Floating-Point Addition and Subtraction on Intel’s 8087

Although you can do basic floating point format operations like addition and subtraction just fine on any CPU, having specialized hardware for it can provide a significant speed boost. Floating-Point Addition and Subtraction on Intel’s 8087. Here Intel’s 8087 was the first mainstream floating-point coprocessor to provide this option to a wide audience, with [Ken Shirriff] recently reverse-engineering using an 8087 die how these basic operations were implemented.

The real-world speed-up of even simple operations like adding two floating point numbers compared to the 8086 CPU was on the order of a hundred times, which is very relevant the moment you start doing interesting things with spreadsheets, not to mention rendering 3D scenes in CAD software or even games. As always, the devil is in the details, with sneaky infinities and edge cases also providing the biggest potential for speed-ups in dedicated silicon, along with the large circuitry spent on the shifter. With floating point values being very much about aligning values with shifting by several bits, this circuitry along with the detecting of over- and underflows is the key element why the 8087 and its successors were so crucial in making floating-point operations at all feasible in PC applications.

How this shifting works in theory is detailed in the article by [Ken], along with how the 8087 implements this in its circuits. Naturally, a large part of this is implemented in microcode, the listing for which is also provided. From this it’s quite clear how what seems like a simple set of operations is actually quite complex, making even the now much maligned x87 ISA an improvement over doing it all in integer-based software.