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