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I know that IEEE754 double floats (64-bit floating number) is known to provide 52 bits of precision (or 53 bits including implicit 1). But I do not know the exact meaning of the precision.

Suppose we want to approximate a rational number $v$ using 64-bit floats, denoting the approximate version by $v'$. Clearly there exists an error $ e = |v-v'|$. Does the precision mean that $e$ is bounded by some number, like $ e < 2^{-53}$?

How many discrete points can be expressive in $[-1/2, 1/2)$ with IEEE 754 double floats?

user9414424
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  • Your title and your question are only loosely related. In the title you would have to explore the bias, reserved exponents and denormal numbers. For the question in the text one only would have to correct that $2^{-53}$ is the relative error for normal floating point numbers. A better related question would be for the number of floating point numbers in $[1/4,1/2)$. – Lutz Lehmann Nov 29 '19 at 13:22
  • Thank you for your comment. In fact, I'm not interested in the range suggested. – user9414424 Nov 29 '19 at 13:31
  • Does the Wikipedia article Double-precision floating-point format contain the information you wanted? – Somos Nov 29 '19 at 15:57

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