From what I remember from a lecture I had of a course I'm attending called "introduction to computational science", floating-point numbers are distributed logarithmically. What does it mean? And how can I visualize it?
I've a slide where it is said:
We assume that all binary numbers are normalized. Between powers of 2, the floating point numbers are equidistant.
I think this is related to the logarithmic distribution or spacing of the floating point numbers, but I don't understand exactly what it means.
I've also below the statement taken from the same slide this picture:
Apart from the range between $0$ and $0.25$, it seems that the number or density of floating point numbers is decreasing, if this picture actually represents the distribution of floating-point numbers.
Why is that?
Why there's this exception between $0$ and $0.25$?
This statement is referring to the fact that there are the same number of floating point numbers representable between $1$ and $2$ as between $2^k$ and $2^{k+1}$ for any $k$. This is because the mantissa of $x$ and $2x$ have the same representation as a floating point number, only the exponent of $2$ changes.