Not sure if wolfram alpha may be able to help you or not, but you can give
it a command like the below and it will give you back an approximation
fit {0.0,0.1},{0.1,0.5},{0.2,0.3}example: http://www.wolframalpha.com/input/?i=fit+%7B0.0%2C0.1%7D%2C%7B0.1%2C0.5%7D%2C%7B0.2%2C0.3%7D On Tue, Sep 2, 2014 at 1:28 PM, Ethan Duni <ethan.d...@gmail.com> wrote: > Well, your standard options for computing 2 to a fractional power are > either polynomial approximation or table look-up. If I'm reading it > correctly, the approach you quoted there is a second-order polynomial > approximation. You can gain accuracy at the cost of complexity by dialing > up the polynomial order. > > Alternatively you can use a table look-up, along with some interpolation. > That will take more memory, but hopefully fewer operations per output. How > favorable either approach is will depend on your target architecture and > your resource constraints. > > Another option is to use a successive approximation type approach, like > Newton's root-finding method. That can get a little hairier than the above > approaches, since it can (in general) require a variable number of > iterations to converge for different inputs. Although that can be > advantageous in certain situations, for example if you don't care about the > peak complexity but simply want to bring down the average complexity > subject to a given required accuracy. > > E > > > On Tue, Sep 2, 2014 at 1:10 PM, Paul Stoffregen <p...@pjrc.com> wrote: > > > I'm hoping to find a fast approximation for exp2(), which I can implement > > in 32 bit fixed point. So far, the best I've turned up by searching is > > this from the archives. > > > > http://www.musicdsp.org/showone.php?id=106 > > > > n = input + 1.0; > > n = n * n; > > n = n * 2.0 / 3.0; > > n = n + 4.0 / 3.0; > > n = n / 2.0; > > > > Some quick tests show the error gets to about 0.34% (not including small > > errors I'll add with 32 bit fixed point representation) when the input > > around 0.72. > > > > Does anyone know of any other approximations? I'm hoping for error under > > 0.1%, if that's even possible with a simple/fast algorithm? > > > > -- > > dupswapdrop -- the music-dsp mailing list and website: > > subscription info, FAQ, source code archive, list archive, book reviews, > > dsp links > > http://music.columbia.edu/cmc/music-dsp > > http://music.columbia.edu/mailman/listinfo/music-dsp > > > -- > dupswapdrop -- the music-dsp mailing list and website: > subscription info, FAQ, source code archive, list archive, book reviews, > dsp links > http://music.columbia.edu/cmc/music-dsp > http://music.columbia.edu/mailman/listinfo/music-dsp > -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
