1//===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//
2//
3//                     The LLVM Compiler Infrastructure
4//
5// This file is distributed under the University of Illinois Open Source
6// License. See LICENSE.TXT for details.
7//
8//===----------------------------------------------------------------------===//
9///
10/// \file
11/// \brief
12/// This file declares a class to represent arbitrary precision floating point
13/// values and provide a variety of arithmetic operations on them.
14///
15//===----------------------------------------------------------------------===//
16
17#ifndef LLVM_ADT_APFLOAT_H
18#define LLVM_ADT_APFLOAT_H
19
20#include "llvm/ADT/APInt.h"
21
22namespace llvm {
23
24struct fltSemantics;
25class APSInt;
26class StringRef;
27
28/// Enum that represents what fraction of the LSB truncated bits of an fp number
29/// represent.
30///
31/// This essentially combines the roles of guard and sticky bits.
32enum lostFraction { // Example of truncated bits:
33  lfExactlyZero,    // 000000
34  lfLessThanHalf,   // 0xxxxx  x's not all zero
35  lfExactlyHalf,    // 100000
36  lfMoreThanHalf    // 1xxxxx  x's not all zero
37};
38
39/// \brief A self-contained host- and target-independent arbitrary-precision
40/// floating-point software implementation.
41///
42/// APFloat uses bignum integer arithmetic as provided by static functions in
43/// the APInt class.  The library will work with bignum integers whose parts are
44/// any unsigned type at least 16 bits wide, but 64 bits is recommended.
45///
46/// Written for clarity rather than speed, in particular with a view to use in
47/// the front-end of a cross compiler so that target arithmetic can be correctly
48/// performed on the host.  Performance should nonetheless be reasonable,
49/// particularly for its intended use.  It may be useful as a base
50/// implementation for a run-time library during development of a faster
51/// target-specific one.
52///
53/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
54/// implemented operations.  Currently implemented operations are add, subtract,
55/// multiply, divide, fused-multiply-add, conversion-to-float,
56/// conversion-to-integer and conversion-from-integer.  New rounding modes
57/// (e.g. away from zero) can be added with three or four lines of code.
58///
59/// Four formats are built-in: IEEE single precision, double precision,
60/// quadruple precision, and x87 80-bit extended double (when operating with
61/// full extended precision).  Adding a new format that obeys IEEE semantics
62/// only requires adding two lines of code: a declaration and definition of the
63/// format.
64///
65/// All operations return the status of that operation as an exception bit-mask,
66/// so multiple operations can be done consecutively with their results or-ed
67/// together.  The returned status can be useful for compiler diagnostics; e.g.,
68/// inexact, underflow and overflow can be easily diagnosed on constant folding,
69/// and compiler optimizers can determine what exceptions would be raised by
70/// folding operations and optimize, or perhaps not optimize, accordingly.
71///
72/// At present, underflow tininess is detected after rounding; it should be
73/// straight forward to add support for the before-rounding case too.
74///
75/// The library reads hexadecimal floating point numbers as per C99, and
76/// correctly rounds if necessary according to the specified rounding mode.
77/// Syntax is required to have been validated by the caller.  It also converts
78/// floating point numbers to hexadecimal text as per the C99 %a and %A
79/// conversions.  The output precision (or alternatively the natural minimal
80/// precision) can be specified; if the requested precision is less than the
81/// natural precision the output is correctly rounded for the specified rounding
82/// mode.
83///
84/// It also reads decimal floating point numbers and correctly rounds according
85/// to the specified rounding mode.
86///
87/// Conversion to decimal text is not currently implemented.
88///
89/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
90/// signed exponent, and the significand as an array of integer parts.  After
91/// normalization of a number of precision P the exponent is within the range of
92/// the format, and if the number is not denormal the P-th bit of the
93/// significand is set as an explicit integer bit.  For denormals the most
94/// significant bit is shifted right so that the exponent is maintained at the
95/// format's minimum, so that the smallest denormal has just the least
96/// significant bit of the significand set.  The sign of zeroes and infinities
97/// is significant; the exponent and significand of such numbers is not stored,
98/// but has a known implicit (deterministic) value: 0 for the significands, 0
99/// for zero exponent, all 1 bits for infinity exponent.  For NaNs the sign and
100/// significand are deterministic, although not really meaningful, and preserved
101/// in non-conversion operations.  The exponent is implicitly all 1 bits.
102///
103/// APFloat does not provide any exception handling beyond default exception
104/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
105/// by encoding Signaling NaNs with the first bit of its trailing significand as
106/// 0.
107///
108/// TODO
109/// ====
110///
111/// Some features that may or may not be worth adding:
112///
113/// Binary to decimal conversion (hard).
114///
115/// Optional ability to detect underflow tininess before rounding.
116///
117/// New formats: x87 in single and double precision mode (IEEE apart from
118/// extended exponent range) (hard).
119///
120/// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
121///
122class APFloat {
123public:
124
125  /// A signed type to represent a floating point numbers unbiased exponent.
126  typedef signed short ExponentType;
127
128  /// \name Floating Point Semantics.
129  /// @{
130
131  static const fltSemantics IEEEhalf;
132  static const fltSemantics IEEEsingle;
133  static const fltSemantics IEEEdouble;
134  static const fltSemantics IEEEquad;
135  static const fltSemantics PPCDoubleDouble;
136  static const fltSemantics x87DoubleExtended;
137
138  /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
139  /// anything real.
140  static const fltSemantics Bogus;
141
142  /// @}
143
144  static unsigned int semanticsPrecision(const fltSemantics &);
145
146  /// IEEE-754R 5.11: Floating Point Comparison Relations.
147  enum cmpResult {
148    cmpLessThan,
149    cmpEqual,
150    cmpGreaterThan,
151    cmpUnordered
152  };
153
154  /// IEEE-754R 4.3: Rounding-direction attributes.
155  enum roundingMode {
156    rmNearestTiesToEven,
157    rmTowardPositive,
158    rmTowardNegative,
159    rmTowardZero,
160    rmNearestTiesToAway
161  };
162
163  /// IEEE-754R 7: Default exception handling.
164  ///
165  /// opUnderflow or opOverflow are always returned or-ed with opInexact.
166  enum opStatus {
167    opOK = 0x00,
168    opInvalidOp = 0x01,
169    opDivByZero = 0x02,
170    opOverflow = 0x04,
171    opUnderflow = 0x08,
172    opInexact = 0x10
173  };
174
175  /// Category of internally-represented number.
176  enum fltCategory {
177    fcInfinity,
178    fcNaN,
179    fcNormal,
180    fcZero
181  };
182
183  /// Convenience enum used to construct an uninitialized APFloat.
184  enum uninitializedTag {
185    uninitialized
186  };
187
188  /// \name Constructors
189  /// @{
190
191  APFloat(const fltSemantics &); // Default construct to 0.0
192  APFloat(const fltSemantics &, StringRef);
193  APFloat(const fltSemantics &, integerPart);
194  APFloat(const fltSemantics &, uninitializedTag);
195  APFloat(const fltSemantics &, const APInt &);
196  explicit APFloat(double d);
197  explicit APFloat(float f);
198  APFloat(const APFloat &);
199  APFloat(APFloat &&);
200  ~APFloat();
201
202  /// @}
203
204  /// \brief Returns whether this instance allocated memory.
205  bool needsCleanup() const { return partCount() > 1; }
206
207  /// \name Convenience "constructors"
208  /// @{
209
210  /// Factory for Positive and Negative Zero.
211  ///
212  /// \param Negative True iff the number should be negative.
213  static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
214    APFloat Val(Sem, uninitialized);
215    Val.makeZero(Negative);
216    return Val;
217  }
218
219  /// Factory for Positive and Negative Infinity.
220  ///
221  /// \param Negative True iff the number should be negative.
222  static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
223    APFloat Val(Sem, uninitialized);
224    Val.makeInf(Negative);
225    return Val;
226  }
227
228  /// Factory for QNaN values.
229  ///
230  /// \param Negative - True iff the NaN generated should be negative.
231  /// \param type - The unspecified fill bits for creating the NaN, 0 by
232  /// default.  The value is truncated as necessary.
233  static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
234                        unsigned type = 0) {
235    if (type) {
236      APInt fill(64, type);
237      return getQNaN(Sem, Negative, &fill);
238    } else {
239      return getQNaN(Sem, Negative, nullptr);
240    }
241  }
242
243  /// Factory for QNaN values.
244  static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
245                         const APInt *payload = nullptr) {
246    return makeNaN(Sem, false, Negative, payload);
247  }
248
249  /// Factory for SNaN values.
250  static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
251                         const APInt *payload = nullptr) {
252    return makeNaN(Sem, true, Negative, payload);
253  }
254
255  /// Returns the largest finite number in the given semantics.
256  ///
257  /// \param Negative - True iff the number should be negative
258  static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
259
260  /// Returns the smallest (by magnitude) finite number in the given semantics.
261  /// Might be denormalized, which implies a relative loss of precision.
262  ///
263  /// \param Negative - True iff the number should be negative
264  static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
265
266  /// Returns the smallest (by magnitude) normalized finite number in the given
267  /// semantics.
268  ///
269  /// \param Negative - True iff the number should be negative
270  static APFloat getSmallestNormalized(const fltSemantics &Sem,
271                                       bool Negative = false);
272
273  /// Returns a float which is bitcasted from an all one value int.
274  ///
275  /// \param BitWidth - Select float type
276  /// \param isIEEE   - If 128 bit number, select between PPC and IEEE
277  static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
278
279  /// @}
280
281  /// Used to insert APFloat objects, or objects that contain APFloat objects,
282  /// into FoldingSets.
283  void Profile(FoldingSetNodeID &NID) const;
284
285  /// \name Arithmetic
286  /// @{
287
288  opStatus add(const APFloat &, roundingMode);
289  opStatus subtract(const APFloat &, roundingMode);
290  opStatus multiply(const APFloat &, roundingMode);
291  opStatus divide(const APFloat &, roundingMode);
292  /// IEEE remainder.
293  opStatus remainder(const APFloat &);
294  /// C fmod, or llvm frem.
295  opStatus mod(const APFloat &, roundingMode);
296  opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
297  opStatus roundToIntegral(roundingMode);
298  /// IEEE-754R 5.3.1: nextUp/nextDown.
299  opStatus next(bool nextDown);
300
301  /// \brief Operator+ overload which provides the default
302  /// \c nmNearestTiesToEven rounding mode and *no* error checking.
303  APFloat operator+(const APFloat &RHS) const {
304    APFloat Result = *this;
305    Result.add(RHS, rmNearestTiesToEven);
306    return Result;
307  }
308
309  /// \brief Operator- overload which provides the default
310  /// \c nmNearestTiesToEven rounding mode and *no* error checking.
311  APFloat operator-(const APFloat &RHS) const {
312    APFloat Result = *this;
313    Result.subtract(RHS, rmNearestTiesToEven);
314    return Result;
315  }
316
317  /// \brief Operator* overload which provides the default
318  /// \c nmNearestTiesToEven rounding mode and *no* error checking.
319  APFloat operator*(const APFloat &RHS) const {
320    APFloat Result = *this;
321    Result.multiply(RHS, rmNearestTiesToEven);
322    return Result;
323  }
324
325  /// \brief Operator/ overload which provides the default
326  /// \c nmNearestTiesToEven rounding mode and *no* error checking.
327  APFloat operator/(const APFloat &RHS) const {
328    APFloat Result = *this;
329    Result.divide(RHS, rmNearestTiesToEven);
330    return Result;
331  }
332
333  /// @}
334
335  /// \name Sign operations.
336  /// @{
337
338  void changeSign();
339  void clearSign();
340  void copySign(const APFloat &);
341
342  /// \brief A static helper to produce a copy of an APFloat value with its sign
343  /// copied from some other APFloat.
344  static APFloat copySign(APFloat Value, const APFloat &Sign) {
345    Value.copySign(Sign);
346    return std::move(Value);
347  }
348
349  /// @}
350
351  /// \name Conversions
352  /// @{
353
354  opStatus convert(const fltSemantics &, roundingMode, bool *);
355  opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
356                            bool *) const;
357  opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
358  opStatus convertFromAPInt(const APInt &, bool, roundingMode);
359  opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
360                                          bool, roundingMode);
361  opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
362                                          bool, roundingMode);
363  opStatus convertFromString(StringRef, roundingMode);
364  APInt bitcastToAPInt() const;
365  double convertToDouble() const;
366  float convertToFloat() const;
367
368  /// @}
369
370  /// The definition of equality is not straightforward for floating point, so
371  /// we won't use operator==.  Use one of the following, or write whatever it
372  /// is you really mean.
373  bool operator==(const APFloat &) const = delete;
374
375  /// IEEE comparison with another floating point number (NaNs compare
376  /// unordered, 0==-0).
377  cmpResult compare(const APFloat &) const;
378
379  /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
380  bool bitwiseIsEqual(const APFloat &) const;
381
382  /// Write out a hexadecimal representation of the floating point value to DST,
383  /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
384  /// Return the number of characters written, excluding the terminating NUL.
385  unsigned int convertToHexString(char *dst, unsigned int hexDigits,
386                                  bool upperCase, roundingMode) const;
387
388  /// \name IEEE-754R 5.7.2 General operations.
389  /// @{
390
391  /// IEEE-754R isSignMinus: Returns true if and only if the current value is
392  /// negative.
393  ///
394  /// This applies to zeros and NaNs as well.
395  bool isNegative() const { return sign; }
396
397  /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
398  ///
399  /// This implies that the current value of the float is not zero, subnormal,
400  /// infinite, or NaN following the definition of normality from IEEE-754R.
401  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
402
403  /// Returns true if and only if the current value is zero, subnormal, or
404  /// normal.
405  ///
406  /// This means that the value is not infinite or NaN.
407  bool isFinite() const { return !isNaN() && !isInfinity(); }
408
409  /// Returns true if and only if the float is plus or minus zero.
410  bool isZero() const { return category == fcZero; }
411
412  /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
413  /// denormal.
414  bool isDenormal() const;
415
416  /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
417  bool isInfinity() const { return category == fcInfinity; }
418
419  /// Returns true if and only if the float is a quiet or signaling NaN.
420  bool isNaN() const { return category == fcNaN; }
421
422  /// Returns true if and only if the float is a signaling NaN.
423  bool isSignaling() const;
424
425  /// @}
426
427  /// \name Simple Queries
428  /// @{
429
430  fltCategory getCategory() const { return category; }
431  const fltSemantics &getSemantics() const { return *semantics; }
432  bool isNonZero() const { return category != fcZero; }
433  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
434  bool isPosZero() const { return isZero() && !isNegative(); }
435  bool isNegZero() const { return isZero() && isNegative(); }
436
437  /// Returns true if and only if the number has the smallest possible non-zero
438  /// magnitude in the current semantics.
439  bool isSmallest() const;
440
441  /// Returns true if and only if the number has the largest possible finite
442  /// magnitude in the current semantics.
443  bool isLargest() const;
444
445  /// @}
446
447  APFloat &operator=(const APFloat &);
448  APFloat &operator=(APFloat &&);
449
450  /// \brief Overload to compute a hash code for an APFloat value.
451  ///
452  /// Note that the use of hash codes for floating point values is in general
453  /// frought with peril. Equality is hard to define for these values. For
454  /// example, should negative and positive zero hash to different codes? Are
455  /// they equal or not? This hash value implementation specifically
456  /// emphasizes producing different codes for different inputs in order to
457  /// be used in canonicalization and memoization. As such, equality is
458  /// bitwiseIsEqual, and 0 != -0.
459  friend hash_code hash_value(const APFloat &Arg);
460
461  /// Converts this value into a decimal string.
462  ///
463  /// \param FormatPrecision The maximum number of digits of
464  ///   precision to output.  If there are fewer digits available,
465  ///   zero padding will not be used unless the value is
466  ///   integral and small enough to be expressed in
467  ///   FormatPrecision digits.  0 means to use the natural
468  ///   precision of the number.
469  /// \param FormatMaxPadding The maximum number of zeros to
470  ///   consider inserting before falling back to scientific
471  ///   notation.  0 means to always use scientific notation.
472  ///
473  /// Number       Precision    MaxPadding      Result
474  /// ------       ---------    ----------      ------
475  /// 1.01E+4              5             2       10100
476  /// 1.01E+4              4             2       1.01E+4
477  /// 1.01E+4              5             1       1.01E+4
478  /// 1.01E-2              5             2       0.0101
479  /// 1.01E-2              4             2       0.0101
480  /// 1.01E-2              4             1       1.01E-2
481  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
482                unsigned FormatMaxPadding = 3) const;
483
484  /// If this value has an exact multiplicative inverse, store it in inv and
485  /// return true.
486  bool getExactInverse(APFloat *inv) const;
487
488  /// \brief Enumeration of \c ilogb error results.
489  enum IlogbErrorKinds {
490    IEK_Zero = INT_MIN+1,
491    IEK_NaN = INT_MIN,
492    IEK_Inf = INT_MAX
493  };
494
495  /// \brief Returns the exponent of the internal representation of the APFloat.
496  ///
497  /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
498  /// For special APFloat values, this returns special error codes:
499  ///
500  ///   NaN -> \c IEK_NaN
501  ///   0   -> \c IEK_Zero
502  ///   Inf -> \c IEK_Inf
503  ///
504  friend int ilogb(const APFloat &Arg) {
505    if (Arg.isNaN())
506      return IEK_NaN;
507    if (Arg.isZero())
508      return IEK_Zero;
509    if (Arg.isInfinity())
510      return IEK_Inf;
511
512    return Arg.exponent;
513  }
514
515  /// \brief Returns: X * 2^Exp for integral exponents.
516  friend APFloat scalbn(APFloat X, int Exp);
517
518private:
519
520  /// \name Simple Queries
521  /// @{
522
523  integerPart *significandParts();
524  const integerPart *significandParts() const;
525  unsigned int partCount() const;
526
527  /// @}
528
529  /// \name Significand operations.
530  /// @{
531
532  integerPart addSignificand(const APFloat &);
533  integerPart subtractSignificand(const APFloat &, integerPart);
534  lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
535  lostFraction multiplySignificand(const APFloat &, const APFloat *);
536  lostFraction divideSignificand(const APFloat &);
537  void incrementSignificand();
538  void initialize(const fltSemantics *);
539  void shiftSignificandLeft(unsigned int);
540  lostFraction shiftSignificandRight(unsigned int);
541  unsigned int significandLSB() const;
542  unsigned int significandMSB() const;
543  void zeroSignificand();
544  /// Return true if the significand excluding the integral bit is all ones.
545  bool isSignificandAllOnes() const;
546  /// Return true if the significand excluding the integral bit is all zeros.
547  bool isSignificandAllZeros() const;
548
549  /// @}
550
551  /// \name Arithmetic on special values.
552  /// @{
553
554  opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
555  opStatus divideSpecials(const APFloat &);
556  opStatus multiplySpecials(const APFloat &);
557  opStatus modSpecials(const APFloat &);
558
559  /// @}
560
561  /// \name Special value setters.
562  /// @{
563
564  void makeLargest(bool Neg = false);
565  void makeSmallest(bool Neg = false);
566  void makeNaN(bool SNaN = false, bool Neg = false,
567               const APInt *fill = nullptr);
568  static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
569                         const APInt *fill);
570  void makeInf(bool Neg = false);
571  void makeZero(bool Neg = false);
572
573  /// @}
574
575  /// \name Miscellany
576  /// @{
577
578  bool convertFromStringSpecials(StringRef str);
579  opStatus normalize(roundingMode, lostFraction);
580  opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
581  cmpResult compareAbsoluteValue(const APFloat &) const;
582  opStatus handleOverflow(roundingMode);
583  bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
584  opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
585                                        roundingMode, bool *) const;
586  opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
587                                    roundingMode);
588  opStatus convertFromHexadecimalString(StringRef, roundingMode);
589  opStatus convertFromDecimalString(StringRef, roundingMode);
590  char *convertNormalToHexString(char *, unsigned int, bool,
591                                 roundingMode) const;
592  opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
593                                        roundingMode);
594
595  /// @}
596
597  APInt convertHalfAPFloatToAPInt() const;
598  APInt convertFloatAPFloatToAPInt() const;
599  APInt convertDoubleAPFloatToAPInt() const;
600  APInt convertQuadrupleAPFloatToAPInt() const;
601  APInt convertF80LongDoubleAPFloatToAPInt() const;
602  APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
603  void initFromAPInt(const fltSemantics *Sem, const APInt &api);
604  void initFromHalfAPInt(const APInt &api);
605  void initFromFloatAPInt(const APInt &api);
606  void initFromDoubleAPInt(const APInt &api);
607  void initFromQuadrupleAPInt(const APInt &api);
608  void initFromF80LongDoubleAPInt(const APInt &api);
609  void initFromPPCDoubleDoubleAPInt(const APInt &api);
610
611  void assign(const APFloat &);
612  void copySignificand(const APFloat &);
613  void freeSignificand();
614
615  /// The semantics that this value obeys.
616  const fltSemantics *semantics;
617
618  /// A binary fraction with an explicit integer bit.
619  ///
620  /// The significand must be at least one bit wider than the target precision.
621  union Significand {
622    integerPart part;
623    integerPart *parts;
624  } significand;
625
626  /// The signed unbiased exponent of the value.
627  ExponentType exponent;
628
629  /// What kind of floating point number this is.
630  ///
631  /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
632  /// Using the extra bit keeps it from failing under VisualStudio.
633  fltCategory category : 3;
634
635  /// Sign bit of the number.
636  unsigned int sign : 1;
637};
638
639/// See friend declarations above.
640///
641/// These additional declarations are required in order to compile LLVM with IBM
642/// xlC compiler.
643hash_code hash_value(const APFloat &Arg);
644APFloat scalbn(APFloat X, int Exp);
645
646/// \brief Returns the absolute value of the argument.
647inline APFloat abs(APFloat X) {
648  X.clearSign();
649  return X;
650}
651
652/// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
653/// both are not NaN. If either argument is a NaN, returns the other argument.
654LLVM_READONLY
655inline APFloat minnum(const APFloat &A, const APFloat &B) {
656  if (A.isNaN())
657    return B;
658  if (B.isNaN())
659    return A;
660  return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
661}
662
663/// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
664/// both are not NaN. If either argument is a NaN, returns the other argument.
665LLVM_READONLY
666inline APFloat maxnum(const APFloat &A, const APFloat &B) {
667  if (A.isNaN())
668    return B;
669  if (B.isNaN())
670    return A;
671  return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
672}
673
674} // namespace llvm
675
676#endif // LLVM_ADT_APFLOAT_H
677