include/llvm/ADT/APFloat.h

   1 //===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//
   2 //
   3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   4 // See https://llvm.org/LICENSE.txt for license information.
   5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8 ///
   9 /// \file
  10 /// \brief
  11 /// This file declares a class to represent arbitrary precision floating point
  12 /// values and provide a variety of arithmetic operations on them.
  13 ///
  14 //===----------------------------------------------------------------------===//
  15
  16 #ifndef LLVM_ADT_APFLOAT_H
  17 #define LLVM_ADT_APFLOAT_H
  18
  19 #include "llvm/ADT/APInt.h"
  20 #include "llvm/ADT/ArrayRef.h"
  21 #include "llvm/Support/ErrorHandling.h"
  22 #include <memory>
  23
  24 #define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL)                             \
  25   do {                                                                         \
  26     if (usesLayout<IEEEFloat>(getSemantics()))                                 \
  27       return U.IEEE.METHOD_CALL;                                               \
  28     if (usesLayout<DoubleAPFloat>(getSemantics()))                             \
  29       return U.Double.METHOD_CALL;                                             \
  30     llvm_unreachable("Unexpected semantics");                                  \
  31   } while (false)
  32
  33 namespace llvm {
  34
  35 struct fltSemantics;
  36 class APSInt;
  37 class StringRef;
  38 class APFloat;
  39 class raw_ostream;
  40
  41 template <typename T> class SmallVectorImpl;
  42
  43 /// Enum that represents what fraction of the LSB truncated bits of an fp number
  44 /// represent.
  45 ///
  46 /// This essentially combines the roles of guard and sticky bits.
  47 enum lostFraction { // Example of truncated bits:
  48   lfExactlyZero,    // 000000
  49   lfLessThanHalf,   // 0xxxxx  x's not all zero
  50   lfExactlyHalf,    // 100000
  51   lfMoreThanHalf    // 1xxxxx  x's not all zero
  52 };
  53
  54 /// A self-contained host- and target-independent arbitrary-precision
  55 /// floating-point software implementation.
  56 ///
  57 /// APFloat uses bignum integer arithmetic as provided by static functions in
  58 /// the APInt class.  The library will work with bignum integers whose parts are
  59 /// any unsigned type at least 16 bits wide, but 64 bits is recommended.
  60 ///
  61 /// Written for clarity rather than speed, in particular with a view to use in
  62 /// the front-end of a cross compiler so that target arithmetic can be correctly
  63 /// performed on the host.  Performance should nonetheless be reasonable,
  64 /// particularly for its intended use.  It may be useful as a base
  65 /// implementation for a run-time library during development of a faster
  66 /// target-specific one.
  67 ///
  68 /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
  69 /// implemented operations.  Currently implemented operations are add, subtract,
  70 /// multiply, divide, fused-multiply-add, conversion-to-float,
  71 /// conversion-to-integer and conversion-from-integer.  New rounding modes
  72 /// (e.g. away from zero) can be added with three or four lines of code.
  73 ///
  74 /// Four formats are built-in: IEEE single precision, double precision,
  75 /// quadruple precision, and x87 80-bit extended double (when operating with
  76 /// full extended precision).  Adding a new format that obeys IEEE semantics
  77 /// only requires adding two lines of code: a declaration and definition of the
  78 /// format.
  79 ///
  80 /// All operations return the status of that operation as an exception bit-mask,
  81 /// so multiple operations can be done consecutively with their results or-ed
  82 /// together.  The returned status can be useful for compiler diagnostics; e.g.,
  83 /// inexact, underflow and overflow can be easily diagnosed on constant folding,
  84 /// and compiler optimizers can determine what exceptions would be raised by
  85 /// folding operations and optimize, or perhaps not optimize, accordingly.
  86 ///
  87 /// At present, underflow tininess is detected after rounding; it should be
  88 /// straight forward to add support for the before-rounding case too.
  89 ///
  90 /// The library reads hexadecimal floating point numbers as per C99, and
  91 /// correctly rounds if necessary according to the specified rounding mode.
  92 /// Syntax is required to have been validated by the caller.  It also converts
  93 /// floating point numbers to hexadecimal text as per the C99 %a and %A
  94 /// conversions.  The output precision (or alternatively the natural minimal
  95 /// precision) can be specified; if the requested precision is less than the
  96 /// natural precision the output is correctly rounded for the specified rounding
  97 /// mode.
  98 ///
  99 /// It also reads decimal floating point numbers and correctly rounds according
 100 /// to the specified rounding mode.
 101 ///
 102 /// Conversion to decimal text is not currently implemented.
 103 ///
 104 /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
 105 /// signed exponent, and the significand as an array of integer parts.  After
 106 /// normalization of a number of precision P the exponent is within the range of
 107 /// the format, and if the number is not denormal the P-th bit of the
 108 /// significand is set as an explicit integer bit.  For denormals the most
 109 /// significant bit is shifted right so that the exponent is maintained at the
 110 /// format's minimum, so that the smallest denormal has just the least
 111 /// significant bit of the significand set.  The sign of zeroes and infinities
 112 /// is significant; the exponent and significand of such numbers is not stored,
 113 /// but has a known implicit (deterministic) value: 0 for the significands, 0
 114 /// for zero exponent, all 1 bits for infinity exponent.  For NaNs the sign and
 115 /// significand are deterministic, although not really meaningful, and preserved
 116 /// in non-conversion operations.  The exponent is implicitly all 1 bits.
 117 ///
 118 /// APFloat does not provide any exception handling beyond default exception
 119 /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
 120 /// by encoding Signaling NaNs with the first bit of its trailing significand as
 121 /// 0.
 122 ///
 123 /// TODO
 124 /// ====
 125 ///
 126 /// Some features that may or may not be worth adding:
 127 ///
 128 /// Binary to decimal conversion (hard).
 129 ///
 130 /// Optional ability to detect underflow tininess before rounding.
 131 ///
 132 /// New formats: x87 in single and double precision mode (IEEE apart from
 133 /// extended exponent range) (hard).
 134 ///
 135 /// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
 136 ///
 137
 138 // This is the common type definitions shared by APFloat and its internal
 139 // implementation classes. This struct should not define any non-static data
 140 // members.
 141 struct APFloatBase {
 142   typedef APInt::WordType integerPart;
 143   static const unsigned integerPartWidth = APInt::APINT_BITS_PER_WORD;
 144
 145   /// A signed type to represent a floating point numbers unbiased exponent.
 146   typedef signed short ExponentType;
 147
 148   /// \name Floating Point Semantics.
 149   /// @{
 150   enum Semantics {
 151     S_IEEEhalf,
 152     S_IEEEsingle,
 153     S_IEEEdouble,
 154     S_x87DoubleExtended,
 155     S_IEEEquad,
 156     S_PPCDoubleDouble
 157   };
 158
 159   static const llvm::fltSemantics &EnumToSemantics(Semantics S);
 160   static Semantics SemanticsToEnum(const llvm::fltSemantics &Sem);
 161
 162   static const fltSemantics &IEEEhalf() LLVM_READNONE;
 163   static const fltSemantics &IEEEsingle() LLVM_READNONE;
 164   static const fltSemantics &IEEEdouble() LLVM_READNONE;
 165   static const fltSemantics &IEEEquad() LLVM_READNONE;
 166   static const fltSemantics &PPCDoubleDouble() LLVM_READNONE;
 167   static const fltSemantics &x87DoubleExtended() LLVM_READNONE;
 168
 169   /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
 170   /// anything real.
 171   static const fltSemantics &Bogus() LLVM_READNONE;
 172
 173   /// @}
 174
 175   /// IEEE-754R 5.11: Floating Point Comparison Relations.
 176   enum cmpResult {
 177     cmpLessThan,
 178     cmpEqual,
 179     cmpGreaterThan,
 180     cmpUnordered
 181   };
 182
 183   /// IEEE-754R 4.3: Rounding-direction attributes.
 184   enum roundingMode {
 185     rmNearestTiesToEven,
 186     rmTowardPositive,
 187     rmTowardNegative,
 188     rmTowardZero,
 189     rmNearestTiesToAway
 190   };
 191
 192   /// IEEE-754R 7: Default exception handling.
 193   ///
 194   /// opUnderflow or opOverflow are always returned or-ed with opInexact.
 195   enum opStatus {
 196     opOK = 0x00,
 197     opInvalidOp = 0x01,
 198     opDivByZero = 0x02,
 199     opOverflow = 0x04,
 200     opUnderflow = 0x08,
 201     opInexact = 0x10
 202   };
 203
 204   /// Category of internally-represented number.
 205   enum fltCategory {
 206     fcInfinity,
 207     fcNaN,
 208     fcNormal,
 209     fcZero
 210   };
 211
 212   /// Convenience enum used to construct an uninitialized APFloat.
 213   enum uninitializedTag {
 214     uninitialized
 215   };
 216
 217   /// Enumeration of \c ilogb error results.
 218   enum IlogbErrorKinds {
 219     IEK_Zero = INT_MIN + 1,
 220     IEK_NaN = INT_MIN,
 221     IEK_Inf = INT_MAX
 222   };
 223
 224   static unsigned int semanticsPrecision(const fltSemantics &);
 225   static ExponentType semanticsMinExponent(const fltSemantics &);
 226   static ExponentType semanticsMaxExponent(const fltSemantics &);
 227   static unsigned int semanticsSizeInBits(const fltSemantics &);
 228
 229   /// Returns the size of the floating point number (in bits) in the given
 230   /// semantics.
 231   static unsigned getSizeInBits(const fltSemantics &Sem);
 232 };
 233
 234 namespace detail {
 235
 236 class IEEEFloat final : public APFloatBase {
 237 public:
 238   /// \name Constructors
 239   /// @{
 240
 241   IEEEFloat(const fltSemantics &); // Default construct to 0.0
 242   IEEEFloat(const fltSemantics &, integerPart);
 243   IEEEFloat(const fltSemantics &, uninitializedTag);
 244   IEEEFloat(const fltSemantics &, const APInt &);
 245   explicit IEEEFloat(double d);
 246   explicit IEEEFloat(float f);
 247   IEEEFloat(const IEEEFloat &);
 248   IEEEFloat(IEEEFloat &&);
 249   ~IEEEFloat();
 250
 251   /// @}
 252
 253   /// Returns whether this instance allocated memory.
 254   bool needsCleanup() const { return partCount() > 1; }
 255
 256   /// \name Convenience "constructors"
 257   /// @{
 258
 259   /// @}
 260
 261   /// \name Arithmetic
 262   /// @{
 263
 264   opStatus add(const IEEEFloat &, roundingMode);
 265   opStatus subtract(const IEEEFloat &, roundingMode);
 266   opStatus multiply(const IEEEFloat &, roundingMode);
 267   opStatus divide(const IEEEFloat &, roundingMode);
 268   /// IEEE remainder.
 269   opStatus remainder(const IEEEFloat &);
 270   /// C fmod, or llvm frem.
 271   opStatus mod(const IEEEFloat &);
 272   opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);
 273   opStatus roundToIntegral(roundingMode);
 274   /// IEEE-754R 5.3.1: nextUp/nextDown.
 275   opStatus next(bool nextDown);
 276
 277   /// @}
 278
 279   /// \name Sign operations.
 280   /// @{
 281
 282   void changeSign();
 283
 284   /// @}
 285
 286   /// \name Conversions
 287   /// @{
 288
 289   opStatus convert(const fltSemantics &, roundingMode, bool *);
 290   opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,
 291                             roundingMode, bool *) const;
 292   opStatus convertFromAPInt(const APInt &, bool, roundingMode);
 293   opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
 294                                           bool, roundingMode);
 295   opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
 296                                           bool, roundingMode);
 297   opStatus convertFromString(StringRef, roundingMode);
 298   APInt bitcastToAPInt() const;
 299   double convertToDouble() const;
 300   float convertToFloat() const;
 301
 302   /// @}
 303
 304   /// The definition of equality is not straightforward for floating point, so
 305   /// we won't use operator==.  Use one of the following, or write whatever it
 306   /// is you really mean.
 307   bool operator==(const IEEEFloat &) const = delete;
 308
 309   /// IEEE comparison with another floating point number (NaNs compare
 310   /// unordered, 0==-0).
 311   cmpResult compare(const IEEEFloat &) const;
 312
 313   /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
 314   bool bitwiseIsEqual(const IEEEFloat &) const;
 315
 316   /// Write out a hexadecimal representation of the floating point value to DST,
 317   /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
 318   /// Return the number of characters written, excluding the terminating NUL.
 319   unsigned int convertToHexString(char *dst, unsigned int hexDigits,
 320                                   bool upperCase, roundingMode) const;
 321
 322   /// \name IEEE-754R 5.7.2 General operations.
 323   /// @{
 324
 325   /// IEEE-754R isSignMinus: Returns true if and only if the current value is
 326   /// negative.
 327   ///
 328   /// This applies to zeros and NaNs as well.
 329   bool isNegative() const { return sign; }
 330
 331   /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
 332   ///
 333   /// This implies that the current value of the float is not zero, subnormal,
 334   /// infinite, or NaN following the definition of normality from IEEE-754R.
 335   bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
 336
 337   /// Returns true if and only if the current value is zero, subnormal, or
 338   /// normal.
 339   ///
 340   /// This means that the value is not infinite or NaN.
 341   bool isFinite() const { return !isNaN() && !isInfinity(); }
 342
 343   /// Returns true if and only if the float is plus or minus zero.
 344   bool isZero() const { return category == fcZero; }
 345
 346   /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
 347   /// denormal.
 348   bool isDenormal() const;
 349
 350   /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
 351   bool isInfinity() const { return category == fcInfinity; }
 352
 353   /// Returns true if and only if the float is a quiet or signaling NaN.
 354   bool isNaN() const { return category == fcNaN; }
 355
 356   /// Returns true if and only if the float is a signaling NaN.
 357   bool isSignaling() const;
 358
 359   /// @}
 360
 361   /// \name Simple Queries
 362   /// @{
 363
 364   fltCategory getCategory() const { return category; }
 365   const fltSemantics &getSemantics() const { return *semantics; }
 366   bool isNonZero() const { return category != fcZero; }
 367   bool isFiniteNonZero() const { return isFinite() && !isZero(); }
 368   bool isPosZero() const { return isZero() && !isNegative(); }
 369   bool isNegZero() const { return isZero() && isNegative(); }
 370
 371   /// Returns true if and only if the number has the smallest possible non-zero
 372   /// magnitude in the current semantics.
 373   bool isSmallest() const;
 374
 375   /// Returns true if and only if the number has the largest possible finite
 376   /// magnitude in the current semantics.
 377   bool isLargest() const;
 378
 379   /// Returns true if and only if the number is an exact integer.
 380   bool isInteger() const;
 381
 382   /// @}
 383
 384   IEEEFloat &operator=(const IEEEFloat &);
 385   IEEEFloat &operator=(IEEEFloat &&);
 386
 387   /// Overload to compute a hash code for an APFloat value.
 388   ///
 389   /// Note that the use of hash codes for floating point values is in general
 390   /// frought with peril. Equality is hard to define for these values. For
 391   /// example, should negative and positive zero hash to different codes? Are
 392   /// they equal or not? This hash value implementation specifically
 393   /// emphasizes producing different codes for different inputs in order to
 394   /// be used in canonicalization and memoization. As such, equality is
 395   /// bitwiseIsEqual, and 0 != -0.
 396   friend hash_code hash_value(const IEEEFloat &Arg);
 397
 398   /// Converts this value into a decimal string.
 399   ///
 400   /// \param FormatPrecision The maximum number of digits of
 401   ///   precision to output.  If there are fewer digits available,
 402   ///   zero padding will not be used unless the value is
 403   ///   integral and small enough to be expressed in
 404   ///   FormatPrecision digits.  0 means to use the natural
 405   ///   precision of the number.
 406   /// \param FormatMaxPadding The maximum number of zeros to
 407   ///   consider inserting before falling back to scientific
 408   ///   notation.  0 means to always use scientific notation.
 409   ///
 410   /// \param TruncateZero Indicate whether to remove the trailing zero in
 411   ///   fraction part or not. Also setting this parameter to false forcing
 412   ///   producing of output more similar to default printf behavior.
 413   ///   Specifically the lower e is used as exponent delimiter and exponent
 414   ///   always contains no less than two digits.
 415   ///
 416   /// Number       Precision    MaxPadding      Result
 417   /// ------       ---------    ----------      ------
 418   /// 1.01E+4              5             2       10100
 419   /// 1.01E+4              4             2       1.01E+4
 420   /// 1.01E+4              5             1       1.01E+4
 421   /// 1.01E-2              5             2       0.0101
 422   /// 1.01E-2              4             2       0.0101
 423   /// 1.01E-2              4             1       1.01E-2
 424   void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
 425                 unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;
 426
 427   /// If this value has an exact multiplicative inverse, store it in inv and
 428   /// return true.
 429   bool getExactInverse(APFloat *inv) const;
 430
 431   /// Returns the exponent of the internal representation of the APFloat.
 432   ///
 433   /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
 434   /// For special APFloat values, this returns special error codes:
 435   ///
 436   ///   NaN -> \c IEK_NaN
 437   ///   0   -> \c IEK_Zero
 438   ///   Inf -> \c IEK_Inf
 439   ///
 440   friend int ilogb(const IEEEFloat &Arg);
 441
 442   /// Returns: X * 2^Exp for integral exponents.
 443   friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);
 444
 445   friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);
 446
 447   /// \name Special value setters.
 448   /// @{
 449
 450   void makeLargest(bool Neg = false);
 451   void makeSmallest(bool Neg = false);
 452   void makeNaN(bool SNaN = false, bool Neg = false,
 453                const APInt *fill = nullptr);
 454   void makeInf(bool Neg = false);
 455   void makeZero(bool Neg = false);
 456   void makeQuiet();
 457
 458   /// Returns the smallest (by magnitude) normalized finite number in the given
 459   /// semantics.
 460   ///
 461   /// \param Negative - True iff the number should be negative
 462   void makeSmallestNormalized(bool Negative = false);
 463
 464   /// @}
 465
 466   cmpResult compareAbsoluteValue(const IEEEFloat &) const;
 467
 468 private:
 469   /// \name Simple Queries
 470   /// @{
 471
 472   integerPart *significandParts();
 473   const integerPart *significandParts() const;
 474   unsigned int partCount() const;
 475
 476   /// @}
 477
 478   /// \name Significand operations.
 479   /// @{
 480
 481   integerPart addSignificand(const IEEEFloat &);
 482   integerPart subtractSignificand(const IEEEFloat &, integerPart);
 483   lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
 484   lostFraction multiplySignificand(const IEEEFloat &, const IEEEFloat *);
 485   lostFraction divideSignificand(const IEEEFloat &);
 486   void incrementSignificand();
 487   void initialize(const fltSemantics *);
 488   void shiftSignificandLeft(unsigned int);
 489   lostFraction shiftSignificandRight(unsigned int);
 490   unsigned int significandLSB() const;
 491   unsigned int significandMSB() const;
 492   void zeroSignificand();
 493   /// Return true if the significand excluding the integral bit is all ones.
 494   bool isSignificandAllOnes() const;
 495   /// Return true if the significand excluding the integral bit is all zeros.
 496   bool isSignificandAllZeros() const;
 497
 498   /// @}
 499
 500   /// \name Arithmetic on special values.
 501   /// @{
 502
 503   opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);
 504   opStatus divideSpecials(const IEEEFloat &);
 505   opStatus multiplySpecials(const IEEEFloat &);
 506   opStatus modSpecials(const IEEEFloat &);
 507
 508   /// @}
 509
 510   /// \name Miscellany
 511   /// @{
 512
 513   bool convertFromStringSpecials(StringRef str);
 514   opStatus normalize(roundingMode, lostFraction);
 515   opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);
 516   opStatus handleOverflow(roundingMode);
 517   bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
 518   opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,
 519                                         unsigned int, bool, roundingMode,
 520                                         bool *) const;
 521   opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
 522                                     roundingMode);
 523   opStatus convertFromHexadecimalString(StringRef, roundingMode);
 524   opStatus convertFromDecimalString(StringRef, roundingMode);
 525   char *convertNormalToHexString(char *, unsigned int, bool,
 526                                  roundingMode) const;
 527   opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
 528                                         roundingMode);
 529
 530   /// @}
 531
 532   APInt convertHalfAPFloatToAPInt() const;
 533   APInt convertFloatAPFloatToAPInt() const;
 534   APInt convertDoubleAPFloatToAPInt() const;
 535   APInt convertQuadrupleAPFloatToAPInt() const;
 536   APInt convertF80LongDoubleAPFloatToAPInt() const;
 537   APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
 538   void initFromAPInt(const fltSemantics *Sem, const APInt &api);
 539   void initFromHalfAPInt(const APInt &api);
 540   void initFromFloatAPInt(const APInt &api);
 541   void initFromDoubleAPInt(const APInt &api);
 542   void initFromQuadrupleAPInt(const APInt &api);
 543   void initFromF80LongDoubleAPInt(const APInt &api);
 544   void initFromPPCDoubleDoubleAPInt(const APInt &api);
 545
 546   void assign(const IEEEFloat &);
 547   void copySignificand(const IEEEFloat &);
 548   void freeSignificand();
 549
 550   /// Note: this must be the first data member.
 551   /// The semantics that this value obeys.
 552   const fltSemantics *semantics;
 553
 554   /// A binary fraction with an explicit integer bit.
 555   ///
 556   /// The significand must be at least one bit wider than the target precision.
 557   union Significand {
 558     integerPart part;
 559     integerPart *parts;
 560   } significand;
 561
 562   /// The signed unbiased exponent of the value.
 563   ExponentType exponent;
 564
 565   /// What kind of floating point number this is.
 566   ///
 567   /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
 568   /// Using the extra bit keeps it from failing under VisualStudio.
 569   fltCategory category : 3;
 570
 571   /// Sign bit of the number.
 572   unsigned int sign : 1;
 573 };
 574
 575 hash_code hash_value(const IEEEFloat &Arg);
 576 int ilogb(const IEEEFloat &Arg);
 577 IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode);
 578 IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);
 579
 580 // This mode implements more precise float in terms of two APFloats.
 581 // The interface and layout is designed for arbitray underlying semantics,
 582 // though currently only PPCDoubleDouble semantics are supported, whose
 583 // corresponding underlying semantics are IEEEdouble.
 584 class DoubleAPFloat final : public APFloatBase {
 585   // Note: this must be the first data member.
 586   const fltSemantics *Semantics;
 587   std::unique_ptr<APFloat[]> Floats;
 588
 589   opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,
 590                    const APFloat &cc, roundingMode RM);
 591
 592   opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,
 593                           DoubleAPFloat &Out, roundingMode RM);
 594
 595 public:
 596   DoubleAPFloat(const fltSemantics &S);
 597   DoubleAPFloat(const fltSemantics &S, uninitializedTag);
 598   DoubleAPFloat(const fltSemantics &S, integerPart);
 599   DoubleAPFloat(const fltSemantics &S, const APInt &I);
 600   DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);
 601   DoubleAPFloat(const DoubleAPFloat &RHS);
 602   DoubleAPFloat(DoubleAPFloat &&RHS);
 603
 604   DoubleAPFloat &operator=(const DoubleAPFloat &RHS);
 605
 606   DoubleAPFloat &operator=(DoubleAPFloat &&RHS) {
 607     if (this != &RHS) {
 608       this->~DoubleAPFloat();
 609       new (this) DoubleAPFloat(std::move(RHS));
 610     }
 611     return *this;
 612   }
 613
 614   bool needsCleanup() const { return Floats != nullptr; }
 615
 616   APFloat &getFirst() { return Floats[0]; }
 617   const APFloat &getFirst() const { return Floats[0]; }
 618   APFloat &getSecond() { return Floats[1]; }
 619   const APFloat &getSecond() const { return Floats[1]; }
 620
 621   opStatus add(const DoubleAPFloat &RHS, roundingMode RM);
 622   opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);
 623   opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);
 624   opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);
 625   opStatus remainder(const DoubleAPFloat &RHS);
 626   opStatus mod(const DoubleAPFloat &RHS);
 627   opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
 628                             const DoubleAPFloat &Addend, roundingMode RM);
 629   opStatus roundToIntegral(roundingMode RM);
 630   void changeSign();
 631   cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;
 632
 633   fltCategory getCategory() const;
 634   bool isNegative() const;
 635
 636   void makeInf(bool Neg);
 637   void makeZero(bool Neg);
 638   void makeLargest(bool Neg);
 639   void makeSmallest(bool Neg);
 640   void makeSmallestNormalized(bool Neg);
 641   void makeNaN(bool SNaN, bool Neg, const APInt *fill);
 642
 643   cmpResult compare(const DoubleAPFloat &RHS) const;
 644   bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;
 645   APInt bitcastToAPInt() const;
 646   opStatus convertFromString(StringRef, roundingMode);
 647   opStatus next(bool nextDown);
 648
 649   opStatus convertToInteger(MutableArrayRef<integerPart> Input,
 650                             unsigned int Width, bool IsSigned, roundingMode RM,
 651                             bool *IsExact) const;
 652   opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);
 653   opStatus convertFromSignExtendedInteger(const integerPart *Input,
 654                                           unsigned int InputSize, bool IsSigned,
 655                                           roundingMode RM);
 656   opStatus convertFromZeroExtendedInteger(const integerPart *Input,
 657                                           unsigned int InputSize, bool IsSigned,
 658                                           roundingMode RM);
 659   unsigned int convertToHexString(char *DST, unsigned int HexDigits,
 660                                   bool UpperCase, roundingMode RM) const;
 661
 662   bool isDenormal() const;
 663   bool isSmallest() const;
 664   bool isLargest() const;
 665   bool isInteger() const;
 666
 667   void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
 668                 unsigned FormatMaxPadding, bool TruncateZero = true) const;
 669
 670   bool getExactInverse(APFloat *inv) const;
 671
 672   friend int ilogb(const DoubleAPFloat &Arg);
 673   friend DoubleAPFloat scalbn(DoubleAPFloat X, int Exp, roundingMode);
 674   friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);
 675   friend hash_code hash_value(const DoubleAPFloat &Arg);
 676 };
 677
 678 hash_code hash_value(const DoubleAPFloat &Arg);
 679
 680 } // End detail namespace
 681
 682 // This is a interface class that is currently forwarding functionalities from
 683 // detail::IEEEFloat.
 684 class APFloat : public APFloatBase {
 685   typedef detail::IEEEFloat IEEEFloat;
 686   typedef detail::DoubleAPFloat DoubleAPFloat;
 687
 688   static_assert(std::is_standard_layout<IEEEFloat>::value, "");
 689
 690   union Storage {
 691     const fltSemantics *semantics;
 692     IEEEFloat IEEE;
 693     DoubleAPFloat Double;
 694
 695     explicit Storage(IEEEFloat F, const fltSemantics &S);
 696     explicit Storage(DoubleAPFloat F, const fltSemantics &S)
 697         : Double(std::move(F)) {
 698       assert(&S == &PPCDoubleDouble());
 699     }
 700
 701     template <typename... ArgTypes>
 702     Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {
 703       if (usesLayout<IEEEFloat>(Semantics)) {
 704         new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);
 705         return;
 706       }
 707       if (usesLayout<DoubleAPFloat>(Semantics)) {
 708         new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);
 709         return;
 710       }
 711       llvm_unreachable("Unexpected semantics");
 712     }
 713
 714     ~Storage() {
 715       if (usesLayout<IEEEFloat>(*semantics)) {
 716         IEEE.~IEEEFloat();
 717         return;
 718       }
 719       if (usesLayout<DoubleAPFloat>(*semantics)) {
 720         Double.~DoubleAPFloat();
 721         return;
 722       }
 723       llvm_unreachable("Unexpected semantics");
 724     }
 725
 726     Storage(const Storage &RHS) {
 727       if (usesLayout<IEEEFloat>(*RHS.semantics)) {
 728         new (this) IEEEFloat(RHS.IEEE);
 729         return;
 730       }
 731       if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
 732         new (this) DoubleAPFloat(RHS.Double);
 733         return;
 734       }
 735       llvm_unreachable("Unexpected semantics");
 736     }
 737
 738     Storage(Storage &&RHS) {
 739       if (usesLayout<IEEEFloat>(*RHS.semantics)) {
 740         new (this) IEEEFloat(std::move(RHS.IEEE));
 741         return;
 742       }
 743       if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
 744         new (this) DoubleAPFloat(std::move(RHS.Double));
 745         return;
 746       }
 747       llvm_unreachable("Unexpected semantics");
 748     }
 749
 750     Storage &operator=(const Storage &RHS) {
 751       if (usesLayout<IEEEFloat>(*semantics) &&
 752           usesLayout<IEEEFloat>(*RHS.semantics)) {
 753         IEEE = RHS.IEEE;
 754       } else if (usesLayout<DoubleAPFloat>(*semantics) &&
 755                  usesLayout<DoubleAPFloat>(*RHS.semantics)) {
 756         Double = RHS.Double;
 757       } else if (this != &RHS) {
 758         this->~Storage();
 759         new (this) Storage(RHS);
 760       }
 761       return *this;
 762     }
 763
 764     Storage &operator=(Storage &&RHS) {
 765       if (usesLayout<IEEEFloat>(*semantics) &&
 766           usesLayout<IEEEFloat>(*RHS.semantics)) {
 767         IEEE = std::move(RHS.IEEE);
 768       } else if (usesLayout<DoubleAPFloat>(*semantics) &&
 769                  usesLayout<DoubleAPFloat>(*RHS.semantics)) {
 770         Double = std::move(RHS.Double);
 771       } else if (this != &RHS) {
 772         this->~Storage();
 773         new (this) Storage(std::move(RHS));
 774       }
 775       return *this;
 776     }
 777   } U;
 778
 779   template <typename T> static bool usesLayout(const fltSemantics &Semantics) {
 780     static_assert(std::is_same<T, IEEEFloat>::value ||
 781                   std::is_same<T, DoubleAPFloat>::value, "");
 782     if (std::is_same<T, DoubleAPFloat>::value) {
 783       return &Semantics == &PPCDoubleDouble();
 784     }
 785     return &Semantics != &PPCDoubleDouble();
 786   }
 787
 788   IEEEFloat &getIEEE() {
 789     if (usesLayout<IEEEFloat>(*U.semantics))
 790       return U.IEEE;
 791     if (usesLayout<DoubleAPFloat>(*U.semantics))
 792       return U.Double.getFirst().U.IEEE;
 793     llvm_unreachable("Unexpected semantics");
 794   }
 795
 796   const IEEEFloat &getIEEE() const {
 797     if (usesLayout<IEEEFloat>(*U.semantics))
 798       return U.IEEE;
 799     if (usesLayout<DoubleAPFloat>(*U.semantics))
 800       return U.Double.getFirst().U.IEEE;
 801     llvm_unreachable("Unexpected semantics");
 802   }
 803
 804   void makeZero(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeZero(Neg)); }
 805
 806   void makeInf(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeInf(Neg)); }
 807
 808   void makeNaN(bool SNaN, bool Neg, const APInt *fill) {
 809     APFLOAT_DISPATCH_ON_SEMANTICS(makeNaN(SNaN, Neg, fill));
 810   }
 811
 812   void makeLargest(bool Neg) {
 813     APFLOAT_DISPATCH_ON_SEMANTICS(makeLargest(Neg));
 814   }
 815
 816   void makeSmallest(bool Neg) {
 817     APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallest(Neg));
 818   }
 819
 820   void makeSmallestNormalized(bool Neg) {
 821     APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallestNormalized(Neg));
 822   }
 823
 824   // FIXME: This is due to clang 3.3 (or older version) always checks for the
 825   // default constructor in an array aggregate initialization, even if no
 826   // elements in the array is default initialized.
 827   APFloat() : U(IEEEdouble()) {
 828     llvm_unreachable("This is a workaround for old clang.");
 829   }
 830
 831   explicit APFloat(IEEEFloat F, const fltSemantics &S) : U(std::move(F), S) {}
 832   explicit APFloat(DoubleAPFloat F, const fltSemantics &S)
 833       : U(std::move(F), S) {}
 834
 835   cmpResult compareAbsoluteValue(const APFloat &RHS) const {
 836     assert(&getSemantics() == &RHS.getSemantics() &&
 837            "Should only compare APFloats with the same semantics");
 838     if (usesLayout<IEEEFloat>(getSemantics()))
 839       return U.IEEE.compareAbsoluteValue(RHS.U.IEEE);
 840     if (usesLayout<DoubleAPFloat>(getSemantics()))
 841       return U.Double.compareAbsoluteValue(RHS.U.Double);
 842     llvm_unreachable("Unexpected semantics");
 843   }
 844
 845 public:
 846   APFloat(const fltSemantics &Semantics) : U(Semantics) {}
 847   APFloat(const fltSemantics &Semantics, StringRef S);
 848   APFloat(const fltSemantics &Semantics, integerPart I) : U(Semantics, I) {}
 849   // TODO: Remove this constructor. This isn't faster than the first one.
 850   APFloat(const fltSemantics &Semantics, uninitializedTag)
 851       : U(Semantics, uninitialized) {}
 852   APFloat(const fltSemantics &Semantics, const APInt &I) : U(Semantics, I) {}
 853   explicit APFloat(double d) : U(IEEEFloat(d), IEEEdouble()) {}
 854   explicit APFloat(float f) : U(IEEEFloat(f), IEEEsingle()) {}
 855   APFloat(const APFloat &RHS) = default;
 856   APFloat(APFloat &&RHS) = default;
 857
 858   ~APFloat() = default;
 859
 860   bool needsCleanup() const { APFLOAT_DISPATCH_ON_SEMANTICS(needsCleanup()); }
 861
 862   /// Factory for Positive and Negative Zero.
 863   ///
 864   /// \param Negative True iff the number should be negative.
 865   static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
 866     APFloat Val(Sem, uninitialized);
 867     Val.makeZero(Negative);
 868     return Val;
 869   }
 870
 871   /// Factory for Positive and Negative Infinity.
 872   ///
 873   /// \param Negative True iff the number should be negative.
 874   static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
 875     APFloat Val(Sem, uninitialized);
 876     Val.makeInf(Negative);
 877     return Val;
 878   }
 879
 880   /// Factory for NaN values.
 881   ///
 882   /// \param Negative - True iff the NaN generated should be negative.
 883   /// \param payload - The unspecified fill bits for creating the NaN, 0 by
 884   /// default.  The value is truncated as necessary.
 885   static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
 886                         uint64_t payload = 0) {
 887     if (payload) {
 888       APInt intPayload(64, payload);
 889       return getQNaN(Sem, Negative, &intPayload);
 890     } else {
 891       return getQNaN(Sem, Negative, nullptr);
 892     }
 893   }
 894
 895   /// Factory for QNaN values.
 896   static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
 897                          const APInt *payload = nullptr) {
 898     APFloat Val(Sem, uninitialized);
 899     Val.makeNaN(false, Negative, payload);
 900     return Val;
 901   }
 902
 903   /// Factory for SNaN values.
 904   static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
 905                          const APInt *payload = nullptr) {
 906     APFloat Val(Sem, uninitialized);
 907     Val.makeNaN(true, Negative, payload);
 908     return Val;
 909   }
 910
 911   /// Returns the largest finite number in the given semantics.
 912   ///
 913   /// \param Negative - True iff the number should be negative
 914   static APFloat getLargest(const fltSemantics &Sem, bool Negative = false) {
 915     APFloat Val(Sem, uninitialized);
 916     Val.makeLargest(Negative);
 917     return Val;
 918   }
 919
 920   /// Returns the smallest (by magnitude) finite number in the given semantics.
 921   /// Might be denormalized, which implies a relative loss of precision.
 922   ///
 923   /// \param Negative - True iff the number should be negative
 924   static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false) {
 925     APFloat Val(Sem, uninitialized);
 926     Val.makeSmallest(Negative);
 927     return Val;
 928   }
 929
 930   /// Returns the smallest (by magnitude) normalized finite number in the given
 931   /// semantics.
 932   ///
 933   /// \param Negative - True iff the number should be negative
 934   static APFloat getSmallestNormalized(const fltSemantics &Sem,
 935                                        bool Negative = false) {
 936     APFloat Val(Sem, uninitialized);
 937     Val.makeSmallestNormalized(Negative);
 938     return Val;
 939   }
 940
 941   /// Returns a float which is bitcasted from an all one value int.
 942   ///
 943   /// \param BitWidth - Select float type
 944   /// \param isIEEE   - If 128 bit number, select between PPC and IEEE
 945   static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
 946
 947   /// Used to insert APFloat objects, or objects that contain APFloat objects,
 948   /// into FoldingSets.
 949   void Profile(FoldingSetNodeID &NID) const;
 950
 951   opStatus add(const APFloat &RHS, roundingMode RM) {
 952     assert(&getSemantics() == &RHS.getSemantics() &&
 953            "Should only call on two APFloats with the same semantics");
 954     if (usesLayout<IEEEFloat>(getSemantics()))
 955       return U.IEEE.add(RHS.U.IEEE, RM);
 956     if (usesLayout<DoubleAPFloat>(getSemantics()))
 957       return U.Double.add(RHS.U.Double, RM);
 958     llvm_unreachable("Unexpected semantics");
 959   }
 960   opStatus subtract(const APFloat &RHS, roundingMode RM) {
 961     assert(&getSemantics() == &RHS.getSemantics() &&
 962            "Should only call on two APFloats with the same semantics");
 963     if (usesLayout<IEEEFloat>(getSemantics()))
 964       return U.IEEE.subtract(RHS.U.IEEE, RM);
 965     if (usesLayout<DoubleAPFloat>(getSemantics()))
 966       return U.Double.subtract(RHS.U.Double, RM);
 967     llvm_unreachable("Unexpected semantics");
 968   }
 969   opStatus multiply(const APFloat &RHS, roundingMode RM) {
 970     assert(&getSemantics() == &RHS.getSemantics() &&
 971            "Should only call on two APFloats with the same semantics");
 972     if (usesLayout<IEEEFloat>(getSemantics()))
 973       return U.IEEE.multiply(RHS.U.IEEE, RM);
 974     if (usesLayout<DoubleAPFloat>(getSemantics()))
 975       return U.Double.multiply(RHS.U.Double, RM);
 976     llvm_unreachable("Unexpected semantics");
 977   }
 978   opStatus divide(const APFloat &RHS, roundingMode RM) {
 979     assert(&getSemantics() == &RHS.getSemantics() &&
 980            "Should only call on two APFloats with the same semantics");
 981     if (usesLayout<IEEEFloat>(getSemantics()))
 982       return U.IEEE.divide(RHS.U.IEEE, RM);
 983     if (usesLayout<DoubleAPFloat>(getSemantics()))
 984       return U.Double.divide(RHS.U.Double, RM);
 985     llvm_unreachable("Unexpected semantics");
 986   }
 987   opStatus remainder(const APFloat &RHS) {
 988     assert(&getSemantics() == &RHS.getSemantics() &&
 989            "Should only call on two APFloats with the same semantics");
 990     if (usesLayout<IEEEFloat>(getSemantics()))
 991       return U.IEEE.remainder(RHS.U.IEEE);
 992     if (usesLayout<DoubleAPFloat>(getSemantics()))
 993       return U.Double.remainder(RHS.U.Double);
 994     llvm_unreachable("Unexpected semantics");
 995   }
 996   opStatus mod(const APFloat &RHS) {
 997     assert(&getSemantics() == &RHS.getSemantics() &&
 998            "Should only call on two APFloats with the same semantics");
 999     if (usesLayout<IEEEFloat>(getSemantics()))
1000       return U.IEEE.mod(RHS.U.IEEE);
1001     if (usesLayout<DoubleAPFloat>(getSemantics()))
1002       return U.Double.mod(RHS.U.Double);
1003     llvm_unreachable("Unexpected semantics");
1004   }
1005   opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend,
1006                             roundingMode RM) {
1007     assert(&getSemantics() == &Multiplicand.getSemantics() &&
1008            "Should only call on APFloats with the same semantics");
1009     assert(&getSemantics() == &Addend.getSemantics() &&
1010            "Should only call on APFloats with the same semantics");
1011     if (usesLayout<IEEEFloat>(getSemantics()))
1012       return U.IEEE.fusedMultiplyAdd(Multiplicand.U.IEEE, Addend.U.IEEE, RM);
1013     if (usesLayout<DoubleAPFloat>(getSemantics()))
1014       return U.Double.fusedMultiplyAdd(Multiplicand.U.Double, Addend.U.Double,
1015                                        RM);
1016     llvm_unreachable("Unexpected semantics");
1017   }
1018   opStatus roundToIntegral(roundingMode RM) {
1019     APFLOAT_DISPATCH_ON_SEMANTICS(roundToIntegral(RM));
1020   }
1021
1022   // TODO: bool parameters are not readable and a source of bugs.
1023   // Do something.
1024   opStatus next(bool nextDown) {
1025     APFLOAT_DISPATCH_ON_SEMANTICS(next(nextDown));
1026   }
1027
1028   /// Add two APFloats, rounding ties to the nearest even.
1029   /// No error checking.
1030   APFloat operator+(const APFloat &RHS) const {
1031     APFloat Result(*this);
1032     (void)Result.add(RHS, rmNearestTiesToEven);
1033     return Result;
1034   }
1035
1036   /// Subtract two APFloats, rounding ties to the nearest even.
1037   /// No error checking.
1038   APFloat operator-(const APFloat &RHS) const {
1039     APFloat Result(*this);
1040     (void)Result.subtract(RHS, rmNearestTiesToEven);
1041     return Result;
1042   }
1043
1044   /// Multiply two APFloats, rounding ties to the nearest even.
1045   /// No error checking.
1046   APFloat operator*(const APFloat &RHS) const {
1047     APFloat Result(*this);
1048     (void)Result.multiply(RHS, rmNearestTiesToEven);
1049     return Result;
1050   }
1051
1052   /// Divide the first APFloat by the second, rounding ties to the nearest even.
1053   /// No error checking.
1054   APFloat operator/(const APFloat &RHS) const {
1055     APFloat Result(*this);
1056     (void)Result.divide(RHS, rmNearestTiesToEven);
1057     return Result;
1058   }
1059
1060   void changeSign() { APFLOAT_DISPATCH_ON_SEMANTICS(changeSign()); }
1061   void clearSign() {
1062     if (isNegative())
1063       changeSign();
1064   }
1065   void copySign(const APFloat &RHS) {
1066     if (isNegative() != RHS.isNegative())
1067       changeSign();
1068   }
1069
1070   /// A static helper to produce a copy of an APFloat value with its sign
1071   /// copied from some other APFloat.
1072   static APFloat copySign(APFloat Value, const APFloat &Sign) {
1073     Value.copySign(Sign);
1074     return Value;
1075   }
1076
1077   opStatus convert(const fltSemantics &ToSemantics, roundingMode RM,
1078                    bool *losesInfo);
1079   opStatus convertToInteger(MutableArrayRef<integerPart> Input,
1080                             unsigned int Width, bool IsSigned, roundingMode RM,
1081                             bool *IsExact) const {
1082     APFLOAT_DISPATCH_ON_SEMANTICS(
1083         convertToInteger(Input, Width, IsSigned, RM, IsExact));
1084   }
1085   opStatus convertToInteger(APSInt &Result, roundingMode RM,
1086                             bool *IsExact) const;
1087   opStatus convertFromAPInt(const APInt &Input, bool IsSigned,
1088                             roundingMode RM) {
1089     APFLOAT_DISPATCH_ON_SEMANTICS(convertFromAPInt(Input, IsSigned, RM));
1090   }
1091   opStatus convertFromSignExtendedInteger(const integerPart *Input,
1092                                           unsigned int InputSize, bool IsSigned,
1093                                           roundingMode RM) {
1094     APFLOAT_DISPATCH_ON_SEMANTICS(
1095         convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM));
1096   }
1097   opStatus convertFromZeroExtendedInteger(const integerPart *Input,
1098                                           unsigned int InputSize, bool IsSigned,
1099                                           roundingMode RM) {
1100     APFLOAT_DISPATCH_ON_SEMANTICS(
1101         convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM));
1102   }
1103   opStatus convertFromString(StringRef, roundingMode);
1104   APInt bitcastToAPInt() const {
1105     APFLOAT_DISPATCH_ON_SEMANTICS(bitcastToAPInt());
1106   }
1107   double convertToDouble() const { return getIEEE().convertToDouble(); }
1108   float convertToFloat() const { return getIEEE().convertToFloat(); }
1109
1110   bool operator==(const APFloat &) const = delete;
1111
1112   cmpResult compare(const APFloat &RHS) const {
1113     assert(&getSemantics() == &RHS.getSemantics() &&
1114            "Should only compare APFloats with the same semantics");
1115     if (usesLayout<IEEEFloat>(getSemantics()))
1116       return U.IEEE.compare(RHS.U.IEEE);
1117     if (usesLayout<DoubleAPFloat>(getSemantics()))
1118       return U.Double.compare(RHS.U.Double);
1119     llvm_unreachable("Unexpected semantics");
1120   }
1121
1122   bool bitwiseIsEqual(const APFloat &RHS) const {
1123     if (&getSemantics() != &RHS.getSemantics())
1124       return false;
1125     if (usesLayout<IEEEFloat>(getSemantics()))
1126       return U.IEEE.bitwiseIsEqual(RHS.U.IEEE);
1127     if (usesLayout<DoubleAPFloat>(getSemantics()))
1128       return U.Double.bitwiseIsEqual(RHS.U.Double);
1129     llvm_unreachable("Unexpected semantics");
1130   }
1131
1132   /// We don't rely on operator== working on double values, as
1133   /// it returns true for things that are clearly not equal, like -0.0 and 0.0.
1134   /// As such, this method can be used to do an exact bit-for-bit comparison of
1135   /// two floating point values.
1136   ///
1137   /// We leave the version with the double argument here because it's just so
1138   /// convenient to write "2.0" and the like.  Without this function we'd
1139   /// have to duplicate its logic everywhere it's called.
1140   bool isExactlyValue(double V) const {
1141     bool ignored;
1142     APFloat Tmp(V);
1143     Tmp.convert(getSemantics(), APFloat::rmNearestTiesToEven, &ignored);
1144     return bitwiseIsEqual(Tmp);
1145   }
1146
1147   unsigned int convertToHexString(char *DST, unsigned int HexDigits,
1148                                   bool UpperCase, roundingMode RM) const {
1149     APFLOAT_DISPATCH_ON_SEMANTICS(
1150         convertToHexString(DST, HexDigits, UpperCase, RM));
1151   }
1152
1153   bool isZero() const { return getCategory() == fcZero; }
1154   bool isInfinity() const { return getCategory() == fcInfinity; }
1155   bool isNaN() const { return getCategory() == fcNaN; }
1156
1157   bool isNegative() const { return getIEEE().isNegative(); }
1158   bool isDenormal() const { APFLOAT_DISPATCH_ON_SEMANTICS(isDenormal()); }
1159   bool isSignaling() const { return getIEEE().isSignaling(); }
1160
1161   bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
1162   bool isFinite() const { return !isNaN() && !isInfinity(); }
1163
1164   fltCategory getCategory() const { return getIEEE().getCategory(); }
1165   const fltSemantics &getSemantics() const { return *U.semantics; }
1166   bool isNonZero() const { return !isZero(); }
1167   bool isFiniteNonZero() const { return isFinite() && !isZero(); }
1168   bool isPosZero() const { return isZero() && !isNegative(); }
1169   bool isNegZero() const { return isZero() && isNegative(); }
1170   bool isSmallest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isSmallest()); }
1171   bool isLargest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isLargest()); }
1172   bool isInteger() const { APFLOAT_DISPATCH_ON_SEMANTICS(isInteger()); }
1173
1174   APFloat &operator=(const APFloat &RHS) = default;
1175   APFloat &operator=(APFloat &&RHS) = default;
1176
1177   void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
1178                 unsigned FormatMaxPadding = 3, bool TruncateZero = true) const {
1179     APFLOAT_DISPATCH_ON_SEMANTICS(
1180         toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero));
1181   }
1182
1183   void print(raw_ostream &) const;
1184   void dump() const;
1185
1186   bool getExactInverse(APFloat *inv) const {
1187     APFLOAT_DISPATCH_ON_SEMANTICS(getExactInverse(inv));
1188   }
1189
1190   friend hash_code hash_value(const APFloat &Arg);
1191   friend int ilogb(const APFloat &Arg) { return ilogb(Arg.getIEEE()); }
1192   friend APFloat scalbn(APFloat X, int Exp, roundingMode RM);
1193   friend APFloat frexp(const APFloat &X, int &Exp, roundingMode RM);
1194   friend IEEEFloat;
1195   friend DoubleAPFloat;
1196 };
1197
1198 /// See friend declarations above.
1199 ///
1200 /// These additional declarations are required in order to compile LLVM with IBM
1201 /// xlC compiler.
1202 hash_code hash_value(const APFloat &Arg);
1203 inline APFloat scalbn(APFloat X, int Exp, APFloat::roundingMode RM) {
1204   if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1205     return APFloat(scalbn(X.U.IEEE, Exp, RM), X.getSemantics());
1206   if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1207     return APFloat(scalbn(X.U.Double, Exp, RM), X.getSemantics());
1208   llvm_unreachable("Unexpected semantics");
1209 }
1210
1211 /// Equivalent of C standard library function.
1212 ///
1213 /// While the C standard says Exp is an unspecified value for infinity and nan,
1214 /// this returns INT_MAX for infinities, and INT_MIN for NaNs.
1215 inline APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM) {
1216   if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1217     return APFloat(frexp(X.U.IEEE, Exp, RM), X.getSemantics());
1218   if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1219     return APFloat(frexp(X.U.Double, Exp, RM), X.getSemantics());
1220   llvm_unreachable("Unexpected semantics");
1221 }
1222 /// Returns the absolute value of the argument.
1223 inline APFloat abs(APFloat X) {
1224   X.clearSign();
1225   return X;
1226 }
1227
1228 /// Returns the negated value of the argument.
1229 inline APFloat neg(APFloat X) {
1230   X.changeSign();
1231   return X;
1232 }
1233
1234 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
1235 /// both are not NaN. If either argument is a NaN, returns the other argument.
1236 LLVM_READONLY
1237 inline APFloat minnum(const APFloat &A, const APFloat &B) {
1238   if (A.isNaN())
1239     return B;
1240   if (B.isNaN())
1241     return A;
1242   return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
1243 }
1244
1245 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
1246 /// both are not NaN. If either argument is a NaN, returns the other argument.
1247 LLVM_READONLY
1248 inline APFloat maxnum(const APFloat &A, const APFloat &B) {
1249   if (A.isNaN())
1250     return B;
1251   if (B.isNaN())
1252     return A;
1253   return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
1254 }
1255
1256 /// Implements IEEE 754-2018 minimum semantics. Returns the smaller of 2
1257 /// arguments, propagating NaNs and treating -0 as less than +0.
1258 LLVM_READONLY
1259 inline APFloat minimum(const APFloat &A, const APFloat &B) {
1260   if (A.isNaN())
1261     return A;
1262   if (B.isNaN())
1263     return B;
1264   if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1265     return A.isNegative() ? A : B;
1266   return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
1267 }
1268
1269 /// Implements IEEE 754-2018 maximum semantics. Returns the larger of 2
1270 /// arguments, propagating NaNs and treating -0 as less than +0.
1271 LLVM_READONLY
1272 inline APFloat maximum(const APFloat &A, const APFloat &B) {
1273   if (A.isNaN())
1274     return A;
1275   if (B.isNaN())
1276     return B;
1277   if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1278     return A.isNegative() ? B : A;
1279   return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
1280 }
1281
1282 } // namespace llvm
1283
1284 #undef APFLOAT_DISPATCH_ON_SEMANTICS
1285 #endif // LLVM_ADT_APFLOAT_H