/***************************************************************************** Copyright (C) 2008 University of Southern California Copyright (C) 2009-2010 University of Utah All Rights Reserved. Purpose: Useful tools involving Omega manipulation. Notes: History: 01/2006 Created by Chun Chen. 03/2009 Upgrade Omega's interaction with compiler to IR_Code, by Chun Chen. *****************************************************************************/ #include // #include #include "omegatools.hh" #include "ir_code.hh" #include "chill_error.hh" using namespace omega; namespace { struct DependenceLevel { Relation r; int level; int dir; // direction upto current level: // -1:negative, 0: undetermined, 1: postive std::vector lbounds; std::vector ubounds; DependenceLevel(const Relation &_r, int _dims): r(_r), level(0), dir(0), lbounds(_dims), ubounds(_dims) {} }; } std::string tmp_e() { static int counter = 1; return std::string("e")+to_string(counter++); } //----------------------------------------------------------------------------- // Convert expression tree to omega relation. "destroy" means shallow // deallocation of "repr", not freeing the actual code inside. // ----------------------------------------------------------------------------- void exp2formula(IR_Code *ir, Relation &r, F_And *f_root, std::vector &freevars, CG_outputRepr *repr, Variable_ID lhs, char side, IR_CONDITION_TYPE rel, bool destroy) { // void exp2formula(IR_Code *ir, Relation &r, F_And *f_root, std::vector &freevars, // CG_outputRepr *repr, Variable_ID lhs, char side, char rel, bool destroy) { switch (ir->QueryExpOperation(repr)) { case IR_OP_CONSTANT: { std::vector v = ir->QueryExpOperand(repr); IR_ConstantRef *ref = static_cast(ir->Repr2Ref(v[0])); if (!ref->is_integer()) throw ir_exp_error("non-integer constant coefficient"); coef_t c = ref->integer(); if (rel == IR_COND_GE || rel == IR_COND_GT) { GEQ_Handle h = f_root->add_GEQ(); h.update_coef(lhs, 1); if (rel == IR_COND_GE) h.update_const(-c); else h.update_const(-c-1); } else if (rel == IR_COND_LE || rel == IR_COND_LT) { GEQ_Handle h = f_root->add_GEQ(); h.update_coef(lhs, -1); if (rel == IR_COND_LE) h.update_const(c); else h.update_const(c-1); } else if (rel == IR_COND_EQ) { EQ_Handle h = f_root->add_EQ(); h.update_coef(lhs, 1); h.update_const(-c); } else throw std::invalid_argument("unsupported condition type"); delete v[0]; delete ref; if (destroy) delete repr; break; } case IR_OP_VARIABLE: { std::vector v = ir->QueryExpOperand(repr); IR_ScalarRef *ref = static_cast(ir->Repr2Ref(v[0])); std::string s = ref->name(); Variable_ID e = find_index(r, s, side); if (e == NULL) { // must be free variable Free_Var_Decl *t = NULL; for (unsigned i = 0; i < freevars.size(); i++) { std::string ss = freevars[i]->base_name(); if (s == ss) { t = freevars[i]; break; } } if (t == NULL) { t = new Free_Var_Decl(s); freevars.insert(freevars.end(), t); } e = r.get_local(t); } if (rel == IR_COND_GE || rel == IR_COND_GT) { GEQ_Handle h = f_root->add_GEQ(); h.update_coef(lhs, 1); h.update_coef(e, -1); if (rel == IR_COND_GT) h.update_const(-1); } else if (rel == IR_COND_LE || rel == IR_COND_LT) { GEQ_Handle h = f_root->add_GEQ(); h.update_coef(lhs, -1); h.update_coef(e, 1); if (rel == IR_COND_LT) h.update_const(-1); } else if (rel == IR_COND_EQ) { EQ_Handle h = f_root->add_EQ(); h.update_coef(lhs, 1); h.update_coef(e, -1); } else throw std::invalid_argument("unsupported condition type"); // delete v[0]; delete ref; if (destroy) delete repr; break; } case IR_OP_ASSIGNMENT: { std::vector v = ir->QueryExpOperand(repr); exp2formula(ir, r, f_root, freevars, v[0], lhs, side, rel, true); if (destroy) delete repr; break; } case IR_OP_PLUS: { F_Exists *f_exists = f_root->add_exists(); Variable_ID e1 = f_exists->declare(tmp_e()); Variable_ID e2 = f_exists->declare(tmp_e()); F_And *f_and = f_exists->add_and(); if (rel == IR_COND_GE || rel == IR_COND_GT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, 1); h.update_coef(e1, -1); h.update_coef(e2, -1); if (rel == IR_COND_GT) h.update_const(-1); } else if (rel == IR_COND_LE || rel == IR_COND_LT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, -1); h.update_coef(e1, 1); h.update_coef(e2, 1); if (rel == IR_COND_LT) h.update_const(-1); } else if (rel == IR_COND_EQ) { EQ_Handle h = f_and->add_EQ(); h.update_coef(lhs, 1); h.update_coef(e1, -1); h.update_coef(e2, -1); } else throw std::invalid_argument("unsupported condition type"); std::vector v = ir->QueryExpOperand(repr); exp2formula(ir, r, f_and, freevars, v[0], e1, side, IR_COND_EQ, true); exp2formula(ir, r, f_and, freevars, v[1], e2, side, IR_COND_EQ, true); if (destroy) delete repr; break; } case IR_OP_MINUS: { F_Exists *f_exists = f_root->add_exists(); Variable_ID e1 = f_exists->declare(tmp_e()); Variable_ID e2 = f_exists->declare(tmp_e()); F_And *f_and = f_exists->add_and(); if (rel == IR_COND_GE || rel == IR_COND_GT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, 1); h.update_coef(e1, -1); h.update_coef(e2, 1); if (rel == IR_COND_GT) h.update_const(-1); } else if (rel == IR_COND_LE || rel == IR_COND_LT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, -1); h.update_coef(e1, 1); h.update_coef(e2, -1); if (rel == IR_COND_LT) h.update_const(-1); } else if (rel == IR_COND_EQ) { EQ_Handle h = f_and->add_EQ(); h.update_coef(lhs, 1); h.update_coef(e1, -1); h.update_coef(e2, 1); } else throw std::invalid_argument("unsupported condition type"); std::vector v = ir->QueryExpOperand(repr); exp2formula(ir, r, f_and, freevars, v[0], e1, side, IR_COND_EQ, true); exp2formula(ir, r, f_and, freevars, v[1], e2, side, IR_COND_EQ, true); if (destroy) delete repr; break; } case IR_OP_MULTIPLY: { std::vector v = ir->QueryExpOperand(repr); coef_t coef; CG_outputRepr *term; if (ir->QueryExpOperation(v[0]) == IR_OP_CONSTANT) { IR_ConstantRef *ref = static_cast(ir->Repr2Ref(v[0])); coef = ref->integer(); delete v[0]; delete ref; term = v[1]; } else if (ir->QueryExpOperation(v[1]) == IR_OP_CONSTANT) { IR_ConstantRef *ref = static_cast(ir->Repr2Ref(v[1])); coef = ref->integer(); delete v[1]; delete ref; term = v[0]; } else throw ir_exp_error("not presburger expression"); F_Exists *f_exists = f_root->add_exists(); Variable_ID e = f_exists->declare(tmp_e()); F_And *f_and = f_exists->add_and(); if (rel == IR_COND_GE || rel == IR_COND_GT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, 1); h.update_coef(e, -coef); if (rel == IR_COND_GT) h.update_const(-1); } else if (rel == IR_COND_LE || rel == IR_COND_LT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, -1); h.update_coef(e, coef); if (rel == IR_COND_LT) h.update_const(-1); } else if (rel == IR_COND_EQ) { EQ_Handle h = f_and->add_EQ(); h.update_coef(lhs, 1); h.update_coef(e, -coef); } else throw std::invalid_argument("unsupported condition type"); exp2formula(ir, r, f_and, freevars, term, e, side, IR_COND_EQ, true); if (destroy) delete repr; break; } case IR_OP_DIVIDE: { std::vector v = ir->QueryExpOperand(repr); assert(ir->QueryExpOperation(v[1]) == IR_OP_CONSTANT); IR_ConstantRef *ref = static_cast(ir->Repr2Ref(v[1])); coef_t coef = ref->integer(); delete v[1]; delete ref; F_Exists *f_exists = f_root->add_exists(); Variable_ID e = f_exists->declare(tmp_e()); F_And *f_and = f_exists->add_and(); if (rel == IR_COND_GE || rel == IR_COND_GT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, coef); h.update_coef(e, -1); if (rel == IR_COND_GT) h.update_const(-1); } else if (rel == IR_COND_LE || rel == IR_COND_LT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, -coef); h.update_coef(e, 1); if (rel == IR_COND_LT) h.update_const(-1); } else if (rel == IR_COND_EQ) { EQ_Handle h = f_and->add_EQ(); h.update_coef(lhs, coef); h.update_coef(e, -1); } else throw std::invalid_argument("unsupported condition type"); exp2formula(ir, r, f_and, freevars, v[0], e, side, IR_COND_EQ, true); if (destroy) delete repr; break; } case IR_OP_POSITIVE: { std::vector v = ir->QueryExpOperand(repr); exp2formula(ir, r, f_root, freevars, v[0], lhs, side, rel, true); if (destroy) delete repr; break; } case IR_OP_NEGATIVE: { std::vector v = ir->QueryExpOperand(repr); F_Exists *f_exists = f_root->add_exists(); Variable_ID e = f_exists->declare(tmp_e()); F_And *f_and = f_exists->add_and(); if (rel == IR_COND_GE || rel == IR_COND_GT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, 1); h.update_coef(e, 1); if (rel == IR_COND_GT) h.update_const(-1); } else if (rel == IR_COND_LE || rel == IR_COND_LT) { GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, -1); h.update_coef(e, -1); if (rel == IR_COND_LT) h.update_const(-1); } else if (rel == IR_COND_EQ) { EQ_Handle h = f_and->add_EQ(); h.update_coef(lhs, 1); h.update_coef(e, 1); } else throw std::invalid_argument("unsupported condition type"); exp2formula(ir, r, f_and, freevars, v[0], e, side, IR_COND_EQ, true); if (destroy) delete repr; break; } case IR_OP_MIN: { std::vector v = ir->QueryExpOperand(repr); F_Exists *f_exists = f_root->add_exists(); if (rel == IR_COND_GE || rel == IR_COND_GT) { F_Or *f_or = f_exists->add_and()->add_or(); for (int i = 0; i < v.size(); i++) { Variable_ID e = f_exists->declare(tmp_e()); F_And *f_and = f_or->add_and(); GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, 1); h.update_coef(e, -1); if (rel == IR_COND_GT) h.update_const(-1); exp2formula(ir, r, f_and, freevars, v[i], e, side, IR_COND_EQ, true); } } else if (rel == IR_COND_LE || rel == IR_COND_LT) { F_And *f_and = f_exists->add_and(); for (int i = 0; i < v.size(); i++) { Variable_ID e = f_exists->declare(tmp_e()); GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, -1); h.update_coef(e, 1); if (rel == IR_COND_LT) h.update_const(-1); exp2formula(ir, r, f_and, freevars, v[i], e, side, IR_COND_EQ, true); } } else if (rel == IR_COND_EQ) { F_Or *f_or = f_exists->add_and()->add_or(); for (int i = 0; i < v.size(); i++) { Variable_ID e = f_exists->declare(tmp_e()); F_And *f_and = f_or->add_and(); EQ_Handle h = f_and->add_EQ(); h.update_coef(lhs, 1); h.update_coef(e, -1); exp2formula(ir, r, f_and, freevars, v[i], e, side, IR_COND_EQ, false); for (int j = 0; j < v.size(); j++) if (j != i) { Variable_ID e2 = f_exists->declare(tmp_e()); GEQ_Handle h2 = f_and->add_GEQ(); h2.update_coef(e, -1); h2.update_coef(e2, 1); exp2formula(ir, r, f_and, freevars, v[j], e2, side, IR_COND_EQ, false); } } for (int i = 0; i < v.size(); i++) delete v[i]; } else throw std::invalid_argument("unsupported condition type"); if (destroy) delete repr; } case IR_OP_MAX: { std::vector v = ir->QueryExpOperand(repr); F_Exists *f_exists = f_root->add_exists(); if (rel == IR_COND_LE || rel == IR_COND_LT) { F_Or *f_or = f_exists->add_and()->add_or(); for (int i = 0; i < v.size(); i++) { Variable_ID e = f_exists->declare(tmp_e()); F_And *f_and = f_or->add_and(); GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, -1); h.update_coef(e, 1); if (rel == IR_COND_LT) h.update_const(-1); exp2formula(ir, r, f_and, freevars, v[i], e, side, IR_COND_EQ, true); } } else if (rel == IR_COND_GE || rel == IR_COND_GT) { F_And *f_and = f_exists->add_and(); for (int i = 0; i < v.size(); i++) { Variable_ID e = f_exists->declare(tmp_e()); GEQ_Handle h = f_and->add_GEQ(); h.update_coef(lhs, 1); h.update_coef(e, -1); if (rel == IR_COND_GT) h.update_const(-1); exp2formula(ir, r, f_and, freevars, v[i], e, side, IR_COND_EQ, true); } } else if (rel == IR_COND_EQ) { F_Or *f_or = f_exists->add_and()->add_or(); for (int i = 0; i < v.size(); i++) { Variable_ID e = f_exists->declare(tmp_e()); F_And *f_and = f_or->add_and(); EQ_Handle h = f_and->add_EQ(); h.update_coef(lhs, 1); h.update_coef(e, -1); exp2formula(ir, r, f_and, freevars, v[i], e, side, IR_COND_EQ, false); for (int j = 0; j < v.size(); j++) if (j != i) { Variable_ID e2 = f_exists->declare(tmp_e()); GEQ_Handle h2 = f_and->add_GEQ(); h2.update_coef(e, 1); h2.update_coef(e2, -1); exp2formula(ir, r, f_and, freevars, v[j], e2, side, IR_COND_EQ, false); } } for (int i = 0; i < v.size(); i++) delete v[i]; } else throw std::invalid_argument("unsupported condition type"); if (destroy) delete repr; } case IR_OP_NULL: break; default: throw ir_exp_error("unsupported operand type"); } } //----------------------------------------------------------------------------- // Build dependence relation for two array references. // ----------------------------------------------------------------------------- Relation arrays2relation(IR_Code *ir, std::vector &freevars, const IR_ArrayRef *ref_src, const Relation &IS_w, const IR_ArrayRef *ref_dst, const Relation &IS_r) { Relation &IS1 = const_cast(IS_w); Relation &IS2 = const_cast(IS_r); Relation r(IS1.n_set(), IS2.n_set()); for (int i = 1; i <= IS1.n_set(); i++) r.name_input_var(i, IS1.set_var(i)->name()); for (int i = 1; i <= IS2.n_set(); i++) r.name_output_var(i, IS2.set_var(i)->name()+"'"); IR_Symbol *sym_src = ref_src->symbol(); IR_Symbol *sym_dst = ref_dst->symbol(); if (*sym_src != *sym_dst) { r.add_or(); // False Relation delete sym_src; delete sym_dst; return r; } else { delete sym_src; delete sym_dst; } F_And *f_root = r.add_and(); for (int i = 0; i < ref_src->n_dim(); i++) { F_Exists *f_exists = f_root->add_exists(); Variable_ID e1 = f_exists->declare(tmp_e()); Variable_ID e2 = f_exists->declare(tmp_e()); F_And *f_and = f_exists->add_and(); CG_outputRepr *repr_src = ref_src->index(i); CG_outputRepr *repr_dst = ref_dst->index(i); bool has_complex_formula = false; try { exp2formula(ir, r, f_and, freevars, repr_src, e1, 'w', IR_COND_EQ, false); exp2formula(ir, r, f_and, freevars, repr_dst, e2, 'r', IR_COND_EQ, false); } catch (const ir_exp_error &e) { has_complex_formula = true; } if (!has_complex_formula) { EQ_Handle h = f_and->add_EQ(); h.update_coef(e1, 1); h.update_coef(e2, -1); } repr_src->clear(); repr_dst->clear(); delete repr_src; delete repr_dst; } // add iteration space restriction r = Restrict_Domain(r, copy(IS1)); r = Restrict_Range(r, copy(IS2)); // reset the output variable names lost in restriction for (int i = 1; i <= IS2.n_set(); i++) r.name_output_var(i, IS2.set_var(i)->name()+"'"); return r; } //----------------------------------------------------------------------------- // Convert array dependence relation into set of dependence vectors, assuming // ref_w is lexicographically before ref_r in the source code. // ----------------------------------------------------------------------------- std::pair, std::vector > relation2dependences (const IR_ArrayRef *ref_src, const IR_ArrayRef *ref_dst, const Relation &r) { assert(r.n_inp() == r.n_out()); std::vector dependences1, dependences2; std::stack working; working.push(DependenceLevel(r, r.n_inp())); while (!working.empty()) { DependenceLevel dep = working.top(); working.pop(); // No dependence exists, move on. if (!dep.r.is_satisfiable()) continue; if (dep.level == r.n_inp()) { DependenceVector dv; // for loop independent dependence, use lexical order to // determine the correct source and destination if (dep.dir == 0) { if (*ref_src == *ref_dst) continue; // trivial self zero-dependence if (ref_src->is_write()) { if (ref_dst->is_write()) dv.type = DEP_W2W; else dv.type = DEP_W2R; } else { if (ref_dst->is_write()) dv.type = DEP_R2W; else dv.type = DEP_R2R; } } else if (dep.dir == 1) { if (ref_src->is_write()) { if (ref_dst->is_write()) dv.type = DEP_W2W; else dv.type = DEP_W2R; } else { if (ref_dst->is_write()) dv.type = DEP_R2W; else dv.type = DEP_R2R; } } else { // dep.dir == -1 if (ref_dst->is_write()) { if (ref_src->is_write()) dv.type = DEP_W2W; else dv.type = DEP_W2R; } else { if (ref_src->is_write()) dv.type = DEP_R2W; else dv.type = DEP_R2R; } } dv.lbounds = dep.lbounds; dv.ubounds = dep.ubounds; dv.sym = ref_src->symbol(); if (dep.dir == 0 || dep.dir == 1) dependences1.push_back(dv); else dependences2.push_back(dv); } else { // now work on the next dimension level int level = ++dep.level; coef_t lbound, ubound; Relation delta = Deltas(copy(dep.r)); delta.query_variable_bounds(delta.set_var(level), lbound, ubound); if (dep.dir == 0) { if (lbound > 0) { dep.dir = 1; dep.lbounds[level-1] = lbound; dep.ubounds[level-1] = ubound; working.push(dep); } else if (ubound < 0) { dep.dir = -1; dep.lbounds[level-1] = -ubound; dep.ubounds[level-1] = -lbound; working.push(dep); } else { // split the dependence vector into flow- and anti-dependence // for the first non-zero distance, also separate zero distance // at this level. { DependenceLevel dep2 = dep; dep2.lbounds[level-1] = 0; dep2.ubounds[level-1] = 0; F_And *f_root = dep2.r.and_with_and(); EQ_Handle h = f_root->add_EQ(); h.update_coef(dep2.r.input_var(level), 1); h.update_coef(dep2.r.output_var(level), -1); working.push(dep2); } if (lbound < 0 && *ref_src != *ref_dst) { DependenceLevel dep2 = dep; F_And *f_root = dep2.r.and_with_and(); GEQ_Handle h = f_root->add_GEQ(); h.update_coef(dep2.r.input_var(level), 1); h.update_coef(dep2.r.output_var(level), -1); h.update_const(-1); // get tighter bounds under new constraints coef_t lbound, ubound; delta = Deltas(copy(dep2.r)); delta.query_variable_bounds(delta.set_var(level), lbound, ubound); dep2.dir = -1; dep2.lbounds[level-1] = max(-ubound,static_cast(1)); // use max() to avoid Omega retardness dep2.ubounds[level-1] = -lbound; working.push(dep2); } if (ubound > 0) { DependenceLevel dep2 = dep; F_And *f_root = dep2.r.and_with_and(); GEQ_Handle h = f_root->add_GEQ(); h.update_coef(dep2.r.input_var(level), -1); h.update_coef(dep2.r.output_var(level), 1); h.update_const(-1); // get tighter bonds under new constraints coef_t lbound, ubound; delta = Deltas(copy(dep2.r)); delta.query_variable_bounds(delta.set_var(level), lbound, ubound); dep2.dir = 1; dep2.lbounds[level-1] = max(lbound,static_cast(1)); // use max() to avoid Omega retardness dep2.ubounds[level-1] = ubound; working.push(dep2); } } } // now deal with dependence vector with known direction // determined at previous levels else { // For messy bounds, further test to see if the dependence distance // can be reduced to positive/negative. This is an omega hack. if (lbound == negInfinity && ubound == posInfinity) { { Relation t = dep.r; F_And *f_root = t.and_with_and(); GEQ_Handle h = f_root->add_GEQ(); h.update_coef(t.input_var(level), 1); h.update_coef(t.output_var(level), -1); h.update_const(-1); if (!t.is_satisfiable()) { lbound = 0; } } { Relation t = dep.r; F_And *f_root = t.and_with_and(); GEQ_Handle h = f_root->add_GEQ(); h.update_coef(t.input_var(level), -1); h.update_coef(t.output_var(level), 1); h.update_const(-1); if (!t.is_satisfiable()) { ubound = 0; } } } // Same thing as above, test to see if zero dependence // distance possible. if (lbound == 0 || ubound == 0) { Relation t = dep.r; F_And *f_root = t.and_with_and(); EQ_Handle h = f_root->add_EQ(); h.update_coef(t.input_var(level), 1); h.update_coef(t.output_var(level), -1); if (!t.is_satisfiable()) { if (lbound == 0) lbound = 1; if (ubound == 0) ubound = -1; } } if (dep.dir == -1) { dep.lbounds[level-1] = -ubound; dep.ubounds[level-1] = -lbound; } else { // dep.dir == 1 dep.lbounds[level-1] = lbound; dep.ubounds[level-1] = ubound; } working.push(dep); } } } return std::make_pair(dependences1, dependences2); } //----------------------------------------------------------------------------- // Convert a boolean expression to omega relation. "destroy" means shallow // deallocation of "repr", not freeing the actual code inside. //----------------------------------------------------------------------------- void exp2constraint(IR_Code *ir, Relation &r, F_And *f_root, std::vector &freevars, CG_outputRepr *repr, bool destroy) { IR_CONDITION_TYPE cond = ir->QueryBooleanExpOperation(repr); switch (cond) { case IR_COND_LT: case IR_COND_LE: case IR_COND_EQ: case IR_COND_GT: case IR_COND_GE: { F_Exists *f_exist = f_root->add_exists(); Variable_ID e = f_exist->declare(); F_And *f_and = f_exist->add_and(); std::vector op = ir->QueryExpOperand(repr); exp2formula(ir, r, f_and, freevars, op[0], e, 's', IR_COND_EQ, true); exp2formula(ir, r, f_and, freevars, op[1], e, 's', cond, true); if (destroy) delete repr; break; } case IR_COND_NE: { F_Exists *f_exist = f_root->add_exists(); Variable_ID e = f_exist->declare(); F_Or *f_or = f_exist->add_or(); F_And *f_and = f_or->add_and(); std::vector op = ir->QueryExpOperand(repr); exp2formula(ir, r, f_and, freevars, op[0], e, 's', IR_COND_EQ, false); exp2formula(ir, r, f_and, freevars, op[1], e, 's', IR_COND_GT, false); f_and = f_or->add_and(); exp2formula(ir, r, f_and, freevars, op[0], e, 's', IR_COND_EQ, true); exp2formula(ir, r, f_and, freevars, op[1], e, 's', IR_COND_LT, true); if (destroy) delete repr; break; } default: throw ir_exp_error("unrecognized conditional expression"); } } // inline void exp2formula(IR_Code *ir, Relation &r, F_And *f_root, // std::vector &freevars, // const CG_outputRepr *repr, Variable_ID lhs, char side, char rel) { // exp2formula(ir, r, f_root, freevars, const_cast(repr), lhs, side, rel, false); // } //----------------------------------------------------------------------------- // Convert suif expression tree to omega relation. //----------------------------------------------------------------------------- // void suif2formula(Relation &r, F_And *f_root, // std::vector &freevars, // operand op, Variable_ID lhs, // char side, char rel) { // if (op.is_immed()) { // immed im = op.immediate(); // if (im.is_integer()) { // int c = im.integer(); // if (rel == '>') { // GEQ_Handle h = f_root->add_GEQ(); // h.update_coef(lhs, 1); // h.update_const(-1*c); // } // else if (rel == '<') { // GEQ_Handle h = f_root->add_GEQ(); // h.update_coef(lhs, -1); // h.update_const(c); // } // else { // '=' // EQ_Handle h = f_root->add_EQ(); // h.update_coef(lhs, 1); // h.update_const(-1*c); // } // } // else { // return; //add Function in the future // } // } // else if (op.is_symbol()) { // String s = op.symbol()->name(); // Variable_ID e = find_index(r, s, side); // if (e == NULL) { // must be free variable // Free_Var_Decl *t = NULL; // for (unsigned i = 0; i < freevars.size(); i++) { // String ss = freevars[i]->base_name(); // if (s == ss) { // t = freevars[i]; // break; // } // } // if (t == NULL) { // t = new Free_Var_Decl(s); // freevars.insert(freevars.end(), t); // } // e = r.get_local(t); // } // if (rel == '>') { // GEQ_Handle h = f_root->add_GEQ(); // h.update_coef(lhs, 1); // h.update_coef(e, -1); // } // else if (rel == '<') { // GEQ_Handle h = f_root->add_GEQ(); // h.update_coef(lhs, -1); // h.update_coef(e, 1); // } // else { // '=' // EQ_Handle h = f_root->add_EQ(); // h.update_coef(lhs, 1); // h.update_coef(e, -1); // } // } // else if (op.is_instr()) // suif2formula(r, f_root, freevars, op.instr(), lhs, side, rel); // } // void suif2formula(Relation &r, F_And *f_root, // std::vector &freevars, // instruction *ins, Variable_ID lhs, // char side, char rel) { // if (ins->opcode() == io_cpy) { // suif2formula(r, f_root, freevars, ins->src_op(0), lhs, side, rel); // } // else if (ins->opcode() == io_add || ins->opcode() == io_sub) { // F_Exists *f_exists = f_root->add_exists(); // Variable_ID e1 = f_exists->declare(tmp_e()); // Variable_ID e2 = f_exists->declare(tmp_e()); // F_And *f_and = f_exists->add_and(); // int add_or_sub = ins->opcode() == io_add ? 1 : -1; // if (rel == '>') { // GEQ_Handle h = f_and->add_GEQ(); // h.update_coef(lhs, 1); // h.update_coef(e1, -1); // h.update_coef(e2, -1 * add_or_sub); // } // else if (rel == '<') { // GEQ_Handle h = f_and->add_GEQ(); // h.update_coef(lhs, -1); // h.update_coef(e1, 1); // h.update_coef(e2, 1 * add_or_sub); // } // else { // '=' // EQ_Handle h = f_and->add_EQ(); // h.update_coef(lhs, 1); // h.update_coef(e1, -1); // h.update_coef(e2, -1 * add_or_sub); // } // suif2formula(r, f_and, freevars, ins->src_op(0), e1, side, '='); // suif2formula(r, f_and, freevars, ins->src_op(1), e2, side, '='); // } // else if (ins->opcode() == io_mul) { // operand op1 = ins->src_op(0); // operand op2 = ins->src_op(1); // if (!op1.is_immed() && !op2.is_immed()) // return; // add Function in the future // else { // operand op; // immed im; // if (op1.is_immed()) { // im = op1.immediate(); // op = op2; // } // else { // im = op2.immediate(); // op = op1; // } // if (!im.is_integer()) // return; //add Function in the future // else { // int c = im.integer(); // F_Exists *f_exists = f_root->add_exists(); // Variable_ID e = f_exists->declare(tmp_e()); // F_And *f_and = f_exists->add_and(); // if (rel == '>') { // GEQ_Handle h = f_and->add_GEQ(); // h.update_coef(lhs, 1); // h.update_coef(e, -c); // } // else if (rel == '<') { // GEQ_Handle h = f_and->add_GEQ(); // h.update_coef(lhs, -1); // h.update_coef(e, c); // } // else { // EQ_Handle h = f_and->add_EQ(); // h.update_coef(lhs, 1); // h.update_coef(e, -c); // } // suif2formula(r, f_and, freevars, op, e, side, '='); // } // } // } // else if (ins->opcode() == io_div) { // operand op1 = ins->src_op(0); // operand op2 = ins->src_op(1); // if (!op2.is_immed()) // return; //add Function in the future // else { // immed im = op2.immediate(); // if (!im.is_integer()) // return; //add Function in the future // else { // int c = im.integer(); // F_Exists *f_exists = f_root->add_exists(); // Variable_ID e = f_exists->declare(tmp_e()); // F_And *f_and = f_exists->add_and(); // if (rel == '>') { // GEQ_Handle h = f_and->add_GEQ(); // h.update_coef(lhs, c); // h.update_coef(e, -1); // } // else if (rel == '<') { // GEQ_Handle h = f_and->add_GEQ(); // h.update_coef(lhs, -c); // h.update_coef(e, 1); // } // else { // EQ_Handle h = f_and->add_EQ(); // h.update_coef(lhs, c); // h.update_coef(e, -1); // } // suif2formula(r, f_and, freevars, op1, e, side, '='); // } // } // } // else if (ins->opcode() == io_neg) { // F_Exists *f_exists = f_root->add_exists(); // Variable_ID e = f_exists->declare(tmp_e()); // F_And *f_and = f_exists->add_and(); // if (rel == '>') { // GEQ_Handle h = f_and->add_GEQ(); // h.update_coef(lhs, 1); // h.update_coef(e, 1); // } // else if (rel == '<') { // GEQ_Handle h = f_and->add_GEQ(); // h.update_coef(lhs, -1); // h.update_coef(e, -1); // } // else { // EQ_Handle h = f_and->add_EQ(); // h.update_coef(lhs, 1); // h.update_coef(e, 1); // } // suif2formula(r, f_and, freevars, ins->src_op(0), e, side, '='); // } // else if (ins->opcode() == io_min) { // operand op1 = ins->src_op(0); // operand op2 = ins->src_op(1); // F_Exists *f_exists = f_root->add_exists(); // Variable_ID e1 = f_exists->declare(tmp_e()); // Variable_ID e2 = f_exists->declare(tmp_e()); // F_And *f_and = f_exists->add_and(); // if (rel == '>') { // F_Or *f_or = f_and->add_or(); // F_And *f_and1 = f_or->add_and(); // GEQ_Handle h1 = f_and1->add_GEQ(); // h1.update_coef(lhs, 1); // h1.update_coef(e1, -1); // F_And *f_and2 = f_or->add_and(); // GEQ_Handle h2 = f_and2->add_GEQ(); // h2.update_coef(lhs, 1); // h2.update_coef(e2, -1); // } // else if (rel == '<') { // GEQ_Handle h1 = f_and->add_GEQ(); // h1.update_coef(lhs, -1); // h1.update_coef(e1, 1); // GEQ_Handle h2 = f_and->add_GEQ(); // h2.update_coef(lhs, -1); // h2.update_coef(e2, 1); // } // else { // F_Or *f_or = f_and->add_or(); // F_And *f_and1 = f_or->add_and(); // EQ_Handle h1 = f_and1->add_EQ(); // h1.update_coef(lhs, 1); // h1.update_coef(e1, -1); // GEQ_Handle h2 = f_and1->add_GEQ(); // h2.update_coef(e1, -1); // h2.update_coef(e2, 1); // F_And *f_and2 = f_or->add_and(); // EQ_Handle h3 = f_and2->add_EQ(); // h3.update_coef(lhs, 1); // h3.update_coef(e2, -1); // GEQ_Handle h4 = f_and2->add_GEQ(); // h4.update_coef(e1, 1); // h4.update_coef(e2, -1); // } // suif2formula(r, f_and, freevars, op1, e1, side, '='); // suif2formula(r, f_and, freevars, op2, e2, side, '='); // } // else if (ins->opcode() == io_max) { // operand op1 = ins->src_op(0); // operand op2 = ins->src_op(1); // F_Exists *f_exists = f_root->add_exists(); // Variable_ID e1 = f_exists->declare(tmp_e()); // Variable_ID e2 = f_exists->declare(tmp_e()); // F_And *f_and = f_exists->add_and(); // if (rel == '>') { // GEQ_Handle h1 = f_and->add_GEQ(); // h1.update_coef(lhs, 1); // h1.update_coef(e1, -1); // GEQ_Handle h2 = f_and->add_GEQ(); // h2.update_coef(lhs, 1); // h2.update_coef(e2, -1); // } // else if (rel == '<') { // F_Or *f_or = f_and->add_or(); // F_And *f_and1 = f_or->add_and(); // GEQ_Handle h1 = f_and1->add_GEQ(); // h1.update_coef(lhs, -1); // h1.update_coef(e1, 1); // F_And *f_and2 = f_or->add_and(); // GEQ_Handle h2 = f_and2->add_GEQ(); // h2.update_coef(lhs, -1); // h2.update_coef(e2, 1); // } // else { // F_Or *f_or = f_and->add_or(); // F_And *f_and1 = f_or->add_and(); // EQ_Handle h1 = f_and1->add_EQ(); // h1.update_coef(lhs, 1); // h1.update_coef(e1, -1); // GEQ_Handle h2 = f_and1->add_GEQ(); // h2.update_coef(e1, 1); // h2.update_coef(e2, -1); // F_And *f_and2 = f_or->add_and(); // EQ_Handle h3 = f_and2->add_EQ(); // h3.update_coef(lhs, 1); // h3.update_coef(e2, -1); // GEQ_Handle h4 = f_and2->add_GEQ(); // h4.update_coef(e1, -1); // h4.update_coef(e2, 1); // } // suif2formula(r, f_and, freevars, op1, e1, side, '='); // suif2formula(r, f_and, freevars, op2, e2, side, '='); // } // } //----------------------------------------------------------------------------- // Generate iteration space constraints //----------------------------------------------------------------------------- // void add_loop_stride_constraints(Relation &r, F_And *f_root, // std::vector &freevars, // tree_for *tnf, char side) { // std::string name(tnf->index()->name()); // int dim = 0; // for (;dim < r.n_set(); dim++) // if (r.set_var(dim+1)->name() == name) // break; // Relation bound = get_loop_bound(r, dim); // operand op = tnf->step_op(); // if (!op.is_null()) { // if (op.is_immed()) { // immed im = op.immediate(); // if (im.is_integer()) { // int c = im.integer(); // if (c != 1 && c != -1) // add_loop_stride(r, bound, dim, c); // } // else // assert(0); // messy stride // } // else // assert(0); // messy stride // } // } // void add_loop_bound_constraints(IR_Code *ir, Relation &r, F_And *f_root, // std::vector &freevars, // tree_for *tnf, // char upper_or_lower, char side, IR_CONDITION_TYPE rel) { // Variable_ID v = find_index(r, tnf->index()->name(), side); // tree_node_list *tnl; // if (upper_or_lower == 'u') // tnl = tnf->ub_list(); // else // tnl = tnf->lb_list(); // tree_node_list_iter iter(tnl); // while (!iter.is_empty()) { // tree_node *tn = iter.step(); // if (tn->kind() != TREE_INSTR) // break; // messy bounds // instruction *ins = static_cast(tn)->instr(); // if (upper_or_lower == 'u' && (tnf->test() == FOR_SLT || tnf->test() == FOR_ULT)) { // operand op1(ins->clone()); // operand op2(new in_ldc(type_s32, operand(), immed(1))); // instruction *t = new in_rrr(io_sub, op1.type(), operand(), op1, op2); // CG_suifRepr *repr = new CG_suifRepr(operand(t)); // exp2formula(ir, r, f_root, freevars, repr, v, side, rel, true); // delete t; // } // else if (tnf->test() == FOR_SLT || tnf->test() == FOR_SLTE || tnf->test() == FOR_ULT || tnf->test() == FOR_ULTE) { // CG_suifRepr *repr = new CG_suifRepr(operand(ins)); // exp2formula(ir, r, f_root, freevars, repr, v, side, rel, true); // } // else // assert(0); // } // } // Relation loop_iteration_space(std::vector &freevars, // tree_node *tn, std::vector &loops) { // Relation r(loops.size()); // for (unsigned i = 0; i < loops.size(); i++) { // String s = loops[i]->index()->name(); // r.name_set_var(i+1, s); // } // F_And *f_root = r.add_and(); // std::vector outer = find_outer_loops(tn); // std::vector loops_lex(loops.size(), LEX_UNKNOWN); // for (unsigned i = 0; i < outer.size(); i++) { // unsigned j; // for (j = 0; j < loops.size(); j++) { // if (outer[i] == loops[j]) { // loops_lex[j] = LEX_MATCH; // break; // } else if (outer[i]->index() == loops[j]->index()) { // loops_lex[j] = lexical_order(outer[i],loops[j]); // break; // } // } // if (j != loops.size()) { // add_loop_bound_constraints(r, f_root, freevars, outer[i], 'l', 's', '>'); // add_loop_bound_constraints(r, f_root, freevars, outer[i], 'u', 's', '<'); // add_loop_stride_constraints(r,f_root, freevars, outer[i], 's'); // } // } // // Add degenerated constraints for non-enclosing loops for this // // statement. We treat low-dim space as part of whole // // iteration space. // LexicalOrderType lex = LEX_MATCH; // for (unsigned i = 0; i < loops.size(); i++) { // if (loops_lex[i] != 0) { // if (lex == LEX_MATCH) // lex = loops_lex[i]; // continue; // } // if (lex == LEX_MATCH) { // for (unsigned j = i+1; j < loops.size(); j++) { // if (loops_lex[j] == LEX_BEFORE || loops_lex[j] == LEX_AFTER) { // lex = loops_lex[j]; // break; // } // } // } // if (lex == LEX_MATCH) // lex = lexical_order(tn, loops[i]); // if (lex == LEX_BEFORE) // add_loop_bound_constraints(r, f_root, freevars, loops[i], 'l', 's', '='); // else // add_loop_bound_constraints(r, f_root, freevars, loops[i], 'u', 's', '='); // } // return r; // } // Relation arrays2relation(std::vector &freevars, // in_array *ia_w, const Relation &IS1_, // in_array *ia_r, const Relation &IS2_) { // Relation &IS1 = const_cast(IS1_); // Relation &IS2 = const_cast(IS2_); // Relation r(IS1.n_set(), IS2.n_set()); // for (int i = 1; i <= IS1.n_set(); i++) // r.name_input_var(i, IS1.set_var(i)->name()); // for (int i = 1; i <= IS2.n_set(); i++) // r.name_output_var(i, IS2.set_var(i)->name()+"'"); // if (get_sym_of_array(ia_w) != get_sym_of_array(ia_r)) { // r.add_or(); // False Relation // return r; // } // F_And *f_root = r.add_and(); // for (unsigned i = 0; i < ia_w->dims(); i++) { // F_Exists *f_exists = f_root->add_exists(); // Variable_ID e = f_exists->declare(tmp_e()); // F_And *f_and = f_exists->add_and(); // suif2formula(r, f_and, freevars, ia_w->index(i), e, 'w', '='); // suif2formula(r, f_and, freevars, ia_r->index(i), e, 'r', '='); // } // // add iteration space restriction // r = Restrict_Domain(r, copy(IS1)); // r = Restrict_Range(r, copy(IS2)); // // reset the output variable names lost in restriction // for (int i = 1; i <= IS2.n_set(); i++) // r.name_output_var(i, IS2.set_var(i)->name()+"'"); // return r; // } // std::vector relation2dependences (IR_Code *ir, in_array *ia_w, in_array *ia_r, const Relation &r) { // assert(r.n_inp() == r.n_out()); // std::vector dependences; // std::stack working; // working.push(DependenceLevel(r, r.n_inp())); // while (!working.empty()) { // DependenceLevel dep = working.top(); // working.pop(); // // No dependence exists, move on. // if (!dep.r.is_satisfiable()) // continue; // if (dep.level == r.n_inp()) { // DependenceVector dv; // // for loop independent dependence, use lexical order to // // determine the correct source and destination // if (dep.dir == 0) { // LexicalOrderType order = lexical_order(ia_w->parent(), ia_r->parent()); // if (order == LEX_MATCH) // continue; //trivial self zero-dependence // else if (order == LEX_AFTER) { // dv.src = new IR_suifArrayRef(ir, ia_r); // dv.dst = new IR_suifArrayRef(ir, ia_w); // } // else { // dv.src = new IR_suifArrayRef(ir, ia_w); // dv.dst = new IR_suifArrayRef(ir,ia_r); // } // } // else if (dep.dir == 1) { // dv.src = new IR_suifArrayRef(ir, ia_w); // dv.dst = new IR_suifArrayRef(ir, ia_r); // } // else { // dep.dir == -1 // dv.src = new IR_suifArrayRef(ir, ia_r); // dv.dst = new IR_suifArrayRef(ir, ia_w); // } // dv.lbounds = dep.lbounds; // dv.ubounds = dep.ubounds; // // // set the dependence type // // if (is_lhs(dv.source) && is_lhs(dv.dest)) // // dv.type = 'o'; // // else if (!is_lhs(dv.source) && ! is_lhs(dv.dest)) // // dv.type = 'i'; // // else if (is_lhs(dv.source)) // // dv.type = 'f'; // // else // // dv.type = 'a'; // dependences.push_back(dv); // } // else { // // now work on the next dimension level // int level = ++dep.level; // coef_t lbound, ubound; // Relation delta = Deltas(copy(dep.r)); // delta.query_variable_bounds(delta.set_var(level), lbound, ubound); // if (dep.dir == 0) { // if (lbound > 0) { // dep.dir = 1; // dep.lbounds[level-1] = lbound; // dep.ubounds[level-1] = ubound; // working.push(dep); // } // else if (ubound < 0) { // dep.dir = -1; // dep.lbounds[level-1] = -ubound; // dep.ubounds[level-1] = -lbound; // working.push(dep); // } // else { // // split the dependence vector into flow- and anti-dependence // // for the first non-zero distance, also separate zero distance // // at this level. // { // DependenceLevel dep2 = dep; // dep2.lbounds[level-1] = 0; // dep2.ubounds[level-1] = 0; // F_And *f_root = dep2.r.and_with_and(); // EQ_Handle h = f_root->add_EQ(); // h.update_coef(dep2.r.input_var(level), 1); // h.update_coef(dep2.r.output_var(level), -1); // working.push(dep2); // } // if (lbound < 0 && ia_w != ia_r) { // DependenceLevel dep2 = dep; // F_And *f_root = dep2.r.and_with_and(); // GEQ_Handle h = f_root->add_GEQ(); // h.update_coef(dep2.r.input_var(level), 1); // h.update_coef(dep2.r.output_var(level), -1); // h.update_const(-1); // // get tighter bounds under new constraints // coef_t lbound, ubound; // delta = Deltas(copy(dep2.r)); // delta.query_variable_bounds(delta.set_var(level), // lbound, ubound); // dep2.dir = -1; // dep2.lbounds[level-1] = max(-ubound,static_cast(1)); // use max() to avoid Omega retardness // dep2.ubounds[level-1] = -lbound; // working.push(dep2); // } // if (ubound > 0) { // DependenceLevel dep2 = dep; // F_And *f_root = dep2.r.and_with_and(); // GEQ_Handle h = f_root->add_GEQ(); // h.update_coef(dep2.r.input_var(level), -1); // h.update_coef(dep2.r.output_var(level), 1); // h.update_const(-1); // // get tighter bonds under new constraints // coef_t lbound, ubound; // delta = Deltas(copy(dep2.r)); // delta.query_variable_bounds(delta.set_var(level), // lbound, ubound); // dep2.dir = 1; // dep2.lbounds[level-1] = max(lbound,static_cast(1)); // use max() to avoid Omega retardness // dep2.ubounds[level-1] = ubound; // working.push(dep2); // } // } // } // // now deal with dependence vector with known direction // // determined at previous levels // else { // // For messy bounds, further test to see if the dependence distance // // can be reduced to positive/negative. This is an omega hack. // if (lbound == negInfinity && ubound == posInfinity) { // { // Relation t = dep.r; // F_And *f_root = t.and_with_and(); // GEQ_Handle h = f_root->add_GEQ(); // h.update_coef(t.input_var(level), 1); // h.update_coef(t.output_var(level), -1); // h.update_const(-1); // if (!t.is_satisfiable()) { // lbound = 0; // } // } // { // Relation t = dep.r; // F_And *f_root = t.and_with_and(); // GEQ_Handle h = f_root->add_GEQ(); // h.update_coef(t.input_var(level), -1); // h.update_coef(t.output_var(level), 1); // h.update_const(-1); // if (!t.is_satisfiable()) { // ubound = 0; // } // } // } // // Same thing as above, test to see if zero dependence // // distance possible. // if (lbound == 0 || ubound == 0) { // Relation t = dep.r; // F_And *f_root = t.and_with_and(); // EQ_Handle h = f_root->add_EQ(); // h.update_coef(t.input_var(level), 1); // h.update_coef(t.output_var(level), -1); // if (!t.is_satisfiable()) { // if (lbound == 0) // lbound = 1; // if (ubound == 0) // ubound = -1; // } // } // if (dep.dir == -1) { // dep.lbounds[level-1] = -ubound; // dep.ubounds[level-1] = -lbound; // } // else { // dep.dir == 1 // dep.lbounds[level-1] = lbound; // dep.ubounds[level-1] = ubound; // } // working.push(dep); // } // } // } // return dependences; // } //----------------------------------------------------------------------------- // Determine whether the loop (starting from 0) in the iteration space // has only one iteration. //----------------------------------------------------------------------------- bool is_single_loop_iteration(const Relation &r, int level, const Relation &known) { int n = r.n_set(); Relation r1 = Intersection(copy(r), Extend_Set(copy(known), n-known.n_set())); Relation mapping(n, n); F_And *f_root = mapping.add_and(); for (int i = 1; i <= level; i++) { EQ_Handle h = f_root->add_EQ(); h.update_coef(mapping.input_var(i), 1); h.update_coef(mapping.output_var(i), -1); } r1 = Range(Restrict_Domain(mapping, r1)); r1.simplify(); Variable_ID v = r1.set_var(level); for (DNF_Iterator di(r1.query_DNF()); di; di++) { bool is_single = false; for (EQ_Iterator ei((*di)->EQs()); ei; ei++) if ((*ei).get_coef(v) != 0 && !(*ei).has_wildcards()) { is_single = true; break; } if (!is_single) return false; } return true; } bool is_single_iteration(const Relation &r, int dim) { assert(r.is_set()); const int n = r.n_set(); if (dim >= n) return true; Relation bound = get_loop_bound(r, dim); // if (!bound.has_single_conjunct()) // return false; // Conjunct *c = bound.query_DNF()->single_conjunct(); for (DNF_Iterator di(bound.query_DNF()); di; di++) { bool is_single = false; for (EQ_Iterator ei((*di)->EQs()); ei; ei++) if (!(*ei).has_wildcards()) { is_single = true; break; } if (!is_single) return false; } return true; // Relation r = copy(r_); // const int n = r.n_set(); // if (dim >= n) // return true; // Relation bound = get_loop_bound(r, dim); // bound = Approximate(bound); // Conjunct *c = bound.query_DNF()->single_conjunct(); // return c->n_GEQs() == 0; // Relation r = copy(r_); // r.simplify(); // const int n = r.n_set(); // if (dim >= n) // return true; // for (DNF_Iterator i(r.query_DNF()); i; i++) { // std::vector is_single(n); // for (int j = 0; j < dim; j++) // is_single[j] = true; // for (int j = dim; j < n; j++) // is_single[j] = false; // bool found_new_single = true; // while (found_new_single) { // found_new_single = false; // for (EQ_Iterator j = (*i)->EQs(); j; j++) { // int saved_pos = -1; // for (Constr_Vars_Iter k(*j); k; k++) // if ((*k).var->kind() == Set_Var || (*k).var->kind() == Input_Var) { // int pos = (*k).var->get_position() - 1; // if (!is_single[pos]) // if (saved_pos == -1) // saved_pos = pos; // else { // saved_pos = -1; // break; // } // } // if (saved_pos != -1) { // is_single[saved_pos] = true; // found_new_single = true; // } // } // if (is_single[dim]) // break; // } // if (!is_single[dim]) // return false; // } // return true; } //----------------------------------------------------------------------------- // Set/get the value of a variable which is know to be constant. //----------------------------------------------------------------------------- void assign_const(Relation &r, int dim, int val) { const int n = r.n_out(); Relation mapping(n, n); F_And *f_root = mapping.add_and(); for (int i = 1; i <= n; i++) { if (i != dim+1) { EQ_Handle h = f_root->add_EQ(); h.update_coef(mapping.output_var(i), 1); h.update_coef(mapping.input_var(i), -1); } else { EQ_Handle h = f_root->add_EQ(); h.update_coef(mapping.output_var(i), 1); h.update_const(-val); } } r = Composition(mapping, r); } int get_const(const Relation &r, int dim, Var_Kind type) { // Relation rr = copy(r); Relation &rr = const_cast(r); Variable_ID v; switch (type) { // case Set_Var: // v = rr.set_var(dim+1); // break; case Input_Var: v = rr.input_var(dim+1); break; case Output_Var: v = rr.output_var(dim+1); break; default: throw std::invalid_argument("unsupported variable type"); } for (DNF_Iterator di(rr.query_DNF()); di; di++) for (EQ_Iterator ei = (*di)->EQs(); ei; ei++) if ((*ei).is_const(v)) return (*ei).get_const(); throw std::runtime_error("cannot get variable's constant value"); } //--------------------------------------------------------------------------- // Get the bound for a specific loop. //--------------------------------------------------------------------------- Relation get_loop_bound(const Relation &r, int dim) { assert(r.is_set()); const int n = r.n_set(); // Relation r1 = project_onto_levels(copy(r), dim+1, true); Relation mapping(n,n); F_And *f_root = mapping.add_and(); for (int i = 1; i <= dim+1; i++) { EQ_Handle h = f_root->add_EQ(); h.update_coef(mapping.input_var(i), 1); h.update_coef(mapping.output_var(i), -1); } Relation r1 = Range(Restrict_Domain(mapping, copy(r))); for (int i = 1; i <= n; i++) r1.name_set_var(i, const_cast(r).set_var(i)->name()); r1.setup_names(); Relation r2 = Project(copy(r1), dim+1, Set_Var); return Gist(r1, r2, 1); } Relation get_loop_bound(const Relation &r, int level, const Relation &known) { int n = r.n_set(); Relation r1 = Intersection(copy(r), Extend_Set(copy(known), n-known.n_set())); Relation mapping(n, n); F_And *f_root = mapping.add_and(); for (int i = 1; i <= level; i++) { EQ_Handle h = f_root->add_EQ(); h.update_coef(mapping.input_var(i), 1); h.update_coef(mapping.output_var(i), -1); } r1 = Range(Restrict_Domain(mapping, r1)); Relation r2 = Project(copy(r1), level, Set_Var); r1 = Gist(r1, r2, 1); for (int i = 1; i <= n; i++) r1.name_set_var(i, const_cast(r).set_var(i)->name()); r1.setup_names(); return r1; } Relation get_max_loop_bound(const std::vector &r, int dim) { if (r.size() == 0) return Relation::Null(); const int n = r[0].n_set(); Relation res(Relation::False(n)); for (int i = 0; i < r.size(); i++) { Relation &t = const_cast(r[i]); if (t.is_satisfiable()) res = Union(get_loop_bound(t, dim), res); } res.simplify(); return res; } Relation get_min_loop_bound(const std::vector &r, int dim) { if (r.size() == 0) return Relation::Null(); const int n = r[0].n_set(); Relation res(Relation::True(n)); for (int i = 0; i < r.size(); i++) { Relation &t = const_cast(r[i]); if (t.is_satisfiable()) res = Intersection(get_loop_bound(t, dim), res); } res.simplify(); return res; } //----------------------------------------------------------------------------- // Add strident to a loop. // Issues: // - Don't work with relations with multiple disjuncts. // - Omega's dealing with max lower bound is awkward. //----------------------------------------------------------------------------- void add_loop_stride(Relation &r, const Relation &bound_, int dim, int stride) { F_And *f_root = r.and_with_and(); Relation &bound = const_cast(bound_); for (DNF_Iterator di(bound.query_DNF()); di; di++) { F_Exists *f_exists = f_root->add_exists(); Variable_ID e1 = f_exists->declare(tmp_e()); Variable_ID e2 = f_exists->declare(tmp_e()); F_And *f_and = f_exists->add_and(); EQ_Handle stride_eq = f_and->add_EQ(); stride_eq.update_coef(e1, 1); stride_eq.update_coef(e2, stride); if (!r.is_set()) stride_eq.update_coef(r.output_var(dim+1), -1); else stride_eq.update_coef(r.set_var(dim+1), -1); F_Or *f_or = f_and->add_or(); for (GEQ_Iterator gi = (*di)->GEQs(); gi; gi++) { if ((*gi).get_coef(bound.set_var(dim+1)) > 0) { // copy the lower bound constraint EQ_Handle h1 = f_or->add_and()->add_EQ(); GEQ_Handle h2 = f_and->add_GEQ(); for (Constr_Vars_Iter ci(*gi); ci; ci++) { switch ((*ci).var->kind()) { // case Set_Var: case Input_Var: { int pos = (*ci).var->get_position(); if (pos == dim + 1) { h1.update_coef(e1, (*ci).coef); h2.update_coef(e1, (*ci).coef); } else { if (!r.is_set()) { h1.update_coef(r.output_var(pos), (*ci).coef); h2.update_coef(r.output_var(pos), (*ci).coef); } else { h1.update_coef(r.set_var(pos), (*ci).coef); h2.update_coef(r.set_var(pos), (*ci).coef); } } break; } case Global_Var: { Global_Var_ID g = (*ci).var->get_global_var(); h1.update_coef(r.get_local(g, (*ci).var->function_of()), (*ci).coef); h2.update_coef(r.get_local(g, (*ci).var->function_of()), (*ci).coef); break; } default: break; } } h1.update_const((*gi).get_const()); h2.update_const((*gi).get_const()); } } } } bool is_inner_loop_depend_on_level(const Relation &r, int level, const Relation &known) { Relation r1 = Intersection(copy(r), Extend_Set(copy(known), r.n_set()-known.n_set())); Relation r2 = copy(r1); for (int i = level+1; i <= r2.n_set(); i++) r2 = Project(r2, r2.set_var(i)); r2.simplify(2, 4); Relation r3 = Gist(r1, r2); Variable_ID v = r3.set_var(level); for (DNF_Iterator di(r3.query_DNF()); di; di++) { for (EQ_Iterator ei = (*di)->EQs(); ei; ei++) if ((*ei).get_coef(v) != 0) return true; for (GEQ_Iterator gi = (*di)->GEQs(); gi; gi++) if ((*gi).get_coef(v) != 0) return true; } return false; } //----------------------------------------------------------------------------- // Suppose loop dim is i. Replace i with i+adjustment in loop bounds. // e.g. do i = 1, n // do j = i, n // after call with dim = 0 and adjustment = 1: // do i = 1, n // do j = i+1, n // ----------------------------------------------------------------------------- Relation adjust_loop_bound(const Relation &r, int level, int adjustment) { if (adjustment == 0) return copy(r); const int n = r.n_set(); Relation r1 = copy(r); for (int i = level+1; i <= r1.n_set(); i++) r1 = Project(r1, r1.set_var(i)); r1.simplify(2, 4); Relation r2 = Gist(copy(r), copy(r1)); Relation mapping(n, n); F_And *f_root = mapping.add_and(); for (int i = 1; i <= n; i++) if (i == level) { EQ_Handle h = f_root->add_EQ(); h.update_coef(mapping.input_var(level), -1); h.update_coef(mapping.output_var(level), 1); h.update_const(static_cast(adjustment)); } else { EQ_Handle h = f_root->add_EQ(); h.update_coef(mapping.input_var(i), -1); h.update_coef(mapping.output_var(i), 1); } r2 = Range(Restrict_Domain(mapping, r2)); r1 = Intersection(r1, r2); r1.simplify(); for (int i = 1; i <= n; i++) r1.name_set_var(i, const_cast(r).set_var(i)->name()); r1.setup_names(); return r1; } // commented out on 07/14/2010 // void adjust_loop_bound(Relation &r, int dim, int adjustment, std::vector globals) { // assert(r.is_set()); // if (adjustment == 0) // return; // const int n = r.n_set(); // Tuple name(n); // for (int i = 1; i <= n; i++) // name[i] = r.set_var(i)->name(); // Relation r1 = project_onto_levels(copy(r), dim+1, true); // Relation r2 = Gist(copy(r), copy(r1)); // // remove old bogus global variable conditions since we are going to // // update the value. // if (globals.size() > 0) // r1 = Gist(r1, project_onto_levels(copy(r), 0, true)); // Relation r4 = Relation::True(n); // for (DNF_Iterator di(r2.query_DNF()); di; di++) { // for (EQ_Iterator ei = (*di)->EQs(); ei; ei++) { // EQ_Handle h = r4.and_with_EQ(*ei); // Variable_ID v = r2.set_var(dim+1); // coef_t c = (*ei).get_coef(v); // if (c != 0) // h.update_const(c*adjustment); // for (int i = 0; i < globals.size(); i++) { // Variable_ID v = r2.get_local(globals[i]); // coef_t c = (*ei).get_coef(v); // if (c != 0) // h.update_const(c*adjustment); // } // } // for (GEQ_Iterator gi = (*di)->GEQs(); gi; gi++) { // GEQ_Handle h = r4.and_with_GEQ(*gi); // Variable_ID v = r2.set_var(dim+1); // coef_t c = (*gi).get_coef(v); // if (c != 0) // h.update_const(c*adjustment); // for (int i = 0; i < globals.size(); i++) { // Variable_ID v = r2.get_local(globals[i]); // coef_t c = (*gi).get_coef(v); // if (c != 0) // h.update_const(c*adjustment); // } // } // } // r = Intersection(r1, r4); // // } // // else // // r = Intersection(r1, r2); // for (int i = 1; i <= n; i++) // r.name_set_var(i, name[i]); // r.setup_names(); // } // void adjust_loop_bound(Relation &r, int dim, int adjustment) { // assert(r.is_set()); // const int n = r.n_set(); // Tuple name(n); // for (int i = 1; i <= n; i++) // name[i] = r.set_var(i)->name(); // Relation r1 = project_onto_levels(copy(r), dim+1, true); // Relation r2 = Gist(r, copy(r1)); // Relation r3(n, n); // F_And *f_root = r3.add_and(); // for (int i = 0; i < n; i++) { // EQ_Handle h = f_root->add_EQ(); // h.update_coef(r3.output_var(i+1), 1); // h.update_coef(r3.input_var(i+1), -1); // if (i == dim) // h.update_const(adjustment); // } // r2 = Range(Restrict_Domain(r3, r2)); // r = Intersection(r1, r2); // for (int i = 1; i <= n; i++) // r.name_set_var(i, name[i]); // r.setup_names(); // } // void adjust_loop_bound(Relation &r, int dim, Free_Var_Decl *global_var, int adjustment) { // assert(r.is_set()); // const int n = r.n_set(); // Tuple name(n); // for (int i = 1; i <= n; i++) // name[i] = r.set_var(i)->name(); // Relation r1 = project_onto_levels(copy(r), dim+1, true); // Relation r2 = Gist(r, copy(r1)); // Relation r3(n); // Variable_ID v = r2.get_local(global_var); // for (DNF_Iterator di(r2.query_DNF()); di; di++) { // for (EQ_Iterator ei = (*di)->EQs(); ei; ei++) { // coef_t c = (*ei).get_coef(v); // EQ_Handle h = r3.and_with_EQ(*ei); // if (c != 0) // h.update_const(c*adjustment); // } // for (GEQ_Iterator gi = (*di)->GEQs(); gi; gi++) { // coef_t c = (*gi).get_coef(v); // GEQ_Handle h = r3.and_with_GEQ(*gi); // if (c != 0) // h.update_const(c*adjustment); // } // } // r = Intersection(r1, r3); // for (int i = 1; i <= n; i++) // r.name_set_var(i, name[i]); // r.setup_names(); // } //------------------------------------------------------------------------------ // If the dimension has value posInfinity, the statement should be privatized // at this dimension. //------------------------------------------------------------------------------ // boolean is_private_statement(const Relation &r, int dim) { // int n; // if (r.is_set()) // n = r.n_set(); // else // n = r.n_out(); // if (dim >= n) // return false; // try { // coef_t c; // if (r.is_set()) // c = get_const(r, dim, Set_Var); // else // c = get_const(r, dim, Output_Var); // if (c == posInfinity) // return true; // else // return false; // } // catch (loop_error e){ // } // return false; // } // // ---------------------------------------------------------------------------- // // Calculate v mod dividend based on equations inside relation r. // // Return posInfinity if it is not a constant. // // ---------------------------------------------------------------------------- // static coef_t mod_(const Relation &r_, Variable_ID v, int dividend, std::set &working_on) { // assert(dividend > 0); // if (v->kind() == Forall_Var || v->kind() == Exists_Var || v->kind() == Wildcard_Var) // return posInfinity; // working_on.insert(v); // Relation &r = const_cast(r_); // Conjunct *c = r.query_DNF()->single_conjunct(); // for (EQ_Iterator ei(c->EQs()); ei; ei++) { // int coef = mod((*ei).get_coef(v), dividend); // if (coef != 1 && coef != dividend - 1 ) // continue; // coef_t result = 0; // for (Constr_Vars_Iter cvi(*ei); cvi; cvi++) // if ((*cvi).var != v) { // int p = mod((*cvi).coef, dividend); // if (p == 0) // continue; // if (working_on.find((*cvi).var) != working_on.end()) { // result = posInfinity; // break; // } // coef_t q = mod_(r, (*cvi).var, dividend, working_on); // if (q == posInfinity) { // result = posInfinity; // break; // } // result += p * q; // } // if (result != posInfinity) { // result += (*ei).get_const(); // if (coef == 1) // result = -result; // working_on.erase(v); // return mod(result, dividend); // } // } // working_on.erase(v); // return posInfinity; // } // coef_t mod(const Relation &r, Variable_ID v, int dividend) { // std::set working_on = std::set(); // return mod_(r, v, dividend, working_on); // } //----------------------------------------------------------------------------- // Generate mapping relation for permuation. //----------------------------------------------------------------------------- Relation permute_relation(const std::vector &pi) { const int n = pi.size(); Relation r(n, n); F_And *f_root = r.add_and(); for (int i = 0; i < n; i++) { EQ_Handle h = f_root->add_EQ(); h.update_coef(r.output_var(i+1), 1); h.update_coef(r.input_var(pi[i]+1), -1); } return r; } //--------------------------------------------------------------------------- // Find the position index variable in a Relation by name. //--------------------------------------------------------------------------- Variable_ID find_index(Relation &r, const std::string &s, char side) { // Omega quirks: assure the names are propagated inside the relation r.setup_names(); if (r.is_set()) { // side == 's' for (int i = 1; i <= r.n_set(); i++) { std::string ss = r.set_var(i)->name(); if (s == ss) { return r.set_var(i); } } } else if (side == 'w') { for (int i = 1; i <= r.n_inp(); i++) { std::string ss = r.input_var(i)->name(); if (s == ss) { return r.input_var(i); } } } else { // side == 'r' for (int i = 1; i <= r.n_out(); i++) { std::string ss = r.output_var(i)->name(); if (s+"'" == ss) { return r.output_var(i); } } } return NULL; } // EQ_Handle get_eq(const Relation &r, int dim, Var_Kind type) { // Variable_ID v; // switch (type) { // case Set_Var: // v = r.set_var(dim+1); // break; // case Input_Var: // v = r.input_var(dim+1); // break; // case Output_Var: // v = r.output_var(dim+1); // break; // default: // return NULL; // } // for (DNF_iterator di(r.query_DNF()); di; di++) // for (EQ_Iterator ei = (*di)->EQs(); ei; ei++) // if ((*ei).get_coef(v) != 0) // return (*ei); // return NULL; // } // std::Pair split_loop(const Relation &r, const Relation &cond) { // Relation r1 = Intersection(copy(r), copy(cond)); // Relation r2 = Intersection(copy(r), Complement(copy(cond))); // return std::Pair(r1, r2); // }