Mandelbrot fractal optimization

Question

This is the code that outputs the mandelbrot fractal in the .ppm file. How can I optimize this?

#include<bits/stdc++.h>
using namespace std;

int findMandelbrot(double cr, double ci, int max_iterations)
{
    int i = 0;
    double zr = 0.0, zi = 0.0;
    while (i < max_iterations && zr * zr + zi * zi < 4.0)
    {
        double temp = zr * zr - zi * zi + cr;
        zi = 2.0 * zr * zi + ci;
        zr = temp;
        ++i;
    }
    return i;
}

double mapToReal(int x, int imageWidth, double minR, double maxR)
{
    double range = maxR - minR;
    return x * (range / imageWidth) + minR;
}

double mapToImaginary(int y, int imageHeight, double minI, double maxI)
{
    double range = maxI - minI;
    return y * (range / imageHeight) + minI;
}

int main()
{
    ifstream f("input.txt");
    int imageWidth, imageHeight, maxN;
    double minR, maxR, minI, maxI;

    if (!f)
    {
        cout << "Could not open file!" << endl;
        return 1;
    }

    f >> imageWidth >> imageHeight >> maxN;
    f >> minR >> maxR >> minI >> maxI;

    ofstream g("output_image.ppm");
    g << "P3" << endl;
    g << imageWidth << " " << imageHeight << endl;
    g << "255" << endl;


    double start = clock();

    for (int i = 0; i < imageHeight; i++)
    {
        for (int j = 0; j < imageWidth; j++)
        {
            double cr = mapToReal(j, imageWidth, minR, maxR);
            double ci = mapToImaginary(i, imageHeight, minI, maxI);

            int n = findMandelbrot(cr, ci, maxN);

            int r = ((int)sqrt(n) % 256);
            int gr = (2*n % 256);
            int b = (n % 256);

            g << r << " " << gr << " " << b << " ";
        }
        g << endl;

        if(i == imageHeight / 2) break;
    }

    cout << "Finished!" << endl;

    double stop = clock();

    cout << (stop-start)/CLOCKS_PER_SEC;
    return 0;
}

I go to the Height / 2 image, because in Photoshop I can just copy the other half. I thought of logarithmic power, but tried something and worked only with integers ...

Answer 1

So this is a hot loop:

int i = 0;
double zr = 0.0, zi = 0.0;
while (i < max_iterations && zr * zr + zi * zi < 4.0)
{
    double temp = zr * zr - zi * zi + cr;
    zi = 2.0 * zr * zi + ci;
    zr = temp;
    ++i;
}
return i;

I know how to implement non-integer power in fast CPU instructions, but it will not save you from binding, since it does not work for complex numbers at all. Also, std :: complex help will not be used. You won’t get anything to pay for non-linking and, of course, you won’t be able to apply optimization as you find them. Therefore, the best I can do is:

int i = max_iterations;
double zr = 0.0, zi = 0.0;
do {
    double temp = zr * zr - zi * zi + cr;
    zi = 2.0 * zr * zi + ci;
    zr = temp;
} while (--i && zr * zr + zi * zi < 4.0)
return max_iterations - i;

, , . , , :

int i = max_iterations;
double zr = 0.0, zi = 0.0;
do {
    double tempr = zr * zr - zi * zi + cr;
    double tempi = zr * zi;
    zi = tempi + tempi + ci;
    zr = tempr;
} while (--i && zr * zr + zi * zi < 4.0);
return max_iterations - i;

, .

Answer 2

findMandelbrot zr * zr zi * zi , , . , , - ...

int findMandelbrot (double cr, double ci, int max_iterations)
{
  int i = 0;
  double zr = 0.0, zi = 0.0;
  double zr2 = 0.0, zi2 = 0.0;
  while (i < max_iterations && zr2 + zi2 < 4.0) {
    double temp = zr2 - zi2 + cr;
    zi = 2.0 * zr * zi + ci;
    zr = temp;
    zr2 = zr * zr;
    zi2 = zi * zi;
    ++i;
  }
  return(i - 1);
}