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// This file declares a class to represent arbitrary precision floating
11// point values and provide a variety of arithmetic operations on them.
12//
13//===----------------------------------------------------------------------===//
14
15/*  A self-contained host- and target-independent arbitrary-precision
16    floating-point software implementation.  It uses bignum integer
17    arithmetic as provided by static functions in the APInt class.
18    The library will work with bignum integers whose parts are any
19    unsigned type at least 16 bits wide, but 64 bits is recommended.
20
21    Written for clarity rather than speed, in particular with a view
22    to use in the front-end of a cross compiler so that target
23    arithmetic can be correctly performed on the host.  Performance
24    should nonetheless be reasonable, particularly for its intended
25    use.  It may be useful as a base implementation for a run-time
26    library during development of a faster target-specific one.
27
28    All 5 rounding modes in the IEEE-754R draft are handled correctly
29    for all implemented operations.  Currently implemented operations
30    are add, subtract, multiply, divide, fused-multiply-add,
31    conversion-to-float, conversion-to-integer and
32    conversion-from-integer.  New rounding modes (e.g. away from zero)
33    can be added with three or four lines of code.
34
35    Four formats are built-in: IEEE single precision, double
36    precision, quadruple precision, and x87 80-bit extended double
37    (when operating with full extended precision).  Adding a new
38    format that obeys IEEE semantics only requires adding two lines of
39    code: a declaration and definition of the format.
40
41    All operations return the status of that operation as an exception
42    bit-mask, so multiple operations can be done consecutively with
43    their results or-ed together.  The returned status can be useful
44    for compiler diagnostics; e.g., inexact, underflow and overflow
45    can be easily diagnosed on constant folding, and compiler
46    optimizers can determine what exceptions would be raised by
47    folding operations and optimize, or perhaps not optimize,
48    accordingly.
49
50    At present, underflow tininess is detected after rounding; it
51    should be straight forward to add support for the before-rounding
52    case too.
53
54    The library reads hexadecimal floating point numbers as per C99,
55    and correctly rounds if necessary according to the specified
56    rounding mode.  Syntax is required to have been validated by the
57    caller.  It also converts floating point numbers to hexadecimal
58    text as per the C99 %a and %A conversions.  The output precision
59    (or alternatively the natural minimal precision) can be specified;
60    if the requested precision is less than the natural precision the
61    output is correctly rounded for the specified rounding mode.
62
63    It also reads decimal floating point numbers and correctly rounds
64    according to the specified rounding mode.
65
66    Conversion to decimal text is not currently implemented.
67
68    Non-zero finite numbers are represented internally as a sign bit,
69    a 16-bit signed exponent, and the significand as an array of
70    integer parts.  After normalization of a number of precision P the
71    exponent is within the range of the format, and if the number is
72    not denormal the P-th bit of the significand is set as an explicit
73    integer bit.  For denormals the most significant bit is shifted
74    right so that the exponent is maintained at the format's minimum,
75    so that the smallest denormal has just the least significant bit
76    of the significand set.  The sign of zeroes and infinities is
77    significant; the exponent and significand of such numbers is not
78    stored, but has a known implicit (deterministic) value: 0 for the
79    significands, 0 for zero exponent, all 1 bits for infinity
80    exponent.  For NaNs the sign and significand are deterministic,
81    although not really meaningful, and preserved in non-conversion
82    operations.  The exponent is implicitly all 1 bits.
83
84    TODO
85    ====
86
87    Some features that may or may not be worth adding:
88
89    Binary to decimal conversion (hard).
90
91    Optional ability to detect underflow tininess before rounding.
92
93    New formats: x87 in single and double precision mode (IEEE apart
94    from extended exponent range) (hard).
95
96    New operations: sqrt, IEEE remainder, C90 fmod, nextafter,
97    nexttoward.
98*/
99
100#ifndef LLVM_FLOAT_H
101#define LLVM_FLOAT_H
102
103// APInt contains static functions implementing bignum arithmetic.
104#include "llvm/ADT/APInt.h"
105
106namespace llvm {
107
108  /* Exponents are stored as signed numbers.  */
109  typedef signed short exponent_t;
110
111  struct fltSemantics;
112  class APSInt;
113  class StringRef;
114
115  /* When bits of a floating point number are truncated, this enum is
116     used to indicate what fraction of the LSB those bits represented.
117     It essentially combines the roles of guard and sticky bits.  */
118  enum lostFraction {           // Example of truncated bits:
119    lfExactlyZero,              // 000000
120    lfLessThanHalf,             // 0xxxxx  x's not all zero
121    lfExactlyHalf,              // 100000
122    lfMoreThanHalf              // 1xxxxx  x's not all zero
123  };
124
125  class APFloat {
126  public:
127
128    /* We support the following floating point semantics.  */
129    static const fltSemantics IEEEhalf;
130    static const fltSemantics IEEEsingle;
131    static const fltSemantics IEEEdouble;
132    static const fltSemantics IEEEquad;
133    static const fltSemantics PPCDoubleDouble;
134    static const fltSemantics x87DoubleExtended;
135    /* And this pseudo, used to construct APFloats that cannot
136       conflict with anything real. */
137    static const fltSemantics Bogus;
138
139    static unsigned int semanticsPrecision(const fltSemantics &);
140
141    /* Floating point numbers have a four-state comparison relation.  */
142    enum cmpResult {
143      cmpLessThan,
144      cmpEqual,
145      cmpGreaterThan,
146      cmpUnordered
147    };
148
149    /* IEEE-754R gives five rounding modes.  */
150    enum roundingMode {
151      rmNearestTiesToEven,
152      rmTowardPositive,
153      rmTowardNegative,
154      rmTowardZero,
155      rmNearestTiesToAway
156    };
157
158    // Operation status.  opUnderflow or opOverflow are always returned
159    // or-ed with opInexact.
160    enum opStatus {
161      opOK          = 0x00,
162      opInvalidOp   = 0x01,
163      opDivByZero   = 0x02,
164      opOverflow    = 0x04,
165      opUnderflow   = 0x08,
166      opInexact     = 0x10
167    };
168
169    // Category of internally-represented number.
170    enum fltCategory {
171      fcInfinity,
172      fcNaN,
173      fcNormal,
174      fcZero
175    };
176
177    enum uninitializedTag {
178      uninitialized
179    };
180
181    // Constructors.
182    APFloat(const fltSemantics &); // Default construct to 0.0
183    APFloat(const fltSemantics &, StringRef);
184    APFloat(const fltSemantics &, integerPart);
185    APFloat(const fltSemantics &, fltCategory, bool negative);
186    APFloat(const fltSemantics &, uninitializedTag);
187    explicit APFloat(double d);
188    explicit APFloat(float f);
189    explicit APFloat(const APInt &, bool isIEEE = false);
190    APFloat(const APFloat &);
191    ~APFloat();
192
193    // Convenience "constructors"
194    static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
195      return APFloat(Sem, fcZero, Negative);
196    }
197    static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
198      return APFloat(Sem, fcInfinity, Negative);
199    }
200
201    /// getNaN - Factory for QNaN values.
202    ///
203    /// \param Negative - True iff the NaN generated should be negative.
204    /// \param type - The unspecified fill bits for creating the NaN, 0 by
205    /// default.  The value is truncated as necessary.
206    static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
207                          unsigned type = 0) {
208      if (type) {
209        APInt fill(64, type);
210        return getQNaN(Sem, Negative, &fill);
211      } else {
212        return getQNaN(Sem, Negative, 0);
213      }
214    }
215
216    /// getQNan - Factory for QNaN values.
217    static APFloat getQNaN(const fltSemantics &Sem,
218                           bool Negative = false,
219                           const APInt *payload = 0) {
220      return makeNaN(Sem, false, Negative, payload);
221    }
222
223    /// getSNan - Factory for SNaN values.
224    static APFloat getSNaN(const fltSemantics &Sem,
225                           bool Negative = false,
226                           const APInt *payload = 0) {
227      return makeNaN(Sem, true, Negative, payload);
228    }
229
230    /// getLargest - Returns the largest finite number in the given
231    /// semantics.
232    ///
233    /// \param Negative - True iff the number should be negative
234    static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
235
236    /// getSmallest - Returns the smallest (by magnitude) finite number
237    /// in the given semantics.  Might be denormalized, which implies a
238    /// relative loss of precision.
239    ///
240    /// \param Negative - True iff the number should be negative
241    static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
242
243    /// getSmallestNormalized - Returns the smallest (by magnitude)
244    /// normalized finite number in the given semantics.
245    ///
246    /// \param Negative - True iff the number should be negative
247    static APFloat getSmallestNormalized(const fltSemantics &Sem,
248                                         bool Negative = false);
249
250    /// getAllOnesValue - Returns a float which is bitcasted from
251    /// an all one value int.
252    ///
253    /// \param BitWidth - Select float type
254    /// \param isIEEE   - If 128 bit number, select between PPC and IEEE
255    static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
256
257    /// Profile - Used to insert APFloat objects, or objects that contain
258    ///  APFloat objects, into FoldingSets.
259    void Profile(FoldingSetNodeID& NID) const;
260
261    /// @brief Used by the Bitcode serializer to emit APInts to Bitcode.
262    void Emit(Serializer& S) const;
263
264    /// @brief Used by the Bitcode deserializer to deserialize APInts.
265    static APFloat ReadVal(Deserializer& D);
266
267    /* Arithmetic.  */
268    opStatus add(const APFloat &, roundingMode);
269    opStatus subtract(const APFloat &, roundingMode);
270    opStatus multiply(const APFloat &, roundingMode);
271    opStatus divide(const APFloat &, roundingMode);
272    /* IEEE remainder. */
273    opStatus remainder(const APFloat &);
274    /* C fmod, or llvm frem. */
275    opStatus mod(const APFloat &, roundingMode);
276    opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
277    opStatus roundToIntegral(roundingMode);
278
279    /* Sign operations.  */
280    void changeSign();
281    void clearSign();
282    void copySign(const APFloat &);
283
284    /* Conversions.  */
285    opStatus convert(const fltSemantics &, roundingMode, bool *);
286    opStatus convertToInteger(integerPart *, unsigned int, bool,
287                              roundingMode, bool *) const;
288    opStatus convertToInteger(APSInt&, roundingMode, bool *) const;
289    opStatus convertFromAPInt(const APInt &,
290                              bool, roundingMode);
291    opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
292                                            bool, roundingMode);
293    opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
294                                            bool, roundingMode);
295    opStatus convertFromString(StringRef, roundingMode);
296    APInt bitcastToAPInt() const;
297    double convertToDouble() const;
298    float convertToFloat() const;
299
300    /* The definition of equality is not straightforward for floating point,
301       so we won't use operator==.  Use one of the following, or write
302       whatever it is you really mean. */
303    // bool operator==(const APFloat &) const;     // DO NOT IMPLEMENT
304
305    /* IEEE comparison with another floating point number (NaNs
306       compare unordered, 0==-0). */
307    cmpResult compare(const APFloat &) const;
308
309    /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
310    bool bitwiseIsEqual(const APFloat &) const;
311
312    /* Write out a hexadecimal representation of the floating point
313       value to DST, which must be of sufficient size, in the C99 form
314       [-]0xh.hhhhp[+-]d.  Return the number of characters written,
315       excluding the terminating NUL.  */
316    unsigned int convertToHexString(char *dst, unsigned int hexDigits,
317                                    bool upperCase, roundingMode) const;
318
319    /* Simple queries.  */
320    fltCategory getCategory() const { return category; }
321    const fltSemantics &getSemantics() const { return *semantics; }
322    bool isZero() const { return category == fcZero; }
323    bool isNonZero() const { return category != fcZero; }
324    bool isNormal() const { return category == fcNormal; }
325    bool isNaN() const { return category == fcNaN; }
326    bool isInfinity() const { return category == fcInfinity; }
327    bool isNegative() const { return sign; }
328    bool isPosZero() const { return isZero() && !isNegative(); }
329    bool isNegZero() const { return isZero() && isNegative(); }
330
331    APFloat& operator=(const APFloat &);
332
333    /// \brief Overload to compute a hash code for an APFloat value.
334    ///
335    /// Note that the use of hash codes for floating point values is in general
336    /// frought with peril. Equality is hard to define for these values. For
337    /// example, should negative and positive zero hash to different codes? Are
338    /// they equal or not? This hash value implementation specifically
339    /// emphasizes producing different codes for different inputs in order to
340    /// be used in canonicalization and memoization. As such, equality is
341    /// bitwiseIsEqual, and 0 != -0.
342    friend hash_code hash_value(const APFloat &Arg);
343
344    /// Converts this value into a decimal string.
345    ///
346    /// \param FormatPrecision The maximum number of digits of
347    ///   precision to output.  If there are fewer digits available,
348    ///   zero padding will not be used unless the value is
349    ///   integral and small enough to be expressed in
350    ///   FormatPrecision digits.  0 means to use the natural
351    ///   precision of the number.
352    /// \param FormatMaxPadding The maximum number of zeros to
353    ///   consider inserting before falling back to scientific
354    ///   notation.  0 means to always use scientific notation.
355    ///
356    /// Number       Precision    MaxPadding      Result
357    /// ------       ---------    ----------      ------
358    /// 1.01E+4              5             2       10100
359    /// 1.01E+4              4             2       1.01E+4
360    /// 1.01E+4              5             1       1.01E+4
361    /// 1.01E-2              5             2       0.0101
362    /// 1.01E-2              4             2       0.0101
363    /// 1.01E-2              4             1       1.01E-2
364    void toString(SmallVectorImpl<char> &Str,
365                  unsigned FormatPrecision = 0,
366                  unsigned FormatMaxPadding = 3) const;
367
368    /// getExactInverse - If this value has an exact multiplicative inverse,
369    /// store it in inv and return true.
370    bool getExactInverse(APFloat *inv) const;
371
372  private:
373
374    /* Trivial queries.  */
375    integerPart *significandParts();
376    const integerPart *significandParts() const;
377    unsigned int partCount() const;
378
379    /* Significand operations.  */
380    integerPart addSignificand(const APFloat &);
381    integerPart subtractSignificand(const APFloat &, integerPart);
382    lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
383    lostFraction multiplySignificand(const APFloat &, const APFloat *);
384    lostFraction divideSignificand(const APFloat &);
385    void incrementSignificand();
386    void initialize(const fltSemantics *);
387    void shiftSignificandLeft(unsigned int);
388    lostFraction shiftSignificandRight(unsigned int);
389    unsigned int significandLSB() const;
390    unsigned int significandMSB() const;
391    void zeroSignificand();
392
393    /* Arithmetic on special values.  */
394    opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
395    opStatus divideSpecials(const APFloat &);
396    opStatus multiplySpecials(const APFloat &);
397    opStatus modSpecials(const APFloat &);
398
399    /* Miscellany.  */
400    static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
401                           const APInt *fill);
402    void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
403    opStatus normalize(roundingMode, lostFraction);
404    opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
405    cmpResult compareAbsoluteValue(const APFloat &) const;
406    opStatus handleOverflow(roundingMode);
407    bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
408    opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
409                                          roundingMode, bool *) const;
410    opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
411                                      roundingMode);
412    opStatus convertFromHexadecimalString(StringRef, roundingMode);
413    opStatus convertFromDecimalString(StringRef, roundingMode);
414    char *convertNormalToHexString(char *, unsigned int, bool,
415                                   roundingMode) const;
416    opStatus roundSignificandWithExponent(const integerPart *, unsigned int,
417                                          int, roundingMode);
418
419    APInt convertHalfAPFloatToAPInt() const;
420    APInt convertFloatAPFloatToAPInt() const;
421    APInt convertDoubleAPFloatToAPInt() const;
422    APInt convertQuadrupleAPFloatToAPInt() const;
423    APInt convertF80LongDoubleAPFloatToAPInt() const;
424    APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
425    void initFromAPInt(const APInt& api, bool isIEEE = false);
426    void initFromHalfAPInt(const APInt& api);
427    void initFromFloatAPInt(const APInt& api);
428    void initFromDoubleAPInt(const APInt& api);
429    void initFromQuadrupleAPInt(const APInt &api);
430    void initFromF80LongDoubleAPInt(const APInt& api);
431    void initFromPPCDoubleDoubleAPInt(const APInt& api);
432
433    void assign(const APFloat &);
434    void copySignificand(const APFloat &);
435    void freeSignificand();
436
437    /* What kind of semantics does this value obey?  */
438    const fltSemantics *semantics;
439
440    /* Significand - the fraction with an explicit integer bit.  Must be
441       at least one bit wider than the target precision.  */
442    union Significand
443    {
444      integerPart part;
445      integerPart *parts;
446    } significand;
447
448    /* The exponent - a signed number.  */
449    exponent_t exponent;
450
451    /* What kind of floating point number this is.  */
452    /* Only 2 bits are required, but VisualStudio incorrectly sign extends
453       it.  Using the extra bit keeps it from failing under VisualStudio */
454    fltCategory category: 3;
455
456    /* The sign bit of this number.  */
457    unsigned int sign: 1;
458
459    /* For PPCDoubleDouble, we have a second exponent and sign (the second
460       significand is appended to the first one, although it would be wrong to
461       regard these as a single number for arithmetic purposes).  These fields
462       are not meaningful for any other type. */
463    exponent_t exponent2 : 11;
464    unsigned int sign2: 1;
465  };
466} /* namespace llvm */
467
468#endif /* LLVM_FLOAT_H */
469