For a given IEEE-754 floating point number X, if
2^E <= abs(X) < 2^(E+1)
then the distance from X to the next largest representable floating point number (epsilon) is:
epsilon = 2^(E-52) % For a 64-bit float (double precision)
epsilon = 2^(E-23) % For a 32-bit float (single precision)
epsilon = 2^(E-10) % For a 16-bit float (half precision)
The above equations allow us to compute the following:
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For half precision…
If you want an accuracy of +/-0.5 (or 2^-1), the maximum size that the number can be is 2^10. Any larger than this and the distance between floating point numbers is greater than 0.5.
If you want an accuracy of +/-0.0005 (about 2^-11), the maximum size that the number can be is 1. Any larger than this and the distance between floating point numbers is greater than 0.0005.
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For single precision…
If you want an accuracy of +/-0.5 (or 2^-1), the maximum size that the number can be is 2^23. Any larger than this and the distance between floating point numbers is greater than 0.5.
If you want an accuracy of +/-0.0005 (about 2^-11), the maximum size that the number can be is 2^13. Any larger than this and the distance between floating point numbers is greater than 0.0005.
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For double precision…
If you want an accuracy of +/-0.5 (or 2^-1), the maximum size that the number can be is 2^52. Any larger than this and the distance between floating point numbers is greater than 0.5.
If you want an accuracy of +/-0.0005 (about 2^-11), the maximum size that the number can be is 2^42. Any larger than this and the distance between floating point numbers is greater than 0.0005.