Intel's Pentium processor (1993) can compute sines, logarithms, and other special functions. To do this, it has a ROM with 304 floating-point constants. I reverse-engineered this ROM and extracted the constants. You can see pi in the ROM, binary 11.001001..., encoded in the transistor pattern. 1/n - ThreadSky

righto.com • 50 days ago

Intel's Pentium processor (1993) can compute sines, logarithms, and other special functions. To do this, it has a ROM with 304 floating-point constants. I reverse-engineered this ROM and extracted the constants. You can see pi in the ROM, binary 11.001001..., encoded in the transistor pattern. 1/n

Comments

joocifer.bsky.social•50 days ago

Still one of the best solutions to tracking down a problem ever, kudos to both your original effort and your willingness to share the details so well.

blenderbuch.bsky.social•49 days ago

So interesting! Thanks 👍

righto.com•50 days ago

The photo shows one of the Pentium's tiny transistors; it has 3.1 million in total. Each transistor acts as a switch between the "source" and "drain", controlled by the "gate".

righto.com•50 days ago

The Pentium's constant ROM consists of a grid of transistors. Each spot in the grid either has a transistor (for a 1 bit) or no transistor (for a 0 bit). The diagram below shows 8 of the 26144 bits in the ROM. The 4 vertical stripes are 4 transistors (0 bits) while the 4 gaps hold 1 bits.

righto.com•50 days ago

This closeup of the Pentium's constant ROM shows the vertical metal wiring that is connected to the silicon. Data exits the ROM through this wiring. The photo shows the bottom layer of metal; the Pentium has two more metal layers that I removed for this photo. 4/n

bugbear6502.bsky.social•50 days ago

Wow - that's a fabulously clear image

righto.com•50 days ago

This image shows the grid structure of the Pentium's constant ROM. Floating-point numbers have an exponent part and a significand part. In the decimal number 6.02×10^23, 23 is the exponent and 6.02 is the significand. The ROM is similar, except in binary. 5/n

righto.com•50 days ago

I wrote a blog post that goes into much more detail, including a look at how the approximation polynomials are optimized. So check it out: https://www.righto.com/2025/01/pentium-floating-point-ROM.html

darkhorse74.bsky.social•47 days ago

Amazing read! I read at your website, referred to by erratarob. Read the pentium FP error post a while ago, happy to see this new one! Great research and writing. Excited to follow you here, not the bad place :-)

righto.com•50 days ago

After all this technical information, you might prefer my thread on a remarkable Navajo weaving of the Pentium. (The constant ROM is in the upper right.)

https://bsky.app/profile/did:plc:svh6dgjnpkdl4dhxahj4xvkv/post/3lbrwysonos2r

frederik.hans.engineer•49 days ago

I remember feeling like a hack for a similar implementation in a class in uni (only for the sin function).😅

retrodes.net•48 days ago

Lookup tables feel like cheating, but they are FAST.

piewpiewpiew.bsky.social•49 days ago

Definitely not a hack. This approach is actually pretty common. One other example is from Direct Digital Synthesizer. Most implementation uses LUT to store sine/cosine values.

zjhitni.bsky.social•49 days ago

wow! great post... thanks!

Comments

Posting Rules

Reply