Source Code Cross Referenced for Monomial.java in  » Testing » KeY » de » uka » ilkd » key » rule » metaconstruct » arith » Java Source Code / Java DocumentationJava Source Code and Java Documentation

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Java Source Code / Java Documentation » Testing » KeY » de.uka.ilkd.key.rule.metaconstruct.arith 
Source Cross Referenced  Class Diagram Java Document (Java Doc) 


001:        // This file is part of KeY - Integrated Deductive Software Design
002:        // Copyright (C) 2001-2007 Universitaet Karlsruhe, Germany
003:        //                         Universitaet Koblenz-Landau, Germany
004:        //                         Chalmers University of Technology, Sweden
005:        //
006:        // The KeY system is protected by the GNU General Public License. 
007:        // See LICENSE.TXT for details.
008:        //
009:        //
010:
011:        package de.uka.ilkd.key.rule.metaconstruct.arith;
012:
013:        import java.math.BigInteger;
014:
015:        import de.uka.ilkd.key.java.Services;
016:        import de.uka.ilkd.key.java.expression.literal.IntLiteral;
017:        import de.uka.ilkd.key.logic.*;
018:        import de.uka.ilkd.key.logic.ldt.IntegerLDT;
019:        import de.uka.ilkd.key.logic.op.AbstractMetaOperator;
020:        import de.uka.ilkd.key.logic.op.Operator;
021:        import de.uka.ilkd.key.logic.op.TermSymbol;
022:        import de.uka.ilkd.key.util.Debug;
023:        import de.uka.ilkd.key.util.LRUCache;
024:
025:        /**
026:         * Class for analysing and modifying monomial expressions over the integers
027:         */
028:        public class Monomial {
029:
030:            private final ListOfTerm parts;
031:            private final BigInteger coefficient;
032:
033:            private Monomial(final ListOfTerm parts,
034:                    final BigInteger coefficient) {
035:                this .parts = parts;
036:                this .coefficient = coefficient;
037:            }
038:
039:            private static final LRUCache monomialCache = new LRUCache(2000);
040:
041:            public static final Monomial ONE = new Monomial(
042:                    SLListOfTerm.EMPTY_LIST, BigInteger.ONE);
043:
044:            public static Monomial create(Term monoTerm, Services services) {
045:                Monomial res = (Monomial) monomialCache.get(monoTerm);
046:                if (res == null) {
047:                    res = createHelp(monoTerm, services);
048:                    monomialCache.put(monoTerm, res);
049:                }
050:                return res;
051:            }
052:
053:            private static Monomial createHelp(Term monomial, Services services) {
054:                final Analyser a = new Analyser(services);
055:                a.analyse(monomial);
056:                return new Monomial(a.parts, a.coeff);
057:            }
058:
059:            public Monomial setCoefficient(BigInteger c) {
060:                return new Monomial(parts, c);
061:            }
062:
063:            public Monomial multiply(BigInteger c) {
064:                return new Monomial(parts, coefficient.multiply(c));
065:            }
066:
067:            public Monomial multiply(Monomial m) {
068:                return new Monomial(parts.prepend(m.parts), coefficient
069:                        .multiply(m.coefficient));
070:            }
071:
072:            public Monomial addToCoefficient(BigInteger c) {
073:                return new Monomial(parts, coefficient.add(c));
074:            }
075:
076:            /**
077:             * @return true iff the monomial <code>this</code> divides the monomial
078:             *         <code>m</code>
079:             */
080:            public boolean divides(Monomial m) {
081:                if (m.coefficient.signum() == 0)
082:                    return true;
083:                if (this .coefficient.signum() == 0)
084:                    return false;
085:                if (m.coefficient.remainder(this .coefficient).signum() != 0)
086:                    return false;
087:
088:                return difference(this .parts, m.parts).isEmpty();
089:            }
090:
091:            /**
092:             * @return true iff the variables/parts of <code>this</code> subsume the
093:             *         variables of <code>m</code>, i.e., if each variable that
094:             *         occurs in <code>m</code> occurs in the same or a higher power
095:             *         in <code>this</code>
096:             */
097:            public boolean variablesSubsume(Monomial m) {
098:                return this .parts.size() >= m.parts.size()
099:                        && difference(m.parts, this .parts).isEmpty();
100:            }
101:
102:            public boolean variablesEqual(Monomial m) {
103:                return this .parts.size() == m.parts.size()
104:                        && this .variablesSubsume(m);
105:            }
106:
107:            public boolean variablesDisjoint(Monomial m) {
108:                return difference(m.parts, this .parts).size() == m.parts.size();
109:            }
110:
111:            /**
112:             * @return true iff the coefficient of <code>m</code> can be made smaller
113:             *         (absolutely) by subtracting a multiple of <code>this</code>
114:             */
115:            public boolean reducible(Monomial m) {
116:                final BigInteger a = m.coefficient;
117:                final BigInteger c = this .coefficient;
118:
119:                if (LexPathOrdering.compare(a.add(c), a) >= 0
120:                        && LexPathOrdering.compare(a.subtract(c), a) >= 0)
121:                    return false;
122:
123:                return difference(this .parts, m.parts).isEmpty();
124:            }
125:
126:            /**
127:             * @return the result of dividing the monomial <code>m</code> by the
128:             *         monomial <code>this</code>
129:             */
130:            public Monomial reduce(Monomial m) {
131:                final BigInteger a = m.coefficient;
132:                final BigInteger c = this .coefficient;
133:
134:                if (a.signum() == 0 || c.signum() == 0)
135:                    return new Monomial(SLListOfTerm.EMPTY_LIST,
136:                            BigInteger.ZERO);
137:
138:                return new Monomial(difference(m.parts, this .parts),
139:                        LexPathOrdering.divide(a, c));
140:            }
141:
142:            /**
143:             * @return the result of dividing the least common reducible (LCR) of
144:             *         monomial <code>m</code> and <code>this</code> by the monomial
145:             *         <code>this</code>
146:             */
147:            public Monomial divideLCR(Monomial m) {
148:                Debug.assertFalse(coefficient.signum() == 0);
149:                Debug.assertFalse(m.coefficient.signum() == 0);
150:
151:                final ListOfTerm newParts = difference(m.parts, this .parts);
152:
153:                final BigInteger gcd = coefficient.abs().gcd(
154:                        m.coefficient.abs());
155:                return new Monomial(newParts, m.coefficient.divide(gcd));
156:
157:                /*
158:                 The code for groebner bases over the integers. We do not use that
159:                 anymore and instead compute groebner bases over the rationals
160:                 (using pseudo-reduction)
161:                 
162:                // in case one the coefficient of one of the monomials divides the other
163:                // coefficient: simply make sure that the leading terms cancel out each
164:                // other. this makes the whole algorithm a bit more robust concerning
165:                // signs
166:                if ( coefficient.remainder ( m.coefficient ).signum () == 0 )
167:                    return new Monomial ( newParts, BigInteger.ONE );
168:                if ( m.coefficient.remainder ( coefficient ).signum () == 0 )
169:                    return new Monomial ( newParts, m.coefficient.divide ( coefficient ) );
170:
171:                BigInteger cofactor = cofactor ( coefficient, m.coefficient );
172:                // (any)one of the two cofactors has to be negated
173:                if ( coefficient.compareTo ( m.coefficient ) < 0 )
174:                    cofactor = cofactor.negate ();
175:                
176:                return new Monomial ( newParts, cofactor );
177:                 */
178:            }
179:
180:            /**
181:             * Extended euclidian algorithm for computing cofactors. This satisfies the
182:             * equation <code>gcd(a,b)=a*cofactor(a,b)+b*cofactor(b,a)</code>
183:             */
184:            private BigInteger cofactor(BigInteger v0, BigInteger v1) {
185:                final boolean neg = v0.signum() < 0;
186:                v0 = v0.abs();
187:                v1 = v1.abs();
188:                BigInteger c0 = BigInteger.ONE;
189:                BigInteger c1 = BigInteger.ZERO;
190:                while (v1.signum() != 0) {
191:                    final BigInteger[] divRem = v0.divideAndRemainder(v1);
192:                    v0 = v1;
193:                    v1 = divRem[1];
194:                    final BigInteger newC = c0.subtract(c1.multiply(divRem[0]));
195:                    c0 = c1;
196:                    c1 = newC;
197:                }
198:                if (neg)
199:                    return c0.negate();
200:                return c0;
201:            }
202:
203:            public Term toTerm(Services services) {
204:                final TermSymbol mul = services.getTypeConverter()
205:                        .getIntegerLDT().getArithMultiplication();
206:                Term res = null;
207:
208:                final IteratorOfTerm it = parts.iterator();
209:                if (it.hasNext()) {
210:                    res = it.next();
211:                    while (it.hasNext())
212:                        res = TermFactory.DEFAULT.createFunctionTerm(mul, res,
213:                                it.next());
214:                }
215:
216:                final IntLiteral lit = new IntLiteral(coefficient.toString());
217:                final Term cTerm = services.getTypeConverter()
218:                        .convertToLogicElement(lit);
219:
220:                if (res == null)
221:                    res = cTerm;
222:                else if (!BigInteger.ONE.equals(coefficient))
223:                    res = TermFactory.DEFAULT.createFunctionTerm(mul, res,
224:                            cTerm);
225:
226:                return res;
227:            }
228:
229:            public String toString() {
230:                final StringBuffer res = new StringBuffer();
231:                res.append(coefficient);
232:
233:                final IteratorOfTerm it = parts.iterator();
234:                while (it.hasNext())
235:                    res.append(" * " + it.next());
236:
237:                return res.toString();
238:            }
239:
240:            private static class Analyser {
241:                public BigInteger coeff = BigInteger.ONE;
242:                public ListOfTerm parts = SLListOfTerm.EMPTY_LIST;
243:                private final Services services;
244:                private final Operator numbers, mul;
245:
246:                public Analyser(final Services services) {
247:                    this .services = services;
248:                    final IntegerLDT intLDT = services.getTypeConverter()
249:                            .getIntegerLDT();
250:                    numbers = intLDT.getNumberSymbol();
251:                    mul = intLDT.getArithMultiplication();
252:                }
253:
254:                public void analyse(Term monomial) {
255:                    if (monomial.op() == mul) {
256:                        analyse(monomial.sub(0));
257:                        analyse(monomial.sub(1));
258:                    } else if (monomial.op() == numbers) {
259:                        final BigInteger c = new BigInteger(
260:                                AbstractMetaOperator.convertToDecimalString(
261:                                        monomial, services));
262:                        coeff = coeff.multiply(c);
263:                    } else {
264:                        parts = parts.prepend(monomial);
265:                    }
266:                }
267:            }
268:
269:            public boolean equals(Object o) {
270:                if (o == this )
271:                    return true;
272:
273:                if (!(o instanceof  Monomial))
274:                    return false;
275:
276:                final Monomial m = (Monomial) o;
277:
278:                if (!coefficient.equals(m.coefficient))
279:                    return false;
280:                if (parts.size() != m.parts.size())
281:                    return false;
282:                return difference(parts, m.parts).isEmpty();
283:            }
284:
285:            public int hashCode() {
286:                int res = coefficient.hashCode();
287:                final IteratorOfTerm it = parts.iterator();
288:                while (it.hasNext())
289:                    res += it.next().hashCode();
290:                return res;
291:            }
292:
293:            /**
294:             * @return the list of all terms that occur in <code>a</code> but not in
295:             *         <code>b</code>. multiplicity is treated as well here, so this
296:             *         is really difference of multisets
297:             */
298:            private static ListOfTerm difference(ListOfTerm a, ListOfTerm b) {
299:                ListOfTerm res = a;
300:                final IteratorOfTerm it = b.iterator();
301:                while (it.hasNext() && !res.isEmpty())
302:                    res = res.removeFirst(it.next());
303:                return res;
304:            }
305:
306:            public BigInteger getCoefficient() {
307:                return coefficient;
308:            }
309:
310:            public ListOfTerm getParts() {
311:                return parts;
312:            }
313:
314:            public boolean variablesAreCoprime(Monomial m) {
315:                return difference(parts, m.parts).equals(parts);
316:            }
317:
318:        }
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