Where can I find an original reference for this integer square root algorithm
The wikipedia article on Methods of computing square roots: base 2 presents a strikingly similar snippet of C-code [a], but the link to the source is dead. Let's try to do better.

The snippets from both wikipedia and the question are very similar to Martin Guy's widely circulated C implementation [b]. which contains a comment: From a book on programming abaci by Mr C. Woo. Search engine use suggests this is [1] - one edition seems to be from 1930; it has been reprinted, e.g. [2].  

The age of the method is bound to be on the order of two millenniums - the original reference might be difficult to obtain.

A purportedly[z] very similar Algorithm has been presented by TIJ Rolfe, who in turn refers to [3].




Woo, C.C. The Fundamental Operations in Bead Arithmetic. How to Use the Chinese Abacus, China Lace Co., Ltd., Hong Kong
Kwa Tak Ming, C. C. Woo, The Fundamental Operations in Bead Arithmetic. How to Use the Chinese Abacus, Literary Licensing, LLC, United States, 2012, 9781258466855
Hart, W.L. "College Algebra" 4th ed., Boston, 1955, p.424