Why do my functions not work in parallel?

Question

I tried to use OpenMP in my C program for creating the Mandelbrot set. I use two functions f(z) and d(z) defined in the file. When I use them inside a parallel section direct code:

dc = 5*z*z*z*z*dc + 1; 
z = z*z*z*z*z +c;

it works. When I use functions:

dc = d(z)*dc +1;
z = f(z);

It works without OpenMP (good image) but not with OpenMP (bad image).

How should it be done?

See below full code:

#include <complex.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <omp.h> //OpenM

/*
fork of 
mandelbrot-book how to write a book about the Mandelbrot set by Claude Heiland-Alle
https://code.mathr.co.uk/mandelbrot-book/blob/HEAD:/book/


gcc e.c -lm -Wall -fopenmp

./a.out >ed.ppm   // P6 = binary Portable PixMap see https://en.wikipedia.org/wiki/Netpbm#File_formats


*/

const double pi = 3.141592653589793;

double _Complex c;
double _Complex z;
double _Complex dc;
/*
 int q = 5 ;
complex double f(complex double z, int q){ return cpow(z,q) + c;}
complex double d(complex double z, int q) {return q*cpow(z, q-1); }

*/
complex double f(complex double z){ return z*z*z*z*z + c;}
complex double d(complex double z) {return 5*z*z*z*z; }




double cnorm(double _Complex z) // https://stackoverflow.com/questions/6363247/what-is-a-complex-data-type-and-an-imaginary-data-type-in-c
{
  return creal(z) * creal(z) + cimag(z) * cimag(z);
}

void hsv2rgb(double h, double s, double v, int *red, int *grn, int *blu) {
  double i, f, p, q, t, r, g, b;
  int ii;
  if (s == 0.0) { r = g = b = v; } else {
    h = 6 * (h - floor(h));
    ii = i = floor(h);
    f = h - i;
    p = v * (1 - s);
    q = v * (1 - (s * f));
    t = v * (1 - (s * (1 - f)));
    switch(ii) {
      case 0: r = v; g = t; b = p; break;
      case 1: r = q; g = v; b = p; break;
      case 2: r = p; g = v; b = t; break;
      case 3: r = p; g = q; b = v; break;
      case 4: r = t; g = p; b = v; break;
      default:r = v; g = p; b = q; break;
    }
  }
  *red = fmin(fmax(255 * r + 0.5, 0), 255);
  *grn = fmin(fmax(255 * g + 0.5, 0), 255);
  *blu = fmin(fmax(255 * b + 0.5, 0), 255);
}

int main()
{
  int aa = 4;
  int w = 800 * aa;
  int h = 800 * aa;
  int n = 1024;
  double r = 2;
  double px = r / (h/2);
  double r2 = 25 * 25;
  unsigned char *img = malloc(3 * w * h);
  int i,j;
  #pragma omp parallel for //schedule(dynamic) private (c,dc,i,j,z) shared(w,h,n,r,px,r2)
  
  for ( j = 0; j < h; ++j)
  {
    double y = (h/2 - (j + 0.5)) / (h/2) * r;
    for (i = 0; i < w; ++i)
    {
      double x =  (i + 0.5 - w/2) / (h/2) * r; // for q=2 add -0.5
      c = x + I * y;
      //double _Complex 
      dc = 0; // first derivative of zn with respect to c
      //double _Complex z = 0;
      z = 0;
      int k;
      for (k = 0; k < n; ++k)
      { 
      
        //complex double temp = z*z*z*z; // optimisation ?
        
        // works for openmp
        //dc = 5*z*z*z*z*dc + 1; 
        //z = z*z*z*z*z +c;
        
        
        // not works for openmp
        dc = d(z)*dc +1;
        z = f(z);
        
        if (cnorm(z) > r2)
          break;
      }
      
      // color
      double hue = 0, sat = 0, val = 1; // interior color = white
      
      if (k < n) 
      { // exterior and boundary color
        double _Complex de = 2 * z * log(cabs(z)) / dc;
        hue = fmod(1 + carg(de) / (2 * pi), 1); // ? slope of de
        sat = 0.25;
        val = tanh(cabs(de) / px / aa);
      }
      
      // hsv to rgb conversion
      int red, grn, blu;
      hsv2rgb(hue, sat, val, &red, &grn, &blu);
      // save rgb color to array
      img[3*(j * w + i)+0] = red;
      img[3*(j * w + i)+1] = grn;
      img[3*(j * w + i)+2] = blu;
    }
  }
  
  //
  printf("P6\n%d %d\n255\n", w, h);
  fwrite(img, 3 * w * h, 1, stdout);
  free(img);
  
  
  return 0;
}

Answer 1

Here's a version of your code that works and produces the image correctly:

#include <complex.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <omp.h> //OpenM

/*
fork of 
mandelbrot-book how to write a book about the Mandelbrot set by Claude Heiland-Alle
https://code.mathr.co.uk/mandelbrot-book/blob/HEAD:/book/


gcc e.c -lm -Wall -fopenmp

./a.out >ed.ppm   // P6 = binary Portable PixMap see https://en.wikipedia.org/wiki/Netpbm#File_formats


*/

const double pi = 3.141592653589793;

/*
 int q = 5 ;
complex double f(complex double z, int q){ return cpow(z,q) + c;}
complex double d(complex double z, int q) {return q*cpow(z, q-1); }

*/
complex double f(complex double z, complex double c){ return z*z*z*z*z + c;}
complex double d(complex double z) {return 5*z*z*z*z; }




double cnorm(double _Complex z) // https://stackoverflow.com/questions/6363247/what-is-a-complex-data-type-and-an-imaginary-data-type-in-c
{
  return creal(z) * creal(z) + cimag(z) * cimag(z);
}

void hsv2rgb(double h, double s, double v, int *red, int *grn, int *blu) {
  double i, f, p, q, t, r, g, b;
  int ii;
  if (s == 0.0) { r = g = b = v; } else {
    h = 6 * (h - floor(h));
    ii = i = floor(h);
    f = h - i;
    p = v * (1 - s);
    q = v * (1 - (s * f));
    t = v * (1 - (s * (1 - f)));
    switch(ii) {
      case 0: r = v; g = t; b = p; break;
      case 1: r = q; g = v; b = p; break;
      case 2: r = p; g = v; b = t; break;
      case 3: r = p; g = q; b = v; break;
      case 4: r = t; g = p; b = v; break;
      default:r = v; g = p; b = q; break;
    }
  }
  *red = fmin(fmax(255 * r + 0.5, 0), 255);
  *grn = fmin(fmax(255 * g + 0.5, 0), 255);
  *blu = fmin(fmax(255 * b + 0.5, 0), 255);
}

int main()
{
  const int aa = 4;
  const int w = 800 * aa;
  const int h = 800 * aa;
  const int n = 1024;
  const double r = 2;
  const double px = r / (h/2);
  const double r2 = 25 * 25;
  unsigned char *img = malloc(3 * w * h);

  #pragma omp parallel for schedule(dynamic)
  for (int j = 0; j < h; ++j)
  {
    double _Complex c;
    double _Complex z;
    double _Complex dc;
    double y = (h/2 - (j + 0.5)) / (h/2) * r;
    for (int i = 0; i < w; ++i)
    {
      double x =  (i + 0.5 - w/2) / (h/2) * r; // for q=2 add -0.5
      c = x + I * y;
      //double _Complex 
      dc = 0; // first derivative of zn with respect to c
      //double _Complex z = 0;
      z = 0;
      int k;
      for (k = 0; k < n; ++k)
      { 
      
        //complex double temp = z*z*z*z; // optimisation ?
        
        // works for openmp
        //dc = 5*z*z*z*z*dc + 1; 
        //z = z*z*z*z*z +c;
        
        
        // not works for openmp
        dc = d(z)*dc +1;
        z = f(z,c);
        
        if (cnorm(z) > r2)
          break;
      }
      
      // color
      double hue = 0, sat = 0, val = 1; // interior color = white
      
      if (k < n) 
      { // exterior and boundary color
        double _Complex de = 2 * z * log(cabs(z)) / dc;
        hue = fmod(1 + carg(de) / (2 * pi), 1); // ? slope of de
        sat = 0.25;
        val = tanh(cabs(de) / px / aa);
      }
      
      // hsv to rgb conversion
      int red, grn, blu;
      hsv2rgb(hue, sat, val, &red, &grn, &blu);
      // save rgb color to array
      img[3*(j * w + i)+0] = red;
      img[3*(j * w + i)+1] = grn;
      img[3*(j * w + i)+2] = blu;
    }
  }
  
  //
  printf("P6\n%d %d\n255\n", w, h);
  fwrite(img, 3 * w * h, 1, stdout);
  free(img);
  
  
  return 0;
}

The important changes is that I declared i, j, c, z, dc withing the parallel region and passed c to the function f. Why this works now, and didn't before, is a bit of a mystery, but I assume that, because c, z, dc were global, they could not be made private.