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Why is it that when I put this equation in matlab it equals 0 but when I do (2^52+1) -2^52 it gives me 1, aren't they the same equation. I think I kind of understand how 64bit float can't represent odd numbers past 2^53-1 but these numbers are not even close to that

cantcode22
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    Using python's decimal module you can see that `sqrt(2^52 +1)` has a decimal expansion that begins `67108864.00000000745`. There isn't enough precision in a 52-bit mantissa to hold that. The decimal part is lopped off entirely. – John Coleman Nov 08 '21 at 21:46
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    so does that mean the computer is able to hold the value 2^52+1 exactly but isnt able to hold sqrt(2^52+1) exactly? – cantcode22 Nov 08 '21 at 22:32

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There are 2^52 double precision numbers between 2^52 and 2^53-1 which the sqrt function maps to (approximately) the interval [2^26, sqrt(2)*2^26]. The latter contains just 2^52/sqrt(2) numbers, which means a lot of numbers x must map to the same sqrt(x).

chtz
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