//
// Subroutine of explain
// A step of explanation for x and y
//
void Egraph::expExplainAlongPath ( Enode * x, Enode * y )
{
Enode * v = expHighestNode( x );
Enode * to = expHighestNode( y );
while ( v != to )
{
Enode * p = v->getExpParent( );
assert( p != NULL );
Enode * r = v->getExpReason( );
// If it is not a congruence edge
if ( r != NULL )
{
if ( !isDup1( r ) )
{
assert( r->isTerm( ) );
explanation.push_back( r );
storeDup1( r );
}
}
// Otherwise it is a congruence edge
// This means that the edge is linking nodes
// like (v)f(a1,...,an) (p)f(b1,...,bn), and that
// a1,...,an = b1,...bn. For each pair ai,bi
// we have therefore to compute the reasons
else
{
assert( v->getCar( ) == p->getCar( ) );
assert( v->getArity( ) == p->getArity( ) );
expEnqueueArguments( v, p );
}
#ifdef PRODUCE_PROOF
if ( config.produce_inter > 0
&& config.logic != QF_AX )
{
cgraph.addCNode( v );
cgraph.addCNode( p );
cgraph.addCEdge( v, p, r );
}
#endif
expUnion( v, p );
v = expHighestNode( p );
}
}
double eval_enode(Enode * const e, unordered_map<Enode*, double> const & var_map) {
if (e->isVar()) {
auto const it = var_map.find(e);
if (it == var_map.cend()) {
throw runtime_error("variable not found");
} else {
// Variable is found in var_map
return it->second;
}
} else if (e->isConstant()) {
double const v = e->getValue();
return v;
} else if (e->isSymb()) {
throw runtime_error("eval_enode: Symb");
} else if (e->isNumb()) {
throw runtime_error("eval_enode: Numb");
} else if (e->isTerm()) {
assert(e->getArity() >= 1);
enodeid_t id = e->getCar()->getId();
double ret = 0.0;
Enode * tmp = e;
switch (id) {
case ENODE_ID_PLUS:
ret = eval_enode(tmp->get1st(), var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret + eval_enode(tmp->getCar(), var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_MINUS:
ret = eval_enode(tmp->get1st(), var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret - eval_enode(tmp->getCar(), var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_UMINUS:
ret = eval_enode(tmp->get1st(), var_map);
assert(tmp->getArity() == 1);
return (- ret);
case ENODE_ID_TIMES:
ret = eval_enode(tmp->get1st(), var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret * eval_enode(tmp->getCar(), var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_DIV:
ret = eval_enode(tmp->get1st(), var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret / eval_enode(tmp->getCar(), var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_ACOS:
assert(e->getArity() == 1);
return acos(eval_enode(e->get1st(), var_map));
case ENODE_ID_ASIN:
assert(e->getArity() == 1);
return asin(eval_enode(e->get1st(), var_map));
case ENODE_ID_ATAN:
assert(e->getArity() == 1);
return atan(eval_enode(e->get1st(), var_map));
case ENODE_ID_ATAN2:
assert(e->getArity() == 2);
return atan2(eval_enode(e->get1st(), var_map),
eval_enode(e->get2nd(), var_map));
case ENODE_ID_MIN:
assert(e->getArity() == 2);
return fmin(eval_enode(e->get1st(), var_map),
eval_enode(e->get2nd(), var_map));
case ENODE_ID_MAX:
assert(e->getArity() == 2);
return fmax(eval_enode(e->get1st(), var_map),
eval_enode(e->get2nd(), var_map));
case ENODE_ID_MATAN:
assert(e->getArity() == 1);
throw runtime_error("eval_enode: MATAN");
case ENODE_ID_SAFESQRT:
assert(e->getArity() == 1);
throw runtime_error("eval_enode: SAFESQRT");
case ENODE_ID_SQRT:
assert(e->getArity() == 1);
return sqrt(eval_enode(e->get1st(), var_map));
case ENODE_ID_EXP:
assert(e->getArity() == 1);
return exp(eval_enode(e->get1st(), var_map));
case ENODE_ID_LOG:
assert(e->getArity() == 1);
return log(eval_enode(e->get1st(), var_map));
case ENODE_ID_POW:
assert(e->getArity() == 2);
return pow(eval_enode(e->get1st(), var_map),
eval_enode(e->get2nd(), var_map));
case ENODE_ID_ABS:
assert(e->getArity() == 1);
return fabs(eval_enode(e->get1st(), var_map));
case ENODE_ID_SIN:
assert(e->getArity() == 1);
return sin(eval_enode(e->get1st(), var_map));
case ENODE_ID_COS:
assert(e->getArity() == 1);
return cos(eval_enode(e->get1st(), var_map));
case ENODE_ID_TAN:
assert(e->getArity() == 1);
return tan(eval_enode(e->get1st(), var_map));
case ENODE_ID_SINH:
assert(e->getArity() == 1);
return sinh(eval_enode(e->get1st(), var_map));
case ENODE_ID_COSH:
assert(e->getArity() == 1);
return cosh(eval_enode(e->get1st(), var_map));
case ENODE_ID_TANH:
assert(e->getArity() == 1);
return tanh(eval_enode(e->get1st(), var_map));
default:
throw runtime_error("eval_enode: Unknown Term");
}
} else if (e->isList()) {
throw runtime_error("eval_enode: List");
} else if (e->isDef()) {
throw runtime_error("eval_enode: Def");
} else if (e->isEnil()) {
throw runtime_error("eval_enode: Nil");
} else {
throw runtime_error("eval_enode: unknown case");
}
throw runtime_error("Not implemented yet: eval_enode");
}
double deriv_enode(Enode * const e, Enode * const v, unordered_map<Enode*, double> const & var_map) {
if (e == v) {
return 1.0;
}
if (e->isVar()) {
auto const it = var_map.find(e);
if (it == var_map.cend()) {
throw runtime_error("variable not found");
} else {
// Variable is found in var_map
return 0.0;
}
} else if (e->isConstant()) {
return 0.0;
} else if (e->isSymb()) {
throw runtime_error("eval_enode: Symb");
} else if (e->isNumb()) {
throw runtime_error("eval_enode: Numb");
} else if (e->isTerm()) {
assert(e->getArity() >= 1);
enodeid_t id = e->getCar()->getId();
double ret = 0.0;
Enode * tmp = e;
switch (id) {
case ENODE_ID_PLUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret + deriv_enode(tmp->getCar(), v, var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_MINUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret - deriv_enode(tmp->getCar(), v, var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_UMINUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
assert(tmp->getArity() == 1);
return (- ret);
case ENODE_ID_TIMES: {
// (f * g)' = f' * g + f * g'
if (tmp->getArity() != 2) {
throw runtime_error("deriv_enode: only support arity = 2 case for multiplication");
}
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return f_ * g + f * g_;
}
case ENODE_ID_DIV: {
// (f / g)' = (f' * g - f * g') / g^2
if (tmp->getArity() != 2) {
throw runtime_error("deriv_enode: only support arity = 2 case for division");
}
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return (f_ * g - f * g_) / (g * g);
}
case ENODE_ID_ACOS: {
// (acos f)' = -(1 / sqrt(1 - f^2)) f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return - (1 / sqrt(1 - f * f)) * f_;
}
case ENODE_ID_ASIN: {
// (asin f)' = (1 / sqrt(1 - f^2)) f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 1 / sqrt(1 - f * f) * f_;
}
case ENODE_ID_ATAN: {
// (atan f)' = (1 / (1 + f^2)) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 1 / (1 + f * f) * f_;
}
case ENODE_ID_ATAN2: {
// atan2(x,y)' = -y / (x^2 + y^2) dx + x / (x^2 + y^2) dy
// = (-y dx + x dy) / (x^2 + y^2)
assert(e->getArity() == 2);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return (-g * f_ + f * g_) / (f * f + g * g);
}
case ENODE_ID_MIN:
assert(e->getArity() == 2);
throw runtime_error("deriv_enode: no support for min");
case ENODE_ID_MAX:
assert(e->getArity() == 2);
throw runtime_error("deriv_enode: no support for max");
case ENODE_ID_MATAN:
assert(e->getArity() == 1);
throw runtime_error("deriv_enode: no support for matan");
case ENODE_ID_SAFESQRT:
assert(e->getArity() == 1);
throw runtime_error("deriv_enode: no support for safesqrt");
case ENODE_ID_SQRT: {
// (sqrt(f))' = 1/2 * 1/(sqrt(f)) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 0.5 * 1 / sqrt(f) * f_;
}
case ENODE_ID_EXP: {
// (exp f)' = (exp f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return exp(f) * f_;
}
case ENODE_ID_LOG: {
// (log f)' = f' / f
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return f_ / f;
}
case ENODE_ID_POW: {
// (f^g)' = f^g (f' * g / f + g' * ln g)
assert(e->getArity() == 2);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return pow(f, g) * (f_ * g / f + g_ * log(g));
}
case ENODE_ID_ABS: {
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
if (f > 0) {
return f_;
} else {
return - f_;
}
}
case ENODE_ID_SIN: {
// (sin f)' = (cos f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return cos(f) * f_;
}
case ENODE_ID_COS: {
// (cos f)' = - (sin f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return - sin(f) * f_;
}
case ENODE_ID_TAN: {
// (tan f)' = (1 + tan^2 f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return (1 + tan(f) * tan(f)) * f_;
}
case ENODE_ID_SINH: {
// (sinh f)' = (e^f + e^(-f))/2 * f'
// = cosh(f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return cosh(f) * f_;
}
case ENODE_ID_COSH: {
// (cosh f)' = (e^f - e^(-f))/2 * f'
// = sinh(f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return sinh(f) * f_;
}
case ENODE_ID_TANH: {
// (tanh f)' = (sech^2 f) * f'
// = (1 - tanh(f) ^ 2) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return (1 - tanh(f) * tanh(f)) * f_;
}
default:
throw runtime_error("deriv_enode: Unknown Term");
}
} else if (e->isList()) {
throw runtime_error("deriv_enode: List");
} else if (e->isDef()) {
throw runtime_error("deriv_enode: Def");
} else if (e->isEnil()) {
throw runtime_error("deriv_enode: Nil");
} else {
throw runtime_error("deriv_enode: unknown case");
}
throw runtime_error("Not implemented yet: deriv_enode");
}
// Translate an Enode e into ibex::ExprNode.
// Note: As a side-effect, update var_map : string -> ibex::Variable
// Note: Use subst map (Enode ->ibex::Interval)
ExprNode const * translate_enode_to_exprnode(map<string, Variable const> & var_map, Enode * const e, unordered_map<Enode*, ibex::Interval> const & subst) {
// TODO(soonhok): for the simple case such as 0 <= x or x <= 10.
// Handle it as a domain specification instead of constraints.
if (e->isVar()) {
auto const subst_it = subst.find(e);
if (subst_it != subst.cend()) {
auto const i = subst_it->second;
return &ExprConstant::new_scalar(i);
}
string const & var_name = e->getCar()->getNameFull();
auto const it = var_map.find(var_name);
if (it == var_map.cend()) {
// The variable is new, we need to make one.
Variable v(var_name.c_str());
// double const lb = e->getLowerBound();
// double const ub = e->getUpperBound();
var_map.emplace(var_name, v);
return v.symbol;
} else {
// Variable is found in var_map
Variable const & v = it->second;
return v.symbol;
}
} else if (e->isConstant()) {
double const lb = e->getValueLowerBound();
double const ub = e->getValueUpperBound();
return &ExprConstant::new_scalar(ibex::Interval(lb, ub));
} else if (e->isSymb()) {
throw logic_error("translateEnodeExprNode: Symb");
} else if (e->isNumb()) {
throw logic_error("translateEnodeExprNode: Numb");
} else if (e->isTerm()) {
assert(e->getArity() >= 1);
enodeid_t id = e->getCar()->getId();
ExprNode const * ret = nullptr;
Enode * tmp = e;
switch (id) {
case ENODE_ID_PLUS:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = &(*ret + *translate_enode_to_exprnode(var_map, tmp->getCar(), subst));
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_MINUS:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = &(*ret - *translate_enode_to_exprnode(var_map, tmp->getCar(), subst));
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_UMINUS:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
assert(tmp->getArity() == 1);
return &(- *ret);
case ENODE_ID_TIMES:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = &(*ret * *translate_enode_to_exprnode(var_map, tmp->getCar(), subst));
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_DIV:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = &(*ret / *translate_enode_to_exprnode(var_map, tmp->getCar(), subst));
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_ACOS:
assert(e->getArity() == 1);
return &acos(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_ASIN:
assert(e->getArity() == 1);
return &asin(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_ATAN:
assert(e->getArity() == 1);
return &atan(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_ATAN2:
assert(e->getArity() == 2);
return &atan2(*translate_enode_to_exprnode(var_map, e->get1st(), subst), *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
case ENODE_ID_MIN:
assert(e->getArity() == 2);
return &min(*translate_enode_to_exprnode(var_map, e->get1st(), subst), *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
case ENODE_ID_MAX:
assert(e->getArity() == 2);
return &max(*translate_enode_to_exprnode(var_map, e->get1st(), subst), *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
case ENODE_ID_MATAN:
// TODO(soonhok): MATAN
throw logic_error("translateEnodeExprNode: MATAN");
case ENODE_ID_SAFESQRT:
// TODO(soonhok): SAFESQRT
throw logic_error("translateEnodeExprNode: SAFESQRT");
case ENODE_ID_SQRT:
assert(e->getArity() == 1);
return &sqrt(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_EXP:
assert(e->getArity() == 1);
return &exp(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_LOG:
assert(e->getArity() == 1);
return &log(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_POW: {
assert(e->getArity() == 2);
bool is_1st_constant = false;
bool is_1st_int = false;
bool is_2nd_constant = false;
bool is_2nd_int = false;
double dbl_1st = 0.0;
int int_1st = 0;
double dbl_2nd = 0.0;
int int_2nd = 0;
if (e->get1st()->isConstant()) {
dbl_1st = e->get1st()->getValue();
is_1st_constant = true;
double tmp;
if (modf(dbl_1st, &tmp) == 0.0) {
is_1st_int = true;
int_1st = static_cast<int>(tmp);
}
}
if (e->get2nd()->isConstant()) {
dbl_2nd = e->get2nd()->getValue();
is_2nd_constant = true;
double tmp;
if (modf(dbl_2nd, &tmp) == 0.0) {
is_2nd_int = true;
int_2nd = static_cast<int>(tmp);
}
}
if (is_1st_constant && is_2nd_constant) {
// Both of them are constant, just compute and return a number
return &ExprConstant::new_scalar(pow(dbl_1st, dbl_2nd));
}
// Now, either of them is non-constant.
if (is_1st_int) {
return &pow(int_1st, *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
}
if (is_1st_constant) {
return &pow(dbl_1st, *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
}
if (is_2nd_int) {
return &pow(*translate_enode_to_exprnode(var_map, e->get1st(), subst), int_2nd);
}
if (is_2nd_constant) {
return &pow(*translate_enode_to_exprnode(var_map, e->get1st(), subst), dbl_2nd);
}
return &pow(*translate_enode_to_exprnode(var_map, e->get1st(), subst), *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
}
case ENODE_ID_ABS:
assert(e->getArity() == 1);
return &abs(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_SIN:
assert(e->getArity() == 1);
return &sin(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_COS:
assert(e->getArity() == 1);
return &cos(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_TAN:
assert(e->getArity() == 1);
return &tan(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_SINH:
assert(e->getArity() == 1);
return &sinh(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_COSH:
assert(e->getArity() == 1);
return &cosh(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_TANH:
assert(e->getArity() == 1);
return &tanh(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
default:
throw logic_error("translateEnodeExprNode: Unknown Term");
}
} else if (e->isList()) {
throw logic_error("translateEnodeExprNode: List");
} else if (e->isDef()) {
throw logic_error("translateEnodeExprNode: Def");
} else if (e->isEnil()) {
throw logic_error("translateEnodeExprNode: Nil");
} else {
throw logic_error("translateEnodeExprNode: unknown case");
}
throw logic_error("Not implemented yet: translateEnodeExprNode");
}