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The stack circuitry of the Intel 8087 floating point chip, reverse-engineered
14 hours ago
- The Intel 8087 floating-point coprocessor, introduced in 1980, performed floating-point operations up to 100 times faster than early microprocessors, benefiting applications like AutoCAD and spreadsheets.
- The 8087 was a complex chip with 40,000 to 75,000 transistors, featuring a datapath, constant ROM, microcode ROM, and stack-based architecture with eight 80-bit registers and tag bits.
- Its stack design used a top-of-stack pointer and offset-addressing, but suffered from stack overflow issues and was difficult for compilers, requiring extensive workarounds like saving the full stack to memory.
- Despite drawbacks, the 8087 was a commercial success, establishing Intel Israel and influencing the IEEE 754 floating-point standard; its stack approach was later replaced by SSE and AVX in modern processors.
Conditions in the Intel 8087 floating-point chip's microcode
14 hours ago
- The Intel 8087 coprocessor accelerated floating-point calculations up to 100 times on IBM PCs using microcoded algorithms.
- The chip's microcode ROM contains 1648 micro-instructions that control internal operations like data movement and arithmetic.
- The microcode engine supports conditional jumps, subroutine calls, and returns based on 49 different conditions.
- Conditions are selected via distributed multiplexers that reduce wiring by processing signals near their source on the die.
- Condition types include opcode tests, register tags (empty, zero, normal, special), sign comparisons, rounding mode exceptions, and more.
- Detailed hardware analysis, including die photos and multiplexer layouts, was used to reverse-engineer the microcode.
- The FABS and FCHS instructions share a microcode routine that uses a condition on the opcode's bottom bit to differentiate behavior.
- Some conditions are specialized, such as detecting stack overflow/underflow or denormalized numbers for exception handling.
The adder at the heart of Intel's 8087 floating-point chip
14 hours ago
- Intel released the 8087 floating-point coprocessor in 1980, featuring a 69-bit adder that accelerated math operations up to 100 times, including transcendental functions.
- The adder uses a Manchester carry chain combined with a carry-skip technique to speed up addition by breaking it into 4-bit blocks.
- Key concepts include Generate, Propagate, and Delete signals that allow parallel computation of carry values, with NMOS pass transistors and precharging for performance.
- The adder takes 69-bit inputs (including rounding bits) and produces a 70-bit output, requiring two clock cycles per addition due to block count.
- Surrounding circuitry like the Skip Shifter and Sum Shifter enables efficient multiplication, division, and square root operations in hardware.
- The adder's design balances complexity and performance, being simpler than later adders like the Kogge-Stone, but crucial for the 8087's arithmetic capabilities.

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intel 8087

The stack circuitry of the Intel 8087 floating point chip, reverse-engineered

Conditions in the Intel 8087 floating-point chip's microcode

The adder at the heart of Intel's 8087 floating-point chip