Comment by GuB-42
4 years ago
I think the binary representation is the essence of floating point numbers, and if you go beyond the "sometimes, the result is slightly wrong" stage, you have to understand it.
And so far the explanation in the article is the best I found, not least because subnormal numbers appear naturally.
There is a mathematical foundation behind it of course, but it is not easy for a programmer like me. I think it is better to think in term of bits and the integers they make, because that's what the computer sees. And going this way, you get NaN-boxing and serialization as a bonus.
Now, I tend to be most comfortable with a "machine first", bottom-up, low level approach to problems. Mathematical and architectural concepts are fine and all, but unless I have some idea about how it looks like in memory and the kind of instructions being run, I tend to feel lost. Some people may be more comfortable with high level reasoning, we don't all have the same approach, that's what I call real diversity and it is a good thing.
Sorry, I didn't mean to downplay the value of using concrete examples. I absolutely agree that everyone learns better from concrete settings, which is why my original comment fixed the parameters for people to play with. I was referring more to the discussions of how exponents are stored biased, the leading bit in the mantissa is implied = 1 (except for subnormals), and so on. All these are distracting features that can (and should) be covered once the reader has a strong intuition of the more fundamental aspects.