From 58ef9bec071383744fb703ff08df9806f25e4095 Mon Sep 17 00:00:00 2001 From: srcarroll <50210727+srcarroll@users.noreply.github.com> Date: Thu, 14 Mar 2024 19:18:56 -0500 Subject: [PATCH] [mlir][math] Implement alternative decomposition for tanh (#85025) The previous implementation decomposes `tanh(x)` into `(exp(2x) - 1)/(exp(2x)+1), x < 0` `(1 - exp(-2x))/(1 + exp(-2x)), x >= 0` This is fine as it avoids overflow with the exponential, but the whole decomposition is computed for both cases unconditionally, then the result is chosen based off the sign of the input. This results in doing two expensive `exp` computations. The proposed change avoids doing the whole computation twice by exploiting the reflection symmetry `tanh(-x) = -tanh(x)`. We can "normalize" the input to be positive by setting `y = sign(x) * x`, where the sign of `x` is computed as `sign(x) = (float)(x > 0) * (-2) + 1`. Then compute `z = tanh(y)` with the decomposition above for `x >=0` and "denormalize" the result `z * sign(x)` to retain the sign. The reason it is done this way is that it is very amenable to vectorization. This method trades the duplicate decomposition computations (which takes 5 instructions including an extra expensive `exp` and `div`) for 4 cheap instructions to compute the signs value 1. `arith.cmpf` (which is a pre-existing instruction in the previous impl) 2. `arith.sitofp` 3. `arith.mulf` 4. `arith.addf` and 1 more instruction to get the right sign in the result 5. `arith.mulf`. Moreover, numerically, this implementation will yield the exact same results as the previous implementation. --- .../Math/Transforms/ExpandPatterns.cpp | 40 +++++++++++-------- mlir/test/Dialect/Math/expand-math.mlir | 19 +++++---- 2 files changed, 32 insertions(+), 27 deletions(-) diff --git a/mlir/lib/Dialect/Math/Transforms/ExpandPatterns.cpp b/mlir/lib/Dialect/Math/Transforms/ExpandPatterns.cpp index 989a3e5536ec66f..1750171b81a10ea 100644 --- a/mlir/lib/Dialect/Math/Transforms/ExpandPatterns.cpp +++ b/mlir/lib/Dialect/Math/Transforms/ExpandPatterns.cpp @@ -91,34 +91,40 @@ static LogicalResult convertCoshOp(math::CoshOp op, PatternRewriter &rewriter) { } /// Expands tanh op into -/// 1) 1-exp^{-2x} / 1+exp^{-2x}, if x => 0 -/// 2) exp^{2x}-1 / exp^{2x}+1 , if x < 0 +/// 1-exp^{-2x} / 1+exp^{-2x} +/// To avoid overflow we exploit the reflection symmetry `tanh(-x) = -tanh(x)`. +/// We compute a "signs" value which is -1 if input is negative and +1 if input +/// is positive. Then multiply the input by this value, guaranteeing that the +/// result is positive, which also guarantees `exp^{-2x * sign(x)}` is in (0, +/// 1]. Expand the computation on the input `x * sign(x)`, then multiply the +/// result by `sign(x)` to retain sign of the real result. static LogicalResult convertTanhOp(math::TanhOp op, PatternRewriter &rewriter) { auto floatType = op.getOperand().getType(); Location loc = op.getLoc(); + Value zero = createFloatConst(loc, floatType, 0.0, rewriter); Value one = createFloatConst(loc, floatType, 1.0, rewriter); - Value two = createFloatConst(loc, floatType, 2.0, rewriter); - Value doubledX = rewriter.create(loc, op.getOperand(), two); + Value negTwo = createFloatConst(loc, floatType, -2.0, rewriter); + + // Compute sign(x) = cast(x < 0) * (-2) + 1 + Value sign = rewriter.create(loc, arith::CmpFPredicate::OLT, + op.getOperand(), zero); + sign = rewriter.create(loc, floatType, sign); + sign = rewriter.create(loc, sign, negTwo); + sign = rewriter.create(loc, sign, one); - // Case 1: tanh(x) = 1-exp^{-2x} / 1+exp^{-2x} - Value negDoubledX = rewriter.create(loc, doubledX); + // Normalize input to positive value: y = sign(x) * x + Value positiveX = rewriter.create(loc, sign, op.getOperand()); + + // Decompose on normalized input + Value negDoubledX = rewriter.create(loc, negTwo, positiveX); Value exp2x = rewriter.create(loc, negDoubledX); Value dividend = rewriter.create(loc, one, exp2x); Value divisor = rewriter.create(loc, one, exp2x); Value positiveRes = rewriter.create(loc, dividend, divisor); - // Case 2: tanh(x) = exp^{2x}-1 / exp^{2x}+1 - exp2x = rewriter.create(loc, doubledX); - dividend = rewriter.create(loc, exp2x, one); - divisor = rewriter.create(loc, exp2x, one); - Value negativeRes = rewriter.create(loc, dividend, divisor); + // Multiply result by sign(x) to retain signs from negative inputs + rewriter.replaceOpWithNewOp(op, sign, positiveRes); - // tanh(x) = x >= 0 ? positiveRes : negativeRes - Value zero = createFloatConst(loc, floatType, 0.0, rewriter); - Value cmpRes = rewriter.create(loc, arith::CmpFPredicate::OGE, - op.getOperand(), zero); - rewriter.replaceOpWithNewOp(op, cmpRes, positiveRes, - negativeRes); return success(); } diff --git a/mlir/test/Dialect/Math/expand-math.mlir b/mlir/test/Dialect/Math/expand-math.mlir index 6ee65b085dad1b6..86ee5c8620472b4 100644 --- a/mlir/test/Dialect/Math/expand-math.mlir +++ b/mlir/test/Dialect/Math/expand-math.mlir @@ -7,19 +7,18 @@ func.func @tanh(%arg: f32) -> f32 { } // CHECK-DAG: %[[ZERO:.+]] = arith.constant 0.000000e+00 : f32 // CHECK-DAG: %[[ONE:.+]] = arith.constant 1.000000e+00 : f32 -// CHECK-DAG: %[[TWO:.+]] = arith.constant 2.000000e+00 : f32 -// CHECK: %[[DOUBLEDX:.+]] = arith.mulf %arg0, %[[TWO]] : f32 -// CHECK: %[[NEGDOUBLEDX:.+]] = arith.negf %[[DOUBLEDX]] : f32 +// CHECK-DAG: %[[TWO:.+]] = arith.constant -2.000000e+00 : f32 +// CHECK: %[[VAL0:.+]] = arith.cmpf olt, %arg0, %[[ZERO]] : f32 +// CHECK: %[[VAL1:.+]] = arith.sitofp %[[VAL0]] : i1 to f32 +// CHECK: %[[VAL2:.+]] = arith.mulf %[[VAL1]], %[[TWO]] : f32 +// CHECK: %[[SIGN:.+]] = arith.addf %[[VAL2]], %[[ONE]] : f32 +// CHECK: %[[POSX:.+]] = arith.mulf %[[SIGN]], %arg0 : f32 +// CHECK: %[[NEGDOUBLEDX:.+]] = arith.mulf %[[POSX]], %[[TWO]] : f32 // CHECK: %[[EXP1:.+]] = math.exp %[[NEGDOUBLEDX]] : f32 // CHECK: %[[DIVIDEND1:.+]] = arith.subf %[[ONE]], %[[EXP1]] : f32 // CHECK: %[[DIVISOR1:.+]] = arith.addf %[[EXP1]], %[[ONE]] : f32 -// CHECK: %[[RES1:.+]] = arith.divf %[[DIVIDEND1]], %[[DIVISOR1]] : f32 -// CHECK: %[[EXP2:.+]] = math.exp %[[DOUBLEDX]] : f32 -// CHECK: %[[DIVIDEND2:.+]] = arith.subf %[[EXP2]], %[[ONE]] : f32 -// CHECK: %[[DIVISOR2:.+]] = arith.addf %[[EXP2]], %[[ONE]] : f32 -// CHECK: %[[RES2:.+]] = arith.divf %[[DIVIDEND2]], %[[DIVISOR2]] : f32 -// CHECK: %[[COND:.+]] = arith.cmpf oge, %arg0, %[[ZERO]] : f32 -// CHECK: %[[RESULT:.+]] = arith.select %[[COND]], %[[RES1]], %[[RES2]] : f32 +// CHECK: %[[POSRES:.+]] = arith.divf %[[DIVIDEND1]], %[[DIVISOR1]] : f32 +// CHECK: %[[RESULT:.+]] = arith.mulf %[[SIGN]], %[[POSRES]] : f32 // CHECK: return %[[RESULT]] // -----