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Course: CAST Ethhics, Spring 2010School: Rochester
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Muscanell Dina Lab 3: CORDIC Algorithm & Custom Instructions ESD II 0618-562-41 1/28/10 Abstract: TheCORDICalgorithmisanabbreviationforCOordinateRotationDIgitalComputer. TheCORDICalgorithmisusedtocalculatehyperbolicandtrigonometricfunctions.The CORDICalgorithmiscommonlyimplementedwhenthereisnohardwaremultiplieravailable. ThepurposeofthislabistoimplementrotationofaVGAimageusingbothsoftwareanda...
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Muscanell Dina Lab 3: CORDIC Algorithm & Custom Instructions ESD II 0618-562-41 1/28/10
Abstract: TheCORDICalgorithmisanabbreviationforCOordinateRotationDIgitalComputer. TheCORDICalgorithmisusedtocalculatehyperbolicandtrigonometricfunctions.The CORDICalgorithmiscommonlyimplementedwhenthereisnohardwaremultiplieravailable. ThepurposeofthislabistoimplementrotationofaVGAimageusingbothsoftwareanda hardwareacceleratorwritteninVHDL. Acustominstructionisusedtooffloadprocessingfromsoftwaretoahardware accelerator.ThebasicoperationofNiosIIcustominstructionlogicistoreceiveinputonthe dataaand/ordatabport,anddriveouttheanswerontheresultport.Thecustominstruction logicprovidesaresultbasedontheinputsprovidedbytheNiosIIprocessor.Acustom instructionisawaytoreduceacomplexsequenceofstandardinstructionstoasingle instructionimplementedinhardware
Theoryofoperation TheSOPC(systemonaprogrammablechip)forthisprojectwillcontainmultiple memories,apixelbuffer,VGAandmultipleothercomponents.ThestandardversionCPUmust beusedwiththehardwaremultipleenabled.Aphaselockedloopiscreatedwiththreeoutput clocks.A50Mhzclockwillhaveanoffsetof3nsfortheSDRAM,a50Mhzclockforthephase lockedloopanda25MhzclockfortheVGA.CustomInstructionswerealsocreatedinthein theCPUofthesystem.ThecustominstructionwillnotbevisibleintheSOPCbuilderwindow becauseitislocatedintheCPU.Thecustominstructionwillacceleratetimecriticaloperations. ThecustominstructionlogicconnectsdirectlytotheNiosIIarithmeticlogicunit(ALU).Ablock diagramoftheconnectioncanbefoundinfigure1. Figure1:
Source:http://www.altera.com/literature/ug/ug_nios2_custom_instruction.pdf
Discussion TheobjectiveofpartoneofthelabwastowritetheCORDICalgorithmwhichisanalgorithmto calculatehyperbolicandtrigfunctions.TheCORDICalgorithmwillonlyrequireprocessesfor addition,subtraction,abitshifterandalookuptable.Astatemachineisusedtodecode betweenidle,workinganddonefortheCORDICalgorithm.Whenthestatemachineisinthe workingstate,themathwillbeperformedtofindtheresult(cos&sin)oftheanglethatwas inputtotheCORDICalgorithm.Theworkingstateisheldhighfor8clockcycles.Aftereight clockcyclesthedonestatewillbeentered,andtheresultwillbecomevalid.Thevariable resultis32bits,butthecosineandsineproducedbytheCORDICalgorithmareonly9bits each.Thebitsinbetweenwillneedtobefilledwithzeros.Theresultmuststay32bits becausetheCORDICalgorithmwilllaterbecomeacustominstructionwhichonlyaccepts32bit values.InordertoverifytheCORDICalgorithmisworkingcorrectly,atestbenchmustbe written.Thetestbenchwillgivetwoinputangles,anangleof30degreesandanangleof90 degrees.
Figure2:ModelSimtestedangleof30degrees
ThisModelSimscreenshotsshowsaninputtestangleof30degrees.TheresultwillgetCos X&SinY.Forexampleonthefirstiteration:Angle30degrees45Degrees=14.549121 whenconvertingtheresultfromhexadecimal00DE0081intodecimal.Themostsignificantbit ofZ(Z(15))willdecidetoaddorsubtractintheCORDICalgorithm.Thenextiterationwillgo throughandtesttheinputangleof90degrees. Figure2:ModelSimtestedangleof90degrees
TheresultwillgettheCosX&SinYwhichisapproximately65.791inthedonestate.Sincethe verificationprocessiscompletethenextpartofthelabprocedurewillbeperformed,whichis buildingthesystemonaprogrammablechipwiththecorrectcomponentsandwritingatoplevel VHDLentity.ThetoplevelmustensurethattheVGAclockwillaccordingbeassignedtothe25 MhzclockorelsetheVGAwillnotdisplaytheimageforrotation.TheNiosIDEprogramwill thenbeusedtodisplayanddebugtheimage.TheimagefileofarhinocerosandtwoC programsareloaded,aCprogramforthepixelbufferandaCprogramtodraw(display)the image.Theimagewilltakealongtimetoloadonthemonitor,sincethiscurrentimageisbeing loadedfromsoftware.Bypressingkey1orkey2theimagewillrotateonthescreen.When rotatingtheimageitwilltakeanoticeablylongtime.Nowwewillcomparetheimagerotation processusinghardware.Inthenextpartofthelabthecustominstructionsareaddedinthe rotationwillbefoundwhenloadingtheimagefromhardware.Theverificationprocessis processorandwillactashardwareaccelerators.Anoticeabledifferenceinthespeedofimage completefortheCORDICalgorithmsoitwillbeaddedasacustominstructionintheprocessor foundinSOPC.SincetheCORDICalgorithmgeneratestheangleindegreesandtheC programusesradians,adjustmentsmustbemadetothedrawimageCprogramtochangethe appropriatevariablesfromradianstodegrees.
Figure4:Cprogramchangingradiantodegrees
void interrupt_handler(void *context, alt_u32 id) { if (id==PIO_0_IRQ) { theta += 10.0; if (theta > 90.0) theta = 0; IOWR_32DIRECT(PIO_0_BASE,12,0); return; } }
NowthecustominstructionthatwasgeneratedwillbeimplementedintheCcode.The accordingparameterstoimplementyourcustominstructionarefoundinthesystem.hfile locatedintheNiosIDEprogram.WhenyoubuildyourprojectinNiosIDEthesystem.hfilewill begeneratedandfilledwithimportantinformationsuchascomponentnamesandaddresses. Figure5:ImplementingtheCustomInstruction
int sin_cos =0; sin_cos=ALT_CI_LAB3_INST((theta << 8),0);
Noticethatthevariablethetaisshifted8bitsandtheresultwillbesavedintothesineand cosineresult.Thevariablesin_cosisa32bitvaluethatwillholdthesamedataasresultfrom theCORDIC.Sincesineandcosineareonlyninebitseachthetaisshiftedeightbitstomask offthefirsteightzeros.NowaVHDLmodulecalledfindsourcewillbecreatedtocalculatethe positionsforthexsourcepixelsandysourcepixels.Thesourcepixelsarefoundfromworking backwardsusingthedestinationpixels.Inthefindsourcemodelitwilltakeintwoinputs sin_cosandx_ydestinationwhichwillbesavedintoregisterscalledDataAandDataB.DataA andDataBarecustominstructionregisterswhicharealways32bits,thesenamesareusedto mapsignalsaccordinglyfromyourVHDLmoduletothenewcustominstruction.TheXandY centervalueswillbestoredasconstantstomakethefindsourcemoduleeasiertounderstand. Themathtofindthesourceofxandycanbeperformedconcurrently.Theprogrammermust becarefulwhenmultiplyingtwodecimalstogether,propermaskingwillbeneededinorderto generatethecorrectresult.Theprogrammershouldalsorememberthatwhensubtraction happensinVHDLthattheactualoperationperformedisatwoscomplement.Oncethefind
sourcefileissuccessfulwritten,atestbenchwillbeusedtoverifyfindsourceisworking correctly.
Figure6:FindSourceDataA=90degreesDataB=1
TheresultwillneedtobelookedattofindthecorrectbitsforXandY.Thevariablesbelow calledXsourceandYsourcewillhelpeasilytellthecorrectbits,ratherthansearchingthrough the32bitvariableresultforthecorrectbits.Nowwehaveverifiedthatfindsourceisworking correctlyitwillalsobeaddedasacustominstruction.Thesameprocesswillbeusedtoadda
custominstructionasdescribedearlier.OncethesystemisregeneratedtheNiosIDEwillbe openedagaintomodifytheCprogram.Againthecustominstructionwillneedtobeaddedfrom thesystem.hfileaccordingly.Thistimetheresultfromthefindsourcecustominstructionwillbe savedintoavariablecalledsource_xy.Thedestination_xyvariableisalsocreatedwhichwill receivetheXvariableshifted16bitsplustheYvariable.
Figure7:ModifyingCprogramforfindingthesourcepixels
for (y=0;y<PB->y_resolution;y++) { y_off = y-y_cent; for (x=0;x<PB->x_resolution;x++) { // find the x and y offset from center x_off = x-x_cent; int destinatation_xy; destinatation_xy = ( x << 16) + y; int source_xy; //saving the source_xy from the custom instruction source_xy //these x_source y_source = ALT_CI_FIND_SOURCE_INST(sin_cos,destinatation_xy); are the equations to find the source pixels = ((source_xy >> 16) & 0x000000FF); = ((source_xy) & 0x000000FF);
Oncethecustominstructionisinstantiatedthesource_xywillneedtobebrokenupintothejust thexsourceandtheysource.OncetheCprogramiscomplied,usethedebugmodeinthe IDEtodisplayandrotatetheimage.Thereisasignificantdifferenceinspeedwhenusingthe hardwareimagerotationcomparedtothesoftware.Thehardwareimagerotatesanddisplays quicker.
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