floating point number imprecision while iterating

Question

I have a function that computes a point in 3d spaced based on a value in range [0, 1]. The problem I\'m facing is, that a binary floating-point number canno

Answer 1

binary floating-point number cannot represent exactly 1

Proof that it can can be found here.

Most accurate representation = 1.0E0

There could be problems with

1. fractional numbers that would have infinite fractional digits in radix of 2
2. numbers that are too small to exactly represent without losing precision
3. numbers that are too large to represent without losing precision.

But 1.0 is none of them!

However 0.1 is a problem case, violating point number 1, look at this:

Most accurate representation = 1.00000001490116119384765625E-1

So if you add up 0.1 ten times, you will get 1.00000001490116119384765625E-0 which is greater than 1.0.

(examples are in IEEE754 single precision 32 bit floating point numbers)

Possible solution:

int i;
for (i=0; i <= 10; i++) {
    t=i/10.0;
    curves_error error = curves_bezier(points, point, t);
    if (error != curves_no_error) {
        printf("Error with t = %f.\n", t);
    }
    else {
        printf("t = %f is ok.\n", t);
    }
}

This way, the error of the binary format does not get summed up!

(Note: I used extra curly braces for the if and else statements. Do that, you'll thank yourself one day.)