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Table of Contents

• ↓ Floating-point addition and subtraction
• ↓ Relevant hardware details of the 8087
• ↓ The addition/subtraction microcode
• ↓ The leading zeros circuitry
• ↓ Conclusions
• ↓ Notes and references
• ↓ Top Alternatives to arcfn.com

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

"In 1980, Intel introduced the 8087, a chip that made floating-point operations much faster in the IBM PC and other systems. Although the 8087 supports advanced operations such as tangents, square roots, and logarithms, this article focuses on basic arithmetic operations: addition and subtraction. The 8087 provided a spectacular speed improvement over the 8086 processor, speeding up addition by a factor of almost 100, and complicated operations by even more.1 In this article, I examine the 8087's microcode and circuitry to explain exactly how floating-point addition and subtraction are implemented, including numerous special cases for infinities and other special values."

"To explore the 8087's circuitry, I popped the lid off a chip with a chisel and used a microscope to create the high-resolution image below. The microcode ROM is the large rectangular region in the center of the die, holding the 1648 micro-instructions that control the chip. The bottom half of the chip (red box) is the datapath, the circuitry that performs floating-point calculations on 80-bit values.2"

"Zooming in on the datapath shows the functional blocks that are important for addition and subtraction. The key component is the integer adder, located in the center. It receives one argument from the B register and another argument from a component such as the temporary registers or the stack registers. The adder's output is stored in the sum register. The shifter can shift the bits in a value to the left or the right. The shifter occupies a lot of space on the die because its circuitry allows a value to be rapidly shifted by an arbitrary number of bits. Floating-point operations make heavy use of the shifter to align values; the leading zero circuitry counts the number of zero bits or bytes on the left of a value so they can be shifted away. The exponent converter processes exponents, detecting overflows and underflows. These specialized circuits helped the 8087 achieve its high performance."

Key Topics & Focus Areas for arcfn.com:

Floating-point addition and subtraction

Relevant hardware details of the 8087

The addition/subtraction microcode

The leading zeros circuitry

Conclusions

Notes and references