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Table of Contents

• ↓ Details of the 8087
• ↓ The 8087's microcode
• ↓ The FSCALE microcode
• ↓ Handling empty or special arguments
• ↓ Handling a non-normal result
• ↓ Helper subroutine: creating a denormal
• ↓ Top Alternatives to righto.com

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"Computer history, restoring vintage computers, IC reverse engineering, and whatever"

"In the 1970s, floating-point arithmetic was a mess. Computer manufacturers had a dozen incompatible arithmetic standards. Moreover, floating-point systems were designed around hardware simplicity rather than mathematical rigor, leading to problems with numerical stability. This changed when Intel introduced the 8087 floating-point coprocessor chip in 1980, designed to be as accurate as possible, even in the corner cases. The 8087 became popular because it could be installed in the IBM PC, making floating-point operations up to 100 times faster in applications ranging from spreadsheets to CAD. But more importantly, the 8087 became the floating-point standard used by most computers today."

"The 8087 implemented its instructions in complex low-level code called microcode. I'm part of a group, the Opcode Collective, that is reverse-engineering this microcode, and I've recently made some progress. In this post, I examine the microcode for one of the 8087's instructions—FSCALE—and describe how this microcode works. The FSCALE (Floating-point Scale) instruction provides a quick way to scale a number by a power of two, much faster than a multiplication. I figured that FSCALE was a simple, almost trivial instruction that would be straightforward to understand and explain. Spoiler: it is not simple. FSCALE uses over 140 micro-instructions and three levels of subroutine calls to handle many special cases. But the FSCALE microcode illustrates many interesting parts of the 8087, such as the shifter, the adder, and the exponent converter, and also reveals a hidden feature of the 8087, so hopefully you will find it interesting."

"To explore the microcode, I opened up an 8087 chip and created a high-resolution image with a microscope. The large microcode ROM is in the center, holding the 1648 micro-instructions that control the chip. The microcode engine on the left steps through the microcode, handling jumps and subroutine calls. The bottom half of the chip is the "datapath", the circuitry that performs floating-point calculations; it is split into a 16-bit datapath for the number's exponent and a 64-bit datapath for the number's significand (also known as the fractional part)."

Key Topics & Focus Areas for righto.com:

Details of the 8087

The 8087's microcode

The FSCALE microcode

Handling empty or special arguments

Handling a non-normal result

Helper subroutine: creating a denormal