CORDIC
An algorithm that computes sine, cosine, arctangent and square roots using nothing but shifts, additions and a small lookup table.
Jack Volder devised it at Convair in 1959 for the navigation computer of the B-58 bomber, which had no room for a hardware multiplier. The trick is to rotate a vector towards the target angle in ever-smaller steps, each angle chosen so that the rotation amounts to dividing by a power of two — a shift. Every iteration yields roughly one bit of precision; sixteen rounds, sixteen bits.
The same idea later ran inside calculators like the HP-35 and Intel's 8087 floating-point coprocessor. Today it survives wherever multipliers are expensive or absent: in FPGAs, in microcontrollers without an FPU, and as a dedicated hardware block in parts such as the STM32G4. Results come out in fixed point, so scaling remains the programmer's problem.