
Rockbox mail archiveSubject: Re: math function for calculatorRe: math function for calculator
From: Didier Simoneau <didier.simoneau_at_tnivaliosys.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 logn) or big  >memoryhungry lookup tables  Although for this application where our app  >is 32K endofstory, 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 / (105100) = 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 20040503 Page template was last modified "Tue Sep 7 00:00:02 2021" The Rockbox Crew  Privacy Policy 