Old calculator with reverb ram

[Gerson W. Barbosa]

(12-03-2017 12:34 PM)jebem Wrote:  

(12-01-2017 06:45 PM)Gerson W. Barbosa Wrote:  By using repeated square root, one could even compute logarithms. For instance, the natural logarithm of 2 can be computed with 6 or 7 correct decimal places on it, I would guess.

Gerson.

Are you referring to the Briggs works that i presume were also used in the HP-35 as the base to calculate logarithms?

Olá, José!

I’m using a small improvement for better accuracy I made to an old algorithm based on repeated square root extraction, as described here:

http://www.hpmuseum.org/forum/thread-5907.html

Here is an estimation of ln(2) on a 12-digit RPN calculator using this method:


2
√ -> 1.41421356237
√ -> 1.18920711500
√ -> 1.09050773266
√ -> 1.04427378242
√ -> 1.02189714865
√ -> 1.01088928605
√ -> 1.00542990111
√ -> 1.00271127505
√ -> 1.00135471989
√ -> 1.00067713069
√ -> 1.00033850805
√ -> 1.00016923970 (*)
2 * -> 2.00033847940
1 - -> 1.00033847940
√ -> 1.00016922538
1 - -> 0.00016922538
4096 x -> 0.693147156480

PS.:

(*) For best accuracy, keep pressing the √ key until you get a result close to 1.0001 (or 0.9999, for arguments less than 1), as in this example. The final multiplication constant will be 2^n, where n is the number of the successive square root operations. In this case n = 12, hence 4096 (2^12).

This might have been useful 50 years ago :-)