New Square-Root Chip Math Cuts Energy Use 77% for Phones

Square roots aren't just a math class memory. Computers use them constantly when you snap a photo, apply a filter, compress a video, or run an AI model on your phone. But the exact circuits that calculate them are heavy — they eat up battery and take up precious space inside a chip. This new research from Prateek Goyal and Sujit Kumar Sahoo introduces a simpler way to do those calculations using only basic arithmetic and shifts. Their design, called EOSQR, estimates square roots in small segments instead of computing the full precise value.

The savings are striking. Compared with an exact "restoring array" square-root circuit, EOSQR needs about 62% fewer chip resources, uses 77% less power, and gets results in less than half the time. And compared with other approximate square-root designs meant to be highly accurate, EOSQR made the fewest errors. So you lose only a tiny bit of precision, but you gain a lot of speed and efficiency. The researchers tested it on a standard chip called an FPGA—basically a programmable test microchip—to confirm the real-world numbers.

They also checked whether these small math errors actually hurt when doing meaningful jobs. The answer: no. EOSQR powered Sobel edge detection (finding boundaries in photos), K-means color quantization (reducing an image's color count), and K-nearest-neighbour classification (a common AI task). In all three, the output stayed visually clean and classification remained accurate. That means cameras, drones, or wearable devices could do real-time image processing without exhausting their batteries or needing heavy hardware.

The catch is that "approximate" means the answer won't always match a perfect square-root calculation. For editing selfies or tagging objects in a video, you'll never notice. But if you're designing a bridge or guiding a spacecraft where tiny errors multiply, you still want exact math. This work is part of a broader push to make computing deliberately "good enough" while being dramatically cheaper, smaller, and faster—a trade-off that could power the next generation of always-on AI devices.