I’m currently reading the Julia documentation/tutorial and I think I don’t really understand how nextfloat(x) and prevfloat(x) are computed. Reading the document I thought they would be respectively x + eps(x) and x - eps(x) , however if it seems to be the case for nextfloat(x), it is not for prevfloat(x).

The thing you’re missing is that eps(0.9999999999999999) is half of eps(1.0) due to how floating point numbers work. The way these results are computed by Julia is that nextfloat(x) is just the result of reinterpreting x as an Integer, adding 1, and reinterpreting back as a floating point number (or subtracting for prevfloat).

To elaborate on that, values that are exactly powers of 2—like 1.0—are on the cusp between a smaller eps size and the next bigger eps size. And since eps(x) is defined such that eps(x) = nextfloat(x) - x, that means that eps(x) is going to be bigger than x - prevfloat(x) for powers of two; for all other values of x, nextfloat(x) - x and x - prevfloat(x) are equal. There’s a case to be made for either definition of eps(x) on the cusp, but the larger value is conventional.