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 
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.
needsCleanup()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.
copySign(APFloat Value,const APFloat & Sign)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.
isNegative()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.
isNormal()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.
isFinite()407   bool isFinite() const { return !isNaN() && !isInfinity(); }
408 
409   /// Returns true if and only if the float is plus or minus zero.
isZero()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.
isInfinity()417   bool isInfinity() const { return category == fcInfinity; }
418 
419   /// Returns true if and only if the float is a quiet or signaling NaN.
isNaN()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 
getCategory()430   fltCategory getCategory() const { return category; }
getSemantics()431   const fltSemantics &getSemantics() const { return *semantics; }
isNonZero()432   bool isNonZero() const { return category != fcZero; }
isFiniteNonZero()433   bool isFiniteNonZero() const { return isFinite() && !isZero(); }
isPosZero()434   bool isPosZero() const { return isZero() && !isNegative(); }
isNegZero()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   ///
ilogb(const APFloat & Arg)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 
518 private:
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.
643 hash_code hash_value(const APFloat &Arg);
644 APFloat scalbn(APFloat X, int Exp);
645 
646 /// \brief Returns the absolute value of the argument.
abs(APFloat X)647 inline 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.
654 LLVM_READONLY
minnum(const APFloat & A,const APFloat & B)655 inline 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.
665 LLVM_READONLY
maxnum(const APFloat & A,const APFloat & B)666 inline 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