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Intel introduced the 8087 floating-point chip in 1980 to make math faster. The chip does tangents, square roots, and so forth, but fundamentally everything is computed through additions and subtractions, performed by an adder at the heart of the chip. Let's look at the adder's circuitry... 1/N

The 8087 patent goes into a fair bit of detail on the algorithms. Square root is essentially the same as long square root by hand, except in binary. It's like long division but you keep appending blocks of two bits. patents.google.com/patent/USRE3...

patents.google.comUSRE33629E - Numeric data processor - Google PatentsA floating point, integrated, arithmetic circuit is organized around a file format having a floating point numeric domain exceeding that of any single or double precision floating point numbers, long ...

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