 0000000..54aa779
--- /dev/null
+++ b/gui/constants.pas
@@ -0,0 +1,8 @@
+unit constants;
+
+interface
+  const cmAbout = 1001;
+  const cmGenerate = 1002;
+  
+implementation
+end.
diff --git a/gui/gui.pas b/gui/gui.pas
new file mode 100644
index 0000000..bab439a
--- /dev/null
+++ b/gui/gui.pas
@@ -0,0 +1,214 @@
+uses
+  Process, SysUtils,
+  App, Dialogs, Objects, Menus, Drivers, Views, MsgBox,
+  utils, constants;
+
+type
+  PGenerateData = ^TGenerateData;
+  TGenerateData = record
+    path: string[128];
+    width: string[16];
+    height: string[16];
+    power: string[64];
+    zoom: string[64];
+    centerX: string[64];
+    centerY: string[64];
+  end;
+  
+  PGeneratorWindow = ^TGeneratorWindow;
+  TGeneratorWindow = object(TDialog)
+    winRect: TRect;
+    curY: integer;
+  
+    constructor Init;
+    procedure addField(caption: string; maxLength: integer);
+    procedure addButton(caption: string; command: integer);
+  end;
+  
+  TMSApp = object(TApplication)
+    GeneratorWindow: PGeneratorWindow;
+  
+    procedure InitStatusLine; virtual;
+    procedure InitMenuBar; virtual;
+    procedure HandleEvent(var Event: TEvent); virtual;
+    
+    procedure NewWindow();
+    procedure GenerateMandelbrotSetImage();
+    procedure ShowAbout();
+    procedure ShowSuccess(fname: string; t: extended);
+  end;
+  
+var
+  MSApp: TMSApp;
+  GenerateData: TGenerateData;
+  
+procedure TMSApp.GenerateMandelbrotSetImage();
+var
+  s: AnsiString;
+  startTime: int64;
+  success: boolean;
+begin
+  GeneratorWindow^.GetData(GenerateData);
+  startTime := getTimestamp();
+  
+  with GenerateData do begin
+    success := RunCommand('../main', [
+      width,
+      height,
+      power,
+      zoom,
+      centerX,
+      centerY,
+      path
+    ], s);
+  end;
+  
+  if (success) then begin
+    ShowSuccess(s, (getTimestamp() - startTime) / 1000);
+  end;
+end;
+
+procedure TGeneratorWindow.addField(caption: string; maxLength: integer);
+var
+  il: PInputLine;
+  r: TRect;
+begin
+  caption := wrapFirstLetter(caption, '~');
+
+  r.assign(14, curY, winRect.b.x - 2, curY + 1);
+  il := New(PInputLine, Init(r, maxLength));
+  Insert(il);
+  r.assign(2, curY, 13, curY + 1);
+  Insert(New(PLabel, Init(r, caption, il)));
+  
+  curY := curY + 2;
+end;
+
+procedure TGeneratorWindow.addButton(caption: string; command: integer);
+var
+  r: TRect;
+begin
+  r.assign(3, curY, winRect.b.x - 1, curY + 1);
+  Insert(New(PButton, Init(r, caption, command, bfNormal)));
+  
+  curY := curY + 2;
+end;
+  
+constructor TGeneratorWindow.Init();
+var
+  wr: TRect;
+begin
+  wr.assign(0, 0, 60, 19);
+  inherited Init(wr, 'Generator');
+  Options := Options or ofCentered;
+  HelpCtx := $F000;
+  
+  winRect := wr;
+  curY := 2;
+  
+  with GenerateData do begin
+    path := './images';
+    width := '512';
+    height := '512';
+    power := '2';
+    zoom := '1';
+    centerX := '0';
+    centerY := '0';
+  end;
+  
+  addField('Path:', 128);
+  addField('Width:', 16);
+  addField('Height:', 16);
+  addField('Power:', 64);
+  addField('Zoom:', 64);
+  addField('Center X:', 64);
+  addField('Center Y:', 64);
+  
+  addButton('Generate', cmGenerate);
+end;
+  
+procedure TMSApp.NewWindow();
+begin
+  GeneratorWindow := New(PGeneratorWindow, Init);
+  GeneratorWindow^.SetData(GenerateData);
+  InsertWindow(GeneratorWindow);
+end;
+  
+procedure TMSApp.ShowAbout();
+begin
+  MessageBox(
+    #3'Multibrot Set Generator GUI'#13 +
+    #3'Developed by Artem K.'#13 +
+    #3'MF BMSTU 2019', 
+    nil, 
+    mfInformation or mfOkButton
+  );
+end;
+
+procedure TMSApp.ShowSuccess(fname: string; t: extended);
+begin
+  MessageBox(
+    #3'Set image was generated!'#13 +
+    'File name: ' + fname + #13 +
+    'Time spent: ' + FloatToStr(t) + ' s',
+    nil, 
+    mfInformation or mfOkButton
+  );
+end;
+  
+procedure TMSApp.HandleEvent(var Event: TEvent);
+begin
+  inherited HandleEvent(Event);
+  
+  if Event.What = evCommand then begin
+    case Event.Command of
+      cmNew: begin
+        NewWindow();
+        ClearEvent(Event);
+      end;
+      cmAbout: begin
+        ShowAbout();
+        ClearEvent(Event);
+      end;
+      cmGenerate: begin
+        GenerateMandelbrotSetImage();
+        ClearEvent(Event);
+      end;
+    end;
+  end;
+end;
+
+procedure TMSApp.InitStatusLine();
+var
+  r: TRect;
+begin
+  GetExtent(r);
+  r.a.y := r.b.y - 1;
+  New(StatusLine, Init(r,
+    NewStatusDef(0, $EFFF,
+      NewStatusKey('~Alt+X~ Exit', kbAltX, cmQuit,
+      NewStatusKey('~F3~ New', kbF3, cmNew,
+      nil 
+    )), nil)
+  ));
+end;
+
+procedure TMSApp.InitMenuBar();
+var
+  r: TRect;
+begin
+  GetExtent(r);
+  r.b.y := r.a.y + 1;
+  MenuBar := New(PMenuBar, Init(r, NewMenu(
+    NewItem('~N~ew', '', kbNoKey, cmNew, hcNew,
+    NewItem('~A~bout', '', kbNoKey, cmAbout, hcNoContext,
+    NewItem('~E~xit', 'Alt+X', kbAltX, cmQuit, hcExit,
+    nil)))))
+  );
+end;
+
+begin
+  MSApp.Init();
+  MSApp.Run();
+  MSApp.Done();
+end.
diff --git a/gui/utils.pas b/gui/utils.pas
new file mode 100644
index 0000000..f5a269f
--- /dev/null
+++ b/gui/utils.pas
@@ -0,0 +1,34 @@
+unit utils;
+
+interface
+
+uses SysUtils;
+
+function wrapFirstLetter(s: string; wrapper: string): string;
+function getTimestamp(): int64;
+
+
+implementation
+
+function wrapFirstLetter(s: string; wrapper: string): string;
+var
+  i: integer;
+  ts: string;
+begin
+  ts := '';
+  for i := 2 to length(s) do begin
+    ts := ts + s[i];
+  end;
+  s := wrapper + s[1] + wrapper + ts;
+  wrapFirstLetter := s;
+end;
+
+function GetTimestamp(): int64;
+var
+  ts: TTimeStamp;
+begin
+  ts := DateTimeToTimestamp(Now());
+  GetTimestamp := ts.time + ts.date * 24 * 60 * 60 * 1000;
+end;
+
+end.
diff --git a/images/generated/.gitignore b/images/generated/.gitignore
new file mode 100644
index 0000000..c96a04f
--- /dev/null
+++ b/images/generated/.gitignore
@@ -0,0 +1,2 @@
+*
+!.gitignore
\ No newline at end of file
diff --git a/images/k.bmp b/images/k.bmp
new file mode 100644
index 0000000000000000000000000000000000000000..67d7aa569649dba0ef46c6108dd6d227421e70b4
GIT binary patch
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diff --git a/main.pas b/main.pas
new file mode 100644
index 0000000..760bfb8
--- /dev/null
+++ b/main.pas
@@ -0,0 +1,240 @@
+uses sysutils, BMPImage, ucomplex;
+
+type
+  TArgs = record
+    width: longint; // TryStrToInt wants longint
+    height: longint;
+    power: longint;
+    zoom: extended;
+    center_x: extended;
+    center_y: extended;
+    out_path: string;
+  end;
+  TPxData = array of array of TColor;
+
+const save_path = './images/generated/';
+const help_text = 'Usage: command <width = 512> <height = 512> <power = 2> <zoom = 1> <centerX = 0> <centerY = 0> <out_path = ./images>';
+
+function get_filename(base_name: string; zoom: extended; center_x: extended; center_y: extended): string;
+var
+  z, cx, cy: string;
+begin
+  z := FloatToStr(zoom);
+  cx := FloatToStr(center_x);
+  cy := FloatToStr(center_y);
+
+  get_filename := base_name + '_(z=' + z + ';cx=' + cx + ';cy=' + cy + ').bmp'
+end;
+
+type Point2D = object
+  x: extended;
+  y: extended;
+
+  procedure update(px: extended; py: extended);
+end;
+
+procedure Point2D.update(px: extended; py: extended);
+begin
+  x := px;
+  y := py;
+end;
+
+{function f(x: integer): integer;
+begin
+  f := round(2 * sin(x) + 3);
+end;
+
+function check_a(x: integer; y: integer): boolean;
+begin
+  check_a := sqr(x - 50) + sqr(y - 50) - 6 <= 900;
+end;
+
+function fr(x: integer; c: integer): integer;
+begin
+  fr := sqr(x) + c;
+end;}
+
+function fc(x: complex; c: complex; n: integer): complex;
+begin
+  fc := complex_sum(x.power(n), c);
+end;
+
+function translate_point(p: Point2D; width: integer; height: integer): Point2D;
+var
+  base_zoom: integer;
+begin
+  base_zoom := round(width * 0.8) div 2;
+  p.update((p.x - width / 2) / base_zoom, (p.y - height / 2) / base_zoom);
+  translate_point := p;
+end;
+
+function multibrot_check(x: extended; y: extended; n: integer): integer;
+// f defined as f(x) = x^2 + c, where c (complex number) is a constant
+// point (x, y) is in Mandelbrot's set if f(f(...f(0))) converges, c = x + yi
+var
+  i: integer;
+  v, c: complex;
+begin
+  i := 0;
+  v.update(0, 0);
+  while (i < 255) and (v.length() <= 2) do begin
+    c.update(x, y);
+    v := fc(v, c, n);
+    inc(i);
+  end;
+  multibrot_check := i;
+end;
+
+procedure setDefaultArgs(var args: TArgs);
+begin
+  with args do begin
+    width := 512;
+    height := 512;
+    power := 2;
+    zoom := 1;
+    center_x := 0;
+    center_y := 0;
+    out_path := './images';
+  end;
+end;
+
+function getArgs(var args: TArgs): boolean;
+var
+  error: boolean;
+begin
+  error := false;
+
+  if (ParamCount > 7) then begin
+    error := true;
+  end else begin
+    if (ParamCount >= 1) then begin
+      if (not TryStrToInt(ParamStr(1), args.width)) then error := true;
+    end;
+    if (ParamCount >= 2) then begin
+      if (not TryStrToInt(ParamStr(2), args.height)) then error := true;
+    end;
+    if (ParamCount >= 3) then begin
+      if (not TryStrToInt(ParamStr(3), args.power)) then error := true;
+    end;
+    if (ParamCount >= 4) then begin
+      if (not TryStrToFloat(ParamStr(4), args.zoom)) then error := true;
+    end;
+    if (ParamCount >= 5) then begin
+      if (not TryStrToFloat(ParamStr(5), args.center_x)) then error := true;
+    end;
+    if (ParamCount >= 6) then begin
+      if (not TryStrToFloat(ParamStr(6), args.center_y)) then error := true;
+    end;
+    if (ParamCount = 7) then begin
+      args.out_path := ParamStr(7);
+    end;
+  end;
+
+  getArgs := not error;
+end;
+
+function generateMultibrot(
+  width: integer; height: integer; 
+  power: longint; zoom: extended; center_x: extended; center_y: extended
+): TPxData;
+var
+  color: TColor;
+  i, j, mb_out: integer;
+  p: Point2D;
+  palette: array[0..255] of TColor;
+  px_data: TPxData;
+begin
+    setLength(px_data, width, height);
+
+    color.reset();
+
+    for i := 0 to 254 do begin
+      palette[i].set_color(i, abs(64 - i), abs(128 - i));
+    end;
+    palette[255].set_color(0, 0, 0);
+
+    for i := 0 to width - 1 do begin
+      for j := 0 to height - 1 do begin
+        p.update(i, j);
+        p := translate_point(p, width, height);
+
+        p.x := (p.x / zoom) + center_x;
+        p.y := (p.y / zoom) + center_y;
+
+        color.reset();
+        if ((abs(p.x) < 0.000001) or (abs(p.y) < 0.000001)) then begin
+          color.g := 255;
+        end else begin
+          mb_out := multibrot_check(p.x, p.y, power);
+          color := palette[mb_out];
+        end;
+
+        px_data[i][j] := color;
+      end;
+    end;
+
+    generateMultibrot := px_data;
+end;
+
+var
+  args: TArgs;
+  img: TBMPImage;
+  out_path, fname: string;
+  px_data: TPxData;
+begin
+  {img.init();
+  img.open('./images/k.bmp');
+
+  // draw sin
+  for i := 0 to img.get_width() - 1 do begin
+    color.set_color(255, 0, 0);
+    img.pixel_data[i][f(i)] := color;
+  end;
+  // convert color
+  for i := 0 to img.get_width() - 1 do begin
+    for j := 0 to img.get_height() - 1 do begin
+      color := img.pixel_data[i][j];
+      new_color.r := color.b;
+      new_color.g := color.g;
+      new_color.b := color.r;
+      img.pixel_data[i][j] := new_color;
+    end;
+  end;
+
+  img.set_width(400);
+  img.set_height(400);
+  img.save('./images/generated/k_generic.bmp', false);
+  img.done();}
+
+  setDefaultArgs(args);
+
+  if (getArgs(args)) then begin
+    px_data := generateMultibrot(args.width, args.height, args.power, args.zoom, args.center_x, args.center_y);
+
+    img.init(px_data);
+
+    fname := get_filename('mb' + IntToStr(args.power) + '_set', args.zoom, args.center_x, args.center_y);
+    out_path := args.out_path + '/' + fname;
+
+    img.save(out_path, false);
+    img.done();
+
+    writeln(fname);
+
+    {color.set_color(255, 255, 255);
+    img.init(100, 100, color);
+    color.set_color(0, 255, 0);
+    for i := 0 to img.get_width() - 1 do begin
+      for j := 0 to img.get_height() - 1 do begin
+        if (check_a(i, j)) then begin
+          img.pixel_data[i][j] := color;
+        end;
+      end;
+    end;
+    img.save('./images/generated/circle.bmp', false);
+    img.done();}
+  end else begin
+    writeln(help_text);
+  end;
+end.
+
diff --git a/ucomplex.pas b/ucomplex.pas
new file mode 100644
index 0000000..d0603b6
--- /dev/null
+++ b/ucomplex.pas
@@ -0,0 +1,71 @@
+unit ucomplex;
+
+interface
+
+type complex = object
+  r: extended;
+  i: extended;
+  function length(): extended;
+  function squared(): complex;
+  function mult(a: complex): complex;
+  function power(n: integer): complex;
+  procedure update(re: extended; im: extended);
+end;
+
+function complex_sum(a: complex; b: complex): complex;
+
+implementation
+
+procedure complex.update(re: extended; im: extended);
+begin
+  r := re;
+  i := im;
+end;
+
+function complex.length(): extended;
+begin
+  length := sqrt(r * r + i * i);
+end;
+
+function complex.squared(): complex;
+var
+  res: complex;
+begin
+  res.r := sqr(r) - sqr(i);
+  res.i := 2 * r * i;
+  squared := res;
+end;
+
+function complex.mult(a: complex): complex;
+var
+  res: complex;
+begin
+  res.r := r * a.r - i * a.i;
+  res.i := r * a.i + i * a.r;
+  mult := res;
+end;
+
+function complex.power(n: integer): complex;
+var
+  j: integer;
+  c, res: complex;
+begin
+  c.update(r, i);
+  res.update(r, i);
+  for j := 1 to n - 1 do begin
+    res := res.mult(c);
+  end;
+  power := res;
+end;
+
+function complex_sum(a: complex; b: complex): complex;
+var
+  res: complex;
+begin
+  res.r := a.r + b.r;
+  res.i := a.i + b.i;
+  complex_sum := res;
+end;
+
+begin
+end.