That's not true, there are plenty of cases where using equivalence is just fine. Integer arithmetic, and algorithms that are more reliably written not to contain any empty intervals are two examples.
There is no uncertainty. There is a guarantee that a == b (if we ignore the off-by-one error in your post), because IEEE operations are guaranteed to be accurate within half an ulp. You can safely perform addition, subtraction, and multiplication, and truncated or floored division, within the 24-bit integer range for single-precision floats and the 53-bit integer range for doubles. This is why people can safely use integers in Javascript.
i guess that's what a i get for not double checking my math. here's a revised version that (as long as i haven't made any other math mistakes) still fits within a 32 bit signed int but doesn't guarantee simple equality:
float a = 0.0;
float b = 10000.0;
for (int i = 0; i < 100000000; ++i)
a+=1.0;
b *= b;
why in the world would you use a float instead of an int for addition, subtraction, and multiplication, and truncated or floored division, within the 24-bit integer range? it seems like there's no benefit to offset the facts that floating point operations are slower than integer operations and that ints can store integers 7 or 8 bits larger.
and what happens when you go beyond 24 bits? since it's a float no error or warning will be thrown, but now equivalence won't work for numbers that are easily stored by an int.
Why aren't you capitalizing your sentences? Are you too lazy to write properly?
Where did I say I'd use floating point numbers for integer math? Yes, let's move the conversation to a direction it never existed so that you can pretend you were right.
(The place I'd use it would be in a Javascript implementation, or a Lua implementation, and other situations where I'm designing a programming language where I want the simplicity of having only one numerical type. And that would be a 53-bit range, not 24-bit.)
If you mean arithmetic on floating point numbers that only store integers, then no equivalence is not ok, because there are examples where bit equivalence fails. One example is repeatedly adding 1.0 to a float something like 1 trillion times versus multiplying 1000000.0 by 1000000.0
What do you mean by
algorithms that are more reliably written not to contain any empty intervals are two examples.
Obviously I'm referring to integer operations within a 52-bit or 23-bit range, not outside the ability of floating point representations to represent integers!
> What do you mean by
I mean exactly that sort of thing. Algorithms that, for example, divide a line into intervals, where empty intervals are not needed, or desired, and are generally risky with respect to the probability of having a correct implementation. An example of this would be computations of the area of a union of rectangles. You might make a segment tree -- and avoid having degenerate rectangles in your segment tree.