The 1950s algorithm that still powers modern navigation and handheld scientific calculators
In short: Before modern processors had dedicated hardware for complex math, engineers needed a way to calculate trigonometry and logarithms without expensive multipliers. The solution was CORDIC, a clever digit-by-digit algorithm that replaces heavy multiplication with simple additions and bit shifts, proving that sometimes the most efficient path is the most indirect.
Conceived in 1956 by Jack E. Volder at Convair, CORDIC (Coordinate Rotation Digital Computer) was designed to replace bulky analog resolvers in the B-58 bomber's navigation computer. By using a sequence of scaled rotations, the algorithm could compute trigonometric functions, square roots, and logarithms using only addition, subtraction, and bit shifting. This made it ideal for early digital systems that lacked hardware multipliers, such as the MOS 6502 or Zilog Z80 processors.
The mechanism relies on precomputed angles and scale factors. In rotation mode, the algorithm iteratively rotates a vector until it matches a target angle; in vectoring mode, it rotates the vector until its y-coordinate reaches zero. Because each rotation step involves a tangent value equal to a power of two, the multiplication can be replaced by a simple bit shift. This efficiency allowed CORDIC to become a staple in diverse hardware, from the Apollo program's Lunar Roving Vehicle to the iconic HP-35 handheld calculator in 1972.
While modern general-purpose CPUs now include robust floating-point units that make software-based CORDIC largely unnecessary, the algorithm remains highly relevant in specialized fields. It is a standard component in FPGA development and is used in microcontrollers like the STM32G4 series to accelerate mixed-signal tasks, such as motor control and human-machine interfaces. Because it requires a low gate count compared to power series approximations, CORDIC remains a preferred choice for time-constrained, safety-critical, and low-power applications where minimizing hardware complexity is paramount.
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Sources
- Summary by Intellect · source: CORDIC
- Also: Wikidata — CORDIC · CC0
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