Reverse-Engineering Intel 8087 FSCALE Microcode Reveals Complexity and Hidden Features

The 8087 Floating-Point Coprocessor

Introduced in 1980, Intel's 8087 floating-point coprocessor standardized floating-point arithmetic, addressing the previous lack of compatibility and numerical stability issues across computer manufacturers. It significantly accelerated floating-point operations in applications like spreadsheets and CAD, becoming a foundational standard for subsequent floating-point systems.

Reverse-Engineering the FSCALE Instruction

A group known as the Opcode Collective is engaged in reverse-engineering the 8087's microcode. Recent progress includes a detailed examination of the FSCALE (Floating-point Scale) instruction. This instruction scales a number by a power of two, offering a faster alternative to multiplication.

Unexpected Complexity in FSCALE

Despite appearing simple, the FSCALE instruction's microcode is complex, utilizing over 140 micro-instructions and three levels of subroutine calls. This complexity is necessary to manage numerous special cases during scaling operations. The analysis of FSCALE's microcode provides insights into the 8087's internal architecture, including its shifter, adder, and exponent converter.

Methodology and Discoveries

The reverse-engineering process involved creating a high-resolution image of an 8087 chip using a microscope. This allowed for the examination of the microcode ROM, which contains 1648 micro-instructions, the microcode engine, and the datapath circuitry. The detailed study of the FSCALE microcode also led to the discovery of a previously hidden feature within the 8087 chip.