Head

GCC Code Coverage Report

Directory:	.		Exec	Total	Coverage
File:	src/theory/arith/arith_utilities.h	Lines:	74	111	66.7 %
Date:	2021-11-06	Branches:	52	139	37.4 %


/******************************************************************************
 * Top contributors (to current version):
 *   Tim King, Andrew Reynolds, Andres Noetzli
 *
 * This file is part of the cvc5 project.
 *
 * Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
 * in the top-level source directory and their institutional affiliations.
 * All rights reserved.  See the file COPYING in the top-level source
 * directory for licensing information.
 * ****************************************************************************
 *
 * Common functions for dealing with nodes.
 */

#include "cvc5_private.h"

#ifndef CVC5__THEORY__ARITH__ARITH_UTILITIES_H
#define CVC5__THEORY__ARITH__ARITH_UTILITIES_H

#include <unordered_map>
#include <unordered_set>
#include <vector>

#include "context/cdhashset.h"
#include "expr/node.h"
#include "expr/subs.h"
#include "theory/arith/arithvar.h"
#include "util/dense_map.h"
#include "util/integer.h"
#include "util/rational.h"

namespace cvc5 {
namespace theory {
namespace arith {

//Sets of Nodes
typedef std::unordered_set<Node> NodeSet;
typedef std::unordered_set<TNode> TNodeSet;
typedef context::CDHashSet<Node> CDNodeSet;

//Maps from Nodes -> ArithVars, and vice versa
typedef std::unordered_map<Node, ArithVar> NodeToArithVarMap;
typedef DenseMap<Node> ArithVarToNodeMap;

inline Node mkRationalNode(const Rational& q){
  return NodeManager::currentNM()->mkConst<Rational>(q);
}

inline Node mkBoolNode(bool b){
  return NodeManager::currentNM()->mkConst<bool>(b);
}

/** \f$ k \in {LT, LEQ, EQ, GEQ, GT} \f$ */
inline bool isRelationOperator(Kind k){
  using namespace kind;

  switch(k){
  case LT:
  case LEQ:
  case EQUAL:
  case GEQ:
  case GT:
    return true;
  default:
    return false;
  }
}

/**
 * Given a relational kind, k, return the kind k' s.t.
 * swapping the lefthand and righthand side is equivalent.
 *
 * The following equivalence should hold,
 *   (k l r) <=> (k' r l)
 */
inline Kind reverseRelationKind(Kind k){
  using namespace kind;

  switch(k){
  case LT:    return GT;
  case LEQ:   return GEQ;
  case EQUAL: return EQUAL;
  case GEQ:   return LEQ;
  case GT:    return LT;

  default:
    Unreachable();
  }
}

inline bool evaluateConstantPredicate(Kind k, const Rational& left, const Rational& right){
  using namespace kind;

  switch(k){
  case LT:    return left <  right;
  case LEQ:   return left <= right;
  case EQUAL: return left == right;
  case GEQ:   return left >= right;
  case GT:    return left >  right;
  default:
    Unreachable();
    return true;
  }
}

/**
 * Returns the appropriate coefficient for the infinitesimal given the kind
 * for an arithmetic atom inorder to represent strict inequalities as inequalities.
 *   x < c  becomes  x <= c + (-1) * \f$ \delta \f$
 *   x > c  becomes  x >= x + ( 1) * \f$ \delta \f$
 * Non-strict inequalities have a coefficient of zero.
 */
inline int deltaCoeff(Kind k){
  switch(k){
  case kind::LT:
    return -1;
  case kind::GT:
    return 1;
  default:
    return 0;
  }
}

/**
 * Given a literal to TheoryArith return a single kind to
 * to indicate its underlying structure.
 * The function returns the following in each case:
 * - (K left right) -> K where is a wildcard for EQUAL, LT, GT, LEQ, or GEQ:
 * - (NOT (EQUAL left right)) -> DISTINCT
 * - (NOT (LEQ left right))   -> GT
 * - (NOT (GEQ left right))   -> LT
 * - (NOT (LT left right))    -> GEQ
 * - (NOT (GT left right))    -> LEQ
 * If none of these match, it returns UNDEFINED_KIND.
 */
inline Kind oldSimplifiedKind(TNode literal){
  switch(literal.getKind()){
  case kind::LT:
  case kind::GT:
  case kind::LEQ:
  case kind::GEQ:
  case kind::EQUAL:
    return literal.getKind();
  case  kind::NOT:
    {
      TNode atom = literal[0];
      switch(atom.getKind()){
      case  kind::LEQ: //(not (LEQ x c)) <=> (GT x c)
        return  kind::GT;
      case  kind::GEQ: //(not (GEQ x c)) <=> (LT x c)
        return  kind::LT;
      case  kind::LT: //(not (LT x c)) <=> (GEQ x c)
        return  kind::GEQ;
      case  kind::GT: //(not (GT x c) <=> (LEQ x c)
        return  kind::LEQ;
      case  kind::EQUAL:
        return  kind::DISTINCT;
      default:
        Unreachable();
        return  kind::UNDEFINED_KIND;
      }
    }
  default:
    Unreachable();
    return kind::UNDEFINED_KIND;
  }
}

inline Kind negateKind(Kind k){
  switch(k){
  case kind::LT:       return kind::GEQ;
  case kind::GT:       return kind::LEQ;
  case kind::LEQ:      return kind::GT;
  case kind::GEQ:      return kind::LT;
  case kind::EQUAL:    return kind::DISTINCT;
  case kind::DISTINCT: return kind::EQUAL;
  default:
    return kind::UNDEFINED_KIND;
  }
}

inline Node negateConjunctionAsClause(TNode conjunction){
  Assert(conjunction.getKind() == kind::AND);
  NodeBuilder orBuilder(kind::OR);

  for(TNode::iterator i = conjunction.begin(), end=conjunction.end(); i != end; ++i){
    TNode child = *i;
    Node negatedChild = NodeBuilder(kind::NOT) << (child);
    orBuilder << negatedChild;
  }
  return orBuilder;
}

inline Node maybeUnaryConvert(NodeBuilder& builder)
{
  Assert(builder.getKind() == kind::OR || builder.getKind() == kind::AND
         || builder.getKind() == kind::PLUS || builder.getKind() == kind::MULT);
  Assert(builder.getNumChildren() >= 1);
  if(builder.getNumChildren() == 1){
    return builder[0];
  }else{
    return builder;
  }
}

inline void flattenAnd(Node n, std::vector<TNode>& out){
  Assert(n.getKind() == kind::AND);
  for(Node::iterator i=n.begin(), i_end=n.end(); i != i_end; ++i){
    Node curr = *i;
    if(curr.getKind() == kind::AND){
      flattenAnd(curr, out);
    }else{
      out.push_back(curr);
    }
  }
}

inline Node flattenAnd(Node n){
  std::vector<TNode> out;
  flattenAnd(n, out);
  return NodeManager::currentNM()->mkNode(kind::AND, out);
}

// Returns an node that is the identity of a select few kinds.
inline Node getIdentity(Kind k){
  switch(k){
  case kind::AND:
    return mkBoolNode(true);
  case kind::PLUS:
    return mkRationalNode(0);
  case kind::MULT:
  case kind::NONLINEAR_MULT:
    return mkRationalNode(1);
  default: Unreachable(); return Node::null();  // silence warning
  }
}

inline Node safeConstructNary(NodeBuilder& nb)
{
  switch (nb.getNumChildren()) {
    case 0:
      return getIdentity(nb.getKind());
    case 1:
      return nb[0];
    default:
      return (Node)nb;
  }
}

inline Node safeConstructNary(Kind k, const std::vector<Node>& children) {
  switch (children.size()) {
    case 0:
      return getIdentity(k);
    case 1:
      return children[0];
    default:
      return NodeManager::currentNM()->mkNode(k, children);
  }
}

// Returns the multiplication of a and b.
inline Node mkMult(Node a, Node b) {
  return NodeManager::currentNM()->mkNode(kind::MULT, a, b);
}

// Return a constraint that is equivalent to term being is in the range
// [start, end). This includes start and excludes end.
inline Node mkInRange(Node term, Node start, Node end) {
  NodeManager* nm = NodeManager::currentNM();
  Node above_start = nm->mkNode(kind::LEQ, start, term);
  Node below_end = nm->mkNode(kind::LT, term, end);
  return nm->mkNode(kind::AND, above_start, below_end);
}

// Creates an expression that constrains q to be equal to one of two expressions
// when n is 0 or not. Useful for division by 0 logic.
//   (ite (= n 0) (= q if_zero) (= q not_zero))
inline Node mkOnZeroIte(Node n, Node q, Node if_zero, Node not_zero) {
  Node zero = mkRationalNode(0);
  return n.eqNode(zero).iteNode(q.eqNode(if_zero), q.eqNode(not_zero));
}

inline Node mkPi()
{
  return NodeManager::currentNM()->mkNullaryOperator(
      NodeManager::currentNM()->realType(), kind::PI);
}
/** Join kinds, where k1 and k2 are arithmetic relations returns an
 * arithmetic relation ret such that
 * if (a <k1> b) and (a <k2> b), then (a <ret> b).
 */
Kind joinKinds(Kind k1, Kind k2);

/** Transitive kinds, where k1 and k2 are arithmetic relations returns an
 * arithmetic relation ret such that
 * if (a <k1> b) and (b <k2> c) then (a <ret> c).
 */
Kind transKinds(Kind k1, Kind k2);

/** Is k a transcendental function kind? */
bool isTranscendentalKind(Kind k);
/**
 * Get a lower/upper approximation of the constant r within the given
 * level of precision. In other words, this returns a constant c' such that
 *   c' <= c <= c' + 1/(10^prec) if isLower is true, or
 *   c' + 1/(10^prec) <= c <= c' if isLower is false.
 * where c' is a rational of the form n/d for some n and d <= 10^prec.
 */
Node getApproximateConstant(Node c, bool isLower, unsigned prec);

/** print rational approximation of cr with precision prec on trace c */
void printRationalApprox(const char* c, Node cr, unsigned prec = 5);

/** Arithmetic substitute
 *
 * This computes the substitution n { subs }, but with the caveat
 * that subterms of n that belong to a theory other than arithmetic are
 * not traversed. In other words, terms that belong to other theories are
 * treated as atomic variables. For example:
 *   (5*f(x) + 7*x ){ x -> 3 } returns 5*f(x) + 7*3.
 */
Node arithSubstitute(Node n, const Subs& sub);

/** Make the node u >= a ^ a >= l */
Node mkBounded(Node l, Node a, Node u);

Rational leastIntGreaterThan(const Rational&);

Rational greatestIntLessThan(const Rational&);

/** Negates a node in arithmetic proof normal form. */
Node negateProofLiteral(TNode n);

}  // namespace arith
}  // namespace theory
}  // namespace cvc5

#endif /* CVC5__THEORY__ARITH__ARITH_UTILITIES_H */


Generated by: GCOVR (Version 3.2)

Line	Exec	Source
1		/******************************************************************************
2		* Top contributors (to current version):
3		* Tim King, Andrew Reynolds, Andres Noetzli
4		*
5		* This file is part of the cvc5 project.
6		*
7		* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
8		* in the top-level source directory and their institutional affiliations.
9		* All rights reserved. See the file COPYING in the top-level source
10		* directory for licensing information.
11		* ****************************************************************************
12		*
13		* Common functions for dealing with nodes.
14		*/
15
16		#include "cvc5_private.h"
17
18		#ifndef CVC5__THEORY__ARITH__ARITH_UTILITIES_H
19		#define CVC5__THEORY__ARITH__ARITH_UTILITIES_H
20
21		#include <unordered_map>
22		#include <unordered_set>
23		#include <vector>
24
25		#include "context/cdhashset.h"
26		#include "expr/node.h"
27		#include "expr/subs.h"
28		#include "theory/arith/arithvar.h"
29		#include "util/dense_map.h"
30		#include "util/integer.h"
31		#include "util/rational.h"
32
33		namespace cvc5 {
34		namespace theory {
35		namespace arith {
36
37		//Sets of Nodes
38		typedef std::unordered_set<Node> NodeSet;
39		typedef std::unordered_set<TNode> TNodeSet;
40		typedef context::CDHashSet<Node> CDNodeSet;
41
42		//Maps from Nodes -> ArithVars, and vice versa
43		typedef std::unordered_map<Node, ArithVar> NodeToArithVarMap;
44		typedef DenseMap<Node> ArithVarToNodeMap;
45
46	157259079	inline Node mkRationalNode(const Rational& q){
47	157259079	return NodeManager::currentNM()->mkConst<Rational>(q);
48		}
49
50	11097	inline Node mkBoolNode(bool b){
51	11097	return NodeManager::currentNM()->mkConst<bool>(b);
52		}
53
54		/** \f$ k \in {LT, LEQ, EQ, GEQ, GT} \f$ */
55	254649472	inline bool isRelationOperator(Kind k){
56		using namespace kind;
57
58	254649472	switch(k){
59	13352232	case LT:
60		case LEQ:
61		case EQUAL:
62		case GEQ:
63		case GT:
64	13352232	return true;
65	241297240	default:
66	241297240	return false;
67		}
68		}
69
70		/**
71		* Given a relational kind, k, return the kind k' s.t.
72		* swapping the lefthand and righthand side is equivalent.
73		*
74		* The following equivalence should hold,
75		* (k l r) <=> (k' r l)
76		*/
77	79390	inline Kind reverseRelationKind(Kind k){
78		using namespace kind;
79
80	79390	switch(k){
81	12622	case LT: return GT;
82	3768	case LEQ: return GEQ;
83	11299	case EQUAL: return EQUAL;
84	41848	case GEQ: return LEQ;
85	9853	case GT: return LT;
86
87		default:
88		Unreachable();
89		}
90		}
91
92	379968	inline bool evaluateConstantPredicate(Kind k, const Rational& left, const Rational& right){
93		using namespace kind;
94
95	379968	switch(k){
96		case LT: return left < right;
97	30561	case LEQ: return left <= right;
98	211003	case EQUAL: return left == right;
99	138404	case GEQ: return left >= right;
100		case GT: return left > right;
101		default:
102		Unreachable();
103		return true;
104		}
105		}
106
107		/**
108		* Returns the appropriate coefficient for the infinitesimal given the kind
109		* for an arithmetic atom inorder to represent strict inequalities as inequalities.
110		* x < c becomes x <= c + (-1) * \f$ \delta \f$
111		* x > c becomes x >= x + ( 1) * \f$ \delta \f$
112		* Non-strict inequalities have a coefficient of zero.
113		*/
114	1210241	inline int deltaCoeff(Kind k){
115	1210241	switch(k){
116	321081	case kind::LT:
117	321081	return -1;
118		case kind::GT:
119		return 1;
120	889160	default:
121	889160	return 0;
122		}
123		}
124
125		/**
126		* Given a literal to TheoryArith return a single kind to
127		* to indicate its underlying structure.
128		* The function returns the following in each case:
129		* - (K left right) -> K where is a wildcard for EQUAL, LT, GT, LEQ, or GEQ:
130		* - (NOT (EQUAL left right)) -> DISTINCT
131		* - (NOT (LEQ left right)) -> GT
132		* - (NOT (GEQ left right)) -> LT
133		* - (NOT (LT left right)) -> GEQ
134		* - (NOT (GT left right)) -> LEQ
135		* If none of these match, it returns UNDEFINED_KIND.
136		*/
137	1768	inline Kind oldSimplifiedKind(TNode literal){
138	1768	switch(literal.getKind()){
139	1768	case kind::LT:
140		case kind::GT:
141		case kind::LEQ:
142		case kind::GEQ:
143		case kind::EQUAL:
144	1768	return literal.getKind();
145		case kind::NOT:
146		{
147		TNode atom = literal[0];
148		switch(atom.getKind()){
149		case kind::LEQ: //(not (LEQ x c)) <=> (GT x c)
150		return kind::GT;
151		case kind::GEQ: //(not (GEQ x c)) <=> (LT x c)
152		return kind::LT;
153		case kind::LT: //(not (LT x c)) <=> (GEQ x c)
154		return kind::GEQ;
155		case kind::GT: //(not (GT x c) <=> (LEQ x c)
156		return kind::LEQ;
157		case kind::EQUAL:
158		return kind::DISTINCT;
159		default:
160		Unreachable();
161		return kind::UNDEFINED_KIND;
162		}
163		}
164		default:
165		Unreachable();
166		return kind::UNDEFINED_KIND;
167		}
168		}
169
170	56339	inline Kind negateKind(Kind k){
171	56339	switch(k){
172		case kind::LT: return kind::GEQ;
173		case kind::GT: return kind::LEQ;
174	19261	case kind::LEQ: return kind::GT;
175	37060	case kind::GEQ: return kind::LT;
176	18	case kind::EQUAL: return kind::DISTINCT;
177		case kind::DISTINCT: return kind::EQUAL;
178		default:
179		return kind::UNDEFINED_KIND;
180		}
181		}
182
183		inline Node negateConjunctionAsClause(TNode conjunction){
184		Assert(conjunction.getKind() == kind::AND);
185		NodeBuilder orBuilder(kind::OR);
186
187		for(TNode::iterator i = conjunction.begin(), end=conjunction.end(); i != end; ++i){
188		TNode child = *i;
189		Node negatedChild = NodeBuilder(kind::NOT) << (child);
190		orBuilder << negatedChild;
191		}
192		return orBuilder;
193		}
194
195		inline Node maybeUnaryConvert(NodeBuilder& builder)
196		{
197		Assert(builder.getKind() == kind::OR \|\| builder.getKind() == kind::AND
198		\|\| builder.getKind() == kind::PLUS \|\| builder.getKind() == kind::MULT);
199		Assert(builder.getNumChildren() >= 1);
200		if(builder.getNumChildren() == 1){
201		return builder[0];
202		}else{
203		return builder;
204		}
205		}
206
207	5323	inline void flattenAnd(Node n, std::vector<TNode>& out){
208	5323	Assert(n.getKind() == kind::AND);
209	20335	for(Node::iterator i=n.begin(), i_end=n.end(); i != i_end; ++i){
210	30024	Node curr = *i;
211	15012	if(curr.getKind() == kind::AND){
212	3044	flattenAnd(curr, out);
213		}else{
214	11968	out.push_back(curr);
215		}
216		}
217	5323	}
218
219	2279	inline Node flattenAnd(Node n){
220	4558	std::vector<TNode> out;
221	2279	flattenAnd(n, out);
222	4558	return NodeManager::currentNM()->mkNode(kind::AND, out);
223		}
224
225		// Returns an node that is the identity of a select few kinds.
226	1807	inline Node getIdentity(Kind k){
227	1807	switch(k){
228		case kind::AND:
229		return mkBoolNode(true);
230		case kind::PLUS:
231		return mkRationalNode(0);
232	1807	case kind::MULT:
233		case kind::NONLINEAR_MULT:
234	1807	return mkRationalNode(1);
235		default: Unreachable(); return Node::null(); // silence warning
236		}
237		}
238
239	4229590	inline Node safeConstructNary(NodeBuilder& nb)
240		{
241	4229590	switch (nb.getNumChildren()) {
242		case 0:
243		return getIdentity(nb.getKind());
244	3509693	case 1:
245	3509693	return nb[0];
246	719897	default:
247	719897	return (Node)nb;
248		}
249		}
250
251	43071	inline Node safeConstructNary(Kind k, const std::vector<Node>& children) {
252	43071	switch (children.size()) {
253	1807	case 0:
254	1807	return getIdentity(k);
255	21141	case 1:
256	21141	return children[0];
257	20123	default:
258	20123	return NodeManager::currentNM()->mkNode(k, children);
259		}
260		}
261
262		// Returns the multiplication of a and b.
263		inline Node mkMult(Node a, Node b) {
264		return NodeManager::currentNM()->mkNode(kind::MULT, a, b);
265		}
266
267		// Return a constraint that is equivalent to term being is in the range
268		// [start, end). This includes start and excludes end.
269	102	inline Node mkInRange(Node term, Node start, Node end) {
270	102	NodeManager* nm = NodeManager::currentNM();
271	204	Node above_start = nm->mkNode(kind::LEQ, start, term);
272	204	Node below_end = nm->mkNode(kind::LT, term, end);
273	204	return nm->mkNode(kind::AND, above_start, below_end);
274		}
275
276		// Creates an expression that constrains q to be equal to one of two expressions
277		// when n is 0 or not. Useful for division by 0 logic.
278		// (ite (= n 0) (= q if_zero) (= q not_zero))
279		inline Node mkOnZeroIte(Node n, Node q, Node if_zero, Node not_zero) {
280		Node zero = mkRationalNode(0);
281		return n.eqNode(zero).iteNode(q.eqNode(if_zero), q.eqNode(not_zero));
282		}
283
284	1654	inline Node mkPi()
285		{
286		return NodeManager::currentNM()->mkNullaryOperator(
287	1654	NodeManager::currentNM()->realType(), kind::PI);
288		}
289		/** Join kinds, where k1 and k2 are arithmetic relations returns an
290		* arithmetic relation ret such that
291		* if (a <k1> b) and (a <k2> b), then (a <ret> b).
292		*/
293		Kind joinKinds(Kind k1, Kind k2);
294
295		/** Transitive kinds, where k1 and k2 are arithmetic relations returns an
296		* arithmetic relation ret such that
297		* if (a <k1> b) and (b <k2> c) then (a <ret> c).
298		*/
299		Kind transKinds(Kind k1, Kind k2);
300
301		/** Is k a transcendental function kind? */
302		bool isTranscendentalKind(Kind k);
303		/**
304		* Get a lower/upper approximation of the constant r within the given
305		* level of precision. In other words, this returns a constant c' such that
306		* c' <= c <= c' + 1/(10^prec) if isLower is true, or
307		* c' + 1/(10^prec) <= c <= c' if isLower is false.
308		* where c' is a rational of the form n/d for some n and d <= 10^prec.
309		*/
310		Node getApproximateConstant(Node c, bool isLower, unsigned prec);
311
312		/** print rational approximation of cr with precision prec on trace c */
313		void printRationalApprox(const char* c, Node cr, unsigned prec = 5);
314
315		/** Arithmetic substitute
316		*
317		* This computes the substitution n { subs }, but with the caveat
318		* that subterms of n that belong to a theory other than arithmetic are
319		* not traversed. In other words, terms that belong to other theories are
320		* treated as atomic variables. For example:
321		* (5f(x) + 7x ){ x -> 3 } returns 5f(x) + 73.
322		*/
323		Node arithSubstitute(Node n, const Subs& sub);
324
325		/** Make the node u >= a ^ a >= l */
326		Node mkBounded(Node l, Node a, Node u);
327
328		Rational leastIntGreaterThan(const Rational&);
329
330		Rational greatestIntLessThan(const Rational&);
331
332		/** Negates a node in arithmetic proof normal form. */
333		Node negateProofLiteral(TNode n);
334
335		} // namespace arith
336		} // namespace theory
337		} // namespace cvc5
338
339		#endif /* CVC5__THEORY__ARITH__ARITH_UTILITIES_H */