One time, not long ago, I was looking through the floating point library, specifically FEXP (standard precision EXP) for the IBM 1130 and I think I noticed where they were doing range reduction to some oddball limits. I wonder if they were using the CORDIC algorithms? This code would have been written earlier than '65. The date seems reasonable for CORDIC and too early for BKM.
I see the CORDIC algorithms were first developed at the aeronautics division of Convair which just so happens to be a place where my entire family worked at one time or another between '51 and '69. We had nothing to do with them...
Not impossible but I would say doubtful. Your mention of range reduction struck a memory.
Volder's CORDIC IEEE paper which generalizes cordic to other elementary functions dates to around 1967 if I recall correctly. In the seventies I was a teenager and had my first TI scientific calculator given to me. It was the thing that prompted me to teach my self how to code and find out how these things worked. So off to my local university 26 miles away and I scavenged the libraries and computer rooms for answers. The uni had at that time 360 and 370 mainframes which were eventually replaced some years with Amdahl improvements. In the general access computer labs were the manuals of most use to students, held in those bolt thru trays so you couldn't steal them! But none contained any documentation on how the scientific library routines were implemented. For that I had to sneak into the special book room in the building that housed the university systems programmers. It was like finding that mega stash of playboys your dirty uncle hid in his tool shed.
Knowing I had limited time for this mission impossible before being discovered I flipped through all the manuals as fast as I could. By some luck I found the Fortran code very quickly. It was nothing like what I expected. Convoluted and arcane with many if branches on input range. The trig functions had some obvious reductions to quarter angle or finer but then the code lost me. In all cases the final calculation was a unique (to that branch) rational polynomial. I had the sense that some masterful math PHD (of which IBM had many) had handcrafted and tuned the whole thing. I was evicted from the building before I could spend quality time studying the code so my memory is limited and fading.
Now you can say the 360 family does not equal 1130, fair enough. The general design choice at the time and still today was if you had four banger floating point hardware you used either rational polynomials or chebyshev polynomial approximations
not Taylor series!. I don't know how many times over the years I have had to educate engineers you don't use Taylor series for anything. And if you only had an integer CPU then CORDIC. I was under the impression the 1130 did have some form of floating point assist and it certainly had a fortran implementation which makes the 360 style fortran library more likely in my mind. Besides CORDIC is not how those egg heads at IBM would roll.
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