/**
  @file 

  @ingroup cudd

  @brief %ADD ITE function and satellites.

  @author Fabio Somenzi

  @copyright@parblock
  Copyright (c) 1995-2015, Regents of the University of Colorado

  All rights reserved.

  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions
  are met:

  Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

  Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer in the
  documentation and/or other materials provided with the distribution.

  Neither the name of the University of Colorado nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
  COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
  @endparblock

*/

#include "util.h"
#include "cuddInt.h"

/*---------------------------------------------------------------------------*/
/* Constant declarations                                                     */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Stucture declarations                                                     */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Type declarations                                                         */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Variable declarations                                                     */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Macro declarations                                                        */
/*---------------------------------------------------------------------------*/

/** \cond */

/*---------------------------------------------------------------------------*/
/* Static function prototypes                                                */
/*---------------------------------------------------------------------------*/

static void addVarToConst (DdNode *f, DdNode **gp, DdNode **hp, DdNode *one, DdNode *zero);

/** \endcond */


/*---------------------------------------------------------------------------*/
/* Definition of exported functions                                          */
/*---------------------------------------------------------------------------*/


/**
  @brief Implements ITE(f,g,h).

  @details This procedure assumes that f is a 0-1 %ADD.

  @return a pointer to the resulting %ADD if successful; NULL
  otherwise.

  @sideeffect None

  @see Cudd_bddIte Cudd_addIteConstant Cudd_addApply

*/
DdNode *
Cudd_addIte(
  DdManager * dd,
  DdNode * f,
  DdNode * g,
  DdNode * h)
{
    DdNode *res;

    do {
	dd->reordered = 0;
	res = cuddAddIteRecur(dd,f,g,h);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_addIte */


/**
  @brief Implements ITEconstant for %ADDs.

  @details f must be a 0-1 %ADD.  No new nodes are created. This
  function can be used, for instance, to check that g has a constant
  value (specified by h) whenever f is 1. If the constant value is
  unknown, then one should use Cudd_addEvalConst.

  @return a pointer to the resulting %ADD (which may or may not be
  constant) or DD_NON_CONSTANT.

  @sideeffect None

  @see Cudd_addIte Cudd_addEvalConst Cudd_bddIteConstant

*/
DdNode *
Cudd_addIteConstant(
  DdManager * dd,
  DdNode * f,
  DdNode * g,
  DdNode * h)
{
    DdNode *one,*zero;
    DdNode *Fv,*Fnv,*Gv,*Gnv,*Hv,*Hnv,*r,*t,*e;
    int topf,topg,toph,v;

    statLine(dd);
    /* Trivial cases. */
    if (f == (one = DD_ONE(dd))) {	/* ITE(1,G,H) = G */
        return(g);
    }
    if (f == (zero = DD_ZERO(dd))) {	/* ITE(0,G,H) = H */
        return(h);
    }

    /* From now on, f is known not to be a constant. */
    addVarToConst(f,&g,&h,one,zero);

    /* Check remaining one variable cases. */
    if (g == h) { 			/* ITE(F,G,G) = G */
        return(g);
    }
    if (cuddIsConstant(g) && cuddIsConstant(h)) {
        return(DD_NON_CONSTANT);
    }

    topf = cuddI(dd,f->index);
    topg = cuddI(dd,g->index);
    toph = cuddI(dd,h->index);
    v = ddMin(topg,toph);

    /* ITE(F,G,H) = (x,G,H) (non constant) if F = (x,1,0), x < top(G,H). */
    if (topf < v && cuddIsConstant(cuddT(f)) && cuddIsConstant(cuddE(f))) {
	return(DD_NON_CONSTANT);
    }

    /* Check cache. */
    r = cuddConstantLookup(dd,DD_ADD_ITE_CONSTANT_TAG,f,g,h);
    if (r != NULL) {
        return(r);
    }

    /* Compute cofactors. */
    if (topf <= v) {
	v = ddMin(topf,v);	/* v = top_var(F,G,H) */
        Fv = cuddT(f); Fnv = cuddE(f);
    } else {
        Fv = Fnv = f;
    }
    if (topg == v) {
        Gv = cuddT(g); Gnv = cuddE(g);
    } else {
        Gv = Gnv = g;
    }
    if (toph == v) {
        Hv = cuddT(h); Hnv = cuddE(h);
    } else {
        Hv = Hnv = h;
    }
    
    /* Recursive step. */
    t = Cudd_addIteConstant(dd,Fv,Gv,Hv);
    if (t == DD_NON_CONSTANT || !cuddIsConstant(t)) {
	cuddCacheInsert(dd, DD_ADD_ITE_CONSTANT_TAG, f, g, h, DD_NON_CONSTANT);
	return(DD_NON_CONSTANT);
    }
    e = Cudd_addIteConstant(dd,Fnv,Gnv,Hnv);
    if (e == DD_NON_CONSTANT || !cuddIsConstant(e) || t != e) {
	cuddCacheInsert(dd, DD_ADD_ITE_CONSTANT_TAG, f, g, h, DD_NON_CONSTANT);
	return(DD_NON_CONSTANT);
    }
    cuddCacheInsert(dd, DD_ADD_ITE_CONSTANT_TAG, f, g, h, t);
    return(t);

} /* end of Cudd_addIteConstant */


/**
  @brief Checks whether %ADD g is constant whenever %ADD f is 1.

  @details f must be a 0-1 %ADD.  If f is identically 0, the check is
  assumed to be successful, and the background value is returned.  No
  new nodes are created.

  @return a pointer to the resulting %ADD (which may or may not be
  constant) or DD_NON_CONSTANT.

  @sideeffect None

  @see Cudd_addIteConstant Cudd_addLeq

*/
DdNode *
Cudd_addEvalConst(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    DdNode *zero;
    DdNode *Fv,*Fnv,*Gv,*Gnv,*r,*t,*e;
    int topf,topg;

#ifdef DD_DEBUG
    assert(!Cudd_IsComplement(f));
#endif

    statLine(dd);
    /* Terminal cases. */
    if (f == DD_ONE(dd) || cuddIsConstant(g)) {
        return(g);
    }
    if (f == (zero = DD_ZERO(dd))) {
        return(dd->background);
    }

#ifdef DD_DEBUG
    assert(!cuddIsConstant(f));
#endif
    /* From now on, f and g are known not to be constants. */

    topf = cuddI(dd,f->index);
    topg = cuddI(dd,g->index);

    /* Check cache. */
    r = cuddConstantLookup(dd,DD_ADD_EVAL_CONST_TAG,f,g,g);
    if (r != NULL) {
        return(r);
    }

    /* Compute cofactors. */
    if (topf <= topg) {
        Fv = cuddT(f); Fnv = cuddE(f);
    } else {
        Fv = Fnv = f;
    }
    if (topg <= topf) {
        Gv = cuddT(g); Gnv = cuddE(g);
    } else {
        Gv = Gnv = g;
    }
    
    /* Recursive step. */
    if (Fv != zero) {
	t = Cudd_addEvalConst(dd,Fv,Gv);
	if (t == DD_NON_CONSTANT || !cuddIsConstant(t)) {
	    cuddCacheInsert2(dd, Cudd_addEvalConst, f, g, DD_NON_CONSTANT);
	    return(DD_NON_CONSTANT);
	}
	if (Fnv != zero) {
	    e = Cudd_addEvalConst(dd,Fnv,Gnv);
	    if (e == DD_NON_CONSTANT || !cuddIsConstant(e) || t != e) {
		cuddCacheInsert2(dd, Cudd_addEvalConst, f, g, DD_NON_CONSTANT);
		return(DD_NON_CONSTANT);
	    }
	}
	cuddCacheInsert2(dd,Cudd_addEvalConst,f,g,t);
	return(t);
    } else { /* Fnv must be != zero */
	e = Cudd_addEvalConst(dd,Fnv,Gnv);
	cuddCacheInsert2(dd, Cudd_addEvalConst, f, g, e);
	return(e);
    }

} /* end of Cudd_addEvalConst */


/**
  @brief Computes the complement of an %ADD a la C language.

  @details The complement of 0 is 1 and the complement of everything
  else is 0.

  @return a pointer to the resulting %ADD if successful; NULL otherwise.

  @sideeffect None

  @see Cudd_addNegate

*/
DdNode *
Cudd_addCmpl(
  DdManager * dd,
  DdNode * f)
{
    DdNode *res;

    do {
	dd->reordered = 0;
	res = cuddAddCmplRecur(dd,f);
    } while (dd->reordered == 1);
    if (dd->errorCode == CUDD_TIMEOUT_EXPIRED && dd->timeoutHandler) {
        dd->timeoutHandler(dd, dd->tohArg);
    }
    return(res);

} /* end of Cudd_addCmpl */


/**
  @brief Determines whether f is less than or equal to g.

  @details No new nodes are created. This procedure works for arbitrary ADDs.
  For 0-1 ADDs Cudd_addEvalConst is more efficient.

  @return 1 if f is less than or equal to g; 0 otherwise.

  @sideeffect None

  @see Cudd_addIteConstant Cudd_addEvalConst Cudd_bddLeq

*/
int
Cudd_addLeq(
  DdManager * dd,
  DdNode * f,
  DdNode * g)
{
    DdNode *tmp, *fv, *fvn, *gv, *gvn;
    int topf, topg, res;

    /* Terminal cases. */
    if (f == g) return(1);

    statLine(dd);
    if (cuddIsConstant(f)) {
	if (cuddIsConstant(g)) return(cuddV(f) <= cuddV(g));
	if (f == DD_MINUS_INFINITY(dd)) return(1);
	if (f == DD_PLUS_INFINITY(dd)) return(0); /* since f != g */
    }
    if (g == DD_PLUS_INFINITY(dd)) return(1);
    if (g == DD_MINUS_INFINITY(dd)) return(0); /* since f != g */

    /* Check cache. */
    tmp = cuddCacheLookup2(dd,(DD_CTFP)Cudd_addLeq,f,g);
    if (tmp != NULL) {
	return(tmp == DD_ONE(dd));
    }

    /* Compute cofactors. One of f and g is not constant. */
    topf = cuddI(dd,f->index);
    topg = cuddI(dd,g->index);
    if (topf <= topg) {
	fv = cuddT(f); fvn = cuddE(f);
    } else {
	fv = fvn = f;
    }
    if (topg <= topf) {
	gv = cuddT(g); gvn = cuddE(g);
    } else {
	gv = gvn = g;
    }

    res = Cudd_addLeq(dd,fvn,gvn) && Cudd_addLeq(dd,fv,gv);

    /* Store result in cache and return. */
    cuddCacheInsert2(dd,(DD_CTFP) Cudd_addLeq,f,g,
		     Cudd_NotCond(DD_ONE(dd),res==0));
    return(res);

} /* end of Cudd_addLeq */


/*---------------------------------------------------------------------------*/
/* Definition of internal functions                                          */
/*---------------------------------------------------------------------------*/


/**
  @brief Implements the recursive step of Cudd_addIte(f,g,h).

  @return a pointer to the resulting %ADD if successful; NULL
  otherwise.

  @sideeffect None

  @see Cudd_addIte

*/
DdNode *
cuddAddIteRecur(
  DdManager * dd,
  DdNode * f,
  DdNode * g,
  DdNode * h)
{
    DdNode *one,*zero;
    DdNode *r,*Fv,*Fnv,*Gv,*Gnv,*Hv,*Hnv,*t,*e;
    int topf,topg,toph,v;
    unsigned int index;

    statLine(dd);
    /* Trivial cases. */

    /* One variable cases. */
    if (f == (one = DD_ONE(dd))) {	/* ITE(1,G,H) = G */
        return(g);
    }
    if (f == (zero = DD_ZERO(dd))) {	/* ITE(0,G,H) = H */
        return(h);
    }

    /* From now on, f is known to not be a constant. */
    addVarToConst(f,&g,&h,one,zero);

    /* Check remaining one variable cases. */
    if (g == h) {			/* ITE(F,G,G) = G */
        return(g);
    }

    if (g == one) {			/* ITE(F,1,0) = F */
        if (h == zero) return(f);
    }

    topf = cuddI(dd,f->index);
    topg = cuddI(dd,g->index);
    toph = cuddI(dd,h->index);
    v = ddMin(topg,toph);

    /* A shortcut: ITE(F,G,H) = (x,G,H) if F=(x,1,0), x < top(G,H). */
    if (topf < v && cuddT(f) == one && cuddE(f) == zero) {
	r = cuddUniqueInter(dd,(int)f->index,g,h);
	return(r);
    }
    if (topf < v && cuddT(f) == zero && cuddE(f) == one) {
	r = cuddUniqueInter(dd,(int)f->index,h,g);
	return(r);
    }

    /* Check cache. */
    r = cuddCacheLookup(dd,DD_ADD_ITE_TAG,f,g,h);
    if (r != NULL) {
        return(r);
    }

    checkWhetherToGiveUp(dd);

    /* Compute cofactors. */
    index = f->index;
    if (topf <= v) {
	v = ddMin(topf,v);	/* v = top_var(F,G,H) */
        Fv = cuddT(f); Fnv = cuddE(f);
    } else {
        Fv = Fnv = f;
    }
    if (topg == v) {
	index = g->index;
        Gv = cuddT(g); Gnv = cuddE(g);
    } else {
        Gv = Gnv = g;
    }
    if (toph == v) {
	index = h->index;
        Hv = cuddT(h); Hnv = cuddE(h);
    } else {
        Hv = Hnv = h;
    }
    
    /* Recursive step. */
    t = cuddAddIteRecur(dd,Fv,Gv,Hv);
    if (t == NULL) return(NULL);
    cuddRef(t);

    e = cuddAddIteRecur(dd,Fnv,Gnv,Hnv);
    if (e == NULL) {
	Cudd_RecursiveDeref(dd,t);
	return(NULL);
    }
    cuddRef(e);

    r = (t == e) ? t : cuddUniqueInter(dd,index,t,e);
    if (r == NULL) {
	Cudd_RecursiveDeref(dd,t);
	Cudd_RecursiveDeref(dd,e);
	return(NULL);
    }
    cuddDeref(t);
    cuddDeref(e);

    cuddCacheInsert(dd,DD_ADD_ITE_TAG,f,g,h,r);

    return(r);

} /* end of cuddAddIteRecur */


/**
  @brief Performs the recursive step of Cudd_addCmpl.

  @return a pointer to the resulting %ADD if successful; NULL
  otherwise.

  @sideeffect None

  @see Cudd_addCmpl

*/
DdNode *
cuddAddCmplRecur(
  DdManager * dd,
  DdNode * f)
{
    DdNode *one,*zero;
    DdNode *r,*Fv,*Fnv,*t,*e;

    statLine(dd);
    one = DD_ONE(dd);
    zero = DD_ZERO(dd); 

    if (cuddIsConstant(f)) {
        if (f == zero) {
	    return(one);
	} else {
	    return(zero);
	}
    }
    r = cuddCacheLookup1(dd,Cudd_addCmpl,f);
    if (r != NULL) {
	return(r);
    }
    checkWhetherToGiveUp(dd);
    Fv = cuddT(f);
    Fnv = cuddE(f);
    t = cuddAddCmplRecur(dd,Fv);
    if (t == NULL) return(NULL);
    cuddRef(t);
    e = cuddAddCmplRecur(dd,Fnv);
    if (e == NULL) {
	Cudd_RecursiveDeref(dd,t);
	return(NULL);
    }
    cuddRef(e);
    r = (t == e) ? t : cuddUniqueInter(dd,(int)f->index,t,e);
    if (r == NULL) {
	Cudd_RecursiveDeref(dd, t);
	Cudd_RecursiveDeref(dd, e);
	return(NULL);
    }
    cuddDeref(t);
    cuddDeref(e);
    cuddCacheInsert1(dd,Cudd_addCmpl,f,r);
    return(r);

} /* end of cuddAddCmplRecur */


/*---------------------------------------------------------------------------*/
/* Definition of static functions                                            */
/*---------------------------------------------------------------------------*/


/**
  @brief Replaces variables with constants if possible (part of
  canonical form).

  @sideeffect None

*/
static void
addVarToConst(
  DdNode * f,
  DdNode ** gp,
  DdNode ** hp,
  DdNode * one,
  DdNode * zero)
{
    DdNode *g = *gp;
    DdNode *h = *hp;

    if (f == g) { /* ITE(F,F,H) = ITE(F,1,H) = F + H */
	*gp = one;
    }

    if (f == h) { /* ITE(F,G,F) = ITE(F,G,0) = F * G */
	*hp = zero;
    }

} /* end of addVarToConst */