IEEE-754 floating-point precision: How much error is allowed?

The IEEE-754 standard requires that so called "basic operations" (which include addition, multiplication, division and square root) are correctly rounded . This means that there is a unique allowed answer, and it is the closest representable floating-point number to the so-called "infinitely precise" result of the operation.

In binary, the first 58 bits of the arbitrary precision answer is 1011111111111111111111110101010101111111111111111011010001...

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