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//===-- ArrayExprRewriter.cpp ---------------------------------------------===//
//
// The KLEE Symbolic Virtual Machine
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
#include "klee/Expr/ArrayExprRewriter.h"
#include "klee/ADT/BitArray.h"
#include "klee/Expr/ArrayExprVisitor.h"
#include "klee/Support/Casting.h"
#include <llvm/ADT/APInt.h>
#include <cassert>
#include <cstdint>
#include <set>
#include <utility>
using namespace klee;
ref<Expr>
ExprRewriter::createOptExpr(const ref<Expr> &e, const array2idx_ty &arrays,
const mapIndexOptimizedExpr_ty &idx_valIdx) {
return rewrite(e, arrays, idx_valIdx);
}
ref<Expr> ExprRewriter::rewrite(const ref<Expr> &e, const array2idx_ty &arrays,
const mapIndexOptimizedExpr_ty &idx_valIdx) {
ref<Expr> notFound;
std::vector<ref<Expr>> eqExprs;
bool invert = false;
for (auto &element : arrays) {
const Array *arr = element.first;
std::vector<ref<Expr>> indexes = element.second;
IndexTransformationExprVisitor idxt_v(arr);
idxt_v.visit(e);
assert((idxt_v.getWidth() % element.first->range == 0) &&
"Read is not aligned");
Expr::Width width = idxt_v.getWidth() / element.first->range;
if (auto e = idxt_v.getMul()) {
// If we have a MulExpr in the index, we can optimize our search by
// skipping all those indexes that are not multiple of such value.
// In fact, they will be rejected by the MulExpr interpreter since it
// will not find any integer solution
auto ce = dyn_cast<ConstantExpr>(e);
assert(ce && "Not a constant expression");
llvm::APInt val = ce->getAPValue();
uint64_t mulVal = val.getZExtValue();
// So far we try to limit this optimization, but we may try some more
// aggressive conditions (i.e. mulVal > width)
if (width == 1 && mulVal > 1)
width = mulVal;
}
for (std::vector<ref<Expr>>::const_iterator index_it = indexes.begin();
index_it != indexes.end(); ++index_it) {
if (idx_valIdx.find((*index_it)) == idx_valIdx.end()) {
continue;
}
auto opt_indexes = idx_valIdx.at((*index_it));
if (opt_indexes.empty()) {
// We continue with other solutions
continue;
} else if (opt_indexes.size() == 1) {
// We treat this case as a special one, and we create an EqExpr (e.g.
// k==i)
eqExprs.push_back(createEqExpr((*index_it), opt_indexes[0]));
} else {
Expr::Width idxWidth = (*index_it).get()->getWidth();
unsigned set = 0;
BitArray ba(arr->size / width);
for (auto &vals : opt_indexes) {
auto ce = dyn_cast<ConstantExpr>(vals);
llvm::APInt v = ce->getAPValue();
ba.set(v.getZExtValue() / width);
set++;
}
if (set > 0 && set < arr->size / width)
invert =
((float)set / (float)(arr->size / width)) > 0.5 ? true : false;
int start = -1;
for (unsigned i = 0; i < arr->size / width; ++i) {
if ((!invert && ba.get(i)) || (invert && !ba.get(i))) {
if (start < 0)
start = i;
} else {
if (start >= 0) {
if (i - start == 1) {
eqExprs.push_back(createEqExpr(
(*index_it),
ConstantExpr::create(start * width, idxWidth)));
} else {
// create range expr
ref<Expr> s = ConstantExpr::create(start * width, idxWidth);
ref<Expr> e = ConstantExpr::create((i - 1) * width, idxWidth);
eqExprs.push_back(createRangeExpr((*index_it), s, e));
}
start = -1;
}
}
}
if (start >= 0) {
if ((arr->size / width) - start == 1) {
eqExprs.push_back(createEqExpr(
(*index_it), ConstantExpr::create(start * width, idxWidth)));
} else {
// create range expr
ref<Expr> s = ConstantExpr::create(start * width, idxWidth);
ref<Expr> e = ConstantExpr::create(
((arr->size / width) - 1) * width, idxWidth);
eqExprs.push_back(createRangeExpr((*index_it), s, e));
}
}
}
}
}
if (eqExprs.empty()) {
return notFound;
} else if (eqExprs.size() == 1) {
if (isa<AndExpr>(eqExprs[0])) {
return EqExpr::alloc(
ConstantExpr::alloc(invert ? 0 : 1, (eqExprs[0])->getWidth()),
eqExprs[0]);
}
return invert ? NotExpr::alloc(eqExprs[0]) : eqExprs[0];
} else {
// We have found at least 2 indexes, we combine them using an OrExpr (e.g.
// k==i|k==j)
ref<Expr> orExpr = concatenateOrExpr(eqExprs.begin(), eqExprs.end());
// Create Eq expression for true branch
return EqExpr::alloc(
ConstantExpr::alloc(invert ? 0 : 1, (orExpr)->getWidth()), orExpr);
}
}
ref<Expr> ExprRewriter::concatenateOrExpr(
const std::vector<ref<Expr>>::const_iterator begin,
const std::vector<ref<Expr>>::const_iterator end) {
if (begin + 2 == end) {
return OrExpr::alloc(ZExtExpr::alloc((*begin), Expr::Int32),
ZExtExpr::alloc((*(begin + 1)), Expr::Int32));
} else {
return OrExpr::alloc(ZExtExpr::alloc((*begin), Expr::Int32),
concatenateOrExpr(begin + 1, end));
}
}
ref<Expr> ExprRewriter::createEqExpr(const ref<Expr> &index,
const ref<Expr> &valIndex) {
return EqExpr::alloc(valIndex, index);
}
ref<Expr> ExprRewriter::createRangeExpr(const ref<Expr> &index,
const ref<Expr> &valStart,
const ref<Expr> &valEnd) {
return AndExpr::alloc(UleExpr::alloc(valStart, index),
UleExpr::alloc(index, valEnd));
}
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