Tableless Calculation of Circular Functions on Dyadic Rationals

I would like to tell a story. A story about beautiful mathematical relationship that elucidates the computational view on classic subject of trigonometry. All stories need language, and for this particular an algorithmic language ought do well. What makes algorithmic? From our perspective as functional programming community, provides means express computation in terms functions, with no implementation-imposed limitations. We develop new algorithm trigonometric functions dyadic rationals, together used it, Scheme. provide mechanically-derived inverses target functions. address efficiency accuracy concerns pertain implementation proposed either hardware or software.