APFloat.h revision a30b0ee959b53e83ed3697ee0b704a493829dc04 
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    Conversion to and from decimal text is not currently implemented.
64
65    Non-zero finite numbers are represented internally as a sign bit,
66    a 16-bit signed exponent, and the significand as an array of
67    integer parts.  After normalization of a number of precision P the
68    exponent is within the range of the format, and if the number is
69    not denormal the P-th bit of the significand is set as an explicit
70    integer bit.  For denormals the most significant bit is shifted
71    right so that the exponent is maintained at the format's minimum,
72    so that the smallest denormal has just the least significant bit
73    of the significand set.  The sign of zeroes and infinities is
74    significant; the exponent and significand of such numbers is not
75    stored, but has a known implicit (deterministic) value: 0 for the
76    significands, 0 for zero exponent, all 1 bits for infinity
77    exponent.  For NaNs the sign and significand are deterministic,
78    although not really meaningful, and preserved in non-conversion
79    operations.  The exponent is implicitly all 1 bits.
80
81    TODO
82    ====
83
84    Some features that may or may not be worth adding:
85
86    Conversions to and from decimal strings (hard).
87
88    Optional ability to detect underflow tininess before rounding.
89
90    New formats: x87 in single and double precision mode (IEEE apart
91    from extended exponent range) and IBM two-double extended
92    precision (hard).
93
94    New operations: sqrt, IEEE remainder, C90 fmod, nextafter,
95    nexttoward.
96*/
97
98#ifndef LLVM_FLOAT_H
99#define LLVM_FLOAT_H
100
101// APInt contains static functions implementing bignum arithmetic.
102#include "llvm/ADT/APInt.h"
103#include "llvm/CodeGen/ValueTypes.h"
104
105namespace llvm {
106
107  /* Exponents are stored as signed numbers.  */
108  typedef signed short exponent_t;
109
110  struct fltSemantics;
111
112  /* When bits of a floating point number are truncated, this enum is
113     used to indicate what fraction of the LSB those bits represented.
114     It essentially combines the roles of guard and sticky bits.  */
115  enum lostFraction {		// Example of truncated bits:
116    lfExactlyZero,		// 000000
117    lfLessThanHalf,		// 0xxxxx  x's not all zero
118    lfExactlyHalf,		// 100000
119    lfMoreThanHalf		// 1xxxxx  x's not all zero
120  };
121
122  class APFloat {
123  public:
124
125    /* We support the following floating point semantics.  */
126    static const fltSemantics IEEEsingle;
127    static const fltSemantics IEEEdouble;
128    static const fltSemantics IEEEquad;
129    static const fltSemantics x87DoubleExtended;
130    /* And this psuedo, used to construct APFloats that cannot
131       conflict with anything real. */
132    static const fltSemantics Bogus;
133
134    static unsigned int semanticsPrecision(const fltSemantics &);
135
136    /* Floating point numbers have a four-state comparison relation.  */
137    enum cmpResult {
138      cmpLessThan,
139      cmpEqual,
140      cmpGreaterThan,
141      cmpUnordered
142    };
143
144    /* IEEE-754R gives five rounding modes.  */
145    enum roundingMode {
146      rmNearestTiesToEven,
147      rmTowardPositive,
148      rmTowardNegative,
149      rmTowardZero,
150      rmNearestTiesToAway
151    };
152
153    /* Operation status.  opUnderflow or opOverflow are always returned
154       or-ed with opInexact.  */
155    enum opStatus {
156      opOK          = 0x00,
157      opInvalidOp   = 0x01,
158      opDivByZero   = 0x02,
159      opOverflow    = 0x04,
160      opUnderflow   = 0x08,
161      opInexact     = 0x10
162    };
163
164    /* Category of internally-represented number.  */
165    enum fltCategory {
166      fcInfinity,
167      fcNaN,
168      fcNormal,
169      fcZero
170    };
171
172    /* Constructors.  */
173    APFloat(const fltSemantics &, const char *);
174    APFloat(const fltSemantics &, integerPart);
175    APFloat(const fltSemantics &, fltCategory, bool negative);
176    explicit APFloat(double d);
177    explicit APFloat(float f);
178    explicit APFloat(const APInt &);
179    APFloat(const APFloat &);
180    ~APFloat();
181
182    /* Arithmetic.  */
183    opStatus add(const APFloat &, roundingMode);
184    opStatus subtract(const APFloat &, roundingMode);
185    opStatus multiply(const APFloat &, roundingMode);
186    opStatus divide(const APFloat &, roundingMode);
187    opStatus mod(const APFloat &, roundingMode);
188    void copySign(const APFloat &);
189    opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
190    void changeSign();    // neg
191    void clearSign();     // abs
192
193    /* Conversions.  */
194    opStatus convert(const fltSemantics &, roundingMode);
195    opStatus convertToInteger(integerPart *, unsigned int, bool,
196			      roundingMode) const;
197    opStatus convertFromInteger(const integerPart *, unsigned int, bool,
198				roundingMode);
199    opStatus convertFromString(const char *, roundingMode);
200    APInt convertToAPInt() const;
201    double convertToDouble() const;
202    float convertToFloat() const;
203
204    /* The definition of equality is not straightforward for floating point,
205       so we won't use operator==.  Use one of the following, or write
206       whatever it is you really mean. */
207    // bool operator==(const APFloat &) const;     // DO NOT IMPLEMENT
208
209    /* IEEE comparison with another floating point number (NaNs
210       compare unordered, 0==-0). */
211    cmpResult compare(const APFloat &) const;
212
213    /* Write out a hexadecimal representation of the floating point
214       value to DST, which must be of sufficient size, in the C99 form
215       [-]0xh.hhhhp[+-]d.  Return the number of characters written,
216       excluding the terminating NUL.  */
217    unsigned int convertToHexString(char *dst, unsigned int hexDigits,
218                                    bool upperCase, roundingMode) const;
219
220    /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
221    bool bitwiseIsEqual(const APFloat &) const;
222
223    /* Simple queries.  */
224    fltCategory getCategory() const { return category; }
225    const fltSemantics &getSemantics() const { return *semantics; }
226    bool isZero() const { return category == fcZero; }
227    bool isNonZero() const { return category != fcZero; }
228    bool isNegative() const { return sign; }
229    bool isPosZero() const { return isZero() && !isNegative(); }
230    bool isNegZero() const { return isZero() && isNegative(); }
231
232    APFloat& operator=(const APFloat &);
233
234    /* Return an arbitrary integer value usable for hashing. */
235    uint32_t getHashValue() const;
236
237  private:
238
239    /* Trivial queries.  */
240    integerPart *significandParts();
241    const integerPart *significandParts() const;
242    unsigned int partCount() const;
243
244    /* Significand operations.  */
245    integerPart addSignificand(const APFloat &);
246    integerPart subtractSignificand(const APFloat &, integerPart);
247    lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
248    lostFraction multiplySignificand(const APFloat &, const APFloat *);
249    lostFraction divideSignificand(const APFloat &);
250    void incrementSignificand();
251    void initialize(const fltSemantics *);
252    void shiftSignificandLeft(unsigned int);
253    lostFraction shiftSignificandRight(unsigned int);
254    unsigned int significandLSB() const;
255    unsigned int significandMSB() const;
256    void zeroSignificand();
257
258    /* Arithmetic on special values.  */
259    opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
260    opStatus divideSpecials(const APFloat &);
261    opStatus multiplySpecials(const APFloat &);
262
263    /* Miscellany.  */
264    opStatus normalize(roundingMode, lostFraction);
265    opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
266    cmpResult compareAbsoluteValue(const APFloat &) const;
267    opStatus handleOverflow(roundingMode);
268    bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
269    opStatus convertFromUnsignedInteger(integerPart *, unsigned int,
270                                        roundingMode);
271    lostFraction combineLostFractions(lostFraction, lostFraction);
272    opStatus convertFromHexadecimalString(const char *, roundingMode);
273    char *convertNormalToHexString(char *, unsigned int, bool,
274                                   roundingMode) const;
275    APInt convertFloatAPFloatToAPInt() const;
276    APInt convertDoubleAPFloatToAPInt() const;
277    APInt convertF80LongDoubleAPFloatToAPInt() const;
278    void initFromAPInt(const APInt& api);
279    void initFromFloatAPInt(const APInt& api);
280    void initFromDoubleAPInt(const APInt& api);
281    void initFromF80LongDoubleAPInt(const APInt& api);
282
283    void assign(const APFloat &);
284    void copySignificand(const APFloat &);
285    void freeSignificand();
286
287    /* What kind of semantics does this value obey?  */
288    const fltSemantics *semantics;
289
290    /* Significand - the fraction with an explicit integer bit.  Must be
291       at least one bit wider than the target precision.  */
292    union Significand
293    {
294      integerPart part;
295      integerPart *parts;
296    } significand;
297
298    /* The exponent - a signed number.  */
299    exponent_t exponent;
300
301    /* What kind of floating point number this is.  */
302    /* Only 2 bits are required, but VisualStudio incorrectly sign extends
303       it.  Using the extra bit keeps it from failing under VisualStudio */
304    fltCategory category: 3;
305
306    /* The sign bit of this number.  */
307    unsigned int sign: 1;
308  };
309} /* namespace llvm */
310
311#endif /* LLVM_FLOAT_H */
312