Home | Notifications | New Note | Local | Federated | Search | Logout
Note Detail
Reply to @kenshirriff@oldbytes.space
Ken Shirriff@kenshirriff@oldbytes.space (2026-09-27 02:05:06)
The 8087 chip implements its algorithms in microcode, specialized low-level code inside the chip. By examining the microcode ROM under a microscope, the Opcode Collective extracted the bits and I reverse-engineered the algorithm.
---Attachments---
image: https://assets.oldbytes.space/assets.oldbytes.space/media_attachments/files/117/338/425/014/611/055/original/5ce63607afd9ba14.png
image: https://assets.oldbytes.space/assets.oldbytes.space/media_attachments/files/117/338/426/271/805/716/original/59e1d6ad620678a6.png
---Reply---
Ken Shirriff@kenshirriff@oldbytes.space (2026-09-27 02:05:29)
For details on how the 8087 calculates tangents by using the CORDIC algorithm combined with polynomials, see my latest article:
https://www.righto.com/2026/09/8087-tangent-cordic.html
Reply
---Replies---
Ken Shirriff@kenshirriff@oldbytes.space (2026-09-27 02:07:54)
Credits: I've been working on this with the members of the "Opcode Collective", especially Smartest Blob and @gloriouscow, who used ML to convert ROM images to microcode data and extensively analyzed the contents.
Photo of the CORDIC II computer from "The Birth of CORDIC", by Jack Volder, the creator of CORDIC: https://web.archive.org/web/20160304064804if_/http://late-dpedago.urv.cat/site_media/papers/fulltext_2.pdf