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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 
151  static const fltSemantics &IEEEhalf() LLVM_READNONE;
153  static const fltSemantics &IEEEdouble() LLVM_READNONE;
154  static const fltSemantics &IEEEquad() LLVM_READNONE;
155  static const fltSemantics &PPCDoubleDouble() LLVM_READNONE;
156  static const fltSemantics &x87DoubleExtended() LLVM_READNONE;
157 
158  /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
159  /// anything real.
160  static const fltSemantics &Bogus() LLVM_READNONE;
161 
162  /// @}
163 
164  /// IEEE-754R 5.11: Floating Point Comparison Relations.
165  enum cmpResult {
170  };
171 
172  /// IEEE-754R 4.3: Rounding-direction attributes.
179  };
180 
181  /// IEEE-754R 7: Default exception handling.
182  ///
183  /// opUnderflow or opOverflow are always returned or-ed with opInexact.
184  enum opStatus {
185  opOK = 0x00,
186  opInvalidOp = 0x01,
187  opDivByZero = 0x02,
188  opOverflow = 0x04,
189  opUnderflow = 0x08,
190  opInexact = 0x10
191  };
192 
193  /// Category of internally-represented number.
194  enum fltCategory {
199  };
200 
201  /// Convenience enum used to construct an uninitialized APFloat.
204  };
205 
206  /// Enumeration of \c ilogb error results.
208  IEK_Zero = INT_MIN + 1,
209  IEK_NaN = INT_MIN,
210  IEK_Inf = INT_MAX
211  };
212 
213  static unsigned int semanticsPrecision(const fltSemantics &);
214  static ExponentType semanticsMinExponent(const fltSemantics &);
215  static ExponentType semanticsMaxExponent(const fltSemantics &);
216  static unsigned int semanticsSizeInBits(const fltSemantics &);
217 
218  /// Returns the size of the floating point number (in bits) in the given
219  /// semantics.
220  static unsigned getSizeInBits(const fltSemantics &Sem);
221 };
222 
223 namespace detail {
224 
225 class IEEEFloat final : public APFloatBase {
226 public:
227  /// \name Constructors
228  /// @{
229 
230  IEEEFloat(const fltSemantics &); // Default construct to 0.0
233  IEEEFloat(const fltSemantics &, const APInt &);
234  explicit IEEEFloat(double d);
235  explicit IEEEFloat(float f);
236  IEEEFloat(const IEEEFloat &);
237  IEEEFloat(IEEEFloat &&);
238  ~IEEEFloat();
239 
240  /// @}
241 
242  /// Returns whether this instance allocated memory.
243  bool needsCleanup() const { return partCount() > 1; }
244 
245  /// \name Convenience "constructors"
246  /// @{
247 
248  /// @}
249 
250  /// \name Arithmetic
251  /// @{
252 
254  opStatus subtract(const IEEEFloat &, roundingMode);
255  opStatus multiply(const IEEEFloat &, roundingMode);
256  opStatus divide(const IEEEFloat &, roundingMode);
257  /// IEEE remainder.
258  opStatus remainder(const IEEEFloat &);
259  /// C fmod, or llvm frem.
260  opStatus mod(const IEEEFloat &);
261  opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);
262  opStatus roundToIntegral(roundingMode);
263  /// IEEE-754R 5.3.1: nextUp/nextDown.
264  opStatus next(bool nextDown);
265 
266  /// @}
267 
268  /// \name Sign operations.
269  /// @{
270 
271  void changeSign();
272 
273  /// @}
274 
275  /// \name Conversions
276  /// @{
277 
278  opStatus convert(const fltSemantics &, roundingMode, bool *);
279  opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,
280  roundingMode, bool *) const;
281  opStatus convertFromAPInt(const APInt &, bool, roundingMode);
282  opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
283  bool, roundingMode);
284  opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
285  bool, roundingMode);
286  opStatus convertFromString(StringRef, roundingMode);
287  APInt bitcastToAPInt() const;
288  double convertToDouble() const;
289  float convertToFloat() const;
290 
291  /// @}
292 
293  /// The definition of equality is not straightforward for floating point, so
294  /// we won't use operator==. Use one of the following, or write whatever it
295  /// is you really mean.
296  bool operator==(const IEEEFloat &) const = delete;
297 
298  /// IEEE comparison with another floating point number (NaNs compare
299  /// unordered, 0==-0).
300  cmpResult compare(const IEEEFloat &) const;
301 
302  /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
303  bool bitwiseIsEqual(const IEEEFloat &) const;
304 
305  /// Write out a hexadecimal representation of the floating point value to DST,
306  /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
307  /// Return the number of characters written, excluding the terminating NUL.
308  unsigned int convertToHexString(char *dst, unsigned int hexDigits,
309  bool upperCase, roundingMode) const;
310 
311  /// \name IEEE-754R 5.7.2 General operations.
312  /// @{
313 
314  /// IEEE-754R isSignMinus: Returns true if and only if the current value is
315  /// negative.
316  ///
317  /// This applies to zeros and NaNs as well.
318  bool isNegative() const { return sign; }
319 
320  /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
321  ///
322  /// This implies that the current value of the float is not zero, subnormal,
323  /// infinite, or NaN following the definition of normality from IEEE-754R.
324  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
325 
326  /// Returns true if and only if the current value is zero, subnormal, or
327  /// normal.
328  ///
329  /// This means that the value is not infinite or NaN.
330  bool isFinite() const { return !isNaN() && !isInfinity(); }
331 
332  /// Returns true if and only if the float is plus or minus zero.
333  bool isZero() const { return category == fcZero; }
334 
335  /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
336  /// denormal.
337  bool isDenormal() const;
338 
339  /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
340  bool isInfinity() const { return category == fcInfinity; }
341 
342  /// Returns true if and only if the float is a quiet or signaling NaN.
343  bool isNaN() const { return category == fcNaN; }
344 
345  /// Returns true if and only if the float is a signaling NaN.
346  bool isSignaling() const;
347 
348  /// @}
349 
350  /// \name Simple Queries
351  /// @{
352 
353  fltCategory getCategory() const { return category; }
354  const fltSemantics &getSemantics() const { return *semantics; }
355  bool isNonZero() const { return category != fcZero; }
356  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
357  bool isPosZero() const { return isZero() && !isNegative(); }
358  bool isNegZero() const { return isZero() && isNegative(); }
359 
360  /// Returns true if and only if the number has the smallest possible non-zero
361  /// magnitude in the current semantics.
362  bool isSmallest() const;
363 
364  /// Returns true if and only if the number has the largest possible finite
365  /// magnitude in the current semantics.
366  bool isLargest() const;
367 
368  /// Returns true if and only if the number is an exact integer.
369  bool isInteger() const;
370 
371  /// @}
372 
373  IEEEFloat &operator=(const IEEEFloat &);
374  IEEEFloat &operator=(IEEEFloat &&);
375 
376  /// Overload to compute a hash code for an APFloat value.
377  ///
378  /// Note that the use of hash codes for floating point values is in general
379  /// frought with peril. Equality is hard to define for these values. For
380  /// example, should negative and positive zero hash to different codes? Are
381  /// they equal or not? This hash value implementation specifically
382  /// emphasizes producing different codes for different inputs in order to
383  /// be used in canonicalization and memoization. As such, equality is
384  /// bitwiseIsEqual, and 0 != -0.
385  friend hash_code hash_value(const IEEEFloat &Arg);
386 
387  /// Converts this value into a decimal string.
388  ///
389  /// \param FormatPrecision The maximum number of digits of
390  /// precision to output. If there are fewer digits available,
391  /// zero padding will not be used unless the value is
392  /// integral and small enough to be expressed in
393  /// FormatPrecision digits. 0 means to use the natural
394  /// precision of the number.
395  /// \param FormatMaxPadding The maximum number of zeros to
396  /// consider inserting before falling back to scientific
397  /// notation. 0 means to always use scientific notation.
398  ///
399  /// \param TruncateZero Indicate whether to remove the trailing zero in
400  /// fraction part or not. Also setting this parameter to false forcing
401  /// producing of output more similar to default printf behavior.
402  /// Specifically the lower e is used as exponent delimiter and exponent
403  /// always contains no less than two digits.
404  ///
405  /// Number Precision MaxPadding Result
406  /// ------ --------- ---------- ------
407  /// 1.01E+4 5 2 10100
408  /// 1.01E+4 4 2 1.01E+4
409  /// 1.01E+4 5 1 1.01E+4
410  /// 1.01E-2 5 2 0.0101
411  /// 1.01E-2 4 2 0.0101
412  /// 1.01E-2 4 1 1.01E-2
413  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
414  unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;
415 
416  /// If this value has an exact multiplicative inverse, store it in inv and
417  /// return true.
418  bool getExactInverse(APFloat *inv) const;
419 
420  /// Returns the exponent of the internal representation of the APFloat.
421  ///
422  /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
423  /// For special APFloat values, this returns special error codes:
424  ///
425  /// NaN -> \c IEK_NaN
426  /// 0 -> \c IEK_Zero
427  /// Inf -> \c IEK_Inf
428  ///
429  friend int ilogb(const IEEEFloat &Arg);
430 
431  /// Returns: X * 2^Exp for integral exponents.
432  friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);
433 
434  friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);
435 
436  /// \name Special value setters.
437  /// @{
438 
439  void makeLargest(bool Neg = false);
440  void makeSmallest(bool Neg = false);
441  void makeNaN(bool SNaN = false, bool Neg = false,
442  const APInt *fill = nullptr);
443  void makeInf(bool Neg = false);
444  void makeZero(bool Neg = false);
445  void makeQuiet();
446 
447  /// Returns the smallest (by magnitude) normalized finite number in the given
448  /// semantics.
449  ///
450  /// \param Negative - True iff the number should be negative
451  void makeSmallestNormalized(bool Negative = false);
452 
453  /// @}
454 
455  cmpResult compareAbsoluteValue(const IEEEFloat &) const;
456 
457 private:
458  /// \name Simple Queries
459  /// @{
460 
461  integerPart *significandParts();
462  const integerPart *significandParts() const;
463  unsigned int partCount() const;
464 
465  /// @}
466 
467  /// \name Significand operations.
468  /// @{
469 
470  integerPart addSignificand(const IEEEFloat &);
471  integerPart subtractSignificand(const IEEEFloat &, integerPart);
472  lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
473  lostFraction multiplySignificand(const IEEEFloat &, const IEEEFloat *);
474  lostFraction divideSignificand(const IEEEFloat &);
475  void incrementSignificand();
476  void initialize(const fltSemantics *);
477  void shiftSignificandLeft(unsigned int);
478  lostFraction shiftSignificandRight(unsigned int);
479  unsigned int significandLSB() const;
480  unsigned int significandMSB() const;
481  void zeroSignificand();
482  /// Return true if the significand excluding the integral bit is all ones.
483  bool isSignificandAllOnes() const;
484  /// Return true if the significand excluding the integral bit is all zeros.
485  bool isSignificandAllZeros() const;
486 
487  /// @}
488 
489  /// \name Arithmetic on special values.
490  /// @{
491 
492  opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);
493  opStatus divideSpecials(const IEEEFloat &);
494  opStatus multiplySpecials(const IEEEFloat &);
495  opStatus modSpecials(const IEEEFloat &);
496 
497  /// @}
498 
499  /// \name Miscellany
500  /// @{
501 
502  bool convertFromStringSpecials(StringRef str);
503  opStatus normalize(roundingMode, lostFraction);
504  opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);
505  opStatus handleOverflow(roundingMode);
506  bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
507  opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,
508  unsigned int, bool, roundingMode,
509  bool *) const;
510  opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
511  roundingMode);
512  opStatus convertFromHexadecimalString(StringRef, roundingMode);
513  opStatus convertFromDecimalString(StringRef, roundingMode);
514  char *convertNormalToHexString(char *, unsigned int, bool,
515  roundingMode) const;
516  opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
517  roundingMode);
518 
519  /// @}
520 
521  APInt convertHalfAPFloatToAPInt() const;
522  APInt convertFloatAPFloatToAPInt() const;
523  APInt convertDoubleAPFloatToAPInt() const;
524  APInt convertQuadrupleAPFloatToAPInt() const;
525  APInt convertF80LongDoubleAPFloatToAPInt() const;
526  APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
527  void initFromAPInt(const fltSemantics *Sem, const APInt &api);
528  void initFromHalfAPInt(const APInt &api);
529  void initFromFloatAPInt(const APInt &api);
530  void initFromDoubleAPInt(const APInt &api);
531  void initFromQuadrupleAPInt(const APInt &api);
532  void initFromF80LongDoubleAPInt(const APInt &api);
533  void initFromPPCDoubleDoubleAPInt(const APInt &api);
534 
535  void assign(const IEEEFloat &);
536  void copySignificand(const IEEEFloat &);
537  void freeSignificand();
538 
539  /// Note: this must be the first data member.
540  /// The semantics that this value obeys.
541  const fltSemantics *semantics;
542 
543  /// A binary fraction with an explicit integer bit.
544  ///
545  /// The significand must be at least one bit wider than the target precision.
546  union Significand {
547  integerPart part;
548  integerPart *parts;
549  } significand;
550 
551  /// The signed unbiased exponent of the value.
552  ExponentType exponent;
553 
554  /// What kind of floating point number this is.
555  ///
556  /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
557  /// Using the extra bit keeps it from failing under VisualStudio.
558  fltCategory category : 3;
559 
560  /// Sign bit of the number.
561  unsigned int sign : 1;
562 };
563 
565 int ilogb(const IEEEFloat &Arg);
567 IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);
568 
569 // This mode implements more precise float in terms of two APFloats.
570 // The interface and layout is designed for arbitray underlying semantics,
571 // though currently only PPCDoubleDouble semantics are supported, whose
572 // corresponding underlying semantics are IEEEdouble.
573 class DoubleAPFloat final : public APFloatBase {
574  // Note: this must be the first data member.
575  const fltSemantics *Semantics;
576  std::unique_ptr<APFloat[]> Floats;
577 
578  opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,
579  const APFloat &cc, roundingMode RM);
580 
581  opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,
582  DoubleAPFloat &Out, roundingMode RM);
583 
584 public:
585  DoubleAPFloat(const fltSemantics &S);
588  DoubleAPFloat(const fltSemantics &S, const APInt &I);
589  DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);
590  DoubleAPFloat(const DoubleAPFloat &RHS);
592 
593  DoubleAPFloat &operator=(const DoubleAPFloat &RHS);
594 
596  if (this != &RHS) {
597  this->~DoubleAPFloat();
598  new (this) DoubleAPFloat(std::move(RHS));
599  }
600  return *this;
601  }
602 
603  bool needsCleanup() const { return Floats != nullptr; }
604 
605  APFloat &getFirst() { return Floats[0]; }
606  const APFloat &getFirst() const { return Floats[0]; }
607  APFloat &getSecond() { return Floats[1]; }
608  const APFloat &getSecond() const { return Floats[1]; }
609 
610  opStatus add(const DoubleAPFloat &RHS, roundingMode RM);
611  opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);
612  opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);
613  opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);
614  opStatus remainder(const DoubleAPFloat &RHS);
615  opStatus mod(const DoubleAPFloat &RHS);
616  opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
617  const DoubleAPFloat &Addend, roundingMode RM);
618  opStatus roundToIntegral(roundingMode RM);
619  void changeSign();
620  cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;
621 
622  fltCategory getCategory() const;
623  bool isNegative() const;
624 
625  void makeInf(bool Neg);
626  void makeZero(bool Neg);
627  void makeLargest(bool Neg);
628  void makeSmallest(bool Neg);
629  void makeSmallestNormalized(bool Neg);
630  void makeNaN(bool SNaN, bool Neg, const APInt *fill);
631 
632  cmpResult compare(const DoubleAPFloat &RHS) const;
633  bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;
634  APInt bitcastToAPInt() const;
635  opStatus convertFromString(StringRef, roundingMode);
636  opStatus next(bool nextDown);
637 
638  opStatus convertToInteger(MutableArrayRef<integerPart> Input,
639  unsigned int Width, bool IsSigned, roundingMode RM,
640  bool *IsExact) const;
641  opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);
642  opStatus convertFromSignExtendedInteger(const integerPart *Input,
643  unsigned int InputSize, bool IsSigned,
644  roundingMode RM);
645  opStatus convertFromZeroExtendedInteger(const integerPart *Input,
646  unsigned int InputSize, bool IsSigned,
647  roundingMode RM);
648  unsigned int convertToHexString(char *DST, unsigned int HexDigits,
649  bool UpperCase, roundingMode RM) const;
650 
651  bool isDenormal() const;
652  bool isSmallest() const;
653  bool isLargest() const;
654  bool isInteger() const;
655 
656  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
657  unsigned FormatMaxPadding, bool TruncateZero = true) const;
658 
659  bool getExactInverse(APFloat *inv) const;
660 
661  friend int ilogb(const DoubleAPFloat &Arg);
662  friend DoubleAPFloat scalbn(DoubleAPFloat X, int Exp, roundingMode);
663  friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);
664  friend hash_code hash_value(const DoubleAPFloat &Arg);
665 };
666 
668 
669 } // End detail namespace
670 
671 // This is a interface class that is currently forwarding functionalities from
672 // detail::IEEEFloat.
673 class APFloat : public APFloatBase {
676 
677  static_assert(std::is_standard_layout<IEEEFloat>::value, "");
678 
679  union Storage {
680  const fltSemantics *semantics;
681  IEEEFloat IEEE;
682  DoubleAPFloat Double;
683 
684  explicit Storage(IEEEFloat F, const fltSemantics &S);
685  explicit Storage(DoubleAPFloat F, const fltSemantics &S)
686  : Double(std::move(F)) {
687  assert(&S == &PPCDoubleDouble());
688  }
689 
690  template <typename... ArgTypes>
691  Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {
692  if (usesLayout<IEEEFloat>(Semantics)) {
693  new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);
694  return;
695  }
696  if (usesLayout<DoubleAPFloat>(Semantics)) {
697  new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);
698  return;
699  }
700  llvm_unreachable("Unexpected semantics");
701  }
702 
703  ~Storage() {
704  if (usesLayout<IEEEFloat>(*semantics)) {
705  IEEE.~IEEEFloat();
706  return;
707  }
708  if (usesLayout<DoubleAPFloat>(*semantics)) {
709  Double.~DoubleAPFloat();
710  return;
711  }
712  llvm_unreachable("Unexpected semantics");
713  }
714 
715  Storage(const Storage &RHS) {
716  if (usesLayout<IEEEFloat>(*RHS.semantics)) {
717  new (this) IEEEFloat(RHS.IEEE);
718  return;
719  }
720  if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
721  new (this) DoubleAPFloat(RHS.Double);
722  return;
723  }
724  llvm_unreachable("Unexpected semantics");
725  }
726 
727  Storage(Storage &&RHS) {
728  if (usesLayout<IEEEFloat>(*RHS.semantics)) {
729  new (this) IEEEFloat(std::move(RHS.IEEE));
730  return;
731  }
732  if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
733  new (this) DoubleAPFloat(std::move(RHS.Double));
734  return;
735  }
736  llvm_unreachable("Unexpected semantics");
737  }
738 
739  Storage &operator=(const Storage &RHS) {
740  if (usesLayout<IEEEFloat>(*semantics) &&
741  usesLayout<IEEEFloat>(*RHS.semantics)) {
742  IEEE = RHS.IEEE;
743  } else if (usesLayout<DoubleAPFloat>(*semantics) &&
744  usesLayout<DoubleAPFloat>(*RHS.semantics)) {
745  Double = RHS.Double;
746  } else if (this != &RHS) {
747  this->~Storage();
748  new (this) Storage(RHS);
749  }
750  return *this;
751  }
752 
753  Storage &operator=(Storage &&RHS) {
754  if (usesLayout<IEEEFloat>(*semantics) &&
755  usesLayout<IEEEFloat>(*RHS.semantics)) {
756  IEEE = std::move(RHS.IEEE);
757  } else if (usesLayout<DoubleAPFloat>(*semantics) &&
758  usesLayout<DoubleAPFloat>(*RHS.semantics)) {
759  Double = std::move(RHS.Double);
760  } else if (this != &RHS) {
761  this->~Storage();
762  new (this) Storage(std::move(RHS));
763  }
764  return *this;
765  }
766  } U;
767 
768  template <typename T> static bool usesLayout(const fltSemantics &Semantics) {
769  static_assert(std::is_same<T, IEEEFloat>::value ||
770  std::is_same<T, DoubleAPFloat>::value, "");
771  if (std::is_same<T, DoubleAPFloat>::value) {
772  return &Semantics == &PPCDoubleDouble();
773  }
774  return &Semantics != &PPCDoubleDouble();
775  }
776 
777  IEEEFloat &getIEEE() {
778  if (usesLayout<IEEEFloat>(*U.semantics))
779  return U.IEEE;
780  if (usesLayout<DoubleAPFloat>(*U.semantics))
781  return U.Double.getFirst().U.IEEE;
782  llvm_unreachable("Unexpected semantics");
783  }
784 
785  const IEEEFloat &getIEEE() const {
786  if (usesLayout<IEEEFloat>(*U.semantics))
787  return U.IEEE;
788  if (usesLayout<DoubleAPFloat>(*U.semantics))
789  return U.Double.getFirst().U.IEEE;
790  llvm_unreachable("Unexpected semantics");
791  }
792 
793  void makeZero(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeZero(Neg)); }
794 
795  void makeInf(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeInf(Neg)); }
796 
797  void makeNaN(bool SNaN, bool Neg, const APInt *fill) {
798  APFLOAT_DISPATCH_ON_SEMANTICS(makeNaN(SNaN, Neg, fill));
799  }
800 
801  void makeLargest(bool Neg) {
802  APFLOAT_DISPATCH_ON_SEMANTICS(makeLargest(Neg));
803  }
804 
805  void makeSmallest(bool Neg) {
806  APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallest(Neg));
807  }
808 
809  void makeSmallestNormalized(bool Neg) {
810  APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallestNormalized(Neg));
811  }
812 
813  // FIXME: This is due to clang 3.3 (or older version) always checks for the
814  // default constructor in an array aggregate initialization, even if no
815  // elements in the array is default initialized.
816  APFloat() : U(IEEEdouble()) {
817  llvm_unreachable("This is a workaround for old clang.");
818  }
819 
820  explicit APFloat(IEEEFloat F, const fltSemantics &S) : U(std::move(F), S) {}
821  explicit APFloat(DoubleAPFloat F, const fltSemantics &S)
822  : U(std::move(F), S) {}
823 
824  cmpResult compareAbsoluteValue(const APFloat &RHS) const {
825  assert(&getSemantics() == &RHS.getSemantics() &&
826  "Should only compare APFloats with the same semantics");
827  if (usesLayout<IEEEFloat>(getSemantics()))
828  return U.IEEE.compareAbsoluteValue(RHS.U.IEEE);
829  if (usesLayout<DoubleAPFloat>(getSemantics()))
830  return U.Double.compareAbsoluteValue(RHS.U.Double);
831  llvm_unreachable("Unexpected semantics");
832  }
833 
834 public:
835  APFloat(const fltSemantics &Semantics) : U(Semantics) {}
836  APFloat(const fltSemantics &Semantics, StringRef S);
837  APFloat(const fltSemantics &Semantics, integerPart I) : U(Semantics, I) {}
838  // TODO: Remove this constructor. This isn't faster than the first one.
840  : U(Semantics, uninitialized) {}
841  APFloat(const fltSemantics &Semantics, const APInt &I) : U(Semantics, I) {}
842  explicit APFloat(double d) : U(IEEEFloat(d), IEEEdouble()) {}
843  explicit APFloat(float f) : U(IEEEFloat(f), IEEEsingle()) {}
844  APFloat(const APFloat &RHS) = default;
845  APFloat(APFloat &&RHS) = default;
846 
847  ~APFloat() = default;
848 
850 
851  /// Factory for Positive and Negative Zero.
852  ///
853  /// \param Negative True iff the number should be negative.
854  static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
855  APFloat Val(Sem, uninitialized);
856  Val.makeZero(Negative);
857  return Val;
858  }
859 
860  /// Factory for Positive and Negative Infinity.
861  ///
862  /// \param Negative True iff the number should be negative.
863  static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
864  APFloat Val(Sem, uninitialized);
865  Val.makeInf(Negative);
866  return Val;
867  }
868 
869  /// Factory for NaN values.
870  ///
871  /// \param Negative - True iff the NaN generated should be negative.
872  /// \param payload - The unspecified fill bits for creating the NaN, 0 by
873  /// default. The value is truncated as necessary.
874  static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
875  uint64_t payload = 0) {
876  if (payload) {
877  APInt intPayload(64, payload);
878  return getQNaN(Sem, Negative, &intPayload);
879  } else {
880  return getQNaN(Sem, Negative, nullptr);
881  }
882  }
883 
884  /// Factory for QNaN values.
885  static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
886  const APInt *payload = nullptr) {
887  APFloat Val(Sem, uninitialized);
888  Val.makeNaN(false, Negative, payload);
889  return Val;
890  }
891 
892  /// Factory for SNaN values.
893  static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
894  const APInt *payload = nullptr) {
895  APFloat Val(Sem, uninitialized);
896  Val.makeNaN(true, Negative, payload);
897  return Val;
898  }
899 
900  /// Returns the largest finite number in the given semantics.
901  ///
902  /// \param Negative - True iff the number should be negative
903  static APFloat getLargest(const fltSemantics &Sem, bool Negative = false) {
904  APFloat Val(Sem, uninitialized);
905  Val.makeLargest(Negative);
906  return Val;
907  }
908 
909  /// Returns the smallest (by magnitude) finite number in the given semantics.
910  /// Might be denormalized, which implies a relative loss of precision.
911  ///
912  /// \param Negative - True iff the number should be negative
913  static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false) {
914  APFloat Val(Sem, uninitialized);
915  Val.makeSmallest(Negative);
916  return Val;
917  }
918 
919  /// Returns the smallest (by magnitude) normalized finite number in the given
920  /// semantics.
921  ///
922  /// \param Negative - True iff the number should be negative
924  bool Negative = false) {
925  APFloat Val(Sem, uninitialized);
926  Val.makeSmallestNormalized(Negative);
927  return Val;
928  }
929 
930  /// Returns a float which is bitcasted from an all one value int.
931  ///
932  /// \param BitWidth - Select float type
933  /// \param isIEEE - If 128 bit number, select between PPC and IEEE
934  static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
935 
936  /// Used to insert APFloat objects, or objects that contain APFloat objects,
937  /// into FoldingSets.
938  void Profile(FoldingSetNodeID &NID) const;
939 
941  assert(&getSemantics() == &RHS.getSemantics() &&
942  "Should only call on two APFloats with the same semantics");
943  if (usesLayout<IEEEFloat>(getSemantics()))
944  return U.IEEE.add(RHS.U.IEEE, RM);
945  if (usesLayout<DoubleAPFloat>(getSemantics()))
946  return U.Double.add(RHS.U.Double, RM);
947  llvm_unreachable("Unexpected semantics");
948  }
950  assert(&getSemantics() == &RHS.getSemantics() &&
951  "Should only call on two APFloats with the same semantics");
952  if (usesLayout<IEEEFloat>(getSemantics()))
953  return U.IEEE.subtract(RHS.U.IEEE, RM);
954  if (usesLayout<DoubleAPFloat>(getSemantics()))
955  return U.Double.subtract(RHS.U.Double, RM);
956  llvm_unreachable("Unexpected semantics");
957  }
959  assert(&getSemantics() == &RHS.getSemantics() &&
960  "Should only call on two APFloats with the same semantics");
961  if (usesLayout<IEEEFloat>(getSemantics()))
962  return U.IEEE.multiply(RHS.U.IEEE, RM);
963  if (usesLayout<DoubleAPFloat>(getSemantics()))
964  return U.Double.multiply(RHS.U.Double, RM);
965  llvm_unreachable("Unexpected semantics");
966  }
968  assert(&getSemantics() == &RHS.getSemantics() &&
969  "Should only call on two APFloats with the same semantics");
970  if (usesLayout<IEEEFloat>(getSemantics()))
971  return U.IEEE.divide(RHS.U.IEEE, RM);
972  if (usesLayout<DoubleAPFloat>(getSemantics()))
973  return U.Double.divide(RHS.U.Double, RM);
974  llvm_unreachable("Unexpected semantics");
975  }
976  opStatus remainder(const APFloat &RHS) {
977  assert(&getSemantics() == &RHS.getSemantics() &&
978  "Should only call on two APFloats with the same semantics");
979  if (usesLayout<IEEEFloat>(getSemantics()))
980  return U.IEEE.remainder(RHS.U.IEEE);
981  if (usesLayout<DoubleAPFloat>(getSemantics()))
982  return U.Double.remainder(RHS.U.Double);
983  llvm_unreachable("Unexpected semantics");
984  }
985  opStatus mod(const APFloat &RHS) {
986  assert(&getSemantics() == &RHS.getSemantics() &&
987  "Should only call on two APFloats with the same semantics");
988  if (usesLayout<IEEEFloat>(getSemantics()))
989  return U.IEEE.mod(RHS.U.IEEE);
990  if (usesLayout<DoubleAPFloat>(getSemantics()))
991  return U.Double.mod(RHS.U.Double);
992  llvm_unreachable("Unexpected semantics");
993  }
994  opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend,
995  roundingMode RM) {
996  assert(&getSemantics() == &Multiplicand.getSemantics() &&
997  "Should only call on APFloats with the same semantics");
998  assert(&getSemantics() == &Addend.getSemantics() &&
999  "Should only call on APFloats with the same semantics");
1000  if (usesLayout<IEEEFloat>(getSemantics()))
1001  return U.IEEE.fusedMultiplyAdd(Multiplicand.U.IEEE, Addend.U.IEEE, RM);
1002  if (usesLayout<DoubleAPFloat>(getSemantics()))
1003  return U.Double.fusedMultiplyAdd(Multiplicand.U.Double, Addend.U.Double,
1004  RM);
1005  llvm_unreachable("Unexpected semantics");
1006  }
1008  APFLOAT_DISPATCH_ON_SEMANTICS(roundToIntegral(RM));
1009  }
1010 
1011  // TODO: bool parameters are not readable and a source of bugs.
1012  // Do something.
1013  opStatus next(bool nextDown) {
1014  APFLOAT_DISPATCH_ON_SEMANTICS(next(nextDown));
1015  }
1016 
1017  /// Add two APFloats, rounding ties to the nearest even.
1018  /// No error checking.
1019  APFloat operator+(const APFloat &RHS) const {
1020  APFloat Result(*this);
1021  (void)Result.add(RHS, rmNearestTiesToEven);
1022  return Result;
1023  }
1024 
1025  /// Subtract two APFloats, rounding ties to the nearest even.
1026  /// No error checking.
1027  APFloat operator-(const APFloat &RHS) const {
1028  APFloat Result(*this);
1029  (void)Result.subtract(RHS, rmNearestTiesToEven);
1030  return Result;
1031  }
1032 
1033  /// Multiply two APFloats, rounding ties to the nearest even.
1034  /// No error checking.
1035  APFloat operator*(const APFloat &RHS) const {
1036  APFloat Result(*this);
1037  (void)Result.multiply(RHS, rmNearestTiesToEven);
1038  return Result;
1039  }
1040 
1041  /// Divide the first APFloat by the second, rounding ties to the nearest even.
1042  /// No error checking.
1043  APFloat operator/(const APFloat &RHS) const {
1044  APFloat Result(*this);
1045  (void)Result.divide(RHS, rmNearestTiesToEven);
1046  return Result;
1047  }
1048 
1050  void clearSign() {
1051  if (isNegative())
1052  changeSign();
1053  }
1054  void copySign(const APFloat &RHS) {
1055  if (isNegative() != RHS.isNegative())
1056  changeSign();
1057  }
1058 
1059  /// A static helper to produce a copy of an APFloat value with its sign
1060  /// copied from some other APFloat.
1061  static APFloat copySign(APFloat Value, const APFloat &Sign) {
1062  Value.copySign(Sign);
1063  return Value;
1064  }
1065 
1066  opStatus convert(const fltSemantics &ToSemantics, roundingMode RM,
1067  bool *losesInfo);
1069  unsigned int Width, bool IsSigned, roundingMode RM,
1070  bool *IsExact) const {
1072  convertToInteger(Input, Width, IsSigned, RM, IsExact));
1073  }
1074  opStatus convertToInteger(APSInt &Result, roundingMode RM,
1075  bool *IsExact) const;
1076  opStatus convertFromAPInt(const APInt &Input, bool IsSigned,
1077  roundingMode RM) {
1078  APFLOAT_DISPATCH_ON_SEMANTICS(convertFromAPInt(Input, IsSigned, RM));
1079  }
1081  unsigned int InputSize, bool IsSigned,
1082  roundingMode RM) {
1084  convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM));
1085  }
1087  unsigned int InputSize, bool IsSigned,
1088  roundingMode RM) {
1090  convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM));
1091  }
1092  opStatus convertFromString(StringRef, roundingMode);
1094  APFLOAT_DISPATCH_ON_SEMANTICS(bitcastToAPInt());
1095  }
1096  double convertToDouble() const { return getIEEE().convertToDouble(); }
1097  float convertToFloat() const { return getIEEE().convertToFloat(); }
1098 
1099  bool operator==(const APFloat &) const = delete;
1100 
1101  cmpResult compare(const APFloat &RHS) const {
1102  assert(&getSemantics() == &RHS.getSemantics() &&
1103  "Should only compare APFloats with the same semantics");
1104  if (usesLayout<IEEEFloat>(getSemantics()))
1105  return U.IEEE.compare(RHS.U.IEEE);
1106  if (usesLayout<DoubleAPFloat>(getSemantics()))
1107  return U.Double.compare(RHS.U.Double);
1108  llvm_unreachable("Unexpected semantics");
1109  }
1110 
1111  bool bitwiseIsEqual(const APFloat &RHS) const {
1112  if (&getSemantics() != &RHS.getSemantics())
1113  return false;
1114  if (usesLayout<IEEEFloat>(getSemantics()))
1115  return U.IEEE.bitwiseIsEqual(RHS.U.IEEE);
1116  if (usesLayout<DoubleAPFloat>(getSemantics()))
1117  return U.Double.bitwiseIsEqual(RHS.U.Double);
1118  llvm_unreachable("Unexpected semantics");
1119  }
1120 
1121  /// We don't rely on operator== working on double values, as
1122  /// it returns true for things that are clearly not equal, like -0.0 and 0.0.
1123  /// As such, this method can be used to do an exact bit-for-bit comparison of
1124  /// two floating point values.
1125  ///
1126  /// We leave the version with the double argument here because it's just so
1127  /// convenient to write "2.0" and the like. Without this function we'd
1128  /// have to duplicate its logic everywhere it's called.
1129  bool isExactlyValue(double V) const {
1130  bool ignored;
1131  APFloat Tmp(V);
1132  Tmp.convert(getSemantics(), APFloat::rmNearestTiesToEven, &ignored);
1133  return bitwiseIsEqual(Tmp);
1134  }
1135 
1136  unsigned int convertToHexString(char *DST, unsigned int HexDigits,
1137  bool UpperCase, roundingMode RM) const {
1139  convertToHexString(DST, HexDigits, UpperCase, RM));
1140  }
1141 
1142  bool isZero() const { return getCategory() == fcZero; }
1143  bool isInfinity() const { return getCategory() == fcInfinity; }
1144  bool isNaN() const { return getCategory() == fcNaN; }
1145 
1146  bool isNegative() const { return getIEEE().isNegative(); }
1148  bool isSignaling() const { return getIEEE().isSignaling(); }
1149 
1150  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
1151  bool isFinite() const { return !isNaN() && !isInfinity(); }
1152 
1153  fltCategory getCategory() const { return getIEEE().getCategory(); }
1154  const fltSemantics &getSemantics() const { return *U.semantics; }
1155  bool isNonZero() const { return !isZero(); }
1156  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
1157  bool isPosZero() const { return isZero() && !isNegative(); }
1158  bool isNegZero() const { return isZero() && isNegative(); }
1162 
1163  APFloat &operator=(const APFloat &RHS) = default;
1164  APFloat &operator=(APFloat &&RHS) = default;
1165 
1166  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
1167  unsigned FormatMaxPadding = 3, bool TruncateZero = true) const {
1169  toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero));
1170  }
1171 
1172  void print(raw_ostream &) const;
1173  void dump() const;
1174 
1175  bool getExactInverse(APFloat *inv) const {
1176  APFLOAT_DISPATCH_ON_SEMANTICS(getExactInverse(inv));
1177  }
1178 
1179  friend hash_code hash_value(const APFloat &Arg);
1180  friend int ilogb(const APFloat &Arg) { return ilogb(Arg.getIEEE()); }
1181  friend APFloat scalbn(APFloat X, int Exp, roundingMode RM);
1182  friend APFloat frexp(const APFloat &X, int &Exp, roundingMode RM);
1183  friend IEEEFloat;
1185 };
1186 
1187 /// See friend declarations above.
1188 ///
1189 /// These additional declarations are required in order to compile LLVM with IBM
1190 /// xlC compiler.
1193  if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1194  return APFloat(scalbn(X.U.IEEE, Exp, RM), X.getSemantics());
1195  if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1196  return APFloat(scalbn(X.U.Double, Exp, RM), X.getSemantics());
1197  llvm_unreachable("Unexpected semantics");
1198 }
1199 
1200 /// Equivalent of C standard library function.
1201 ///
1202 /// While the C standard says Exp is an unspecified value for infinity and nan,
1203 /// this returns INT_MAX for infinities, and INT_MIN for NaNs.
1204 inline APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM) {
1205  if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1206  return APFloat(frexp(X.U.IEEE, Exp, RM), X.getSemantics());
1207  if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1208  return APFloat(frexp(X.U.Double, Exp, RM), X.getSemantics());
1209  llvm_unreachable("Unexpected semantics");
1210 }
1211 /// Returns the absolute value of the argument.
1213  X.clearSign();
1214  return X;
1215 }
1216 
1217 /// Returns the negated value of the argument.
1219  X.changeSign();
1220  return X;
1221 }
1222 
1223 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
1224 /// both are not NaN. If either argument is a NaN, returns the other argument.
1226 inline APFloat minnum(const APFloat &A, const APFloat &B) {
1227  if (A.isNaN())
1228  return B;
1229  if (B.isNaN())
1230  return A;
1231  return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
1232 }
1233 
1234 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
1235 /// both are not NaN. If either argument is a NaN, returns the other argument.
1237 inline APFloat maxnum(const APFloat &A, const APFloat &B) {
1238  if (A.isNaN())
1239  return B;
1240  if (B.isNaN())
1241  return A;
1242  return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
1243 }
1244 
1245 /// Implements IEEE 754-2018 minimum semantics. Returns the smaller of 2
1246 /// arguments, propagating NaNs and treating -0 as less than +0.
1248 inline APFloat minimum(const APFloat &A, const APFloat &B) {
1249  if (A.isNaN())
1250  return A;
1251  if (B.isNaN())
1252  return B;
1253  if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1254  return A.isNegative() ? A : B;
1255  return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
1256 }
1257 
1258 /// Implements IEEE 754-2018 maximum semantics. Returns the larger of 2
1259 /// arguments, propagating NaNs and treating -0 as less than +0.
1261 inline APFloat maximum(const APFloat &A, const APFloat &B) {
1262  if (A.isNaN())
1263  return A;
1264  if (B.isNaN())
1265  return B;
1266  if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1267  return A.isNegative() ? B : A;
1268  return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
1269 }
1270 
1271 } // namespace llvm
1272 
1273 #undef APFLOAT_DISPATCH_ON_SEMANTICS
1274 #endif // LLVM_ADT_APFLOAT_H
friend int ilogb(const APFloat &Arg)
Definition: APFloat.h:1180
opStatus roundToIntegral(roundingMode RM)
Definition: APFloat.h:1007
static APFloat getNaN(const fltSemantics &Sem, bool Negative=false, uint64_t payload=0)
Factory for NaN values.
Definition: APFloat.h:874
static const fltSemantics & IEEEquad() LLVM_READNONE
Definition: APFloat.cpp:125
fltCategory
Category of internally-represented number.
Definition: APFloat.h:194
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
bool isZero() const
Definition: APFloat.h:1142
opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM)
Definition: APFloat.h:1076
APFloat(const fltSemantics &Semantics)
Definition: APFloat.h:835
This class represents lattice values for constants.
Definition: AllocatorList.h:23
APFloat(double d)
Definition: APFloat.h:842
fltCategory getCategory() const
Definition: APFloat.h:1153
float convertToFloat() const
Definition: APFloat.h:1097
static unsigned getSizeInBits(const fltSemantics &Sem)
Returns the size of the floating point number (in bits) in the given semantics.
Definition: APFloat.cpp:169
F(f)
const fltSemantics & getSemantics() const
Definition: APFloat.h:1154
static APFloat getZero(const fltSemantics &Sem, bool Negative=false)
Factory for Positive and Negative Zero.
Definition: APFloat.h:854
Bits in a word.
Definition: APInt.h:78
LLVM_READONLY APFloat maximum(const APFloat &A, const APFloat &B)
Implements IEEE 754-2018 maximum semantics.
Definition: APFloat.h:1261
void changeSign()
Definition: APFloat.h:1049
opStatus next(bool nextDown)
Definition: APFloat.h:1013
APFloat(const fltSemantics &Semantics, const APInt &I)
Definition: APFloat.h:841
bool isNonZero() const
Definition: APFloat.h:355
bool isNegative() const
IEEE-754R isSignMinus: Returns true if and only if the current value is negative. ...
Definition: APFloat.h:318
opStatus convertToInteger(MutableArrayRef< integerPart > Input, unsigned int Width, bool IsSigned, roundingMode RM, bool *IsExact) const
Definition: APFloat.h:1068
opStatus convertFromSignExtendedInteger(const integerPart *Input, unsigned int InputSize, bool IsSigned, roundingMode RM)
Definition: APFloat.h:1080
opStatus divide(const APFloat &RHS, roundingMode RM)
Definition: APFloat.h:967
static APFloat getSmallest(const fltSemantics &Sem, bool Negative=false)
Returns the smallest (by magnitude) finite number in the given semantics.
Definition: APFloat.h:913
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:1183
bool isNonZero() const
Definition: APFloat.h:1155
roundingMode
IEEE-754R 4.3: Rounding-direction attributes.
Definition: APFloat.h:173
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:1035
LLVM_READONLY APFloat minimum(const APFloat &A, const APFloat &B)
Implements IEEE 754-2018 minimum semantics.
Definition: APFloat.h:1248
APFloat operator-(const APFloat &RHS) const
Subtract two APFloats, rounding ties to the nearest even.
Definition: APFloat.h:1027
static ExponentType semanticsMaxExponent(const fltSemantics &)
Definition: APFloat.cpp:158
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:1143
opStatus convert(const fltSemantics &ToSemantics, roundingMode RM, bool *losesInfo)
Definition: APFloat.cpp:4443
static unsigned int semanticsSizeInBits(const fltSemantics &)
Definition: APFloat.cpp:165
void toString(SmallVectorImpl< char > &Str, unsigned FormatPrecision=0, unsigned FormatMaxPadding=3, bool TruncateZero=true) const
Definition: APFloat.h:1166
friend DoubleAPFloat
Definition: APFloat.h:1184
bool isNaN() const
Returns true if and only if the float is a quiet or signaling NaN.
Definition: APFloat.h:343
hash_code hash_value(const APFloat &Arg)
See friend declarations above.
Definition: APFloat.cpp:4430
opStatus subtract(const APFloat &RHS, roundingMode RM)
Definition: APFloat.h:949
cmpResult
IEEE-754R 5.11: Floating Point Comparison Relations.
Definition: APFloat.h:165
static const fltSemantics & IEEEdouble() LLVM_READNONE
Definition: APFloat.cpp:122
static APFloat getInf(const fltSemantics &Sem, bool Negative=false)
Factory for Positive and Negative Infinity.
Definition: APFloat.h:863
static ExponentType semanticsMinExponent(const fltSemantics &)
Definition: APFloat.cpp:162
uninitializedTag
Convenience enum used to construct an uninitialized APFloat.
Definition: APFloat.h:202
static const unsigned integerPartWidth
Definition: APFloat.h:143
IlogbErrorKinds
Enumeration of ilogb error results.
Definition: APFloat.h:207
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:1061
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:353
bool isNegZero() const
Definition: APFloat.h:1158
void clearSign()
Definition: APFloat.h:1050
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:1146
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:843
bool isNaN() const
Definition: APFloat.h:1144
bool isLargest() const
Definition: APFloat.h:1160
double convertToDouble() const
Definition: APFloat.h:1096
APFloat scalbn(APFloat X, int Exp, APFloat::roundingMode RM)
Definition: APFloat.h:1192
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:1129
opStatus multiply(const APFloat &RHS, roundingMode RM)
Definition: APFloat.h:958
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:1019
static const fltSemantics & x87DoubleExtended() LLVM_READNONE
Definition: APFloat.cpp:128
APFloat operator/(const APFloat &RHS) const
Divide the first APFloat by the second, rounding ties to the nearest even.
Definition: APFloat.h:1043
#define llvm_unreachable(msg)
Marks that the current location is not supposed to be reachable.
void copySign(const APFloat &RHS)
Definition: APFloat.h:1054
LLVM_READONLY APFloat maxnum(const APFloat &A, const APFloat &B)
Implements IEEE maxNum semantics.
Definition: APFloat.h:1237
signed short ExponentType
A signed type to represent a floating point numbers unbiased exponent.
Definition: APFloat.h:146
bool isFinite() const
Definition: APFloat.h:1151
bool needsCleanup() const
Definition: APFloat.h:849
static const fltSemantics & IEEEsingle() LLVM_READNONE
Definition: APFloat.cpp:119
bool isInteger() const
Definition: APFloat.h:1161
DoubleAPFloat & operator=(DoubleAPFloat &&RHS)
Definition: APFloat.h:595
static const fltSemantics & IEEEhalf() LLVM_READNONE
Definition: APFloat.cpp:116
bool isFiniteNonZero() const
Definition: APFloat.h:356
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:357
bool isFinite() const
Returns true if and only if the current value is zero, subnormal, or normal.
Definition: APFloat.h:330
bool isFiniteNonZero() const
Definition: APFloat.h:1156
#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:1218
APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM)
Equivalent of C standard library function.
Definition: APFloat.h:1204
bool needsCleanup() const
Definition: APFloat.h:603
static unsigned int semanticsPrecision(const fltSemantics &)
Definition: APFloat.cpp:154
bool isDenormal() const
Definition: APFloat.h:1147
uint64_t WordType
Definition: APInt.h:71
const fltSemantics & getSemantics() const
Definition: APFloat.h:354
APInt::WordType integerPart
Definition: APFloat.h:142
bool getExactInverse(APFloat *inv) const
Definition: APFloat.h:1175
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:893
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:606
bool isZero() const
Returns true if and only if the float is plus or minus zero.
Definition: APFloat.h:333
opStatus mod(const APFloat &RHS)
Definition: APFloat.h:985
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:1136
static const fltSemantics & PPCDoubleDouble() LLVM_READNONE
Definition: APFloat.cpp:134
opStatus add(const APFloat &RHS, roundingMode RM)
Definition: APFloat.h:940
static bool isZero(Value *V, const DataLayout &DL, DominatorTree *DT, AssumptionCache *AC)
Definition: Lint.cpp:545
opStatus
IEEE-754R 7: Default exception handling.
Definition: APFloat.h:184
bool isPosZero() const
Definition: APFloat.h:1157
#define LLVM_READNONE
Definition: Compiler.h:176
#define I(x, y, z)
Definition: MD5.cpp:58
APFloat abs(APFloat X)
Returns the absolute value of the argument.
Definition: APFloat.h:1212
bool isNormal() const
Definition: APFloat.h:1150
static const fltSemantics & Bogus() LLVM_READNONE
A Pseudo fltsemantic used to construct APFloats that cannot conflict with anything real...
Definition: APFloat.cpp:131
#define LLVM_READONLY
Definition: Compiler.h:183
static APFloat getLargest(const fltSemantics &Sem, bool Negative=false)
Returns the largest finite number in the given semantics.
Definition: APFloat.h:903
static APFloat getSmallestNormalized(const fltSemantics &Sem, bool Negative=false)
Returns the smallest (by magnitude) normalized finite number in the given semantics.
Definition: APFloat.h:923
const APFloat & getSecond() const
Definition: APFloat.h:608
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:358
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend, roundingMode RM)
Definition: APFloat.h:994
opStatus remainder(const APFloat &RHS)
Definition: APFloat.h:976
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:72
bool needsCleanup() const
Returns whether this instance allocated memory.
Definition: APFloat.h:243
bool bitwiseIsEqual(const APFloat &RHS) const
Definition: APFloat.h:1111
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:1086
APInt bitcastToAPInt() const
Definition: APFloat.h:1093
bool operator==(uint64_t V1, const APInt &V2)
Definition: APInt.h:1966
APFloat(const fltSemantics &Semantics, integerPart I)
Definition: APFloat.h:837
bool isInfinity() const
IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
Definition: APFloat.h:340
bool isSmallest() const
Definition: APFloat.h:1159
bool isSignaling() const
Definition: APFloat.h:1148
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:885
APFloat(const fltSemantics &Semantics, uninitializedTag)
Definition: APFloat.h:839
LLVM_READONLY APFloat minnum(const APFloat &A, const APFloat &B)
Implements IEEE minNum semantics.
Definition: APFloat.h:1226
int ilogb(const IEEEFloat &Arg)
Definition: APFloat.cpp:3788
cmpResult compare(const APFloat &RHS) const
Definition: APFloat.h:1101
bool isNormal() const
IEEE-754R isNormal: Returns true if and only if the current value is normal.
Definition: APFloat.h:324