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/// This file declares a class to represent arbitrary precision floating point
11/// values and provide a variety of arithmetic operations on them.
12///
13//===----------------------------------------------------------------------===//
14
15#ifndef LLVM_ADT_APFLOAT_H
16#define LLVM_ADT_APFLOAT_H
17
18#include "llvm/ADT/APInt.h"
19#include "llvm/ADT/ArrayRef.h"
20#include "llvm/ADT/FloatingPointMode.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
33namespace llvm {
34
35struct fltSemantics;
36class APSInt;
37class StringRef;
38class APFloat;
39class raw_ostream;
40
41template <typename T> class Expected;
42template <typename T> class SmallVectorImpl;
43
44/// Enum that represents what fraction of the LSB truncated bits of an fp number
45/// represent.
46///
47/// This essentially combines the roles of guard and sticky bits.
48enum lostFraction { // Example of truncated bits:
49  lfExactlyZero,    // 000000
50  lfLessThanHalf,   // 0xxxxx  x's not all zero
51  lfExactlyHalf,    // 100000
52  lfMoreThanHalf    // 1xxxxx  x's not all zero
53};
54
55/// A self-contained host- and target-independent arbitrary-precision
56/// floating-point software implementation.
57///
58/// APFloat uses bignum integer arithmetic as provided by static functions in
59/// the APInt class.  The library will work with bignum integers whose parts are
60/// any unsigned type at least 16 bits wide, but 64 bits is recommended.
61///
62/// Written for clarity rather than speed, in particular with a view to use in
63/// the front-end of a cross compiler so that target arithmetic can be correctly
64/// performed on the host.  Performance should nonetheless be reasonable,
65/// particularly for its intended use.  It may be useful as a base
66/// implementation for a run-time library during development of a faster
67/// target-specific one.
68///
69/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
70/// implemented operations.  Currently implemented operations are add, subtract,
71/// multiply, divide, fused-multiply-add, conversion-to-float,
72/// conversion-to-integer and conversion-from-integer.  New rounding modes
73/// (e.g. away from zero) can be added with three or four lines of code.
74///
75/// Four formats are built-in: IEEE single precision, double precision,
76/// quadruple precision, and x87 80-bit extended double (when operating with
77/// full extended precision).  Adding a new format that obeys IEEE semantics
78/// only requires adding two lines of code: a declaration and definition of the
79/// format.
80///
81/// All operations return the status of that operation as an exception bit-mask,
82/// so multiple operations can be done consecutively with their results or-ed
83/// together.  The returned status can be useful for compiler diagnostics; e.g.,
84/// inexact, underflow and overflow can be easily diagnosed on constant folding,
85/// and compiler optimizers can determine what exceptions would be raised by
86/// folding operations and optimize, or perhaps not optimize, accordingly.
87///
88/// At present, underflow tininess is detected after rounding; it should be
89/// straight forward to add support for the before-rounding case too.
90///
91/// The library reads hexadecimal floating point numbers as per C99, and
92/// correctly rounds if necessary according to the specified rounding mode.
93/// Syntax is required to have been validated by the caller.  It also converts
94/// floating point numbers to hexadecimal text as per the C99 %a and %A
95/// conversions.  The output precision (or alternatively the natural minimal
96/// precision) can be specified; if the requested precision is less than the
97/// natural precision the output is correctly rounded for the specified rounding
98/// mode.
99///
100/// It also reads decimal floating point numbers and correctly rounds according
101/// to the specified rounding mode.
102///
103/// Conversion to decimal text is not currently implemented.
104///
105/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
106/// signed exponent, and the significand as an array of integer parts.  After
107/// normalization of a number of precision P the exponent is within the range of
108/// the format, and if the number is not denormal the P-th bit of the
109/// significand is set as an explicit integer bit.  For denormals the most
110/// significant bit is shifted right so that the exponent is maintained at the
111/// format's minimum, so that the smallest denormal has just the least
112/// significant bit of the significand set.  The sign of zeroes and infinities
113/// is significant; the exponent and significand of such numbers is not stored,
114/// but has a known implicit (deterministic) value: 0 for the significands, 0
115/// for zero exponent, all 1 bits for infinity exponent.  For NaNs the sign and
116/// significand are deterministic, although not really meaningful, and preserved
117/// in non-conversion operations.  The exponent is implicitly all 1 bits.
118///
119/// APFloat does not provide any exception handling beyond default exception
120/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
121/// by encoding Signaling NaNs with the first bit of its trailing significand as
122/// 0.
123///
124/// TODO
125/// ====
126///
127/// Some features that may or may not be worth adding:
128///
129/// Binary to decimal conversion (hard).
130///
131/// Optional ability to detect underflow tininess before rounding.
132///
133/// New formats: x87 in single and double precision mode (IEEE apart from
134/// extended exponent range) (hard).
135///
136/// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
137///
138
139// This is the common type definitions shared by APFloat and its internal
140// implementation classes. This struct should not define any non-static data
141// members.
142struct APFloatBase {
143  typedef APInt::WordType integerPart;
144  static constexpr unsigned integerPartWidth = APInt::APINT_BITS_PER_WORD;
145
146  /// A signed type to represent a floating point numbers unbiased exponent.
147  typedef int32_t ExponentType;
148
149  /// \name Floating Point Semantics.
150  /// @{
151  enum Semantics {
152    S_IEEEhalf,
153    S_BFloat,
154    S_IEEEsingle,
155    S_IEEEdouble,
156    S_IEEEquad,
157    S_PPCDoubleDouble,
158    // 8-bit floating point number following IEEE-754 conventions with bit
159    // layout S1E5M2 as described in https://arxiv.org/abs/2209.05433.
160    S_Float8E5M2,
161    // 8-bit floating point number mostly following IEEE-754 conventions
162    // and bit layout S1E5M2 described in https://arxiv.org/abs/2206.02915,
163    // with expanded range and with no infinity or signed zero.
164    // NaN is represented as negative zero. (FN -> Finite, UZ -> unsigned zero).
165    // This format's exponent bias is 16, instead of the 15 (2 ** (5 - 1) - 1)
166    // that IEEE precedent would imply.
167    S_Float8E5M2FNUZ,
168    // 8-bit floating point number mostly following IEEE-754 conventions with
169    // bit layout S1E4M3 as described in https://arxiv.org/abs/2209.05433.
170    // Unlike IEEE-754 types, there are no infinity values, and NaN is
171    // represented with the exponent and mantissa bits set to all 1s.
172    S_Float8E4M3FN,
173    // 8-bit floating point number mostly following IEEE-754 conventions
174    // and bit layout S1E4M3 described in https://arxiv.org/abs/2206.02915,
175    // with expanded range and with no infinity or signed zero.
176    // NaN is represented as negative zero. (FN -> Finite, UZ -> unsigned zero).
177    // This format's exponent bias is 8, instead of the 7 (2 ** (4 - 1) - 1)
178    // that IEEE precedent would imply.
179    S_Float8E4M3FNUZ,
180    // 8-bit floating point number mostly following IEEE-754 conventions
181    // and bit layout S1E4M3 with expanded range and with no infinity or signed
182    // zero.
183    // NaN is represented as negative zero. (FN -> Finite, UZ -> unsigned zero).
184    // This format's exponent bias is 11, instead of the 7 (2 ** (4 - 1) - 1)
185    // that IEEE precedent would imply.
186    S_Float8E4M3B11FNUZ,
187    // Floating point number that occupies 32 bits or less of storage, providing
188    // improved range compared to half (16-bit) formats, at (potentially)
189    // greater throughput than single precision (32-bit) formats.
190    S_FloatTF32,
191
192    S_x87DoubleExtended,
193    S_MaxSemantics = S_x87DoubleExtended,
194  };
195
196  static const llvm::fltSemantics &EnumToSemantics(Semantics S);
197  static Semantics SemanticsToEnum(const llvm::fltSemantics &Sem);
198
199  static const fltSemantics &IEEEhalf() LLVM_READNONE;
200  static const fltSemantics &BFloat() LLVM_READNONE;
201  static const fltSemantics &IEEEsingle() LLVM_READNONE;
202  static const fltSemantics &IEEEdouble() LLVM_READNONE;
203  static const fltSemantics &IEEEquad() LLVM_READNONE;
204  static const fltSemantics &PPCDoubleDouble() LLVM_READNONE;
205  static const fltSemantics &Float8E5M2() LLVM_READNONE;
206  static const fltSemantics &Float8E5M2FNUZ() LLVM_READNONE;
207  static const fltSemantics &Float8E4M3FN() LLVM_READNONE;
208  static const fltSemantics &Float8E4M3FNUZ() LLVM_READNONE;
209  static const fltSemantics &Float8E4M3B11FNUZ() LLVM_READNONE;
210  static const fltSemantics &FloatTF32() LLVM_READNONE;
211  static const fltSemantics &x87DoubleExtended() LLVM_READNONE;
212
213  /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
214  /// anything real.
215  static const fltSemantics &Bogus() LLVM_READNONE;
216
217  /// @}
218
219  /// IEEE-754R 5.11: Floating Point Comparison Relations.
220  enum cmpResult {
221    cmpLessThan,
222    cmpEqual,
223    cmpGreaterThan,
224    cmpUnordered
225  };
226
227  /// IEEE-754R 4.3: Rounding-direction attributes.
228  using roundingMode = llvm::RoundingMode;
229
230  static constexpr roundingMode rmNearestTiesToEven =
231                                                RoundingMode::NearestTiesToEven;
232  static constexpr roundingMode rmTowardPositive = RoundingMode::TowardPositive;
233  static constexpr roundingMode rmTowardNegative = RoundingMode::TowardNegative;
234  static constexpr roundingMode rmTowardZero     = RoundingMode::TowardZero;
235  static constexpr roundingMode rmNearestTiesToAway =
236                                                RoundingMode::NearestTiesToAway;
237
238  /// IEEE-754R 7: Default exception handling.
239  ///
240  /// opUnderflow or opOverflow are always returned or-ed with opInexact.
241  ///
242  /// APFloat models this behavior specified by IEEE-754:
243  ///   "For operations producing results in floating-point format, the default
244  ///    result of an operation that signals the invalid operation exception
245  ///    shall be a quiet NaN."
246  enum opStatus {
247    opOK = 0x00,
248    opInvalidOp = 0x01,
249    opDivByZero = 0x02,
250    opOverflow = 0x04,
251    opUnderflow = 0x08,
252    opInexact = 0x10
253  };
254
255  /// Category of internally-represented number.
256  enum fltCategory {
257    fcInfinity,
258    fcNaN,
259    fcNormal,
260    fcZero
261  };
262
263  /// Convenience enum used to construct an uninitialized APFloat.
264  enum uninitializedTag {
265    uninitialized
266  };
267
268  /// Enumeration of \c ilogb error results.
269  enum IlogbErrorKinds {
270    IEK_Zero = INT_MIN + 1,
271    IEK_NaN = INT_MIN,
272    IEK_Inf = INT_MAX
273  };
274
275  static unsigned int semanticsPrecision(const fltSemantics &);
276  static ExponentType semanticsMinExponent(const fltSemantics &);
277  static ExponentType semanticsMaxExponent(const fltSemantics &);
278  static unsigned int semanticsSizeInBits(const fltSemantics &);
279  static unsigned int semanticsIntSizeInBits(const fltSemantics&, bool);
280
281  // Returns true if any number described by \p Src can be precisely represented
282  // by a normal (not subnormal) value in \p Dst.
283  static bool isRepresentableAsNormalIn(const fltSemantics &Src,
284                                        const fltSemantics &Dst);
285
286  /// Returns the size of the floating point number (in bits) in the given
287  /// semantics.
288  static unsigned getSizeInBits(const fltSemantics &Sem);
289};
290
291namespace detail {
292
293class IEEEFloat final : public APFloatBase {
294public:
295  /// \name Constructors
296  /// @{
297
298  IEEEFloat(const fltSemantics &); // Default construct to +0.0
299  IEEEFloat(const fltSemantics &, integerPart);
300  IEEEFloat(const fltSemantics &, uninitializedTag);
301  IEEEFloat(const fltSemantics &, const APInt &);
302  explicit IEEEFloat(double d);
303  explicit IEEEFloat(float f);
304  IEEEFloat(const IEEEFloat &);
305  IEEEFloat(IEEEFloat &&);
306  ~IEEEFloat();
307
308  /// @}
309
310  /// Returns whether this instance allocated memory.
311  bool needsCleanup() const { return partCount() > 1; }
312
313  /// \name Convenience "constructors"
314  /// @{
315
316  /// @}
317
318  /// \name Arithmetic
319  /// @{
320
321  opStatus add(const IEEEFloat &, roundingMode);
322  opStatus subtract(const IEEEFloat &, roundingMode);
323  opStatus multiply(const IEEEFloat &, roundingMode);
324  opStatus divide(const IEEEFloat &, roundingMode);
325  /// IEEE remainder.
326  opStatus remainder(const IEEEFloat &);
327  /// C fmod, or llvm frem.
328  opStatus mod(const IEEEFloat &);
329  opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);
330  opStatus roundToIntegral(roundingMode);
331  /// IEEE-754R 5.3.1: nextUp/nextDown.
332  opStatus next(bool nextDown);
333
334  /// @}
335
336  /// \name Sign operations.
337  /// @{
338
339  void changeSign();
340
341  /// @}
342
343  /// \name Conversions
344  /// @{
345
346  opStatus convert(const fltSemantics &, roundingMode, bool *);
347  opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,
348                            roundingMode, bool *) const;
349  opStatus convertFromAPInt(const APInt &, bool, roundingMode);
350  opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
351                                          bool, roundingMode);
352  opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
353                                          bool, roundingMode);
354  Expected<opStatus> convertFromString(StringRef, roundingMode);
355  APInt bitcastToAPInt() const;
356  double convertToDouble() const;
357  float convertToFloat() const;
358
359  /// @}
360
361  /// The definition of equality is not straightforward for floating point, so
362  /// we won't use operator==.  Use one of the following, or write whatever it
363  /// is you really mean.
364  bool operator==(const IEEEFloat &) const = delete;
365
366  /// IEEE comparison with another floating point number (NaNs compare
367  /// unordered, 0==-0).
368  cmpResult compare(const IEEEFloat &) const;
369
370  /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
371  bool bitwiseIsEqual(const IEEEFloat &) const;
372
373  /// Write out a hexadecimal representation of the floating point value to DST,
374  /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
375  /// Return the number of characters written, excluding the terminating NUL.
376  unsigned int convertToHexString(char *dst, unsigned int hexDigits,
377                                  bool upperCase, roundingMode) const;
378
379  /// \name IEEE-754R 5.7.2 General operations.
380  /// @{
381
382  /// IEEE-754R isSignMinus: Returns true if and only if the current value is
383  /// negative.
384  ///
385  /// This applies to zeros and NaNs as well.
386  bool isNegative() const { return sign; }
387
388  /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
389  ///
390  /// This implies that the current value of the float is not zero, subnormal,
391  /// infinite, or NaN following the definition of normality from IEEE-754R.
392  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
393
394  /// Returns true if and only if the current value is zero, subnormal, or
395  /// normal.
396  ///
397  /// This means that the value is not infinite or NaN.
398  bool isFinite() const { return !isNaN() && !isInfinity(); }
399
400  /// Returns true if and only if the float is plus or minus zero.
401  bool isZero() const { return category == fcZero; }
402
403  /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
404  /// denormal.
405  bool isDenormal() const;
406
407  /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
408  bool isInfinity() const { return category == fcInfinity; }
409
410  /// Returns true if and only if the float is a quiet or signaling NaN.
411  bool isNaN() const { return category == fcNaN; }
412
413  /// Returns true if and only if the float is a signaling NaN.
414  bool isSignaling() const;
415
416  /// @}
417
418  /// \name Simple Queries
419  /// @{
420
421  fltCategory getCategory() const { return category; }
422  const fltSemantics &getSemantics() const { return *semantics; }
423  bool isNonZero() const { return category != fcZero; }
424  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
425  bool isPosZero() const { return isZero() && !isNegative(); }
426  bool isNegZero() const { return isZero() && isNegative(); }
427
428  /// Returns true if and only if the number has the smallest possible non-zero
429  /// magnitude in the current semantics.
430  bool isSmallest() const;
431
432  /// Returns true if this is the smallest (by magnitude) normalized finite
433  /// number in the given semantics.
434  bool isSmallestNormalized() const;
435
436  /// Returns true if and only if the number has the largest possible finite
437  /// magnitude in the current semantics.
438  bool isLargest() const;
439
440  /// Returns true if and only if the number is an exact integer.
441  bool isInteger() const;
442
443  /// @}
444
445  IEEEFloat &operator=(const IEEEFloat &);
446  IEEEFloat &operator=(IEEEFloat &&);
447
448  /// Overload to compute a hash code for an APFloat value.
449  ///
450  /// Note that the use of hash codes for floating point values is in general
451  /// frought with peril. Equality is hard to define for these values. For
452  /// example, should negative and positive zero hash to different codes? Are
453  /// they equal or not? This hash value implementation specifically
454  /// emphasizes producing different codes for different inputs in order to
455  /// be used in canonicalization and memoization. As such, equality is
456  /// bitwiseIsEqual, and 0 != -0.
457  friend hash_code hash_value(const IEEEFloat &Arg);
458
459  /// Converts this value into a decimal string.
460  ///
461  /// \param FormatPrecision The maximum number of digits of
462  ///   precision to output.  If there are fewer digits available,
463  ///   zero padding will not be used unless the value is
464  ///   integral and small enough to be expressed in
465  ///   FormatPrecision digits.  0 means to use the natural
466  ///   precision of the number.
467  /// \param FormatMaxPadding The maximum number of zeros to
468  ///   consider inserting before falling back to scientific
469  ///   notation.  0 means to always use scientific notation.
470  ///
471  /// \param TruncateZero Indicate whether to remove the trailing zero in
472  ///   fraction part or not. Also setting this parameter to false forcing
473  ///   producing of output more similar to default printf behavior.
474  ///   Specifically the lower e is used as exponent delimiter and exponent
475  ///   always contains no less than two digits.
476  ///
477  /// Number       Precision    MaxPadding      Result
478  /// ------       ---------    ----------      ------
479  /// 1.01E+4              5             2       10100
480  /// 1.01E+4              4             2       1.01E+4
481  /// 1.01E+4              5             1       1.01E+4
482  /// 1.01E-2              5             2       0.0101
483  /// 1.01E-2              4             2       0.0101
484  /// 1.01E-2              4             1       1.01E-2
485  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
486                unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;
487
488  /// If this value has an exact multiplicative inverse, store it in inv and
489  /// return true.
490  bool getExactInverse(APFloat *inv) const;
491
492  // If this is an exact power of two, return the exponent while ignoring the
493  // sign bit. If it's not an exact power of 2, return INT_MIN
494  LLVM_READONLY
495  int getExactLog2Abs() const;
496
497  // If this is an exact power of two, return the exponent. If it's not an exact
498  // power of 2, return INT_MIN
499  LLVM_READONLY
500  int getExactLog2() const {
501    return isNegative() ? INT_MIN : getExactLog2Abs();
502  }
503
504  /// Returns the exponent of the internal representation of the APFloat.
505  ///
506  /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
507  /// For special APFloat values, this returns special error codes:
508  ///
509  ///   NaN -> \c IEK_NaN
510  ///   0   -> \c IEK_Zero
511  ///   Inf -> \c IEK_Inf
512  ///
513  friend int ilogb(const IEEEFloat &Arg);
514
515  /// Returns: X * 2^Exp for integral exponents.
516  friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);
517
518  friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);
519
520  /// \name Special value setters.
521  /// @{
522
523  void makeLargest(bool Neg = false);
524  void makeSmallest(bool Neg = false);
525  void makeNaN(bool SNaN = false, bool Neg = false,
526               const APInt *fill = nullptr);
527  void makeInf(bool Neg = false);
528  void makeZero(bool Neg = false);
529  void makeQuiet();
530
531  /// Returns the smallest (by magnitude) normalized finite number in the given
532  /// semantics.
533  ///
534  /// \param Negative - True iff the number should be negative
535  void makeSmallestNormalized(bool Negative = false);
536
537  /// @}
538
539  cmpResult compareAbsoluteValue(const IEEEFloat &) const;
540
541private:
542  /// \name Simple Queries
543  /// @{
544
545  integerPart *significandParts();
546  const integerPart *significandParts() const;
547  unsigned int partCount() const;
548
549  /// @}
550
551  /// \name Significand operations.
552  /// @{
553
554  integerPart addSignificand(const IEEEFloat &);
555  integerPart subtractSignificand(const IEEEFloat &, integerPart);
556  lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
557  lostFraction multiplySignificand(const IEEEFloat &, IEEEFloat);
558  lostFraction multiplySignificand(const IEEEFloat&);
559  lostFraction divideSignificand(const IEEEFloat &);
560  void incrementSignificand();
561  void initialize(const fltSemantics *);
562  void shiftSignificandLeft(unsigned int);
563  lostFraction shiftSignificandRight(unsigned int);
564  unsigned int significandLSB() const;
565  unsigned int significandMSB() const;
566  void zeroSignificand();
567  /// Return true if the significand excluding the integral bit is all ones.
568  bool isSignificandAllOnes() const;
569  bool isSignificandAllOnesExceptLSB() const;
570  /// Return true if the significand excluding the integral bit is all zeros.
571  bool isSignificandAllZeros() const;
572  bool isSignificandAllZerosExceptMSB() const;
573
574  /// @}
575
576  /// \name Arithmetic on special values.
577  /// @{
578
579  opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);
580  opStatus divideSpecials(const IEEEFloat &);
581  opStatus multiplySpecials(const IEEEFloat &);
582  opStatus modSpecials(const IEEEFloat &);
583  opStatus remainderSpecials(const IEEEFloat&);
584
585  /// @}
586
587  /// \name Miscellany
588  /// @{
589
590  bool convertFromStringSpecials(StringRef str);
591  opStatus normalize(roundingMode, lostFraction);
592  opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);
593  opStatus handleOverflow(roundingMode);
594  bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
595  opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,
596                                        unsigned int, bool, roundingMode,
597                                        bool *) const;
598  opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
599                                    roundingMode);
600  Expected<opStatus> convertFromHexadecimalString(StringRef, roundingMode);
601  Expected<opStatus> convertFromDecimalString(StringRef, roundingMode);
602  char *convertNormalToHexString(char *, unsigned int, bool,
603                                 roundingMode) const;
604  opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
605                                        roundingMode);
606  ExponentType exponentNaN() const;
607  ExponentType exponentInf() const;
608  ExponentType exponentZero() const;
609
610  /// @}
611
612  template <const fltSemantics &S> APInt convertIEEEFloatToAPInt() const;
613  APInt convertHalfAPFloatToAPInt() const;
614  APInt convertBFloatAPFloatToAPInt() const;
615  APInt convertFloatAPFloatToAPInt() const;
616  APInt convertDoubleAPFloatToAPInt() const;
617  APInt convertQuadrupleAPFloatToAPInt() const;
618  APInt convertF80LongDoubleAPFloatToAPInt() const;
619  APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
620  APInt convertFloat8E5M2APFloatToAPInt() const;
621  APInt convertFloat8E5M2FNUZAPFloatToAPInt() const;
622  APInt convertFloat8E4M3FNAPFloatToAPInt() const;
623  APInt convertFloat8E4M3FNUZAPFloatToAPInt() const;
624  APInt convertFloat8E4M3B11FNUZAPFloatToAPInt() const;
625  APInt convertFloatTF32APFloatToAPInt() const;
626  void initFromAPInt(const fltSemantics *Sem, const APInt &api);
627  template <const fltSemantics &S> void initFromIEEEAPInt(const APInt &api);
628  void initFromHalfAPInt(const APInt &api);
629  void initFromBFloatAPInt(const APInt &api);
630  void initFromFloatAPInt(const APInt &api);
631  void initFromDoubleAPInt(const APInt &api);
632  void initFromQuadrupleAPInt(const APInt &api);
633  void initFromF80LongDoubleAPInt(const APInt &api);
634  void initFromPPCDoubleDoubleAPInt(const APInt &api);
635  void initFromFloat8E5M2APInt(const APInt &api);
636  void initFromFloat8E5M2FNUZAPInt(const APInt &api);
637  void initFromFloat8E4M3FNAPInt(const APInt &api);
638  void initFromFloat8E4M3FNUZAPInt(const APInt &api);
639  void initFromFloat8E4M3B11FNUZAPInt(const APInt &api);
640  void initFromFloatTF32APInt(const APInt &api);
641
642  void assign(const IEEEFloat &);
643  void copySignificand(const IEEEFloat &);
644  void freeSignificand();
645
646  /// Note: this must be the first data member.
647  /// The semantics that this value obeys.
648  const fltSemantics *semantics;
649
650  /// A binary fraction with an explicit integer bit.
651  ///
652  /// The significand must be at least one bit wider than the target precision.
653  union Significand {
654    integerPart part;
655    integerPart *parts;
656  } significand;
657
658  /// The signed unbiased exponent of the value.
659  ExponentType exponent;
660
661  /// What kind of floating point number this is.
662  ///
663  /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
664  /// Using the extra bit keeps it from failing under VisualStudio.
665  fltCategory category : 3;
666
667  /// Sign bit of the number.
668  unsigned int sign : 1;
669};
670
671hash_code hash_value(const IEEEFloat &Arg);
672int ilogb(const IEEEFloat &Arg);
673IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode);
674IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);
675
676// This mode implements more precise float in terms of two APFloats.
677// The interface and layout is designed for arbitrary underlying semantics,
678// though currently only PPCDoubleDouble semantics are supported, whose
679// corresponding underlying semantics are IEEEdouble.
680class DoubleAPFloat final : public APFloatBase {
681  // Note: this must be the first data member.
682  const fltSemantics *Semantics;
683  std::unique_ptr<APFloat[]> Floats;
684
685  opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,
686                   const APFloat &cc, roundingMode RM);
687
688  opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,
689                          DoubleAPFloat &Out, roundingMode RM);
690
691public:
692  DoubleAPFloat(const fltSemantics &S);
693  DoubleAPFloat(const fltSemantics &S, uninitializedTag);
694  DoubleAPFloat(const fltSemantics &S, integerPart);
695  DoubleAPFloat(const fltSemantics &S, const APInt &I);
696  DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);
697  DoubleAPFloat(const DoubleAPFloat &RHS);
698  DoubleAPFloat(DoubleAPFloat &&RHS);
699
700  DoubleAPFloat &operator=(const DoubleAPFloat &RHS);
701  inline DoubleAPFloat &operator=(DoubleAPFloat &&RHS);
702
703  bool needsCleanup() const { return Floats != nullptr; }
704
705  inline APFloat &getFirst();
706  inline const APFloat &getFirst() const;
707  inline APFloat &getSecond();
708  inline const APFloat &getSecond() const;
709
710  opStatus add(const DoubleAPFloat &RHS, roundingMode RM);
711  opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);
712  opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);
713  opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);
714  opStatus remainder(const DoubleAPFloat &RHS);
715  opStatus mod(const DoubleAPFloat &RHS);
716  opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
717                            const DoubleAPFloat &Addend, roundingMode RM);
718  opStatus roundToIntegral(roundingMode RM);
719  void changeSign();
720  cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;
721
722  fltCategory getCategory() const;
723  bool isNegative() const;
724
725  void makeInf(bool Neg);
726  void makeZero(bool Neg);
727  void makeLargest(bool Neg);
728  void makeSmallest(bool Neg);
729  void makeSmallestNormalized(bool Neg);
730  void makeNaN(bool SNaN, bool Neg, const APInt *fill);
731
732  cmpResult compare(const DoubleAPFloat &RHS) const;
733  bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;
734  APInt bitcastToAPInt() const;
735  Expected<opStatus> convertFromString(StringRef, roundingMode);
736  opStatus next(bool nextDown);
737
738  opStatus convertToInteger(MutableArrayRef<integerPart> Input,
739                            unsigned int Width, bool IsSigned, roundingMode RM,
740                            bool *IsExact) const;
741  opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);
742  opStatus convertFromSignExtendedInteger(const integerPart *Input,
743                                          unsigned int InputSize, bool IsSigned,
744                                          roundingMode RM);
745  opStatus convertFromZeroExtendedInteger(const integerPart *Input,
746                                          unsigned int InputSize, bool IsSigned,
747                                          roundingMode RM);
748  unsigned int convertToHexString(char *DST, unsigned int HexDigits,
749                                  bool UpperCase, roundingMode RM) const;
750
751  bool isDenormal() const;
752  bool isSmallest() const;
753  bool isSmallestNormalized() const;
754  bool isLargest() const;
755  bool isInteger() const;
756
757  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
758                unsigned FormatMaxPadding, bool TruncateZero = true) const;
759
760  bool getExactInverse(APFloat *inv) const;
761
762  LLVM_READONLY
763  int getExactLog2() const;
764  LLVM_READONLY
765  int getExactLog2Abs() const;
766
767  friend DoubleAPFloat scalbn(const DoubleAPFloat &X, int Exp, roundingMode);
768  friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);
769  friend hash_code hash_value(const DoubleAPFloat &Arg);
770};
771
772hash_code hash_value(const DoubleAPFloat &Arg);
773DoubleAPFloat scalbn(const DoubleAPFloat &Arg, int Exp, IEEEFloat::roundingMode RM);
774DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, IEEEFloat::roundingMode);
775
776} // End detail namespace
777
778// This is a interface class that is currently forwarding functionalities from
779// detail::IEEEFloat.
780class APFloat : public APFloatBase {
781  typedef detail::IEEEFloat IEEEFloat;
782  typedef detail::DoubleAPFloat DoubleAPFloat;
783
784  static_assert(std::is_standard_layout<IEEEFloat>::value);
785
786  union Storage {
787    const fltSemantics *semantics;
788    IEEEFloat IEEE;
789    DoubleAPFloat Double;
790
791    explicit Storage(IEEEFloat F, const fltSemantics &S);
792    explicit Storage(DoubleAPFloat F, const fltSemantics &S)
793        : Double(std::move(F)) {
794      assert(&S == &PPCDoubleDouble());
795    }
796
797    template <typename... ArgTypes>
798    Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {
799      if (usesLayout<IEEEFloat>(Semantics)) {
800        new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);
801        return;
802      }
803      if (usesLayout<DoubleAPFloat>(Semantics)) {
804        new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);
805        return;
806      }
807      llvm_unreachable("Unexpected semantics");
808    }
809
810    ~Storage() {
811      if (usesLayout<IEEEFloat>(*semantics)) {
812        IEEE.~IEEEFloat();
813        return;
814      }
815      if (usesLayout<DoubleAPFloat>(*semantics)) {
816        Double.~DoubleAPFloat();
817        return;
818      }
819      llvm_unreachable("Unexpected semantics");
820    }
821
822    Storage(const Storage &RHS) {
823      if (usesLayout<IEEEFloat>(*RHS.semantics)) {
824        new (this) IEEEFloat(RHS.IEEE);
825        return;
826      }
827      if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
828        new (this) DoubleAPFloat(RHS.Double);
829        return;
830      }
831      llvm_unreachable("Unexpected semantics");
832    }
833
834    Storage(Storage &&RHS) {
835      if (usesLayout<IEEEFloat>(*RHS.semantics)) {
836        new (this) IEEEFloat(std::move(RHS.IEEE));
837        return;
838      }
839      if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
840        new (this) DoubleAPFloat(std::move(RHS.Double));
841        return;
842      }
843      llvm_unreachable("Unexpected semantics");
844    }
845
846    Storage &operator=(const Storage &RHS) {
847      if (usesLayout<IEEEFloat>(*semantics) &&
848          usesLayout<IEEEFloat>(*RHS.semantics)) {
849        IEEE = RHS.IEEE;
850      } else if (usesLayout<DoubleAPFloat>(*semantics) &&
851                 usesLayout<DoubleAPFloat>(*RHS.semantics)) {
852        Double = RHS.Double;
853      } else if (this != &RHS) {
854        this->~Storage();
855        new (this) Storage(RHS);
856      }
857      return *this;
858    }
859
860    Storage &operator=(Storage &&RHS) {
861      if (usesLayout<IEEEFloat>(*semantics) &&
862          usesLayout<IEEEFloat>(*RHS.semantics)) {
863        IEEE = std::move(RHS.IEEE);
864      } else if (usesLayout<DoubleAPFloat>(*semantics) &&
865                 usesLayout<DoubleAPFloat>(*RHS.semantics)) {
866        Double = std::move(RHS.Double);
867      } else if (this != &RHS) {
868        this->~Storage();
869        new (this) Storage(std::move(RHS));
870      }
871      return *this;
872    }
873  } U;
874
875  template <typename T> static bool usesLayout(const fltSemantics &Semantics) {
876    static_assert(std::is_same<T, IEEEFloat>::value ||
877                  std::is_same<T, DoubleAPFloat>::value);
878    if (std::is_same<T, DoubleAPFloat>::value) {
879      return &Semantics == &PPCDoubleDouble();
880    }
881    return &Semantics != &PPCDoubleDouble();
882  }
883
884  IEEEFloat &getIEEE() {
885    if (usesLayout<IEEEFloat>(*U.semantics))
886      return U.IEEE;
887    if (usesLayout<DoubleAPFloat>(*U.semantics))
888      return U.Double.getFirst().U.IEEE;
889    llvm_unreachable("Unexpected semantics");
890  }
891
892  const IEEEFloat &getIEEE() const {
893    if (usesLayout<IEEEFloat>(*U.semantics))
894      return U.IEEE;
895    if (usesLayout<DoubleAPFloat>(*U.semantics))
896      return U.Double.getFirst().U.IEEE;
897    llvm_unreachable("Unexpected semantics");
898  }
899
900  void makeZero(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeZero(Neg)); }
901
902  void makeInf(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeInf(Neg)); }
903
904  void makeNaN(bool SNaN, bool Neg, const APInt *fill) {
905    APFLOAT_DISPATCH_ON_SEMANTICS(makeNaN(SNaN, Neg, fill));
906  }
907
908  void makeLargest(bool Neg) {
909    APFLOAT_DISPATCH_ON_SEMANTICS(makeLargest(Neg));
910  }
911
912  void makeSmallest(bool Neg) {
913    APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallest(Neg));
914  }
915
916  void makeSmallestNormalized(bool Neg) {
917    APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallestNormalized(Neg));
918  }
919
920  explicit APFloat(IEEEFloat F, const fltSemantics &S) : U(std::move(F), S) {}
921  explicit APFloat(DoubleAPFloat F, const fltSemantics &S)
922      : U(std::move(F), S) {}
923
924  cmpResult compareAbsoluteValue(const APFloat &RHS) const {
925    assert(&getSemantics() == &RHS.getSemantics() &&
926           "Should only compare APFloats with the same semantics");
927    if (usesLayout<IEEEFloat>(getSemantics()))
928      return U.IEEE.compareAbsoluteValue(RHS.U.IEEE);
929    if (usesLayout<DoubleAPFloat>(getSemantics()))
930      return U.Double.compareAbsoluteValue(RHS.U.Double);
931    llvm_unreachable("Unexpected semantics");
932  }
933
934public:
935  APFloat(const fltSemantics &Semantics) : U(Semantics) {}
936  APFloat(const fltSemantics &Semantics, StringRef S);
937  APFloat(const fltSemantics &Semantics, integerPart I) : U(Semantics, I) {}
938  template <typename T,
939            typename = std::enable_if_t<std::is_floating_point<T>::value>>
940  APFloat(const fltSemantics &Semantics, T V) = delete;
941  // TODO: Remove this constructor. This isn't faster than the first one.
942  APFloat(const fltSemantics &Semantics, uninitializedTag)
943      : U(Semantics, uninitialized) {}
944  APFloat(const fltSemantics &Semantics, const APInt &I) : U(Semantics, I) {}
945  explicit APFloat(double d) : U(IEEEFloat(d), IEEEdouble()) {}
946  explicit APFloat(float f) : U(IEEEFloat(f), IEEEsingle()) {}
947  APFloat(const APFloat &RHS) = default;
948  APFloat(APFloat &&RHS) = default;
949
950  ~APFloat() = default;
951
952  bool needsCleanup() const { APFLOAT_DISPATCH_ON_SEMANTICS(needsCleanup()); }
953
954  /// Factory for Positive and Negative Zero.
955  ///
956  /// \param Negative True iff the number should be negative.
957  static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
958    APFloat Val(Sem, uninitialized);
959    Val.makeZero(Negative);
960    return Val;
961  }
962
963  /// Factory for Positive and Negative Infinity.
964  ///
965  /// \param Negative True iff the number should be negative.
966  static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
967    APFloat Val(Sem, uninitialized);
968    Val.makeInf(Negative);
969    return Val;
970  }
971
972  /// Factory for NaN values.
973  ///
974  /// \param Negative - True iff the NaN generated should be negative.
975  /// \param payload - The unspecified fill bits for creating the NaN, 0 by
976  /// default.  The value is truncated as necessary.
977  static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
978                        uint64_t payload = 0) {
979    if (payload) {
980      APInt intPayload(64, payload);
981      return getQNaN(Sem, Negative, &intPayload);
982    } else {
983      return getQNaN(Sem, Negative, nullptr);
984    }
985  }
986
987  /// Factory for QNaN values.
988  static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
989                         const APInt *payload = nullptr) {
990    APFloat Val(Sem, uninitialized);
991    Val.makeNaN(false, Negative, payload);
992    return Val;
993  }
994
995  /// Factory for SNaN values.
996  static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
997                         const APInt *payload = nullptr) {
998    APFloat Val(Sem, uninitialized);
999    Val.makeNaN(true, Negative, payload);
1000    return Val;
1001  }
1002
1003  /// Returns the largest finite number in the given semantics.
1004  ///
1005  /// \param Negative - True iff the number should be negative
1006  static APFloat getLargest(const fltSemantics &Sem, bool Negative = false) {
1007    APFloat Val(Sem, uninitialized);
1008    Val.makeLargest(Negative);
1009    return Val;
1010  }
1011
1012  /// Returns the smallest (by magnitude) finite number in the given semantics.
1013  /// Might be denormalized, which implies a relative loss of precision.
1014  ///
1015  /// \param Negative - True iff the number should be negative
1016  static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false) {
1017    APFloat Val(Sem, uninitialized);
1018    Val.makeSmallest(Negative);
1019    return Val;
1020  }
1021
1022  /// Returns the smallest (by magnitude) normalized finite number in the given
1023  /// semantics.
1024  ///
1025  /// \param Negative - True iff the number should be negative
1026  static APFloat getSmallestNormalized(const fltSemantics &Sem,
1027                                       bool Negative = false) {
1028    APFloat Val(Sem, uninitialized);
1029    Val.makeSmallestNormalized(Negative);
1030    return Val;
1031  }
1032
1033  /// Returns a float which is bitcasted from an all one value int.
1034  ///
1035  /// \param Semantics - type float semantics
1036  static APFloat getAllOnesValue(const fltSemantics &Semantics);
1037
1038  /// Used to insert APFloat objects, or objects that contain APFloat objects,
1039  /// into FoldingSets.
1040  void Profile(FoldingSetNodeID &NID) const;
1041
1042  opStatus add(const APFloat &RHS, roundingMode RM) {
1043    assert(&getSemantics() == &RHS.getSemantics() &&
1044           "Should only call on two APFloats with the same semantics");
1045    if (usesLayout<IEEEFloat>(getSemantics()))
1046      return U.IEEE.add(RHS.U.IEEE, RM);
1047    if (usesLayout<DoubleAPFloat>(getSemantics()))
1048      return U.Double.add(RHS.U.Double, RM);
1049    llvm_unreachable("Unexpected semantics");
1050  }
1051  opStatus subtract(const APFloat &RHS, roundingMode RM) {
1052    assert(&getSemantics() == &RHS.getSemantics() &&
1053           "Should only call on two APFloats with the same semantics");
1054    if (usesLayout<IEEEFloat>(getSemantics()))
1055      return U.IEEE.subtract(RHS.U.IEEE, RM);
1056    if (usesLayout<DoubleAPFloat>(getSemantics()))
1057      return U.Double.subtract(RHS.U.Double, RM);
1058    llvm_unreachable("Unexpected semantics");
1059  }
1060  opStatus multiply(const APFloat &RHS, roundingMode RM) {
1061    assert(&getSemantics() == &RHS.getSemantics() &&
1062           "Should only call on two APFloats with the same semantics");
1063    if (usesLayout<IEEEFloat>(getSemantics()))
1064      return U.IEEE.multiply(RHS.U.IEEE, RM);
1065    if (usesLayout<DoubleAPFloat>(getSemantics()))
1066      return U.Double.multiply(RHS.U.Double, RM);
1067    llvm_unreachable("Unexpected semantics");
1068  }
1069  opStatus divide(const APFloat &RHS, roundingMode RM) {
1070    assert(&getSemantics() == &RHS.getSemantics() &&
1071           "Should only call on two APFloats with the same semantics");
1072    if (usesLayout<IEEEFloat>(getSemantics()))
1073      return U.IEEE.divide(RHS.U.IEEE, RM);
1074    if (usesLayout<DoubleAPFloat>(getSemantics()))
1075      return U.Double.divide(RHS.U.Double, RM);
1076    llvm_unreachable("Unexpected semantics");
1077  }
1078  opStatus remainder(const APFloat &RHS) {
1079    assert(&getSemantics() == &RHS.getSemantics() &&
1080           "Should only call on two APFloats with the same semantics");
1081    if (usesLayout<IEEEFloat>(getSemantics()))
1082      return U.IEEE.remainder(RHS.U.IEEE);
1083    if (usesLayout<DoubleAPFloat>(getSemantics()))
1084      return U.Double.remainder(RHS.U.Double);
1085    llvm_unreachable("Unexpected semantics");
1086  }
1087  opStatus mod(const APFloat &RHS) {
1088    assert(&getSemantics() == &RHS.getSemantics() &&
1089           "Should only call on two APFloats with the same semantics");
1090    if (usesLayout<IEEEFloat>(getSemantics()))
1091      return U.IEEE.mod(RHS.U.IEEE);
1092    if (usesLayout<DoubleAPFloat>(getSemantics()))
1093      return U.Double.mod(RHS.U.Double);
1094    llvm_unreachable("Unexpected semantics");
1095  }
1096  opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend,
1097                            roundingMode RM) {
1098    assert(&getSemantics() == &Multiplicand.getSemantics() &&
1099           "Should only call on APFloats with the same semantics");
1100    assert(&getSemantics() == &Addend.getSemantics() &&
1101           "Should only call on APFloats with the same semantics");
1102    if (usesLayout<IEEEFloat>(getSemantics()))
1103      return U.IEEE.fusedMultiplyAdd(Multiplicand.U.IEEE, Addend.U.IEEE, RM);
1104    if (usesLayout<DoubleAPFloat>(getSemantics()))
1105      return U.Double.fusedMultiplyAdd(Multiplicand.U.Double, Addend.U.Double,
1106                                       RM);
1107    llvm_unreachable("Unexpected semantics");
1108  }
1109  opStatus roundToIntegral(roundingMode RM) {
1110    APFLOAT_DISPATCH_ON_SEMANTICS(roundToIntegral(RM));
1111  }
1112
1113  // TODO: bool parameters are not readable and a source of bugs.
1114  // Do something.
1115  opStatus next(bool nextDown) {
1116    APFLOAT_DISPATCH_ON_SEMANTICS(next(nextDown));
1117  }
1118
1119  /// Negate an APFloat.
1120  APFloat operator-() const {
1121    APFloat Result(*this);
1122    Result.changeSign();
1123    return Result;
1124  }
1125
1126  /// Add two APFloats, rounding ties to the nearest even.
1127  /// No error checking.
1128  APFloat operator+(const APFloat &RHS) const {
1129    APFloat Result(*this);
1130    (void)Result.add(RHS, rmNearestTiesToEven);
1131    return Result;
1132  }
1133
1134  /// Subtract two APFloats, rounding ties to the nearest even.
1135  /// No error checking.
1136  APFloat operator-(const APFloat &RHS) const {
1137    APFloat Result(*this);
1138    (void)Result.subtract(RHS, rmNearestTiesToEven);
1139    return Result;
1140  }
1141
1142  /// Multiply two APFloats, rounding ties to the nearest even.
1143  /// No error checking.
1144  APFloat operator*(const APFloat &RHS) const {
1145    APFloat Result(*this);
1146    (void)Result.multiply(RHS, rmNearestTiesToEven);
1147    return Result;
1148  }
1149
1150  /// Divide the first APFloat by the second, rounding ties to the nearest even.
1151  /// No error checking.
1152  APFloat operator/(const APFloat &RHS) const {
1153    APFloat Result(*this);
1154    (void)Result.divide(RHS, rmNearestTiesToEven);
1155    return Result;
1156  }
1157
1158  void changeSign() { APFLOAT_DISPATCH_ON_SEMANTICS(changeSign()); }
1159  void clearSign() {
1160    if (isNegative())
1161      changeSign();
1162  }
1163  void copySign(const APFloat &RHS) {
1164    if (isNegative() != RHS.isNegative())
1165      changeSign();
1166  }
1167
1168  /// A static helper to produce a copy of an APFloat value with its sign
1169  /// copied from some other APFloat.
1170  static APFloat copySign(APFloat Value, const APFloat &Sign) {
1171    Value.copySign(Sign);
1172    return Value;
1173  }
1174
1175  /// Assuming this is an IEEE-754 NaN value, quiet its signaling bit.
1176  /// This preserves the sign and payload bits.
1177  APFloat makeQuiet() const {
1178    APFloat Result(*this);
1179    Result.getIEEE().makeQuiet();
1180    return Result;
1181  }
1182
1183  opStatus convert(const fltSemantics &ToSemantics, roundingMode RM,
1184                   bool *losesInfo);
1185  opStatus convertToInteger(MutableArrayRef<integerPart> Input,
1186                            unsigned int Width, bool IsSigned, roundingMode RM,
1187                            bool *IsExact) const {
1188    APFLOAT_DISPATCH_ON_SEMANTICS(
1189        convertToInteger(Input, Width, IsSigned, RM, IsExact));
1190  }
1191  opStatus convertToInteger(APSInt &Result, roundingMode RM,
1192                            bool *IsExact) const;
1193  opStatus convertFromAPInt(const APInt &Input, bool IsSigned,
1194                            roundingMode RM) {
1195    APFLOAT_DISPATCH_ON_SEMANTICS(convertFromAPInt(Input, IsSigned, RM));
1196  }
1197  opStatus convertFromSignExtendedInteger(const integerPart *Input,
1198                                          unsigned int InputSize, bool IsSigned,
1199                                          roundingMode RM) {
1200    APFLOAT_DISPATCH_ON_SEMANTICS(
1201        convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM));
1202  }
1203  opStatus convertFromZeroExtendedInteger(const integerPart *Input,
1204                                          unsigned int InputSize, bool IsSigned,
1205                                          roundingMode RM) {
1206    APFLOAT_DISPATCH_ON_SEMANTICS(
1207        convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM));
1208  }
1209  Expected<opStatus> convertFromString(StringRef, roundingMode);
1210  APInt bitcastToAPInt() const {
1211    APFLOAT_DISPATCH_ON_SEMANTICS(bitcastToAPInt());
1212  }
1213
1214  /// Converts this APFloat to host double value.
1215  ///
1216  /// \pre The APFloat must be built using semantics, that can be represented by
1217  /// the host double type without loss of precision. It can be IEEEdouble and
1218  /// shorter semantics, like IEEEsingle and others.
1219  double convertToDouble() const;
1220
1221  /// Converts this APFloat to host float value.
1222  ///
1223  /// \pre The APFloat must be built using semantics, that can be represented by
1224  /// the host float type without loss of precision. It can be IEEEsingle and
1225  /// shorter semantics, like IEEEhalf.
1226  float convertToFloat() const;
1227
1228  bool operator==(const APFloat &RHS) const { return compare(RHS) == cmpEqual; }
1229
1230  bool operator!=(const APFloat &RHS) const { return compare(RHS) != cmpEqual; }
1231
1232  bool operator<(const APFloat &RHS) const {
1233    return compare(RHS) == cmpLessThan;
1234  }
1235
1236  bool operator>(const APFloat &RHS) const {
1237    return compare(RHS) == cmpGreaterThan;
1238  }
1239
1240  bool operator<=(const APFloat &RHS) const {
1241    cmpResult Res = compare(RHS);
1242    return Res == cmpLessThan || Res == cmpEqual;
1243  }
1244
1245  bool operator>=(const APFloat &RHS) const {
1246    cmpResult Res = compare(RHS);
1247    return Res == cmpGreaterThan || Res == cmpEqual;
1248  }
1249
1250  cmpResult compare(const APFloat &RHS) const {
1251    assert(&getSemantics() == &RHS.getSemantics() &&
1252           "Should only compare APFloats with the same semantics");
1253    if (usesLayout<IEEEFloat>(getSemantics()))
1254      return U.IEEE.compare(RHS.U.IEEE);
1255    if (usesLayout<DoubleAPFloat>(getSemantics()))
1256      return U.Double.compare(RHS.U.Double);
1257    llvm_unreachable("Unexpected semantics");
1258  }
1259
1260  bool bitwiseIsEqual(const APFloat &RHS) const {
1261    if (&getSemantics() != &RHS.getSemantics())
1262      return false;
1263    if (usesLayout<IEEEFloat>(getSemantics()))
1264      return U.IEEE.bitwiseIsEqual(RHS.U.IEEE);
1265    if (usesLayout<DoubleAPFloat>(getSemantics()))
1266      return U.Double.bitwiseIsEqual(RHS.U.Double);
1267    llvm_unreachable("Unexpected semantics");
1268  }
1269
1270  /// We don't rely on operator== working on double values, as
1271  /// it returns true for things that are clearly not equal, like -0.0 and 0.0.
1272  /// As such, this method can be used to do an exact bit-for-bit comparison of
1273  /// two floating point values.
1274  ///
1275  /// We leave the version with the double argument here because it's just so
1276  /// convenient to write "2.0" and the like.  Without this function we'd
1277  /// have to duplicate its logic everywhere it's called.
1278  bool isExactlyValue(double V) const {
1279    bool ignored;
1280    APFloat Tmp(V);
1281    Tmp.convert(getSemantics(), APFloat::rmNearestTiesToEven, &ignored);
1282    return bitwiseIsEqual(Tmp);
1283  }
1284
1285  unsigned int convertToHexString(char *DST, unsigned int HexDigits,
1286                                  bool UpperCase, roundingMode RM) const {
1287    APFLOAT_DISPATCH_ON_SEMANTICS(
1288        convertToHexString(DST, HexDigits, UpperCase, RM));
1289  }
1290
1291  bool isZero() const { return getCategory() == fcZero; }
1292  bool isInfinity() const { return getCategory() == fcInfinity; }
1293  bool isNaN() const { return getCategory() == fcNaN; }
1294
1295  bool isNegative() const { return getIEEE().isNegative(); }
1296  bool isDenormal() const { APFLOAT_DISPATCH_ON_SEMANTICS(isDenormal()); }
1297  bool isSignaling() const { return getIEEE().isSignaling(); }
1298
1299  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
1300  bool isFinite() const { return !isNaN() && !isInfinity(); }
1301
1302  fltCategory getCategory() const { return getIEEE().getCategory(); }
1303  const fltSemantics &getSemantics() const { return *U.semantics; }
1304  bool isNonZero() const { return !isZero(); }
1305  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
1306  bool isPosZero() const { return isZero() && !isNegative(); }
1307  bool isNegZero() const { return isZero() && isNegative(); }
1308  bool isPosInfinity() const { return isInfinity() && !isNegative(); }
1309  bool isNegInfinity() const { return isInfinity() && isNegative(); }
1310  bool isSmallest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isSmallest()); }
1311  bool isLargest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isLargest()); }
1312  bool isInteger() const { APFLOAT_DISPATCH_ON_SEMANTICS(isInteger()); }
1313  bool isIEEE() const { return usesLayout<IEEEFloat>(getSemantics()); }
1314
1315  bool isSmallestNormalized() const {
1316    APFLOAT_DISPATCH_ON_SEMANTICS(isSmallestNormalized());
1317  }
1318
1319  /// Return the FPClassTest which will return true for the value.
1320  FPClassTest classify() const;
1321
1322  APFloat &operator=(const APFloat &RHS) = default;
1323  APFloat &operator=(APFloat &&RHS) = default;
1324
1325  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
1326                unsigned FormatMaxPadding = 3, bool TruncateZero = true) const {
1327    APFLOAT_DISPATCH_ON_SEMANTICS(
1328        toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero));
1329  }
1330
1331  void print(raw_ostream &) const;
1332  void dump() const;
1333
1334  bool getExactInverse(APFloat *inv) const {
1335    APFLOAT_DISPATCH_ON_SEMANTICS(getExactInverse(inv));
1336  }
1337
1338  LLVM_READONLY
1339  int getExactLog2Abs() const {
1340    APFLOAT_DISPATCH_ON_SEMANTICS(getExactLog2Abs());
1341  }
1342
1343  LLVM_READONLY
1344  int getExactLog2() const {
1345    APFLOAT_DISPATCH_ON_SEMANTICS(getExactLog2());
1346  }
1347
1348  friend hash_code hash_value(const APFloat &Arg);
1349  friend int ilogb(const APFloat &Arg) { return ilogb(Arg.getIEEE()); }
1350  friend APFloat scalbn(APFloat X, int Exp, roundingMode RM);
1351  friend APFloat frexp(const APFloat &X, int &Exp, roundingMode RM);
1352  friend IEEEFloat;
1353  friend DoubleAPFloat;
1354};
1355
1356/// See friend declarations above.
1357///
1358/// These additional declarations are required in order to compile LLVM with IBM
1359/// xlC compiler.
1360hash_code hash_value(const APFloat &Arg);
1361inline APFloat scalbn(APFloat X, int Exp, APFloat::roundingMode RM) {
1362  if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1363    return APFloat(scalbn(X.U.IEEE, Exp, RM), X.getSemantics());
1364  if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1365    return APFloat(scalbn(X.U.Double, Exp, RM), X.getSemantics());
1366  llvm_unreachable("Unexpected semantics");
1367}
1368
1369/// Equivalent of C standard library function.
1370///
1371/// While the C standard says Exp is an unspecified value for infinity and nan,
1372/// this returns INT_MAX for infinities, and INT_MIN for NaNs.
1373inline APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM) {
1374  if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1375    return APFloat(frexp(X.U.IEEE, Exp, RM), X.getSemantics());
1376  if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1377    return APFloat(frexp(X.U.Double, Exp, RM), X.getSemantics());
1378  llvm_unreachable("Unexpected semantics");
1379}
1380/// Returns the absolute value of the argument.
1381inline APFloat abs(APFloat X) {
1382  X.clearSign();
1383  return X;
1384}
1385
1386/// Returns the negated value of the argument.
1387inline APFloat neg(APFloat X) {
1388  X.changeSign();
1389  return X;
1390}
1391
1392/// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
1393/// both are not NaN. If either argument is a NaN, returns the other argument.
1394LLVM_READONLY
1395inline APFloat minnum(const APFloat &A, const APFloat &B) {
1396  if (A.isNaN())
1397    return B;
1398  if (B.isNaN())
1399    return A;
1400  return B < A ? B : A;
1401}
1402
1403/// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
1404/// both are not NaN. If either argument is a NaN, returns the other argument.
1405LLVM_READONLY
1406inline APFloat maxnum(const APFloat &A, const APFloat &B) {
1407  if (A.isNaN())
1408    return B;
1409  if (B.isNaN())
1410    return A;
1411  return A < B ? B : A;
1412}
1413
1414/// Implements IEEE 754-2018 minimum semantics. Returns the smaller of 2
1415/// arguments, propagating NaNs and treating -0 as less than +0.
1416LLVM_READONLY
1417inline APFloat minimum(const APFloat &A, const APFloat &B) {
1418  if (A.isNaN())
1419    return A;
1420  if (B.isNaN())
1421    return B;
1422  if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1423    return A.isNegative() ? A : B;
1424  return B < A ? B : A;
1425}
1426
1427/// Implements IEEE 754-2018 maximum semantics. Returns the larger of 2
1428/// arguments, propagating NaNs and treating -0 as less than +0.
1429LLVM_READONLY
1430inline APFloat maximum(const APFloat &A, const APFloat &B) {
1431  if (A.isNaN())
1432    return A;
1433  if (B.isNaN())
1434    return B;
1435  if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1436    return A.isNegative() ? B : A;
1437  return A < B ? B : A;
1438}
1439
1440// We want the following functions to be available in the header for inlining.
1441// We cannot define them inline in the class definition of `DoubleAPFloat`
1442// because doing so would instantiate `std::unique_ptr<APFloat[]>` before
1443// `APFloat` is defined, and that would be undefined behavior.
1444namespace detail {
1445
1446DoubleAPFloat &DoubleAPFloat::operator=(DoubleAPFloat &&RHS) {
1447  if (this != &RHS) {
1448    this->~DoubleAPFloat();
1449    new (this) DoubleAPFloat(std::move(RHS));
1450  }
1451  return *this;
1452}
1453
1454APFloat &DoubleAPFloat::getFirst() { return Floats[0]; }
1455const APFloat &DoubleAPFloat::getFirst() const { return Floats[0]; }
1456APFloat &DoubleAPFloat::getSecond() { return Floats[1]; }
1457const APFloat &DoubleAPFloat::getSecond() const { return Floats[1]; }
1458
1459} // namespace detail
1460
1461} // namespace llvm
1462
1463#undef APFLOAT_DISPATCH_ON_SEMANTICS
1464#endif // LLVM_ADT_APFLOAT_H
1465