+bool llvm::CannotBeOrderedLessThanZero(const Value *V, unsigned Depth) {
+ if (const ConstantFP *CFP = dyn_cast<ConstantFP>(V))
+ return !CFP->getValueAPF().isNegative() || CFP->getValueAPF().isZero();
+
+ if (Depth == 6)
+ return false; // Limit search depth.
+
+ const Operator *I = dyn_cast<Operator>(V);
+ if (!I) return false;
+
+ switch (I->getOpcode()) {
+ default: break;
+ case Instruction::FMul:
+ // x*x is always non-negative or a NaN.
+ if (I->getOperand(0) == I->getOperand(1))
+ return true;
+ // Fall through
+ case Instruction::FAdd:
+ case Instruction::FDiv:
+ case Instruction::FRem:
+ return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1) &&
+ CannotBeOrderedLessThanZero(I->getOperand(1), Depth+1);
+ case Instruction::FPExt:
+ case Instruction::FPTrunc:
+ // Widening/narrowing never change sign.
+ return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1);
+ case Instruction::Call:
+ if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(I))
+ switch (II->getIntrinsicID()) {
+ default: break;
+ case Intrinsic::exp:
+ case Intrinsic::exp2:
+ case Intrinsic::fabs:
+ case Intrinsic::sqrt:
+ return true;
+ case Intrinsic::powi:
+ if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
+ // powi(x,n) is non-negative if n is even.
+ if (CI->getBitWidth() <= 64 && CI->getSExtValue() % 2u == 0)
+ return true;
+ }
+ return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1);
+ case Intrinsic::fma:
+ case Intrinsic::fmuladd:
+ // x*x+y is non-negative if y is non-negative.
+ return I->getOperand(0) == I->getOperand(1) &&
+ CannotBeOrderedLessThanZero(I->getOperand(2), Depth+1);
+ }
+ break;
+ }
+ return false;
+}
+