ExpandOps.cpp

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//===- ExpandOps.cpp - Pass to legalize Arith ops for LLVM lowering --===//
//
// 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/ArithCommon/CeilFloorDivExpansion.h"
#include "mlir/Dialect/Arith/IR/Arith.h"
#include "mlir/Dialect/Arith/Transforms/Passes.h"
#include "mlir/Dialect/Vector/IR/VectorDialect.h"
#include "mlir/IR/BuiltinTypeInterfaces.h"
#include "mlir/IR/Location.h"
#include "mlir/IR/TypeUtilities.h"
#include "mlir/Transforms/DialectConversion.h"
 
namespace mlir {
namespace arith {
#define GEN_PASS_DEF_ARITHEXPANDOPSPASS
#include "mlir/Dialect/Arith/Transforms/Passes.h.inc"
} // namespace arith
} // namespace mlir
 
using namespace mlir;
 
/// Create an integer or index constant.
static Value createConst(Location loc, Type type, int value,
                         PatternRewriter &rewriter) {
  auto attr = rewriter.getIntegerAttr(getElementTypeOrSelf(type), value);
  if (auto shapedTy = dyn_cast<ShapedType>(type)) {
    return arith::ConstantOp::create(rewriter, loc,
                                     DenseElementsAttr::get(shapedTy, attr));
  }
  return arith::ConstantOp::create(rewriter, loc, attr);
}
 
/// Create an integer constant from an APInt.
static Value createAPIntConst(Location loc, Type type, const APInt &value,
                              PatternRewriter &rewriter) {
  auto attr = IntegerAttr::get(getElementTypeOrSelf(type), value);
  if (auto shapedTy = dyn_cast<ShapedType>(type)) {
    return arith::ConstantOp::create(rewriter, loc,
                                     DenseElementsAttr::get(shapedTy, attr));
  }
  return arith::ConstantOp::create(rewriter, loc, attr);
}
 
/// Create a float constant.
static Value createFloatConst(Location loc, Type type, const APFloat &value,
                              PatternRewriter &rewriter) {
  auto attr = rewriter.getFloatAttr(getElementTypeOrSelf(type), value);
  if (auto shapedTy = dyn_cast<ShapedType>(type)) {
    return arith::ConstantOp::create(rewriter, loc,
                                     DenseElementsAttr::get(shapedTy, attr));
  }
 
  return arith::ConstantOp::create(rewriter, loc, attr);
}
 
/// Creates shapedType using shape from cloneFrom and base type from cloneTo
static Type cloneToShapedType(Type cloneFrom, Type cloneTo) {
  if (auto shapedTy = dyn_cast<ShapedType>(cloneFrom)) {
    return shapedTy.clone(cloneTo);
  }
  return cloneTo;
}
 
namespace {
 
template <typename OpTy, arith::CmpIPredicate pred>
struct MaxMinIOpConverter : public OpRewritePattern<OpTy> {
public:
  using OpRewritePattern<OpTy>::OpRewritePattern;
 
  LogicalResult matchAndRewrite(OpTy op,
                                PatternRewriter &rewriter) const final {
    Value lhs = op.getLhs();
    Value rhs = op.getRhs();
 
    Value cmp = arith::CmpIOp::create(rewriter, op.getLoc(), pred, lhs, rhs);
    rewriter.replaceOpWithNewOp<arith::SelectOp>(op, cmp, lhs, rhs);
    return success();
  }
};
 
template <typename OpTy, arith::CmpFPredicate pred>
struct MaximumMinimumFOpConverter : public OpRewritePattern<OpTy> {
public:
  using OpRewritePattern<OpTy>::OpRewritePattern;
 
  LogicalResult matchAndRewrite(OpTy op,
                                PatternRewriter &rewriter) const final {
    Value lhs = op.getLhs();
    Value rhs = op.getRhs();
 
    Location loc = op.getLoc();
    // If any operand is NaN, 'cmp' will be true (and 'select' returns 'lhs').
    static_assert(pred == arith::CmpFPredicate::UGT ||
                      pred == arith::CmpFPredicate::ULT,
                  "pred must be either UGT or ULT");
    Value cmp = arith::CmpFOp::create(rewriter, loc, pred, lhs, rhs);
    Value select = arith::SelectOp::create(rewriter, loc, cmp, lhs, rhs);
 
    // Handle the case where rhs is NaN: 'isNaN(rhs) ? rhs : select'.
    Value isNaN = arith::CmpFOp::create(rewriter, loc,
                                        arith::CmpFPredicate::UNO, rhs, rhs);
    rewriter.replaceOpWithNewOp<arith::SelectOp>(op, isNaN, rhs, select);
    return success();
  }
};
 
template <typename OpTy, arith::CmpFPredicate pred>
struct MaxNumMinNumFOpConverter : public OpRewritePattern<OpTy> {
public:
  using OpRewritePattern<OpTy>::OpRewritePattern;
 
  LogicalResult matchAndRewrite(OpTy op,
                                PatternRewriter &rewriter) const final {
    Value lhs = op.getLhs();
    Value rhs = op.getRhs();
 
    Location loc = op.getLoc();
    // If any operand is NaN, 'cmp' will be true (and 'select' returns 'lhs').
    static_assert(pred == arith::CmpFPredicate::UGT ||
                      pred == arith::CmpFPredicate::ULT,
                  "pred must be either UGT or ULT");
    Value cmp = arith::CmpFOp::create(rewriter, loc, pred, lhs, rhs);
    Value select = arith::SelectOp::create(rewriter, loc, cmp, lhs, rhs);
 
    // Handle the case where lhs is NaN: 'isNaN(lhs) ? rhs : select'.
    Value isNaN = arith::CmpFOp::create(rewriter, loc,
                                        arith::CmpFPredicate::UNO, lhs, lhs);
    rewriter.replaceOpWithNewOp<arith::SelectOp>(op, isNaN, rhs, select);
    return success();
  }
};
 
struct BFloat16ExtFOpConverter : public OpRewritePattern<arith::ExtFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::ExtFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    auto operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    if (!operandETy.isBF16() || !resultETy.isF32()) {
      return rewriter.notifyMatchFailure(op, "not a ext of bf16 to f32.");
    }
 
    Type i16Ty = cloneToShapedType(operandTy, b.getI16Type());
    Type i32Ty = cloneToShapedType(operandTy, b.getI32Type());
 
    Value bitcast = arith::BitcastOp::create(b, i16Ty, operand);
    Value exti = arith::ExtUIOp::create(b, i32Ty, bitcast);
 
    Value c16 = createConst(op.getLoc(), i32Ty, 16, rewriter);
    Value shl = arith::ShLIOp::create(b, exti, c16);
    Value result = arith::BitcastOp::create(b, resultTy, shl);
 
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
struct BFloat16TruncFOpConverter : public OpRewritePattern<arith::TruncFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::TruncFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    auto operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    if (!operandETy.isF32() || !resultETy.isBF16()) {
      return rewriter.notifyMatchFailure(op, "not a trunc of f32 to bf16.");
    }
 
    if (op.getRoundingmodeAttr()) {
      return rewriter.notifyMatchFailure(
          op, "only applicable to default rounding mode.");
    }
 
    Type i16Ty = cloneToShapedType(operandTy, b.getI16Type());
    Type i32Ty = cloneToShapedType(operandTy, b.getI32Type());
 
    // Algorithm borrowed from this excellent code:
    // https://github.com/pytorch/pytorch/blob/e1502c0cdbfd17548c612f25d5a65b1e4b86224d/c10/util/BFloat16.h#L60-L79
    // There is a magic idea there, to let the addition of the rounding_bias to
    // the mantissa simply overflow into the exponent bits. It's a bit of an
    // aggressive, obfuscating optimization, but it is well-tested code, and it
    // results in more concise and efficient IR.
    // The case of NaN is handled separately (see isNaN and the final select).
    // The case of infinities is NOT handled separately, which deserves an
    // explanation. As the encoding of infinities has zero mantissa, the
    // rounding-bias addition never carries into the exponent so that just gets
    // truncated away, and as bfloat16 and float32 have the same number of
    // exponent bits, that simple truncation is the desired outcome for
    // infinities.
    Value isNan =
        arith::CmpFOp::create(b, arith::CmpFPredicate::UNE, operand, operand);
    // Constant used to make the rounding bias.
    Value c7FFF = createConst(op.getLoc(), i32Ty, 0x7fff, rewriter);
    // Constant used to generate a quiet NaN.
    Value c7FC0I16 = createConst(op.getLoc(), i16Ty, 0x7fc0, rewriter);
    // Small constants used to address bits.
    Value c16 = createConst(op.getLoc(), i32Ty, 16, rewriter);
    Value c1 = createConst(op.getLoc(), i32Ty, 1, rewriter);
    // Reinterpret the input f32 value as bits.
    Value bitcast = arith::BitcastOp::create(b, i32Ty, operand);
    // Read bit 16 as a value in {0,1}.
    Value bit16 =
        arith::AndIOp::create(b, arith::ShRUIOp::create(b, bitcast, c16), c1);
    // Determine the rounding bias to add as either 0x7fff or 0x8000 depending
    // on bit 16, implementing the tie-breaking "to nearest even".
    Value roundingBias = arith::AddIOp::create(b, bit16, c7FFF);
    // Add the rounding bias. Generally we want this to be added to the
    // mantissa, but nothing prevents this to from carrying into the exponent
    // bits, which would feel like a bug, but this is the magic trick here:
    // when that happens, the mantissa gets reset to zero and the exponent
    // gets incremented by the carry... which is actually exactly what we
    // want.
    Value biased = arith::AddIOp::create(b, bitcast, roundingBias);
    // Now that the rounding-bias has been added, truncating the low bits
    // yields the correctly rounded result.
    Value biasedAndShifted = arith::ShRUIOp::create(b, biased, c16);
    Value normalCaseResultI16 =
        arith::TruncIOp::create(b, i16Ty, biasedAndShifted);
    // Select either the above-computed result, or a quiet NaN constant
    // if the input was NaN.
    Value select =
        arith::SelectOp::create(b, isNan, c7FC0I16, normalCaseResultI16);
    Value result = arith::BitcastOp::create(b, resultTy, select);
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
/// In this implementation of extf we take advantage of some key patterns we
/// notice between the binary representation of an F4E2M1 value and its
/// corresponding value in F32.
///
/// Note: x is sign bit
/// | Binary | F4E2M1 | f32[23:32]
/// | x000   | 0.0    | x000 0000 00
/// | x001   | 0.5    | x011 1111 00
/// | x010   | 1.0    | x011 1111 10
/// | x011   | 1.5    | x011 1111 11
/// | x100   | 2.0    | x010 0000 00
/// | x101   | 3.0    | x010 0000 01
/// | x110   | 4.0    | x010 0000 10
/// | x111   | 6.0    | x010 0000 11
///
/// 1) There are only two versions of bits [25:31] in the f32 result
///     F4E2M1 bits[2:3] decide whether:
///       - F32 bits[25:31] = 0011 1111
///       - F32 bits[25:31] = 0010 0000
///     Exception is zero where
///       - F32 bits[25:31] = 0000 0000
///
/// 2) F4E2M1 bits[1:2] = F32 bits[23:24]
///     Exception is 0.5 where
///       - F4E2M1 bits[1:2] = 01, F32 bits[23:24] = 00
///
/// 3) F4E2M1 bits[4] = F32 bits[32] (sign bits are equal)
///
/// 4) F32 bits[1:22] = 0
struct F4E2M1ExtFOpConverter : public OpRewritePattern<arith::ExtFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::ExtFOp op,
                                PatternRewriter &rewriter) const final {
    Location loc = op.getLoc();
    ImplicitLocOpBuilder b(loc, rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    if (!isa<Float4E2M1FNType>(operandETy))
      return rewriter.notifyMatchFailure(op, "not a ext of F4E2M1FN");
 
    Type f32Ty = cloneToShapedType(operandTy, b.getF32Type());
    Type i4Ty = cloneToShapedType(operandTy, b.getI4Type());
    Type i32Ty = cloneToShapedType(operandTy, b.getI32Type());
    Value i4Bits = arith::BitcastOp::create(b, i4Ty, operand);
 
    Value c0x0 = createConst(loc, i4Ty, 0x0, rewriter);
    Value c0x1 = createConst(loc, i4Ty, 0x1, rewriter);
    Value c0x2 = createConst(loc, i4Ty, 0x2, rewriter);
    Value c0x4 = createConst(loc, i4Ty, 0x4, rewriter);
    Value c0x7 = createConst(loc, i4Ty, 0x7, rewriter);
 
    Value i4BitsNoSign = arith::AndIOp::create(b, i4Bits, c0x7);
 
    // Set last Exponent bit and Mantissa.
    Value c0x00000014 = createConst(loc, i32Ty, 0x14, rewriter);
    Value bits1To24 = arith::ShLIOp::create(b, i4BitsNoSign, c0x2);
    Value isHalf =
        arith::CmpIOp::create(b, arith::CmpIPredicate::eq, i4BitsNoSign, c0x1);
    bits1To24 = arith::SelectOp::create(b, isHalf, c0x0, bits1To24);
    bits1To24 = arith::ExtUIOp::create(b, i32Ty, bits1To24);
    bits1To24 = arith::ShLIOp::create(b, bits1To24, c0x00000014);
 
    // Set first 7 bits of Exponent.
    Value zeroExpBits = createConst(loc, i32Ty, 0x00000000, rewriter);
    Value highExpBits = createConst(loc, i32Ty, 0x40000000, rewriter);
    Value lowExpBits = createConst(loc, i32Ty, 0x3f000000, rewriter);
    Value useLargerExp =
        arith::CmpIOp::create(b, arith::CmpIPredicate::uge, i4BitsNoSign, c0x4);
    Value bits25To31 =
        arith::SelectOp::create(b, useLargerExp, highExpBits, lowExpBits);
    Value zeroExp =
        arith::CmpIOp::create(b, arith::CmpIPredicate::eq, i4BitsNoSign, c0x0);
    bits25To31 = arith::SelectOp::create(b, zeroExp, zeroExpBits, bits25To31);
 
    // Set sign.
    Value c0x80000000 = createConst(loc, i32Ty, 0x80000000, rewriter);
    Value c0x8 = createConst(loc, i4Ty, 0x8, rewriter);
    Value negative =
        arith::CmpIOp::create(b, arith::CmpIPredicate::uge, i4Bits, c0x8);
    Value bit32 =
        arith::SelectOp::create(b, negative, c0x80000000, zeroExpBits);
 
    // Add segments together.
    Value bits1To31 = arith::AddIOp::create(b, bits1To24, bits25To31);
    Value bits1To32 = arith::AddIOp::create(b, bits1To31, bit32);
    Value result = arith::BitcastOp::create(b, f32Ty, bits1To32);
    if (!isa<Float32Type>(resultETy))
      result = arith::TruncFOp::create(b, resultTy, result);
 
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
struct F8E8M0ExtFOpConverter : public OpRewritePattern<arith::ExtFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::ExtFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    if (!llvm::isa<Float8E8M0FNUType>(operandETy)) {
      return rewriter.notifyMatchFailure(op, "not a ext of F8E8M0FNU");
    }
 
    Type i8Ty = cloneToShapedType(operandTy, b.getI8Type());
    Type i32Ty = cloneToShapedType(operandTy, b.getI32Type());
    Type f32Ty = cloneToShapedType(operandTy, b.getF32Type());
 
    Value bitcast = arith::BitcastOp::create(b, i8Ty, operand);
    Value cF32MantissaWidth = createConst(op->getLoc(), i32Ty, 23, rewriter);
    Value exti = arith::ExtUIOp::create(b, i32Ty, bitcast);
    Value f32Bits = arith::ShLIOp::create(b, exti, cF32MantissaWidth);
 
    // If FastMathFlag allows no NaN checks, skip it
    auto fastMath = op.getFastmathAttr();
    bool NoNaN = fastMath
                     ? (fastMath.getValue() & arith::FastMathFlags::nnan) ==
                           arith::FastMathFlags::nnan
                     : false;
    if (!NoNaN) {
      Value cF8NaN = createConst(op.getLoc(), i8Ty, 0xff, rewriter);
      Value cF32NaN = createConst(op.getLoc(), i32Ty, 0xffffffff, rewriter);
      Value isNan =
          arith::CmpIOp::create(b, arith::CmpIPredicate::eq, bitcast, cF8NaN);
      // select for NaNs
      f32Bits = arith::SelectOp::create(b, isNan, cF32NaN, f32Bits);
    }
 
    Value result = arith::BitcastOp::create(b, f32Ty, f32Bits);
    if (resultETy.getIntOrFloatBitWidth() < 32) {
      result = arith::TruncFOp::create(b, resultTy, result, nullptr,
                                       op.getFastmathAttr());
    } else if (resultETy.getIntOrFloatBitWidth() > 32) {
      result = arith::ExtFOp::create(b, resultTy, result, op.getFastmathAttr());
    }
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
/// Conversion from F32 to F4E2M1 according to the OCP Spec:
/// www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf
///
/// The spec requiers us to perform Round to Nearest, Ties to Even.
///
/// This means that after rounding, we should break ties by choosing the option
/// which results in a mantissa of 0 in the least significant digit.
///
/// Table of representable values in F4E2M1:
///
/// Note: x is sign bit
/// | Binary | F4E2M1 | F32[23:32]
/// | x000   | 0.0    | x000 0000 00
/// | x001   | 0.5    | x011 1111 00
/// | x010   | 1.0    | x011 1111 10
/// | x011   | 1.5    | x011 1111 11
/// | x100   | 2.0    | x010 0000 00
/// | x101   | 3.0    | x010 0000 01
/// | x110   | 4.0    | x010 0000 10
/// | x111   | 6.0    | x010 0000 11
///
/// Conversion procedure:
///   Step 1: Clamp to representable bounds.
///   Step 2: Convert exponent by adjusting bias.
///   Step 3: Set mantissa to first bit.
///   Step 4: Special consideration for subnormal and zero exponent.
///   Step 5: Round up if necessary, if mantissa[1:] greater than 1000000 or
///   subnormal.
struct F4E2M1TruncFOpConverter : public OpRewritePattern<arith::TruncFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::TruncFOp op,
                                PatternRewriter &rewriter) const final {
    Location loc = op.getLoc();
    ImplicitLocOpBuilder b(loc, rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    Type i4Ty = cloneToShapedType(operandTy, b.getI4Type());
    Type i8Ty = cloneToShapedType(operandTy, b.getI8Type());
    Type i32Ty = cloneToShapedType(operandTy, b.getI32Type());
    Type f32Ty = cloneToShapedType(operandTy, b.getF32Type());
 
    if (!isa<Float4E2M1FNType>(resultETy))
      return rewriter.notifyMatchFailure(op, "not a trunc of F4E2M1FN");
    if (!isa<Float32Type>(operandETy))
      operand =
          arith::ExtFOp::create(b, f32Ty, operand, arith::FastMathFlagsAttr{});
 
    Value c0x1 = createConst(loc, i4Ty, 1, rewriter);
    Value c0x3 = createConst(loc, i4Ty, 3, rewriter);
    Value c0x00000016 = createConst(loc, i32Ty, 22, rewriter);
    Value c0x00 = createConst(loc, i8Ty, 0x00, rewriter);
    Value c0xff = createConst(loc, i8Ty, 0xff, rewriter);
    Value zeroExpBits = createConst(loc, i32Ty, 0, rewriter);
 
    // Step 0: Clamp to bounds.
    Value cHigherBound = createFloatConst(loc, f32Ty, APFloat(6.0f), rewriter);
    Value cLowerBound = createFloatConst(loc, f32Ty, APFloat(-6.0f), rewriter);
    Value operandClamped = arith::MinNumFOp::create(b, cHigherBound, operand);
    operandClamped = arith::MaxNumFOp::create(b, cLowerBound, operandClamped);
    Value f32Bits = arith::BitcastOp::create(b, i32Ty, operandClamped);
 
    // Step 1: Set sign bit.
    Value cF32ExpManWidth = createConst(loc, i32Ty, 31, rewriter); // 23
    Value f32Sign = arith::ShRUIOp::create(b, f32Bits, cF32ExpManWidth);
    Value f4Sign = arith::TruncIOp::create(b, i4Ty, f32Sign);
    Value f4Bits = arith::ShLIOp::create(b, f4Sign, c0x3);
 
    // Step 2: Convert exponent by adjusting bias.
    Value biasAdjustment = createConst(loc, i32Ty, 0x7e, rewriter);
    Value cF4MantissaWidth = c0x1;                                   // 1
    Value cF32MantissaWidth = createConst(loc, i32Ty, 23, rewriter); // 23
    Value f32SignExp = arith::ShRUIOp::create(b, f32Bits, cF32MantissaWidth);
    Value biasAdjustedSignExp =
        arith::SubIOp::create(b, f32SignExp, biasAdjustment);
    Value f4Exp = arith::TruncIOp::create(b, i4Ty, biasAdjustedSignExp);
    f4Exp = arith::ShLIOp::create(b, f4Exp, cF4MantissaWidth);
    f4Bits = arith::AddIOp::create(b, f4Bits, f4Exp);
 
    // Step 3: Set mantissa to first bit.
    Value cF32FirstBitMask = createConst(loc, i32Ty, 0x400000, rewriter);
    Value man1Bit = arith::AndIOp::create(b, f32Bits, cF32FirstBitMask);
    man1Bit = arith::ShRUIOp::create(b, man1Bit, c0x00000016);
    Value f4Man = arith::TruncIOp::create(b, i4Ty, man1Bit);
    f4Bits = arith::AddIOp::create(b, f4Bits, f4Man);
 
    // Step 4: Special consideration for conversion to 0.5.
    Value cF32MantissaMask = createConst(loc, i32Ty, 0x7fffff, rewriter);
    Value f8Exp = arith::TruncIOp::create(b, i8Ty, biasAdjustedSignExp);
    Value isSubnormal =
        arith::CmpIOp::create(b, arith::CmpIPredicate::sle, f8Exp, c0x00);
    Value isNegOneExp =
        arith::CmpIOp::create(b, arith::CmpIPredicate::eq, f8Exp, c0xff);
    Value man23Bits = arith::AndIOp::create(b, f32Bits, cF32MantissaMask);
    Value isNonZeroMan = arith::CmpIOp::create(b, arith::CmpIPredicate::ugt,
                                               man23Bits, zeroExpBits);
    Value roundToHalf = arith::AndIOp::create(b, isNegOneExp, isNonZeroMan);
    Value isZeroExp =
        arith::CmpIOp::create(b, arith::CmpIPredicate::eq, f8Exp, c0x00);
    Value subnormalF4Bits = createConst(loc, i4Ty, 0xf, rewriter);
    Value halfF4Bits = createConst(loc, i4Ty, 0x0, rewriter);
    Value subResult =
        arith::SelectOp::create(b, isSubnormal, subnormalF4Bits, f4Bits);
    subResult = arith::SelectOp::create(b, roundToHalf, halfF4Bits, subResult);
    f4Bits = arith::SelectOp::create(b, isZeroExp, f4Bits, subResult);
 
    // Step 5: Round up if necessary.
    Value cF32Last22BitMask = createConst(loc, i32Ty, 0x3fffff, rewriter);
    Value cRound = createConst(loc, i32Ty, 0x200000, rewriter); // 010 0000...
    Value man22Bits = arith::AndIOp::create(b, f32Bits, cF32Last22BitMask);
    Value shouldRound =
        arith::CmpIOp::create(b, arith::CmpIPredicate::uge, man22Bits, cRound);
    shouldRound = arith::OrIOp::create(b, shouldRound, isSubnormal);
    Value roundedF4Bits = arith::AddIOp::create(b, f4Bits, c0x1);
    f4Bits = arith::SelectOp::create(b, shouldRound, roundedF4Bits, f4Bits);
 
    Value result = arith::BitcastOp::create(b, resultTy, f4Bits);
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
/*
TruncF to F8E8M0 is expected to extract exponent bits out of F32 type
Since All kinds of Infs and NaNs are mapped to same exponent bits in F32 type,
they all map to NaN in F8E8M0 Type.
*/
struct F8E8M0TruncFOpConverter : public OpRewritePattern<arith::TruncFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::TruncFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultTy = op.getType();
    Type resultETy = getElementTypeOrSelf(resultTy);
    if (!llvm::isa<Float8E8M0FNUType>(resultETy)) {
      return rewriter.notifyMatchFailure(op, "not a truncf to f8E8M0FNU");
    }
 
    if (op.getRoundingmodeAttr()) {
      return rewriter.notifyMatchFailure(
          op, "only applicable to default rounding mode.");
    }
 
    Type i8Ty = cloneToShapedType(operandTy, b.getI8Type());
    Type i32Ty = cloneToShapedType(operandTy, b.getI32Type());
    Type f32Ty = cloneToShapedType(operandTy, b.getF32Type());
 
    if (operandETy.getIntOrFloatBitWidth() < 32) {
      operand = arith::ExtFOp::create(b, f32Ty, operand, op.getFastmathAttr());
    } else if (operandETy.getIntOrFloatBitWidth() > 32) {
      operand = arith::TruncFOp::create(
          b, f32Ty, operand, op.getRoundingmodeAttr(), op.getFastmathAttr());
    }
    Value f32Bits = arith::BitcastOp::create(b, i32Ty, operand);
    Value cF32MantissaWidth = createConst(op->getLoc(), i32Ty, 23, rewriter);
    Value f32SignExp = arith::ShRUIOp::create(b, f32Bits, cF32MantissaWidth);
    Value exp8Bits = arith::TruncIOp::create(b, i8Ty, f32SignExp);
    Value result = arith::BitcastOp::create(b, resultTy, exp8Bits);
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
/// Expand an ExtF from F8E5M2. F8E5M2 uses a 5-bit exponent with bias 15 and a
/// 2-bit mantissa, i.e. it is bit-for-bit the high byte of an IEEE F16 value
/// (same exponent field and bias), including infinities and NaNs. The exact
/// F16 value is therefore obtained by placing the 8 F8E5M2 bits into the high
/// byte of an i16. The F16 value is then converted to the requested result
/// type with the native (LLVM-lowerable) extf/truncf.
struct F8E5M2ExtFOpConverter : public OpRewritePattern<arith::ExtFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::ExtFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    if (!llvm::isa<Float8E5M2Type>(operandETy))
      return rewriter.notifyMatchFailure(op, "not a ext of F8E5M2");
 
    Type i8Ty = cloneToShapedType(operandTy, b.getI8Type());
    Type i16Ty = cloneToShapedType(operandTy, b.getI16Type());
    Type f16Ty = cloneToShapedType(operandTy, b.getF16Type());
 
    Value bitcast = arith::BitcastOp::create(b, i8Ty, operand);
    Value exti = arith::ExtUIOp::create(b, i16Ty, bitcast);
    Value c8 = createConst(op.getLoc(), i16Ty, 8, rewriter);
    Value f16Bits = arith::ShLIOp::create(b, exti, c8);
    Value f16 = arith::BitcastOp::create(b, f16Ty, f16Bits);
 
    Value result = f16;
    if (!resultETy.isF16()) {
      if (resultETy.getIntOrFloatBitWidth() < 16)
        result = arith::TruncFOp::create(b, resultTy, f16, nullptr,
                                         op.getFastmathAttr());
      else
        result = arith::ExtFOp::create(b, resultTy, f16, op.getFastmathAttr());
    }
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
/// Expand a TruncF to F8E5M2. The input is first reduced to F16 (which shares
/// the F8E5M2 exponent layout and bias) using the native truncf, then the low
/// 8 mantissa bits of the F16 value are dropped with round-to-nearest-even.
/// The rounding-bias trick is borrowed from the BF16 converter: adding the
/// bias may carry into the exponent field, which is exactly the desired
/// behavior since F16 and F8E5M2 share the same exponent bias. NaN is handled
/// separately.
struct F8E5M2TruncFOpConverter : public OpRewritePattern<arith::TruncFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::TruncFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    if (!llvm::isa<Float8E5M2Type>(resultETy))
      return rewriter.notifyMatchFailure(op, "not a trunc to F8E5M2");
    if (op.getRoundingmodeAttr())
      return rewriter.notifyMatchFailure(
          op, "only applicable to default rounding mode.");
 
    Type i8Ty = cloneToShapedType(operandTy, b.getI8Type());
    Type i16Ty = cloneToShapedType(operandTy, b.getI16Type());
    Type f16Ty = cloneToShapedType(operandTy, b.getF16Type());
 
    Value h16 = operand;
    if (!operandETy.isF16())
      h16 = arith::TruncFOp::create(b, f16Ty, operand, nullptr,
                                    op.getFastmathAttr());
 
    Value isNan = arith::CmpFOp::create(b, arith::CmpFPredicate::UNE, h16, h16);
    Value h16Bits = arith::BitcastOp::create(b, i16Ty, h16);
    // Rounding bias constants for dropping the low 8 mantissa bits.
    Value c7F = createConst(op.getLoc(), i16Ty, 0x7f, rewriter);
    Value c8 = createConst(op.getLoc(), i16Ty, 8, rewriter);
    Value c1 = createConst(op.getLoc(), i16Ty, 1, rewriter);
    Value bit8 =
        arith::AndIOp::create(b, arith::ShRUIOp::create(b, h16Bits, c8), c1);
    Value roundingBias = arith::AddIOp::create(b, bit8, c7F);
    Value biased = arith::AddIOp::create(b, h16Bits, roundingBias);
    Value biasedAndShifted = arith::ShRUIOp::create(b, biased, c8);
    Value normalCaseResult = arith::TruncIOp::create(b, i8Ty, biasedAndShifted);
    // Quiet NaN for F8E5M2 (exponent all ones, mantissa MSB set).
    Value cNan = createConst(op.getLoc(), i8Ty, 0x7e, rewriter);
    Value select = arith::SelectOp::create(b, isNan, cNan, normalCaseResult);
    Value result = arith::BitcastOp::create(b, resultTy, select);
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
/// Expand an ExtF from F8E4M3FN. F8E4M3FN uses a 4-bit exponent with bias 7, a
/// 3-bit mantissa, no infinities and a single NaN encoding (S.1111.111). The
/// 7 magnitude bits (EEEE.MMM) are placed into the high mantissa/exponent bits
/// of an F16 by shifting left by 7, producing an F16 whose value equals the
/// desired magnitude scaled by 2^-8 (the F16 bias is 15 while F8E4M3FN's is
/// 7). Multiplying by 256 in F32 recovers the true magnitude for both normal
/// and subnormal inputs. The sign bit and the NaN encoding are re-applied
/// explicitly.
struct F8E4M3FNExtFOpConverter : public OpRewritePattern<arith::ExtFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::ExtFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    if (!llvm::isa<Float8E4M3FNType>(operandETy))
      return rewriter.notifyMatchFailure(op, "not a ext of F8E4M3FN");
 
    Type i8Ty = cloneToShapedType(operandTy, b.getI8Type());
    Type i16Ty = cloneToShapedType(operandTy, b.getI16Type());
    Type i32Ty = cloneToShapedType(operandTy, b.getI32Type());
    Type f16Ty = cloneToShapedType(operandTy, b.getF16Type());
    Type f32Ty = cloneToShapedType(operandTy, b.getF32Type());
 
    Value bits = arith::BitcastOp::create(b, i8Ty, operand);
    Value c7F8 = createConst(op.getLoc(), i8Ty, 0x7f, rewriter);
    Value mag8 = arith::AndIOp::create(b, bits, c7F8);
    // Build an F16 equal to the magnitude times 2^-8.
    Value mag16 = arith::ExtUIOp::create(b, i16Ty, mag8);
    Value c7 = createConst(op.getLoc(), i16Ty, 7, rewriter);
    Value g16Bits = arith::ShLIOp::create(b, mag16, c7);
    Value g16 = arith::BitcastOp::create(b, f16Ty, g16Bits);
    Value gF32 = arith::ExtFOp::create(b, f32Ty, g16, op.getFastmathAttr());
    Value c256 =
        createFloatConst(op.getLoc(), f32Ty, APFloat(256.0f), rewriter);
    Value magF32 = arith::MulFOp::create(b, gF32, c256, op.getFastmathAttr());
    // Re-apply the sign bit into the F32 result.
    Value magI32 = arith::BitcastOp::create(b, i32Ty, magF32);
    Value c80I8 = createConst(op.getLoc(), i8Ty, 0x80, rewriter);
    Value sign8 = arith::AndIOp::create(b, bits, c80I8);
    Value sign32 = arith::ExtUIOp::create(b, i32Ty, sign8);
    Value c24 = createConst(op.getLoc(), i32Ty, 24, rewriter);
    Value signBit = arith::ShLIOp::create(b, sign32, c24);
    Value signedI32 = arith::OrIOp::create(b, magI32, signBit);
    Value signedF32 = arith::BitcastOp::create(b, f32Ty, signedI32);
    // NaN encoding is magnitude == 0x7f.
    Value isNan =
        arith::CmpIOp::create(b, arith::CmpIPredicate::eq, mag8, c7F8);
    Value cNan32 = createConst(op.getLoc(), i32Ty, 0x7fc00000, rewriter);
    Value nanSigned = arith::OrIOp::create(b, cNan32, signBit);
    Value nanF32 = arith::BitcastOp::create(b, f32Ty, nanSigned);
    Value resultF32 = arith::SelectOp::create(b, isNan, nanF32, signedF32);
 
    Value result = resultF32;
    if (!resultETy.isF32()) {
      if (resultETy.getIntOrFloatBitWidth() < 32)
        result = arith::TruncFOp::create(b, resultTy, resultF32, nullptr,
                                         op.getFastmathAttr());
      else
        result =
            arith::ExtFOp::create(b, resultTy, resultF32, op.getFastmathAttr());
    }
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
/// Expand a TruncF to F8E4M3FN. The magnitude is scaled by 2^-8 and reduced to
/// F16 (undoing the bias difference so the F16 value equals the magnitude times
/// 2^-8). The low 7 bits of the F16 encoding are then dropped with
/// round-to-nearest-even to recover the 7 magnitude bits. F8E4M3FN has no
/// infinity, so any input that overflows the maximum representable magnitude
/// (448), as well as infinities and NaNs, maps to the F8E4M3FN NaN encoding to
/// match the LLVM APFloat NanOnly overflow behavior and the OCP FP8 (E4M3)
/// spec.
struct F8E4M3FNTruncFOpConverter : public OpRewritePattern<arith::TruncFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::TruncFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    Type resultTy = op.getType();
    Type operandETy = getElementTypeOrSelf(operandTy);
    Type resultETy = getElementTypeOrSelf(resultTy);
 
    if (!llvm::isa<Float8E4M3FNType>(resultETy))
      return rewriter.notifyMatchFailure(op, "not a trunc to F8E4M3FN");
    if (op.getRoundingmodeAttr())
      return rewriter.notifyMatchFailure(
          op, "only applicable to default rounding mode.");
 
    Type i8Ty = cloneToShapedType(operandTy, b.getI8Type());
    Type i16Ty = cloneToShapedType(operandTy, b.getI16Type());
    Type i32Ty = cloneToShapedType(operandTy, b.getI32Type());
    Type f16Ty = cloneToShapedType(operandTy, b.getF16Type());
    Type f32Ty = cloneToShapedType(operandTy, b.getF32Type());
 
    Value f32 = operand;
    if (!operandETy.isF32()) {
      if (operandETy.getIntOrFloatBitWidth() < 32)
        f32 = arith::ExtFOp::create(b, f32Ty, operand, op.getFastmathAttr());
      else
        f32 = arith::TruncFOp::create(b, f32Ty, operand, nullptr,
                                      op.getFastmathAttr());
    }
 
    Value isNan = arith::CmpFOp::create(b, arith::CmpFPredicate::UNE, f32, f32);
    // Split sign and magnitude.
    Value f32Bits = arith::BitcastOp::create(b, i32Ty, f32);
    Value cSignMask = createConst(op.getLoc(), i32Ty, 0x80000000, rewriter);
    Value cAbsMask = createConst(op.getLoc(), i32Ty, 0x7fffffff, rewriter);
    Value signBits = arith::AndIOp::create(b, f32Bits, cSignMask);
    Value absBits = arith::AndIOp::create(b, f32Bits, cAbsMask);
    Value absF32 = arith::BitcastOp::create(b, f32Ty, absBits);
    // F8E4M3FN has no infinity: a magnitude above the round-to-nearest-even
    // overflow boundary (464 = 448 + half an ulp) or an infinity maps to NaN.
    Value cOverflow =
        createFloatConst(op.getLoc(), f32Ty, APFloat(464.0f), rewriter);
    Value isOverflow =
        arith::CmpFOp::create(b, arith::CmpFPredicate::OGT, absF32, cOverflow);
    // Clamp to the F8E4M3FN maximum magnitude (448) so the finite path stays
    // well-defined; overflowing inputs are replaced by NaN below.
    Value cMax =
        createFloatConst(op.getLoc(), f32Ty, APFloat(448.0f), rewriter);
    absF32 = arith::MinNumFOp::create(b, absF32, cMax);
    Value cInv256 =
        createFloatConst(op.getLoc(), f32Ty, APFloat(0.00390625f), rewriter);
    Value scaled = arith::MulFOp::create(b, absF32, cInv256, nullptr);
    Value h16 = arith::TruncFOp::create(b, f16Ty, scaled, nullptr,
                                        op.getFastmathAttr());
    Value h16Bits = arith::BitcastOp::create(b, i16Ty, h16);
    // Drop the low 7 bits with round-to-nearest-even.
    Value c3F = createConst(op.getLoc(), i16Ty, 0x3f, rewriter);
    Value c7 = createConst(op.getLoc(), i16Ty, 7, rewriter);
    Value c1 = createConst(op.getLoc(), i16Ty, 1, rewriter);
    Value bit7 =
        arith::AndIOp::create(b, arith::ShRUIOp::create(b, h16Bits, c7), c1);
    Value roundingBias = arith::AddIOp::create(b, bit7, c3F);
    Value biased = arith::AddIOp::create(b, h16Bits, roundingBias);
    Value shifted = arith::ShRUIOp::create(b, biased, c7);
    Value mag8 = arith::TruncIOp::create(b, i8Ty, shifted);
    Value c7F8 = createConst(op.getLoc(), i8Ty, 0x7f, rewriter);
    mag8 = arith::AndIOp::create(b, mag8, c7F8);
    // Re-apply the sign.
    Value c24 = createConst(op.getLoc(), i32Ty, 24, rewriter);
    Value sign8 = arith::TruncIOp::create(
        b, i8Ty, arith::ShRUIOp::create(b, signBits, c24));
    Value res8 = arith::OrIOp::create(b, mag8, sign8);
    // NaN input or an overflowing/infinite magnitude maps to the NaN encoding.
    Value isNanOrOverflow = arith::OrIOp::create(b, isNan, isOverflow);
    Value cNan8 = createConst(op.getLoc(), i8Ty, 0x7f, rewriter);
    Value res = arith::SelectOp::create(b, isNanOrOverflow, cNan8, res8);
    Value result = arith::BitcastOp::create(b, resultTy, res);
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
struct ScalingExtFOpConverter : public OpRewritePattern<arith::ScalingExtFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::ScalingExtFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    Value inputOperand = op.getIn();
    Value scaleOperand = op.getScale();
    Type scaleTy = scaleOperand.getType();
    Type scaleETy = getElementTypeOrSelf(scaleOperand);
    // allow implicit exponent extraction from 16/32 bits floats
    if (scaleETy.getIntOrFloatBitWidth() >= 16) {
      scaleETy = b.getF8E8M0Type();
      scaleTy = cloneToShapedType(scaleTy, scaleETy);
      scaleOperand = arith::TruncFOp::create(b, scaleTy, scaleOperand, nullptr,
                                             op.getFastmathAttr());
    }
    // Catch scale types like f8E5M2.
    if (!llvm::isa<Float8E8M0FNUType>(scaleETy)) {
      return rewriter.notifyMatchFailure(
          op, "scaling_extf is using scales of type which can not be converted "
              "to f8E8M0FNU");
    }
    Type resultTy = op.getType();
    // extf on scale will essentially create floating point number
    // of type resulTy that is 2^scale and will also propagate NaNs
    Value scaleExt =
        arith::ExtFOp::create(b, resultTy, scaleOperand, op.getFastmathAttr());
    Value inputExt =
        arith::ExtFOp::create(b, resultTy, inputOperand, op.getFastmathAttr());
    Value result =
        arith::MulFOp::create(b, inputExt, scaleExt, op.getFastmathAttr());
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
/*
Expands arith.ScalingTruncFOp(in, scale) into
  scale = arith.truncf(scale) : scaleTy -> f8E8M0FNU
  result = arith.truncf(in / (2^scale))
 */
struct ScalingTruncFOpConverter
    : public OpRewritePattern<arith::ScalingTruncFOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::ScalingTruncFOp op,
                                PatternRewriter &rewriter) const final {
    ImplicitLocOpBuilder b(op.getLoc(), rewriter);
    Value inputOperand = op.getIn();
    Value scaleOperand = op.getScale();
    Type scaleTy = scaleOperand.getType();
    Type scaleETy = getElementTypeOrSelf(scaleOperand);
    // allow implicit exponent extraction from 16/32 bits floats
    if (scaleETy.getIntOrFloatBitWidth() >= 16) {
      scaleETy = b.getF8E8M0Type();
      scaleTy = cloneToShapedType(scaleTy, scaleETy);
      scaleOperand = arith::TruncFOp::create(b, scaleTy, scaleOperand, nullptr,
                                             op.getFastmathAttr());
    }
    if (!llvm::isa<Float8E8M0FNUType>(scaleETy)) {
      return rewriter.notifyMatchFailure(
          op, "scaling_truncf is using scales type which can not be converted "
              "to f8E8M0FNU");
    }
    Type resultTy = op.getType();
    Type inputTy = inputOperand.getType();
    // this will create a floating point number of type
    // inputTy that is 2^scale and will also propagate NaNs
    scaleOperand =
        arith::ExtFOp::create(b, inputTy, scaleOperand, op.getFastmathAttr());
    Value result = arith::DivFOp::create(b, inputOperand, scaleOperand,
                                         op.getFastmathAttr());
    Value resultCast = arith::TruncFOp::create(
        b, resultTy, result, op.getRoundingmodeAttr(), op.getFastmathAttr());
    rewriter.replaceOp(op, resultCast);
    return success();
  }
};
 
/// Expands `arith.flush_denormals` into integer arithmetic.
///
/// For an IEEE-like floating-point value with a sign|exponent|mantissa bit
/// layout, a value is denormal iff its biased exponent field is zero and its
/// stored mantissa is non-zero. When the exponent field is zero, the value is
/// either pos/neg 0 (mantissa = 0) or a denormal (mantissa != 0); in both
/// cases, clearing the mantissa bits produces the desired sign-preserved zero
/// (a no-op for pos/neg 0, a flush for denormals). When the exponent field is
/// non-zero, the value passes through unchanged.
///
/// Pseudocode:
///   bits        = bitcast(x, iN)
///   expIsZero   = (bits & expMask) == 0
///   cleared     = bits & ~manMask
///   resultBits  = select(expIsZero, cleared, bits)
///   result      = bitcast(resultBits, floatTy)
struct FlushDenormalsOpConverter
    : public OpRewritePattern<arith::FlushDenormalsOp> {
  using Base::Base;
  LogicalResult matchAndRewrite(arith::FlushDenormalsOp op,
                                PatternRewriter &rewriter) const final {
    Location loc = op.getLoc();
    ImplicitLocOpBuilder b(loc, rewriter);
    Value operand = op.getOperand();
    Type operandTy = operand.getType();
    auto floatTy = dyn_cast<FloatType>(getElementTypeOrSelf(operandTy));
    if (!floatTy)
      return rewriter.notifyMatchFailure(op, "operand is not a float type");
 
    const llvm::fltSemantics &sem = floatTy.getFloatSemantics();
    // Restrict to IEEE-like encodings, where the sign bit is the MSB and
    // denormals are exactly "biased exponent == 0 and non-zero mantissa".
    if (!llvm::APFloatBase::isIEEELikeFP(sem))
      return rewriter.notifyMatchFailure(
          op, "only IEEE-like floating-point types are supported");
 
    unsigned totalBits = llvm::APFloatBase::semanticsSizeInBits(sem);
    unsigned precision = llvm::APFloatBase::semanticsPrecision(sem);
    // Stored mantissa bits = precision - 1 (implicit leading bit not stored).
    // Exponent field bits = totalBits - 1 (sign) - storedMantissa.
    if (precision < 1 || precision > totalBits)
      return rewriter.notifyMatchFailure(op, "unexpected float semantics");
    unsigned mantissaBits = precision - 1;
    unsigned expBits = totalBits - 1 - mantissaBits;
    if (expBits == 0 || mantissaBits == 0)
      return rewriter.notifyMatchFailure(
          op, "degenerate float encoding has no exponent or mantissa");
 
    Type intTy =
        cloneToShapedType(operandTy, rewriter.getIntegerType(totalBits));
    Value bits = arith::BitcastOp::create(b, intTy, operand);
    APInt expMaskVal =
        APInt::getBitsSet(totalBits, mantissaBits, mantissaBits + expBits);
    APInt clearMantissaMaskVal = ~APInt::getLowBitsSet(totalBits, mantissaBits);
    APInt zeroVal = APInt::getZero(totalBits);
    Value expMask = createAPIntConst(loc, intTy, expMaskVal, rewriter);
    Value clearMantissaMask =
        createAPIntConst(loc, intTy, clearMantissaMaskVal, rewriter);
    Value zero = createAPIntConst(loc, intTy, zeroVal, rewriter);
 
    // expField == 0
    Value expField = arith::AndIOp::create(b, bits, expMask);
    Value expIsZero =
        arith::CmpIOp::create(b, arith::CmpIPredicate::eq, expField, zero);
 
    // Clear mantissa bits: when exp == 0, this produces pos/neg 0.0.
    Value cleared = arith::AndIOp::create(b, bits, clearMantissaMask);
    Value resultBits = arith::SelectOp::create(b, expIsZero, cleared, bits);
    Value result = arith::BitcastOp::create(b, operandTy, resultBits);
 
    rewriter.replaceOp(op, result);
    return success();
  }
};
 
struct ArithExpandOpsPass
    : public arith::impl::ArithExpandOpsPassBase<ArithExpandOpsPass> {
  using ArithExpandOpsPassBase::ArithExpandOpsPassBase;
 
  void runOnOperation() override {
    RewritePatternSet patterns(&getContext());
    ConversionTarget target(getContext());
 
    arith::populateCeilFloorDivExpandOpsPatterns(patterns);
    arith::populateExpandScalingExtTruncPatterns(patterns);
 
    target.addLegalDialect<arith::ArithDialect>();
    target.addLegalDialect<vector::VectorDialect>();
 
    // clang-format off
    target.addIllegalOp<
      arith::CeilDivSIOp,
      arith::CeilDivUIOp,
      arith::FloorDivSIOp,
      arith::ScalingExtFOp,
      arith::ScalingTruncFOp
    >();
    // clang-format on
 
    // The min/max ops also have a direct arith-to-llvm lowering to the
    // `llvm.intr.maximum`/`minimum`/... (and smax/umax/...) intrinsics, which
    // are a single hardware instruction on many targets. Only expand them into
    // cmpf/cmpi + select when requested, so pipelines that run arith-to-llvm
    // can keep the intrinsic lowering. The float and integer ops are gated
    // separately.
    if (includeMinMaxF) {
      arith::populateExpandMinMaxFPatterns(patterns);
      // clang-format off
      target.addIllegalOp<
        arith::MaximumFOp,
        arith::MinimumFOp,
        arith::MaxNumFOp,
        arith::MinNumFOp
      >();
      // clang-format on
    }
    if (includeMinMaxI) {
      arith::populateExpandMinMaxIPatterns(patterns);
      // clang-format off
      target.addIllegalOp<
        arith::MaxSIOp,
        arith::MaxUIOp,
        arith::MinSIOp,
        arith::MinUIOp
      >();
      // clang-format on
    }
 
    if (includeBf16)
      arith::populateExpandBFloat16Patterns(patterns);
    if (includeF8E8M0)
      arith::populateExpandF8E8M0Patterns(patterns);
    if (includeF4E2M1)
      arith::populateExpandF4E2M1Patterns(patterns);
    if (includeF8E5M2)
      arith::populateExpandF8E5M2Patterns(patterns);
    if (includeF8E4M3FN)
      arith::populateExpandF8E4M3FNPatterns(patterns);
    if (includeFlushDenormals) {
      arith::populateExpandFlushDenormalsPatterns(patterns);
      // Only IEEE-like floating-point types are expanded by the pattern;
      // leave `arith.flush_denormals` on other types alone.
      target.addDynamicallyLegalOp<arith::FlushDenormalsOp>(
          [](arith::FlushDenormalsOp op) {
            auto floatTy =
                dyn_cast<FloatType>(getElementTypeOrSelf(op.getType()));
            if (!floatTy)
              return true;
            return !llvm::APFloatBase::isIEEELikeFP(
                floatTy.getFloatSemantics());
          });
    }
 
    target.addDynamicallyLegalOp<arith::ExtFOp>([=](arith::ExtFOp op) {
      Type inETy = getElementTypeOrSelf(op.getOperand().getType());
      Type outETy = getElementTypeOrSelf(op.getType());
      bool legalTypes = true;
      if (includeBf16)
        legalTypes &= !(inETy.isBF16() && outETy.isF32());
      if (includeF8E8M0)
        legalTypes &= !llvm::isa<Float8E8M0FNUType>(inETy);
      if (includeF4E2M1)
        legalTypes &= !llvm::isa<Float4E2M1FNType>(inETy);
      if (includeF8E5M2)
        legalTypes &= !llvm::isa<Float8E5M2Type>(inETy);
      if (includeF8E4M3FN)
        legalTypes &= !llvm::isa<Float8E4M3FNType>(inETy);
      return legalTypes;
    });
 
    target.addDynamicallyLegalOp<arith::TruncFOp>([=](arith::TruncFOp op) {
      Type inETy = getElementTypeOrSelf(op.getOperand().getType());
      Type outETy = getElementTypeOrSelf(op.getType());
      bool legalTypes = true;
      if (includeBf16)
        legalTypes &= !(inETy.isF32() && outETy.isBF16());
      if (includeF8E8M0)
        legalTypes &= !(llvm::isa<Float8E8M0FNUType>(outETy));
      if (includeF4E2M1)
        legalTypes &= !llvm::isa<Float4E2M1FNType>(outETy);
      if (includeF8E5M2)
        legalTypes &= !llvm::isa<Float8E5M2Type>(outETy);
      if (includeF8E4M3FN)
        legalTypes &= !llvm::isa<Float8E4M3FNType>(outETy);
      return legalTypes;
    });
 
    // clang-format on
    if (failed(applyPartialConversion(getOperation(), target,
                                      std::move(patterns))))
      signalPassFailure();
  }
};
 
} // namespace
 
void mlir::arith::populateExpandBFloat16Patterns(RewritePatternSet &patterns) {
  patterns.add<BFloat16ExtFOpConverter, BFloat16TruncFOpConverter>(
      patterns.getContext());
}
 
void mlir::arith::populateExpandF4E2M1Patterns(RewritePatternSet &patterns) {
  patterns.add<F4E2M1ExtFOpConverter, F4E2M1TruncFOpConverter>(
      patterns.getContext());
}
 
void mlir::arith::populateExpandF8E5M2Patterns(RewritePatternSet &patterns) {
  patterns.add<F8E5M2ExtFOpConverter, F8E5M2TruncFOpConverter>(
      patterns.getContext());
}
 
void mlir::arith::populateExpandF8E4M3FNPatterns(RewritePatternSet &patterns) {
  patterns.add<F8E4M3FNExtFOpConverter, F8E4M3FNTruncFOpConverter>(
      patterns.getContext());
}
 
void mlir::arith::populateExpandF8E8M0Patterns(RewritePatternSet &patterns) {
  patterns.add<F8E8M0ExtFOpConverter, F8E8M0TruncFOpConverter>(
      patterns.getContext());
}
 
void mlir::arith::populateExpandScalingExtTruncPatterns(
    RewritePatternSet &patterns) {
  patterns.add<ScalingExtFOpConverter, ScalingTruncFOpConverter>(
      patterns.getContext());
}
 
void mlir::arith::populateExpandFlushDenormalsPatterns(
    RewritePatternSet &patterns) {
  patterns.add<FlushDenormalsOpConverter>(patterns.getContext());
}
 
void mlir::arith::populateExpandMinMaxFPatterns(RewritePatternSet &patterns) {
  // clang-format off
  patterns.add<
    MaximumMinimumFOpConverter<MaximumFOp, arith::CmpFPredicate::UGT>,
    MaximumMinimumFOpConverter<MinimumFOp, arith::CmpFPredicate::ULT>,
    MaxNumMinNumFOpConverter<MaxNumFOp, arith::CmpFPredicate::UGT>,
    MaxNumMinNumFOpConverter<MinNumFOp, arith::CmpFPredicate::ULT>
   >(patterns.getContext());
  // clang-format on
}
 
void mlir::arith::populateExpandMinMaxIPatterns(RewritePatternSet &patterns) {
  // clang-format off
  patterns.add<
    MaxMinIOpConverter<MaxSIOp, arith::CmpIPredicate::sgt>,
    MaxMinIOpConverter<MaxUIOp, arith::CmpIPredicate::ugt>,
    MaxMinIOpConverter<MinSIOp, arith::CmpIPredicate::slt>,
    MaxMinIOpConverter<MinUIOp, arith::CmpIPredicate::ult>
   >(patterns.getContext());
  // clang-format on
}
 
void mlir::arith::populateExpandMinMaxPatterns(RewritePatternSet &patterns) {
  populateExpandMinMaxFPatterns(patterns);
  populateExpandMinMaxIPatterns(patterns);
}
 
void mlir::arith::populateArithExpandOpsPatterns(RewritePatternSet &patterns) {
  populateCeilFloorDivExpandOpsPatterns(patterns);
  populateExpandScalingExtTruncPatterns(patterns);
  populateExpandMinMaxPatterns(patterns);
}