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
