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   William D. Jones (cr1901@mastodon.social)'s status on Tuesday, 26-Nov-2024 18:56:57 JST William D. Jones

   At some point, I'll learn CORDIC. But part of me doesn't want to because I don't want the magic ruined. Kinda like Rubik's cubes.

   It feels like like a cheat code to calculate complex functions. Like, it shouldn't work at all.

   • Embed this notice
     William D. Jones (cr1901@mastodon.social)'s status on Tuesday, 26-Nov-2024 18:56:57 JST William D. Jones

     in reply to

     • Ken Shirriff

     According to @kenshirriff, the original 8087 uses CORDIC. With all the rounding bullshit that FP arith has to do it surprises me that it's a good fit.

     But I also don't understand it well.

   • Embed this notice
     Rich Felker (dalias@hachyderm.io)'s status on Tuesday, 26-Nov-2024 18:56:57 JST Rich Felker

     in reply to

     • Ken Shirriff

     @cr1901 @kenshirriff CORDIC has no role in arithmetic, only trig functions. The x87 trig insns have always been useless for implementing decent trig functions. Slower & less accurate than the obvious implementations.

   • Embed this notice
     William D. Jones (cr1901@mastodon.social)'s status on Wednesday, 27-Nov-2024 08:55:09 JST William D. Jones

     in reply to

     • Rich Felker
     • Ken Shirriff
     • Steve Canon

     @dalias @kenshirriff Well, @steve deleted his hellsite acct, so context is missing.

     https://x.com/cr1901/status/1601969347899133954

     But according to my FF History, the correct way to do FP trig functions is arg reduce to +/-pi/4:

     https://userpages.cs.umbc.edu/phatak/645/supl/Ng-ArgReduction.pdf

     Then do a polynomial approx. Except I remember Steve saying the polynomial shouldn't be a Taylor series for some reason (slow convergence?).

   • Embed this notice
     Rich Felker (dalias@hachyderm.io)'s status on Wednesday, 27-Nov-2024 08:55:09 JST Rich Felker

     in reply to

     • Ken Shirriff
     • Steve Canon

     @cr1901 @kenshirriff @steve Yes all that is basically correct.

   • Embed this notice
     Rich Felker (dalias@hachyderm.io)'s status on Wednesday, 27-Nov-2024 09:29:40 JST Rich Felker

     in reply to

     • Ken Shirriff
     • Steve Canon

     @steve @cr1901 @kenshirriff What is atan argument reduction? atan isn't periodic.

   • Embed this notice
     Steve Canon (steve@discuss.systems)'s status on Wednesday, 27-Nov-2024 09:29:41 JST Steve Canon

     in reply to

     • Rich Felker
     • Ken Shirriff

     @dalias @cr1901 @kenshirriff what they said. A few steps of CORDIC still useful for atan(2) argument reduction, more if the only fast operation you have is addition. Otherwise use polynomial approximations everywhere.

   • Embed this notice
     Rich Felker (dalias@hachyderm.io)'s status on Wednesday, 27-Nov-2024 09:54:21 JST Rich Felker

     in reply to

     • Ken Shirriff
     • Steve Canon

     @steve @cr1901 @kenshirriff Yes, I didn't immediately realize how that would work for atan but surely there are trig identities or whatnot that should do it, and I guess you apply CORDIC to the inverse functions involved in that.

   • Embed this notice
     Steve Canon (steve@discuss.systems)'s status on Wednesday, 27-Nov-2024 09:54:22 JST Steve Canon

     in reply to

     • Rich Felker
     • Ken Shirriff

     @dalias @cr1901 @kenshirriff expanding a bit more, I would say argument reduction is any process you use to go from evaluating a function on a larger interval to evaluating a related function on a smaller (in the sense of “computationally easier”) interval.

   • Embed this notice
     Steve Canon (steve@discuss.systems)'s status on Wednesday, 27-Nov-2024 09:54:23 JST Steve Canon

     in reply to

     • Rich Felker
     • Ken Shirriff

     @dalias @cr1901 @kenshirriff that doesn’t mean you can’t reduce the argument! log and exp aren’t periodic either (at least, not on the real line), and we do argument reduction for them as well.