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[mlir][math] Fix polynomial math.asin approximation (#101247)

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The polynomial approximation for asin is only good between [-9/16,
9/16]. Values beyond that range must be remapped to achieve good numeric
results. This is done by the equation below:

`arcsin(x) = PI/2 - arcsin(sqrt(1.0 - x*x))`
This commit is contained in:
Rob Suderman 2024-07-31 10:06:20 -07:00 committed by GitHub
parent 28a079223d
commit a3fb301435
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GPG Key ID: B5690EEEBB952194
2 changed files with 38 additions and 3 deletions
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37
mlir/lib/Dialect/Math/Transforms/PolynomialApproximation.cpp
View File

@ -861,7 +861,34 @@ AsinPolynomialApproximation::matchAndRewrite(math::AsinOp op,
return builder.create<arith::MulFOp>(a, b);
};
Value s = mul(operand, operand);
auto sub = [&](Value a, Value b) -> Value {
return builder.create<arith::SubFOp>(a, b);
};
auto abs = [&](Value a) -> Value { return builder.create<math::AbsFOp>(a); };
auto sqrt = [&](Value a) -> Value { return builder.create<math::SqrtOp>(a); };
auto scopy = [&](Value a, Value b) -> Value {
return builder.create<math::CopySignOp>(a, b);
};
auto sel = [&](Value a, Value b, Value c) -> Value {
return builder.create<arith::SelectOp>(a, b, c);
};
Value abso = abs(operand);
Value aa = mul(operand, operand);
Value opp = sqrt(sub(bcast(floatCst(builder, 1.0, elementType)), aa));
Value gt =
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OGT, aa,
bcast(floatCst(builder, 0.5, elementType)));
Value x = sel(gt, opp, abso);
// Asin(x) approximation for x = [-9/16, 9/16]:
Value s = mul(x, x);
Value q = mul(s, s);
Value r = bcast(floatCst(builder, 5.5579749017470502e-2, elementType));
Value t = bcast(floatCst(builder, -6.2027913464120114e-2, elementType));
@ -878,8 +905,12 @@ AsinPolynomialApproximation::matchAndRewrite(math::AsinOp op,
t = fma(t, q, bcast(floatCst(builder, 7.4999999991367292e-2, elementType)));
r = fma(r, s, t);
r = fma(r, s, bcast(floatCst(builder, 1.6666666666670193e-1, elementType)));
t = mul(operand, s);
r = fma(r, t, operand);
t = mul(x, s);
r = fma(r, t, x);
Value rsub = sub(bcast(floatCst(builder, 1.57079632679, elementType)), r);
r = sel(gt, rsub, r);
r = scopy(r, operand);
rewriter.replaceOp(op, r);
return success();

4
mlir/test/mlir-cpu-runner/math-polynomial-approx.mlir
View File

@ -493,6 +493,10 @@ func.func @asin() {
%cst3 = arith.constant -0.25 : f32
call @asin_f32(%cst3) : (f32) -> ()
// CHECK: -1.1197
%cst4 = arith.constant -0.90 : f32
call @asin_f32(%cst4) : (f32) -> ()
// CHECK: 0.25268, 0.384397, 0.597406
%vec_x = arith.constant dense<[0.25, 0.375, 0.5625]> : vector<3xf32>
call @asin_3xf32(%vec_x) : (vector<3xf32>) -> ()