CORDIC: rotate a vector with shifts and adds

Set an angle and a number of steps and watch the vector turn by ever smaller angles, each one only a shift and an add, until it lands on cos and sin.

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Where the numbers come from

gHashTag/t27 specs/fpga/dsp/cordic.t27 (t27#8985): every value on the page is its fn bodies, compiled to wasm (logic.js)
J. E. Volder, The CORDIC trigonometric computing technique, IRE Trans. Electronic Computers EC-8(3), 1959
J. S. Walther, A unified algorithm for elementary functions, AFIPS Spring Joint Computer Conference, 1971
K(n) tends to 0.6072529350088812 (ST DT0087, the CORDIC design tip); the spec recomputes it