LLVM  3.7.0
APFloat.h
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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;
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 {
152  };
153 
154  /// IEEE-754R 4.3: Rounding-direction attributes.
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 {
181  };
182 
183  /// Convenience enum used to construct an uninitialized APFloat.
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);
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  /// Returns the size of the floating point number (in bits) in the given
280  /// semantics.
281  static unsigned getSizeInBits(const fltSemantics &Sem);
282 
283  /// @}
284 
285  /// Used to insert APFloat objects, or objects that contain APFloat objects,
286  /// into FoldingSets.
287  void Profile(FoldingSetNodeID &NID) const;
288 
289  /// \name Arithmetic
290  /// @{
291 
292  opStatus add(const APFloat &, roundingMode);
296  /// IEEE remainder.
297  opStatus remainder(const APFloat &);
298  /// C fmod, or llvm frem.
299  opStatus mod(const APFloat &, roundingMode);
302  /// IEEE-754R 5.3.1: nextUp/nextDown.
303  opStatus next(bool nextDown);
304 
305  /// \brief Operator+ overload which provides the default
306  /// \c nmNearestTiesToEven rounding mode and *no* error checking.
307  APFloat operator+(const APFloat &RHS) const {
308  APFloat Result = *this;
309  Result.add(RHS, rmNearestTiesToEven);
310  return Result;
311  }
312 
313  /// \brief Operator- overload which provides the default
314  /// \c nmNearestTiesToEven rounding mode and *no* error checking.
315  APFloat operator-(const APFloat &RHS) const {
316  APFloat Result = *this;
317  Result.subtract(RHS, rmNearestTiesToEven);
318  return Result;
319  }
320 
321  /// \brief Operator* overload which provides the default
322  /// \c nmNearestTiesToEven rounding mode and *no* error checking.
323  APFloat operator*(const APFloat &RHS) const {
324  APFloat Result = *this;
325  Result.multiply(RHS, rmNearestTiesToEven);
326  return Result;
327  }
328 
329  /// \brief Operator/ overload which provides the default
330  /// \c nmNearestTiesToEven rounding mode and *no* error checking.
331  APFloat operator/(const APFloat &RHS) const {
332  APFloat Result = *this;
333  Result.divide(RHS, rmNearestTiesToEven);
334  return Result;
335  }
336 
337  /// @}
338 
339  /// \name Sign operations.
340  /// @{
341 
342  void changeSign();
343  void clearSign();
344  void copySign(const APFloat &);
345 
346  /// \brief A static helper to produce a copy of an APFloat value with its sign
347  /// copied from some other APFloat.
348  static APFloat copySign(APFloat Value, const APFloat &Sign) {
349  Value.copySign(Sign);
350  return Value;
351  }
352 
353  /// @}
354 
355  /// \name Conversions
356  /// @{
357 
358  opStatus convert(const fltSemantics &, roundingMode, bool *);
359  opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
360  bool *) const;
361  opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
364  bool, roundingMode);
366  bool, roundingMode);
368  APInt bitcastToAPInt() const;
369  double convertToDouble() const;
370  float convertToFloat() const;
371 
372  /// @}
373 
374  /// The definition of equality is not straightforward for floating point, so
375  /// we won't use operator==. Use one of the following, or write whatever it
376  /// is you really mean.
377  bool operator==(const APFloat &) const = delete;
378 
379  /// IEEE comparison with another floating point number (NaNs compare
380  /// unordered, 0==-0).
381  cmpResult compare(const APFloat &) const;
382 
383  /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
384  bool bitwiseIsEqual(const APFloat &) const;
385 
386  /// Write out a hexadecimal representation of the floating point value to DST,
387  /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
388  /// Return the number of characters written, excluding the terminating NUL.
389  unsigned int convertToHexString(char *dst, unsigned int hexDigits,
390  bool upperCase, roundingMode) const;
391 
392  /// \name IEEE-754R 5.7.2 General operations.
393  /// @{
394 
395  /// IEEE-754R isSignMinus: Returns true if and only if the current value is
396  /// negative.
397  ///
398  /// This applies to zeros and NaNs as well.
399  bool isNegative() const { return sign; }
400 
401  /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
402  ///
403  /// This implies that the current value of the float is not zero, subnormal,
404  /// infinite, or NaN following the definition of normality from IEEE-754R.
405  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
406 
407  /// Returns true if and only if the current value is zero, subnormal, or
408  /// normal.
409  ///
410  /// This means that the value is not infinite or NaN.
411  bool isFinite() const { return !isNaN() && !isInfinity(); }
412 
413  /// Returns true if and only if the float is plus or minus zero.
414  bool isZero() const { return category == fcZero; }
415 
416  /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
417  /// denormal.
418  bool isDenormal() const;
419 
420  /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
421  bool isInfinity() const { return category == fcInfinity; }
422 
423  /// Returns true if and only if the float is a quiet or signaling NaN.
424  bool isNaN() const { return category == fcNaN; }
425 
426  /// Returns true if and only if the float is a signaling NaN.
427  bool isSignaling() const;
428 
429  /// @}
430 
431  /// \name Simple Queries
432  /// @{
433 
434  fltCategory getCategory() const { return category; }
435  const fltSemantics &getSemantics() const { return *semantics; }
436  bool isNonZero() const { return category != fcZero; }
437  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
438  bool isPosZero() const { return isZero() && !isNegative(); }
439  bool isNegZero() const { return isZero() && isNegative(); }
440 
441  /// Returns true if and only if the number has the smallest possible non-zero
442  /// magnitude in the current semantics.
443  bool isSmallest() const;
444 
445  /// Returns true if and only if the number has the largest possible finite
446  /// magnitude in the current semantics.
447  bool isLargest() const;
448 
449  /// @}
450 
451  APFloat &operator=(const APFloat &);
453 
454  /// \brief Overload to compute a hash code for an APFloat value.
455  ///
456  /// Note that the use of hash codes for floating point values is in general
457  /// frought with peril. Equality is hard to define for these values. For
458  /// example, should negative and positive zero hash to different codes? Are
459  /// they equal or not? This hash value implementation specifically
460  /// emphasizes producing different codes for different inputs in order to
461  /// be used in canonicalization and memoization. As such, equality is
462  /// bitwiseIsEqual, and 0 != -0.
463  friend hash_code hash_value(const APFloat &Arg);
464 
465  /// Converts this value into a decimal string.
466  ///
467  /// \param FormatPrecision The maximum number of digits of
468  /// precision to output. If there are fewer digits available,
469  /// zero padding will not be used unless the value is
470  /// integral and small enough to be expressed in
471  /// FormatPrecision digits. 0 means to use the natural
472  /// precision of the number.
473  /// \param FormatMaxPadding The maximum number of zeros to
474  /// consider inserting before falling back to scientific
475  /// notation. 0 means to always use scientific notation.
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) 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  /// \brief Enumeration of \c ilogb error results.
494  IEK_Zero = INT_MIN+1,
495  IEK_NaN = INT_MIN,
496  IEK_Inf = INT_MAX
497  };
498 
499  /// \brief Returns the exponent of the internal representation of the APFloat.
500  ///
501  /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
502  /// For special APFloat values, this returns special error codes:
503  ///
504  /// NaN -> \c IEK_NaN
505  /// 0 -> \c IEK_Zero
506  /// Inf -> \c IEK_Inf
507  ///
508  friend int ilogb(const APFloat &Arg) {
509  if (Arg.isNaN())
510  return IEK_NaN;
511  if (Arg.isZero())
512  return IEK_Zero;
513  if (Arg.isInfinity())
514  return IEK_Inf;
515 
516  return Arg.exponent;
517  }
518 
519  /// \brief Returns: X * 2^Exp for integral exponents.
520  friend APFloat scalbn(APFloat X, int Exp);
521 
522 private:
523 
524  /// \name Simple Queries
525  /// @{
526 
527  integerPart *significandParts();
528  const integerPart *significandParts() const;
529  unsigned int partCount() const;
530 
531  /// @}
532 
533  /// \name Significand operations.
534  /// @{
535 
536  integerPart addSignificand(const APFloat &);
537  integerPart subtractSignificand(const APFloat &, integerPart);
538  lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
539  lostFraction multiplySignificand(const APFloat &, const APFloat *);
540  lostFraction divideSignificand(const APFloat &);
541  void incrementSignificand();
542  void initialize(const fltSemantics *);
543  void shiftSignificandLeft(unsigned int);
544  lostFraction shiftSignificandRight(unsigned int);
545  unsigned int significandLSB() const;
546  unsigned int significandMSB() const;
547  void zeroSignificand();
548  /// Return true if the significand excluding the integral bit is all ones.
549  bool isSignificandAllOnes() const;
550  /// Return true if the significand excluding the integral bit is all zeros.
551  bool isSignificandAllZeros() const;
552 
553  /// @}
554 
555  /// \name Arithmetic on special values.
556  /// @{
557 
558  opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
559  opStatus divideSpecials(const APFloat &);
560  opStatus multiplySpecials(const APFloat &);
561  opStatus modSpecials(const APFloat &);
562 
563  /// @}
564 
565  /// \name Special value setters.
566  /// @{
567 
568  void makeLargest(bool Neg = false);
569  void makeSmallest(bool Neg = false);
570  void makeNaN(bool SNaN = false, bool Neg = false,
571  const APInt *fill = nullptr);
572  static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
573  const APInt *fill);
574  void makeInf(bool Neg = false);
575  void makeZero(bool Neg = false);
576 
577  /// @}
578 
579  /// \name Miscellany
580  /// @{
581 
582  bool convertFromStringSpecials(StringRef str);
583  opStatus normalize(roundingMode, lostFraction);
584  opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
585  cmpResult compareAbsoluteValue(const APFloat &) const;
586  opStatus handleOverflow(roundingMode);
587  bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
588  opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
589  roundingMode, bool *) const;
590  opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
591  roundingMode);
592  opStatus convertFromHexadecimalString(StringRef, roundingMode);
593  opStatus convertFromDecimalString(StringRef, roundingMode);
594  char *convertNormalToHexString(char *, unsigned int, bool,
595  roundingMode) const;
596  opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
597  roundingMode);
598 
599  /// @}
600 
601  APInt convertHalfAPFloatToAPInt() const;
602  APInt convertFloatAPFloatToAPInt() const;
603  APInt convertDoubleAPFloatToAPInt() const;
604  APInt convertQuadrupleAPFloatToAPInt() const;
605  APInt convertF80LongDoubleAPFloatToAPInt() const;
606  APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
607  void initFromAPInt(const fltSemantics *Sem, const APInt &api);
608  void initFromHalfAPInt(const APInt &api);
609  void initFromFloatAPInt(const APInt &api);
610  void initFromDoubleAPInt(const APInt &api);
611  void initFromQuadrupleAPInt(const APInt &api);
612  void initFromF80LongDoubleAPInt(const APInt &api);
613  void initFromPPCDoubleDoubleAPInt(const APInt &api);
614 
615  void assign(const APFloat &);
616  void copySignificand(const APFloat &);
617  void freeSignificand();
618 
619  /// The semantics that this value obeys.
620  const fltSemantics *semantics;
621 
622  /// A binary fraction with an explicit integer bit.
623  ///
624  /// The significand must be at least one bit wider than the target precision.
625  union Significand {
626  integerPart part;
627  integerPart *parts;
628  } significand;
629 
630  /// The signed unbiased exponent of the value.
631  ExponentType exponent;
632 
633  /// What kind of floating point number this is.
634  ///
635  /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
636  /// Using the extra bit keeps it from failing under VisualStudio.
637  fltCategory category : 3;
638 
639  /// Sign bit of the number.
640  unsigned int sign : 1;
641 };
642 
643 /// See friend declarations above.
644 ///
645 /// These additional declarations are required in order to compile LLVM with IBM
646 /// xlC compiler.
647 hash_code hash_value(const APFloat &Arg);
648 APFloat scalbn(APFloat X, int Exp);
649 
650 /// \brief Returns the absolute value of the argument.
651 inline APFloat abs(APFloat X) {
652  X.clearSign();
653  return X;
654 }
655 
656 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
657 /// both are not NaN. If either argument is a NaN, returns the other argument.
659 inline APFloat minnum(const APFloat &A, const APFloat &B) {
660  if (A.isNaN())
661  return B;
662  if (B.isNaN())
663  return A;
664  return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
665 }
666 
667 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
668 /// both are not NaN. If either argument is a NaN, returns the other argument.
670 inline APFloat maxnum(const APFloat &A, const APFloat &B) {
671  if (A.isNaN())
672  return B;
673  if (B.isNaN())
674  return A;
675  return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
676 }
677 
678 } // namespace llvm
679 
680 #endif // LLVM_ADT_APFLOAT_H
friend int ilogb(const APFloat &Arg)
Returns the exponent of the internal representation of the APFloat.
Definition: APFloat.h:508
opStatus divide(const APFloat &, roundingMode)
Definition: APFloat.cpp:1709
bool isNonZero() const
Definition: APFloat.h:436
bool isNaN() const
Returns true if and only if the float is a quiet or signaling NaN.
Definition: APFloat.h:424
APFloat & operator=(const APFloat &)
Definition: APFloat.cpp:675
void Profile(FoldingSetNodeID &NID) const
Used to insert APFloat objects, or objects that contain APFloat objects, into FoldingSets.
Definition: APFloat.cpp:835
static const fltSemantics IEEEdouble
Definition: APFloat.h:133
APFloat(const fltSemantics &)
Definition: APFloat.cpp:804
opStatus
IEEE-754R 7: Default exception handling.
Definition: APFloat.h:166
void clearSign()
Definition: APFloat.cpp:1630
friend APFloat scalbn(APFloat X, int Exp)
Returns: X * 2^Exp for integral exponents.
static APFloat getZero(const fltSemantics &Sem, bool Negative=false)
Factory for Positive and Negative Zero.
Definition: APFloat.h:213
static const fltSemantics Bogus
A Pseudo fltsemantic used to construct APFloats that cannot conflict with anything real...
Definition: APFloat.h:140
bool isSignaling() const
Returns true if and only if the float is a signaling NaN.
Definition: APFloat.cpp:3783
bool isFiniteNonZero() const
Definition: APFloat.h:437
opStatus convertFromString(StringRef, roundingMode)
Definition: APFloat.cpp:2645
bool bitwiseIsEqual(const APFloat &) const
Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
Definition: APFloat.cpp:771
static const fltSemantics x87DoubleExtended
Definition: APFloat.h:136
signed short ExponentType
A signed type to represent a floating point numbers unbiased exponent.
Definition: APFloat.h:126
opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode, bool *) const
Definition: APFloat.cpp:2191
static const fltSemantics IEEEquad
Definition: APFloat.h:134
APFloat operator+(const APFloat &RHS) const
Operator+ overload which provides the default nmNearestTiesToEven rounding mode and no error checking...
Definition: APFloat.h:307
void copySign(const APFloat &)
Definition: APFloat.cpp:1637
This file implements a class to represent arbitrary precision integral constant values and operations...
uninitializedTag
Convenience enum used to construct an uninitialized APFloat.
Definition: APFloat.h:184
opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int, bool, roundingMode)
Definition: APFloat.cpp:2320
bool isFinite() const
Returns true if and only if the current value is zero, subnormal, or normal.
Definition: APFloat.h:411
static APFloat getSmallest(const fltSemantics &Sem, bool Negative=false)
Returns the smallest (by magnitude) finite number in the given semantics.
Definition: APFloat.cpp:3427
hash_code hash_value(const APFloat &Arg)
See friend declarations above.
Definition: APFloat.cpp:2848
static unsigned int semanticsPrecision(const fltSemantics &)
Definition: APFloat.cpp:846
double convertToDouble() const
Definition: APFloat.cpp:3116
static APFloat getInf(const fltSemantics &Sem, bool Negative=false)
Factory for Positive and Negative Infinity.
Definition: APFloat.h:222
unsigned int convertToHexString(char *dst, unsigned int hexDigits, bool upperCase, roundingMode) const
Write out a hexadecimal representation of the floating point value to DST, which must be of sufficien...
Definition: APFloat.cpp:2697
opStatus mod(const APFloat &, roundingMode)
C fmod, or llvm frem.
Definition: APFloat.cpp:1765
static APFloat copySign(APFloat Value, const APFloat &Sign)
A static helper to produce a copy of an APFloat value with its sign copied from some other APFloat...
Definition: APFloat.h:348
opStatus convertFromAPInt(const APInt &, bool, roundingMode)
Definition: APFloat.cpp:2272
FoldingSetNodeID - This class is used to gather all the unique data bits of a node.
Definition: FoldingSet.h:297
A self-contained host- and target-independent arbitrary-precision floating-point software implementat...
Definition: APFloat.h:122
friend hash_code hash_value(const APFloat &Arg)
Overload to compute a hash code for an APFloat value.
bool isNegZero() const
Definition: APFloat.h:439
static APFloat getSmallestNormalized(const fltSemantics &Sem, bool Negative=false)
Returns the smallest (by magnitude) normalized finite number in the given semantics.
Definition: APFloat.cpp:3437
cmpResult compare(const APFloat &) const
IEEE comparison with another floating point number (NaNs compare unordered, 0==-0).
Definition: APFloat.cpp:1893
bool operator==(const APFloat &) const =delete
The definition of equality is not straightforward for floating point, so we won't use operator==...
fltCategory
Category of internally-represented number.
Definition: APFloat.h:176
opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode)
Definition: APFloat.cpp:1805
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang","erlang-compatible garbage collector")
opStatus convert(const fltSemantics &, roundingMode, bool *)
APFloat::convert - convert a value of one floating point type to another.
Definition: APFloat.cpp:1972
IlogbErrorKinds
Enumeration of ilogb error results.
Definition: APFloat.h:493
APFloat operator/(const APFloat &RHS) const
Operator/ overload which provides the default nmNearestTiesToEven rounding mode and no error checking...
Definition: APFloat.h:331
void changeSign()
Definition: APFloat.cpp:1623
APFloat scalbn(APFloat X, int Exp)
Definition: APFloat.cpp:3928
fltCategory getCategory() const
Definition: APFloat.h:434
static const fltSemantics IEEEhalf
Definition: APFloat.h:131
LLVM_READONLY APFloat maxnum(const APFloat &A, const APFloat &B)
Implements IEEE maxNum semantics.
Definition: APFloat.h:670
bool needsCleanup() const
Returns whether this instance allocated memory.
Definition: APFloat.h:205
opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int, bool, roundingMode)
Definition: APFloat.cpp:2292
bool isPosZero() const
Definition: APFloat.h:438
static const fltSemantics PPCDoubleDouble
Definition: APFloat.h:135
roundingMode
IEEE-754R 4.3: Rounding-direction attributes.
Definition: APFloat.h:155
lostFraction
Enum that represents what fraction of the LSB truncated bits of an fp number represent.
Definition: APFloat.h:32
bool isNegative() const
IEEE-754R isSignMinus: Returns true if and only if the current value is negative. ...
Definition: APFloat.h:399
opStatus add(const APFloat &, roundingMode)
Definition: APFloat.cpp:1676
bool isDenormal() const
IEEE-754R isSubnormal(): Returns true if and only if the float is a denormal.
Definition: APFloat.cpp:703
opStatus multiply(const APFloat &, roundingMode)
Definition: APFloat.cpp:1690
static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE=false)
Returns a float which is bitcasted from an all one value int.
Definition: APFloat.cpp:3354
Class for arbitrary precision integers.
Definition: APInt.h:73
static APFloat getSNaN(const fltSemantics &Sem, bool Negative=false, const APInt *payload=nullptr)
Factory for SNaN values.
Definition: APFloat.h:250
APInt bitcastToAPInt() const
Definition: APFloat.cpp:3084
static APFloat getLargest(const fltSemantics &Sem, bool Negative=false)
Returns the largest finite number in the given semantics.
Definition: APFloat.cpp:3417
An opaque object representing a hash code.
Definition: Hashing.h:73
static APFloat getNaN(const fltSemantics &Sem, bool Negative=false, unsigned type=0)
Factory for QNaN values.
Definition: APFloat.h:233
void toString(SmallVectorImpl< char > &Str, unsigned FormatPrecision=0, unsigned FormatMaxPadding=3) const
Converts this value into a decimal string.
Definition: APFloat.cpp:3551
static const fltSemantics IEEEsingle
Definition: APFloat.h:132
APFloat operator*(const APFloat &RHS) const
Operator* overload which provides the default nmNearestTiesToEven rounding mode and no error checking...
Definition: APFloat.h:323
opStatus roundToIntegral(roundingMode)
Definition: APFloat.cpp:1849
APFloat abs(APFloat X)
Returns the absolute value of the argument.
Definition: APFloat.h:651
float convertToFloat() const
Definition: APFloat.cpp:3107
bool isSmallest() const
Returns true if and only if the number has the smallest possible non-zero magnitude in the current se...
Definition: APFloat.cpp:710
#define LLVM_READONLY
Definition: Compiler.h:166
APFloat operator-(const APFloat &RHS) const
Operator- overload which provides the default nmNearestTiesToEven rounding mode and no error checking...
Definition: APFloat.h:315
LLVM Value Representation.
Definition: Value.h:69
bool isZero() const
Returns true if and only if the float is plus or minus zero.
Definition: APFloat.h:414
static unsigned getSizeInBits(const fltSemantics &Sem)
Returns the size of the floating point number (in bits) in the given semantics.
Definition: APFloat.cpp:3374
bool isLargest() const
Returns true if and only if the number has the largest possible finite magnitude in the current seman...
Definition: APFloat.cpp:763
bool isInfinity() const
IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
Definition: APFloat.h:421
StringRef - Represent a constant reference to a string, i.e.
Definition: StringRef.h:40
opStatus next(bool nextDown)
IEEE-754R 5.3.1: nextUp/nextDown.
Definition: APFloat.cpp:3796
opStatus remainder(const APFloat &)
IEEE remainder.
Definition: APFloat.cpp:1728
cmpResult
IEEE-754R 5.11: Floating Point Comparison Relations.
Definition: APFloat.h:147
bool getExactInverse(APFloat *inv) const
If this value has an exact multiplicative inverse, store it in inv and return true.
Definition: APFloat.cpp:3754
const fltSemantics & getSemantics() const
Definition: APFloat.h:435
opStatus subtract(const APFloat &, roundingMode)
Definition: APFloat.cpp:1683
static APFloat getQNaN(const fltSemantics &Sem, bool Negative=false, const APInt *payload=nullptr)
Factory for QNaN values.
Definition: APFloat.h:244
LLVM_READONLY APFloat minnum(const APFloat &A, const APFloat &B)
Implements IEEE minNum semantics.
Definition: APFloat.h:659
bool isNormal() const
IEEE-754R isNormal: Returns true if and only if the current value is normal.
Definition: APFloat.h:405
uint64_t integerPart
Definition: APInt.h:33