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APFloat.h
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1 //===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 ///
9 /// \file
10 /// \brief
11 /// This file declares a class to represent arbitrary precision floating point
12 /// values and provide a variety of arithmetic operations on them.
13 ///
14 //===----------------------------------------------------------------------===//
15 
16 #ifndef LLVM_ADT_APFLOAT_H
17 #define LLVM_ADT_APFLOAT_H
18 
19 #include "llvm/ADT/APInt.h"
20 #include "llvm/ADT/ArrayRef.h"
22 #include <memory>
23 
24 #define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL) \
25  do { \
26  if (usesLayout<IEEEFloat>(getSemantics())) \
27  return U.IEEE.METHOD_CALL; \
28  if (usesLayout<DoubleAPFloat>(getSemantics())) \
29  return U.Double.METHOD_CALL; \
30  llvm_unreachable("Unexpected semantics"); \
31  } while (false)
32 
33 namespace llvm {
34 
35 struct fltSemantics;
36 class APSInt;
37 class StringRef;
38 class APFloat;
39 class raw_ostream;
40 
41 template <typename T> class SmallVectorImpl;
42 
43 /// Enum that represents what fraction of the LSB truncated bits of an fp number
44 /// represent.
45 ///
46 /// This essentially combines the roles of guard and sticky bits.
47 enum lostFraction { // Example of truncated bits:
48  lfExactlyZero, // 000000
49  lfLessThanHalf, // 0xxxxx x's not all zero
50  lfExactlyHalf, // 100000
51  lfMoreThanHalf // 1xxxxx x's not all zero
52 };
53 
54 /// A self-contained host- and target-independent arbitrary-precision
55 /// floating-point software implementation.
56 ///
57 /// APFloat uses bignum integer arithmetic as provided by static functions in
58 /// the APInt class. The library will work with bignum integers whose parts are
59 /// any unsigned type at least 16 bits wide, but 64 bits is recommended.
60 ///
61 /// Written for clarity rather than speed, in particular with a view to use in
62 /// the front-end of a cross compiler so that target arithmetic can be correctly
63 /// performed on the host. Performance should nonetheless be reasonable,
64 /// particularly for its intended use. It may be useful as a base
65 /// implementation for a run-time library during development of a faster
66 /// target-specific one.
67 ///
68 /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
69 /// implemented operations. Currently implemented operations are add, subtract,
70 /// multiply, divide, fused-multiply-add, conversion-to-float,
71 /// conversion-to-integer and conversion-from-integer. New rounding modes
72 /// (e.g. away from zero) can be added with three or four lines of code.
73 ///
74 /// Four formats are built-in: IEEE single precision, double precision,
75 /// quadruple precision, and x87 80-bit extended double (when operating with
76 /// full extended precision). Adding a new format that obeys IEEE semantics
77 /// only requires adding two lines of code: a declaration and definition of the
78 /// format.
79 ///
80 /// All operations return the status of that operation as an exception bit-mask,
81 /// so multiple operations can be done consecutively with their results or-ed
82 /// together. The returned status can be useful for compiler diagnostics; e.g.,
83 /// inexact, underflow and overflow can be easily diagnosed on constant folding,
84 /// and compiler optimizers can determine what exceptions would be raised by
85 /// folding operations and optimize, or perhaps not optimize, accordingly.
86 ///
87 /// At present, underflow tininess is detected after rounding; it should be
88 /// straight forward to add support for the before-rounding case too.
89 ///
90 /// The library reads hexadecimal floating point numbers as per C99, and
91 /// correctly rounds if necessary according to the specified rounding mode.
92 /// Syntax is required to have been validated by the caller. It also converts
93 /// floating point numbers to hexadecimal text as per the C99 %a and %A
94 /// conversions. The output precision (or alternatively the natural minimal
95 /// precision) can be specified; if the requested precision is less than the
96 /// natural precision the output is correctly rounded for the specified rounding
97 /// mode.
98 ///
99 /// It also reads decimal floating point numbers and correctly rounds according
100 /// to the specified rounding mode.
101 ///
102 /// Conversion to decimal text is not currently implemented.
103 ///
104 /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
105 /// signed exponent, and the significand as an array of integer parts. After
106 /// normalization of a number of precision P the exponent is within the range of
107 /// the format, and if the number is not denormal the P-th bit of the
108 /// significand is set as an explicit integer bit. For denormals the most
109 /// significant bit is shifted right so that the exponent is maintained at the
110 /// format's minimum, so that the smallest denormal has just the least
111 /// significant bit of the significand set. The sign of zeroes and infinities
112 /// is significant; the exponent and significand of such numbers is not stored,
113 /// but has a known implicit (deterministic) value: 0 for the significands, 0
114 /// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
115 /// significand are deterministic, although not really meaningful, and preserved
116 /// in non-conversion operations. The exponent is implicitly all 1 bits.
117 ///
118 /// APFloat does not provide any exception handling beyond default exception
119 /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
120 /// by encoding Signaling NaNs with the first bit of its trailing significand as
121 /// 0.
122 ///
123 /// TODO
124 /// ====
125 ///
126 /// Some features that may or may not be worth adding:
127 ///
128 /// Binary to decimal conversion (hard).
129 ///
130 /// Optional ability to detect underflow tininess before rounding.
131 ///
132 /// New formats: x87 in single and double precision mode (IEEE apart from
133 /// extended exponent range) (hard).
134 ///
135 /// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
136 ///
137 
138 // This is the common type definitions shared by APFloat and its internal
139 // implementation classes. This struct should not define any non-static data
140 // members.
141 struct APFloatBase {
144 
145  /// A signed type to represent a floating point numbers unbiased exponent.
146  typedef signed short ExponentType;
147 
148  /// \name Floating Point Semantics.
149  /// @{
150  enum Semantics {
157  };
158 
160  static Semantics SemanticsToEnum(const llvm::fltSemantics &Sem);
161 
162  static const fltSemantics &IEEEhalf() LLVM_READNONE;
164  static const fltSemantics &IEEEdouble() LLVM_READNONE;
165  static const fltSemantics &IEEEquad() LLVM_READNONE;
166  static const fltSemantics &PPCDoubleDouble() LLVM_READNONE;
167  static const fltSemantics &x87DoubleExtended() LLVM_READNONE;
168 
169  /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
170  /// anything real.
171  static const fltSemantics &Bogus() LLVM_READNONE;
172 
173  /// @}
174 
175  /// IEEE-754R 5.11: Floating Point Comparison Relations.
176  enum cmpResult {
181  };
182 
183  /// IEEE-754R 4.3: Rounding-direction attributes.
190  };
191 
192  /// IEEE-754R 7: Default exception handling.
193  ///
194  /// opUnderflow or opOverflow are always returned or-ed with opInexact.
195  enum opStatus {
196  opOK = 0x00,
197  opInvalidOp = 0x01,
198  opDivByZero = 0x02,
199  opOverflow = 0x04,
200  opUnderflow = 0x08,
201  opInexact = 0x10
202  };
203 
204  /// Category of internally-represented number.
205  enum fltCategory {
210  };
211 
212  /// Convenience enum used to construct an uninitialized APFloat.
215  };
216 
217  /// Enumeration of \c ilogb error results.
219  IEK_Zero = INT_MIN + 1,
220  IEK_NaN = INT_MIN,
221  IEK_Inf = INT_MAX
222  };
223 
224  static unsigned int semanticsPrecision(const fltSemantics &);
225  static ExponentType semanticsMinExponent(const fltSemantics &);
226  static ExponentType semanticsMaxExponent(const fltSemantics &);
227  static unsigned int semanticsSizeInBits(const fltSemantics &);
228 
229  /// Returns the size of the floating point number (in bits) in the given
230  /// semantics.
231  static unsigned getSizeInBits(const fltSemantics &Sem);
232 };
233 
234 namespace detail {
235 
236 class IEEEFloat final : public APFloatBase {
237 public:
238  /// \name Constructors
239  /// @{
240 
241  IEEEFloat(const fltSemantics &); // Default construct to 0.0
244  IEEEFloat(const fltSemantics &, const APInt &);
245  explicit IEEEFloat(double d);
246  explicit IEEEFloat(float f);
247  IEEEFloat(const IEEEFloat &);
248  IEEEFloat(IEEEFloat &&);
249  ~IEEEFloat();
250 
251  /// @}
252 
253  /// Returns whether this instance allocated memory.
254  bool needsCleanup() const { return partCount() > 1; }
255 
256  /// \name Convenience "constructors"
257  /// @{
258 
259  /// @}
260 
261  /// \name Arithmetic
262  /// @{
263 
265  opStatus subtract(const IEEEFloat &, roundingMode);
266  opStatus multiply(const IEEEFloat &, roundingMode);
267  opStatus divide(const IEEEFloat &, roundingMode);
268  /// IEEE remainder.
269  opStatus remainder(const IEEEFloat &);
270  /// C fmod, or llvm frem.
271  opStatus mod(const IEEEFloat &);
272  opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);
273  opStatus roundToIntegral(roundingMode);
274  /// IEEE-754R 5.3.1: nextUp/nextDown.
275  opStatus next(bool nextDown);
276 
277  /// @}
278 
279  /// \name Sign operations.
280  /// @{
281 
282  void changeSign();
283 
284  /// @}
285 
286  /// \name Conversions
287  /// @{
288 
289  opStatus convert(const fltSemantics &, roundingMode, bool *);
290  opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,
291  roundingMode, bool *) const;
292  opStatus convertFromAPInt(const APInt &, bool, roundingMode);
293  opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
294  bool, roundingMode);
295  opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
296  bool, roundingMode);
297  opStatus convertFromString(StringRef, roundingMode);
298  APInt bitcastToAPInt() const;
299  double convertToDouble() const;
300  float convertToFloat() const;
301 
302  /// @}
303 
304  /// The definition of equality is not straightforward for floating point, so
305  /// we won't use operator==. Use one of the following, or write whatever it
306  /// is you really mean.
307  bool operator==(const IEEEFloat &) const = delete;
308 
309  /// IEEE comparison with another floating point number (NaNs compare
310  /// unordered, 0==-0).
311  cmpResult compare(const IEEEFloat &) const;
312 
313  /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
314  bool bitwiseIsEqual(const IEEEFloat &) const;
315 
316  /// Write out a hexadecimal representation of the floating point value to DST,
317  /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
318  /// Return the number of characters written, excluding the terminating NUL.
319  unsigned int convertToHexString(char *dst, unsigned int hexDigits,
320  bool upperCase, roundingMode) const;
321 
322  /// \name IEEE-754R 5.7.2 General operations.
323  /// @{
324 
325  /// IEEE-754R isSignMinus: Returns true if and only if the current value is
326  /// negative.
327  ///
328  /// This applies to zeros and NaNs as well.
329  bool isNegative() const { return sign; }
330 
331  /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
332  ///
333  /// This implies that the current value of the float is not zero, subnormal,
334  /// infinite, or NaN following the definition of normality from IEEE-754R.
335  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
336 
337  /// Returns true if and only if the current value is zero, subnormal, or
338  /// normal.
339  ///
340  /// This means that the value is not infinite or NaN.
341  bool isFinite() const { return !isNaN() && !isInfinity(); }
342 
343  /// Returns true if and only if the float is plus or minus zero.
344  bool isZero() const { return category == fcZero; }
345 
346  /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
347  /// denormal.
348  bool isDenormal() const;
349 
350  /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
351  bool isInfinity() const { return category == fcInfinity; }
352 
353  /// Returns true if and only if the float is a quiet or signaling NaN.
354  bool isNaN() const { return category == fcNaN; }
355 
356  /// Returns true if and only if the float is a signaling NaN.
357  bool isSignaling() const;
358 
359  /// @}
360 
361  /// \name Simple Queries
362  /// @{
363 
364  fltCategory getCategory() const { return category; }
365  const fltSemantics &getSemantics() const { return *semantics; }
366  bool isNonZero() const { return category != fcZero; }
367  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
368  bool isPosZero() const { return isZero() && !isNegative(); }
369  bool isNegZero() const { return isZero() && isNegative(); }
370 
371  /// Returns true if and only if the number has the smallest possible non-zero
372  /// magnitude in the current semantics.
373  bool isSmallest() const;
374 
375  /// Returns true if and only if the number has the largest possible finite
376  /// magnitude in the current semantics.
377  bool isLargest() const;
378 
379  /// Returns true if and only if the number is an exact integer.
380  bool isInteger() const;
381 
382  /// @}
383 
384  IEEEFloat &operator=(const IEEEFloat &);
385  IEEEFloat &operator=(IEEEFloat &&);
386 
387  /// Overload to compute a hash code for an APFloat value.
388  ///
389  /// Note that the use of hash codes for floating point values is in general
390  /// frought with peril. Equality is hard to define for these values. For
391  /// example, should negative and positive zero hash to different codes? Are
392  /// they equal or not? This hash value implementation specifically
393  /// emphasizes producing different codes for different inputs in order to
394  /// be used in canonicalization and memoization. As such, equality is
395  /// bitwiseIsEqual, and 0 != -0.
396  friend hash_code hash_value(const IEEEFloat &Arg);
397 
398  /// Converts this value into a decimal string.
399  ///
400  /// \param FormatPrecision The maximum number of digits of
401  /// precision to output. If there are fewer digits available,
402  /// zero padding will not be used unless the value is
403  /// integral and small enough to be expressed in
404  /// FormatPrecision digits. 0 means to use the natural
405  /// precision of the number.
406  /// \param FormatMaxPadding The maximum number of zeros to
407  /// consider inserting before falling back to scientific
408  /// notation. 0 means to always use scientific notation.
409  ///
410  /// \param TruncateZero Indicate whether to remove the trailing zero in
411  /// fraction part or not. Also setting this parameter to false forcing
412  /// producing of output more similar to default printf behavior.
413  /// Specifically the lower e is used as exponent delimiter and exponent
414  /// always contains no less than two digits.
415  ///
416  /// Number Precision MaxPadding Result
417  /// ------ --------- ---------- ------
418  /// 1.01E+4 5 2 10100
419  /// 1.01E+4 4 2 1.01E+4
420  /// 1.01E+4 5 1 1.01E+4
421  /// 1.01E-2 5 2 0.0101
422  /// 1.01E-2 4 2 0.0101
423  /// 1.01E-2 4 1 1.01E-2
424  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
425  unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;
426 
427  /// If this value has an exact multiplicative inverse, store it in inv and
428  /// return true.
429  bool getExactInverse(APFloat *inv) const;
430 
431  /// Returns the exponent of the internal representation of the APFloat.
432  ///
433  /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
434  /// For special APFloat values, this returns special error codes:
435  ///
436  /// NaN -> \c IEK_NaN
437  /// 0 -> \c IEK_Zero
438  /// Inf -> \c IEK_Inf
439  ///
440  friend int ilogb(const IEEEFloat &Arg);
441 
442  /// Returns: X * 2^Exp for integral exponents.
443  friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);
444 
445  friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);
446 
447  /// \name Special value setters.
448  /// @{
449 
450  void makeLargest(bool Neg = false);
451  void makeSmallest(bool Neg = false);
452  void makeNaN(bool SNaN = false, bool Neg = false,
453  const APInt *fill = nullptr);
454  void makeInf(bool Neg = false);
455  void makeZero(bool Neg = false);
456  void makeQuiet();
457 
458  /// Returns the smallest (by magnitude) normalized finite number in the given
459  /// semantics.
460  ///
461  /// \param Negative - True iff the number should be negative
462  void makeSmallestNormalized(bool Negative = false);
463 
464  /// @}
465 
466  cmpResult compareAbsoluteValue(const IEEEFloat &) const;
467 
468 private:
469  /// \name Simple Queries
470  /// @{
471 
472  integerPart *significandParts();
473  const integerPart *significandParts() const;
474  unsigned int partCount() const;
475 
476  /// @}
477 
478  /// \name Significand operations.
479  /// @{
480 
481  integerPart addSignificand(const IEEEFloat &);
482  integerPart subtractSignificand(const IEEEFloat &, integerPart);
483  lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
484  lostFraction multiplySignificand(const IEEEFloat &, const IEEEFloat *);
485  lostFraction divideSignificand(const IEEEFloat &);
486  void incrementSignificand();
487  void initialize(const fltSemantics *);
488  void shiftSignificandLeft(unsigned int);
489  lostFraction shiftSignificandRight(unsigned int);
490  unsigned int significandLSB() const;
491  unsigned int significandMSB() const;
492  void zeroSignificand();
493  /// Return true if the significand excluding the integral bit is all ones.
494  bool isSignificandAllOnes() const;
495  /// Return true if the significand excluding the integral bit is all zeros.
496  bool isSignificandAllZeros() const;
497 
498  /// @}
499 
500  /// \name Arithmetic on special values.
501  /// @{
502 
503  opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);
504  opStatus divideSpecials(const IEEEFloat &);
505  opStatus multiplySpecials(const IEEEFloat &);
506  opStatus modSpecials(const IEEEFloat &);
507 
508  /// @}
509 
510  /// \name Miscellany
511  /// @{
512 
513  bool convertFromStringSpecials(StringRef str);
514  opStatus normalize(roundingMode, lostFraction);
515  opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);
516  opStatus handleOverflow(roundingMode);
517  bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
518  opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,
519  unsigned int, bool, roundingMode,
520  bool *) const;
521  opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
522  roundingMode);
523  opStatus convertFromHexadecimalString(StringRef, roundingMode);
524  opStatus convertFromDecimalString(StringRef, roundingMode);
525  char *convertNormalToHexString(char *, unsigned int, bool,
526  roundingMode) const;
527  opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
528  roundingMode);
529 
530  /// @}
531 
532  APInt convertHalfAPFloatToAPInt() const;
533  APInt convertFloatAPFloatToAPInt() const;
534  APInt convertDoubleAPFloatToAPInt() const;
535  APInt convertQuadrupleAPFloatToAPInt() const;
536  APInt convertF80LongDoubleAPFloatToAPInt() const;
537  APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
538  void initFromAPInt(const fltSemantics *Sem, const APInt &api);
539  void initFromHalfAPInt(const APInt &api);
540  void initFromFloatAPInt(const APInt &api);
541  void initFromDoubleAPInt(const APInt &api);
542  void initFromQuadrupleAPInt(const APInt &api);
543  void initFromF80LongDoubleAPInt(const APInt &api);
544  void initFromPPCDoubleDoubleAPInt(const APInt &api);
545 
546  void assign(const IEEEFloat &);
547  void copySignificand(const IEEEFloat &);
548  void freeSignificand();
549 
550  /// Note: this must be the first data member.
551  /// The semantics that this value obeys.
552  const fltSemantics *semantics;
553 
554  /// A binary fraction with an explicit integer bit.
555  ///
556  /// The significand must be at least one bit wider than the target precision.
557  union Significand {
558  integerPart part;
559  integerPart *parts;
560  } significand;
561 
562  /// The signed unbiased exponent of the value.
563  ExponentType exponent;
564 
565  /// What kind of floating point number this is.
566  ///
567  /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
568  /// Using the extra bit keeps it from failing under VisualStudio.
569  fltCategory category : 3;
570 
571  /// Sign bit of the number.
572  unsigned int sign : 1;
573 };
574 
576 int ilogb(const IEEEFloat &Arg);
578 IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);
579 
580 // This mode implements more precise float in terms of two APFloats.
581 // The interface and layout is designed for arbitray underlying semantics,
582 // though currently only PPCDoubleDouble semantics are supported, whose
583 // corresponding underlying semantics are IEEEdouble.
584 class DoubleAPFloat final : public APFloatBase {
585  // Note: this must be the first data member.
586  const fltSemantics *Semantics;
587  std::unique_ptr<APFloat[]> Floats;
588 
589  opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,
590  const APFloat &cc, roundingMode RM);
591 
592  opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,
593  DoubleAPFloat &Out, roundingMode RM);
594 
595 public:
596  DoubleAPFloat(const fltSemantics &S);
599  DoubleAPFloat(const fltSemantics &S, const APInt &I);
600  DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);
601  DoubleAPFloat(const DoubleAPFloat &RHS);
603 
604  DoubleAPFloat &operator=(const DoubleAPFloat &RHS);
605 
607  if (this != &RHS) {
608  this->~DoubleAPFloat();
609  new (this) DoubleAPFloat(std::move(RHS));
610  }
611  return *this;
612  }
613 
614  bool needsCleanup() const { return Floats != nullptr; }
615 
616  APFloat &getFirst() { return Floats[0]; }
617  const APFloat &getFirst() const { return Floats[0]; }
618  APFloat &getSecond() { return Floats[1]; }
619  const APFloat &getSecond() const { return Floats[1]; }
620 
621  opStatus add(const DoubleAPFloat &RHS, roundingMode RM);
622  opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);
623  opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);
624  opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);
625  opStatus remainder(const DoubleAPFloat &RHS);
626  opStatus mod(const DoubleAPFloat &RHS);
627  opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
628  const DoubleAPFloat &Addend, roundingMode RM);
629  opStatus roundToIntegral(roundingMode RM);
630  void changeSign();
631  cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;
632 
633  fltCategory getCategory() const;
634  bool isNegative() const;
635 
636  void makeInf(bool Neg);
637  void makeZero(bool Neg);
638  void makeLargest(bool Neg);
639  void makeSmallest(bool Neg);
640  void makeSmallestNormalized(bool Neg);
641  void makeNaN(bool SNaN, bool Neg, const APInt *fill);
642 
643  cmpResult compare(const DoubleAPFloat &RHS) const;
644  bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;
645  APInt bitcastToAPInt() const;
646  opStatus convertFromString(StringRef, roundingMode);
647  opStatus next(bool nextDown);
648 
649  opStatus convertToInteger(MutableArrayRef<integerPart> Input,
650  unsigned int Width, bool IsSigned, roundingMode RM,
651  bool *IsExact) const;
652  opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);
653  opStatus convertFromSignExtendedInteger(const integerPart *Input,
654  unsigned int InputSize, bool IsSigned,
655  roundingMode RM);
656  opStatus convertFromZeroExtendedInteger(const integerPart *Input,
657  unsigned int InputSize, bool IsSigned,
658  roundingMode RM);
659  unsigned int convertToHexString(char *DST, unsigned int HexDigits,
660  bool UpperCase, roundingMode RM) const;
661 
662  bool isDenormal() const;
663  bool isSmallest() const;
664  bool isLargest() const;
665  bool isInteger() const;
666 
667  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
668  unsigned FormatMaxPadding, bool TruncateZero = true) const;
669 
670  bool getExactInverse(APFloat *inv) const;
671 
672  friend int ilogb(const DoubleAPFloat &Arg);
673  friend DoubleAPFloat scalbn(DoubleAPFloat X, int Exp, roundingMode);
674  friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);
675  friend hash_code hash_value(const DoubleAPFloat &Arg);
676 };
677 
679 
680 } // End detail namespace
681 
682 // This is a interface class that is currently forwarding functionalities from
683 // detail::IEEEFloat.
684 class APFloat : public APFloatBase {
687 
688  static_assert(std::is_standard_layout<IEEEFloat>::value, "");
689 
690  union Storage {
691  const fltSemantics *semantics;
692  IEEEFloat IEEE;
693  DoubleAPFloat Double;
694 
695  explicit Storage(IEEEFloat F, const fltSemantics &S);
696  explicit Storage(DoubleAPFloat F, const fltSemantics &S)
697  : Double(std::move(F)) {
698  assert(&S == &PPCDoubleDouble());
699  }
700 
701  template <typename... ArgTypes>
702  Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {
703  if (usesLayout<IEEEFloat>(Semantics)) {
704  new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);
705  return;
706  }
707  if (usesLayout<DoubleAPFloat>(Semantics)) {
708  new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);
709  return;
710  }
711  llvm_unreachable("Unexpected semantics");
712  }
713 
714  ~Storage() {
715  if (usesLayout<IEEEFloat>(*semantics)) {
716  IEEE.~IEEEFloat();
717  return;
718  }
719  if (usesLayout<DoubleAPFloat>(*semantics)) {
720  Double.~DoubleAPFloat();
721  return;
722  }
723  llvm_unreachable("Unexpected semantics");
724  }
725 
726  Storage(const Storage &RHS) {
727  if (usesLayout<IEEEFloat>(*RHS.semantics)) {
728  new (this) IEEEFloat(RHS.IEEE);
729  return;
730  }
731  if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
732  new (this) DoubleAPFloat(RHS.Double);
733  return;
734  }
735  llvm_unreachable("Unexpected semantics");
736  }
737 
738  Storage(Storage &&RHS) {
739  if (usesLayout<IEEEFloat>(*RHS.semantics)) {
740  new (this) IEEEFloat(std::move(RHS.IEEE));
741  return;
742  }
743  if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
744  new (this) DoubleAPFloat(std::move(RHS.Double));
745  return;
746  }
747  llvm_unreachable("Unexpected semantics");
748  }
749 
750  Storage &operator=(const Storage &RHS) {
751  if (usesLayout<IEEEFloat>(*semantics) &&
752  usesLayout<IEEEFloat>(*RHS.semantics)) {
753  IEEE = RHS.IEEE;
754  } else if (usesLayout<DoubleAPFloat>(*semantics) &&
755  usesLayout<DoubleAPFloat>(*RHS.semantics)) {
756  Double = RHS.Double;
757  } else if (this != &RHS) {
758  this->~Storage();
759  new (this) Storage(RHS);
760  }
761  return *this;
762  }
763 
764  Storage &operator=(Storage &&RHS) {
765  if (usesLayout<IEEEFloat>(*semantics) &&
766  usesLayout<IEEEFloat>(*RHS.semantics)) {
767  IEEE = std::move(RHS.IEEE);
768  } else if (usesLayout<DoubleAPFloat>(*semantics) &&
769  usesLayout<DoubleAPFloat>(*RHS.semantics)) {
770  Double = std::move(RHS.Double);
771  } else if (this != &RHS) {
772  this->~Storage();
773  new (this) Storage(std::move(RHS));
774  }
775  return *this;
776  }
777  } U;
778 
779  template <typename T> static bool usesLayout(const fltSemantics &Semantics) {
780  static_assert(std::is_same<T, IEEEFloat>::value ||
781  std::is_same<T, DoubleAPFloat>::value, "");
782  if (std::is_same<T, DoubleAPFloat>::value) {
783  return &Semantics == &PPCDoubleDouble();
784  }
785  return &Semantics != &PPCDoubleDouble();
786  }
787 
788  IEEEFloat &getIEEE() {
789  if (usesLayout<IEEEFloat>(*U.semantics))
790  return U.IEEE;
791  if (usesLayout<DoubleAPFloat>(*U.semantics))
792  return U.Double.getFirst().U.IEEE;
793  llvm_unreachable("Unexpected semantics");
794  }
795 
796  const IEEEFloat &getIEEE() const {
797  if (usesLayout<IEEEFloat>(*U.semantics))
798  return U.IEEE;
799  if (usesLayout<DoubleAPFloat>(*U.semantics))
800  return U.Double.getFirst().U.IEEE;
801  llvm_unreachable("Unexpected semantics");
802  }
803 
804  void makeZero(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeZero(Neg)); }
805 
806  void makeInf(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeInf(Neg)); }
807 
808  void makeNaN(bool SNaN, bool Neg, const APInt *fill) {
809  APFLOAT_DISPATCH_ON_SEMANTICS(makeNaN(SNaN, Neg, fill));
810  }
811 
812  void makeLargest(bool Neg) {
813  APFLOAT_DISPATCH_ON_SEMANTICS(makeLargest(Neg));
814  }
815 
816  void makeSmallest(bool Neg) {
817  APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallest(Neg));
818  }
819 
820  void makeSmallestNormalized(bool Neg) {
821  APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallestNormalized(Neg));
822  }
823 
824  // FIXME: This is due to clang 3.3 (or older version) always checks for the
825  // default constructor in an array aggregate initialization, even if no
826  // elements in the array is default initialized.
827  APFloat() : U(IEEEdouble()) {
828  llvm_unreachable("This is a workaround for old clang.");
829  }
830 
831  explicit APFloat(IEEEFloat F, const fltSemantics &S) : U(std::move(F), S) {}
832  explicit APFloat(DoubleAPFloat F, const fltSemantics &S)
833  : U(std::move(F), S) {}
834 
835  cmpResult compareAbsoluteValue(const APFloat &RHS) const {
836  assert(&getSemantics() == &RHS.getSemantics() &&
837  "Should only compare APFloats with the same semantics");
838  if (usesLayout<IEEEFloat>(getSemantics()))
839  return U.IEEE.compareAbsoluteValue(RHS.U.IEEE);
840  if (usesLayout<DoubleAPFloat>(getSemantics()))
841  return U.Double.compareAbsoluteValue(RHS.U.Double);
842  llvm_unreachable("Unexpected semantics");
843  }
844 
845 public:
846  APFloat(const fltSemantics &Semantics) : U(Semantics) {}
847  APFloat(const fltSemantics &Semantics, StringRef S);
848  APFloat(const fltSemantics &Semantics, integerPart I) : U(Semantics, I) {}
849  // TODO: Remove this constructor. This isn't faster than the first one.
851  : U(Semantics, uninitialized) {}
852  APFloat(const fltSemantics &Semantics, const APInt &I) : U(Semantics, I) {}
853  explicit APFloat(double d) : U(IEEEFloat(d), IEEEdouble()) {}
854  explicit APFloat(float f) : U(IEEEFloat(f), IEEEsingle()) {}
855  APFloat(const APFloat &RHS) = default;
856  APFloat(APFloat &&RHS) = default;
857 
858  ~APFloat() = default;
859 
861 
862  /// Factory for Positive and Negative Zero.
863  ///
864  /// \param Negative True iff the number should be negative.
865  static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
866  APFloat Val(Sem, uninitialized);
867  Val.makeZero(Negative);
868  return Val;
869  }
870 
871  /// Factory for Positive and Negative Infinity.
872  ///
873  /// \param Negative True iff the number should be negative.
874  static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
875  APFloat Val(Sem, uninitialized);
876  Val.makeInf(Negative);
877  return Val;
878  }
879 
880  /// Factory for NaN values.
881  ///
882  /// \param Negative - True iff the NaN generated should be negative.
883  /// \param payload - The unspecified fill bits for creating the NaN, 0 by
884  /// default. The value is truncated as necessary.
885  static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
886  uint64_t payload = 0) {
887  if (payload) {
888  APInt intPayload(64, payload);
889  return getQNaN(Sem, Negative, &intPayload);
890  } else {
891  return getQNaN(Sem, Negative, nullptr);
892  }
893  }
894 
895  /// Factory for QNaN values.
896  static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
897  const APInt *payload = nullptr) {
898  APFloat Val(Sem, uninitialized);
899  Val.makeNaN(false, Negative, payload);
900  return Val;
901  }
902 
903  /// Factory for SNaN values.
904  static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
905  const APInt *payload = nullptr) {
906  APFloat Val(Sem, uninitialized);
907  Val.makeNaN(true, Negative, payload);
908  return Val;
909  }
910 
911  /// Returns the largest finite number in the given semantics.
912  ///
913  /// \param Negative - True iff the number should be negative
914  static APFloat getLargest(const fltSemantics &Sem, bool Negative = false) {
915  APFloat Val(Sem, uninitialized);
916  Val.makeLargest(Negative);
917  return Val;
918  }
919 
920  /// Returns the smallest (by magnitude) finite number in the given semantics.
921  /// Might be denormalized, which implies a relative loss of precision.
922  ///
923  /// \param Negative - True iff the number should be negative
924  static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false) {
925  APFloat Val(Sem, uninitialized);
926  Val.makeSmallest(Negative);
927  return Val;
928  }
929 
930  /// Returns the smallest (by magnitude) normalized finite number in the given
931  /// semantics.
932  ///
933  /// \param Negative - True iff the number should be negative
935  bool Negative = false) {
936  APFloat Val(Sem, uninitialized);
937  Val.makeSmallestNormalized(Negative);
938  return Val;
939  }
940 
941  /// Returns a float which is bitcasted from an all one value int.
942  ///
943  /// \param BitWidth - Select float type
944  /// \param isIEEE - If 128 bit number, select between PPC and IEEE
945  static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
946 
947  /// Used to insert APFloat objects, or objects that contain APFloat objects,
948  /// into FoldingSets.
949  void Profile(FoldingSetNodeID &NID) const;
950 
952  assert(&getSemantics() == &RHS.getSemantics() &&
953  "Should only call on two APFloats with the same semantics");
954  if (usesLayout<IEEEFloat>(getSemantics()))
955  return U.IEEE.add(RHS.U.IEEE, RM);
956  if (usesLayout<DoubleAPFloat>(getSemantics()))
957  return U.Double.add(RHS.U.Double, RM);
958  llvm_unreachable("Unexpected semantics");
959  }
961  assert(&getSemantics() == &RHS.getSemantics() &&
962  "Should only call on two APFloats with the same semantics");
963  if (usesLayout<IEEEFloat>(getSemantics()))
964  return U.IEEE.subtract(RHS.U.IEEE, RM);
965  if (usesLayout<DoubleAPFloat>(getSemantics()))
966  return U.Double.subtract(RHS.U.Double, RM);
967  llvm_unreachable("Unexpected semantics");
968  }
970  assert(&getSemantics() == &RHS.getSemantics() &&
971  "Should only call on two APFloats with the same semantics");
972  if (usesLayout<IEEEFloat>(getSemantics()))
973  return U.IEEE.multiply(RHS.U.IEEE, RM);
974  if (usesLayout<DoubleAPFloat>(getSemantics()))
975  return U.Double.multiply(RHS.U.Double, RM);
976  llvm_unreachable("Unexpected semantics");
977  }
979  assert(&getSemantics() == &RHS.getSemantics() &&
980  "Should only call on two APFloats with the same semantics");
981  if (usesLayout<IEEEFloat>(getSemantics()))
982  return U.IEEE.divide(RHS.U.IEEE, RM);
983  if (usesLayout<DoubleAPFloat>(getSemantics()))
984  return U.Double.divide(RHS.U.Double, RM);
985  llvm_unreachable("Unexpected semantics");
986  }
987  opStatus remainder(const APFloat &RHS) {
988  assert(&getSemantics() == &RHS.getSemantics() &&
989  "Should only call on two APFloats with the same semantics");
990  if (usesLayout<IEEEFloat>(getSemantics()))
991  return U.IEEE.remainder(RHS.U.IEEE);
992  if (usesLayout<DoubleAPFloat>(getSemantics()))
993  return U.Double.remainder(RHS.U.Double);
994  llvm_unreachable("Unexpected semantics");
995  }
996  opStatus mod(const APFloat &RHS) {
997  assert(&getSemantics() == &RHS.getSemantics() &&
998  "Should only call on two APFloats with the same semantics");
999  if (usesLayout<IEEEFloat>(getSemantics()))
1000  return U.IEEE.mod(RHS.U.IEEE);
1001  if (usesLayout<DoubleAPFloat>(getSemantics()))
1002  return U.Double.mod(RHS.U.Double);
1003  llvm_unreachable("Unexpected semantics");
1004  }
1005  opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend,
1006  roundingMode RM) {
1007  assert(&getSemantics() == &Multiplicand.getSemantics() &&
1008  "Should only call on APFloats with the same semantics");
1009  assert(&getSemantics() == &Addend.getSemantics() &&
1010  "Should only call on APFloats with the same semantics");
1011  if (usesLayout<IEEEFloat>(getSemantics()))
1012  return U.IEEE.fusedMultiplyAdd(Multiplicand.U.IEEE, Addend.U.IEEE, RM);
1013  if (usesLayout<DoubleAPFloat>(getSemantics()))
1014  return U.Double.fusedMultiplyAdd(Multiplicand.U.Double, Addend.U.Double,
1015  RM);
1016  llvm_unreachable("Unexpected semantics");
1017  }
1019  APFLOAT_DISPATCH_ON_SEMANTICS(roundToIntegral(RM));
1020  }
1021 
1022  // TODO: bool parameters are not readable and a source of bugs.
1023  // Do something.
1024  opStatus next(bool nextDown) {
1025  APFLOAT_DISPATCH_ON_SEMANTICS(next(nextDown));
1026  }
1027 
1028  /// Add two APFloats, rounding ties to the nearest even.
1029  /// No error checking.
1030  APFloat operator+(const APFloat &RHS) const {
1031  APFloat Result(*this);
1032  (void)Result.add(RHS, rmNearestTiesToEven);
1033  return Result;
1034  }
1035 
1036  /// Subtract two APFloats, rounding ties to the nearest even.
1037  /// No error checking.
1038  APFloat operator-(const APFloat &RHS) const {
1039  APFloat Result(*this);
1040  (void)Result.subtract(RHS, rmNearestTiesToEven);
1041  return Result;
1042  }
1043 
1044  /// Multiply two APFloats, rounding ties to the nearest even.
1045  /// No error checking.
1046  APFloat operator*(const APFloat &RHS) const {
1047  APFloat Result(*this);
1048  (void)Result.multiply(RHS, rmNearestTiesToEven);
1049  return Result;
1050  }
1051 
1052  /// Divide the first APFloat by the second, rounding ties to the nearest even.
1053  /// No error checking.
1054  APFloat operator/(const APFloat &RHS) const {
1055  APFloat Result(*this);
1056  (void)Result.divide(RHS, rmNearestTiesToEven);
1057  return Result;
1058  }
1059 
1061  void clearSign() {
1062  if (isNegative())
1063  changeSign();
1064  }
1065  void copySign(const APFloat &RHS) {
1066  if (isNegative() != RHS.isNegative())
1067  changeSign();
1068  }
1069 
1070  /// A static helper to produce a copy of an APFloat value with its sign
1071  /// copied from some other APFloat.
1072  static APFloat copySign(APFloat Value, const APFloat &Sign) {
1073  Value.copySign(Sign);
1074  return Value;
1075  }
1076 
1077  opStatus convert(const fltSemantics &ToSemantics, roundingMode RM,
1078  bool *losesInfo);
1080  unsigned int Width, bool IsSigned, roundingMode RM,
1081  bool *IsExact) const {
1083  convertToInteger(Input, Width, IsSigned, RM, IsExact));
1084  }
1085  opStatus convertToInteger(APSInt &Result, roundingMode RM,
1086  bool *IsExact) const;
1087  opStatus convertFromAPInt(const APInt &Input, bool IsSigned,
1088  roundingMode RM) {
1089  APFLOAT_DISPATCH_ON_SEMANTICS(convertFromAPInt(Input, IsSigned, RM));
1090  }
1092  unsigned int InputSize, bool IsSigned,
1093  roundingMode RM) {
1095  convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM));
1096  }
1098  unsigned int InputSize, bool IsSigned,
1099  roundingMode RM) {
1101  convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM));
1102  }
1103  opStatus convertFromString(StringRef, roundingMode);
1105  APFLOAT_DISPATCH_ON_SEMANTICS(bitcastToAPInt());
1106  }
1107  double convertToDouble() const { return getIEEE().convertToDouble(); }
1108  float convertToFloat() const { return getIEEE().convertToFloat(); }
1109 
1110  bool operator==(const APFloat &) const = delete;
1111 
1112  cmpResult compare(const APFloat &RHS) const {
1113  assert(&getSemantics() == &RHS.getSemantics() &&
1114  "Should only compare APFloats with the same semantics");
1115  if (usesLayout<IEEEFloat>(getSemantics()))
1116  return U.IEEE.compare(RHS.U.IEEE);
1117  if (usesLayout<DoubleAPFloat>(getSemantics()))
1118  return U.Double.compare(RHS.U.Double);
1119  llvm_unreachable("Unexpected semantics");
1120  }
1121 
1122  bool bitwiseIsEqual(const APFloat &RHS) const {
1123  if (&getSemantics() != &RHS.getSemantics())
1124  return false;
1125  if (usesLayout<IEEEFloat>(getSemantics()))
1126  return U.IEEE.bitwiseIsEqual(RHS.U.IEEE);
1127  if (usesLayout<DoubleAPFloat>(getSemantics()))
1128  return U.Double.bitwiseIsEqual(RHS.U.Double);
1129  llvm_unreachable("Unexpected semantics");
1130  }
1131 
1132  /// We don't rely on operator== working on double values, as
1133  /// it returns true for things that are clearly not equal, like -0.0 and 0.0.
1134  /// As such, this method can be used to do an exact bit-for-bit comparison of
1135  /// two floating point values.
1136  ///
1137  /// We leave the version with the double argument here because it's just so
1138  /// convenient to write "2.0" and the like. Without this function we'd
1139  /// have to duplicate its logic everywhere it's called.
1140  bool isExactlyValue(double V) const {
1141  bool ignored;
1142  APFloat Tmp(V);
1143  Tmp.convert(getSemantics(), APFloat::rmNearestTiesToEven, &ignored);
1144  return bitwiseIsEqual(Tmp);
1145  }
1146 
1147  unsigned int convertToHexString(char *DST, unsigned int HexDigits,
1148  bool UpperCase, roundingMode RM) const {
1150  convertToHexString(DST, HexDigits, UpperCase, RM));
1151  }
1152 
1153  bool isZero() const { return getCategory() == fcZero; }
1154  bool isInfinity() const { return getCategory() == fcInfinity; }
1155  bool isNaN() const { return getCategory() == fcNaN; }
1156 
1157  bool isNegative() const { return getIEEE().isNegative(); }
1159  bool isSignaling() const { return getIEEE().isSignaling(); }
1160 
1161  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
1162  bool isFinite() const { return !isNaN() && !isInfinity(); }
1163 
1164  fltCategory getCategory() const { return getIEEE().getCategory(); }
1165  const fltSemantics &getSemantics() const { return *U.semantics; }
1166  bool isNonZero() const { return !isZero(); }
1167  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
1168  bool isPosZero() const { return isZero() && !isNegative(); }
1169  bool isNegZero() const { return isZero() && isNegative(); }
1173 
1174  APFloat &operator=(const APFloat &RHS) = default;
1175  APFloat &operator=(APFloat &&RHS) = default;
1176 
1177  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
1178  unsigned FormatMaxPadding = 3, bool TruncateZero = true) const {
1180  toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero));
1181  }
1182 
1183  void print(raw_ostream &) const;
1184  void dump() const;
1185 
1186  bool getExactInverse(APFloat *inv) const {
1187  APFLOAT_DISPATCH_ON_SEMANTICS(getExactInverse(inv));
1188  }
1189 
1190  friend hash_code hash_value(const APFloat &Arg);
1191  friend int ilogb(const APFloat &Arg) { return ilogb(Arg.getIEEE()); }
1192  friend APFloat scalbn(APFloat X, int Exp, roundingMode RM);
1193  friend APFloat frexp(const APFloat &X, int &Exp, roundingMode RM);
1194  friend IEEEFloat;
1196 };
1197 
1198 /// See friend declarations above.
1199 ///
1200 /// These additional declarations are required in order to compile LLVM with IBM
1201 /// xlC compiler.
1204  if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1205  return APFloat(scalbn(X.U.IEEE, Exp, RM), X.getSemantics());
1206  if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1207  return APFloat(scalbn(X.U.Double, Exp, RM), X.getSemantics());
1208  llvm_unreachable("Unexpected semantics");
1209 }
1210 
1211 /// Equivalent of C standard library function.
1212 ///
1213 /// While the C standard says Exp is an unspecified value for infinity and nan,
1214 /// this returns INT_MAX for infinities, and INT_MIN for NaNs.
1215 inline APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM) {
1216  if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1217  return APFloat(frexp(X.U.IEEE, Exp, RM), X.getSemantics());
1218  if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1219  return APFloat(frexp(X.U.Double, Exp, RM), X.getSemantics());
1220  llvm_unreachable("Unexpected semantics");
1221 }
1222 /// Returns the absolute value of the argument.
1224  X.clearSign();
1225  return X;
1226 }
1227 
1228 /// Returns the negated value of the argument.
1230  X.changeSign();
1231  return X;
1232 }
1233 
1234 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
1235 /// both are not NaN. If either argument is a NaN, returns the other argument.
1237 inline APFloat minnum(const APFloat &A, const APFloat &B) {
1238  if (A.isNaN())
1239  return B;
1240  if (B.isNaN())
1241  return A;
1242  return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
1243 }
1244 
1245 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
1246 /// both are not NaN. If either argument is a NaN, returns the other argument.
1248 inline APFloat maxnum(const APFloat &A, const APFloat &B) {
1249  if (A.isNaN())
1250  return B;
1251  if (B.isNaN())
1252  return A;
1253  return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
1254 }
1255 
1256 /// Implements IEEE 754-2018 minimum semantics. Returns the smaller of 2
1257 /// arguments, propagating NaNs and treating -0 as less than +0.
1259 inline APFloat minimum(const APFloat &A, const APFloat &B) {
1260  if (A.isNaN())
1261  return A;
1262  if (B.isNaN())
1263  return B;
1264  if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1265  return A.isNegative() ? A : B;
1266  return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
1267 }
1268 
1269 /// Implements IEEE 754-2018 maximum semantics. Returns the larger of 2
1270 /// arguments, propagating NaNs and treating -0 as less than +0.
1272 inline APFloat maximum(const APFloat &A, const APFloat &B) {
1273  if (A.isNaN())
1274  return A;
1275  if (B.isNaN())
1276  return B;
1277  if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1278  return A.isNegative() ? B : A;
1279  return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
1280 }
1281 
1282 } // namespace llvm
1283 
1284 #undef APFLOAT_DISPATCH_ON_SEMANTICS
1285 #endif // LLVM_ADT_APFLOAT_H
friend int ilogb(const APFloat &Arg)
Definition: APFloat.h:1191
opStatus roundToIntegral(roundingMode RM)
Definition: APFloat.h:1018
static APFloat getNaN(const fltSemantics &Sem, bool Negative=false, uint64_t payload=0)
Factory for NaN values.
Definition: APFloat.h:885
static const fltSemantics & IEEEquad() LLVM_READNONE
Definition: APFloat.cpp:161
fltCategory
Category of internally-represented number.
Definition: APFloat.h:205
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
bool isZero() const
Definition: APFloat.h:1153
opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM)
Definition: APFloat.h:1087
APFloat(const fltSemantics &Semantics)
Definition: APFloat.h:846
This class represents lattice values for constants.
Definition: AllocatorList.h:23
APFloat(double d)
Definition: APFloat.h:853
fltCategory getCategory() const
Definition: APFloat.h:1164
float convertToFloat() const
Definition: APFloat.h:1108
static unsigned getSizeInBits(const fltSemantics &Sem)
Returns the size of the floating point number (in bits) in the given semantics.
Definition: APFloat.cpp:205
F(f)
const fltSemantics & getSemantics() const
Definition: APFloat.h:1165
static APFloat getZero(const fltSemantics &Sem, bool Negative=false)
Factory for Positive and Negative Zero.
Definition: APFloat.h:865
Bits in a word.
Definition: APInt.h:78
static const llvm::fltSemantics & EnumToSemantics(Semantics S)
Definition: APFloat.cpp:116
LLVM_READONLY APFloat maximum(const APFloat &A, const APFloat &B)
Implements IEEE 754-2018 maximum semantics.
Definition: APFloat.h:1272
void changeSign()
Definition: APFloat.h:1060
opStatus next(bool nextDown)
Definition: APFloat.h:1024
APFloat(const fltSemantics &Semantics, const APInt &I)
Definition: APFloat.h:852
bool isNonZero() const
Definition: APFloat.h:366
static Semantics SemanticsToEnum(const llvm::fltSemantics &Sem)
Definition: APFloat.cpp:135
bool isNegative() const
IEEE-754R isSignMinus: Returns true if and only if the current value is negative. ...
Definition: APFloat.h:329
opStatus convertToInteger(MutableArrayRef< integerPart > Input, unsigned int Width, bool IsSigned, roundingMode RM, bool *IsExact) const
Definition: APFloat.h:1079
opStatus convertFromSignExtendedInteger(const integerPart *Input, unsigned int InputSize, bool IsSigned, roundingMode RM)
Definition: APFloat.h:1091
opStatus divide(const APFloat &RHS, roundingMode RM)
Definition: APFloat.h:978
static APFloat getSmallest(const fltSemantics &Sem, bool Negative=false)
Returns the smallest (by magnitude) finite number in the given semantics.
Definition: APFloat.h:924
std::string toString(Error E)
Write all error messages (if any) in E to a string.
Definition: Error.h:966
friend IEEEFloat
Definition: APFloat.h:1194
bool isNonZero() const
Definition: APFloat.h:1166
roundingMode
IEEE-754R 4.3: Rounding-direction attributes.
Definition: APFloat.h:184
This class consists of common code factored out of the SmallVector class to reduce code duplication b...
Definition: APFloat.h:41
APFloat operator*(const APFloat &RHS) const
Multiply two APFloats, rounding ties to the nearest even.
Definition: APFloat.h:1046
LLVM_READONLY APFloat minimum(const APFloat &A, const APFloat &B)
Implements IEEE 754-2018 minimum semantics.
Definition: APFloat.h:1259
APFloat operator-(const APFloat &RHS) const
Subtract two APFloats, rounding ties to the nearest even.
Definition: APFloat.h:1038
static ExponentType semanticsMaxExponent(const fltSemantics &)
Definition: APFloat.cpp:194
This file implements a class to represent arbitrary precision integral constant values and operations...
div rem Hoist decompose integer division and remainder
bool isInfinity() const
Definition: APFloat.h:1154
opStatus convert(const fltSemantics &ToSemantics, roundingMode RM, bool *losesInfo)
Definition: APFloat.cpp:4483
static unsigned int semanticsSizeInBits(const fltSemantics &)
Definition: APFloat.cpp:201
void toString(SmallVectorImpl< char > &Str, unsigned FormatPrecision=0, unsigned FormatMaxPadding=3, bool TruncateZero=true) const
Definition: APFloat.h:1177
friend DoubleAPFloat
Definition: APFloat.h:1195
bool isNaN() const
Returns true if and only if the float is a quiet or signaling NaN.
Definition: APFloat.h:354
hash_code hash_value(const APFloat &Arg)
See friend declarations above.
Definition: APFloat.cpp:4470
opStatus subtract(const APFloat &RHS, roundingMode RM)
Definition: APFloat.h:960
cmpResult
IEEE-754R 5.11: Floating Point Comparison Relations.
Definition: APFloat.h:176
static const fltSemantics & IEEEdouble() LLVM_READNONE
Definition: APFloat.cpp:158
static APFloat getInf(const fltSemantics &Sem, bool Negative=false)
Factory for Positive and Negative Infinity.
Definition: APFloat.h:874
static ExponentType semanticsMinExponent(const fltSemantics &)
Definition: APFloat.cpp:198
uninitializedTag
Convenience enum used to construct an uninitialized APFloat.
Definition: APFloat.h:213
static const unsigned integerPartWidth
Definition: APFloat.h:143
IlogbErrorKinds
Enumeration of ilogb error results.
Definition: APFloat.h:218
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:1072
FoldingSetNodeID - This class is used to gather all the unique data bits of a node.
Definition: FoldingSet.h:305
fltCategory getCategory() const
Definition: APFloat.h:364
bool isNegZero() const
Definition: APFloat.h:1169
void clearSign()
Definition: APFloat.h:1061
static GCRegistry::Add< OcamlGC > B("ocaml", "ocaml 3.10-compatible GC")
void dump(const SparseBitVector< ElementSize > &LHS, raw_ostream &out)
bool isNegative() const
Definition: APFloat.h:1157
MutableArrayRef - Represent a mutable reference to an array (0 or more elements consecutively in memo...
Definition: ArrayRef.h:290
APFloat(float f)
Definition: APFloat.h:854
bool isNaN() const
Definition: APFloat.h:1155
bool isLargest() const
Definition: APFloat.h:1171
double convertToDouble() const
Definition: APFloat.h:1107
APFloat scalbn(APFloat X, int Exp, APFloat::roundingMode RM)
Definition: APFloat.h:1203
bool isExactlyValue(double V) const
We don&#39;t rely on operator== working on double values, as it returns true for things that are clearly ...
Definition: APFloat.h:1140
opStatus multiply(const APFloat &RHS, roundingMode RM)
Definition: APFloat.h:969
amdgpu Simplify well known AMD library false FunctionCallee Value * Arg
static void print(raw_ostream &Out, object::Archive::Kind Kind, T Val)
APFloat operator+(const APFloat &RHS) const
Add two APFloats, rounding ties to the nearest even.
Definition: APFloat.h:1030
static const fltSemantics & x87DoubleExtended() LLVM_READNONE
Definition: APFloat.cpp:164
APFloat operator/(const APFloat &RHS) const
Divide the first APFloat by the second, rounding ties to the nearest even.
Definition: APFloat.h:1054
#define llvm_unreachable(msg)
Marks that the current location is not supposed to be reachable.
void copySign(const APFloat &RHS)
Definition: APFloat.h:1065
LLVM_READONLY APFloat maxnum(const APFloat &A, const APFloat &B)
Implements IEEE maxNum semantics.
Definition: APFloat.h:1248
signed short ExponentType
A signed type to represent a floating point numbers unbiased exponent.
Definition: APFloat.h:146
bool isFinite() const
Definition: APFloat.h:1162
bool needsCleanup() const
Definition: APFloat.h:860
static const fltSemantics & IEEEsingle() LLVM_READNONE
Definition: APFloat.cpp:155
bool isInteger() const
Definition: APFloat.h:1172
DoubleAPFloat & operator=(DoubleAPFloat &&RHS)
Definition: APFloat.h:606
static const fltSemantics & IEEEhalf() LLVM_READNONE
Definition: APFloat.cpp:152
bool isFiniteNonZero() const
Definition: APFloat.h:367
lostFraction
Enum that represents what fraction of the LSB truncated bits of an fp number represent.
Definition: APFloat.h:47
bool isPosZero() const
Definition: APFloat.h:368
static uint64_t add(uint64_t LeftOp, uint64_t RightOp)
Definition: FileCheck.cpp:243
bool isFinite() const
Returns true if and only if the current value is zero, subnormal, or normal.
Definition: APFloat.h:341
bool isFiniteNonZero() const
Definition: APFloat.h:1167
#define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL)
Definition: APFloat.h:24
APFloat neg(APFloat X)
Returns the negated value of the argument.
Definition: APFloat.h:1229
APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM)
Equivalent of C standard library function.
Definition: APFloat.h:1215
bool needsCleanup() const
Definition: APFloat.h:614
static unsigned int semanticsPrecision(const fltSemantics &)
Definition: APFloat.cpp:190
bool isDenormal() const
Definition: APFloat.h:1158
uint64_t WordType
Definition: APInt.h:71
const fltSemantics & getSemantics() const
Definition: APFloat.h:365
APInt::WordType integerPart
Definition: APFloat.h:142
bool getExactInverse(APFloat *inv) const
Definition: APFloat.h:1186
Class for arbitrary precision integers.
Definition: APInt.h:69
static APFloat getSNaN(const fltSemantics &Sem, bool Negative=false, const APInt *payload=nullptr)
Factory for SNaN values.
Definition: APFloat.h:904
static void initialize(TargetLibraryInfoImpl &TLI, const Triple &T, ArrayRef< StringRef > StandardNames)
Initialize the set of available library functions based on the specified target triple.
const APFloat & getFirst() const
Definition: APFloat.h:617
bool isZero() const
Returns true if and only if the float is plus or minus zero.
Definition: APFloat.h:344
opStatus mod(const APFloat &RHS)
Definition: APFloat.h:996
An opaque object representing a hash code.
Definition: Hashing.h:71
unsigned int convertToHexString(char *DST, unsigned int HexDigits, bool UpperCase, roundingMode RM) const
Definition: APFloat.h:1147
static const fltSemantics & PPCDoubleDouble() LLVM_READNONE
Definition: APFloat.cpp:170
opStatus add(const APFloat &RHS, roundingMode RM)
Definition: APFloat.h:951
static bool isZero(Value *V, const DataLayout &DL, DominatorTree *DT, AssumptionCache *AC)
Definition: Lint.cpp:549
opStatus
IEEE-754R 7: Default exception handling.
Definition: APFloat.h:195
bool isPosZero() const
Definition: APFloat.h:1168
#define LLVM_READNONE
Definition: Compiler.h:184
#define I(x, y, z)
Definition: MD5.cpp:58
APFloat abs(APFloat X)
Returns the absolute value of the argument.
Definition: APFloat.h:1223
bool isNormal() const
Definition: APFloat.h:1161
static const fltSemantics & Bogus() LLVM_READNONE
A Pseudo fltsemantic used to construct APFloats that cannot conflict with anything real...
Definition: APFloat.cpp:167
#define LLVM_READONLY
Definition: Compiler.h:191
static APFloat getLargest(const fltSemantics &Sem, bool Negative=false)
Returns the largest finite number in the given semantics.
Definition: APFloat.h:914
static APFloat getSmallestNormalized(const fltSemantics &Sem, bool Negative=false)
Returns the smallest (by magnitude) normalized finite number in the given semantics.
Definition: APFloat.h:934
const APFloat & getSecond() const
Definition: APFloat.h:619
int compare(DigitsT LDigits, int16_t LScale, DigitsT RDigits, int16_t RScale)
Compare two scaled numbers.
Definition: ScaledNumber.h:251
bool isNegZero() const
Definition: APFloat.h:369
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend, roundingMode RM)
Definition: APFloat.h:1005
opStatus remainder(const APFloat &RHS)
Definition: APFloat.h:987
A self-contained host- and target-independent arbitrary-precision floating-point software implementat...
Definition: APFloat.h:141
aarch64 promote const
LLVM Value Representation.
Definition: Value.h:73
bool needsCleanup() const
Returns whether this instance allocated memory.
Definition: APFloat.h:254
bool bitwiseIsEqual(const APFloat &RHS) const
Definition: APFloat.h:1122
This class implements an extremely fast bulk output stream that can only output to a stream...
Definition: raw_ostream.h:45
StringRef - Represent a constant reference to a string, i.e.
Definition: StringRef.h:48
opStatus convertFromZeroExtendedInteger(const integerPart *Input, unsigned int InputSize, bool IsSigned, roundingMode RM)
Definition: APFloat.h:1097
APInt bitcastToAPInt() const
Definition: APFloat.h:1104
bool operator==(uint64_t V1, const APInt &V2)
Definition: APInt.h:1973
APFloat(const fltSemantics &Semantics, integerPart I)
Definition: APFloat.h:848
bool isInfinity() const
IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
Definition: APFloat.h:351
bool isSmallest() const
Definition: APFloat.h:1170
bool isSignaling() const
Definition: APFloat.h:1159
constexpr char Args[]
Key for Kernel::Metadata::mArgs.
static APFloat getQNaN(const fltSemantics &Sem, bool Negative=false, const APInt *payload=nullptr)
Factory for QNaN values.
Definition: APFloat.h:896
APFloat(const fltSemantics &Semantics, uninitializedTag)
Definition: APFloat.h:850
LLVM_READONLY APFloat minnum(const APFloat &A, const APFloat &B)
Implements IEEE minNum semantics.
Definition: APFloat.h:1237
int ilogb(const IEEEFloat &Arg)
Definition: APFloat.cpp:3827
cmpResult compare(const APFloat &RHS) const
Definition: APFloat.h:1112
bool isNormal() const
IEEE-754R isNormal: Returns true if and only if the current value is normal.
Definition: APFloat.h:335