/**CFile*********************************************************************** FileName [cuddMatMult.c] PackageName [cudd] Synopsis [Matrix multiplication functions.] Description [External procedures included in this module: Static procedures included in this module: ] Author [Fabio Somenzi] Copyright [Copyright (c) 1995-2004, Regents of the University of Colorado All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of the University of Colorado nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.] ******************************************************************************/ #include "util.h" #include "cuddInt.h" /*---------------------------------------------------------------------------*/ /* Constant declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Stucture declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Type declarations */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Variable declarations */ /*---------------------------------------------------------------------------*/ #ifndef lint static char rcsid[] DD_UNUSED = "$Id: cuddMatMult.c,v 1.17 2004/08/13 18:04:50 fabio Exp $"; #endif /*---------------------------------------------------------------------------*/ /* Macro declarations */ /*---------------------------------------------------------------------------*/ /**AutomaticStart*************************************************************/ /*---------------------------------------------------------------------------*/ /* Static function prototypes */ /*---------------------------------------------------------------------------*/ static DdNode * addMMRecur (DdManager *dd, DdNode *A, DdNode *B, int topP, int *vars); static DdNode * addTriangleRecur (DdManager *dd, DdNode *f, DdNode *g, int *vars, DdNode *cube); static DdNode * cuddAddOuterSumRecur (DdManager *dd, DdNode *M, DdNode *r, DdNode *c); /**AutomaticEnd***************************************************************/ /*---------------------------------------------------------------------------*/ /* Definition of exported functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Calculates the product of two matrices represented as ADDs.] Description [Calculates the product of two matrices, A and B, represented as ADDs. This procedure implements the quasiring multiplication algorithm. A is assumed to depend on variables x (rows) and z (columns). B is assumed to depend on variables z (rows) and y (columns). The product of A and B then depends on x (rows) and y (columns). Only the z variables have to be explicitly identified; they are the "summation" variables. Returns a pointer to the result if successful; NULL otherwise.] SideEffects [None] SeeAlso [Cudd_addTimesPlus Cudd_addTriangle Cudd_bddAndAbstract] ******************************************************************************/ DdNode * Cudd_addMatrixMultiply( DdManager * dd, DdNode * A, DdNode * B, DdNode ** z, int nz) { int i, nvars, *vars; DdNode *res; /* Array vars says what variables are "summation" variables. */ nvars = dd->size; vars = ALLOC(int,nvars); if (vars == NULL) { dd->errorCode = CUDD_MEMORY_OUT; return(NULL); } for (i = 0; i < nvars; i++) { vars[i] = 0; } for (i = 0; i < nz; i++) { vars[z[i]->index] = 1; } do { dd->reordered = 0; res = addMMRecur(dd,A,B,-1,vars); } while (dd->reordered == 1); FREE(vars); return(res); } /* end of Cudd_addMatrixMultiply */ /**Function******************************************************************** Synopsis [Calculates the product of two matrices represented as ADDs.] Description [Calculates the product of two matrices, A and B, represented as ADDs, using the CMU matrix by matrix multiplication procedure by Clarke et al.. Matrix A has x's as row variables and z's as column variables, while matrix B has z's as row variables and y's as column variables. Returns the pointer to the result if successful; NULL otherwise. The resulting matrix has x's as row variables and y's as column variables.] SideEffects [None] SeeAlso [Cudd_addMatrixMultiply] ******************************************************************************/ DdNode * Cudd_addTimesPlus( DdManager * dd, DdNode * A, DdNode * B, DdNode ** z, int nz) { DdNode *w, *cube, *tmp, *res; int i; tmp = Cudd_addApply(dd,Cudd_addTimes,A,B); if (tmp == NULL) return(NULL); Cudd_Ref(tmp); Cudd_Ref(cube = DD_ONE(dd)); for (i = nz-1; i >= 0; i--) { w = Cudd_addIte(dd,z[i],cube,DD_ZERO(dd)); if (w == NULL) { Cudd_RecursiveDeref(dd,tmp); return(NULL); } Cudd_Ref(w); Cudd_RecursiveDeref(dd,cube); cube = w; } res = Cudd_addExistAbstract(dd,tmp,cube); if (res == NULL) { Cudd_RecursiveDeref(dd,tmp); Cudd_RecursiveDeref(dd,cube); return(NULL); } Cudd_Ref(res); Cudd_RecursiveDeref(dd,cube); Cudd_RecursiveDeref(dd,tmp); Cudd_Deref(res); return(res); } /* end of Cudd_addTimesPlus */ /**Function******************************************************************** Synopsis [Performs the triangulation step for the shortest path computation.] Description [Implements the semiring multiplication algorithm used in the triangulation step for the shortest path computation. f is assumed to depend on variables x (rows) and z (columns). g is assumed to depend on variables z (rows) and y (columns). The product of f and g then depends on x (rows) and y (columns). Only the z variables have to be explicitly identified; they are the "abstraction" variables. Returns a pointer to the result if successful; NULL otherwise. ] SideEffects [None] SeeAlso [Cudd_addMatrixMultiply Cudd_bddAndAbstract] ******************************************************************************/ DdNode * Cudd_addTriangle( DdManager * dd, DdNode * f, DdNode * g, DdNode ** z, int nz) { int i, nvars, *vars; DdNode *res, *cube; nvars = dd->size; vars = ALLOC(int, nvars); if (vars == NULL) { dd->errorCode = CUDD_MEMORY_OUT; return(NULL); } for (i = 0; i < nvars; i++) vars[i] = -1; for (i = 0; i < nz; i++) vars[z[i]->index] = i; cube = Cudd_addComputeCube(dd, z, NULL, nz); if (cube == NULL) { FREE(vars); return(NULL); } cuddRef(cube); do { dd->reordered = 0; res = addTriangleRecur(dd, f, g, vars, cube); } while (dd->reordered == 1); if (res != NULL) cuddRef(res); Cudd_RecursiveDeref(dd,cube); if (res != NULL) cuddDeref(res); FREE(vars); return(res); } /* end of Cudd_addTriangle */ /**Function******************************************************************** Synopsis [Takes the minimum of a matrix and the outer sum of two vectors.] Description [Takes the pointwise minimum of a matrix and the outer sum of two vectors. This procedure is used in the Floyd-Warshall all-pair shortest path algorithm. Returns a pointer to the result if successful; NULL otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ DdNode * Cudd_addOuterSum( DdManager *dd, DdNode *M, DdNode *r, DdNode *c) { DdNode *res; do { dd->reordered = 0; res = cuddAddOuterSumRecur(dd, M, r, c); } while (dd->reordered == 1); return(res); } /* end of Cudd_addOuterSum */ /*---------------------------------------------------------------------------*/ /* Definition of internal functions */ /*---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------*/ /* Definition of static functions */ /*---------------------------------------------------------------------------*/ /**Function******************************************************************** Synopsis [Performs the recursive step of Cudd_addMatrixMultiply.] Description [Performs the recursive step of Cudd_addMatrixMultiply. Returns a pointer to the result if successful; NULL otherwise.] SideEffects [None] ******************************************************************************/ static DdNode * addMMRecur( DdManager * dd, DdNode * A, DdNode * B, int topP, int * vars) { DdNode *zero, *At, /* positive cofactor of first operand */ *Ae, /* negative cofactor of first operand */ *Bt, /* positive cofactor of second operand */ *Be, /* negative cofactor of second operand */ *t, /* positive cofactor of result */ *e, /* negative cofactor of result */ *scaled, /* scaled result */ *add_scale, /* ADD representing the scaling factor */ *res; int i; /* loop index */ double scale; /* scaling factor */ int index; /* index of the top variable */ CUDD_VALUE_TYPE value; unsigned int topA, topB, topV; DD_CTFP cacheOp; statLine(dd); zero = DD_ZERO(dd); if (A == zero || B == zero) { return(zero); } if (cuddIsConstant(A) && cuddIsConstant(B)) { /* Compute the scaling factor. It is 2^k, where k is the ** number of summation variables below the current variable. ** Indeed, these constants represent blocks of 2^k identical ** constant values in both A and B. */ value = cuddV(A) * cuddV(B); for (i = 0; i < dd->size; i++) { if (vars[i]) { if (dd->perm[i] > topP) { value *= (CUDD_VALUE_TYPE) 2; } } } res = cuddUniqueConst(dd, value); return(res); } /* Standardize to increase cache efficiency. Clearly, A*B != B*A ** in matrix multiplication. However, which matrix is which is ** determined by the variables appearing in the ADDs and not by ** which one is passed as first argument. */ if (A > B) { DdNode *tmp = A; A = B; B = tmp; } topA = cuddI(dd,A->index); topB = cuddI(dd,B->index); topV = ddMin(topA,topB); cacheOp = (DD_CTFP) addMMRecur; res = cuddCacheLookup2(dd,cacheOp,A,B); if (res != NULL) { /* If the result is 0, there is no need to normalize. ** Otherwise we count the number of z variables between ** the current depth and the top of the ADDs. These are ** the missing variables that determine the size of the ** constant blocks. */ if (res == zero) return(res); scale = 1.0; for (i = 0; i < dd->size; i++) { if (vars[i]) { if (dd->perm[i] > topP && (unsigned) dd->perm[i] < topV) { scale *= 2; } } } if (scale > 1.0) { cuddRef(res); add_scale = cuddUniqueConst(dd,(CUDD_VALUE_TYPE)scale); if (add_scale == NULL) { Cudd_RecursiveDeref(dd, res); return(NULL); } cuddRef(add_scale); scaled = cuddAddApplyRecur(dd,Cudd_addTimes,res,add_scale); if (scaled == NULL) { Cudd_RecursiveDeref(dd, add_scale); Cudd_RecursiveDeref(dd, res); return(NULL); } cuddRef(scaled); Cudd_RecursiveDeref(dd, add_scale); Cudd_RecursiveDeref(dd, res); res = scaled; cuddDeref(res); } return(res); } /* compute the cofactors */ if (topV == topA) { At = cuddT(A); Ae = cuddE(A); } else { At = Ae = A; } if (topV == topB) { Bt = cuddT(B); Be = cuddE(B); } else { Bt = Be = B; } t = addMMRecur(dd, At, Bt, (int)topV, vars); if (t == NULL) return(NULL); cuddRef(t); e = addMMRecur(dd, Ae, Be, (int)topV, vars); if (e == NULL) { Cudd_RecursiveDeref(dd, t); return(NULL); } cuddRef(e); index = dd->invperm[topV]; if (vars[index] == 0) { /* We have split on either the rows of A or the columns ** of B. We just need to connect the two subresults, ** which correspond to two submatrices of the result. */ res = (t == e) ? t : cuddUniqueInter(dd,index,t,e); if (res == NULL) { Cudd_RecursiveDeref(dd, t); Cudd_RecursiveDeref(dd, e); return(NULL); } cuddRef(res); cuddDeref(t); cuddDeref(e); } else { /* we have simultaneously split on the columns of A and ** the rows of B. The two subresults must be added. */ res = cuddAddApplyRecur(dd,Cudd_addPlus,t,e); if (res == NULL) { Cudd_RecursiveDeref(dd, t); Cudd_RecursiveDeref(dd, e); return(NULL); } cuddRef(res); Cudd_RecursiveDeref(dd, t); Cudd_RecursiveDeref(dd, e); } cuddCacheInsert2(dd,cacheOp,A,B,res); /* We have computed (and stored in the computed table) a minimal ** result; that is, a result that assumes no summation variables ** between the current depth of the recursion and its top ** variable. We now take into account the z variables by properly ** scaling the result. */ if (res != zero) { scale = 1.0; for (i = 0; i < dd->size; i++) { if (vars[i]) { if (dd->perm[i] > topP && (unsigned) dd->perm[i] < topV) { scale *= 2; } } } if (scale > 1.0) { add_scale = cuddUniqueConst(dd,(CUDD_VALUE_TYPE)scale); if (add_scale == NULL) { Cudd_RecursiveDeref(dd, res); return(NULL); } cuddRef(add_scale); scaled = cuddAddApplyRecur(dd,Cudd_addTimes,res,add_scale); if (scaled == NULL) { Cudd_RecursiveDeref(dd, res); Cudd_RecursiveDeref(dd, add_scale); return(NULL); } cuddRef(scaled); Cudd_RecursiveDeref(dd, add_scale); Cudd_RecursiveDeref(dd, res); res = scaled; } } cuddDeref(res); return(res); } /* end of addMMRecur */ /**Function******************************************************************** Synopsis [Performs the recursive step of Cudd_addTriangle.] Description [Performs the recursive step of Cudd_addTriangle. Returns a pointer to the result if successful; NULL otherwise.] SideEffects [None] ******************************************************************************/ static DdNode * addTriangleRecur( DdManager * dd, DdNode * f, DdNode * g, int * vars, DdNode *cube) { DdNode *fv, *fvn, *gv, *gvn, *t, *e, *res; CUDD_VALUE_TYPE value; int top, topf, topg, index; statLine(dd); if (f == DD_PLUS_INFINITY(dd) || g == DD_PLUS_INFINITY(dd)) { return(DD_PLUS_INFINITY(dd)); } if (cuddIsConstant(f) && cuddIsConstant(g)) { value = cuddV(f) + cuddV(g); res = cuddUniqueConst(dd, value); return(res); } if (f < g) { DdNode *tmp = f; f = g; g = tmp; } if (f->ref != 1 || g->ref != 1) { res = cuddCacheLookup(dd, DD_ADD_TRIANGLE_TAG, f, g, cube); if (res != NULL) { return(res); } } topf = cuddI(dd,f->index); topg = cuddI(dd,g->index); top = ddMin(topf,topg); if (top == topf) {fv = cuddT(f); fvn = cuddE(f);} else {fv = fvn = f;} if (top == topg) {gv = cuddT(g); gvn = cuddE(g);} else {gv = gvn = g;} t = addTriangleRecur(dd, fv, gv, vars, cube); if (t == NULL) return(NULL); cuddRef(t); e = addTriangleRecur(dd, fvn, gvn, vars, cube); if (e == NULL) { Cudd_RecursiveDeref(dd, t); return(NULL); } cuddRef(e); index = dd->invperm[top]; if (vars[index] < 0) { res = (t == e) ? t : cuddUniqueInter(dd,index,t,e); if (res == NULL) { Cudd_RecursiveDeref(dd, t); Cudd_RecursiveDeref(dd, e); return(NULL); } cuddDeref(t); cuddDeref(e); } else { res = cuddAddApplyRecur(dd,Cudd_addMinimum,t,e); if (res == NULL) { Cudd_RecursiveDeref(dd, t); Cudd_RecursiveDeref(dd, e); return(NULL); } cuddRef(res); Cudd_RecursiveDeref(dd, t); Cudd_RecursiveDeref(dd, e); cuddDeref(res); } if (f->ref != 1 || g->ref != 1) { cuddCacheInsert(dd, DD_ADD_TRIANGLE_TAG, f, g, cube, res); } return(res); } /* end of addTriangleRecur */ /**Function******************************************************************** Synopsis [Performs the recursive step of Cudd_addOuterSum.] Description [Performs the recursive step of Cudd_addOuterSum. Returns a pointer to the result if successful; NULL otherwise.] SideEffects [None] SeeAlso [] ******************************************************************************/ static DdNode * cuddAddOuterSumRecur( DdManager *dd, DdNode *M, DdNode *r, DdNode *c) { DdNode *P, *R, *Mt, *Me, *rt, *re, *ct, *ce, *Rt, *Re; int topM, topc, topr; int v, index; statLine(dd); /* Check special cases. */ if (r == DD_PLUS_INFINITY(dd) || c == DD_PLUS_INFINITY(dd)) return(M); if (cuddIsConstant(c) && cuddIsConstant(r)) { R = cuddUniqueConst(dd,Cudd_V(c)+Cudd_V(r)); cuddRef(R); if (cuddIsConstant(M)) { if (cuddV(R) <= cuddV(M)) { cuddDeref(R); return(R); } else { Cudd_RecursiveDeref(dd,R); return(M); } } else { P = Cudd_addApply(dd,Cudd_addMinimum,R,M); cuddRef(P); Cudd_RecursiveDeref(dd,R); cuddDeref(P); return(P); } } /* Check the cache. */ R = cuddCacheLookup(dd,DD_ADD_OUT_SUM_TAG,M,r,c); if (R != NULL) return(R); topM = cuddI(dd,M->index); topr = cuddI(dd,r->index); topc = cuddI(dd,c->index); v = ddMin(topM,ddMin(topr,topc)); /* Compute cofactors. */ if (topM == v) { Mt = cuddT(M); Me = cuddE(M); } else { Mt = Me = M; } if (topr == v) { rt = cuddT(r); re = cuddE(r); } else { rt = re = r; } if (topc == v) { ct = cuddT(c); ce = cuddE(c); } else { ct = ce = c; } /* Recursively solve. */ Rt = cuddAddOuterSumRecur(dd,Mt,rt,ct); if (Rt == NULL) return(NULL); cuddRef(Rt); Re = cuddAddOuterSumRecur(dd,Me,re,ce); if (Re == NULL) { Cudd_RecursiveDeref(dd, Rt); return(NULL); } cuddRef(Re); index = dd->invperm[v]; R = (Rt == Re) ? Rt : cuddUniqueInter(dd,index,Rt,Re); if (R == NULL) { Cudd_RecursiveDeref(dd, Rt); Cudd_RecursiveDeref(dd, Re); return(NULL); } cuddDeref(Rt); cuddDeref(Re); /* Store the result in the cache. */ cuddCacheInsert(dd,DD_ADD_OUT_SUM_TAG,M,r,c,R); return(R); } /* end of cuddAddOuterSumRecur */