1//===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//
2//
3//                     The LLVM Compiler Infrastructure
4//
5// This file is distributed under the University of Illinois Open Source
6// License. See LICENSE.TXT for details.
7//
8//===----------------------------------------------------------------------===//
9///
10/// \file
11/// \brief
12/// This file declares a class to represent arbitrary precision floating point
13/// values and provide a variety of arithmetic operations on them.
14///
15//===----------------------------------------------------------------------===//
16
17#ifndef LLVM_ADT_APFLOAT_H
18#define LLVM_ADT_APFLOAT_H
19
20#include "llvm/ADT/APInt.h"
21
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(APFloat &&);
200  ~APFloat();
201
202  /// @}
203
204  /// \brief Returns whether this instance allocated memory.
205  bool needsCleanup() const { return partCount() > 1; }
206
207  /// \name Convenience "constructors"
208  /// @{
209
210  /// Factory for Positive and Negative Zero.
211  ///
212  /// \param Negative True iff the number should be negative.
213  static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
214    APFloat Val(Sem, uninitialized);
215    Val.makeZero(Negative);
216    return Val;
217  }
218
219  /// Factory for Positive and Negative Infinity.
220  ///
221  /// \param Negative True iff the number should be negative.
222  static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
223    APFloat Val(Sem, uninitialized);
224    Val.makeInf(Negative);
225    return Val;
226  }
227
228  /// Factory for QNaN values.
229  ///
230  /// \param Negative - True iff the NaN generated should be negative.
231  /// \param type - The unspecified fill bits for creating the NaN, 0 by
232  /// default.  The value is truncated as necessary.
233  static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
234                        unsigned type = 0) {
235    if (type) {
236      APInt fill(64, type);
237      return getQNaN(Sem, Negative, &fill);
238    } else {
239      return getQNaN(Sem, Negative, nullptr);
240    }
241  }
242
243  /// Factory for QNaN values.
244  static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
245                         const APInt *payload = nullptr) {
246    return makeNaN(Sem, false, Negative, payload);
247  }
248
249  /// Factory for SNaN values.
250  static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
251                         const APInt *payload = nullptr) {
252    return makeNaN(Sem, true, Negative, payload);
253  }
254
255  /// Returns the largest finite number in the given semantics.
256  ///
257  /// \param Negative - True iff the number should be negative
258  static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
259
260  /// Returns the smallest (by magnitude) finite number in the given semantics.
261  /// Might be denormalized, which implies a relative loss of precision.
262  ///
263  /// \param Negative - True iff the number should be negative
264  static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
265
266  /// Returns the smallest (by magnitude) normalized finite number in the given
267  /// semantics.
268  ///
269  /// \param Negative - True iff the number should be negative
270  static APFloat getSmallestNormalized(const fltSemantics &Sem,
271                                       bool Negative = false);
272
273  /// Returns a float which is bitcasted from an all one value int.
274  ///
275  /// \param BitWidth - Select float type
276  /// \param isIEEE   - If 128 bit number, select between PPC and IEEE
277  static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
278
279  /// @}
280
281  /// Used to insert APFloat objects, or objects that contain APFloat objects,
282  /// into FoldingSets.
283  void Profile(FoldingSetNodeID &NID) const;
284
285  /// \brief Used by the Bitcode serializer to emit APInts to Bitcode.
286  void Emit(Serializer &S) const;
287
288  /// \brief Used by the Bitcode deserializer to deserialize APInts.
289  static APFloat ReadVal(Deserializer &D);
290
291  /// \name Arithmetic
292  /// @{
293
294  opStatus add(const APFloat &, roundingMode);
295  opStatus subtract(const APFloat &, roundingMode);
296  opStatus multiply(const APFloat &, roundingMode);
297  opStatus divide(const APFloat &, roundingMode);
298  /// IEEE remainder.
299  opStatus remainder(const APFloat &);
300  /// C fmod, or llvm frem.
301  opStatus mod(const APFloat &, roundingMode);
302  opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
303  opStatus roundToIntegral(roundingMode);
304  /// IEEE-754R 5.3.1: nextUp/nextDown.
305  opStatus next(bool nextDown);
306
307  /// @}
308
309  /// \name Sign operations.
310  /// @{
311
312  void changeSign();
313  void clearSign();
314  void copySign(const APFloat &);
315
316  /// @}
317
318  /// \name Conversions
319  /// @{
320
321  opStatus convert(const fltSemantics &, roundingMode, bool *);
322  opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
323                            bool *) const;
324  opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
325  opStatus convertFromAPInt(const APInt &, bool, roundingMode);
326  opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
327                                          bool, roundingMode);
328  opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
329                                          bool, roundingMode);
330  opStatus convertFromString(StringRef, roundingMode);
331  APInt bitcastToAPInt() const;
332  double convertToDouble() const;
333  float convertToFloat() const;
334
335  /// @}
336
337  /// The definition of equality is not straightforward for floating point, so
338  /// we won't use operator==.  Use one of the following, or write whatever it
339  /// is you really mean.
340  bool operator==(const APFloat &) const LLVM_DELETED_FUNCTION;
341
342  /// IEEE comparison with another floating point number (NaNs compare
343  /// unordered, 0==-0).
344  cmpResult compare(const APFloat &) const;
345
346  /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
347  bool bitwiseIsEqual(const APFloat &) const;
348
349  /// Write out a hexadecimal representation of the floating point value to DST,
350  /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
351  /// Return the number of characters written, excluding the terminating NUL.
352  unsigned int convertToHexString(char *dst, unsigned int hexDigits,
353                                  bool upperCase, roundingMode) const;
354
355  /// \name IEEE-754R 5.7.2 General operations.
356  /// @{
357
358  /// IEEE-754R isSignMinus: Returns true if and only if the current value is
359  /// negative.
360  ///
361  /// This applies to zeros and NaNs as well.
362  bool isNegative() const { return sign; }
363
364  /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
365  ///
366  /// This implies that the current value of the float is not zero, subnormal,
367  /// infinite, or NaN following the definition of normality from IEEE-754R.
368  bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
369
370  /// Returns true if and only if the current value is zero, subnormal, or
371  /// normal.
372  ///
373  /// This means that the value is not infinite or NaN.
374  bool isFinite() const { return !isNaN() && !isInfinity(); }
375
376  /// Returns true if and only if the float is plus or minus zero.
377  bool isZero() const { return category == fcZero; }
378
379  /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
380  /// denormal.
381  bool isDenormal() const;
382
383  /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
384  bool isInfinity() const { return category == fcInfinity; }
385
386  /// Returns true if and only if the float is a quiet or signaling NaN.
387  bool isNaN() const { return category == fcNaN; }
388
389  /// Returns true if and only if the float is a signaling NaN.
390  bool isSignaling() const;
391
392  /// @}
393
394  /// \name Simple Queries
395  /// @{
396
397  fltCategory getCategory() const { return category; }
398  const fltSemantics &getSemantics() const { return *semantics; }
399  bool isNonZero() const { return category != fcZero; }
400  bool isFiniteNonZero() const { return isFinite() && !isZero(); }
401  bool isPosZero() const { return isZero() && !isNegative(); }
402  bool isNegZero() const { return isZero() && isNegative(); }
403
404  /// Returns true if and only if the number has the smallest possible non-zero
405  /// magnitude in the current semantics.
406  bool isSmallest() const;
407
408  /// Returns true if and only if the number has the largest possible finite
409  /// magnitude in the current semantics.
410  bool isLargest() const;
411
412  /// @}
413
414  APFloat &operator=(const APFloat &);
415  APFloat &operator=(APFloat &&);
416
417  /// \brief Overload to compute a hash code for an APFloat value.
418  ///
419  /// Note that the use of hash codes for floating point values is in general
420  /// frought with peril. Equality is hard to define for these values. For
421  /// example, should negative and positive zero hash to different codes? Are
422  /// they equal or not? This hash value implementation specifically
423  /// emphasizes producing different codes for different inputs in order to
424  /// be used in canonicalization and memoization. As such, equality is
425  /// bitwiseIsEqual, and 0 != -0.
426  friend hash_code hash_value(const APFloat &Arg);
427
428  /// Converts this value into a decimal string.
429  ///
430  /// \param FormatPrecision The maximum number of digits of
431  ///   precision to output.  If there are fewer digits available,
432  ///   zero padding will not be used unless the value is
433  ///   integral and small enough to be expressed in
434  ///   FormatPrecision digits.  0 means to use the natural
435  ///   precision of the number.
436  /// \param FormatMaxPadding The maximum number of zeros to
437  ///   consider inserting before falling back to scientific
438  ///   notation.  0 means to always use scientific notation.
439  ///
440  /// Number       Precision    MaxPadding      Result
441  /// ------       ---------    ----------      ------
442  /// 1.01E+4              5             2       10100
443  /// 1.01E+4              4             2       1.01E+4
444  /// 1.01E+4              5             1       1.01E+4
445  /// 1.01E-2              5             2       0.0101
446  /// 1.01E-2              4             2       0.0101
447  /// 1.01E-2              4             1       1.01E-2
448  void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
449                unsigned FormatMaxPadding = 3) const;
450
451  /// If this value has an exact multiplicative inverse, store it in inv and
452  /// return true.
453  bool getExactInverse(APFloat *inv) const;
454
455private:
456
457  /// \name Simple Queries
458  /// @{
459
460  integerPart *significandParts();
461  const integerPart *significandParts() const;
462  unsigned int partCount() const;
463
464  /// @}
465
466  /// \name Significand operations.
467  /// @{
468
469  integerPart addSignificand(const APFloat &);
470  integerPart subtractSignificand(const APFloat &, integerPart);
471  lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
472  lostFraction multiplySignificand(const APFloat &, const APFloat *);
473  lostFraction divideSignificand(const APFloat &);
474  void incrementSignificand();
475  void initialize(const fltSemantics *);
476  void shiftSignificandLeft(unsigned int);
477  lostFraction shiftSignificandRight(unsigned int);
478  unsigned int significandLSB() const;
479  unsigned int significandMSB() const;
480  void zeroSignificand();
481  /// Return true if the significand excluding the integral bit is all ones.
482  bool isSignificandAllOnes() const;
483  /// Return true if the significand excluding the integral bit is all zeros.
484  bool isSignificandAllZeros() const;
485
486  /// @}
487
488  /// \name Arithmetic on special values.
489  /// @{
490
491  opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
492  opStatus divideSpecials(const APFloat &);
493  opStatus multiplySpecials(const APFloat &);
494  opStatus modSpecials(const APFloat &);
495
496  /// @}
497
498  /// \name Special value setters.
499  /// @{
500
501  void makeLargest(bool Neg = false);
502  void makeSmallest(bool Neg = false);
503  void makeNaN(bool SNaN = false, bool Neg = false,
504               const APInt *fill = nullptr);
505  static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
506                         const APInt *fill);
507  void makeInf(bool Neg = false);
508  void makeZero(bool Neg = false);
509
510  /// @}
511
512  /// \name Miscellany
513  /// @{
514
515  bool convertFromStringSpecials(StringRef str);
516  opStatus normalize(roundingMode, lostFraction);
517  opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
518  cmpResult compareAbsoluteValue(const APFloat &) const;
519  opStatus handleOverflow(roundingMode);
520  bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
521  opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
522                                        roundingMode, bool *) const;
523  opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
524                                    roundingMode);
525  opStatus convertFromHexadecimalString(StringRef, roundingMode);
526  opStatus convertFromDecimalString(StringRef, roundingMode);
527  char *convertNormalToHexString(char *, unsigned int, bool,
528                                 roundingMode) const;
529  opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
530                                        roundingMode);
531
532  /// @}
533
534  APInt convertHalfAPFloatToAPInt() const;
535  APInt convertFloatAPFloatToAPInt() const;
536  APInt convertDoubleAPFloatToAPInt() const;
537  APInt convertQuadrupleAPFloatToAPInt() const;
538  APInt convertF80LongDoubleAPFloatToAPInt() const;
539  APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
540  void initFromAPInt(const fltSemantics *Sem, const APInt &api);
541  void initFromHalfAPInt(const APInt &api);
542  void initFromFloatAPInt(const APInt &api);
543  void initFromDoubleAPInt(const APInt &api);
544  void initFromQuadrupleAPInt(const APInt &api);
545  void initFromF80LongDoubleAPInt(const APInt &api);
546  void initFromPPCDoubleDoubleAPInt(const APInt &api);
547
548  void assign(const APFloat &);
549  void copySignificand(const APFloat &);
550  void freeSignificand();
551
552  /// The semantics that this value obeys.
553  const fltSemantics *semantics;
554
555  /// A binary fraction with an explicit integer bit.
556  ///
557  /// The significand must be at least one bit wider than the target precision.
558  union Significand {
559    integerPart part;
560    integerPart *parts;
561  } significand;
562
563  /// The signed unbiased exponent of the value.
564  ExponentType exponent;
565
566  /// What kind of floating point number this is.
567  ///
568  /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
569  /// Using the extra bit keeps it from failing under VisualStudio.
570  fltCategory category : 3;
571
572  /// Sign bit of the number.
573  unsigned int sign : 1;
574};
575
576/// See friend declaration above.
577///
578/// This additional declaration is required in order to compile LLVM with IBM
579/// xlC compiler.
580hash_code hash_value(const APFloat &Arg);
581} // namespace llvm
582
583#endif // LLVM_ADT_APFLOAT_H
584