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1、1038IEEETRANSACTIONSONCOMPUTERS,VOL.39,NO.8,AUGUST1990On-LineCORDICAlgorithmsHAIXIANGLIN,STUDENTMEMBER,IEEE,ANDHENKJ.SIPS,MEMBER,IEEEA&ha&--TheCORDICalgorithmsprovideinafastwaythecalculationsofanumberofarithmeticbasicfunctions.ACORDICcalculationtakesO(n
2、)stepsforafunction,wherenisthewordlengthoftheoperands.Thespeedislimitedbytheon-linecarrypropagationintheaddersandtheIA)throughput.Speedarithmetic6canheimprovedbyintroducingredundancyinthecalculationunit1timediagramcircuitandIDthroughputbydoingI/otransfe
3、rswhilecalculat-ing.Thelatterischaracteristicfortheclassofsocalledon-lineX,Y$+Sarithmetic.Atthesametime,thepinrequirementsarelimited2'wtoasingledigitperoperand.Thispaperintroducesanumberon-line&iofnewalgorithmstomakeanon-lineCORDICimplementa-arithmetict
4、ion.Theon-lineCORDICalgorithmtakesn+6clockcyclesunit62i621ztocomputeaCORDICfunction.Itisestimatedthatanimple-iidenotesthei-thon-linedigitofzmentationoftheproposedalgorithmis6to7timesasfastasthetraditionalCORDICapproachforGivens’rotation,and7ii?~~;:‘~~~~
5、::ito8timesasfastforSVDcomputation.Fig.1.Chainedon-linecomputation.IndexTerms-Computerarithmetic,CORDIC,digitpipelin-ing,on-linealgorithms.on-linearithmetic.ForSVDtheirapproachisestimatedtobe4timesasfastastheapproachin[111,sincetheuseofredundantaddersal
6、lowsforafasterclockperiod.I.INTRODUCTIONInthispaper,weintroduceanon-lineCORDICalgorithmON-LINEcomputations,theinputoperandsandresultswithanon-linedelay6of65658(independentofthewordIf;’owthrougharithmeticunitsinadigitbydigitmanner,lengthnoftheoperands).I
7、tisalsoshownthatbyusingthestartingwiththemostsignificantdigit.Anon-linealgorithmproposedscheme,Givens’rotationandthediagonalizationofissaidtohaveanon-linedelayof6,ifforthegenerationofa2x2matrixinSVDcomputationcanbecomputedinn+13thejthdigitoftheresult,(j
8、+S)digitsoftheinputoperandsandn+22clockcycles,respectively.Thepaperisorganizedarerequired[l].Fig.1showstheprincipleofon-linecompu-asfollows.InSectionII,thearithmeticfunctionswhichcantationandillustratesthatdigiton-linearithmeticu
