Does anybody know any efficient algorithm to compute the inverse of a number in a fixed point DSP? I have to perform the division and I have about 30 cicles to do it. I thought that a good way is to do a/b = a * inv(b). Right now the inverse is computed by series approximation exploiting the log properties, but I think there are far better ideas, like using somehow a lookup table. Any guess is welcome. Luca

# Division

Started by ●November 17, 2003

Reply by ●November 17, 20032003-11-17

Hello Luca, You can use a seed (determined by you value of b) fed into a Newton-Raphson algorithm for 1/b. Clay "Luca Baradel" <lbaradel@lsil.com> wrote in message news:bpbptk$h9q$1@news.lsil.com...> Does anybody know any efficient algorithm to compute the inverse of anumber> in a fixed point DSP? I have to perform the division and I have about 30 > cicles to do it. > I thought that a good way is to do > > a/b = a * inv(b). > > Right now the inverse is computed by series approximation exploiting thelog> properties, but I think there are far better ideas, like using somehow a > lookup table. > > Any guess is welcome. > > Luca > >

Reply by ●November 17, 20032003-11-17

most DSP manufacturers include application notes on how to do division with their fixed-point DSPs. i know TI does. did you try looking there? there is a clever way to do it, i remember. julius On Mon, 17 Nov 2003, Luca Baradel wrote:> Does anybody know any efficient algorithm to compute the inverse of a number > in a fixed point DSP? I have to perform the division and I have about 30 > cicles to do it. > I thought that a good way is to do > > a/b = a * inv(b). > > Right now the inverse is computed by series approximation exploiting the log > properties, but I think there are far better ideas, like using somehow a > lookup table. > > Any guess is welcome. > > Luca > > >-- The most rigorous proofs will be shown by vigorous handwaving. http://www.mit.edu/~kusuma opinion of author is not necessarily of the institute

Reply by ●November 18, 20032003-11-18

Luca Baradel wrote:> > Does anybody know any efficient algorithm to compute the inverse of a number > in a fixed point DSP?Determine the first guess by the table lookup, then use the Newton's method for solving equation. That is faster then making a straight division. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com

Reply by ●November 18, 20032003-11-18

Luca Baradel wrote:> Does anybody know any efficient algorithm to compute the inverse > of a number in a fixed point DSP? I have to perform the division > and I have about 30 cicles to do it. > I thought that a good way is to do > > a/b = a * inv(b). > > Right now the inverse is computed by series approximation > exploiting the log properties, but I think there are far better > ideas, like using somehow a lookup table. > > Any guess is welcome. > > LucaDon't forget to check these two: 1. if b is constant, do the inv(b) manually / at compile time. 2. check if your DSP has a function for the first guess. there might be a sort of 8bit approximation for 1/x or so. Bernhard

Reply by ●November 20, 20032003-11-20

Luca Baradel wrote:> Does anybody know any efficient algorithm to compute the inverse of a number > in a fixed point DSP? I have to perform the division and I have about 30 > cicles to do it. > I thought that a good way is to do > > a/b = a * inv(b). > > Right now the inverse is computed by series approximation exploiting the log > properties, but I think there are far better ideas, like using somehow a > lookup table. > > Any guess is welcome. > > LucaYou do know that the direct method would only take 1 cycle per bit if this is, e.g., a TI TMS 5xxx DSP, right? (See the SUBC instruction.) 30 cycles is a goodly amount of bits. -- % Randy Yates % "...the answer lies within your soul %% Fuquay-Varina, NC % 'cause no one knows which side %%% 919-577-9882 % the coin will fall." %%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO http://home.earthlink.net/~yatescr

Reply by ●November 21, 20032003-11-21

Randy Yates <yates@ieee.org> wrote in message news:<IqYub.11311$Wy4.5784@newsread2.news.atl.earthlink.net>...> Luca Baradel wrote: > > > Does anybody know any efficient algorithm to compute the inverse of a number > > in a fixed point DSP? I have to perform the division and I have about 30 > > cicles to do it. > > I thought that a good way is to do > > > > a/b = a * inv(b). > > > > Right now the inverse is computed by series approximation exploiting the log > > properties, but I think there are far better ideas, like using somehow a > > lookup table. > > > > Any guess is welcome. > > > > Luca > > You do know that the direct method would only take 1 cycle per bit if > this is, e.g., a TI TMS 5xxx DSP, right? (See the SUBC instruction.) > 30 cycles is a goodly amount of bits.Whether you can achieve the desired precision for your quotient in 30 cycles depends on how many bits of precision you want. Usually you can compute a 16 bit quotient it on most fixed point 16 bit DSPs with single-cycle shift and add/subtract instructions, quite easily within 30 cycles. The initial seed (the guess for the reciprocal) will determine how fast the Newton-Raphson iterations converge. You can use a look-up table to pick an appropriate seed value. --Kal.