Die Analysis of the 8087 Math Coprocessor's Fast Bit Shifter
owl writes:
https://www.righto.com/2020/05/die-analysis-of-8087-math-coprocessors.html
Floating-point numbers are very useful for scientific programming, but early microprocessors only supported integers directly.1 Although floating-point was common in mainframes back in the 1950s and 1960s, it wasn't until 1980 that Intel introduced the 8087 floating-point coprocessor for microcomputers.2 Adding this chip to a microcomputer such as the IBM PC made floating-point operations up to 100 times faster. This was a huge benefit for applications such as AutoCAD, spreadsheets, or flight simulators.3 The downside was the 8087 chip cost hundreds of dollars.4
It's hard to implement floating-point operations so they are computed quickly and accurately. Problems can arise from overflow, rounding, transcendental operations, and numerous edge cases. Prior to the 8087, each manufacturer had their own incompatible ad hoc implementation of floating point. Intel, however, enlisted numerical analysis expert William Kahan to design accurate floating point based on rigorous principles.5 The result was the floating-point architecture of the 8087. This became the IEEE 754 standard used in almost all modern computers, so I consider the 8087 one of the most influential chips ever designed.
To explore how the 8087 works, I opened up an 8087 chip and took photos of the silicon die with a microscope. Containing 40,000 transistors, the 8087 pushed chip manufacturing to the limit; in comparison, the companion 8086 microprocessor only had 29,000 transistors. To make the chip possible, Intel developed new techniques. In this article, I focus on the high-speed binary shifter. The shifter takes up a large fraction of the chip's area, so minimizing its area was vital to making the 8087 possible.
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