A new reverse-engineering writeup shows the Intel 8087's tangent function is not the simple CORDIC algorithm everyone assumed it to be.
The 8087, Intel's first math coprocessor, shipped in 1980 to give x86 machines hardware support for floating-point and trigonometric math they otherwise had to fake in software. A fresh look at the chip's internals, tracing its microcode step by step, finds that its tangent routine layers extra steps on top of CORDIC (Coordinate Rotation Digital Computer), the classic technique for computing trig functions using only shifts and adds. That means the textbook explanation of "the 8087 uses CORDIC" undersells what the chip actually does. The writeup treats CORDIC as a starting point, not the whole answer.
That distinction matters beyond trivia. CORDIC's supposed simplicity is why it still shows up in modern low-power chips and FPGAs whenever engineers need trig functions without a full multiplier. Finding that even one of its most famous implementations quietly added extra machinery is a reminder that how something is taught and how it was actually built often diverge once real hardware constraints show up.
Forty-six years after the 8087 shipped, people are still pulling its microcode apart and finding new wrinkles - a decent argument that legacy chips have more to teach than their spec sheets ever let on.