Question

I would like some advise on how to optimise the following while loop:

double minor_interval   = 0.1;
double major_interval   = 1.0;

double start            = 0.0;
double finish           = 10.0;

printf("Start\r\n");

while (start < finish)
{
    printf("Minor interval: %.20f\r\n", start);

    double m = fmod(start, major_interval);
    printf("m: %.20f\r\n", m);

    if (m == 0)
        printf("At major interval: %.20f\r\n", start);

    start += minor_interval;
}

printf("Finished\r\n");

Essentially, I am incrementing a counter in the loop by the minor interval and would like to know every time around the loop if I am at a major interval. Picture this as drawing a ruler with millimeter intervals, and every time I get to a major interval, I want to draw a centimetre. Given inaccuracies in floating point arithmetic, how can I modify the above loop to implement the functionality I require? I have tried different methods of comparing the result of the modulus using a tolerance with no luck. Note that the minor and major intervals can be any values i.e. minor = 0.4 and major = 1.6 (to draw quarter mile increments).

Thanks in advance.

Answer 1

I would implement this with a for loop over an int variable i. Using integers avoids rounding problems due to the limitations of floating point arithmetic. [See What Every Computer Scientist Should Know About Floating-Point Arithmetic.]

Let i run from 0 to iFinish-1 and set time equal to start + i*minor_interval. The value of iFinish can be found by rounding (finish-start)/minor_interval to the nearest int.

Major axis updates can be handled in a similar way. Round major_interval/minor_interval to the nearest int, say k. Then update major axis marks every k-th iteration.

In terms of code it looks like this:

double round(double r) {
    return (r > 0.0) ? floor(r + 0.5) : ceil(r - 0.5);
}
...
int iFinish = round((finish-start)/minor_interval);
int k = round(major_interval/minor_interval);
for (int i=0; i<iFinish; i++)
{
    double time = start + i*minor_interval;
    bool isMajor = (i%k == 0);
    ...
}