The arc tan flaw in early HP35 ROM is elucidated


Hi everybody,

“And now I see with eye serene, the very pulse of the Machine".
William Wordsworth

The arc tan flaw in early HP35 ROM is elucidated on my page:

Best regards,



Hello, Jacques;

and congratulations. This is a remarkable mind job, indeed. I did not read it completely, just got to the middle of it, and then I scrolled to the end jut to have a look at the tables and graphics. I could not help congratulating you then.

Although I do not have an HP35, this work of yours is very elucidating, indeed.


Luiz (Brazil)


Thank you Luiz,

Reading your words “remarkable mind job”, I think to the man who debugged this code, under maximum pressure, in 1972.

Think that the code is crammed in 768 words: no room left in these 3 ROMS. Only one “no operation” at fixed address 00045 in ROM 0 (there is no key code “45”) ; you can’t move it, you can’t use it.

It was a kind of constant-sum game. For 2 instructions added somewhere (and that was the case with the exp(ln((2.02))) problem), 2 other instructions had to be removed, and in the same ROM!

You wrote you do not own an HP 35 ; in fact the algorithms evolved of course (Classic, Woodstock, Spice …), mainly on the precision issue. But the approach in the transcendental functions remained the same. Here, the name of Dave Cochran must be cited. He is the man who implemented Cordic in the 9100 and 35 calculators, based on the J.E. Meggitt’s paper, and made it possible.


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