[llvm] [DAG] Combine manual reciprocal square root refinement into FRSQRTS. (PR #172067)

[Valeriy Savchenko via llvm-commits]

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@@ -28356,6 +28339,71 @@ static SDValue performCTPOPCombine(SDNode *N,
   return DAG.getNegative(NegPopCount, DL, VT);
 }
 
+// Combine manual Newton-Raphson reciprocal square root refinement patterns
+// into FRSQRTS instructions.
+//
+// The Newton-Raphson iteration for rsqrt is:
+//   r' = r * (1.5 - 0.5 * x * r * r)
+//
+// This appears as:
+//   fma(r, 1.5, mul(mul(mul(x, -0.5), r), r * r))
+//   where r = frsqrte(x) is the initial estimate.
+//
+// We convert this to use FRSQRTS: r * frsqrts(x * r, r).
+static SDValue
+performRSQRTRefinementCombine(SDNode *N, SelectionDAG &DAG,
+                              const AArch64Subtarget *Subtarget) {
+  using namespace SDPatternMatch;
+
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SavchenkoValeriy wrote:

>From my little experimentation, it looks like the target `frsqrts` version produces bit-equivalent results to `(fma(-(x * r), r, 3.0) * 0.5) * r`, but that also can't be used for a formal proof.

https://github.com/llvm/llvm-project/pull/172067