/**CFile**************************************************************** FileName [dsdProc.c] PackageName [DSD: Disjoint-support decomposition package.] Synopsis [The core procedures of the package.] Author [Alan Mishchenko] Affiliation [UC Berkeley] Date [Ver. 8.0. Started - September 22, 2003.] Revision [$Id: dsdProc.c,v 1.0 2002/22/09 00:00:00 alanmi Exp $] ***********************************************************************/ #include "dsdInt.h" //////////////////////////////////////////////////////////////////////// /// FUNCTION DECLARATIONS /// //////////////////////////////////////////////////////////////////////// // the most important procedures void dsdKernelDecompose( Dsd_Manager_t * pDsdMan, DdNode ** pbFuncs, int nFuncs ); static Dsd_Node_t * dsdKernelDecompose_rec( Dsd_Manager_t * pDsdMan, DdNode * F ); // additional procedures static Dsd_Node_t * dsdKernelFindContainingComponent( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pWhere, DdNode * Var, int * fPolarity ); static int dsdKernelFindCommonComponents( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pL, Dsd_Node_t * pH, Dsd_Node_t *** pCommon, Dsd_Node_t ** pLastDiffL, Dsd_Node_t ** pLastDiffH ); static void dsdKernelComputeSumOfComponents( Dsd_Manager_t * pDsdMan, Dsd_Node_t ** pCommon, int nCommon, DdNode ** pCompF, DdNode ** pCompS, int fExor ); static int dsdKernelCheckContainment( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pL, Dsd_Node_t * pH, Dsd_Node_t ** pLarge, Dsd_Node_t ** pSmall ); // list copying static void dsdKernelCopyListPlusOne( Dsd_Node_t * p, Dsd_Node_t * First, Dsd_Node_t ** ppList, int nListSize ); static void dsdKernelCopyListPlusOneMinusOne( Dsd_Node_t * p, Dsd_Node_t * First, Dsd_Node_t ** ppList, int nListSize, int Skipped ); // debugging procedures static int dsdKernelVerifyDecomposition( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pDE ); //////////////////////////////////////////////////////////////////////// /// STATIC VARIABLES /// //////////////////////////////////////////////////////////////////////// // the counter of marks static int s_Mark; // debugging flag static int s_Show = 0; // temporary var used for debugging static int Depth = 0; static int s_Loops1; static int s_Loops2; static int s_Loops3; static int s_Pivot; static int s_PivotNo; static int s_Common; static int s_CommonNo; static int s_Case4Calls; static int s_Case4CallsSpecial; static int s_Case5; static int s_Loops2Useless; static int s_DecNodesTotal; static int s_DecNodesUsed; // statistical variables static int s_nDecBlocks; static int s_nLiterals; static int s_nExorGates; static int s_nReusedBlocks; static int s_nCascades; static float s_nArea; static float s_MaxDelay; static long s_Time; static int s_nInvertors; static int s_nPrimeBlocks; static int HashSuccess = 0; static int HashFailure = 0; static int s_CacheEntries; //////////////////////////////////////////////////////////////////////// /// DECOMPOSITION FUNCTIONS /// //////////////////////////////////////////////////////////////////////// /**Function************************************************************* Synopsis [Performs DSD for the array of functions represented by BDDs.] Description [This function takes the DSD manager, which should be previously allocated by the call to Dsd_ManagerStart(). The resulting DSD tree is stored in the DSD manager (pDsdMan->pRoots, pDsdMan->nRoots). Access to the tree is through the APIs of the manager. The resulting tree is a shared DSD DAG for the functions given in the array. For one function the resulting DAG is always a tree. The root node pointers can be complemented, as discussed in the literature referred to in "dsd.h". This procedure can be called repeatedly for different functions. There is no need to remove the decomposition tree after it is returned, because the next call to the DSD manager will "recycle" the tree. The user should not modify or dereference any data associated with the nodes of the DSD trees (the user can only change the contents of a temporary mark associated with each node by the calling to Dsd_NodeSetMark()). All the decomposition trees and intermediate nodes will be removed when the DSD manager is deallocated at the end by calling Dsd_ManagerStop().] SideEffects [] SeeAlso [] ***********************************************************************/ void Dsd_Decompose( Dsd_Manager_t * pDsdMan, DdNode ** pbFuncs, int nFuncs ) { DdManager * dd = pDsdMan->dd; int i; long clk; Dsd_Node_t * pTemp; int SumMaxGateSize = 0; int nDecOutputs = 0; int nCBFOutputs = 0; /* s_Loops1 = 0; s_Loops2 = 0; s_Loops3 = 0; s_Case4Calls = 0; s_Case4CallsSpecial = 0; s_Case5 = 0; s_Loops2Useless = 0; */ // resize the number of roots in the manager if ( pDsdMan->nRootsAlloc < nFuncs ) { if ( pDsdMan->nRootsAlloc > 0 ) free( pDsdMan->pRoots ); pDsdMan->nRootsAlloc = nFuncs; pDsdMan->pRoots = (Dsd_Node_t **) malloc( pDsdMan->nRootsAlloc * sizeof(Dsd_Node_t *) ); } if ( pDsdMan->fVerbose ) printf( "\nDecomposability statistics for individual outputs:\n" ); // set the counter of decomposition nodes s_nDecBlocks = 0; // perform decomposition for all outputs clk = clock(); pDsdMan->nRoots = 0; s_nCascades = 0; for ( i = 0; i < nFuncs; i++ ) { int nLiteralsPrev; int nDecBlocksPrev; int nExorGatesPrev; int nReusedBlocksPres; int nCascades; int MaxBlock; int nPrimeBlocks; long clk; clk = clock(); nLiteralsPrev = s_nLiterals; nDecBlocksPrev = s_nDecBlocks; nExorGatesPrev = s_nExorGates; nReusedBlocksPres = s_nReusedBlocks; nPrimeBlocks = s_nPrimeBlocks; pDsdMan->pRoots[ pDsdMan->nRoots++ ] = dsdKernelDecompose_rec( pDsdMan, pbFuncs[i] ); Dsd_TreeNodeGetInfoOne( pDsdMan->pRoots[i], &nCascades, &MaxBlock ); s_nCascades = ddMax( s_nCascades, nCascades ); pTemp = Dsd_Regular(pDsdMan->pRoots[i]); if ( pTemp->Type != DSD_NODE_PRIME || pTemp->nDecs != Extra_bddSuppSize(dd,pTemp->S) ) nDecOutputs++; if ( MaxBlock < 3 ) nCBFOutputs++; SumMaxGateSize += MaxBlock; if ( pDsdMan->fVerbose ) { printf("#%02d: ", i ); printf("Ins=%2d. ", Cudd_SupportSize(dd,pbFuncs[i]) ); printf("Gts=%3d. ", Dsd_TreeCountNonTerminalNodesOne( pDsdMan->pRoots[i] ) ); printf("Pri=%3d. ", Dsd_TreeCountPrimeNodesOne( pDsdMan->pRoots[i] ) ); printf("Max=%3d. ", MaxBlock ); printf("Reuse=%2d. ", s_nReusedBlocks-nReusedBlocksPres ); printf("Csc=%2d. ", nCascades ); printf("T= %.2f s. ", (float)(clock()-clk)/(float)(CLOCKS_PER_SEC) ) ; printf("Bdd=%2d. ", Cudd_DagSize(pbFuncs[i]) ); printf("\n"); fflush( stdout ); } } assert( pDsdMan->nRoots == nFuncs ); if ( pDsdMan->fVerbose ) { printf( "\n" ); printf( "The cumulative decomposability statistics:\n" ); printf( " Total outputs = %5d\n", nFuncs ); printf( " Decomposable outputs = %5d\n", nDecOutputs ); printf( " Completely decomposable outputs = %5d\n", nCBFOutputs ); printf( " The sum of max gate sizes = %5d\n", SumMaxGateSize ); printf( " Shared BDD size = %5d\n", Cudd_SharingSize( pbFuncs, nFuncs ) ); printf( " Decomposition entries = %5d\n", st_count( pDsdMan->Table ) ); printf( " Pure decomposition time = %.2f sec\n", (float)(clock() - clk)/(float)(CLOCKS_PER_SEC) ); } /* printf( "s_Loops1 = %d.\n", s_Loops1 ); printf( "s_Loops2 = %d.\n", s_Loops2 ); printf( "s_Loops3 = %d.\n", s_Loops3 ); printf( "s_Case4Calls = %d.\n", s_Case4Calls ); printf( "s_Case4CallsSpecial = %d.\n", s_Case4CallsSpecial ); printf( "s_Case5 = %d.\n", s_Case5 ); printf( "s_Loops2Useless = %d.\n", s_Loops2Useless ); */ } /**Function************************************************************* Synopsis [The main function of this module. Recursive implementation of DSD.] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ Dsd_Node_t * dsdKernelDecompose_rec( Dsd_Manager_t * pDsdMan, DdNode * bFunc0 ) { DdManager * dd = pDsdMan->dd; DdNode * bLow; DdNode * bLowR; DdNode * bHigh; int VarInt; DdNode * bVarCur; Dsd_Node_t * pVarCurDE; // works only if var indices start from 0!!! DdNode * bSuppNew = NULL, * bTemp; int fContained; int nSuppLH; int nSuppL; int nSuppH; // various decomposition nodes Dsd_Node_t * pThis, * pL, * pH, * pLR, * pHR; Dsd_Node_t * pSmallR, * pLargeR; Dsd_Node_t * pTableEntry; // treat the complemented case DdNode * bF = Cudd_Regular(bFunc0); int fCompF = (int)(bF != bFunc0); // check cache if ( st_lookup( pDsdMan->Table, (char*)bF, (char**)&pTableEntry ) ) { // the entry is present HashSuccess++; return Dsd_NotCond( pTableEntry, fCompF ); } HashFailure++; Depth++; // proceed to consider "four cases" ////////////////////////////////////////////////////////////////////// // TERMINAL CASES - CASES 1 and 2 ////////////////////////////////////////////////////////////////////// bLow = cuddE(bF); bLowR = Cudd_Regular(bLow); bHigh = cuddT(bF); VarInt = bF->index; bVarCur = dd->vars[VarInt]; pVarCurDE = pDsdMan->pInputs[VarInt]; // works only if var indices start from 0!!! bSuppNew = NULL; if ( bLowR->index == CUDD_CONST_INDEX || bHigh->index == CUDD_CONST_INDEX ) { // one of the cofactors in the constant if ( bHigh == b1 ) // bHigh cannot be equal to b0, because then it will be complemented if ( bLow == b0 ) // bLow cannot be equal to b1, because then the node will have bLow == bHigh ///////////////////////////////////////////////////////////////// // bLow == 0, bHigh == 1, F = x'&0 + x&1 = x ///////////////////////////////////////////////////////////////// { // create the elementary variable node assert(0); // should be already in the hash table pThis = Dsd_TreeNodeCreate( DSD_NODE_BUF, 1, s_nDecBlocks++ ); pThis->pDecs[0] = NULL; } else // if ( bLow != constant ) ///////////////////////////////////////////////////////////////// // bLow != const, bHigh == 1, F = x'&bLow + x&1 = bLow + x --- DSD_NODE_OR(x,bLow) ///////////////////////////////////////////////////////////////// { pL = dsdKernelDecompose_rec( pDsdMan, bLow ); pLR = Dsd_Regular( pL ); bSuppNew = Cudd_bddAnd( dd, bVarCur, pLR->S ); Cudd_Ref(bSuppNew); if ( pLR->Type == DSD_NODE_OR && pL == pLR ) // OR and no complement { // add to the components pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, pL->nDecs+1, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, pVarCurDE, pL->pDecs, pL->nDecs ); } else // all other cases { // create a new 2-input OR-gate pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, 2, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, pVarCurDE, &pL, 1 ); } } else // if ( bHigh != const ) // meaning that bLow should be a constant { pH = dsdKernelDecompose_rec( pDsdMan, bHigh ); pHR = Dsd_Regular( pH ); bSuppNew = Cudd_bddAnd( dd, bVarCur, pHR->S ); Cudd_Ref(bSuppNew); if ( bLow == b0 ) ///////////////////////////////////////////////////////////////// // Low == 0, High != 1, F = x'&0+x&High = (x'+High')'--- NOR(x',High') ///////////////////////////////////////////////////////////////// if ( pHR->Type == DSD_NODE_OR && pH != pHR ) // DSD_NODE_OR and complement { // add to the components pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, pHR->nDecs+1, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, Dsd_Not(pVarCurDE), pHR->pDecs, pHR->nDecs ); pThis = Dsd_Not(pThis); } else // all other cases { // create a new 2-input NOR gate pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, 2, s_nDecBlocks++ ); pH = Dsd_Not(pH); dsdKernelCopyListPlusOne( pThis, Dsd_Not(pVarCurDE), &pH, 1 ); pThis = Dsd_Not(pThis); } else // if ( bLow == b1 ) ///////////////////////////////////////////////////////////////// // Low == 1, High != 1, F = x'&1 + x&High = x' + High --- DSD_NODE_OR(x',High) ///////////////////////////////////////////////////////////////// if ( pHR->Type == DSD_NODE_OR && pH == pHR ) // OR and no complement { // add to the components pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, pH->nDecs+1, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, Dsd_Not(pVarCurDE), pH->pDecs, pH->nDecs ); } else // all other cases { // create a new 2-input OR-gate pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, 2, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, Dsd_Not(pVarCurDE), &pH, 1 ); } } goto EXIT; } // else if ( bLow != const && bHigh != const ) // the case of equal cofactors (up to complementation) if ( bLowR == bHigh ) ///////////////////////////////////////////////////////////////// // Low == G, High == G', F = x'&G + x&G' = (x(+)G) --- EXOR(x,Low) ///////////////////////////////////////////////////////////////// { pL = dsdKernelDecompose_rec( pDsdMan, bLow ); pLR = Dsd_Regular( pL ); bSuppNew = Cudd_bddAnd( dd, bVarCur, pLR->S ); Cudd_Ref(bSuppNew); if ( pLR->Type == DSD_NODE_EXOR ) // complemented or not - does not matter! { // add to the components pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, pLR->nDecs+1, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, pVarCurDE, pLR->pDecs, pLR->nDecs ); if ( pL != pLR ) pThis = Dsd_Not( pThis ); } else // all other cases { // create a new 2-input EXOR-gate pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, 2, s_nDecBlocks++ ); if ( pL != pLR ) // complemented { dsdKernelCopyListPlusOne( pThis, pVarCurDE, &pLR, 1 ); pThis = Dsd_Not( pThis ); } else // non-complemented dsdKernelCopyListPlusOne( pThis, pVarCurDE, &pL, 1 ); } goto EXIT; } ////////////////////////////////////////////////////////////////////// // solve subproblems ////////////////////////////////////////////////////////////////////// pL = dsdKernelDecompose_rec( pDsdMan, bLow ); pH = dsdKernelDecompose_rec( pDsdMan, bHigh ); pLR = Dsd_Regular( pL ); pHR = Dsd_Regular( pH ); assert( pLR->Type == DSD_NODE_BUF || pLR->Type == DSD_NODE_OR || pLR->Type == DSD_NODE_EXOR || pLR->Type == DSD_NODE_PRIME ); assert( pHR->Type == DSD_NODE_BUF || pHR->Type == DSD_NODE_OR || pHR->Type == DSD_NODE_EXOR || pHR->Type == DSD_NODE_PRIME ); /* if ( Depth == 1 ) { // PRK(bLow,pDecTreeTotal->nInputs); // PRK(bHigh,pDecTreeTotal->nInputs); if ( s_Show ) { PRD( pL ); PRD( pH ); } } */ // compute the new support bTemp = Cudd_bddAnd( dd, pLR->S, pHR->S ); Cudd_Ref( bTemp ); nSuppL = Extra_bddSuppSize( dd, pLR->S ); nSuppH = Extra_bddSuppSize( dd, pHR->S ); nSuppLH = Extra_bddSuppSize( dd, bTemp ); bSuppNew = Cudd_bddAnd( dd, bTemp, bVarCur ); Cudd_Ref( bSuppNew ); Cudd_RecursiveDeref( dd, bTemp ); // several possibilities are possible // (1) support of one component contains another // (2) none of the supports is contained in another fContained = dsdKernelCheckContainment( pDsdMan, pLR, pHR, &pLargeR, &pSmallR ); ////////////////////////////////////////////////////////////////////// // CASE 3.b One of the cofactors in a constant (OR and EXOR) ////////////////////////////////////////////////////////////////////// // the support of the larger component should contain the support of the smaller // it is possible to have PRIME function in this role // for example: F = ITE( a+b, c(+)d, e+f ), F0 = ITE( b, c(+)d, e+f ), F1 = c(+)d if ( fContained ) { Dsd_Node_t * pSmall, * pLarge; int c, iCompLarge; // the number of the component is Large is equal to the whole of Small int fLowIsLarge; DdNode * bFTemp; // the changed input function Dsd_Node_t * pDETemp, * pDENew; Dsd_Node_t * pComp = NULL; int nComp; if ( pSmallR == pLR ) { // Low is Small => High is Large pSmall = pL; pLarge = pH; fLowIsLarge = 0; } else { // vice versa pSmall = pH; pLarge = pL; fLowIsLarge = 1; } // treat the situation when the larger is PRIME if ( pLargeR->Type == DSD_NODE_PRIME ) //&& pLargeR->nDecs != pSmallR->nDecs ) { // QUESTION: Is it possible for pLargeR->nDecs > 3 // and pSmall contained as one of input in pLarge? // Yes, for example F = a'c + a & MUX(b,c',d) = a'c + abc' + ab'd is non-decomposable // Consider the function H(a->xy) = F( xy, b, c, d ) // H0 = H(x=0) = F(0,b,c,d) = c // H1 = F(x=1) = F(y,b,c,d) - non-decomposable // // QUESTION: Is it possible that pLarge is PRIME(3) and pSmall is OR(2), // which is not contained in PRIME as one input? // Yes, for example F = abcd + b'c'd' + a'c'd' = PRIME(ab, c, d) // F(a=0) = c'd' = NOT(OR(a,d)) F(a=1) = bcd + b'c'd' = PRIME(b,c,d) // To find decomposition, we have to prove that F(a=1)|b=0 = F(a=0) // Is it possible that (pLargeR->nDecs == pSmallR->nDecs) and yet this case holds? // Yes, consider the function such that F(a=0) = PRIME(a,b+c,d,e) and F(a=1) = OR(b,c,d,e) // They have the same number of inputs and it is possible that they will be the cofactors // as discribed in the previous example. // find the component, which when substituted for 0 or 1, produces the desired result int g, fFoundComp; // {0,1} depending on whether setting cofactor to 0 or 1 worked out DdNode * bLarge, * bSmall; if ( fLowIsLarge ) { bLarge = bLow; bSmall = bHigh; } else { bLarge = bHigh; bSmall = bLow; } for ( g = 0; g < pLargeR->nDecs; g++ ) // if ( g != c ) { pDETemp = pLargeR->pDecs[g]; // cannot be complemented if ( Dsd_CheckRootFunctionIdentity( dd, bLarge, bSmall, pDETemp->G, b1 ) ) { fFoundComp = 1; break; } s_Loops1++; if ( Dsd_CheckRootFunctionIdentity( dd, bLarge, bSmall, Cudd_Not(pDETemp->G), b1 ) ) { fFoundComp = 0; break; } s_Loops1++; } if ( g != pLargeR->nDecs ) { // decomposition is found if ( fFoundComp ) if ( fLowIsLarge ) bFTemp = Cudd_bddOr( dd, bVarCur, pLargeR->pDecs[g]->G ); else bFTemp = Cudd_bddOr( dd, Cudd_Not(bVarCur), pLargeR->pDecs[g]->G ); else if ( fLowIsLarge ) bFTemp = Cudd_bddAnd( dd, Cudd_Not(bVarCur), pLargeR->pDecs[g]->G ); else bFTemp = Cudd_bddAnd( dd, bVarCur, pLargeR->pDecs[g]->G ); Cudd_Ref( bFTemp ); pDENew = dsdKernelDecompose_rec( pDsdMan, bFTemp ); pDENew = Dsd_Regular( pDENew ); Cudd_RecursiveDeref( dd, bFTemp ); // get the new gate pThis = Dsd_TreeNodeCreate( DSD_NODE_PRIME, pLargeR->nDecs, s_nDecBlocks++ ); dsdKernelCopyListPlusOneMinusOne( pThis, pDENew, pLargeR->pDecs, pLargeR->nDecs, g ); goto EXIT; } } // try to find one component in the pLarger that is equal to the whole of pSmaller for ( c = 0; c < pLargeR->nDecs; c++ ) if ( pLargeR->pDecs[c] == pSmall || pLargeR->pDecs[c] == Dsd_Not(pSmall) ) { iCompLarge = c; break; } // assign the equal component if ( c != pLargeR->nDecs ) // the decomposition is possible! { pComp = pLargeR->pDecs[iCompLarge]; nComp = 1; } else // the decomposition is still possible { // for example F = OR(ab,c,d), F(a=0) = OR(c,d), F(a=1) = OR(b,c,d) // supp(F0) is contained in supp(F1), Polarity(F(a=0)) == Polarity(F(a=1)) // try to find a group of common components if ( pLargeR->Type == pSmallR->Type && (pLargeR->Type == DSD_NODE_EXOR || pSmallR->Type == DSD_NODE_OR&& ((pLarge==pLargeR) == (pSmall==pSmallR))) ) { Dsd_Node_t ** pCommon, * pLastDiffL = NULL, * pLastDiffH = NULL; int nCommon = dsdKernelFindCommonComponents( pDsdMan, pLargeR, pSmallR, &pCommon, &pLastDiffL, &pLastDiffH ); // if all the components of pSmall are contained in pLarge, // then the decomposition exists if ( nCommon == pSmallR->nDecs ) { pComp = pSmallR; nComp = pSmallR->nDecs; } } } if ( pComp ) // the decomposition is possible! { // Dsd_Node_t * pComp = pLargeR->pDecs[iCompLarge]; Dsd_Node_t * pCompR = Dsd_Regular( pComp ); int fComp1 = (int)( pLarge != pLargeR ); int fComp2 = (int)( pComp != pCompR ); int fComp3 = (int)( pSmall != pSmallR ); DdNode * bFuncComp; // the function of the given component DdNode * bFuncNew; // the function of the input component if ( pLargeR->Type == DSD_NODE_OR ) // Figure 4 of Matsunaga's paper { // the decomposition exists only if the polarity assignment // along the paths is the same if ( (fComp1 ^ fComp2) == fComp3 ) { // decomposition exists = consider 4 cases // consideration of cases leads to the following conclusion // fComp1 gives the polarity of the resulting DSD_NODE_OR gate // fComp2 gives the polarity of the common component feeding into the DSD_NODE_OR gate // // | fComp1 pL/ |pS // <> .........<=>....... <> | // | / | // [OR] [OR] | fComp3 // / \ fComp2 / | \ | // <> <> .......<=>... /..|..<> | // / \ / | \| // [OR] [C] S1 S2 C // / \ // <> \ // / \ // [OR] [x] // / \ // S1 S2 // // at this point we have the function F (bFTemp) and the common component C (bFuncComp) // to get the remainder, R, in the relationship F = R + C, supp(R) & supp(C) = 0 // we compute the following R = Exist( F - C, supp(C) ) bFTemp = (fComp1)? Cudd_Not( bF ): bF; bFuncComp = (fComp2)? Cudd_Not( pCompR->G ): pCompR->G; bFuncNew = Cudd_bddAndAbstract( dd, bFTemp, Cudd_Not(bFuncComp), pCompR->S ); Cudd_Ref( bFuncNew ); // there is no need to copy the dec entry list first, because pComp is a component // which will not be destroyed by the recursive call to decomposition pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew ); assert( Dsd_IsComplement(pDENew) ); // follows from the consideration of cases Cudd_RecursiveDeref( dd, bFuncNew ); // get the new gate if ( nComp == 1 ) { pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, 2, s_nDecBlocks++ ); pThis->pDecs[0] = pDENew; pThis->pDecs[1] = pComp; // takes the complement } else { // pComp is not complemented pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, nComp+1, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, pDENew, pComp->pDecs, nComp ); } if ( fComp1 ) pThis = Dsd_Not( pThis ); goto EXIT; } } else if ( pLargeR->Type == DSD_NODE_EXOR ) // Figure 5 of Matsunaga's paper (with correction) { // decomposition always exists = consider 4 cases // consideration of cases leads to the following conclusion // fComp3 gives the COMPLEMENT of the polarity of the resulting EXOR gate // (if fComp3 is 0, the EXOR gate is complemented, and vice versa) // // | fComp1 pL/ |pS // <> .........<=>....... /....| fComp3 // | / | // [XOR] [XOR] | // / \ fComp2==0 / | \ | // / \ / | \ | // / \ / | \| // [OR] [C] S1 S2 C // / \ // <> \ // / \ // [XOR] [x] // / \ // S1 S2 // assert( fComp2 == 0 ); // find the functionality of the lower gates bFTemp = (fComp3)? bF: Cudd_Not( bF ); bFuncNew = Cudd_bddXor( dd, bFTemp, pComp->G ); Cudd_Ref( bFuncNew ); pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew ); assert( !Dsd_IsComplement(pDENew) ); // follows from the consideration of cases Cudd_RecursiveDeref( dd, bFuncNew ); // get the new gate if ( nComp == 1 ) { pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, 2, s_nDecBlocks++ ); pThis->pDecs[0] = pDENew; pThis->pDecs[1] = pComp; } else { // pComp is not complemented pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, nComp+1, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, pDENew, pComp->pDecs, nComp ); } if ( !fComp3 ) pThis = Dsd_Not( pThis ); goto EXIT; } } } // this case was added to fix the trivial bug found November 4, 2002 in Japan // by running the example provided by T. Sasao if ( nSuppLH == nSuppL + nSuppH ) // the supports of the components are disjoint { // create a new component of the type ITE( a, pH, pL ) pThis = Dsd_TreeNodeCreate( DSD_NODE_PRIME, 3, s_nDecBlocks++ ); if ( dd->perm[pLR->S->index] < dd->perm[pHR->S->index] ) // pLR is higher in the varible order { pThis->pDecs[1] = pLR; pThis->pDecs[2] = pHR; } else // pHR is higher in the varible order { pThis->pDecs[1] = pHR; pThis->pDecs[2] = pLR; } // add the first component pThis->pDecs[0] = pVarCurDE; goto EXIT; } ////////////////////////////////////////////////////////////////////// // CASE 3.a Neither of the cofactors is a constant (OR, EXOR, PRIME) ////////////////////////////////////////////////////////////////////// // the component types are identical // and if they are OR, they are either both complemented or both not complemented // and if they are PRIME, their dec numbers should be the same if ( pLR->Type == pHR->Type && pLR->Type != DSD_NODE_BUF && (pLR->Type != DSD_NODE_OR || ( pL == pLR && pH == pHR || pL != pLR && pH != pHR ) ) && (pLR->Type != DSD_NODE_PRIME || pLR->nDecs == pHR->nDecs) ) { // array to store common comps in pL and pH Dsd_Node_t ** pCommon, * pLastDiffL = NULL, * pLastDiffH = NULL; int nCommon = dsdKernelFindCommonComponents( pDsdMan, pLR, pHR, &pCommon, &pLastDiffL, &pLastDiffH ); if ( nCommon ) { if ( pLR->Type == DSD_NODE_OR ) // Figure 2 of Matsunaga's paper { // at this point we have the function F and the group of common components C // to get the remainder, R, in the relationship F = R + C, supp(R) & supp(C) = 0 // we compute the following R = Exist( F - C, supp(C) ) // compute the sum total of the common components and the union of their supports DdNode * bCommF, * bCommS, * bFTemp, * bFuncNew; Dsd_Node_t * pDENew; dsdKernelComputeSumOfComponents( pDsdMan, pCommon, nCommon, &bCommF, &bCommS, 0 ); Cudd_Ref( bCommF ); Cudd_Ref( bCommS ); bFTemp = ( pL != pLR )? Cudd_Not(bF): bF; bFuncNew = Cudd_bddAndAbstract( dd, bFTemp, Cudd_Not(bCommF), bCommS ); Cudd_Ref( bFuncNew ); Cudd_RecursiveDeref( dd, bCommF ); Cudd_RecursiveDeref( dd, bCommS ); // get the new gate // copy the components first, then call the decomposition // because decomposition will distroy the list used for copying pThis = Dsd_TreeNodeCreate( DSD_NODE_OR, nCommon + 1, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, NULL, pCommon, nCommon ); // call the decomposition recursively pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew ); // assert( !Dsd_IsComplement(pDENew) ); // follows from the consideration of cases Cudd_RecursiveDeref( dd, bFuncNew ); // add the first component pThis->pDecs[0] = pDENew; if ( pL != pLR ) pThis = Dsd_Not( pThis ); goto EXIT; } else if ( pLR->Type == DSD_NODE_EXOR ) // Figure 3 of Matsunaga's paper { // compute the sum total of the common components and the union of their supports DdNode * bCommF, * bFuncNew; Dsd_Node_t * pDENew; int fCompExor; dsdKernelComputeSumOfComponents( pDsdMan, pCommon, nCommon, &bCommF, NULL, 1 ); Cudd_Ref( bCommF ); bFuncNew = Cudd_bddXor( dd, bF, bCommF ); Cudd_Ref( bFuncNew ); Cudd_RecursiveDeref( dd, bCommF ); // get the new gate // copy the components first, then call the decomposition // because decomposition will distroy the list used for copying pThis = Dsd_TreeNodeCreate( DSD_NODE_EXOR, nCommon + 1, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, NULL, pCommon, nCommon ); // call the decomposition recursively pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew ); Cudd_RecursiveDeref( dd, bFuncNew ); // remember the fact that it was complemented fCompExor = Dsd_IsComplement(pDENew); pDENew = Dsd_Regular(pDENew); // add the first component pThis->pDecs[0] = pDENew; if ( fCompExor ) pThis = Dsd_Not( pThis ); goto EXIT; } else if ( pLR->Type == DSD_NODE_PRIME && (nCommon == pLR->nDecs-1 || nCommon == pLR->nDecs) ) { // for example the function F(a,b,c,d) = ITE(b,c,a(+)d) produces // two cofactors F(a=0) = PRIME(b,c,d) and F(a=1) = PRIME(b,c,d) // with exactly the same list of common components Dsd_Node_t * pDENew; DdNode * bFuncNew; int fCompComp = 0; // this flag can be {0,1,2} // if it is 0 there is no identity // if it is 1/2, the cofactored functions are equal in the direct/complemented polarity if ( nCommon == pLR->nDecs ) { // all the components are the same // find the formal input, in which pLow and pHigh differ (if such input exists) int m; Dsd_Node_t * pTempL, * pTempH; s_Common++; for ( m = 0; m < pLR->nDecs; m++ ) { pTempL = pLR->pDecs[m]; // cannot be complemented pTempH = pHR->pDecs[m]; // cannot be complemented if ( Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, pTempL->G, Cudd_Not(pTempH->G) ) && Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, Cudd_Not(pTempL->G), pTempH->G ) ) { pLastDiffL = pTempL; pLastDiffH = pTempH; assert( pLastDiffL == pLastDiffH ); fCompComp = 2; break; } s_Loops2++; s_Loops2++; /* if ( s_Loops2 % 10000 == 0 ) { int i; for ( i = 0; i < pLR->nDecs; i++ ) printf( " %d(s=%d)", pLR->pDecs[i]->Type, Extra_bddSuppSize(dd, pLR->pDecs[i]->S) ); printf( "\n" ); } */ } // if ( pLR->nDecs == Extra_bddSuppSize(dd, pLR->S) ) // s_Loops2Useless += pLR->nDecs * 2; if ( fCompComp ) { // put the equal components into pCommon, so that they could be copied into the new dec entry nCommon = 0; for ( m = 0; m < pLR->nDecs; m++ ) if ( pLR->pDecs[m] != pLastDiffL ) pCommon[nCommon++] = pLR->pDecs[m]; assert( nCommon = pLR->nDecs-1 ); } } else { // the differing components are known - check that they have compatible PRIME function s_CommonNo++; // find the numbers of different components assert( pLastDiffL ); assert( pLastDiffH ); // also, they cannot be complemented, because the decomposition type is PRIME if ( Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, Cudd_Not(pLastDiffL->G), Cudd_Not(pLastDiffH->G) ) && Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, pLastDiffL->G, pLastDiffH->G ) ) fCompComp = 1; else if ( Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, pLastDiffL->G, Cudd_Not(pLastDiffH->G) ) && Dsd_CheckRootFunctionIdentity( dd, bLow, bHigh, Cudd_Not(pLastDiffL->G), pLastDiffH->G ) ) fCompComp = 2; s_Loops3 += 4; } if ( fCompComp ) { if ( fCompComp == 1 ) // it is true that bLow(G=0) == bHigh(H=0) && bLow(G=1) == bHigh(H=1) bFuncNew = Cudd_bddIte( dd, bVarCur, pLastDiffH->G, pLastDiffL->G ); else // it is true that bLow(G=0) == bHigh(H=1) && bLow(G=1) == bHigh(H=0) bFuncNew = Cudd_bddIte( dd, bVarCur, Cudd_Not(pLastDiffH->G), pLastDiffL->G ); Cudd_Ref( bFuncNew ); // get the new gate // copy the components first, then call the decomposition // because decomposition will distroy the list used for copying pThis = Dsd_TreeNodeCreate( DSD_NODE_PRIME, pLR->nDecs, s_nDecBlocks++ ); dsdKernelCopyListPlusOne( pThis, NULL, pCommon, nCommon ); // create a new component pDENew = dsdKernelDecompose_rec( pDsdMan, bFuncNew ); Cudd_RecursiveDeref( dd, bFuncNew ); // the BDD of the argument function in PRIME decomposition, should be regular pDENew = Dsd_Regular(pDENew); // add the first component pThis->pDecs[0] = pDENew; goto EXIT; } } // end of PRIME type } // end of existing common components } // end of CASE 3.a // if ( Depth != 1) // { //CASE4: ////////////////////////////////////////////////////////////////////// // CASE 4 ////////////////////////////////////////////////////////////////////// { // estimate the number of entries in the list int nEntriesMax = pDsdMan->nInputs - dd->perm[VarInt]; // create the new decomposition entry int nEntries = 0; DdNode * SuppL, * SuppH, * SuppL_init, * SuppH_init; Dsd_Node_t *pHigher, *pLower, * pTemp, * pDENew; int levTopSuppL; int levTopSuppH; int levTop; pThis = Dsd_TreeNodeCreate( DSD_NODE_PRIME, nEntriesMax, s_nDecBlocks++ ); pThis->pDecs[ nEntries++ ] = pVarCurDE; // other entries will be added to this list one-by-one during analysis // count how many times does it happen that the decomposition entries are s_Case4Calls++; // consider the simplest case: when the supports are equal // and at least one of the components // is the PRIME without decompositions, or // when both of them are without decomposition if ( (((pLR->Type == DSD_NODE_PRIME && nSuppL == pLR->nDecs) || (pHR->Type == DSD_NODE_PRIME && nSuppH == pHR->nDecs)) && pLR->S == pHR->S) || ((pLR->Type == DSD_NODE_PRIME && nSuppL == pLR->nDecs) && (pHR->Type == DSD_NODE_PRIME && nSuppH == pHR->nDecs)) ) { s_Case4CallsSpecial++; // walk through both supports and create the decomposition list composed of simple entries SuppL = pLR->S; SuppH = pHR->S; do { // determine levels levTopSuppL = cuddI(dd,SuppL->index); levTopSuppH = cuddI(dd,SuppH->index); // skip the topmost variable in both supports if ( levTopSuppL <= levTopSuppH ) { levTop = levTopSuppL; SuppL = cuddT(SuppL); } else levTop = levTopSuppH; if ( levTopSuppH <= levTopSuppL ) SuppH = cuddT(SuppH); // set the new decomposition entry pThis->pDecs[ nEntries++ ] = pDsdMan->pInputs[ dd->invperm[levTop] ]; } while ( SuppL != b1 || SuppH != b1 ); } else { // compare two different decomposition lists SuppL_init = pLR->S; SuppH_init = pHR->S; // start references (because these supports will change) SuppL = pLR->S; Cudd_Ref( SuppL ); SuppH = pHR->S; Cudd_Ref( SuppH ); while ( SuppL != b1 || SuppH != b1 ) { // determine the top level in cofactors and // whether they have the same top level int TopLevL = cuddI(dd,SuppL->index); int TopLevH = cuddI(dd,SuppH->index); int TopLevel = TopLevH; int fEqualLevel = 0; DdNode * bVarTop; DdNode * bSuppSubract; if ( TopLevL < TopLevH ) { pHigher = pLR; pLower = pHR; TopLevel = TopLevL; } else if ( TopLevL > TopLevH ) { pHigher = pHR; pLower = pLR; } else fEqualLevel = 1; assert( TopLevel != CUDD_CONST_INDEX ); // find the currently top variable in the decomposition lists bVarTop = dd->vars[dd->invperm[TopLevel]]; if ( !fEqualLevel ) { // find the lower support DdNode * bSuppLower = (TopLevL < TopLevH)? SuppH_init: SuppL_init; // find the first component in pHigher // whose support does not overlap with supp(Lower) // and remember the previous component int fPolarity; Dsd_Node_t * pPrev = NULL; // the pointer to the component proceeding pCur Dsd_Node_t * pCur = pHigher; // the first component not contained in supp(Lower) while ( Extra_bddSuppOverlapping( dd, pCur->S, bSuppLower ) ) { // get the next component pPrev = pCur; pCur = dsdKernelFindContainingComponent( pDsdMan, pCur, bVarTop, &fPolarity ); }; // look for the possibility to subtract more than one component if ( pPrev == NULL || pPrev->Type == DSD_NODE_PRIME ) { // if there is no previous component, or if the previous component is PRIME // there is no way to subtract more than one component // add the new decomposition entry (it is already regular) pThis->pDecs[ nEntries++ ] = pCur; // assign the support to be subtracted from both components bSuppSubract = pCur->S; } else // all other types { // go through the decomposition list of pPrev and find components // whose support does not overlap with supp(Lower) Dsd_Node_t ** pNonOverlap = ALLOC( Dsd_Node_t *, dd->size ); int i, nNonOverlap = 0; for ( i = 0; i < pPrev->nDecs; i++ ) { pTemp = Dsd_Regular( pPrev->pDecs[i] ); if ( !Extra_bddSuppOverlapping( dd, pTemp->S, bSuppLower ) ) pNonOverlap[ nNonOverlap++ ] = pPrev->pDecs[i]; } assert( nNonOverlap > 0 ); if ( nNonOverlap == 1 ) { // one one component was found, which is the original one assert( Dsd_Regular(pNonOverlap[0]) == pCur); // add the new decomposition entry pThis->pDecs[ nEntries++ ] = pCur; // assign the support to be subtracted from both components bSuppSubract = pCur->S; } else // more than one components was found { // find the OR (EXOR) of the non-overlapping components DdNode * bCommF; dsdKernelComputeSumOfComponents( pDsdMan, pNonOverlap, nNonOverlap, &bCommF, NULL, (int)(pPrev->Type==DSD_NODE_EXOR) ); Cudd_Ref( bCommF ); // create a new gated pDENew = dsdKernelDecompose_rec( pDsdMan, bCommF ); Cudd_RecursiveDeref(dd, bCommF); // make it regular... it must be regular already assert( !Dsd_IsComplement(pDENew) ); // add the new decomposition entry pThis->pDecs[ nEntries++ ] = pDENew; // assign the support to be subtracted from both components bSuppSubract = pDENew->S; } free( pNonOverlap ); } // subtract its support from the support of upper component if ( TopLevL < TopLevH ) { SuppL = Cudd_bddExistAbstract( dd, bTemp = SuppL, bSuppSubract ); Cudd_Ref( SuppL ); Cudd_RecursiveDeref(dd, bTemp); } else { SuppH = Cudd_bddExistAbstract( dd, bTemp = SuppH, bSuppSubract ); Cudd_Ref( SuppH ); Cudd_RecursiveDeref(dd, bTemp); } } // end of if ( !fEqualLevel ) else // if ( fEqualLevel ) -- they have the same top level var { Dsd_Node_t ** pMarkedLeft = ALLOC( Dsd_Node_t *, dd->size ); // the pointers to the marked blocks char * pMarkedPols = ALLOC( char, dd->size ); // polarities of the marked blocks int nMarkedLeft = 0; int fPolarity = 0; Dsd_Node_t * pTempL = pLR; int fPolarityCurH = 0; Dsd_Node_t * pPrevH = NULL, * pCurH = pHR; int fPolarityCurL = 0; Dsd_Node_t * pPrevL = NULL, * pCurL = pLR; // = pMarkedLeft[0]; int index = 1; // set the new mark s_Mark++; // go over the dec list of pL, mark all components that contain the given variable assert( Extra_bddSuppContainVar( dd, pLR->S, bVarTop ) ); assert( Extra_bddSuppContainVar( dd, pHR->S, bVarTop ) ); do { pTempL->Mark = s_Mark; pMarkedLeft[ nMarkedLeft ] = pTempL; pMarkedPols[ nMarkedLeft ] = fPolarity; nMarkedLeft++; } while ( pTempL = dsdKernelFindContainingComponent( pDsdMan, pTempL, bVarTop, &fPolarity ) ); // go over the dec list of pH, and find the component that is marked and the previos one // (such component always exists, because they have common variables) while ( pCurH->Mark != s_Mark ) { pPrevH = pCurH; pCurH = dsdKernelFindContainingComponent( pDsdMan, pCurH, bVarTop, &fPolarityCurH ); assert( pCurH ); } // go through the first list once again and find // the component proceeding the one marked found in the second list while ( pCurL != pCurH ) { pPrevL = pCurL; pCurL = pMarkedLeft[index]; fPolarityCurL = pMarkedPols[index]; index++; } // look for the possibility to subtract more than one component if ( !pPrevL || !pPrevH || pPrevL->Type != pPrevH->Type || pPrevL->Type == DSD_NODE_PRIME || fPolarityCurL != fPolarityCurH ) { // there is no way to extract more than one pThis->pDecs[ nEntries++ ] = pCurH; // assign the support to be subtracted from both components bSuppSubract = pCurH->S; } else { // find the equal components in two decomposition lists Dsd_Node_t ** pCommon, * pLastDiffL = NULL, * pLastDiffH = NULL; int nCommon = dsdKernelFindCommonComponents( pDsdMan, pPrevL, pPrevH, &pCommon, &pLastDiffL, &pLastDiffH ); if ( nCommon == 0 || nCommon == 1 ) { // one one component was found, which is the original one // assert( Dsd_Regular(pCommon[0]) == pCurL); // add the new decomposition entry pThis->pDecs[ nEntries++ ] = pCurL; // assign the support to be subtracted from both components bSuppSubract = pCurL->S; } else // more than one components was found { // find the OR (EXOR) of the non-overlapping components DdNode * bCommF; dsdKernelComputeSumOfComponents( pDsdMan, pCommon, nCommon, &bCommF, NULL, (int)(pPrevL->Type==DSD_NODE_EXOR) ); Cudd_Ref( bCommF ); pDENew = dsdKernelDecompose_rec( pDsdMan, bCommF ); assert( !Dsd_IsComplement(pDENew) ); // cannot be complemented because of construction Cudd_RecursiveDeref( dd, bCommF ); // add the new decomposition entry pThis->pDecs[ nEntries++ ] = pDENew; // assign the support to be subtracted from both components bSuppSubract = pDENew->S; } } SuppL = Cudd_bddExistAbstract( dd, bTemp = SuppL, bSuppSubract ), Cudd_Ref( SuppL ); Cudd_RecursiveDeref(dd, bTemp); SuppH = Cudd_bddExistAbstract( dd, bTemp = SuppH, bSuppSubract ), Cudd_Ref( SuppH ); Cudd_RecursiveDeref(dd, bTemp); free( pMarkedLeft ); free( pMarkedPols ); } // end of if ( fEqualLevel ) } // end of decomposition list comparison Cudd_RecursiveDeref( dd, SuppL ); Cudd_RecursiveDeref( dd, SuppH ); } // check that the estimation of the number of entries was okay assert( nEntries <= nEntriesMax ); // if ( nEntries != Extra_bddSuppSize(dd, bSuppNew) ) // s_Case5++; // update the number of entries in the new decomposition list pThis->nDecs = nEntries; } //} EXIT: { // if the component created is complemented, it represents a function without complement // therefore, as it is, without complement, it should recieve the complemented function Dsd_Node_t * pThisR = Dsd_Regular( pThis ); assert( pThisR->G == NULL ); assert( pThisR->S == NULL ); if ( pThisR == pThis ) // set regular function pThisR->G = bF; else // set complemented function pThisR->G = Cudd_Not(bF); Cudd_Ref(bF); // reference the function in the component assert( bSuppNew ); pThisR->S = bSuppNew; // takes the reference from the new support if ( st_insert( pDsdMan->Table, (char*)bF, (char*)pThis ) ) { assert( 0 ); } s_CacheEntries++; #if 0 if ( dsdKernelVerifyDecomposition(dd, pThis) == 0 ) { // write the function, for which verification does not work cout << endl << "Internal verification failed!"" ); // create the variable mask static int s_pVarMask[MAXINPUTS]; int nInputCounter = 0; Cudd_SupportArray( dd, bF, s_pVarMask ); int k; for ( k = 0; k < dd->size; k++ ) if ( s_pVarMask[k] ) nInputCounter++; cout << endl << "The problem function is "" ); DdNode * zNewFunc = Cudd_zddIsopCover( dd, bF, bF ); Cudd_Ref( zNewFunc ); cuddWriteFunctionSop( stdout, dd, zNewFunc, -1, dd->size, "1", s_pVarMask ); Cudd_RecursiveDerefZdd( dd, zNewFunc ); } #endif } Depth--; return Dsd_NotCond( pThis, fCompF ); } //////////////////////////////////////////////////////////////////////// /// OTHER FUNCTIONS /// //////////////////////////////////////////////////////////////////////// /**Function************************************************************* Synopsis [Finds the corresponding decomposition entry.] Description [This function returns the non-complemented pointer to the DecEntry of that component which contains the given variable in its support, or NULL if no such component exists] SideEffects [] SeeAlso [] ***********************************************************************/ Dsd_Node_t * dsdKernelFindContainingComponent( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pWhere, DdNode * Var, int * fPolarity ) { Dsd_Node_t * pTemp; int i; // assert( !Dsd_IsComplement( pWhere ) ); // assert( Extra_bddSuppContainVar( pDsdMan->dd, pWhere->S, Var ) ); if ( pWhere->nDecs == 1 ) return NULL; for( i = 0; i < pWhere->nDecs; i++ ) { pTemp = Dsd_Regular( pWhere->pDecs[i] ); if ( Extra_bddSuppContainVar( pDsdMan->dd, pTemp->S, Var ) ) { *fPolarity = (int)( pTemp != pWhere->pDecs[i] ); return pTemp; } } assert( 0 ); return NULL; } /**Function************************************************************* Synopsis [Find the common decomposition components.] Description [This function determines the common components. It counts the number of common components in the decomposition lists of pL and pH and returns their number and the lists of common components. It assumes that pL and pH are regular pointers. It retuns also the pointers to the last different components encountered in pL and pH.] SideEffects [] SeeAlso [] ***********************************************************************/ int dsdKernelFindCommonComponents( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pL, Dsd_Node_t * pH, Dsd_Node_t *** pCommon, Dsd_Node_t ** pLastDiffL, Dsd_Node_t ** pLastDiffH ) { Dsd_Node_t ** Common = ALLOC( Dsd_Node_t *, pDsdMan->dd->size ); int nCommon = 0; // pointers to the current decomposition entries Dsd_Node_t * pLcur; Dsd_Node_t * pHcur; // the pointers to their supports DdNode * bSLcur; DdNode * bSHcur; // the top variable in the supports int TopVar; // the indices running through the components int iCurL = 0; int iCurH = 0; while ( iCurL < pL->nDecs && iCurH < pH->nDecs ) { // both did not run out pLcur = Dsd_Regular(pL->pDecs[iCurL]); pHcur = Dsd_Regular(pH->pDecs[iCurH]); bSLcur = pLcur->S; bSHcur = pHcur->S; // find out what component is higher in the BDD if ( pDsdMan->dd->perm[bSLcur->index] < pDsdMan->dd->perm[bSHcur->index] ) TopVar = bSLcur->index; else TopVar = bSHcur->index; if ( TopVar == bSLcur->index && TopVar == bSHcur->index ) { // the components may be equal - should match exactly! if ( pL->pDecs[iCurL] == pH->pDecs[iCurH] ) Common[nCommon++] = pL->pDecs[iCurL]; else { *pLastDiffL = pL->pDecs[iCurL]; *pLastDiffH = pH->pDecs[iCurH]; } // skip both iCurL++; iCurH++; } else if ( TopVar == bSLcur->index ) { // the components cannot be equal // skip the top-most one *pLastDiffL = pL->pDecs[iCurL++]; } else // if ( TopVar == bSHcur->index ) { // the components cannot be equal // skip the top-most one *pLastDiffH = pH->pDecs[iCurH++]; } } // if one of the lists still has components, write the first one down if ( iCurL < pL->nDecs ) *pLastDiffL = pL->pDecs[iCurL]; if ( iCurH < pH->nDecs ) *pLastDiffH = pH->pDecs[iCurH]; // return the pointer to the array *pCommon = Common; // return the number of common components free( Common ); return nCommon; } /**Function************************************************************* Synopsis [Computes the sum (OR or EXOR) of the functions of the components.] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ void dsdKernelComputeSumOfComponents( Dsd_Manager_t * pDsdMan, Dsd_Node_t ** pCommon, int nCommon, DdNode ** pCompF, DdNode ** pCompS, int fExor ) { DdManager * dd = pDsdMan->dd; DdNode * bF, * bS, * bFadd, * bTemp; Dsd_Node_t * pDE, * pDER; int i; // start the function bF = b0; Cudd_Ref( bF ); // start the support if ( pCompS ) bS = b1, Cudd_Ref( bS ); assert( nCommon > 0 ); for ( i = 0; i < nCommon; i++ ) { pDE = pCommon[i]; pDER = Dsd_Regular( pDE ); bFadd = (pDE != pDER)? Cudd_Not(pDER->G): pDER->G; // add to the function if ( fExor ) bF = Cudd_bddXor( dd, bTemp = bF, bFadd ); else bF = Cudd_bddOr( dd, bTemp = bF, bFadd ); Cudd_Ref( bF ); Cudd_RecursiveDeref( dd, bTemp ); if ( pCompS ) { // add to the support bS = Cudd_bddAnd( dd, bTemp = bS, pDER->S ); Cudd_Ref( bS ); Cudd_RecursiveDeref( dd, bTemp ); } } // return the function Cudd_Deref( bF ); *pCompF = bF; // return the support if ( pCompS ) Cudd_Deref( bS ), *pCompS = bS; } /**Function************************************************************* Synopsis [Checks support containment of the decomposition components.] Description [This function returns 1 if support of one component is contained in that of another. In this case, pLarge (pSmall) is assigned to point to the larger (smaller) support. If the supports are identical return 0, and does not assign the components.] ] SideEffects [] SeeAlso [] ***********************************************************************/ int dsdKernelCheckContainment( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pL, Dsd_Node_t * pH, Dsd_Node_t ** pLarge, Dsd_Node_t ** pSmall ) { DdManager * dd = pDsdMan->dd; DdNode * bSuppLarge, * bSuppSmall; int RetValue; RetValue = Extra_bddSuppCheckContainment( dd, pL->S, pH->S, &bSuppLarge, &bSuppSmall ); if ( RetValue == 0 ) return 0; if ( pH->S == bSuppLarge ) { *pLarge = pH; *pSmall = pL; } else // if ( pL->S == bSuppLarge ) { *pLarge = pL; *pSmall = pH; } return 1; } /**Function************************************************************* Synopsis [Copies the list of components plus one.] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ void dsdKernelCopyListPlusOne( Dsd_Node_t * p, Dsd_Node_t * First, Dsd_Node_t ** ppList, int nListSize ) { int i; assert( nListSize+1 == p->nDecs ); p->pDecs[0] = First; for( i = 0; i < nListSize; i++ ) p->pDecs[i+1] = ppList[i]; } /**Function************************************************************* Synopsis [Copies the list of components plus one, and skips one.] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ void dsdKernelCopyListPlusOneMinusOne( Dsd_Node_t * p, Dsd_Node_t * First, Dsd_Node_t ** ppList, int nListSize, int iSkipped ) { int i, Counter; assert( nListSize == p->nDecs ); p->pDecs[0] = First; for( i = 0, Counter = 1; i < nListSize; i++ ) if ( i != iSkipped ) p->pDecs[Counter++] = ppList[i]; } /**Function************************************************************* Synopsis [Debugging procedure to compute the functionality of the decomposed structure.] Description [] SideEffects [] SeeAlso [] ***********************************************************************/ int dsdKernelVerifyDecomposition( Dsd_Manager_t * pDsdMan, Dsd_Node_t * pDE ) { DdManager * dd = pDsdMan->dd; Dsd_Node_t * pR = Dsd_Regular(pDE); int fCompP = (int)( pDE != pR ); int RetValue; DdNode * bRes; if ( pR->Type == DSD_NODE_CONST1 ) bRes = b1; else if ( pR->Type == DSD_NODE_BUF ) bRes = pR->G; else if ( pR->Type == DSD_NODE_OR || pR->Type == DSD_NODE_EXOR ) dsdKernelComputeSumOfComponents( pDsdMan, pR->pDecs, pR->nDecs, &bRes, NULL, (int)(pR->Type == DSD_NODE_EXOR) ); else if ( pR->Type == DSD_NODE_PRIME ) { int i; DdNode ** bGVars = ALLOC( DdNode *, dd->size ); // transform the function of this block, so that it depended on inputs // corresponding to the formal inputs DdNode * bNewFunc = Dsd_TreeGetPrimeFunctionOld( dd, pR, 1 ); Cudd_Ref( bNewFunc ); // compose this function with the inputs // create the elementary permutation for ( i = 0; i < dd->size; i++ ) bGVars[i] = dd->vars[i]; // assign functions to be composed for ( i = 0; i < pR->nDecs; i++ ) bGVars[dd->invperm[i]] = pR->pDecs[i]->G; // perform the composition bRes = Cudd_bddVectorCompose( dd, bNewFunc, bGVars ); Cudd_Ref( bRes ); Cudd_RecursiveDeref( dd, bNewFunc ); ///////////////////////////////////////////////////////// RetValue = (int)( bRes == pR->G );//|| bRes == Cudd_Not(pR->G) ); ///////////////////////////////////////////////////////// Cudd_Deref( bRes ); free( bGVars ); } else { assert(0); } Cudd_Ref( bRes ); RetValue = (int)( bRes == pR->G );//|| bRes == Cudd_Not(pR->G) ); Cudd_RecursiveDeref( dd, bRes ); return RetValue; } //////////////////////////////////////////////////////////////////////// /// END OF FILE /// ////////////////////////////////////////////////////////////////////////