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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 
22 namespace llvm {
23 
24 struct fltSemantics;
25 class APSInt;
26 class 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.
32 enum 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 ///
122 class APFloat {
123 public:
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   static ExponentType semanticsMinExponent(const fltSemantics &);
146   static ExponentType semanticsMaxExponent(const fltSemantics &);
147   static unsigned int semanticsSizeInBits(const fltSemantics &);
148 
149   /// IEEE-754R 5.11: Floating Point Comparison Relations.
150   enum cmpResult {
151     cmpLessThan,
152     cmpEqual,
153     cmpGreaterThan,
154     cmpUnordered
155   };
156 
157   /// IEEE-754R 4.3: Rounding-direction attributes.
158   enum roundingMode {
159     rmNearestTiesToEven,
160     rmTowardPositive,
161     rmTowardNegative,
162     rmTowardZero,
163     rmNearestTiesToAway
164   };
165 
166   /// IEEE-754R 7: Default exception handling.
167   ///
168   /// opUnderflow or opOverflow are always returned or-ed with opInexact.
169   enum opStatus {
170     opOK = 0x00,
171     opInvalidOp = 0x01,
172     opDivByZero = 0x02,
173     opOverflow = 0x04,
174     opUnderflow = 0x08,
175     opInexact = 0x10
176   };
177 
178   /// Category of internally-represented number.
179   enum fltCategory {
180     fcInfinity,
181     fcNaN,
182     fcNormal,
183     fcZero
184   };
185 
186   /// Convenience enum used to construct an uninitialized APFloat.
187   enum uninitializedTag {
188     uninitialized
189   };
190 
191   /// \name Constructors
192   /// @{
193 
194   APFloat(const fltSemantics &); // Default construct to 0.0
195   APFloat(const fltSemantics &, StringRef);
196   APFloat(const fltSemantics &, integerPart);
197   APFloat(const fltSemantics &, uninitializedTag);
198   APFloat(const fltSemantics &, const APInt &);
199   explicit APFloat(double d);
200   explicit APFloat(float f);
201   APFloat(const APFloat &);
202   APFloat(APFloat &&);
203   ~APFloat();
204 
205   /// @}
206 
207   /// \brief Returns whether this instance allocated memory.
needsCleanup()208   bool needsCleanup() const { return partCount() > 1; }
209 
210   /// \name Convenience "constructors"
211   /// @{
212 
213   /// Factory for Positive and Negative Zero.
214   ///
215   /// \param Negative True iff the number should be negative.
216   static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
217     APFloat Val(Sem, uninitialized);
218     Val.makeZero(Negative);
219     return Val;
220   }
221 
222   /// Factory for Positive and Negative Infinity.
223   ///
224   /// \param Negative True iff the number should be negative.
225   static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
226     APFloat Val(Sem, uninitialized);
227     Val.makeInf(Negative);
228     return Val;
229   }
230 
231   /// Factory for QNaN values.
232   ///
233   /// \param Negative - True iff the NaN generated should be negative.
234   /// \param type - The unspecified fill bits for creating the NaN, 0 by
235   /// default.  The value is truncated as necessary.
236   static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
237                         unsigned type = 0) {
238     if (type) {
239       APInt fill(64, type);
240       return getQNaN(Sem, Negative, &fill);
241     } else {
242       return getQNaN(Sem, Negative, nullptr);
243     }
244   }
245 
246   /// Factory for QNaN values.
247   static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
248                          const APInt *payload = nullptr) {
249     return makeNaN(Sem, false, Negative, payload);
250   }
251 
252   /// Factory for SNaN values.
253   static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
254                          const APInt *payload = nullptr) {
255     return makeNaN(Sem, true, Negative, payload);
256   }
257 
258   /// Returns the largest finite number in the given semantics.
259   ///
260   /// \param Negative - True iff the number should be negative
261   static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
262 
263   /// Returns the smallest (by magnitude) finite number in the given semantics.
264   /// Might be denormalized, which implies a relative loss of precision.
265   ///
266   /// \param Negative - True iff the number should be negative
267   static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
268 
269   /// Returns the smallest (by magnitude) normalized finite number in the given
270   /// semantics.
271   ///
272   /// \param Negative - True iff the number should be negative
273   static APFloat getSmallestNormalized(const fltSemantics &Sem,
274                                        bool Negative = false);
275 
276   /// Returns a float which is bitcasted from an all one value int.
277   ///
278   /// \param BitWidth - Select float type
279   /// \param isIEEE   - If 128 bit number, select between PPC and IEEE
280   static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
281 
282   /// Returns the size of the floating point number (in bits) in the given
283   /// semantics.
284   static unsigned getSizeInBits(const fltSemantics &Sem);
285 
286   /// @}
287 
288   /// Used to insert APFloat objects, or objects that contain APFloat objects,
289   /// into FoldingSets.
290   void Profile(FoldingSetNodeID &NID) const;
291 
292   /// \name Arithmetic
293   /// @{
294 
295   opStatus add(const APFloat &, roundingMode);
296   opStatus subtract(const APFloat &, roundingMode);
297   opStatus multiply(const APFloat &, roundingMode);
298   opStatus divide(const APFloat &, roundingMode);
299   /// IEEE remainder.
300   opStatus remainder(const APFloat &);
301   /// C fmod, or llvm frem.
302   opStatus mod(const APFloat &);
303   opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
304   opStatus roundToIntegral(roundingMode);
305   /// IEEE-754R 5.3.1: nextUp/nextDown.
306   opStatus next(bool nextDown);
307 
308   /// \brief Operator+ overload which provides the default
309   /// \c nmNearestTiesToEven rounding mode and *no* error checking.
310   APFloat operator+(const APFloat &RHS) const {
311     APFloat Result = *this;
312     Result.add(RHS, rmNearestTiesToEven);
313     return Result;
314   }
315 
316   /// \brief Operator- overload which provides the default
317   /// \c nmNearestTiesToEven rounding mode and *no* error checking.
318   APFloat operator-(const APFloat &RHS) const {
319     APFloat Result = *this;
320     Result.subtract(RHS, rmNearestTiesToEven);
321     return Result;
322   }
323 
324   /// \brief Operator* overload which provides the default
325   /// \c nmNearestTiesToEven rounding mode and *no* error checking.
326   APFloat operator*(const APFloat &RHS) const {
327     APFloat Result = *this;
328     Result.multiply(RHS, rmNearestTiesToEven);
329     return Result;
330   }
331 
332   /// \brief Operator/ overload which provides the default
333   /// \c nmNearestTiesToEven rounding mode and *no* error checking.
334   APFloat operator/(const APFloat &RHS) const {
335     APFloat Result = *this;
336     Result.divide(RHS, rmNearestTiesToEven);
337     return Result;
338   }
339 
340   /// @}
341 
342   /// \name Sign operations.
343   /// @{
344 
345   void changeSign();
346   void clearSign();
347   void copySign(const APFloat &);
348 
349   /// \brief A static helper to produce a copy of an APFloat value with its sign
350   /// copied from some other APFloat.
copySign(APFloat Value,const APFloat & Sign)351   static APFloat copySign(APFloat Value, const APFloat &Sign) {
352     Value.copySign(Sign);
353     return Value;
354   }
355 
356   /// @}
357 
358   /// \name Conversions
359   /// @{
360 
361   opStatus convert(const fltSemantics &, roundingMode, bool *);
362   opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
363                             bool *) const;
364   opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
365   opStatus convertFromAPInt(const APInt &, bool, roundingMode);
366   opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
367                                           bool, roundingMode);
368   opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
369                                           bool, roundingMode);
370   opStatus convertFromString(StringRef, roundingMode);
371   APInt bitcastToAPInt() const;
372   double convertToDouble() const;
373   float convertToFloat() const;
374 
375   /// @}
376 
377   /// The definition of equality is not straightforward for floating point, so
378   /// we won't use operator==.  Use one of the following, or write whatever it
379   /// is you really mean.
380   bool operator==(const APFloat &) const = delete;
381 
382   /// IEEE comparison with another floating point number (NaNs compare
383   /// unordered, 0==-0).
384   cmpResult compare(const APFloat &) const;
385 
386   /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
387   bool bitwiseIsEqual(const APFloat &) const;
388 
389   /// Write out a hexadecimal representation of the floating point value to DST,
390   /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
391   /// Return the number of characters written, excluding the terminating NUL.
392   unsigned int convertToHexString(char *dst, unsigned int hexDigits,
393                                   bool upperCase, roundingMode) const;
394 
395   /// \name IEEE-754R 5.7.2 General operations.
396   /// @{
397 
398   /// IEEE-754R isSignMinus: Returns true if and only if the current value is
399   /// negative.
400   ///
401   /// This applies to zeros and NaNs as well.
isNegative()402   bool isNegative() const { return sign; }
403 
404   /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
405   ///
406   /// This implies that the current value of the float is not zero, subnormal,
407   /// infinite, or NaN following the definition of normality from IEEE-754R.
isNormal()408   bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
409 
410   /// Returns true if and only if the current value is zero, subnormal, or
411   /// normal.
412   ///
413   /// This means that the value is not infinite or NaN.
isFinite()414   bool isFinite() const { return !isNaN() && !isInfinity(); }
415 
416   /// Returns true if and only if the float is plus or minus zero.
isZero()417   bool isZero() const { return category == fcZero; }
418 
419   /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
420   /// denormal.
421   bool isDenormal() const;
422 
423   /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
isInfinity()424   bool isInfinity() const { return category == fcInfinity; }
425 
426   /// Returns true if and only if the float is a quiet or signaling NaN.
isNaN()427   bool isNaN() const { return category == fcNaN; }
428 
429   /// Returns true if and only if the float is a signaling NaN.
430   bool isSignaling() const;
431 
432   /// @}
433 
434   /// \name Simple Queries
435   /// @{
436 
getCategory()437   fltCategory getCategory() const { return category; }
getSemantics()438   const fltSemantics &getSemantics() const { return *semantics; }
isNonZero()439   bool isNonZero() const { return category != fcZero; }
isFiniteNonZero()440   bool isFiniteNonZero() const { return isFinite() && !isZero(); }
isPosZero()441   bool isPosZero() const { return isZero() && !isNegative(); }
isNegZero()442   bool isNegZero() const { return isZero() && isNegative(); }
443 
444   /// Returns true if and only if the number has the smallest possible non-zero
445   /// magnitude in the current semantics.
446   bool isSmallest() const;
447 
448   /// Returns true if and only if the number has the largest possible finite
449   /// magnitude in the current semantics.
450   bool isLargest() const;
451 
452   /// Returns true if and only if the number is an exact integer.
453   bool isInteger() const;
454 
455   /// @}
456 
457   APFloat &operator=(const APFloat &);
458   APFloat &operator=(APFloat &&);
459 
460   /// \brief Overload to compute a hash code for an APFloat value.
461   ///
462   /// Note that the use of hash codes for floating point values is in general
463   /// frought with peril. Equality is hard to define for these values. For
464   /// example, should negative and positive zero hash to different codes? Are
465   /// they equal or not? This hash value implementation specifically
466   /// emphasizes producing different codes for different inputs in order to
467   /// be used in canonicalization and memoization. As such, equality is
468   /// bitwiseIsEqual, and 0 != -0.
469   friend hash_code hash_value(const APFloat &Arg);
470 
471   /// Converts this value into a decimal string.
472   ///
473   /// \param FormatPrecision The maximum number of digits of
474   ///   precision to output.  If there are fewer digits available,
475   ///   zero padding will not be used unless the value is
476   ///   integral and small enough to be expressed in
477   ///   FormatPrecision digits.  0 means to use the natural
478   ///   precision of the number.
479   /// \param FormatMaxPadding The maximum number of zeros to
480   ///   consider inserting before falling back to scientific
481   ///   notation.  0 means to always use scientific notation.
482   ///
483   /// Number       Precision    MaxPadding      Result
484   /// ------       ---------    ----------      ------
485   /// 1.01E+4              5             2       10100
486   /// 1.01E+4              4             2       1.01E+4
487   /// 1.01E+4              5             1       1.01E+4
488   /// 1.01E-2              5             2       0.0101
489   /// 1.01E-2              4             2       0.0101
490   /// 1.01E-2              4             1       1.01E-2
491   void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
492                 unsigned FormatMaxPadding = 3) const;
493 
494   /// If this value has an exact multiplicative inverse, store it in inv and
495   /// return true.
496   bool getExactInverse(APFloat *inv) const;
497 
498   /// \brief Enumeration of \c ilogb error results.
499   enum IlogbErrorKinds {
500     IEK_Zero = INT_MIN+1,
501     IEK_NaN = INT_MIN,
502     IEK_Inf = INT_MAX
503   };
504 
505   /// \brief Returns the exponent of the internal representation of the APFloat.
506   ///
507   /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
508   /// For special APFloat values, this returns special error codes:
509   ///
510   ///   NaN -> \c IEK_NaN
511   ///   0   -> \c IEK_Zero
512   ///   Inf -> \c IEK_Inf
513   ///
ilogb(const APFloat & Arg)514   friend int ilogb(const APFloat &Arg) {
515     if (Arg.isNaN())
516       return IEK_NaN;
517     if (Arg.isZero())
518       return IEK_Zero;
519     if (Arg.isInfinity())
520       return IEK_Inf;
521 
522     return Arg.exponent;
523   }
524 
525   /// \brief Returns: X * 2^Exp for integral exponents.
526   friend APFloat scalbn(APFloat X, int Exp);
527 
528 private:
529 
530   /// \name Simple Queries
531   /// @{
532 
533   integerPart *significandParts();
534   const integerPart *significandParts() const;
535   unsigned int partCount() const;
536 
537   /// @}
538 
539   /// \name Significand operations.
540   /// @{
541 
542   integerPart addSignificand(const APFloat &);
543   integerPart subtractSignificand(const APFloat &, integerPart);
544   lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
545   lostFraction multiplySignificand(const APFloat &, const APFloat *);
546   lostFraction divideSignificand(const APFloat &);
547   void incrementSignificand();
548   void initialize(const fltSemantics *);
549   void shiftSignificandLeft(unsigned int);
550   lostFraction shiftSignificandRight(unsigned int);
551   unsigned int significandLSB() const;
552   unsigned int significandMSB() const;
553   void zeroSignificand();
554   /// Return true if the significand excluding the integral bit is all ones.
555   bool isSignificandAllOnes() const;
556   /// Return true if the significand excluding the integral bit is all zeros.
557   bool isSignificandAllZeros() const;
558 
559   /// @}
560 
561   /// \name Arithmetic on special values.
562   /// @{
563 
564   opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
565   opStatus divideSpecials(const APFloat &);
566   opStatus multiplySpecials(const APFloat &);
567   opStatus modSpecials(const APFloat &);
568 
569   /// @}
570 
571   /// \name Special value setters.
572   /// @{
573 
574   void makeLargest(bool Neg = false);
575   void makeSmallest(bool Neg = false);
576   void makeNaN(bool SNaN = false, bool Neg = false,
577                const APInt *fill = nullptr);
578   static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
579                          const APInt *fill);
580   void makeInf(bool Neg = false);
581   void makeZero(bool Neg = false);
582 
583   /// @}
584 
585   /// \name Miscellany
586   /// @{
587 
588   bool convertFromStringSpecials(StringRef str);
589   opStatus normalize(roundingMode, lostFraction);
590   opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
591   cmpResult compareAbsoluteValue(const APFloat &) const;
592   opStatus handleOverflow(roundingMode);
593   bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
594   opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
595                                         roundingMode, bool *) const;
596   opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
597                                     roundingMode);
598   opStatus convertFromHexadecimalString(StringRef, roundingMode);
599   opStatus convertFromDecimalString(StringRef, roundingMode);
600   char *convertNormalToHexString(char *, unsigned int, bool,
601                                  roundingMode) const;
602   opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
603                                         roundingMode);
604 
605   /// @}
606 
607   APInt convertHalfAPFloatToAPInt() const;
608   APInt convertFloatAPFloatToAPInt() const;
609   APInt convertDoubleAPFloatToAPInt() const;
610   APInt convertQuadrupleAPFloatToAPInt() const;
611   APInt convertF80LongDoubleAPFloatToAPInt() const;
612   APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
613   void initFromAPInt(const fltSemantics *Sem, const APInt &api);
614   void initFromHalfAPInt(const APInt &api);
615   void initFromFloatAPInt(const APInt &api);
616   void initFromDoubleAPInt(const APInt &api);
617   void initFromQuadrupleAPInt(const APInt &api);
618   void initFromF80LongDoubleAPInt(const APInt &api);
619   void initFromPPCDoubleDoubleAPInt(const APInt &api);
620 
621   void assign(const APFloat &);
622   void copySignificand(const APFloat &);
623   void freeSignificand();
624 
625   /// The semantics that this value obeys.
626   const fltSemantics *semantics;
627 
628   /// A binary fraction with an explicit integer bit.
629   ///
630   /// The significand must be at least one bit wider than the target precision.
631   union Significand {
632     integerPart part;
633     integerPart *parts;
634   } significand;
635 
636   /// The signed unbiased exponent of the value.
637   ExponentType exponent;
638 
639   /// What kind of floating point number this is.
640   ///
641   /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
642   /// Using the extra bit keeps it from failing under VisualStudio.
643   fltCategory category : 3;
644 
645   /// Sign bit of the number.
646   unsigned int sign : 1;
647 };
648 
649 /// See friend declarations above.
650 ///
651 /// These additional declarations are required in order to compile LLVM with IBM
652 /// xlC compiler.
653 hash_code hash_value(const APFloat &Arg);
654 APFloat scalbn(APFloat X, int Exp);
655 
656 /// \brief Returns the absolute value of the argument.
abs(APFloat X)657 inline APFloat abs(APFloat X) {
658   X.clearSign();
659   return X;
660 }
661 
662 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
663 /// both are not NaN. If either argument is a NaN, returns the other argument.
664 LLVM_READONLY
minnum(const APFloat & A,const APFloat & B)665 inline APFloat minnum(const APFloat &A, const APFloat &B) {
666   if (A.isNaN())
667     return B;
668   if (B.isNaN())
669     return A;
670   return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
671 }
672 
673 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
674 /// both are not NaN. If either argument is a NaN, returns the other argument.
675 LLVM_READONLY
maxnum(const APFloat & A,const APFloat & B)676 inline APFloat maxnum(const APFloat &A, const APFloat &B) {
677   if (A.isNaN())
678     return B;
679   if (B.isNaN())
680     return A;
681   return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
682 }
683 
684 } // namespace llvm
685 
686 #endif // LLVM_ADT_APFLOAT_H
687