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|
//===- ComplexToStandard.cpp - conversion from Complex to Standard dialect ===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "mlir/Conversion/ComplexToStandard/ComplexToStandard.h"
#include "mlir/Dialect/Arith/IR/Arith.h"
#include "mlir/Dialect/Complex/IR/Complex.h"
#include "mlir/Dialect/Math/IR/Math.h"
#include "mlir/IR/ImplicitLocOpBuilder.h"
#include "mlir/IR/PatternMatch.h"
#include "mlir/Pass/Pass.h"
#include "mlir/Transforms/DialectConversion.h"
#include <memory>
#include <type_traits>
namespace mlir {
#define GEN_PASS_DEF_CONVERTCOMPLEXTOSTANDARD
#include "mlir/Conversion/Passes.h.inc"
} // namespace mlir
using namespace mlir;
namespace {
enum class AbsFn { abs, sqrt, rsqrt };
// Returns the absolute value, its square root or its reciprocal square root.
Value computeAbs(Value real, Value imag, arith::FastMathFlags fmf,
ImplicitLocOpBuilder &b, AbsFn fn = AbsFn::abs) {
Value one = b.create<arith::ConstantOp>(real.getType(),
b.getFloatAttr(real.getType(), 1.0));
Value absReal = b.create<math::AbsFOp>(real, fmf);
Value absImag = b.create<math::AbsFOp>(imag, fmf);
Value max = b.create<arith::MaximumFOp>(absReal, absImag, fmf);
Value min = b.create<arith::MinimumFOp>(absReal, absImag, fmf);
Value ratio = b.create<arith::DivFOp>(min, max, fmf);
Value ratioSq = b.create<arith::MulFOp>(ratio, ratio, fmf);
Value ratioSqPlusOne = b.create<arith::AddFOp>(ratioSq, one, fmf);
Value result;
if (fn == AbsFn::rsqrt) {
ratioSqPlusOne = b.create<math::RsqrtOp>(ratioSqPlusOne, fmf);
min = b.create<math::RsqrtOp>(min, fmf);
max = b.create<math::RsqrtOp>(max, fmf);
}
if (fn == AbsFn::sqrt) {
Value quarter = b.create<arith::ConstantOp>(
real.getType(), b.getFloatAttr(real.getType(), 0.25));
// sqrt(sqrt(a*b)) would avoid the pow, but will overflow more easily.
Value sqrt = b.create<math::SqrtOp>(max, fmf);
Value p025 = b.create<math::PowFOp>(ratioSqPlusOne, quarter, fmf);
result = b.create<arith::MulFOp>(sqrt, p025, fmf);
} else {
Value sqrt = b.create<math::SqrtOp>(ratioSqPlusOne, fmf);
result = b.create<arith::MulFOp>(max, sqrt, fmf);
}
Value isNaN =
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, result, result, fmf);
return b.create<arith::SelectOp>(isNaN, min, result);
}
struct AbsOpConversion : public OpConversionPattern<complex::AbsOp> {
using OpConversionPattern<complex::AbsOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::AbsOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
ImplicitLocOpBuilder b(op.getLoc(), rewriter);
arith::FastMathFlags fmf = op.getFastMathFlagsAttr().getValue();
Value real = b.create<complex::ReOp>(adaptor.getComplex());
Value imag = b.create<complex::ImOp>(adaptor.getComplex());
rewriter.replaceOp(op, computeAbs(real, imag, fmf, b));
return success();
}
};
// atan2(y,x) = -i * log((x + i * y)/sqrt(x**2+y**2))
struct Atan2OpConversion : public OpConversionPattern<complex::Atan2Op> {
using OpConversionPattern<complex::Atan2Op>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::Atan2Op op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
auto type = cast<ComplexType>(op.getType());
Type elementType = type.getElementType();
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
Value lhs = adaptor.getLhs();
Value rhs = adaptor.getRhs();
Value rhsSquared = b.create<complex::MulOp>(type, rhs, rhs, fmf);
Value lhsSquared = b.create<complex::MulOp>(type, lhs, lhs, fmf);
Value rhsSquaredPlusLhsSquared =
b.create<complex::AddOp>(type, rhsSquared, lhsSquared, fmf);
Value sqrtOfRhsSquaredPlusLhsSquared =
b.create<complex::SqrtOp>(type, rhsSquaredPlusLhsSquared, fmf);
Value zero =
b.create<arith::ConstantOp>(elementType, b.getZeroAttr(elementType));
Value one = b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, 1));
Value i = b.create<complex::CreateOp>(type, zero, one);
Value iTimesLhs = b.create<complex::MulOp>(i, lhs, fmf);
Value rhsPlusILhs = b.create<complex::AddOp>(rhs, iTimesLhs, fmf);
Value divResult = b.create<complex::DivOp>(
rhsPlusILhs, sqrtOfRhsSquaredPlusLhsSquared, fmf);
Value logResult = b.create<complex::LogOp>(divResult, fmf);
Value negativeOne = b.create<arith::ConstantOp>(
elementType, b.getFloatAttr(elementType, -1));
Value negativeI = b.create<complex::CreateOp>(type, zero, negativeOne);
rewriter.replaceOpWithNewOp<complex::MulOp>(op, negativeI, logResult, fmf);
return success();
}
};
template <typename ComparisonOp, arith::CmpFPredicate p>
struct ComparisonOpConversion : public OpConversionPattern<ComparisonOp> {
using OpConversionPattern<ComparisonOp>::OpConversionPattern;
using ResultCombiner =
std::conditional_t<std::is_same<ComparisonOp, complex::EqualOp>::value,
arith::AndIOp, arith::OrIOp>;
LogicalResult
matchAndRewrite(ComparisonOp op, typename ComparisonOp::Adaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto loc = op.getLoc();
auto type = cast<ComplexType>(adaptor.getLhs().getType()).getElementType();
Value realLhs = rewriter.create<complex::ReOp>(loc, type, adaptor.getLhs());
Value imagLhs = rewriter.create<complex::ImOp>(loc, type, adaptor.getLhs());
Value realRhs = rewriter.create<complex::ReOp>(loc, type, adaptor.getRhs());
Value imagRhs = rewriter.create<complex::ImOp>(loc, type, adaptor.getRhs());
Value realComparison =
rewriter.create<arith::CmpFOp>(loc, p, realLhs, realRhs);
Value imagComparison =
rewriter.create<arith::CmpFOp>(loc, p, imagLhs, imagRhs);
rewriter.replaceOpWithNewOp<ResultCombiner>(op, realComparison,
imagComparison);
return success();
}
};
// Default conversion which applies the BinaryStandardOp separately on the real
// and imaginary parts. Can for example be used for complex::AddOp and
// complex::SubOp.
template <typename BinaryComplexOp, typename BinaryStandardOp>
struct BinaryComplexOpConversion : public OpConversionPattern<BinaryComplexOp> {
using OpConversionPattern<BinaryComplexOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(BinaryComplexOp op, typename BinaryComplexOp::Adaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto type = cast<ComplexType>(adaptor.getLhs().getType());
auto elementType = cast<FloatType>(type.getElementType());
mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
Value realLhs = b.create<complex::ReOp>(elementType, adaptor.getLhs());
Value realRhs = b.create<complex::ReOp>(elementType, adaptor.getRhs());
Value resultReal = b.create<BinaryStandardOp>(elementType, realLhs, realRhs,
fmf.getValue());
Value imagLhs = b.create<complex::ImOp>(elementType, adaptor.getLhs());
Value imagRhs = b.create<complex::ImOp>(elementType, adaptor.getRhs());
Value resultImag = b.create<BinaryStandardOp>(elementType, imagLhs, imagRhs,
fmf.getValue());
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultReal,
resultImag);
return success();
}
};
template <typename TrigonometricOp>
struct TrigonometricOpConversion : public OpConversionPattern<TrigonometricOp> {
using OpAdaptor = typename OpConversionPattern<TrigonometricOp>::OpAdaptor;
using OpConversionPattern<TrigonometricOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(TrigonometricOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto loc = op.getLoc();
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
Value real =
rewriter.create<complex::ReOp>(loc, elementType, adaptor.getComplex());
Value imag =
rewriter.create<complex::ImOp>(loc, elementType, adaptor.getComplex());
// Trigonometric ops use a set of common building blocks to convert to real
// ops. Here we create these building blocks and call into an op-specific
// implementation in the subclass to combine them.
Value half = rewriter.create<arith::ConstantOp>(
loc, elementType, rewriter.getFloatAttr(elementType, 0.5));
Value exp = rewriter.create<math::ExpOp>(loc, imag, fmf);
Value scaledExp = rewriter.create<arith::MulFOp>(loc, half, exp, fmf);
Value reciprocalExp = rewriter.create<arith::DivFOp>(loc, half, exp, fmf);
Value sin = rewriter.create<math::SinOp>(loc, real, fmf);
Value cos = rewriter.create<math::CosOp>(loc, real, fmf);
auto resultPair =
combine(loc, scaledExp, reciprocalExp, sin, cos, rewriter, fmf);
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultPair.first,
resultPair.second);
return success();
}
virtual std::pair<Value, Value>
combine(Location loc, Value scaledExp, Value reciprocalExp, Value sin,
Value cos, ConversionPatternRewriter &rewriter,
arith::FastMathFlagsAttr fmf) const = 0;
};
struct CosOpConversion : public TrigonometricOpConversion<complex::CosOp> {
using TrigonometricOpConversion<complex::CosOp>::TrigonometricOpConversion;
std::pair<Value, Value> combine(Location loc, Value scaledExp,
Value reciprocalExp, Value sin, Value cos,
ConversionPatternRewriter &rewriter,
arith::FastMathFlagsAttr fmf) const override {
// Complex cosine is defined as;
// cos(x + iy) = 0.5 * (exp(i(x + iy)) + exp(-i(x + iy)))
// Plugging in:
// exp(i(x+iy)) = exp(-y + ix) = exp(-y)(cos(x) + i sin(x))
// exp(-i(x+iy)) = exp(y + i(-x)) = exp(y)(cos(x) + i (-sin(x)))
// and defining t := exp(y)
// We get:
// Re(cos(x + iy)) = (0.5/t + 0.5*t) * cos x
// Im(cos(x + iy)) = (0.5/t - 0.5*t) * sin x
Value sum =
rewriter.create<arith::AddFOp>(loc, reciprocalExp, scaledExp, fmf);
Value resultReal = rewriter.create<arith::MulFOp>(loc, sum, cos, fmf);
Value diff =
rewriter.create<arith::SubFOp>(loc, reciprocalExp, scaledExp, fmf);
Value resultImag = rewriter.create<arith::MulFOp>(loc, diff, sin, fmf);
return {resultReal, resultImag};
}
};
struct DivOpConversion : public OpConversionPattern<complex::DivOp> {
using OpConversionPattern<complex::DivOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::DivOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto loc = op.getLoc();
auto type = cast<ComplexType>(adaptor.getLhs().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
Value lhsReal =
rewriter.create<complex::ReOp>(loc, elementType, adaptor.getLhs());
Value lhsImag =
rewriter.create<complex::ImOp>(loc, elementType, adaptor.getLhs());
Value rhsReal =
rewriter.create<complex::ReOp>(loc, elementType, adaptor.getRhs());
Value rhsImag =
rewriter.create<complex::ImOp>(loc, elementType, adaptor.getRhs());
// Smith's algorithm to divide complex numbers. It is just a bit smarter
// way to compute the following formula:
// (lhsReal + lhsImag * i) / (rhsReal + rhsImag * i)
// = (lhsReal + lhsImag * i) (rhsReal - rhsImag * i) /
// ((rhsReal + rhsImag * i)(rhsReal - rhsImag * i))
// = ((lhsReal * rhsReal + lhsImag * rhsImag) +
// (lhsImag * rhsReal - lhsReal * rhsImag) * i) / ||rhs||^2
//
// Depending on whether |rhsReal| < |rhsImag| we compute either
// rhsRealImagRatio = rhsReal / rhsImag
// rhsRealImagDenom = rhsImag + rhsReal * rhsRealImagRatio
// resultReal = (lhsReal * rhsRealImagRatio + lhsImag) / rhsRealImagDenom
// resultImag = (lhsImag * rhsRealImagRatio - lhsReal) / rhsRealImagDenom
//
// or
//
// rhsImagRealRatio = rhsImag / rhsReal
// rhsImagRealDenom = rhsReal + rhsImag * rhsImagRealRatio
// resultReal = (lhsReal + lhsImag * rhsImagRealRatio) / rhsImagRealDenom
// resultImag = (lhsImag - lhsReal * rhsImagRealRatio) / rhsImagRealDenom
//
// See https://dl.acm.org/citation.cfm?id=368661 for more details.
Value rhsRealImagRatio =
rewriter.create<arith::DivFOp>(loc, rhsReal, rhsImag, fmf);
Value rhsRealImagDenom = rewriter.create<arith::AddFOp>(
loc, rhsImag,
rewriter.create<arith::MulFOp>(loc, rhsRealImagRatio, rhsReal, fmf),
fmf);
Value realNumerator1 = rewriter.create<arith::AddFOp>(
loc,
rewriter.create<arith::MulFOp>(loc, lhsReal, rhsRealImagRatio, fmf),
lhsImag, fmf);
Value resultReal1 = rewriter.create<arith::DivFOp>(loc, realNumerator1,
rhsRealImagDenom, fmf);
Value imagNumerator1 = rewriter.create<arith::SubFOp>(
loc,
rewriter.create<arith::MulFOp>(loc, lhsImag, rhsRealImagRatio, fmf),
lhsReal, fmf);
Value resultImag1 = rewriter.create<arith::DivFOp>(loc, imagNumerator1,
rhsRealImagDenom, fmf);
Value rhsImagRealRatio =
rewriter.create<arith::DivFOp>(loc, rhsImag, rhsReal, fmf);
Value rhsImagRealDenom = rewriter.create<arith::AddFOp>(
loc, rhsReal,
rewriter.create<arith::MulFOp>(loc, rhsImagRealRatio, rhsImag, fmf),
fmf);
Value realNumerator2 = rewriter.create<arith::AddFOp>(
loc, lhsReal,
rewriter.create<arith::MulFOp>(loc, lhsImag, rhsImagRealRatio, fmf),
fmf);
Value resultReal2 = rewriter.create<arith::DivFOp>(loc, realNumerator2,
rhsImagRealDenom, fmf);
Value imagNumerator2 = rewriter.create<arith::SubFOp>(
loc, lhsImag,
rewriter.create<arith::MulFOp>(loc, lhsReal, rhsImagRealRatio, fmf),
fmf);
Value resultImag2 = rewriter.create<arith::DivFOp>(loc, imagNumerator2,
rhsImagRealDenom, fmf);
// Consider corner cases.
// Case 1. Zero denominator, numerator contains at most one NaN value.
Value zero = rewriter.create<arith::ConstantOp>(
loc, elementType, rewriter.getZeroAttr(elementType));
Value rhsRealAbs = rewriter.create<math::AbsFOp>(loc, rhsReal, fmf);
Value rhsRealIsZero = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::OEQ, rhsRealAbs, zero);
Value rhsImagAbs = rewriter.create<math::AbsFOp>(loc, rhsImag, fmf);
Value rhsImagIsZero = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::OEQ, rhsImagAbs, zero);
Value lhsRealIsNotNaN = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::ORD, lhsReal, zero);
Value lhsImagIsNotNaN = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::ORD, lhsImag, zero);
Value lhsContainsNotNaNValue =
rewriter.create<arith::OrIOp>(loc, lhsRealIsNotNaN, lhsImagIsNotNaN);
Value resultIsInfinity = rewriter.create<arith::AndIOp>(
loc, lhsContainsNotNaNValue,
rewriter.create<arith::AndIOp>(loc, rhsRealIsZero, rhsImagIsZero));
Value inf = rewriter.create<arith::ConstantOp>(
loc, elementType,
rewriter.getFloatAttr(
elementType, APFloat::getInf(elementType.getFloatSemantics())));
Value infWithSignOfRhsReal =
rewriter.create<math::CopySignOp>(loc, inf, rhsReal);
Value infinityResultReal =
rewriter.create<arith::MulFOp>(loc, infWithSignOfRhsReal, lhsReal, fmf);
Value infinityResultImag =
rewriter.create<arith::MulFOp>(loc, infWithSignOfRhsReal, lhsImag, fmf);
// Case 2. Infinite numerator, finite denominator.
Value rhsRealFinite = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::ONE, rhsRealAbs, inf);
Value rhsImagFinite = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::ONE, rhsImagAbs, inf);
Value rhsFinite =
rewriter.create<arith::AndIOp>(loc, rhsRealFinite, rhsImagFinite);
Value lhsRealAbs = rewriter.create<math::AbsFOp>(loc, lhsReal, fmf);
Value lhsRealInfinite = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::OEQ, lhsRealAbs, inf);
Value lhsImagAbs = rewriter.create<math::AbsFOp>(loc, lhsImag, fmf);
Value lhsImagInfinite = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::OEQ, lhsImagAbs, inf);
Value lhsInfinite =
rewriter.create<arith::OrIOp>(loc, lhsRealInfinite, lhsImagInfinite);
Value infNumFiniteDenom =
rewriter.create<arith::AndIOp>(loc, lhsInfinite, rhsFinite);
Value one = rewriter.create<arith::ConstantOp>(
loc, elementType, rewriter.getFloatAttr(elementType, 1));
Value lhsRealIsInfWithSign = rewriter.create<math::CopySignOp>(
loc, rewriter.create<arith::SelectOp>(loc, lhsRealInfinite, one, zero),
lhsReal);
Value lhsImagIsInfWithSign = rewriter.create<math::CopySignOp>(
loc, rewriter.create<arith::SelectOp>(loc, lhsImagInfinite, one, zero),
lhsImag);
Value lhsRealIsInfWithSignTimesRhsReal =
rewriter.create<arith::MulFOp>(loc, lhsRealIsInfWithSign, rhsReal, fmf);
Value lhsImagIsInfWithSignTimesRhsImag =
rewriter.create<arith::MulFOp>(loc, lhsImagIsInfWithSign, rhsImag, fmf);
Value resultReal3 = rewriter.create<arith::MulFOp>(
loc, inf,
rewriter.create<arith::AddFOp>(loc, lhsRealIsInfWithSignTimesRhsReal,
lhsImagIsInfWithSignTimesRhsImag, fmf),
fmf);
Value lhsRealIsInfWithSignTimesRhsImag =
rewriter.create<arith::MulFOp>(loc, lhsRealIsInfWithSign, rhsImag, fmf);
Value lhsImagIsInfWithSignTimesRhsReal =
rewriter.create<arith::MulFOp>(loc, lhsImagIsInfWithSign, rhsReal, fmf);
Value resultImag3 = rewriter.create<arith::MulFOp>(
loc, inf,
rewriter.create<arith::SubFOp>(loc, lhsImagIsInfWithSignTimesRhsReal,
lhsRealIsInfWithSignTimesRhsImag, fmf),
fmf);
// Case 3: Finite numerator, infinite denominator.
Value lhsRealFinite = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::ONE, lhsRealAbs, inf);
Value lhsImagFinite = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::ONE, lhsImagAbs, inf);
Value lhsFinite =
rewriter.create<arith::AndIOp>(loc, lhsRealFinite, lhsImagFinite);
Value rhsRealInfinite = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::OEQ, rhsRealAbs, inf);
Value rhsImagInfinite = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::OEQ, rhsImagAbs, inf);
Value rhsInfinite =
rewriter.create<arith::OrIOp>(loc, rhsRealInfinite, rhsImagInfinite);
Value finiteNumInfiniteDenom =
rewriter.create<arith::AndIOp>(loc, lhsFinite, rhsInfinite);
Value rhsRealIsInfWithSign = rewriter.create<math::CopySignOp>(
loc, rewriter.create<arith::SelectOp>(loc, rhsRealInfinite, one, zero),
rhsReal);
Value rhsImagIsInfWithSign = rewriter.create<math::CopySignOp>(
loc, rewriter.create<arith::SelectOp>(loc, rhsImagInfinite, one, zero),
rhsImag);
Value rhsRealIsInfWithSignTimesLhsReal =
rewriter.create<arith::MulFOp>(loc, lhsReal, rhsRealIsInfWithSign, fmf);
Value rhsImagIsInfWithSignTimesLhsImag =
rewriter.create<arith::MulFOp>(loc, lhsImag, rhsImagIsInfWithSign, fmf);
Value resultReal4 = rewriter.create<arith::MulFOp>(
loc, zero,
rewriter.create<arith::AddFOp>(loc, rhsRealIsInfWithSignTimesLhsReal,
rhsImagIsInfWithSignTimesLhsImag, fmf),
fmf);
Value rhsRealIsInfWithSignTimesLhsImag =
rewriter.create<arith::MulFOp>(loc, lhsImag, rhsRealIsInfWithSign, fmf);
Value rhsImagIsInfWithSignTimesLhsReal =
rewriter.create<arith::MulFOp>(loc, lhsReal, rhsImagIsInfWithSign, fmf);
Value resultImag4 = rewriter.create<arith::MulFOp>(
loc, zero,
rewriter.create<arith::SubFOp>(loc, rhsRealIsInfWithSignTimesLhsImag,
rhsImagIsInfWithSignTimesLhsReal, fmf),
fmf);
Value realAbsSmallerThanImagAbs = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::OLT, rhsRealAbs, rhsImagAbs);
Value resultReal = rewriter.create<arith::SelectOp>(
loc, realAbsSmallerThanImagAbs, resultReal1, resultReal2);
Value resultImag = rewriter.create<arith::SelectOp>(
loc, realAbsSmallerThanImagAbs, resultImag1, resultImag2);
Value resultRealSpecialCase3 = rewriter.create<arith::SelectOp>(
loc, finiteNumInfiniteDenom, resultReal4, resultReal);
Value resultImagSpecialCase3 = rewriter.create<arith::SelectOp>(
loc, finiteNumInfiniteDenom, resultImag4, resultImag);
Value resultRealSpecialCase2 = rewriter.create<arith::SelectOp>(
loc, infNumFiniteDenom, resultReal3, resultRealSpecialCase3);
Value resultImagSpecialCase2 = rewriter.create<arith::SelectOp>(
loc, infNumFiniteDenom, resultImag3, resultImagSpecialCase3);
Value resultRealSpecialCase1 = rewriter.create<arith::SelectOp>(
loc, resultIsInfinity, infinityResultReal, resultRealSpecialCase2);
Value resultImagSpecialCase1 = rewriter.create<arith::SelectOp>(
loc, resultIsInfinity, infinityResultImag, resultImagSpecialCase2);
Value resultRealIsNaN = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::UNO, resultReal, zero);
Value resultImagIsNaN = rewriter.create<arith::CmpFOp>(
loc, arith::CmpFPredicate::UNO, resultImag, zero);
Value resultIsNaN =
rewriter.create<arith::AndIOp>(loc, resultRealIsNaN, resultImagIsNaN);
Value resultRealWithSpecialCases = rewriter.create<arith::SelectOp>(
loc, resultIsNaN, resultRealSpecialCase1, resultReal);
Value resultImagWithSpecialCases = rewriter.create<arith::SelectOp>(
loc, resultIsNaN, resultImagSpecialCase1, resultImag);
rewriter.replaceOpWithNewOp<complex::CreateOp>(
op, type, resultRealWithSpecialCases, resultImagWithSpecialCases);
return success();
}
};
struct ExpOpConversion : public OpConversionPattern<complex::ExpOp> {
using OpConversionPattern<complex::ExpOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::ExpOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto loc = op.getLoc();
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
Value real =
rewriter.create<complex::ReOp>(loc, elementType, adaptor.getComplex());
Value imag =
rewriter.create<complex::ImOp>(loc, elementType, adaptor.getComplex());
Value expReal = rewriter.create<math::ExpOp>(loc, real, fmf.getValue());
Value cosImag = rewriter.create<math::CosOp>(loc, imag, fmf.getValue());
Value resultReal =
rewriter.create<arith::MulFOp>(loc, expReal, cosImag, fmf.getValue());
Value sinImag = rewriter.create<math::SinOp>(loc, imag, fmf.getValue());
Value resultImag =
rewriter.create<arith::MulFOp>(loc, expReal, sinImag, fmf.getValue());
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultReal,
resultImag);
return success();
}
};
struct Expm1OpConversion : public OpConversionPattern<complex::Expm1Op> {
using OpConversionPattern<complex::Expm1Op>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::Expm1Op op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
Value exp = b.create<complex::ExpOp>(adaptor.getComplex(), fmf.getValue());
Value real = b.create<complex::ReOp>(elementType, exp);
Value one = b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, 1));
Value realMinusOne = b.create<arith::SubFOp>(real, one, fmf.getValue());
Value imag = b.create<complex::ImOp>(elementType, exp);
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, realMinusOne,
imag);
return success();
}
};
struct LogOpConversion : public OpConversionPattern<complex::LogOp> {
using OpConversionPattern<complex::LogOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::LogOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
Value abs = b.create<complex::AbsOp>(elementType, adaptor.getComplex(),
fmf.getValue());
Value resultReal = b.create<math::LogOp>(elementType, abs, fmf.getValue());
Value real = b.create<complex::ReOp>(elementType, adaptor.getComplex());
Value imag = b.create<complex::ImOp>(elementType, adaptor.getComplex());
Value resultImag =
b.create<math::Atan2Op>(elementType, imag, real, fmf.getValue());
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultReal,
resultImag);
return success();
}
};
struct Log1pOpConversion : public OpConversionPattern<complex::Log1pOp> {
using OpConversionPattern<complex::Log1pOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::Log1pOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlags fmf = op.getFastMathFlagsAttr().getValue();
mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
Value real = b.create<complex::ReOp>(adaptor.getComplex());
Value imag = b.create<complex::ImOp>(adaptor.getComplex());
Value half = b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, 0.5));
Value one = b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, 1));
Value realPlusOne = b.create<arith::AddFOp>(real, one, fmf);
Value absRealPlusOne = b.create<math::AbsFOp>(realPlusOne, fmf);
Value absImag = b.create<math::AbsFOp>(imag, fmf);
Value maxAbs = b.create<arith::MaximumFOp>(absRealPlusOne, absImag, fmf);
Value minAbs = b.create<arith::MinimumFOp>(absRealPlusOne, absImag, fmf);
Value useReal = b.create<arith::CmpFOp>(arith::CmpFPredicate::OGT,
realPlusOne, absImag, fmf);
Value maxMinusOne = b.create<arith::SubFOp>(maxAbs, one, fmf);
Value maxAbsOfRealPlusOneAndImagMinusOne =
b.create<arith::SelectOp>(useReal, real, maxMinusOne);
Value minMaxRatio = b.create<arith::DivFOp>(minAbs, maxAbs, fmf);
Value logOfMaxAbsOfRealPlusOneAndImag =
b.create<math::Log1pOp>(maxAbsOfRealPlusOneAndImagMinusOne, fmf);
Value logOfSqrtPart = b.create<math::Log1pOp>(
b.create<arith::MulFOp>(minMaxRatio, minMaxRatio, fmf), fmf);
Value r = b.create<arith::AddFOp>(
b.create<arith::MulFOp>(half, logOfSqrtPart, fmf),
logOfMaxAbsOfRealPlusOneAndImag, fmf);
Value resultReal = b.create<arith::SelectOp>(
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, r, r, fmf), minAbs,
r);
Value resultImag = b.create<math::Atan2Op>(imag, realPlusOne, fmf);
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultReal,
resultImag);
return success();
}
};
struct MulOpConversion : public OpConversionPattern<complex::MulOp> {
using OpConversionPattern<complex::MulOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::MulOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
auto type = cast<ComplexType>(adaptor.getLhs().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
auto fmfValue = fmf.getValue();
Value lhsReal = b.create<complex::ReOp>(elementType, adaptor.getLhs());
Value lhsRealAbs = b.create<math::AbsFOp>(lhsReal, fmfValue);
Value lhsImag = b.create<complex::ImOp>(elementType, adaptor.getLhs());
Value lhsImagAbs = b.create<math::AbsFOp>(lhsImag, fmfValue);
Value rhsReal = b.create<complex::ReOp>(elementType, adaptor.getRhs());
Value rhsRealAbs = b.create<math::AbsFOp>(rhsReal, fmfValue);
Value rhsImag = b.create<complex::ImOp>(elementType, adaptor.getRhs());
Value rhsImagAbs = b.create<math::AbsFOp>(rhsImag, fmfValue);
Value lhsRealTimesRhsReal =
b.create<arith::MulFOp>(lhsReal, rhsReal, fmfValue);
Value lhsRealTimesRhsRealAbs =
b.create<math::AbsFOp>(lhsRealTimesRhsReal, fmfValue);
Value lhsImagTimesRhsImag =
b.create<arith::MulFOp>(lhsImag, rhsImag, fmfValue);
Value lhsImagTimesRhsImagAbs =
b.create<math::AbsFOp>(lhsImagTimesRhsImag, fmfValue);
Value real = b.create<arith::SubFOp>(lhsRealTimesRhsReal,
lhsImagTimesRhsImag, fmfValue);
Value lhsImagTimesRhsReal =
b.create<arith::MulFOp>(lhsImag, rhsReal, fmfValue);
Value lhsImagTimesRhsRealAbs =
b.create<math::AbsFOp>(lhsImagTimesRhsReal, fmfValue);
Value lhsRealTimesRhsImag =
b.create<arith::MulFOp>(lhsReal, rhsImag, fmfValue);
Value lhsRealTimesRhsImagAbs =
b.create<math::AbsFOp>(lhsRealTimesRhsImag, fmfValue);
Value imag = b.create<arith::AddFOp>(lhsImagTimesRhsReal,
lhsRealTimesRhsImag, fmfValue);
// Handle cases where the "naive" calculation results in NaN values.
Value realIsNan =
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, real, real);
Value imagIsNan =
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, imag, imag);
Value isNan = b.create<arith::AndIOp>(realIsNan, imagIsNan);
Value inf = b.create<arith::ConstantOp>(
elementType,
b.getFloatAttr(elementType,
APFloat::getInf(elementType.getFloatSemantics())));
// Case 1. `lhsReal` or `lhsImag` are infinite.
Value lhsRealIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, lhsRealAbs, inf);
Value lhsImagIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, lhsImagAbs, inf);
Value lhsIsInf = b.create<arith::OrIOp>(lhsRealIsInf, lhsImagIsInf);
Value rhsRealIsNan =
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, rhsReal, rhsReal);
Value rhsImagIsNan =
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, rhsImag, rhsImag);
Value zero =
b.create<arith::ConstantOp>(elementType, b.getZeroAttr(elementType));
Value one = b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, 1));
Value lhsRealIsInfFloat =
b.create<arith::SelectOp>(lhsRealIsInf, one, zero);
lhsReal = b.create<arith::SelectOp>(
lhsIsInf, b.create<math::CopySignOp>(lhsRealIsInfFloat, lhsReal),
lhsReal);
Value lhsImagIsInfFloat =
b.create<arith::SelectOp>(lhsImagIsInf, one, zero);
lhsImag = b.create<arith::SelectOp>(
lhsIsInf, b.create<math::CopySignOp>(lhsImagIsInfFloat, lhsImag),
lhsImag);
Value lhsIsInfAndRhsRealIsNan =
b.create<arith::AndIOp>(lhsIsInf, rhsRealIsNan);
rhsReal = b.create<arith::SelectOp>(
lhsIsInfAndRhsRealIsNan, b.create<math::CopySignOp>(zero, rhsReal),
rhsReal);
Value lhsIsInfAndRhsImagIsNan =
b.create<arith::AndIOp>(lhsIsInf, rhsImagIsNan);
rhsImag = b.create<arith::SelectOp>(
lhsIsInfAndRhsImagIsNan, b.create<math::CopySignOp>(zero, rhsImag),
rhsImag);
// Case 2. `rhsReal` or `rhsImag` are infinite.
Value rhsRealIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, rhsRealAbs, inf);
Value rhsImagIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, rhsImagAbs, inf);
Value rhsIsInf = b.create<arith::OrIOp>(rhsRealIsInf, rhsImagIsInf);
Value lhsRealIsNan =
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, lhsReal, lhsReal);
Value lhsImagIsNan =
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, lhsImag, lhsImag);
Value rhsRealIsInfFloat =
b.create<arith::SelectOp>(rhsRealIsInf, one, zero);
rhsReal = b.create<arith::SelectOp>(
rhsIsInf, b.create<math::CopySignOp>(rhsRealIsInfFloat, rhsReal),
rhsReal);
Value rhsImagIsInfFloat =
b.create<arith::SelectOp>(rhsImagIsInf, one, zero);
rhsImag = b.create<arith::SelectOp>(
rhsIsInf, b.create<math::CopySignOp>(rhsImagIsInfFloat, rhsImag),
rhsImag);
Value rhsIsInfAndLhsRealIsNan =
b.create<arith::AndIOp>(rhsIsInf, lhsRealIsNan);
lhsReal = b.create<arith::SelectOp>(
rhsIsInfAndLhsRealIsNan, b.create<math::CopySignOp>(zero, lhsReal),
lhsReal);
Value rhsIsInfAndLhsImagIsNan =
b.create<arith::AndIOp>(rhsIsInf, lhsImagIsNan);
lhsImag = b.create<arith::SelectOp>(
rhsIsInfAndLhsImagIsNan, b.create<math::CopySignOp>(zero, lhsImag),
lhsImag);
Value recalc = b.create<arith::OrIOp>(lhsIsInf, rhsIsInf);
// Case 3. One of the pairwise products of left hand side with right hand
// side is infinite.
Value lhsRealTimesRhsRealIsInf = b.create<arith::CmpFOp>(
arith::CmpFPredicate::OEQ, lhsRealTimesRhsRealAbs, inf);
Value lhsImagTimesRhsImagIsInf = b.create<arith::CmpFOp>(
arith::CmpFPredicate::OEQ, lhsImagTimesRhsImagAbs, inf);
Value isSpecialCase = b.create<arith::OrIOp>(lhsRealTimesRhsRealIsInf,
lhsImagTimesRhsImagIsInf);
Value lhsRealTimesRhsImagIsInf = b.create<arith::CmpFOp>(
arith::CmpFPredicate::OEQ, lhsRealTimesRhsImagAbs, inf);
isSpecialCase =
b.create<arith::OrIOp>(isSpecialCase, lhsRealTimesRhsImagIsInf);
Value lhsImagTimesRhsRealIsInf = b.create<arith::CmpFOp>(
arith::CmpFPredicate::OEQ, lhsImagTimesRhsRealAbs, inf);
isSpecialCase =
b.create<arith::OrIOp>(isSpecialCase, lhsImagTimesRhsRealIsInf);
Type i1Type = b.getI1Type();
Value notRecalc = b.create<arith::XOrIOp>(
recalc,
b.create<arith::ConstantOp>(i1Type, b.getIntegerAttr(i1Type, 1)));
isSpecialCase = b.create<arith::AndIOp>(isSpecialCase, notRecalc);
Value isSpecialCaseAndLhsRealIsNan =
b.create<arith::AndIOp>(isSpecialCase, lhsRealIsNan);
lhsReal = b.create<arith::SelectOp>(
isSpecialCaseAndLhsRealIsNan, b.create<math::CopySignOp>(zero, lhsReal),
lhsReal);
Value isSpecialCaseAndLhsImagIsNan =
b.create<arith::AndIOp>(isSpecialCase, lhsImagIsNan);
lhsImag = b.create<arith::SelectOp>(
isSpecialCaseAndLhsImagIsNan, b.create<math::CopySignOp>(zero, lhsImag),
lhsImag);
Value isSpecialCaseAndRhsRealIsNan =
b.create<arith::AndIOp>(isSpecialCase, rhsRealIsNan);
rhsReal = b.create<arith::SelectOp>(
isSpecialCaseAndRhsRealIsNan, b.create<math::CopySignOp>(zero, rhsReal),
rhsReal);
Value isSpecialCaseAndRhsImagIsNan =
b.create<arith::AndIOp>(isSpecialCase, rhsImagIsNan);
rhsImag = b.create<arith::SelectOp>(
isSpecialCaseAndRhsImagIsNan, b.create<math::CopySignOp>(zero, rhsImag),
rhsImag);
recalc = b.create<arith::OrIOp>(recalc, isSpecialCase);
recalc = b.create<arith::AndIOp>(isNan, recalc);
// Recalculate real part.
lhsRealTimesRhsReal = b.create<arith::MulFOp>(lhsReal, rhsReal, fmfValue);
lhsImagTimesRhsImag = b.create<arith::MulFOp>(lhsImag, rhsImag, fmfValue);
Value newReal = b.create<arith::SubFOp>(lhsRealTimesRhsReal,
lhsImagTimesRhsImag, fmfValue);
real = b.create<arith::SelectOp>(
recalc, b.create<arith::MulFOp>(inf, newReal, fmfValue), real);
// Recalculate imag part.
lhsImagTimesRhsReal = b.create<arith::MulFOp>(lhsImag, rhsReal, fmfValue);
lhsRealTimesRhsImag = b.create<arith::MulFOp>(lhsReal, rhsImag, fmfValue);
Value newImag = b.create<arith::AddFOp>(lhsImagTimesRhsReal,
lhsRealTimesRhsImag, fmfValue);
imag = b.create<arith::SelectOp>(
recalc, b.create<arith::MulFOp>(inf, newImag, fmfValue), imag);
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, real, imag);
return success();
}
};
struct NegOpConversion : public OpConversionPattern<complex::NegOp> {
using OpConversionPattern<complex::NegOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::NegOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto loc = op.getLoc();
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
Value real =
rewriter.create<complex::ReOp>(loc, elementType, adaptor.getComplex());
Value imag =
rewriter.create<complex::ImOp>(loc, elementType, adaptor.getComplex());
Value negReal = rewriter.create<arith::NegFOp>(loc, real);
Value negImag = rewriter.create<arith::NegFOp>(loc, imag);
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, negReal, negImag);
return success();
}
};
struct SinOpConversion : public TrigonometricOpConversion<complex::SinOp> {
using TrigonometricOpConversion<complex::SinOp>::TrigonometricOpConversion;
std::pair<Value, Value> combine(Location loc, Value scaledExp,
Value reciprocalExp, Value sin, Value cos,
ConversionPatternRewriter &rewriter,
arith::FastMathFlagsAttr fmf) const override {
// Complex sine is defined as;
// sin(x + iy) = -0.5i * (exp(i(x + iy)) - exp(-i(x + iy)))
// Plugging in:
// exp(i(x+iy)) = exp(-y + ix) = exp(-y)(cos(x) + i sin(x))
// exp(-i(x+iy)) = exp(y + i(-x)) = exp(y)(cos(x) + i (-sin(x)))
// and defining t := exp(y)
// We get:
// Re(sin(x + iy)) = (0.5*t + 0.5/t) * sin x
// Im(cos(x + iy)) = (0.5*t - 0.5/t) * cos x
Value sum =
rewriter.create<arith::AddFOp>(loc, scaledExp, reciprocalExp, fmf);
Value resultReal = rewriter.create<arith::MulFOp>(loc, sum, sin, fmf);
Value diff =
rewriter.create<arith::SubFOp>(loc, scaledExp, reciprocalExp, fmf);
Value resultImag = rewriter.create<arith::MulFOp>(loc, diff, cos, fmf);
return {resultReal, resultImag};
}
};
// The algorithm is listed in https://dl.acm.org/doi/pdf/10.1145/363717.363780.
struct SqrtOpConversion : public OpConversionPattern<complex::SqrtOp> {
using OpConversionPattern<complex::SqrtOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::SqrtOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
ImplicitLocOpBuilder b(op.getLoc(), rewriter);
auto type = cast<ComplexType>(op.getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlags fmf = op.getFastMathFlagsAttr().getValue();
auto cst = [&](APFloat v) {
return b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, v));
};
const auto &floatSemantics = elementType.getFloatSemantics();
Value zero = cst(APFloat::getZero(floatSemantics));
Value half = b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, 0.5));
Value real = b.create<complex::ReOp>(elementType, adaptor.getComplex());
Value imag = b.create<complex::ImOp>(elementType, adaptor.getComplex());
Value absSqrt = computeAbs(real, imag, fmf, b, AbsFn::sqrt);
Value argArg = b.create<math::Atan2Op>(imag, real, fmf);
Value sqrtArg = b.create<arith::MulFOp>(argArg, half, fmf);
Value cos = b.create<math::CosOp>(sqrtArg, fmf);
Value sin = b.create<math::SinOp>(sqrtArg, fmf);
// sin(atan2(0, inf)) = 0, sqrt(abs(inf)) = inf, but we can't multiply
// 0 * inf.
Value sinIsZero =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, sin, zero, fmf);
Value resultReal = b.create<arith::MulFOp>(absSqrt, cos, fmf);
Value resultImag = b.create<arith::SelectOp>(
sinIsZero, zero, b.create<arith::MulFOp>(absSqrt, sin, fmf));
if (!arith::bitEnumContainsAll(fmf, arith::FastMathFlags::nnan |
arith::FastMathFlags::ninf)) {
Value inf = cst(APFloat::getInf(floatSemantics));
Value negInf = cst(APFloat::getInf(floatSemantics, true));
Value nan = cst(APFloat::getNaN(floatSemantics));
Value absImag = b.create<math::AbsFOp>(elementType, imag, fmf);
Value absImagIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, absImag, inf, fmf);
Value absImagIsNotInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::ONE, absImag, inf, fmf);
Value realIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, real, inf, fmf);
Value realIsNegInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, real, negInf, fmf);
resultReal = b.create<arith::SelectOp>(
b.create<arith::AndIOp>(realIsNegInf, absImagIsNotInf), zero,
resultReal);
resultReal = b.create<arith::SelectOp>(
b.create<arith::OrIOp>(absImagIsInf, realIsInf), inf, resultReal);
Value imagSignInf = b.create<math::CopySignOp>(inf, imag, fmf);
resultImag = b.create<arith::SelectOp>(
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, absSqrt, absSqrt),
nan, resultImag);
resultImag = b.create<arith::SelectOp>(
b.create<arith::OrIOp>(absImagIsInf, realIsNegInf), imagSignInf,
resultImag);
}
Value resultIsZero =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, absSqrt, zero, fmf);
resultReal = b.create<arith::SelectOp>(resultIsZero, zero, resultReal);
resultImag = b.create<arith::SelectOp>(resultIsZero, zero, resultImag);
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultReal,
resultImag);
return success();
}
};
struct SignOpConversion : public OpConversionPattern<complex::SignOp> {
using OpConversionPattern<complex::SignOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::SignOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
Value real = b.create<complex::ReOp>(elementType, adaptor.getComplex());
Value imag = b.create<complex::ImOp>(elementType, adaptor.getComplex());
Value zero =
b.create<arith::ConstantOp>(elementType, b.getZeroAttr(elementType));
Value realIsZero =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, real, zero);
Value imagIsZero =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, imag, zero);
Value isZero = b.create<arith::AndIOp>(realIsZero, imagIsZero);
auto abs = b.create<complex::AbsOp>(elementType, adaptor.getComplex(), fmf);
Value realSign = b.create<arith::DivFOp>(real, abs, fmf);
Value imagSign = b.create<arith::DivFOp>(imag, abs, fmf);
Value sign = b.create<complex::CreateOp>(type, realSign, imagSign);
rewriter.replaceOpWithNewOp<arith::SelectOp>(op, isZero,
adaptor.getComplex(), sign);
return success();
}
};
template <typename Op>
struct TanTanhOpConversion : public OpConversionPattern<Op> {
using OpConversionPattern<Op>::OpConversionPattern;
LogicalResult
matchAndRewrite(Op op, typename Op::Adaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
ImplicitLocOpBuilder b(op.getLoc(), rewriter);
auto loc = op.getLoc();
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlags fmf = op.getFastMathFlagsAttr().getValue();
const auto &floatSemantics = elementType.getFloatSemantics();
Value real =
b.create<complex::ReOp>(loc, elementType, adaptor.getComplex());
Value imag =
b.create<complex::ImOp>(loc, elementType, adaptor.getComplex());
Value negOne = b.create<arith::ConstantOp>(
elementType, b.getFloatAttr(elementType, -1.0));
if constexpr (std::is_same_v<Op, complex::TanOp>) {
// tan(x+yi) = -i*tanh(-y + xi)
std::swap(real, imag);
real = b.create<arith::MulFOp>(real, negOne, fmf);
}
auto cst = [&](APFloat v) {
return b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, v));
};
Value inf = cst(APFloat::getInf(floatSemantics));
Value four = b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, 4.0));
Value twoReal = b.create<arith::AddFOp>(real, real, fmf);
Value negTwoReal = b.create<arith::MulFOp>(negOne, twoReal, fmf);
Value expTwoRealMinusOne = b.create<math::ExpM1Op>(twoReal, fmf);
Value expNegTwoRealMinusOne = b.create<math::ExpM1Op>(negTwoReal, fmf);
Value realNum =
b.create<arith::SubFOp>(expTwoRealMinusOne, expNegTwoRealMinusOne, fmf);
Value cosImag = b.create<math::CosOp>(imag, fmf);
Value cosImagSq = b.create<arith::MulFOp>(cosImag, cosImag, fmf);
Value twoCosTwoImagPlusOne = b.create<arith::MulFOp>(cosImagSq, four, fmf);
Value sinImag = b.create<math::SinOp>(imag, fmf);
Value imagNum = b.create<arith::MulFOp>(
four, b.create<arith::MulFOp>(cosImag, sinImag, fmf), fmf);
Value expSumMinusTwo =
b.create<arith::AddFOp>(expTwoRealMinusOne, expNegTwoRealMinusOne, fmf);
Value denom =
b.create<arith::AddFOp>(expSumMinusTwo, twoCosTwoImagPlusOne, fmf);
Value isInf = b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ,
expSumMinusTwo, inf, fmf);
Value realLimit = b.create<math::CopySignOp>(negOne, real, fmf);
Value resultReal = b.create<arith::SelectOp>(
isInf, realLimit, b.create<arith::DivFOp>(realNum, denom, fmf));
Value resultImag = b.create<arith::DivFOp>(imagNum, denom, fmf);
if (!arith::bitEnumContainsAll(fmf, arith::FastMathFlags::nnan |
arith::FastMathFlags::ninf)) {
Value absReal = b.create<math::AbsFOp>(real, fmf);
Value zero = b.create<arith::ConstantOp>(
elementType, b.getFloatAttr(elementType, 0.0));
Value nan = cst(APFloat::getNaN(floatSemantics));
Value absRealIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, absReal, inf, fmf);
Value imagIsZero =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, imag, zero, fmf);
Value absRealIsNotInf = b.create<arith::XOrIOp>(
absRealIsInf, b.create<arith::ConstantIntOp>(true, /*width=*/1));
Value imagNumIsNaN = b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO,
imagNum, imagNum, fmf);
Value resultRealIsNaN =
b.create<arith::AndIOp>(imagNumIsNaN, absRealIsNotInf);
Value resultImagIsZero = b.create<arith::OrIOp>(
imagIsZero, b.create<arith::AndIOp>(absRealIsInf, imagNumIsNaN));
resultReal = b.create<arith::SelectOp>(resultRealIsNaN, nan, resultReal);
resultImag =
b.create<arith::SelectOp>(resultImagIsZero, zero, resultImag);
}
if constexpr (std::is_same_v<Op, complex::TanOp>) {
// tan(x+yi) = -i*tanh(-y + xi)
std::swap(resultReal, resultImag);
resultImag = b.create<arith::MulFOp>(resultImag, negOne, fmf);
}
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultReal,
resultImag);
return success();
}
};
struct ConjOpConversion : public OpConversionPattern<complex::ConjOp> {
using OpConversionPattern<complex::ConjOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::ConjOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto loc = op.getLoc();
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
Value real =
rewriter.create<complex::ReOp>(loc, elementType, adaptor.getComplex());
Value imag =
rewriter.create<complex::ImOp>(loc, elementType, adaptor.getComplex());
Value negImag = rewriter.create<arith::NegFOp>(loc, elementType, imag);
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, real, negImag);
return success();
}
};
/// Converts lhs^y = (a+bi)^(c+di) to
/// (a*a+b*b)^(0.5c) * exp(-d*atan2(b,a)) * (cos(q) + i*sin(q)),
/// where q = c*atan2(b,a)+0.5d*ln(a*a+b*b)
static Value powOpConversionImpl(mlir::ImplicitLocOpBuilder &builder,
ComplexType type, Value lhs, Value c, Value d,
arith::FastMathFlags fmf) {
auto elementType = cast<FloatType>(type.getElementType());
Value a = builder.create<complex::ReOp>(lhs);
Value b = builder.create<complex::ImOp>(lhs);
Value abs = builder.create<complex::AbsOp>(lhs, fmf);
Value absToC = builder.create<math::PowFOp>(abs, c, fmf);
Value negD = builder.create<arith::NegFOp>(d, fmf);
Value argLhs = builder.create<math::Atan2Op>(b, a, fmf);
Value negDArgLhs = builder.create<arith::MulFOp>(negD, argLhs, fmf);
Value expNegDArgLhs = builder.create<math::ExpOp>(negDArgLhs, fmf);
Value coeff = builder.create<arith::MulFOp>(absToC, expNegDArgLhs, fmf);
Value lnAbs = builder.create<math::LogOp>(abs, fmf);
Value cArgLhs = builder.create<arith::MulFOp>(c, argLhs, fmf);
Value dLnAbs = builder.create<arith::MulFOp>(d, lnAbs, fmf);
Value q = builder.create<arith::AddFOp>(cArgLhs, dLnAbs, fmf);
Value cosQ = builder.create<math::CosOp>(q, fmf);
Value sinQ = builder.create<math::SinOp>(q, fmf);
Value inf = builder.create<arith::ConstantOp>(
elementType,
builder.getFloatAttr(elementType,
APFloat::getInf(elementType.getFloatSemantics())));
Value zero = builder.create<arith::ConstantOp>(
elementType, builder.getFloatAttr(elementType, 0.0));
Value one = builder.create<arith::ConstantOp>(
elementType, builder.getFloatAttr(elementType, 1.0));
Value complexOne = builder.create<complex::CreateOp>(type, one, zero);
Value complexZero = builder.create<complex::CreateOp>(type, zero, zero);
Value complexInf = builder.create<complex::CreateOp>(type, inf, zero);
// Case 0:
// d^c is 0 if d is 0 and c > 0. 0^0 is defined to be 1.0, see
// Branch Cuts for Complex Elementary Functions or Much Ado About
// Nothing's Sign Bit, W. Kahan, Section 10.
Value absEqZero =
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, abs, zero, fmf);
Value dEqZero =
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, d, zero, fmf);
Value cEqZero =
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, c, zero, fmf);
Value bEqZero =
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, b, zero, fmf);
Value zeroLeC =
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OLE, zero, c, fmf);
Value coeffCosQ = builder.create<arith::MulFOp>(coeff, cosQ, fmf);
Value coeffSinQ = builder.create<arith::MulFOp>(coeff, sinQ, fmf);
Value complexOneOrZero =
builder.create<arith::SelectOp>(cEqZero, complexOne, complexZero);
Value coeffCosSin =
builder.create<complex::CreateOp>(type, coeffCosQ, coeffSinQ);
Value cutoff0 = builder.create<arith::SelectOp>(
builder.create<arith::AndIOp>(
builder.create<arith::AndIOp>(absEqZero, dEqZero), zeroLeC),
complexOneOrZero, coeffCosSin);
// Case 1:
// x^0 is defined to be 1 for any x, see
// Branch Cuts for Complex Elementary Functions or Much Ado About
// Nothing's Sign Bit, W. Kahan, Section 10.
Value rhsEqZero = builder.create<arith::AndIOp>(cEqZero, dEqZero);
Value cutoff1 =
builder.create<arith::SelectOp>(rhsEqZero, complexOne, cutoff0);
// Case 2:
// 1^(c + d*i) = 1 + 0*i
Value lhsEqOne = builder.create<arith::AndIOp>(
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, a, one, fmf),
bEqZero);
Value cutoff2 =
builder.create<arith::SelectOp>(lhsEqOne, complexOne, cutoff1);
// Case 3:
// inf^(c + 0*i) = inf + 0*i, c > 0
Value lhsEqInf = builder.create<arith::AndIOp>(
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, a, inf, fmf),
bEqZero);
Value rhsGt0 = builder.create<arith::AndIOp>(
dEqZero,
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OGT, c, zero, fmf));
Value cutoff3 = builder.create<arith::SelectOp>(
builder.create<arith::AndIOp>(lhsEqInf, rhsGt0), complexInf, cutoff2);
// Case 4:
// inf^(c + 0*i) = 0 + 0*i, c < 0
Value rhsLt0 = builder.create<arith::AndIOp>(
dEqZero,
builder.create<arith::CmpFOp>(arith::CmpFPredicate::OLT, c, zero, fmf));
Value cutoff4 = builder.create<arith::SelectOp>(
builder.create<arith::AndIOp>(lhsEqInf, rhsLt0), complexZero, cutoff3);
return cutoff4;
}
struct PowOpConversion : public OpConversionPattern<complex::PowOp> {
using OpConversionPattern<complex::PowOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::PowOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
mlir::ImplicitLocOpBuilder builder(op.getLoc(), rewriter);
auto type = cast<ComplexType>(adaptor.getLhs().getType());
auto elementType = cast<FloatType>(type.getElementType());
Value c = builder.create<complex::ReOp>(elementType, adaptor.getRhs());
Value d = builder.create<complex::ImOp>(elementType, adaptor.getRhs());
rewriter.replaceOp(op, {powOpConversionImpl(builder, type, adaptor.getLhs(),
c, d, op.getFastmath())});
return success();
}
};
struct RsqrtOpConversion : public OpConversionPattern<complex::RsqrtOp> {
using OpConversionPattern<complex::RsqrtOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::RsqrtOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
auto type = cast<ComplexType>(adaptor.getComplex().getType());
auto elementType = cast<FloatType>(type.getElementType());
arith::FastMathFlags fmf = op.getFastMathFlagsAttr().getValue();
auto cst = [&](APFloat v) {
return b.create<arith::ConstantOp>(elementType,
b.getFloatAttr(elementType, v));
};
const auto &floatSemantics = elementType.getFloatSemantics();
Value zero = cst(APFloat::getZero(floatSemantics));
Value inf = cst(APFloat::getInf(floatSemantics));
Value negHalf = b.create<arith::ConstantOp>(
elementType, b.getFloatAttr(elementType, -0.5));
Value nan = cst(APFloat::getNaN(floatSemantics));
Value real = b.create<complex::ReOp>(elementType, adaptor.getComplex());
Value imag = b.create<complex::ImOp>(elementType, adaptor.getComplex());
Value absRsqrt = computeAbs(real, imag, fmf, b, AbsFn::rsqrt);
Value argArg = b.create<math::Atan2Op>(imag, real, fmf);
Value rsqrtArg = b.create<arith::MulFOp>(argArg, negHalf, fmf);
Value cos = b.create<math::CosOp>(rsqrtArg, fmf);
Value sin = b.create<math::SinOp>(rsqrtArg, fmf);
Value resultReal = b.create<arith::MulFOp>(absRsqrt, cos, fmf);
Value resultImag = b.create<arith::MulFOp>(absRsqrt, sin, fmf);
if (!arith::bitEnumContainsAll(fmf, arith::FastMathFlags::nnan |
arith::FastMathFlags::ninf)) {
Value negOne = b.create<arith::ConstantOp>(
elementType, b.getFloatAttr(elementType, -1));
Value realSignedZero = b.create<math::CopySignOp>(zero, real, fmf);
Value imagSignedZero = b.create<math::CopySignOp>(zero, imag, fmf);
Value negImagSignedZero =
b.create<arith::MulFOp>(negOne, imagSignedZero, fmf);
Value absReal = b.create<math::AbsFOp>(real, fmf);
Value absImag = b.create<math::AbsFOp>(imag, fmf);
Value absImagIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, absImag, inf, fmf);
Value realIsNan =
b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, real, real, fmf);
Value realIsInf =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, absReal, inf, fmf);
Value inIsNanInf = b.create<arith::AndIOp>(absImagIsInf, realIsNan);
Value resultIsZero = b.create<arith::OrIOp>(inIsNanInf, realIsInf);
resultReal =
b.create<arith::SelectOp>(resultIsZero, realSignedZero, resultReal);
resultImag = b.create<arith::SelectOp>(resultIsZero, negImagSignedZero,
resultImag);
}
Value isRealZero =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, real, zero, fmf);
Value isImagZero =
b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, imag, zero, fmf);
Value isZero = b.create<arith::AndIOp>(isRealZero, isImagZero);
resultReal = b.create<arith::SelectOp>(isZero, inf, resultReal);
resultImag = b.create<arith::SelectOp>(isZero, nan, resultImag);
rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, resultReal,
resultImag);
return success();
}
};
struct AngleOpConversion : public OpConversionPattern<complex::AngleOp> {
using OpConversionPattern<complex::AngleOp>::OpConversionPattern;
LogicalResult
matchAndRewrite(complex::AngleOp op, OpAdaptor adaptor,
ConversionPatternRewriter &rewriter) const override {
auto loc = op.getLoc();
auto type = op.getType();
arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
Value real =
rewriter.create<complex::ReOp>(loc, type, adaptor.getComplex());
Value imag =
rewriter.create<complex::ImOp>(loc, type, adaptor.getComplex());
rewriter.replaceOpWithNewOp<math::Atan2Op>(op, imag, real, fmf);
return success();
}
};
} // namespace
void mlir::populateComplexToStandardConversionPatterns(
RewritePatternSet &patterns) {
// clang-format off
patterns.add<
AbsOpConversion,
AngleOpConversion,
Atan2OpConversion,
BinaryComplexOpConversion<complex::AddOp, arith::AddFOp>,
BinaryComplexOpConversion<complex::SubOp, arith::SubFOp>,
ComparisonOpConversion<complex::EqualOp, arith::CmpFPredicate::OEQ>,
ComparisonOpConversion<complex::NotEqualOp, arith::CmpFPredicate::UNE>,
ConjOpConversion,
CosOpConversion,
DivOpConversion,
ExpOpConversion,
Expm1OpConversion,
Log1pOpConversion,
LogOpConversion,
MulOpConversion,
NegOpConversion,
SignOpConversion,
SinOpConversion,
SqrtOpConversion,
TanTanhOpConversion<complex::TanOp>,
TanTanhOpConversion<complex::TanhOp>,
PowOpConversion,
RsqrtOpConversion
>(patterns.getContext());
// clang-format on
}
namespace {
struct ConvertComplexToStandardPass
: public impl::ConvertComplexToStandardBase<ConvertComplexToStandardPass> {
void runOnOperation() override;
};
void ConvertComplexToStandardPass::runOnOperation() {
// Convert to the Standard dialect using the converter defined above.
RewritePatternSet patterns(&getContext());
populateComplexToStandardConversionPatterns(patterns);
ConversionTarget target(getContext());
target.addLegalDialect<arith::ArithDialect, math::MathDialect>();
target.addLegalOp<complex::CreateOp, complex::ImOp, complex::ReOp>();
if (failed(
applyPartialConversion(getOperation(), target, std::move(patterns))))
signalPassFailure();
}
} // namespace
std::unique_ptr<Pass> mlir::createConvertComplexToStandardPass() {
return std::make_unique<ConvertComplexToStandardPass>();
}
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