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Rockbox mail archiveSubject: Re: math function for calculatorRe: math function for calculator
From: Didier Simoneau <didier.simoneau_at_tni-valiosys.com>
Date: Mon, 3 May 2004 16:23:41 +0200 The algorithme is the application of the Newton method to the equation: x^2 = V If V is n digits long, sqrt(V) is approximatly n/2 digits long. So a good initial guess can be obtained by stripping the last n/2 digits of V. Didier Rockbox enthusiast ----- Original Message ----- From: <tinousus_at_yahoo.com> To: "rockbox" <rockbox_at_cool.haxx.se> Sent: Monday, May 03, 2004 12:06 PM Subject: Re: math function for calculator | Woo, really thanks. I use your algorithm and it works like a charm. | | Your algorithm is very efficient especially for my program. | I am using scientific number format, the number needed to | find root is always between 0 and 10. I take the midpoint of | operand and 1 as the initial guess. Most of time, it takes less | than 10 repeat. Average is about 5 times! Math is beautiful! | | Can you tell me the name of the algorithm? | | And do you know the algorithms for other functions like sin,cos, | especially log? | | Isaac | | ------------------ Original Message ------------------ | | >Try this: | > | > | >V/G = N ... (G+N)/2 = G | >repeat until G=N | > | > | >V = Value (for which we are seeking the root) | >G = most recent Guess | >N = New guess | > | > | >Example for root of V=12 with an arbitrary intial guess of 2 | > | > | >find _/12 ... guess 2.000 | >12/2.000 = 6.000 ... (2.000+6.000)/2 = 4.000 | >12/4.000 = 3.000 ... (4.000+3.000)/2 = 3.500 | >12/3.500 = 3.429 ... (3.500+3.429)/2 = 3.465 | >12/3.465 = 3.463 ... (3.465+3.463)/2 = 3.464 | >12/3.464 = 3.464 | > | > | >3.464^2 = 11.999 | > | > | >_/12 is irrational, so to get 12 back out of the other end you will need an | >infinite number of digits after the decimal place, hence the result above | >being 11.999, that is because I decided to offer a result to only 3 decimal | >places. | > | > | >Obviously faster methods can be found, but generally you will need to rely | >on the existence of other mathematical functions (such as log-n) or big | >memory-hungry lookup tables - Although for this application where our app | >is 32K end-of-story, a lookup table of 1..2K would not be harmful. | > | > | >One use of a lookup table might be to get a good initial guess... | >With a table of all known integer squares: | > | > | >_/105 lies somewhere between _/100 (=10) and _/121 (=11) | >121 - 100 = 21 | >21 / (105-100) = 4.200 | >(1) / 4.200 = .238 | > | > | >So an initial guess of 10.238 would be reasonable | >The answer is actually 10.247 | > | > | >If you need clarification on any of that, please ask. | > | > | >ChipBleu | | _______________________________________________ | http://cool.haxx.se/mailman/listinfo/rockbox _______________________________________________ http://cool.haxx.se/mailman/listinfo/rockbox Received on 2004-05-03 Page template was last modified "Tue Sep 7 00:00:02 2021" The Rockbox Crew -- Privacy Policy |