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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 
106 namespace 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 
278     /* Sign operations.  */
279     void changeSign();
280     void clearSign();
281     void copySign(const APFloat &);
282 
283     /* Conversions.  */
284     opStatus convert(const fltSemantics &, roundingMode, bool *);
285     opStatus convertToInteger(integerPart *, unsigned int, bool,
286                               roundingMode, bool *) const;
287     opStatus convertToInteger(APSInt&, roundingMode, bool *) const;
288     opStatus convertFromAPInt(const APInt &,
289                               bool, roundingMode);
290     opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
291                                             bool, roundingMode);
292     opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
293                                             bool, roundingMode);
294     opStatus convertFromString(StringRef, roundingMode);
295     APInt bitcastToAPInt() const;
296     double convertToDouble() const;
297     float convertToFloat() const;
298 
299     /* The definition of equality is not straightforward for floating point,
300        so we won't use operator==.  Use one of the following, or write
301        whatever it is you really mean. */
302     // bool operator==(const APFloat &) const;     // DO NOT IMPLEMENT
303 
304     /* IEEE comparison with another floating point number (NaNs
305        compare unordered, 0==-0). */
306     cmpResult compare(const APFloat &) const;
307 
308     /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
309     bool bitwiseIsEqual(const APFloat &) const;
310 
311     /* Write out a hexadecimal representation of the floating point
312        value to DST, which must be of sufficient size, in the C99 form
313        [-]0xh.hhhhp[+-]d.  Return the number of characters written,
314        excluding the terminating NUL.  */
315     unsigned int convertToHexString(char *dst, unsigned int hexDigits,
316                                     bool upperCase, roundingMode) const;
317 
318     /* Simple queries.  */
getCategory()319     fltCategory getCategory() const { return category; }
getSemantics()320     const fltSemantics &getSemantics() const { return *semantics; }
isZero()321     bool isZero() const { return category == fcZero; }
isNonZero()322     bool isNonZero() const { return category != fcZero; }
isNaN()323     bool isNaN() const { return category == fcNaN; }
isInfinity()324     bool isInfinity() const { return category == fcInfinity; }
isNegative()325     bool isNegative() const { return sign; }
isPosZero()326     bool isPosZero() const { return isZero() && !isNegative(); }
isNegZero()327     bool isNegZero() const { return isZero() && isNegative(); }
328 
329     APFloat& operator=(const APFloat &);
330 
331     /* Return an arbitrary integer value usable for hashing. */
332     uint32_t getHashValue() const;
333 
334     /// Converts this value into a decimal string.
335     ///
336     /// \param FormatPrecision The maximum number of digits of
337     ///   precision to output.  If there are fewer digits available,
338     ///   zero padding will not be used unless the value is
339     ///   integral and small enough to be expressed in
340     ///   FormatPrecision digits.  0 means to use the natural
341     ///   precision of the number.
342     /// \param FormatMaxPadding The maximum number of zeros to
343     ///   consider inserting before falling back to scientific
344     ///   notation.  0 means to always use scientific notation.
345     ///
346     /// Number       Precision    MaxPadding      Result
347     /// ------       ---------    ----------      ------
348     /// 1.01E+4              5             2       10100
349     /// 1.01E+4              4             2       1.01E+4
350     /// 1.01E+4              5             1       1.01E+4
351     /// 1.01E-2              5             2       0.0101
352     /// 1.01E-2              4             2       0.0101
353     /// 1.01E-2              4             1       1.01E-2
354     void toString(SmallVectorImpl<char> &Str,
355                   unsigned FormatPrecision = 0,
356                   unsigned FormatMaxPadding = 3) const;
357 
358     /// getExactInverse - If this value has an exact multiplicative inverse,
359     /// store it in inv and return true.
360     bool getExactInverse(APFloat *inv) const;
361 
362   private:
363 
364     /* Trivial queries.  */
365     integerPart *significandParts();
366     const integerPart *significandParts() const;
367     unsigned int partCount() const;
368 
369     /* Significand operations.  */
370     integerPart addSignificand(const APFloat &);
371     integerPart subtractSignificand(const APFloat &, integerPart);
372     lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
373     lostFraction multiplySignificand(const APFloat &, const APFloat *);
374     lostFraction divideSignificand(const APFloat &);
375     void incrementSignificand();
376     void initialize(const fltSemantics *);
377     void shiftSignificandLeft(unsigned int);
378     lostFraction shiftSignificandRight(unsigned int);
379     unsigned int significandLSB() const;
380     unsigned int significandMSB() const;
381     void zeroSignificand();
382 
383     /* Arithmetic on special values.  */
384     opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
385     opStatus divideSpecials(const APFloat &);
386     opStatus multiplySpecials(const APFloat &);
387     opStatus modSpecials(const APFloat &);
388 
389     /* Miscellany.  */
390     static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
391                            const APInt *fill);
392     void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
393     opStatus normalize(roundingMode, lostFraction);
394     opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
395     cmpResult compareAbsoluteValue(const APFloat &) const;
396     opStatus handleOverflow(roundingMode);
397     bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
398     opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
399                                           roundingMode, bool *) const;
400     opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
401                                       roundingMode);
402     opStatus convertFromHexadecimalString(StringRef, roundingMode);
403     opStatus convertFromDecimalString(StringRef, roundingMode);
404     char *convertNormalToHexString(char *, unsigned int, bool,
405                                    roundingMode) const;
406     opStatus roundSignificandWithExponent(const integerPart *, unsigned int,
407                                           int, roundingMode);
408 
409     APInt convertHalfAPFloatToAPInt() const;
410     APInt convertFloatAPFloatToAPInt() const;
411     APInt convertDoubleAPFloatToAPInt() const;
412     APInt convertQuadrupleAPFloatToAPInt() const;
413     APInt convertF80LongDoubleAPFloatToAPInt() const;
414     APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
415     void initFromAPInt(const APInt& api, bool isIEEE = false);
416     void initFromHalfAPInt(const APInt& api);
417     void initFromFloatAPInt(const APInt& api);
418     void initFromDoubleAPInt(const APInt& api);
419     void initFromQuadrupleAPInt(const APInt &api);
420     void initFromF80LongDoubleAPInt(const APInt& api);
421     void initFromPPCDoubleDoubleAPInt(const APInt& api);
422 
423     void assign(const APFloat &);
424     void copySignificand(const APFloat &);
425     void freeSignificand();
426 
427     /* What kind of semantics does this value obey?  */
428     const fltSemantics *semantics;
429 
430     /* Significand - the fraction with an explicit integer bit.  Must be
431        at least one bit wider than the target precision.  */
432     union Significand
433     {
434       integerPart part;
435       integerPart *parts;
436     } significand;
437 
438     /* The exponent - a signed number.  */
439     exponent_t exponent;
440 
441     /* What kind of floating point number this is.  */
442     /* Only 2 bits are required, but VisualStudio incorrectly sign extends
443        it.  Using the extra bit keeps it from failing under VisualStudio */
444     fltCategory category: 3;
445 
446     /* The sign bit of this number.  */
447     unsigned int sign: 1;
448 
449     /* For PPCDoubleDouble, we have a second exponent and sign (the second
450        significand is appended to the first one, although it would be wrong to
451        regard these as a single number for arithmetic purposes).  These fields
452        are not meaningful for any other type. */
453     exponent_t exponent2 : 11;
454     unsigned int sign2: 1;
455   };
456 } /* namespace llvm */
457 
458 #endif /* LLVM_FLOAT_H */
459