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//===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//

//

// 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

//

//===----------------------------------------------------------------------===//

///

/// \file

/// This file declares a class to represent arbitrary precision floating point

/// values and provide a variety of arithmetic operations on them.

///

//===----------------------------------------------------------------------===//

#ifndef LLVM_ADT_APFLOAT_H

#define LLVM_ADT_APFLOAT_H

#include "llvm/ADT/APInt.h"

#include "llvm/ADT/ArrayRef.h"

#include "llvm/ADT/FloatingPointMode.h"

#include "llvm/Support/ErrorHandling.h"

#include <memory>

#define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL)                             \

  do {                                                                         \

    if (usesLayout<IEEEFloat>(getSemantics()))                                 \

      return U.IEEE.METHOD_CALL;                                               \

    if (usesLayout<DoubleAPFloat>(getSemantics()))                             \

      return U.Double.METHOD_CALL;                                             \

    llvm_unreachable("Unexpected semantics");                                  \

  } while (false)

namespace llvm {

struct fltSemantics;

class APSInt;

class StringRef;

class APFloat;

class raw_ostream;

template <typename T> class Expected;

template <typename T> class SmallVectorImpl;

/// Enum that represents what fraction of the LSB truncated bits of an fp number

/// represent.

///

/// This essentially combines the roles of guard and sticky bits.

enum lostFraction { // Example of truncated bits:

  lfExactlyZero,    // 000000

  lfLessThanHalf,   // 0xxxxx  x's not all zero

  lfExactlyHalf,    // 100000

  lfMoreThanHalf    // 1xxxxx  x's not all zero

};

/// A self-contained host- and target-independent arbitrary-precision

/// floating-point software implementation.

///

/// APFloat uses bignum integer arithmetic as provided by static functions in

/// the APInt class.  The library will work with bignum integers whose parts are

/// any unsigned type at least 16 bits wide, but 64 bits is recommended.

///

/// Written for clarity rather than speed, in particular with a view to use in

/// the front-end of a cross compiler so that target arithmetic can be correctly

/// performed on the host.  Performance should nonetheless be reasonable,

/// particularly for its intended use.  It may be useful as a base

/// implementation for a run-time library during development of a faster

/// target-specific one.

///

/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all

/// implemented operations.  Currently implemented operations are add, subtract,

/// multiply, divide, fused-multiply-add, conversion-to-float,

/// conversion-to-integer and conversion-from-integer.  New rounding modes

/// (e.g. away from zero) can be added with three or four lines of code.

///

/// Four formats are built-in: IEEE single precision, double precision,

/// quadruple precision, and x87 80-bit extended double (when operating with

/// full extended precision).  Adding a new format that obeys IEEE semantics

/// only requires adding two lines of code: a declaration and definition of the

/// format.

///

/// All operations return the status of that operation as an exception bit-mask,

/// so multiple operations can be done consecutively with their results or-ed

/// together.  The returned status can be useful for compiler diagnostics; e.g.,

/// inexact, underflow and overflow can be easily diagnosed on constant folding,

/// and compiler optimizers can determine what exceptions would be raised by

/// folding operations and optimize, or perhaps not optimize, accordingly.

///

/// At present, underflow tininess is detected after rounding; it should be

/// straight forward to add support for the before-rounding case too.

///

/// The library reads hexadecimal floating point numbers as per C99, and

/// correctly rounds if necessary according to the specified rounding mode.

/// Syntax is required to have been validated by the caller.  It also converts

/// floating point numbers to hexadecimal text as per the C99 %a and %A

/// conversions.  The output precision (or alternatively the natural minimal

/// precision) can be specified; if the requested precision is less than the

/// natural precision the output is correctly rounded for the specified rounding

/// mode.

///

/// It also reads decimal floating point numbers and correctly rounds according

/// to the specified rounding mode.

///

/// Conversion to decimal text is not currently implemented.

///

/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit

/// signed exponent, and the significand as an array of integer parts.  After

/// normalization of a number of precision P the exponent is within the range of

/// the format, and if the number is not denormal the P-th bit of the

/// significand is set as an explicit integer bit.  For denormals the most

/// significant bit is shifted right so that the exponent is maintained at the

/// format's minimum, so that the smallest denormal has just the least

/// significant bit of the significand set.  The sign of zeroes and infinities

/// is significant; the exponent and significand of such numbers is not stored,

/// but has a known implicit (deterministic) value: 0 for the significands, 0

/// for zero exponent, all 1 bits for infinity exponent.  For NaNs the sign and

/// significand are deterministic, although not really meaningful, and preserved

/// in non-conversion operations.  The exponent is implicitly all 1 bits.

///

/// APFloat does not provide any exception handling beyond default exception

/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause

/// by encoding Signaling NaNs with the first bit of its trailing significand as

/// 0.

///

/// TODO

/// ====

///

/// Some features that may or may not be worth adding:

///

/// Binary to decimal conversion (hard).

///

/// Optional ability to detect underflow tininess before rounding.

///

/// New formats: x87 in single and double precision mode (IEEE apart from

/// extended exponent range) (hard).

///

/// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.

///

// This is the common type definitions shared by APFloat and its internal

// implementation classes. This struct should not define any non-static data

// members.

struct APFloatBase {

  typedef APInt::WordType integerPart;

  static constexpr unsigned integerPartWidth = APInt::APINT_BITS_PER_WORD;

  /// A signed type to represent a floating point numbers unbiased exponent.

  typedef int32_t ExponentType;

  /// \name Floating Point Semantics.

  /// @{

  enum Semantics {

    S_IEEEhalf,

    S_BFloat,

    S_IEEEsingle,

    S_IEEEdouble,

    S_IEEEquad,

    S_PPCDoubleDouble,

    // 8-bit floating point number following IEEE-754 conventions with bit

    // layout S1E5M2 as described in https://arxiv.org/abs/2209.05433.

    S_Float8E5M2,

    // 8-bit floating point number mostly following IEEE-754 conventions with

    // bit layout S1E4M3 as described in https://arxiv.org/abs/2209.05433.

    // Unlike IEEE-754 types, there are no infinity values, and NaN is

    // represented with the exponent and mantissa bits set to all 1s.

    S_Float8E4M3FN,

    S_x87DoubleExtended,

    S_MaxSemantics = S_x87DoubleExtended,

  };

  static const llvm::fltSemantics &EnumToSemantics(Semantics S);

  static Semantics SemanticsToEnum(const llvm::fltSemantics &Sem);

  static const fltSemantics &IEEEhalf() LLVM_READNONE;

  static const fltSemantics &BFloat() LLVM_READNONE;

  static const fltSemantics &IEEEsingle() LLVM_READNONE;

  static const fltSemantics &IEEEdouble() LLVM_READNONE;

  static const fltSemantics &IEEEquad() LLVM_READNONE;

  static const fltSemantics &PPCDoubleDouble() LLVM_READNONE;

  static const fltSemantics &Float8E5M2() LLVM_READNONE;

  static const fltSemantics &Float8E4M3FN() LLVM_READNONE;

  static const fltSemantics &x87DoubleExtended() LLVM_READNONE;

  /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with

  /// anything real.

  static const fltSemantics &Bogus() LLVM_READNONE;

  /// @}

  /// IEEE-754R 5.11: Floating Point Comparison Relations.

  enum cmpResult {

    cmpLessThan,

    cmpEqual,

    cmpGreaterThan,

    cmpUnordered

  };

  /// IEEE-754R 4.3: Rounding-direction attributes.

  using roundingMode = llvm::RoundingMode;

  static constexpr roundingMode rmNearestTiesToEven =

                                                RoundingMode::NearestTiesToEven;

  static constexpr roundingMode rmTowardPositive = RoundingMode::TowardPositive;

  static constexpr roundingMode rmTowardNegative = RoundingMode::TowardNegative;

  static constexpr roundingMode rmTowardZero     = RoundingMode::TowardZero;

  static constexpr roundingMode rmNearestTiesToAway =

                                                RoundingMode::NearestTiesToAway;

  /// IEEE-754R 7: Default exception handling.

  ///

  /// opUnderflow or opOverflow are always returned or-ed with opInexact.

  ///

  /// APFloat models this behavior specified by IEEE-754:

  ///   "For operations producing results in floating-point format, the default

  ///    result of an operation that signals the invalid operation exception

  ///    shall be a quiet NaN."

  enum opStatus {

    opOK = 0x00,

    opInvalidOp = 0x01,

    opDivByZero = 0x02,

    opOverflow = 0x04,

    opUnderflow = 0x08,

    opInexact = 0x10

  };

  /// Category of internally-represented number.

  enum fltCategory {

    fcInfinity,

    fcNaN,

    fcNormal,

    fcZero

  };

  /// Convenience enum used to construct an uninitialized APFloat.

  enum uninitializedTag {

    uninitialized

  };

  /// Enumeration of \c ilogb error results.

  enum IlogbErrorKinds {

    IEK_Zero = INT_MIN + 1,

    IEK_NaN = INT_MIN,

    IEK_Inf = INT_MAX

  };

  static unsigned int semanticsPrecision(const fltSemantics &);

  static ExponentType semanticsMinExponent(const fltSemantics &);

  static ExponentType semanticsMaxExponent(const fltSemantics &);

  static unsigned int semanticsSizeInBits(const fltSemantics &);

  /// Returns the size of the floating point number (in bits) in the given

  /// semantics.

  static unsigned getSizeInBits(const fltSemantics &Sem);

};

namespace detail {

class IEEEFloat final : public APFloatBase {

public:

  /// \name Constructors

  /// @{

  IEEEFloat(const fltSemantics &); // Default construct to +0.0

  IEEEFloat(const fltSemantics &, integerPart);

  IEEEFloat(const fltSemantics &, uninitializedTag);

  IEEEFloat(const fltSemantics &, const APInt &);

  explicit IEEEFloat(double d);

  explicit IEEEFloat(float f);

  IEEEFloat(const IEEEFloat &);

  IEEEFloat(IEEEFloat &&);

  ~IEEEFloat();

  /// @}

  /// Returns whether this instance allocated memory.

  bool needsCleanup() const { return partCount() > 1; }

  /// \name Convenience "constructors"

  /// @{

  /// @}

  /// \name Arithmetic

  /// @{

  opStatus add(const IEEEFloat &, roundingMode);

  opStatus subtract(const IEEEFloat &, roundingMode);

  opStatus multiply(const IEEEFloat &, roundingMode);

  opStatus divide(const IEEEFloat &, roundingMode);

  /// IEEE remainder.

  opStatus remainder(const IEEEFloat &);

  /// C fmod, or llvm frem.

  opStatus mod(const IEEEFloat &);

  opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);

  opStatus roundToIntegral(roundingMode);

  /// IEEE-754R 5.3.1: nextUp/nextDown.

  opStatus next(bool nextDown);

  /// @}

  /// \name Sign operations.

  /// @{

  void changeSign();

  /// @}

  /// \name Conversions

  /// @{

  opStatus convert(const fltSemantics &, roundingMode, bool *);

  opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,

                            roundingMode, bool *) const;

  opStatus convertFromAPInt(const APInt &, bool, roundingMode);

  opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,

                                          bool, roundingMode);

  opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,

                                          bool, roundingMode);

  Expected<opStatus> convertFromString(StringRef, roundingMode);

  APInt bitcastToAPInt() const;

  double convertToDouble() const;

  float convertToFloat() const;

  /// @}

  /// The definition of equality is not straightforward for floating point, so

  /// we won't use operator==.  Use one of the following, or write whatever it

  /// is you really mean.

  bool operator==(const IEEEFloat &) const = delete;

  /// IEEE comparison with another floating point number (NaNs compare

  /// unordered, 0==-0).

  cmpResult compare(const IEEEFloat &) const;

  /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).

  bool bitwiseIsEqual(const IEEEFloat &) const;

  /// Write out a hexadecimal representation of the floating point value to DST,

  /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.

  /// Return the number of characters written, excluding the terminating NUL.

  unsigned int convertToHexString(char *dst, unsigned int hexDigits,

                                  bool upperCase, roundingMode) const;

  /// \name IEEE-754R 5.7.2 General operations.

  /// @{

  /// IEEE-754R isSignMinus: Returns true if and only if the current value is

  /// negative.

  ///

  /// This applies to zeros and NaNs as well.

  bool isNegative() const { return sign; }

  /// IEEE-754R isNormal: Returns true if and only if the current value is normal.

  ///

  /// This implies that the current value of the float is not zero, subnormal,

  /// infinite, or NaN following the definition of normality from IEEE-754R.

  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }

  /// Returns true if and only if the current value is zero, subnormal, or

  /// normal.

  ///

  /// This means that the value is not infinite or NaN.

  bool isFinite() const { return !isNaN() && !isInfinity(); }

  /// Returns true if and only if the float is plus or minus zero.

  bool isZero() const { return category == fcZero; }

  /// IEEE-754R isSubnormal(): Returns true if and only if the float is a

  /// denormal.

  bool isDenormal() const;

  /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.

  bool isInfinity() const { return category == fcInfinity; }

  /// Returns true if and only if the float is a quiet or signaling NaN.

  bool isNaN() const { return category == fcNaN; }

  /// Returns true if and only if the float is a signaling NaN.

  bool isSignaling() const;

  /// @}

  /// \name Simple Queries

  /// @{

  fltCategory getCategory() const { return category; }

  const fltSemantics &getSemantics() const { return *semantics; }

  bool isNonZero() const { return category != fcZero; }

  bool isFiniteNonZero() const { return isFinite() && !isZero(); }

  bool isPosZero() const { return isZero() && !isNegative(); }

  bool isNegZero() const { return isZero() && isNegative(); }

  /// Returns true if and only if the number has the smallest possible non-zero

  /// magnitude in the current semantics.

  bool isSmallest() const;

  /// Returns true if this is the smallest (by magnitude) normalized finite

  /// number in the given semantics.

  bool isSmallestNormalized() const;

  /// Returns true if and only if the number has the largest possible finite

  /// magnitude in the current semantics.

  bool isLargest() const;

  /// Returns true if and only if the number is an exact integer.

  bool isInteger() const;

  /// @}

  IEEEFloat &operator=(const IEEEFloat &);

  IEEEFloat &operator=(IEEEFloat &&);

  /// Overload to compute a hash code for an APFloat value.

  ///

  /// Note that the use of hash codes for floating point values is in general

  /// frought with peril. Equality is hard to define for these values. For

  /// example, should negative and positive zero hash to different codes? Are

  /// they equal or not? This hash value implementation specifically

  /// emphasizes producing different codes for different inputs in order to

  /// be used in canonicalization and memoization. As such, equality is

  /// bitwiseIsEqual, and 0 != -0.

  friend hash_code hash_value(const IEEEFloat &Arg);

  /// Converts this value into a decimal string.

  ///

  /// \param FormatPrecision The maximum number of digits of

  ///   precision to output.  If there are fewer digits available,

  ///   zero padding will not be used unless the value is

  ///   integral and small enough to be expressed in

  ///   FormatPrecision digits.  0 means to use the natural

  ///   precision of the number.

  /// \param FormatMaxPadding The maximum number of zeros to

  ///   consider inserting before falling back to scientific

  ///   notation.  0 means to always use scientific notation.

  ///

  /// \param TruncateZero Indicate whether to remove the trailing zero in

  ///   fraction part or not. Also setting this parameter to false forcing

  ///   producing of output more similar to default printf behavior.

  ///   Specifically the lower e is used as exponent delimiter and exponent

  ///   always contains no less than two digits.

  ///

  /// Number       Precision    MaxPadding      Result

  /// ------       ---------    ----------      ------

  /// 1.01E+4              5             2       10100

  /// 1.01E+4              4             2       1.01E+4

  /// 1.01E+4              5             1       1.01E+4

  /// 1.01E-2              5             2       0.0101

  /// 1.01E-2              4             2       0.0101

  /// 1.01E-2              4             1       1.01E-2

  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,

                unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;

  /// If this value has an exact multiplicative inverse, store it in inv and

  /// return true.

  bool getExactInverse(APFloat *inv) const;

  /// Returns the exponent of the internal representation of the APFloat.

  ///

  /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).

  /// For special APFloat values, this returns special error codes:

  ///

  ///   NaN -> \c IEK_NaN

  ///   0   -> \c IEK_Zero

  ///   Inf -> \c IEK_Inf

  ///

  friend int ilogb(const IEEEFloat &Arg);

  /// Returns: X * 2^Exp for integral exponents.

  friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);

  friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);

  /// \name Special value setters.

  /// @{

  void makeLargest(bool Neg = false);

  void makeSmallest(bool Neg = false);

  void makeNaN(bool SNaN = false, bool Neg = false,

               const APInt *fill = nullptr);

  void makeInf(bool Neg = false);

  void makeZero(bool Neg = false);

  void makeQuiet();

  /// Returns the smallest (by magnitude) normalized finite number in the given

  /// semantics.

  ///

  /// \param Negative - True iff the number should be negative

  void makeSmallestNormalized(bool Negative = false);

  /// @}

  cmpResult compareAbsoluteValue(const IEEEFloat &) const;

private:

  /// \name Simple Queries

  /// @{

  integerPart *significandParts();

  const integerPart *significandParts() const;

  unsigned int partCount() const;

  /// @}

  /// \name Significand operations.

  /// @{

  integerPart addSignificand(const IEEEFloat &);

  integerPart subtractSignificand(const IEEEFloat &, integerPart);

  lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);

  lostFraction multiplySignificand(const IEEEFloat &, IEEEFloat);

  lostFraction multiplySignificand(const IEEEFloat&);

  lostFraction divideSignificand(const IEEEFloat &);

  void incrementSignificand();

  void initialize(const fltSemantics *);

  void shiftSignificandLeft(unsigned int);

  lostFraction shiftSignificandRight(unsigned int);

  unsigned int significandLSB() const;

  unsigned int significandMSB() const;

  void zeroSignificand();

  /// Return true if the significand excluding the integral bit is all ones.

  bool isSignificandAllOnes() const;

  bool isSignificandAllOnesExceptLSB() const;

  /// Return true if the significand excluding the integral bit is all zeros.

  bool isSignificandAllZeros() const;

  bool isSignificandAllZerosExceptMSB() const;

  /// @}

  /// \name Arithmetic on special values.

  /// @{

  opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);

  opStatus divideSpecials(const IEEEFloat &);

  opStatus multiplySpecials(const IEEEFloat &);

  opStatus modSpecials(const IEEEFloat &);

  opStatus remainderSpecials(const IEEEFloat&);

  /// @}

  /// \name Miscellany

  /// @{

  bool convertFromStringSpecials(StringRef str);

  opStatus normalize(roundingMode, lostFraction);

  opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);

  opStatus handleOverflow(roundingMode);

  bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;

  opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,

                                        unsigned int, bool, roundingMode,

                                        bool *) const;

  opStatus convertFromUnsignedParts(const integerPart *, unsigned int,

                                    roundingMode);

  Expected<opStatus> convertFromHexadecimalString(StringRef, roundingMode);

  Expected<opStatus> convertFromDecimalString(StringRef, roundingMode);

  char *convertNormalToHexString(char *, unsigned int, bool,

                                 roundingMode) const;

  opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,

                                        roundingMode);

  ExponentType exponentNaN() const;

  ExponentType exponentInf() const;

  ExponentType exponentZero() const;

  /// @}

  APInt convertHalfAPFloatToAPInt() const;

  APInt convertBFloatAPFloatToAPInt() const;

  APInt convertFloatAPFloatToAPInt() const;

  APInt convertDoubleAPFloatToAPInt() const;

  APInt convertQuadrupleAPFloatToAPInt() const;

  APInt convertF80LongDoubleAPFloatToAPInt() const;

  APInt convertPPCDoubleDoubleAPFloatToAPInt() const;

  APInt convertFloat8E5M2APFloatToAPInt() const;

  APInt convertFloat8E4M3FNAPFloatToAPInt() const;

  void initFromAPInt(const fltSemantics *Sem, const APInt &api);

  void initFromHalfAPInt(const APInt &api);

  void initFromBFloatAPInt(const APInt &api);

  void initFromFloatAPInt(const APInt &api);

  void initFromDoubleAPInt(const APInt &api);

  void initFromQuadrupleAPInt(const APInt &api);

  void initFromF80LongDoubleAPInt(const APInt &api);

  void initFromPPCDoubleDoubleAPInt(const APInt &api);

  void initFromFloat8E5M2APInt(const APInt &api);

  void initFromFloat8E4M3FNAPInt(const APInt &api);

  void assign(const IEEEFloat &);

  void copySignificand(const IEEEFloat &);

  void freeSignificand();

  /// Note: this must be the first data member.

  /// The semantics that this value obeys.

  const fltSemantics *semantics;

  /// A binary fraction with an explicit integer bit.

  ///

  /// The significand must be at least one bit wider than the target precision.

  union Significand {

    integerPart part;

    integerPart *parts;

  } significand;

  /// The signed unbiased exponent of the value.

  ExponentType exponent;

  /// What kind of floating point number this is.

  ///

  /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.

  /// Using the extra bit keeps it from failing under VisualStudio.

  fltCategory category : 3;

  /// Sign bit of the number.

  unsigned int sign : 1;

};

hash_code hash_value(const IEEEFloat &Arg);

int ilogb(const IEEEFloat &Arg);

IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode);

IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);

// This mode implements more precise float in terms of two APFloats.

// The interface and layout is designed for arbitrary underlying semantics,

// though currently only PPCDoubleDouble semantics are supported, whose

// corresponding underlying semantics are IEEEdouble.

class DoubleAPFloat final : public APFloatBase {

  // Note: this must be the first data member.

  const fltSemantics *Semantics;

  std::unique_ptr<APFloat[]> Floats;

  opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,

                   const APFloat &cc, roundingMode RM);

  opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,

                          DoubleAPFloat &Out, roundingMode RM);

public:

  DoubleAPFloat(const fltSemantics &S);

  DoubleAPFloat(const fltSemantics &S, uninitializedTag);

  DoubleAPFloat(const fltSemantics &S, integerPart);

  DoubleAPFloat(const fltSemantics &S, const APInt &I);

  DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);

  DoubleAPFloat(const DoubleAPFloat &RHS);

  DoubleAPFloat(DoubleAPFloat &&RHS);

  DoubleAPFloat &operator=(const DoubleAPFloat &RHS);

  DoubleAPFloat &operator=(DoubleAPFloat &&RHS) {

    if (this != &RHS) {

      this->~DoubleAPFloat();

      new (this) DoubleAPFloat(std::move(RHS));

    }

    return *this;

  }

  bool needsCleanup() const { return Floats != nullptr; }

  APFloat &getFirst() { return Floats[0]; }

  const APFloat &getFirst() const { return Floats[0]; }

  APFloat &getSecond() { return Floats[1]; }

  const APFloat &getSecond() const { return Floats[1]; }

  opStatus add(const DoubleAPFloat &RHS, roundingMode RM);

  opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);

  opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);

  opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);

  opStatus remainder(const DoubleAPFloat &RHS);

  opStatus mod(const DoubleAPFloat &RHS);

  opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,

                            const DoubleAPFloat &Addend, roundingMode RM);

  opStatus roundToIntegral(roundingMode RM);

  void changeSign();

  cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;

  fltCategory getCategory() const;

  bool isNegative() const;

  void makeInf(bool Neg);

  void makeZero(bool Neg);

  void makeLargest(bool Neg);

  void makeSmallest(bool Neg);

  void makeSmallestNormalized(bool Neg);

  void makeNaN(bool SNaN, bool Neg, const APInt *fill);

  cmpResult compare(const DoubleAPFloat &RHS) const;

  bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;

  APInt bitcastToAPInt() const;

  Expected<opStatus> convertFromString(StringRef, roundingMode);

  opStatus next(bool nextDown);

  opStatus convertToInteger(MutableArrayRef<integerPart> Input,

                            unsigned int Width, bool IsSigned, roundingMode RM,

                            bool *IsExact) const;

  opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);

  opStatus convertFromSignExtendedInteger(const integerPart *Input,

                                          unsigned int InputSize, bool IsSigned,

                                          roundingMode RM);

  opStatus convertFromZeroExtendedInteger(const integerPart *Input,

                                          unsigned int InputSize, bool IsSigned,

                                          roundingMode RM);

  unsigned int convertToHexString(char *DST, unsigned int HexDigits,

                                  bool UpperCase, roundingMode RM) const;

  bool isDenormal() const;

  bool isSmallest() const;

  bool isSmallestNormalized() const;

  bool isLargest() const;

  bool isInteger() const;

  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,

                unsigned FormatMaxPadding, bool TruncateZero = true) const;

  bool getExactInverse(APFloat *inv) const;

  friend DoubleAPFloat scalbn(const DoubleAPFloat &X, int Exp, roundingMode);

  friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);

  friend hash_code hash_value(const DoubleAPFloat &Arg);

};

hash_code hash_value(const DoubleAPFloat &Arg);

} // End detail namespace

// This is a interface class that is currently forwarding functionalities from

// detail::IEEEFloat.

class APFloat : public APFloatBase {

  typedef detail::IEEEFloat IEEEFloat;

  typedef detail::DoubleAPFloat DoubleAPFloat;

  static_assert(std::is_standard_layout<IEEEFloat>::value);

  union Storage {

    const fltSemantics *semantics;

    IEEEFloat IEEE;

    DoubleAPFloat Double;

    explicit Storage(IEEEFloat F, const fltSemantics &S);

    explicit Storage(DoubleAPFloat F, const fltSemantics &S)

        : Double(std::move(F)) {

      assert(&S == &PPCDoubleDouble());

    }

    template <typename... ArgTypes>

    Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {

      if (usesLayout<IEEEFloat>(Semantics)) {

        new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);

        return;

      }

      if (usesLayout<DoubleAPFloat>(Semantics)) {

        new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);

        return;

      }

      llvm_unreachable("Unexpected semantics");

    }

    ~Storage() {

      if (usesLayout<IEEEFloat>(*semantics)) {

        IEEE.~IEEEFloat();

        return;

      }

      if (usesLayout<DoubleAPFloat>(*semantics)) {

        Double.~DoubleAPFloat();

        return;

      }

      llvm_unreachable("Unexpected semantics");

    }

    Storage(const Storage &RHS) {

      if (usesLayout<IEEEFloat>(*RHS.semantics)) {

        new (this) IEEEFloat(RHS.IEEE);

        return;

      }

      if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {

        new (this) DoubleAPFloat(RHS.Double);

        return;

      }

      llvm_unreachable("Unexpected semantics");

    }

    Storage(Storage &&RHS) {

      if (usesLayout<IEEEFloat>(*RHS.semantics)) {

        new (this) IEEEFloat(std::move(RHS.IEEE));

        return;

      }

      if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {

        new (this) DoubleAPFloat(std::move(RHS.Double));

        return;

      }

      llvm_unreachable("Unexpected semantics");

    }

    Storage &operator=(const Storage &RHS) {

      if (usesLayout<IEEEFloat>(*semantics) &&

          usesLayout<IEEEFloat>(*RHS.semantics)) {

        IEEE = RHS.IEEE;

      } else if (usesLayout<DoubleAPFloat>(*semantics) &&

                 usesLayout<DoubleAPFloat>(*RHS.semantics)) {

        Double = RHS.Double;

      } else if (this != &RHS) {

        this->~Storage();

        new (this) Storage(RHS);

      }

      return *this;

    }

    Storage &operator=(Storage &&RHS) {

      if (usesLayout<IEEEFloat>(*semantics) &&

          usesLayout<IEEEFloat>(*RHS.semantics)) {

        IEEE = std::move(RHS.IEEE);

      } else if (usesLayout<DoubleAPFloat>(*semantics) &&

                 usesLayout<DoubleAPFloat>(*RHS.semantics)) {

        Double = std::move(RHS.Double);

      } else if (this != &RHS) {

        this->~Storage();

        new (this) Storage(std::move(RHS));