/3rd_party/llvm/include/llvm/ADT/APFloat.h

  1//== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==//
  2//
  3//                     The LLVM Compiler Infrastructure
  4//
  5// This file is distributed under the University of Illinois Open Source
  6// License. See LICENSE.TXT for details.
  7//
  8//===----------------------------------------------------------------------===//
  9///
 10/// \file
 11/// \brief
 12/// This file declares a class to represent arbitrary precision floating point
 13/// values and provide a variety of arithmetic operations on them.
 14///
 15//===----------------------------------------------------------------------===//
 16
 17#ifndef LLVM_ADT_APFLOAT_H
 18#define LLVM_ADT_APFLOAT_H
 19
 20#include "llvm/ADT/APInt.h"
 21
 22namespace llvm {
 23
 24struct fltSemantics;
 25class APSInt;
 26class StringRef;
 27
 28/// Enum that represents what fraction of the LSB truncated bits of an fp number
 29/// represent.
 30///
 31/// This essentially combines the roles of guard and sticky bits.
 32enum lostFraction { // Example of truncated bits:
 33  lfExactlyZero,    // 000000
 34  lfLessThanHalf,   // 0xxxxx  x's not all zero
 35  lfExactlyHalf,    // 100000
 36  lfMoreThanHalf    // 1xxxxx  x's not all zero
 37};
 38
 39/// \brief A self-contained host- and target-independent arbitrary-precision
 40/// floating-point software implementation.
 41///
 42/// APFloat uses bignum integer arithmetic as provided by static functions in
 43/// the APInt class.  The library will work with bignum integers whose parts are
 44/// any unsigned type at least 16 bits wide, but 64 bits is recommended.
 45///
 46/// Written for clarity rather than speed, in particular with a view to use in
 47/// the front-end of a cross compiler so that target arithmetic can be correctly
 48/// performed on the host.  Performance should nonetheless be reasonable,
 49/// particularly for its intended use.  It may be useful as a base
 50/// implementation for a run-time library during development of a faster
 51/// target-specific one.
 52///
 53/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
 54/// implemented operations.  Currently implemented operations are add, subtract,
 55/// multiply, divide, fused-multiply-add, conversion-to-float,
 56/// conversion-to-integer and conversion-from-integer.  New rounding modes
 57/// (e.g. away from zero) can be added with three or four lines of code.
 58///
 59/// Four formats are built-in: IEEE single precision, double precision,
 60/// quadruple precision, and x87 80-bit extended double (when operating with
 61/// full extended precision).  Adding a new format that obeys IEEE semantics
 62/// only requires adding two lines of code: a declaration and definition of the
 63/// format.
 64///
 65/// All operations return the status of that operation as an exception bit-mask,
 66/// so multiple operations can be done consecutively with their results or-ed
 67/// together.  The returned status can be useful for compiler diagnostics; e.g.,
 68/// inexact, underflow and overflow can be easily diagnosed on constant folding,
 69/// and compiler optimizers can determine what exceptions would be raised by
 70/// folding operations and optimize, or perhaps not optimize, accordingly.
 71///
 72/// At present, underflow tininess is detected after rounding; it should be
 73/// straight forward to add support for the before-rounding case too.
 74///
 75/// The library reads hexadecimal floating point numbers as per C99, and
 76/// correctly rounds if necessary according to the specified rounding mode.
 77/// Syntax is required to have been validated by the caller.  It also converts
 78/// floating point numbers to hexadecimal text as per the C99 %a and %A
 79/// conversions.  The output precision (or alternatively the natural minimal
 80/// precision) can be specified; if the requested precision is less than the
 81/// natural precision the output is correctly rounded for the specified rounding
 82/// mode.
 83///
 84/// It also reads decimal floating point numbers and correctly rounds according
 85/// to the specified rounding mode.
 86///
 87/// Conversion to decimal text is not currently implemented.
 88///
 89/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
 90/// signed exponent, and the significand as an array of integer parts.  After
 91/// normalization of a number of precision P the exponent is within the range of
 92/// the format, and if the number is not denormal the P-th bit of the
 93/// significand is set as an explicit integer bit.  For denormals the most
 94/// significant bit is shifted right so that the exponent is maintained at the
 95/// format's minimum, so that the smallest denormal has just the least
 96/// significant bit of the significand set.  The sign of zeroes and infinities
 97/// is significant; the exponent and significand of such numbers is not stored,
 98/// but has a known implicit (deterministic) value: 0 for the significands, 0
 99/// for zero exponent, all 1 bits for infinity exponent.  For NaNs the sign and
100/// significand are deterministic, although not really meaningful, and preserved
101/// in non-conversion operations.  The exponent is implicitly all 1 bits.
102///
103/// APFloat does not provide any exception handling beyond default exception
104/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
105/// by encoding Signaling NaNs with the first bit of its trailing significand as
106/// 0.
107///
108/// TODO
109/// ====
110///
111/// Some features that may or may not be worth adding:
112///
113/// Binary to decimal conversion (hard).
114///
115/// Optional ability to detect underflow tininess before rounding.
116///
117/// New formats: x87 in single and double precision mode (IEEE apart from
118/// extended exponent range) (hard).
119///
120/// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
121///
122class APFloat {
123public:
124
125  /// A signed type to represent a floating point numbers unbiased exponent.
126  typedef signed short ExponentType;
127
128  /// \name Floating Point Semantics.
129  /// @{
130
131  static const fltSemantics IEEEhalf;
132  static const fltSemantics IEEEsingle;
133  static const fltSemantics IEEEdouble;
134  static const fltSemantics IEEEquad;
135  static const fltSemantics PPCDoubleDouble;
136  static const fltSemantics x87DoubleExtended;
137
138  /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
139  /// anything real.
140  static const fltSemantics Bogus;
141
142  /// @}
143
144  static unsigned int semanticsPrecision(const fltSemantics &);
145
146  /// IEEE-754R 5.11: Floating Point Comparison Relations.
147  enum cmpResult {
148    cmpLessThan,
149    cmpEqual,
150    cmpGreaterThan,
151    cmpUnordered
152  };
153
154  /// IEEE-754R 4.3: Rounding-direction attributes.
155  enum roundingMode {
156    rmNearestTiesToEven,
157    rmTowardPositive,
158    rmTowardNegative,
159    rmTowardZero,
160    rmNearestTiesToAway
161  };
162
163  /// IEEE-754R 7: Default exception handling.
164  ///
165  /// opUnderflow or opOverflow are always returned or-ed with opInexact.
166  enum opStatus {
167    opOK = 0x00,
168    opInvalidOp = 0x01,
169    opDivByZero = 0x02,
170    opOverflow = 0x04,
171    opUnderflow = 0x08,
172    opInexact = 0x10
173  };
174
175  /// Category of internally-represented number.
176  enum fltCategory {
177    fcInfinity,
178    fcNaN,
179    fcNormal,
180    fcZero
181  };
182
183  /// Convenience enum used to construct an uninitialized APFloat.
184  enum uninitializedTag {
185    uninitialized
186  };
187
188  /// \name Constructors
189  /// @{
190
191  APFloat(const fltSemantics &); // Default construct to 0.0
192  APFloat(const fltSemantics &, StringRef);
193  APFloat(const fltSemantics &, integerPart);
194  APFloat(const fltSemantics &, uninitializedTag);
195  APFloat(const fltSemantics &, const APInt &);
196  explicit APFloat(double d);
197  explicit APFloat(float f);
198  APFloat(const APFloat &);
199  ~APFloat();
200
201  /// @}
202
203  /// \brief Returns whether this instance allocated memory.
204  bool needsCleanup() const { return partCount() > 1; }
205
206  /// \name Convenience "constructors"
207  /// @{
208
209  /// Factory for Positive and Negative Zero.
210  ///
211  /// \param Negative True iff the number should be negative.
212  static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
213    APFloat Val(Sem, uninitialized);
214    Val.makeZero(Negative);
215    return Val;
216  }
217
218  /// Factory for Positive and Negative Infinity.
219  ///
220  /// \param Negative True iff the number should be negative.
221  static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
222    APFloat Val(Sem, uninitialized);
223    Val.makeInf(Negative);
224    return Val;
225  }
226
227  /// Factory for QNaN values.
228  ///
229  /// \param Negative - True iff the NaN generated should be negative.
230  /// \param type - The unspecified fill bits for creating the NaN, 0 by
231  /// default.  The value is truncated as necessary.
232  static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
233                        unsigned type = 0) {
234    if (type) {
235      APInt fill(64, type);
236      return getQNaN(Sem, Negative, &fill);
237    } else {
238      return getQNaN(Sem, Negative, 0);
239    }
240  }
241
242  /// Factory for QNaN values.
243  static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
244                         const APInt *payload = 0) {
245    return makeNaN(Sem, false, Negative, payload);
246  }
247
248  /// Factory for SNaN values.
249  static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
250                         const APInt *payload = 0) {
251    return makeNaN(Sem, true, Negative, payload);
252  }
253
254  /// Returns the largest finite number in the given semantics.
255  ///
256  /// \param Negative - True iff the number should be negative
257  static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
258
259  /// Returns the smallest (by magnitude) finite number in the given semantics.
260  /// Might be denormalized, which implies a relative loss of precision.
261  ///
262  /// \param Negative - True iff the number should be negative
263  static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
264
265  /// Returns the smallest (by magnitude) normalized finite number in the given
266  /// semantics.
267  ///
268  /// \param Negative - True iff the number should be negative
269  static APFloat getSmallestNormalized(const fltSemantics &Sem,
270                                       bool Negative = false);
271
272  /// Returns a float which is bitcasted from an all one value int.
273  ///
274  /// \param BitWidth - Select float type
275  /// \param isIEEE   - If 128 bit number, select between PPC and IEEE
276  static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
277
278  /// @}
279
280  /// Used to insert APFloat objects, or objects that contain APFloat objects,
281  /// into FoldingSets.
282  void Profile(FoldingSetNodeID &NID) const;
283
284  /// \brief Used by the Bitcode serializer to emit APInts to Bitcode.
285  void Emit(Serializer &S) const;
286
287  /// \brief Used by the Bitcode deserializer to deserialize APInts.
288  static APFloat ReadVal(Deserializer &D);
289
290  /// \name Arithmetic
291  /// @{
292
293  opStatus add(const APFloat &, roundingMode);
294  opStatus subtract(const APFloat &, roundingMode);
295  opStatus multiply(const APFloat &, roundingMode);
296  opStatus divide(const APFloat &, roundingMode);
297  /// IEEE remainder.
298  opStatus remainder(const APFloat &);
299  /// C fmod, or llvm frem.
300  opStatus mod(const APFloat &, roundingMode);
301  opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
302  opStatus roundToIntegral(roundingMode);
303  /// IEEE-754R 5.3.1: nextUp/nextDown.
304  opStatus next(bool nextDown);
305
306  /// @}
307
308  /// \name Sign operations.
309  /// @{
310
311  void changeSign();
312  void clearSign();
313  void copySign(const APFloat &);
314
315  /// @}
316
317  /// \name Conversions
318  /// @{
319
320  opStatus convert(const fltSemantics &, roundingMode, bool *);
321  opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
322                            bool *) const;
323  opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
324  opStatus convertFromAPInt(const APInt &, bool, roundingMode);
325  opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
326                                          bool, roundingMode);
327  opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
328                                          bool, roundingMode);
329  opStatus convertFromString(StringRef, roundingMode);
330  APInt bitcastToAPInt() const;
331  double convertToDouble() const;
332  float convertToFloat() const;
333
334  /// @}
335
336  /// The definition of equality is not straightforward for floating point, so
337  /// we won't use operator==.  Use one of the following, or write whatever it
338  /// is you really mean.
339  bool operator==(const APFloat &) const LLVM_DELETED_FUNCTION;
340
341  /// IEEE comparison with another floating point number (NaNs compare
342  /// unordered, 0==-0).
343  cmpResult compare(const APFloat &) const;
344
345  /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
346  bool bitwiseIsEqual(const APFloat &) const;
347
348  /// Write out a hexadecimal representation of the floating point value to DST,
349  /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
350  /// Return the number of characters written, excluding the terminating NUL.
351  unsigned int convertToHexString(char *dst, unsigned int hexDigits,
352                                  bool upperCase, roundingMode) const;
353
354  /// \name IEEE-754R 5.7.2 General operations.
355  /// @{
356
357  /// IEEE-754R isSignMinus: Returns true if and only if the current value is
358  /// negative.
359  ///
360  /// This applies to zeros and NaNs as well.
361  bool isNegative() const { return sign; }
362
363  /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
364  ///
365  /// This implies that the current value of the float is not zero, subnormal,
366  /// infinite, or NaN following the definition of normality from IEEE-754R.
367  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
368
369  /// Returns true if and only if the current value is zero, subnormal, or
370  /// normal.
371  ///
372  /// This means that the value is not infinite or NaN.
373  bool isFinite() const { return !isNaN() && !isInfinity(); }
374
375  /// Returns true if and only if the float is plus or minus zero.
376  bool isZero() const { return category == fcZero; }
377
378  /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
379  /// denormal.
380  bool isDenormal() const;
381
382  /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
383  bool isInfinity() const { return category == fcInfinity; }
384
385  /// Returns true if and only if the float is a quiet or signaling NaN.
386  bool isNaN() const { return category == fcNaN; }
387
388  /// Returns true if and only if the float is a signaling NaN.
389  bool isSignaling() const;
390
391  /// @}
392
393  /// \name Simple Queries
394  /// @{
395
396  fltCategory getCategory() const { return category; }
397  const fltSemantics &getSemantics() const { return *semantics; }
398  bool isNonZero() const { return category != fcZero; }
399  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
400  bool isPosZero() const { return isZero() && !isNegative(); }
401  bool isNegZero() const { return isZero() && isNegative(); }
402
403  /// Returns true if and only if the number has the smallest possible non-zero
404  /// magnitude in the current semantics.
405  bool isSmallest() const;
406
407  /// Returns true if and only if the number has the largest possible finite
408  /// magnitude in the current semantics.
409  bool isLargest() const;
410
411  /// @}
412
413  APFloat &operator=(const APFloat &);
414
415  /// \brief Overload to compute a hash code for an APFloat value.
416  ///
417  /// Note that the use of hash codes for floating point values is in general
418  /// frought with peril. Equality is hard to define for these values. For
419  /// example, should negative and positive zero hash to different codes? Are
420  /// they equal or not? This hash value implementation specifically
421  /// emphasizes producing different codes for different inputs in order to
422  /// be used in canonicalization and memoization. As such, equality is
423  /// bitwiseIsEqual, and 0 != -0.
424  friend hash_code hash_value(const APFloat &Arg);
425
426  /// Converts this value into a decimal string.
427  ///
428  /// \param FormatPrecision The maximum number of digits of
429  ///   precision to output.  If there are fewer digits available,
430  ///   zero padding will not be used unless the value is
431  ///   integral and small enough to be expressed in
432  ///   FormatPrecision digits.  0 means to use the natural
433  ///   precision of the number.
434  /// \param FormatMaxPadding The maximum number of zeros to
435  ///   consider inserting before falling back to scientific
436  ///   notation.  0 means to always use scientific notation.
437  ///
438  /// Number       Precision    MaxPadding      Result
439  /// ------       ---------    ----------      ------
440  /// 1.01E+4              5             2       10100
441  /// 1.01E+4              4             2       1.01E+4
442  /// 1.01E+4              5             1       1.01E+4
443  /// 1.01E-2              5             2       0.0101
444  /// 1.01E-2              4             2       0.0101
445  /// 1.01E-2              4             1       1.01E-2
446  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
447                unsigned FormatMaxPadding = 3) const;
448
449  /// If this value has an exact multiplicative inverse, store it in inv and
450  /// return true.
451  bool getExactInverse(APFloat *inv) const;
452
453private:
454
455  /// \name Simple Queries
456  /// @{
457
458  integerPart *significandParts();
459  const integerPart *significandParts() const;
460  unsigned int partCount() const;
461
462  /// @}
463
464  /// \name Significand operations.
465  /// @{
466
467  integerPart addSignificand(const APFloat &);
468  integerPart subtractSignificand(const APFloat &, integerPart);
469  lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
470  lostFraction multiplySignificand(const APFloat &, const APFloat *);
471  lostFraction divideSignificand(const APFloat &);
472  void incrementSignificand();
473  void initialize(const fltSemantics *);
474  void shiftSignificandLeft(unsigned int);
475  lostFraction shiftSignificandRight(unsigned int);
476  unsigned int significandLSB() const;
477  unsigned int significandMSB() const;
478  void zeroSignificand();
479  /// Return true if the significand excluding the integral bit is all ones.
480  bool isSignificandAllOnes() const;
481  /// Return true if the significand excluding the integral bit is all zeros.
482  bool isSignificandAllZeros() const;
483
484  /// @}
485
486  /// \name Arithmetic on special values.
487  /// @{
488
489  opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
490  opStatus divideSpecials(const APFloat &);
491  opStatus multiplySpecials(const APFloat &);
492  opStatus modSpecials(const APFloat &);
493
494  /// @}
495
496  /// \name Special value setters.
497  /// @{
498
499  void makeLargest(bool Neg = false);
500  void makeSmallest(bool Neg = false);
501  void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
502  static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
503                         const APInt *fill);
504  void makeInf(bool Neg = false);
505  void makeZero(bool Neg = false);
506
507  /// @}
508
509  /// \name Miscellany
510  /// @{
511
512  bool convertFromStringSpecials(StringRef str);
513  opStatus normalize(roundingMode, lostFraction);
514  opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
515  cmpResult compareAbsoluteValue(const APFloat &) const;
516  opStatus handleOverflow(roundingMode);
517  bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
518  opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
519                                        roundingMode, bool *) const;
520  opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
521                                    roundingMode);
522  opStatus convertFromHexadecimalString(StringRef, roundingMode);
523  opStatus convertFromDecimalString(StringRef, roundingMode);
524  char *convertNormalToHexString(char *, unsigned int, bool,
525                                 roundingMode) const;
526  opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
527                                        roundingMode);
528
529  /// @}
530
531  APInt convertHalfAPFloatToAPInt() const;
532  APInt convertFloatAPFloatToAPInt() const;
533  APInt convertDoubleAPFloatToAPInt() const;
534  APInt convertQuadrupleAPFloatToAPInt() const;
535  APInt convertF80LongDoubleAPFloatToAPInt() const;
536  APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
537  void initFromAPInt(const fltSemantics *Sem, const APInt &api);
538  void initFromHalfAPInt(const APInt &api);
539  void initFromFloatAPInt(const APInt &api);
540  void initFromDoubleAPInt(const APInt &api);
541  void initFromQuadrupleAPInt(const APInt &api);
542  void initFromF80LongDoubleAPInt(const APInt &api);
543  void initFromPPCDoubleDoubleAPInt(const APInt &api);
544
545  void assign(const APFloat &);
546  void copySignificand(const APFloat &);
547  void freeSignificand();
548
549  /// The semantics that this value obeys.
550  const fltSemantics *semantics;
551
552  /// A binary fraction with an explicit integer bit.
553  ///
554  /// The significand must be at least one bit wider than the target precision.
555  union Significand {
556    integerPart part;
557    integerPart *parts;
558  } significand;
559
560  /// The signed unbiased exponent of the value.
561  ExponentType exponent;
562
563  /// What kind of floating point number this is.
564  ///
565  /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
566  /// Using the extra bit keeps it from failing under VisualStudio.
567  fltCategory category : 3;
568
569  /// Sign bit of the number.
570  unsigned int sign : 1;
571};
572
573/// See friend declaration above.
574///
575/// This additional declaration is required in order to compile LLVM with IBM
576/// xlC compiler.
577hash_code hash_value(const APFloat &Arg);
578} // namespace llvm
579
580#endif // LLVM_ADT_APFLOAT_H