APFloat.h revision 921f0d40ececc91649bff9feeef37a3c89250608 
1//== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==//
2//
3//                     The LLVM Compiler Infrastructure
4//
5// This file was developed by Neil Booth and is distributed under the
6// University of Illinois Open Source 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
113  /* When bits of a floating point number are truncated, this enum is
114     used to indicate what fraction of the LSB those bits represented.
115     It essentially combines the roles of guard and sticky bits.  */
116  enum lostFraction {		// Example of truncated bits:
117    lfExactlyZero,		// 000000
118    lfLessThanHalf,		// 0xxxxx  x's not all zero
119    lfExactlyHalf,		// 100000
120    lfMoreThanHalf		// 1xxxxx  x's not all zero
121  };
122
123  class APFloat {
124  public:
125
126    /* We support the following floating point semantics.  */
127    static const fltSemantics IEEEsingle;
128    static const fltSemantics IEEEdouble;
129    static const fltSemantics IEEEquad;
130    static const fltSemantics PPCDoubleDouble;
131    static const fltSemantics x87DoubleExtended;
132    /* And this psuedo, used to construct APFloats that cannot
133       conflict with anything real. */
134    static const fltSemantics Bogus;
135
136    static unsigned int semanticsPrecision(const fltSemantics &);
137
138    /* Floating point numbers have a four-state comparison relation.  */
139    enum cmpResult {
140      cmpLessThan,
141      cmpEqual,
142      cmpGreaterThan,
143      cmpUnordered
144    };
145
146    /* IEEE-754R gives five rounding modes.  */
147    enum roundingMode {
148      rmNearestTiesToEven,
149      rmTowardPositive,
150      rmTowardNegative,
151      rmTowardZero,
152      rmNearestTiesToAway
153    };
154
155    /* Operation status.  opUnderflow or opOverflow are always returned
156       or-ed with opInexact.  */
157    enum opStatus {
158      opOK          = 0x00,
159      opInvalidOp   = 0x01,
160      opDivByZero   = 0x02,
161      opOverflow    = 0x04,
162      opUnderflow   = 0x08,
163      opInexact     = 0x10
164    };
165
166    /* Category of internally-represented number.  */
167    enum fltCategory {
168      fcInfinity,
169      fcNaN,
170      fcNormal,
171      fcZero
172    };
173
174    /* Constructors.  */
175    APFloat(const fltSemantics &, const char *);
176    APFloat(const fltSemantics &, integerPart);
177    APFloat(const fltSemantics &, fltCategory, bool negative);
178    explicit APFloat(double d);
179    explicit APFloat(float f);
180    explicit APFloat(const APInt &, bool isIEEE = false);
181    APFloat(const APFloat &);
182    ~APFloat();
183
184    /// @brief Used by the Bitcode serializer to emit APInts to Bitcode.
185    void Emit(Serializer& S) const;
186
187    /// @brief Used by the Bitcode deserializer to deserialize APInts.
188    static APFloat ReadVal(Deserializer& D);
189
190    /* Arithmetic.  */
191    opStatus add(const APFloat &, roundingMode);
192    opStatus subtract(const APFloat &, roundingMode);
193    opStatus multiply(const APFloat &, roundingMode);
194    opStatus divide(const APFloat &, roundingMode);
195    opStatus mod(const APFloat &, roundingMode);
196    opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
197
198    /* Sign operations.  */
199    void changeSign();
200    void clearSign();
201    void copySign(const APFloat &);
202
203    /* Conversions.  */
204    opStatus convert(const fltSemantics &, roundingMode);
205    opStatus convertToInteger(integerPart *, unsigned int, bool,
206			      roundingMode) const;
207    opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
208                                            bool, roundingMode);
209    opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
210                                            bool, roundingMode);
211    opStatus convertFromString(const char *, roundingMode);
212    APInt convertToAPInt() const;
213    double convertToDouble() const;
214    float convertToFloat() const;
215
216    /* The definition of equality is not straightforward for floating point,
217       so we won't use operator==.  Use one of the following, or write
218       whatever it is you really mean. */
219    // bool operator==(const APFloat &) const;     // DO NOT IMPLEMENT
220
221    /* IEEE comparison with another floating point number (NaNs
222       compare unordered, 0==-0). */
223    cmpResult compare(const APFloat &) const;
224
225    /* Write out a hexadecimal representation of the floating point
226       value to DST, which must be of sufficient size, in the C99 form
227       [-]0xh.hhhhp[+-]d.  Return the number of characters written,
228       excluding the terminating NUL.  */
229    unsigned int convertToHexString(char *dst, unsigned int hexDigits,
230                                    bool upperCase, roundingMode) const;
231
232    /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
233    bool bitwiseIsEqual(const APFloat &) const;
234
235    /* Simple queries.  */
236    fltCategory getCategory() const { return category; }
237    const fltSemantics &getSemantics() const { return *semantics; }
238    bool isZero() const { return category == fcZero; }
239    bool isNonZero() const { return category != fcZero; }
240    bool isNaN() const { return category == fcNaN; }
241    bool isNegative() const { return sign; }
242    bool isPosZero() const { return isZero() && !isNegative(); }
243    bool isNegZero() const { return isZero() && isNegative(); }
244
245    APFloat& operator=(const APFloat &);
246
247    /* Return an arbitrary integer value usable for hashing. */
248    uint32_t getHashValue() const;
249
250  private:
251
252    /* Trivial queries.  */
253    integerPart *significandParts();
254    const integerPart *significandParts() const;
255    unsigned int partCount() const;
256
257    /* Significand operations.  */
258    integerPart addSignificand(const APFloat &);
259    integerPart subtractSignificand(const APFloat &, integerPart);
260    lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
261    lostFraction multiplySignificand(const APFloat &, const APFloat *);
262    lostFraction divideSignificand(const APFloat &);
263    void incrementSignificand();
264    void initialize(const fltSemantics *);
265    void shiftSignificandLeft(unsigned int);
266    lostFraction shiftSignificandRight(unsigned int);
267    unsigned int significandLSB() const;
268    unsigned int significandMSB() const;
269    void zeroSignificand();
270
271    /* Arithmetic on special values.  */
272    opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
273    opStatus divideSpecials(const APFloat &);
274    opStatus multiplySpecials(const APFloat &);
275
276    /* Miscellany.  */
277    void makeNaN(void);
278    opStatus normalize(roundingMode, lostFraction);
279    opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
280    cmpResult compareAbsoluteValue(const APFloat &) const;
281    opStatus handleOverflow(roundingMode);
282    bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
283    opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
284                                          roundingMode) const;
285    opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
286                                      roundingMode);
287    opStatus convertFromHexadecimalString(const char *, roundingMode);
288    opStatus convertFromDecimalString (const char *, roundingMode);
289    char *convertNormalToHexString(char *, unsigned int, bool,
290                                   roundingMode) const;
291    opStatus roundSignificandWithExponent(const integerPart *, unsigned int,
292                                          int, roundingMode);
293
294    APInt convertFloatAPFloatToAPInt() const;
295    APInt convertDoubleAPFloatToAPInt() const;
296    APInt convertF80LongDoubleAPFloatToAPInt() const;
297    APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
298    void initFromAPInt(const APInt& api, bool isIEEE = false);
299    void initFromFloatAPInt(const APInt& api);
300    void initFromDoubleAPInt(const APInt& api);
301    void initFromF80LongDoubleAPInt(const APInt& api);
302    void initFromPPCDoubleDoubleAPInt(const APInt& api);
303
304    void assign(const APFloat &);
305    void copySignificand(const APFloat &);
306    void freeSignificand();
307
308    /* What kind of semantics does this value obey?  */
309    const fltSemantics *semantics;
310
311    /* Significand - the fraction with an explicit integer bit.  Must be
312       at least one bit wider than the target precision.  */
313    union Significand
314    {
315      integerPart part;
316      integerPart *parts;
317    } significand;
318
319    /* The exponent - a signed number.  */
320    exponent_t exponent;
321
322    /* What kind of floating point number this is.  */
323    /* Only 2 bits are required, but VisualStudio incorrectly sign extends
324       it.  Using the extra bit keeps it from failing under VisualStudio */
325    fltCategory category: 3;
326
327    /* The sign bit of this number.  */
328    unsigned int sign: 1;
329
330    /* For PPCDoubleDouble, we have a second exponent and sign (the second
331       significand is appended to the first one, although it would be wrong to
332       regard these as a single number for arithmetic purposes).  These fields
333       are not meaningful for any other type. */
334    exponent_t exponent2 : 11;
335    unsigned int sign2: 1;
336  };
337} /* namespace llvm */
338
339#endif /* LLVM_FLOAT_H */
340