Coding - Comparison test gone wrong?

I'm sure I just made a silly mistake somewhere, I just don't know where. Observe the highlighted piece of code:

 screenshot

 excerpted for your convenience

Code:

while(x > limit)
    fprintf("x = %.1f, limit = %.1f, x > limit : %d\n", (x), limit, (x>limit));
    fprintf("X before = %f\n", x);
    [x, y, slope] = findNext(x, y, deltaX);
    fprintf("X after = %f\n\n", x);
end

 sample output of the program

Code:

octave:28> run main.m
Input deltaX: -0.1
Initial values:
x = 0.900000
y = -0.700000
slope = -3.000000

Input limit of x: 0.7
x = 0.9, limit = 0.7, x > limit : 1
X before = 0.900000
X after = 0.800000

x = 0.8, limit = 0.7, x > limit : 1
X before = 0.800000
X after = 0.700000

x = 0.7, limit = 0.7, x > limit : 1
X before = 0.700000
X after = 0.600000

Program paused.
x = 0.6
y(0.6) = -0.367017
slope = -0.634426

It doesn't do much, take an initial x value, do stuff with it, decrement by deltaX until it hits limit, abort.

The problem is, x > limit returns true when x = limit (as in this example, x = limit = 0.7)

Code:

fprintf("x = %.1f, limit = %.1f, x > limit : %d\n", (x), limit, (x>limit));

Code:

x = 0.7, limit = 0.7, x > limit : 1

x is higher than limit. When you're printing out x and limit, you only print out the first decimal behind the period. Try to print it all out, and you'll see that x > limit.

I did print out up to the 15th decimal place. Also note how on the Before-After check, x was printed without any formatting, so perhaps the fprintf function did the truncating itself.

But anyway, I got it working with
while (x - limit > 10^(-15))
so I'm assuming it's just some nuances with binary representation of numbers.

The question now is how do I know beforehand that something this simple (decrement step by 0.1) is going to run into this problem? Should I always do the (different > epsilon) check instead of (difference = 0) check?

The question now is how do I know beforehand that something this simple (decrement step by 0.1) is going to run into this problem? Should I always do the (different > epsilon) check instead of (difference = 0) check?

You'll pretty much want to use >= or <= for floating-point compares in place of ==. Integer is fine to use ==, though.