+ break;
+ case Instruction::FMul:
+ // For multiplication, the infinitely precise result has at most
+ // LHSWidth + RHSWidth significant bits; if OpWidth is sufficient
+ // that such a value can be exactly represented, then no double
+ // rounding can possibly occur; we can safely perform the operation
+ // in the destination format if it can represent both sources.
+ if (OpWidth >= LHSWidth + RHSWidth && DstWidth >= SrcWidth) {
+ if (LHSOrig->getType() != CI.getType())
+ LHSOrig = Builder->CreateFPExt(LHSOrig, CI.getType());
+ if (RHSOrig->getType() != CI.getType())
+ RHSOrig = Builder->CreateFPExt(RHSOrig, CI.getType());
+ Instruction *RI =
+ BinaryOperator::CreateFMul(LHSOrig, RHSOrig);
+ RI->copyFastMathFlags(OpI);
+ return RI;
+ }
+ break;
+ case Instruction::FDiv:
+ // For division, we use again use the bound from Figueroa's
+ // dissertation. I am entirely certain that this bound can be
+ // tightened in the unbalanced operand case by an analysis based on
+ // the diophantine rational approximation bound, but the well-known
+ // condition used here is a good conservative first pass.
+ // TODO: Tighten bound via rigorous analysis of the unbalanced case.
+ if (OpWidth >= 2*DstWidth && DstWidth >= SrcWidth) {
+ if (LHSOrig->getType() != CI.getType())
+ LHSOrig = Builder->CreateFPExt(LHSOrig, CI.getType());
+ if (RHSOrig->getType() != CI.getType())
+ RHSOrig = Builder->CreateFPExt(RHSOrig, CI.getType());
+ Instruction *RI =
+ BinaryOperator::CreateFDiv(LHSOrig, RHSOrig);
+ RI->copyFastMathFlags(OpI);
+ return RI;
+ }
+ break;
+ case Instruction::FRem:
+ // Remainder is straightforward. Remainder is always exact, so the
+ // type of OpI doesn't enter into things at all. We simply evaluate
+ // in whichever source type is larger, then convert to the
+ // destination type.
+ if (LHSWidth < SrcWidth)
+ LHSOrig = Builder->CreateFPExt(LHSOrig, RHSOrig->getType());
+ else if (RHSWidth <= SrcWidth)
+ RHSOrig = Builder->CreateFPExt(RHSOrig, LHSOrig->getType());
+ Value *ExactResult = Builder->CreateFRem(LHSOrig, RHSOrig);
+ if (Instruction *RI = dyn_cast<Instruction>(ExactResult))
+ RI->copyFastMathFlags(OpI);
+ return CastInst::CreateFPCast(ExactResult, CI.getType());