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Re^3: Determining the minimum representable increment/decrement possible?

by ExReg (Priest)
on Jun 15, 2016 at 18:52 UTC ( #1165777=note: print w/replies, xml ) Need Help??


in reply to Re^2: Determining the minimum representable increment/decrement possible?
in thread Determining the minimum representable increment/decrement possible?

Excuse me while I clear out my cranial flatus. I was not forcing the maximum precision. I was using the default. If I add the printf "%25.32" as dvido had I would have gotten slightly different results:

0100001110111101100010001110100001001000001011011111000110101110 - 1.9 +041105342991886e+258 1100001110111101100010001110100001001000001011011111000110101110 - 1.9 +041105342991888e+258

It would appear that in this case, 1.9041105342991887e+258 is not possible to store. Using all 53 bits of mantissa, I still get about 15.95 digits instead of the 14. Each case will be different and require converting to binary, twiddling the bits, and seeing what you get.

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Re^4: Determining the minimum representable increment/decrement possible?
by davido (Cardinal) on Jun 15, 2016 at 19:36 UTC

    It would appear that in this case, 1.9041105342991887e+258 is not possible to store.

    That is because 1.9041105342991887e+258 does not fit into m/2^n, and therefore cannot be represented precisely in base 2. You would need a couple more bits to push the rounding error further out, but that's just kicking the can down the road.

    In other words, the binary representation of this floating point value results in a non-terminating sequence, much as 1/3rd results in a non-terminating sequence in base 10.


    Dave

      Very true. But since perl is using double precision on my machine, you will never get that number. You would need quad precision to represent 1.9041105342991887e+258.

        Ignore this. I'm seeing things.


        With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority". I knew I was on the right track :)
        In the absence of evidence, opinion is indistinguishable from prejudice. Not understood.

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