[Mlir-commits] [mlir] [mlir][math] Add Polynomial Approximation for acos, asin op (PR #90962)

[Han-Chung Wang]

================
@@ -821,6 +821,153 @@ Log1pApproximation::matchAndRewrite(math::Log1pOp op,
   return success();
 }
 
+//----------------------------------------------------------------------------//
+// Asin approximation.
+//----------------------------------------------------------------------------//
+
+// Approximates asin(x).
+// This approximation is based on the following stackoverflow post:
+// https://stackoverflow.com/a/42683455
+namespace {
+struct AsinPolynomialApproximation : public OpRewritePattern<math::AsinOp> {
+public:
+  using OpRewritePattern::OpRewritePattern;
+
+  LogicalResult matchAndRewrite(math::AsinOp op,
+                                PatternRewriter &rewriter) const final;
+};
+} // namespace
+LogicalResult
+AsinPolynomialApproximation::matchAndRewrite(math::AsinOp op,
+                                             PatternRewriter &rewriter) const {
+  Value operand = op.getOperand();
+  Type elementType = getElementTypeOrSelf(operand);
+
+  if (!(elementType.isF32() || elementType.isF16()))
+    return rewriter.notifyMatchFailure(op,
+                                       "only f32 and f16 type is supported.");
+  VectorShape shape = vectorShape(operand);
+
+  ImplicitLocOpBuilder builder(op->getLoc(), rewriter);
+  auto bcast = [&](Value value) -> Value {
+    return broadcast(builder, value, shape);
+  };
+
+  auto fma = [&](Value a, Value b, Value c) -> Value {
+    return builder.create<math::FmaOp>(a, b, c);
+  };
+
+  auto mul = [&](Value a, Value b) -> Value {
+    return builder.create<arith::MulFOp>(a, b);
+  };
+
+  Value s = mul(operand, operand);
+  Value q = mul(s, s);
+  Value r = bcast(floatCst(builder, 5.5579749017470502e-2, elementType));
+  Value t = bcast(floatCst(builder, -6.2027913464120114e-2, elementType));
+
+  r = fma(r, q, bcast(floatCst(builder, 5.4224464349245036e-2, elementType)));
----------------
hanhanW wrote:

yeah.. I was going to suggest using Remez algorithm instead of Taylor series. However, aren't these parameters optimized for `[-9/16, 9/16]`? What happens to other input values...?

https://github.com/llvm/llvm-project/pull/90962