Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ames!sun-barr!cs.utexas.edu!uunet!peregrine!ccicpg!conexch!zardoz!tgate!ka3ovk!drilex!axiom!linus!bs From: bs@linus.UUCP (Robert D. Silverman) Newsgroups: comp.arch Subject: Re: hardware complex arithmetic support Keywords: FFT complex arithmetic Message-ID: <64429@linus.UUCP> Date: 18 Aug 89 17:31:53 GMT References: <1672@crdgw1.crd.ge.com> <5858@pt.cs.cmu.edu> <121828@sun.Eng.Sun.COM> <3532@epimass.EPI.CO Reply-To: bs@linus.UUCP (Robert D. Silverman) Organization: The MITRE Corporation, Bedford MA Lines: 31 In article <3532@epimass.EPI.COM> jbuck@epimass.EPI.COM (Joe Buck) writes: :In article <121828@sun.Eng.Sun.COM> rtrauben@sun.UUCP (Richard Trauben) writes: :>The "current/previous" generation of ATT and Texas Instruments digital :>signal processor (DSP) chips provide complex floating point arithmetic :>primitives to speed up the inner-loop multiply/accumulate butterfly :>operation of a fast fourier transform. : :There is no support for complex arithmetic per se in the TI TMS320 :family, and I don't believe there is any in the AT&T chips either. :What is supported is a magic "bit reversal addressing" mode, which :makes it easy to handle the shuffling operation required in an FFT. : :It requires four multiplies, an addition, and a subtraction to do a :complex multiply; you can do this in four cycles on the TMS320C30 by :taking advantage of parallel multiplication and addition/subtraction. This is not quite correct. Usually [on most hardware] multiplies take significantly longer than additions. Two complex numbers can be multiplied in THREE multiplications (not four) at the expense of a couple extra add/subtracts: (a+bi)(c+di) = ac - bd + ((a+b)(c+d) - ac -bd) i One computes a+b and c+d , then does 3 multiplications: ac, bd and (a+b)(c+d) one additional add, and 3 subtracts finishes it. Total: 3 multiplies, 3 adds, 3 subtracts. This can be faster depending on the relative speed of multiplication and addition. It is almost always faster if working in double precision. Bob Silverman