nroot.hpp

00001 /* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
00002 /*
00003  *  Main authors:
00004  *     Christian Schulte <schulte@gecode.org>
00005  *
00006  *  Copyright:
00007  *     Christian Schulte, 2012
00008  *
00009  *  Last modified:
00010  *     $Date: 2016-05-23 22:18:23 +0200 (Mon, 23 May 2016) $ by $Author: schulte $
00011  *     $Revision: 15073 $
00012  *
00013  *  This file is part of Gecode, the generic constraint
00014  *  development environment:
00015  *     http://www.gecode.org
00016  *
00017  *  Permission is hereby granted, free of charge, to any person obtaining
00018  *  a copy of this software and associated documentation files (the
00019  *  "Software"), to deal in the Software without restriction, including
00020  *  without limitation the rights to use, copy, modify, merge, publish,
00021  *  distribute, sublicense, and/or sell copies of the Software, and to
00022  *  permit persons to whom the Software is furnished to do so, subject to
00023  *  the following conditions:
00024  *
00025  *  The above copyright notice and this permission notice shall be
00026  *  included in all copies or substantial portions of the Software.
00027  *
00028  *  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
00029  *  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
00030  *  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
00031  *  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
00032  *  LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
00033  *  OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
00034  *  WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
00035  *
00036  */
00037 
00038 #include <gecode/int/rel.hh>
00039 
00040 #include <climits>
00041 #include <algorithm>
00042 
00043 namespace Gecode { namespace Int { namespace Arithmetic {
00044 
00045   /*
00046    * Positive bounds consistent nth root
00047    *
00048    */
00049 
00050   template<class Ops, bool minus>
00051   forceinline ExecStatus
00052   prop_nroot_plus_bnd(Space& home, IntView x0, IntView x1, const Ops& ops) {
00053     if (minus) {
00054       bool mod;
00055       do {
00056         mod = false;
00057         {
00058           ModEvent me = x1.gq(home,-ops.cnroot(-x0.min()));
00059           if (me_failed(me)) return ES_FAILED;
00060           mod |= me_modified(me);
00061         }
00062         {
00063           ModEvent me = x1.lq(home,-ops.cnroot(-x0.max()));
00064           if (me_failed(me)) return ES_FAILED;
00065           mod |= me_modified(me);
00066         }
00067         {
00068           ModEvent me = x0.gq(home,-ops.tpow(-x1.min()));
00069           if (me_failed(me)) return ES_FAILED;
00070           mod |= me_modified(me);
00071         }
00072         {
00073           ModEvent me = x0.lq(home,-(ops.tpow(-x1.max()-1)+1));
00074           if (me_failed(me)) return ES_FAILED;
00075           mod |= me_modified(me);
00076         }
00077       } while (mod);
00078     } else {
00079       bool mod;
00080       do {
00081         mod = false;
00082         {
00083           ModEvent me = x1.lq(home,ops.fnroot(x0.max()));
00084           if (me_failed(me)) return ES_FAILED;
00085           mod |= me_modified(me);
00086         }
00087         {
00088           ModEvent me = x1.gq(home,ops.fnroot(x0.min()));
00089           if (me_failed(me)) return ES_FAILED;
00090           mod |= me_modified(me);
00091         }
00092         {
00093           ModEvent me = x0.le(home,ops.tpow(x1.max()+1));
00094           if (me_failed(me)) return ES_FAILED;
00095           mod |= me_modified(me);
00096         }
00097         {
00098           ModEvent me = x0.gq(home,ops.tpow(x1.min()));
00099           if (me_failed(me)) return ES_FAILED;
00100           mod |= me_modified(me);
00101         }
00102       } while (mod);
00103     }
00104     return ES_OK;
00105   }
00106 
00107   template<class Ops, bool minus>
00108   forceinline
00109   NrootPlusBnd<Ops,minus>::NrootPlusBnd(Home home, IntView x0, IntView x1,
00110                                         const Ops& o)
00111     : BinaryPropagator<IntView,PC_INT_BND>(home,x0,x1),
00112       ops(o) {}
00113 
00114   template<class Ops, bool minus>
00115   forceinline ExecStatus
00116   NrootPlusBnd<Ops,minus>::post(Home home, IntView x0, IntView x1, Ops ops) {
00117     if (minus) {
00118       GECODE_ME_CHECK(x0.lq(home,0));
00119       GECODE_ME_CHECK(x1.lq(home,0));
00120     } else {
00121       GECODE_ME_CHECK(x0.gq(home,0));
00122       GECODE_ME_CHECK(x1.gq(home,0));
00123     }
00124     (void) new (home) NrootPlusBnd<Ops,minus>(home,x0,x1,ops);
00125     return ES_OK;
00126   }
00127 
00128   template<class Ops, bool minus>
00129   forceinline
00130   NrootPlusBnd<Ops,minus>::NrootPlusBnd(Space& home, bool share,
00131                                         NrootPlusBnd<Ops,minus>& p)
00132     : BinaryPropagator<IntView,PC_INT_BND>(home,share,p),
00133       ops(p.ops) {}
00134 
00135   template<class Ops, bool minus>
00136   Actor*
00137   NrootPlusBnd<Ops,minus>::copy(Space& home, bool share) {
00138     return new (home) NrootPlusBnd<Ops,minus>(home,share,*this);
00139   }
00140 
00141   template<class Ops, bool minus>
00142   ExecStatus
00143   NrootPlusBnd<Ops,minus>::propagate(Space& home, const ModEventDelta&) {
00144     GECODE_ES_CHECK((prop_nroot_plus_bnd<Ops,minus>(home,x0,x1,ops)));
00145     return x1.assigned() ? home.ES_SUBSUMED(*this) : ES_FIX;
00146   }
00147 
00148 
00149   /*
00150    * Bounds consistent nth root
00151    *
00152    */
00153 
00154   template<class Ops>
00155   forceinline ExecStatus
00156   prop_nroot_bnd(Space& home, IntView x0, IntView x1, const Ops& ops) {
00157     assert((x0.min() < 0) && (x0.max() > 0));
00158     assert((x1.min() < 0) && (x1.max() > 0));
00159 
00160     GECODE_ME_CHECK(x1.lq(home,ops.fnroot(x0.max())));
00161     GECODE_ME_CHECK(x1.gq(home,-ops.cnroot(-x0.min())));
00162     GECODE_ME_CHECK(x0.le(home,ops.tpow(x1.max()+1)));
00163     GECODE_ME_CHECK(x0.gq(home,ops.tpow(x1.min()-1)+1));
00164 
00165     return ES_OK;
00166   }
00167 
00168   template<class Ops>
00169   forceinline
00170   NrootBnd<Ops>::NrootBnd(Home home, IntView x0, IntView x1, const Ops& o)
00171     : BinaryPropagator<IntView,PC_INT_BND>(home,x0,x1),
00172       ops(o) {}
00173 
00174   template<class Ops>
00175   forceinline ExecStatus
00176   NrootBnd<Ops>::post(Home home, IntView x0, IntView x1, Ops ops) {
00177     if (static_cast<unsigned int>(ops.exp()) >= sizeof(int) * CHAR_BIT) {
00178       // The integer limits allow only -2, -1, 0, 1 for x1
00179       GECODE_ME_CHECK(x1.lq(home,1));
00180       GECODE_ME_CHECK(x1.gq(home,-2));
00181       // Just rewrite to values that can be handeled without overflow
00182       ops.exp(ops.even() ? 30 : 31);
00183     }
00184 
00185     if (ops.exp() == 0) {
00186       GECODE_ME_CHECK(x1.eq(home,1));
00187       return ES_OK;
00188     } else if (ops.exp() == 1) {
00189       return Rel::EqBnd<IntView,IntView>::post(home,x0,x1);
00190     }
00191 
00192     if (same(x0,x1)) {
00193       assert(ops.exp() > 1);
00194       GECODE_ME_CHECK(x0.lq(home,1));
00195       GECODE_ME_CHECK(x0.gq(home,ops.even() ? 0 : -2));
00196       return ES_OK;
00197     }
00198 
00199     // Limits values such that no overflow can occur
00200     GECODE_ME_CHECK(x1.lq(home,ops.fnroot(Limits::max)));
00201     GECODE_ME_CHECK(x1.gq(home,-ops.cnroot(-Limits::min)));
00202 
00203     if (ops.even()) {
00204       GECODE_ME_CHECK(x0.gq(home,0));
00205       GECODE_ME_CHECK(x1.gq(home,0));
00206     }
00207 
00208     if ((x0.min() >= 0) || (x1.min() >= 0))
00209       return NrootPlusBnd<Ops,false>::post(home,x0,x1,ops);
00210 
00211     if ((x0.max() <= 0) || (x1.max() <= 0))
00212       return NrootPlusBnd<Ops,true>::post(home,x0,x1,ops);
00213 
00214     assert((x0.min() < 0) && (x0.max() > 0));
00215     assert((x1.min() < 0) && (x1.max() > 0));
00216     GECODE_ES_CHECK(prop_nroot_bnd<Ops>(home,x0,x1,ops));
00217     (void) new (home) NrootBnd(home,x0,x1,ops);
00218     return ES_OK;
00219   }
00220 
00221   template<class Ops>
00222   forceinline
00223   NrootBnd<Ops>::NrootBnd(Space& home, bool share, NrootBnd<Ops>& p)
00224     : BinaryPropagator<IntView,PC_INT_BND>(home,share,p),
00225       ops(p.ops) {}
00226 
00227   template<class Ops>
00228   Actor*
00229   NrootBnd<Ops>::copy(Space& home, bool share) {
00230     return new (home) NrootBnd<Ops>(home,share,*this);
00231   }
00232 
00233   template<class Ops>
00234   ExecStatus
00235   NrootBnd<Ops>::propagate(Space& home, const ModEventDelta&) {
00236     assert(!ops.even());
00237     if ((x0.min() >= 0) || (x1.min() >= 0))
00238       GECODE_REWRITE(*this,(NrootPlusBnd<Ops,false>::post(home(*this),x0,x1,ops)));
00239 
00240     if ((x0.max() <= 0) || (x1.max() <= 0))
00241       GECODE_REWRITE(*this,(NrootPlusBnd<Ops,true>::post(home(*this),x0,x1,ops)));
00242 
00243     GECODE_ES_CHECK(prop_nroot_bnd(home,x0,x1,ops));
00244 
00245     return x0.assigned() && x1.assigned() ? home.ES_SUBSUMED(*this) : ES_NOFIX;
00246   }
00247 
00248 
00249   /*
00250    * Domain consistent nth root
00251    *
00252    */
00254   template<class Ops>
00255   class RangesMapPow {
00256   protected:
00258     Ops ops;
00259   public:
00261     forceinline RangesMapPow(const Ops& o) : ops(o) {}
00263     forceinline int min(int x) const {
00264       return ops.tpow(x);
00265     }
00267     forceinline int max(int x) const {
00268       return ops.tpow(x+1)-1;
00269     }
00270   };
00271 
00273   template<class Ops>
00274   class RangesMapNroot {
00275   protected:
00277     Ops ops;
00278   public:
00280     forceinline RangesMapNroot(const Ops& o) : ops(o) {}
00282     forceinline int min(int x) const {
00283       return (x < 0) ? -ops.cnroot(-x) : ops.fnroot(x);
00284     }
00286     forceinline int max(int x) const {
00287       return (x < 0) ? -ops.cnroot(-x) : ops.fnroot(x);
00288     }
00289  };
00290 
00291   template<class Ops, bool minus>
00292   forceinline
00293   NrootPlusDom<Ops,minus>::NrootPlusDom(Home home, IntView x0, IntView x1,
00294                                         const Ops& o)
00295     : BinaryPropagator<IntView,PC_INT_DOM>(home,x0,x1),
00296       ops(o) {}
00297 
00298   template<class Ops, bool minus>
00299   forceinline ExecStatus
00300   NrootPlusDom<Ops,minus>::post(Home home, IntView x0, IntView x1, Ops ops) {
00301     if (minus) {
00302       GECODE_ME_CHECK(x0.lq(home,0));
00303       GECODE_ME_CHECK(x1.lq(home,0));
00304     } else {
00305       GECODE_ME_CHECK(x0.gq(home,0));
00306       GECODE_ME_CHECK(x1.gq(home,0));
00307     }
00308     GECODE_ES_CHECK((prop_nroot_plus_bnd<Ops,minus>(home,x0,x1,ops)));
00309     (void) new (home) NrootPlusDom<Ops,minus>(home,x0,x1,ops);
00310     return ES_OK;
00311   }
00312 
00313   template<class Ops, bool minus>
00314   forceinline
00315   NrootPlusDom<Ops,minus>::NrootPlusDom(Space& home, bool share,
00316                                         NrootPlusDom<Ops,minus>& p)
00317     : BinaryPropagator<IntView,PC_INT_DOM>(home,share,p),
00318       ops(p.ops) {}
00319 
00320   template<class Ops, bool minus>
00321   Actor*
00322   NrootPlusDom<Ops,minus>::copy(Space& home, bool share) {
00323     return new (home) NrootPlusDom<Ops,minus>(home,share,*this);
00324   }
00325 
00326   template<class Ops, bool minus>
00327   PropCost
00328   NrootPlusDom<Ops,minus>::cost(const Space&, const ModEventDelta& med) const {
00329     if (IntView::me(med) == ME_INT_VAL)
00330       return PropCost::unary(PropCost::LO);
00331     else if (IntView::me(med) == ME_INT_DOM)
00332       return PropCost::binary(PropCost::HI);
00333     else
00334       return PropCost::binary(PropCost::LO);
00335   }
00336 
00337   template<class Ops, bool minus>
00338   ExecStatus
00339   NrootPlusDom<Ops,minus>::propagate(Space& home, const ModEventDelta& med) {
00340     if (IntView::me(med) != ME_INT_DOM) {
00341       GECODE_ES_CHECK((prop_nroot_plus_bnd<Ops,minus>(home,x0,x1,ops)));
00342       return x1.assigned() ? home.ES_SUBSUMED(*this)
00343         : home.ES_NOFIX_PARTIAL(*this,IntView::med(ME_INT_DOM));
00344     }
00345 
00346     {
00347       ViewRanges<IntView> r(x0);
00348       RangesMapNroot<Ops> rmn(ops);
00349       Iter::Ranges::Map<ViewRanges<IntView>,RangesMapNroot<Ops>,false>
00350         m(r,rmn);
00351       GECODE_ME_CHECK(x1.inter_r(home,m,false));
00352     }
00353 
00354     {
00355       ViewRanges<IntView> r(x1);
00356       RangesMapPow<Ops> rmp(ops);
00357       Iter::Ranges::Map<ViewRanges<IntView>,RangesMapPow<Ops>,true>
00358         m(r,rmp);
00359       GECODE_ME_CHECK(x0.inter_r(home,m,false));
00360     }
00361 
00362     return x1.assigned() ? home.ES_SUBSUMED(*this) : ES_FIX;
00363   }
00364 
00365 
00366 
00367   template<class Ops>
00368   forceinline
00369   NrootDom<Ops>::NrootDom(Home home, IntView x0, IntView x1, const Ops& o)
00370     : BinaryPropagator<IntView,PC_INT_DOM>(home,x0,x1),
00371       ops(o) {}
00372 
00373   template<class Ops>
00374   forceinline ExecStatus
00375   NrootDom<Ops>::post(Home home, IntView x0, IntView x1, Ops ops) {
00376     if (static_cast<unsigned int>(ops.exp()) >= sizeof(int) * CHAR_BIT) {
00377       // The integer limits allow only -2, -1, 0, 1 for x1
00378       GECODE_ME_CHECK(x1.lq(home,1));
00379       GECODE_ME_CHECK(x1.gq(home,-2));
00380       // Just rewrite to values that can be handeled without overflow
00381       ops.exp(ops.even() ? 30 : 31);
00382     }
00383 
00384     if (ops.exp() == 0) {
00385       GECODE_ME_CHECK(x1.eq(home,1));
00386       return ES_OK;
00387     } else if (ops.exp() == 1) {
00388       return Rel::EqDom<IntView,IntView>::post(home,x0,x1);
00389     }
00390 
00391     if (same(x0,x1)) {
00392       assert(ops.exp() > 1);
00393       GECODE_ME_CHECK(x0.lq(home,1));
00394       GECODE_ME_CHECK(x0.gq(home,ops.even() ? 0 : -2));
00395       return ES_OK;
00396     }
00397 
00398     // Limits values such that no overflow can occur
00399     GECODE_ME_CHECK(x1.lq(home,ops.fnroot(Limits::max)));
00400     GECODE_ME_CHECK(x1.gq(home,-ops.cnroot(-Limits::min)));
00401 
00402     if (ops.even()) {
00403       GECODE_ME_CHECK(x0.gq(home,0));
00404       GECODE_ME_CHECK(x1.gq(home,0));
00405     }
00406 
00407     if ((x0.min() >= 0) || (x1.min() >= 0))
00408       return NrootPlusDom<Ops,false>::post(home,x0,x1,ops);
00409 
00410     if ((x0.max() <= 0) || (x1.max() <= 0))
00411       return NrootPlusDom<Ops,true>::post(home,x0,x1,ops);
00412 
00413     assert((x0.min() < 0) && (x0.max() > 0));
00414     assert((x1.min() < 0) && (x1.max() > 0));
00415     GECODE_ES_CHECK(prop_nroot_bnd<Ops>(home,x0,x1,ops));
00416     (void) new (home) NrootDom(home,x0,x1,ops);
00417     return ES_OK;
00418   }
00419 
00420   template<class Ops>
00421   forceinline
00422   NrootDom<Ops>::NrootDom(Space& home, bool share, NrootDom<Ops>& p)
00423     : BinaryPropagator<IntView,PC_INT_DOM>(home,share,p),
00424       ops(p.ops) {}
00425 
00426   template<class Ops>
00427   Actor*
00428   NrootDom<Ops>::copy(Space& home, bool share) {
00429     return new (home) NrootDom<Ops>(home,share,*this);
00430   }
00431 
00432   template<class Ops>
00433   PropCost
00434   NrootDom<Ops>::cost(const Space&, const ModEventDelta& med) const {
00435     if (IntView::me(med) == ME_INT_VAL)
00436       return PropCost::unary(PropCost::LO);
00437     else if (IntView::me(med) == ME_INT_DOM)
00438       return PropCost::binary(PropCost::HI);
00439     else
00440       return PropCost::binary(PropCost::LO);
00441   }
00442 
00443   template<class Ops>
00444   ExecStatus
00445   NrootDom<Ops>::propagate(Space& home, const ModEventDelta& med) {
00446     assert(!ops.even());
00447     if ((x0.min() >= 0) || (x1.min() >= 0))
00448       GECODE_REWRITE(*this,(NrootPlusDom<Ops,false>::post(home(*this),x0,x1,ops)));
00449 
00450     if ((x0.max() <= 0) || (x1.max() <= 0))
00451       GECODE_REWRITE(*this,(NrootPlusDom<Ops,true>::post(home(*this),x0,x1,ops)));
00452 
00453     if (IntView::me(med) != ME_INT_DOM) {
00454       GECODE_ES_CHECK(prop_nroot_bnd<Ops>(home,x0,x1,ops));
00455       return x0.assigned() && x1.assigned() ? home.ES_SUBSUMED(*this)
00456         : home.ES_NOFIX_PARTIAL(*this,IntView::med(ME_INT_DOM));
00457     }
00458 
00459     {
00460       ViewRanges<IntView> r(x0);
00461       RangesMapNroot<Ops> rmn(ops);
00462       Iter::Ranges::Map<ViewRanges<IntView>,RangesMapNroot<Ops>,false>
00463         m(r,rmn);
00464       GECODE_ME_CHECK(x1.inter_r(home,m,false));
00465     }
00466 
00467     {
00468       ViewRanges<IntView> r(x1);
00469       RangesMapPow<Ops> rmp(ops);
00470       Iter::Ranges::Map<ViewRanges<IntView>,RangesMapPow<Ops>,true>
00471         m(r,rmp);
00472       GECODE_ME_CHECK(x0.inter_r(home,m,false));
00473     }
00474 
00475     return x0.assigned() && x1.assigned() ? home.ES_SUBSUMED(*this) : ES_FIX;
00476   }
00477 
00478 
00479 }}}
00480 
00481 // STATISTICS: int-prop
00482