Rockbox mail archive
Subject: Re: math function for calculator
From: BlueChip (cs_bluechip_at_webtribe.net)
Date: 20040503
>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!
Thank you, and you are most welcome :)
>Can you tell me the name of the algorithm?
Sorry, I have no idea if it has a name  I based it on an estimation theory
I found when trying to calcualte PI for use in a random number generator a
few years ago.
>And do you know the algorithms for other functions like sin,cos,
>especially log?
Sin & cos can be done in code with the "cordic" algorithm  I'm sure google
will aid you with some source code  as this is what is in most calculators
 if not give me a shout and I will dig some out for you  it is FAR too
horrific to try and describe here, and the method I could describe here
is really too chunky and timeconsuming for use in this scenario  check
out cordic, it's really quite nice :)
If I ever find out why I should care what a log is, you will be the first
to know  LOL
I'm sure you should be able to use it to work out how many bits are
required to store a specified number  but I've never worked out how to
actually do it
/me bows his head in shame
Anyway, the point is, sorry, no I have never understood logs let alone
worked on theories for them :(
pihCeulB
>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
>
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Page was last modified "Jan 10 2012" The Rockbox Crew
