[mlir] Add polynomial approximation for math::ExpM1

This approximation matches the one in Eigen.

```
name                      old cpu/op  new cpu/op  delta
BM_mlir_Expm1_f32/10      90.9ns ± 4%  52.2ns ± 4%  -42.60%    (p=0.000 n=74+87)
BM_mlir_Expm1_f32/100      837ns ± 3%   231ns ± 4%  -72.43%    (p=0.000 n=79+69)
BM_mlir_Expm1_f32/1k      8.43µs ± 3%  1.58µs ± 5%  -81.30%    (p=0.000 n=77+83)
BM_mlir_Expm1_f32/10k     83.8µs ± 3%  15.4µs ± 5%  -81.65%    (p=0.000 n=83+69)
BM_eigen_s_Expm1_f32/10   68.8ns ±17%  72.5ns ±14%   +5.40%  (p=0.000 n=118+115)
BM_eigen_s_Expm1_f32/100   694ns ±11%   717ns ± 2%   +3.34%   (p=0.000 n=120+75)
BM_eigen_s_Expm1_f32/1k   7.69µs ± 2%  7.97µs ±11%   +3.56%   (p=0.000 n=95+117)
BM_eigen_s_Expm1_f32/10k  88.0µs ± 1%  89.3µs ± 6%   +1.45%   (p=0.000 n=74+106)
BM_eigen_v_Expm1_f32/10   44.3ns ± 6%  45.0ns ± 8%   +1.45%   (p=0.018 n=81+111)
BM_eigen_v_Expm1_f32/100   351ns ± 1%   360ns ± 9%   +2.58%    (p=0.000 n=73+99)
BM_eigen_v_Expm1_f32/1k   3.31µs ± 1%  3.42µs ± 9%   +3.37%   (p=0.000 n=71+100)
BM_eigen_v_Expm1_f32/10k  33.7µs ± 8%  34.1µs ± 9%   +1.04%    (p=0.007 n=99+98)
```

Reviewed By: ezhulenev

Differential Revision: https://reviews.llvm.org/D101852

mlir/lib/Dialect/Math/Transforms/PolynomialApproximation.cpp

@@ -576,10 +576,65 @@ ExpApproximation::matchAndRewrite(math::ExpOp op,
   return success();
 }
 
+//----------------------------------------------------------------------------//
+// ExpM1 approximation.
+//----------------------------------------------------------------------------//
+
+namespace {
+
+struct ExpM1Approximation : public OpRewritePattern<math::ExpM1Op> {
+public:
+  using OpRewritePattern::OpRewritePattern;
+
+  LogicalResult matchAndRewrite(math::ExpM1Op op,
+                                PatternRewriter &rewriter) const final;
+};
+} // namespace
+
+LogicalResult
+ExpM1Approximation::matchAndRewrite(math::ExpM1Op op,
+                                    PatternRewriter &rewriter) const {
+  auto width = vectorWidth(op.operand().getType(), isF32);
+  if (!width.hasValue())
+    return rewriter.notifyMatchFailure(op, "unsupported operand type");
+
+  ImplicitLocOpBuilder builder(op->getLoc(), rewriter);
+  auto bcast = [&](Value value) -> Value {
+    return broadcast(builder, value, *width);
+  };
+
+  // expm1(x) = exp(x) - 1 = u - 1.
+  // We have to handle it carefully when x is near 0, i.e. u ~= 1,
+  // and when the input is ~= -inf, i.e. u - 1 ~= -1.
+  Value cstOne = bcast(f32Cst(builder, 1.0f));
+  Value cstNegOne = bcast(f32Cst(builder, -1.0f));
+  Value x = op.operand();
+  Value u = builder.create<math::ExpOp>(x);
+  Value uEqOne = builder.create<CmpFOp>(CmpFPredicate::OEQ, u, cstOne);
+  Value uMinusOne = builder.create<SubFOp>(u, cstOne);
+  Value uMinusOneEqNegOne =
+      builder.create<CmpFOp>(CmpFPredicate::OEQ, uMinusOne, cstNegOne);
+  // logU = log(u) ~= x
+  Value logU = builder.create<math::LogOp>(u);
+
+  // Detect exp(x) = +inf; written this way to avoid having to form +inf.
+  Value isInf = builder.create<CmpFOp>(CmpFPredicate::OEQ, logU, u);
+
+  // (u - 1) * (x / ~x)
+  Value expm1 =
+      builder.create<MulFOp>(uMinusOne, builder.create<DivFOp>(x, logU));
+  expm1 = builder.create<SelectOp>(isInf, u, expm1);
+  Value approximation = builder.create<SelectOp>(
+      uEqOne, x, builder.create<SelectOp>(uMinusOneEqNegOne, cstNegOne, expm1));
+  rewriter.replaceOp(op, approximation);
+  return success();
+}
+
 //----------------------------------------------------------------------------//
 
 void mlir::populateMathPolynomialApproximationPatterns(
     RewritePatternSet &patterns) {
   patterns.add<TanhApproximation, LogApproximation, Log2Approximation,
-               Log1pApproximation, ExpApproximation>(patterns.getContext());
+               Log1pApproximation, ExpApproximation, ExpM1Approximation>(
+      patterns.getContext());
 }

mlir/test/Dialect/Math/polynomial-approximation.mlir

@@ -11,7 +11,10 @@ func @scalar(%arg0: f32) -> f32 {
   %1 = math.log %0 : f32
   %2 = math.log2 %1 : f32
   %3 = math.log1p %2 : f32
-  return %3 : f32
+  // CHECK-NOT: exp
+  %4 = math.exp %3 : f32
+  %5 = math.expm1 %4 : f32
+  return %5 : f32
 }
 
 // CHECK-LABEL: @vector
@@ -22,18 +25,8 @@ func @vector(%arg0: vector<8xf32>) -> vector<8xf32> {
   %1 = math.log %0 : vector<8xf32>
   %2 = math.log2 %1 : vector<8xf32>
   %3 = math.log1p %2 : vector<8xf32>
-  return %3 : vector<8xf32>
-}
-
-// CHECK-LABEL: @exp_scalar
-func @exp_scalar(%arg0: f32) -> f32 {
-  %0 = math.exp %arg0 : f32
-  return %0 : f32
-}
-
-// CHECK-LABEL: @exp_vector
-func @exp_vector(%arg0: vector<8xf32>) -> vector<8xf32> {
-  // CHECK-NOT: math.exp
-  %0 = math.exp %arg0 : vector<8xf32>
-  return %0 : vector<8xf32>
+  // CHECK-NOT: exp
+  %4 = math.exp %3 : vector<8xf32>
+  %5 = math.expm1 %4 : vector<8xf32>
+  return %5 : vector<8xf32>
 }

mlir/test/mlir-cpu-runner/math_polynomial_approx.mlir

@@ -186,11 +186,46 @@ func @exp() {
   return
 }
 
+func @expm1() {
+  // CHECK: 1e-10
+  %0 = constant 1.0e-10 : f32
+  %1 = math.expm1 %0 : f32
+  vector.print %1 : f32
+
+  // CHECK: -0.00995016, 0.0100502, 0.648721, 6.38905
+  %2 = constant dense<[-0.01, 0.01, 0.5, 2.0]> : vector<4xf32>
+  %3 = math.expm1 %2 : vector<4xf32>
+  vector.print %3 : vector<4xf32>
+
+  // CHECK: -0.181269, 0, 0.221403, 0.491825, 0.822119, 1.22554, 1.71828, 2.32012
+  %4 = constant dense<[-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2]> : vector<8xf32>
+  %5 = math.expm1 %4 : vector<8xf32>
+  vector.print %5 : vector<8xf32>
+
+  // CHECK: -1
+  %neg_inf = constant 0xff800000 : f32
+  %expm1_neg_inf = math.expm1 %neg_inf : f32
+  vector.print %expm1_neg_inf : f32
+
+  // CHECK: inf
+  %inf = constant 0x7f800000 : f32
+  %expm1_inf = math.expm1 %inf : f32
+  vector.print %expm1_inf : f32
+
+  // CHECK: -1, inf, 1e-10
+  %special_vec = constant dense<[0xff800000, 0x7f800000, 1.0e-10]> : vector<3xf32>
+  %log_special_vec = math.expm1 %special_vec : vector<3xf32>
+  vector.print %log_special_vec : vector<3xf32>
+
+  return
+}
+
 func @main() {
   call @tanh(): () -> ()
   call @log(): () -> ()
   call @log2(): () -> ()
   call @log1p(): () -> ()
   call @exp(): () -> ()
+  call @expm1(): () -> ()
   return
 }