(12C) Signum Function

[Albert Chan]

(03-03-2019 08:17 AM)Thomas Klemm Wrote:  But what happens with a number that uses all the 10 digits like 12.78974364?
When we square this number we get 163.5775424 which is rounded to 10 digits ...
Taking the square root of the rounded value 163.5775424, why can we be sure that we get the original number?

If a number x had an uncertainty factor 1+ε, (x·(1+ε))² = x²·(1+2ε+ε²) ≈ x²·(1+2ε)

So, for squaring, uncertainly doubled (with at most ±½ ulp error).
Square root is just a reverse operation, uncertainly cut in half.
We would expect squaring, then square root, round-trip back to original number.