A puzzle

I am always interested in some of the subtle effects that coding can have on not just the behavior of code, but also its performance. Recently, I stumbled across some benchmarking code – I cannot recall how I actually found it. It was not written in C, so I translated it.

In the process, I realized that a literal translation might not be ideal …

The code is to do with Mandelbrot sets. My first C translation looked like this:

int mandelbrot(float a)

{

float b;

int iterations = 50;

int i;

b = a;

for (i=1; i<=iterations; i++)

{

if (abs(a) > 2)

return (i - 1);

a = pow(a, 2) + b;

}

return (iterations);

}

I then saw a couple of optimizations that I could make:

#define ITERATIONS 50

int mandelbrot(float a)

{

float b;

int i;

b = a;

for (i=1; i<=ITERATIONS; i++)

{

if (abs(a) > 2)

return (i - 1);

a = a * a + b;

}

return (ITERATIONS);

}

I made it clear that iterations was a constant. I could have simply qualified it with const, but I chose to use #define. Call me old fashioned if you like. Both would most likely produce the same result. A good compiler may well optimize this without my help.

Since the code was translated from a language that included an exponentiation operator, using the pow() library function seemed logical, as C has no such operator. As a is simply squared, multiplication seemed better. Again, a smart compiler may well have addressed this.

I then saw another possible enhancement that might be effective:

#define ITERATIONS 50

int mandelbrot(float a)

{

float b;

int i;

b = a;

for (i=1; i<=ITERATIONS; i++)

{

if (abs(b) > 2)

return (i - 1);

b = b * b + a;

}

return (ITERATIONS);

}

Does this improve matters? If so, why? Please let me know your thoughts by email or comment. Sorry, no prizes, but I will follow up this posting with my further thoughts sometime soon.