  The paper presents (human-oriented) specification and (pen-and-paper)
verification of the square root function. The function implements Newton method
and uses a look-up table for initial approximations. Specification is done in
terms of total correctness assertions with use of precise arithmetic and the
mathematical square root $\sqrt{\dots}$, algorithms are presented in
pseudo-code with explicit distinction between precise and machine arithmetic,
verification is done in Floyd-Hoare style and adjustment (matching) of runs of
algorithms with precise arithmetic and with machine arithmetic. The primary
purpose of the paper is to make explicit properties of the machine arithmetic
that are sufficient to make verification presented in the paper. Computer-aided
implementation and validation of the proofs (using some proof-assistant) is the
topic for further studies.
