Old calculator with reverb ram

12032017, 01:54 PM
(This post was last modified: 12042017 01:19 AM by Gerson W. Barbosa.)
Post: #12




RE: Old calculator with reverb ram
(12032017 12:34 PM)jebem Wrote:(12012017 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. 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/thread5907.html Here is an estimation of ln(2) on a 12digit 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 :) 

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