+/// Newton iteration for a function: F(X) is X_{i+1} = X_i - F(X_i)/F'(X_i)
+/// For the reciprocal sqrt, we need to find the zero of the function:
+/// F(X) = 1/X^2 - A [which has a zero at X = 1/sqrt(A)]
+/// =>
+/// X_{i+1} = X_i (1.5 - A X_i^2 / 2)
+/// As a result, we precompute A/2 prior to the iteration loop.
+SDValue DAGCombiner::BuildRsqrtNROneConst(SDValue Arg, SDValue Est,
+ unsigned Iterations) {
+ EVT VT = Arg.getValueType();
+ SDLoc DL(Arg);
+ SDValue ThreeHalves = DAG.getConstantFP(1.5, VT);
+
+ // We now need 0.5 * Arg which we can write as (1.5 * Arg - Arg) so that
+ // this entire sequence requires only one FP constant.
+ SDValue HalfArg = DAG.getNode(ISD::FMUL, DL, VT, ThreeHalves, Arg);
+ AddToWorklist(HalfArg.getNode());
+
+ HalfArg = DAG.getNode(ISD::FSUB, DL, VT, HalfArg, Arg);
+ AddToWorklist(HalfArg.getNode());
+
+ // Newton iterations: Est = Est * (1.5 - HalfArg * Est * Est)
+ for (unsigned i = 0; i < Iterations; ++i) {
+ SDValue NewEst = DAG.getNode(ISD::FMUL, DL, VT, Est, Est);
+ AddToWorklist(NewEst.getNode());
+
+ NewEst = DAG.getNode(ISD::FMUL, DL, VT, HalfArg, NewEst);
+ AddToWorklist(NewEst.getNode());
+
+ NewEst = DAG.getNode(ISD::FSUB, DL, VT, ThreeHalves, NewEst);
+ AddToWorklist(NewEst.getNode());
+
+ Est = DAG.getNode(ISD::FMUL, DL, VT, Est, NewEst);
+ AddToWorklist(Est.getNode());
+ }
+ return Est;
+}