1 //== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
12 /// This file declares a class to represent arbitrary precision floating point
13 /// values and provide a variety of arithmetic operations on them.
15 //===----------------------------------------------------------------------===//
17 #ifndef LLVM_ADT_APFLOAT_H
18 #define LLVM_ADT_APFLOAT_H
20 #include "llvm/ADT/APInt.h"
24 /// A signed type to represent a floating point numbers unbiased exponent.
25 typedef signed short exponent_t;
31 /// Enum that represents what fraction of the LSB truncated bits of an fp number
34 /// This essentially combines the roles of guard and sticky bits.
35 enum lostFraction { // Example of truncated bits:
36 lfExactlyZero, // 000000
37 lfLessThanHalf, // 0xxxxx x's not all zero
38 lfExactlyHalf, // 100000
39 lfMoreThanHalf // 1xxxxx x's not all zero
42 /// \brief A self-contained host- and target-independent arbitrary-precision
43 /// floating-point software implementation.
45 /// APFloat uses bignum integer arithmetic as provided by static functions in
46 /// the APInt class. The library will work with bignum integers whose parts are
47 /// any unsigned type at least 16 bits wide, but 64 bits is recommended.
49 /// Written for clarity rather than speed, in particular with a view to use in
50 /// the front-end of a cross compiler so that target arithmetic can be correctly
51 /// performed on the host. Performance should nonetheless be reasonable,
52 /// particularly for its intended use. It may be useful as a base
53 /// implementation for a run-time library during development of a faster
54 /// target-specific one.
56 /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
57 /// implemented operations. Currently implemented operations are add, subtract,
58 /// multiply, divide, fused-multiply-add, conversion-to-float,
59 /// conversion-to-integer and conversion-from-integer. New rounding modes
60 /// (e.g. away from zero) can be added with three or four lines of code.
62 /// Four formats are built-in: IEEE single precision, double precision,
63 /// quadruple precision, and x87 80-bit extended double (when operating with
64 /// full extended precision). Adding a new format that obeys IEEE semantics
65 /// only requires adding two lines of code: a declaration and definition of the
68 /// All operations return the status of that operation as an exception bit-mask,
69 /// so multiple operations can be done consecutively with their results or-ed
70 /// together. The returned status can be useful for compiler diagnostics; e.g.,
71 /// inexact, underflow and overflow can be easily diagnosed on constant folding,
72 /// and compiler optimizers can determine what exceptions would be raised by
73 /// folding operations and optimize, or perhaps not optimize, accordingly.
75 /// At present, underflow tininess is detected after rounding; it should be
76 /// straight forward to add support for the before-rounding case too.
78 /// The library reads hexadecimal floating point numbers as per C99, and
79 /// correctly rounds if necessary according to the specified rounding mode.
80 /// Syntax is required to have been validated by the caller. It also converts
81 /// floating point numbers to hexadecimal text as per the C99 %a and %A
82 /// conversions. The output precision (or alternatively the natural minimal
83 /// precision) can be specified; if the requested precision is less than the
84 /// natural precision the output is correctly rounded for the specified rounding
87 /// It also reads decimal floating point numbers and correctly rounds according
88 /// to the specified rounding mode.
90 /// Conversion to decimal text is not currently implemented.
92 /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
93 /// signed exponent, and the significand as an array of integer parts. After
94 /// normalization of a number of precision P the exponent is within the range of
95 /// the format, and if the number is not denormal the P-th bit of the
96 /// significand is set as an explicit integer bit. For denormals the most
97 /// significant bit is shifted right so that the exponent is maintained at the
98 /// format's minimum, so that the smallest denormal has just the least
99 /// significant bit of the significand set. The sign of zeroes and infinities
100 /// is significant; the exponent and significand of such numbers is not stored,
101 /// but has a known implicit (deterministic) value: 0 for the significands, 0
102 /// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
103 /// significand are deterministic, although not really meaningful, and preserved
104 /// in non-conversion operations. The exponent is implicitly all 1 bits.
106 /// APFloat does not provide any exception handling beyond default exception
107 /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
108 /// by encoding Signaling NaNs with the first bit of its trailing significand as
114 /// Some features that may or may not be worth adding:
116 /// Binary to decimal conversion (hard).
118 /// Optional ability to detect underflow tininess before rounding.
120 /// New formats: x87 in single and double precision mode (IEEE apart from
121 /// extended exponent range) (hard).
123 /// New operations: sqrt, IEEE remainder, C90 fmod, nextafter, nexttoward.
128 /// \name Floating Point Semantics.
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;
138 /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
140 static const fltSemantics Bogus;
144 static unsigned int semanticsPrecision(const fltSemantics &);
146 /// IEEE-754R 5.11: Floating Point Comparison Relations.
154 /// IEEE-754R 4.3: Rounding-direction attributes.
163 /// IEEE-754R 7: Default exception handling.
165 /// opUnderflow or opOverflow are always returned or-ed with opInexact.
175 /// Category of internally-represented number.
183 /// Convenience enum used to construct an uninitialized APFloat.
184 enum uninitializedTag {
188 /// \name Constructors
191 APFloat(const fltSemantics &); // Default construct to 0.0
192 APFloat(const fltSemantics &, StringRef);
193 APFloat(const fltSemantics &, integerPart);
194 APFloat(const fltSemantics &, fltCategory, bool negative);
195 APFloat(const fltSemantics &, uninitializedTag);
196 APFloat(const fltSemantics &, const APInt &);
197 explicit APFloat(double d);
198 explicit APFloat(float f);
199 APFloat(const APFloat &);
204 /// \name Convenience "constructors"
207 /// Factory for Positive and Negative Zero.
209 /// \param Negative True iff the number should be negative.
210 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
211 return APFloat(Sem, fcZero, Negative);
214 /// Factory for Positive and Negative Infinity.
216 /// \param Negative True iff the number should be negative.
217 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
218 return APFloat(Sem, fcInfinity, Negative);
221 /// Factory for QNaN values.
223 /// \param Negative - True iff the NaN generated should be negative.
224 /// \param type - The unspecified fill bits for creating the NaN, 0 by
225 /// default. The value is truncated as necessary.
226 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
229 APInt fill(64, type);
230 return getQNaN(Sem, Negative, &fill);
232 return getQNaN(Sem, Negative, 0);
236 /// Factory for QNaN values.
237 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
238 const APInt *payload = 0) {
239 return makeNaN(Sem, false, Negative, payload);
242 /// Factory for SNaN values.
243 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
244 const APInt *payload = 0) {
245 return makeNaN(Sem, true, Negative, payload);
248 /// Returns the largest finite number in the given semantics.
250 /// \param Negative - True iff the number should be negative
251 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
253 /// Returns the smallest (by magnitude) finite number in the given semantics.
254 /// Might be denormalized, which implies a relative loss of precision.
256 /// \param Negative - True iff the number should be negative
257 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
259 /// Returns the smallest (by magnitude) normalized finite number in the given
262 /// \param Negative - True iff the number should be negative
263 static APFloat getSmallestNormalized(const fltSemantics &Sem,
264 bool Negative = false);
266 /// Returns a float which is bitcasted from an all one value int.
268 /// \param BitWidth - Select float type
269 /// \param isIEEE - If 128 bit number, select between PPC and IEEE
270 static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
274 /// Used to insert APFloat objects, or objects that contain APFloat objects,
275 /// into FoldingSets.
276 void Profile(FoldingSetNodeID &NID) const;
278 /// \brief Used by the Bitcode serializer to emit APInts to Bitcode.
279 void Emit(Serializer &S) const;
281 /// \brief Used by the Bitcode deserializer to deserialize APInts.
282 static APFloat ReadVal(Deserializer &D);
287 opStatus add(const APFloat &, roundingMode);
288 opStatus subtract(const APFloat &, roundingMode);
289 opStatus multiply(const APFloat &, roundingMode);
290 opStatus divide(const APFloat &, roundingMode);
292 opStatus remainder(const APFloat &);
293 /// C fmod, or llvm frem.
294 opStatus mod(const APFloat &, roundingMode);
295 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
296 opStatus roundToIntegral(roundingMode);
297 /// IEEE-754R 5.3.1: nextUp/nextDown.
298 opStatus next(bool nextDown);
300 /// \name Sign operations.
305 void copySign(const APFloat &);
309 /// \name Conversions
312 opStatus convert(const fltSemantics &, roundingMode, bool *);
313 opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
315 opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
316 opStatus convertFromAPInt(const APInt &, bool, roundingMode);
317 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
319 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
321 opStatus convertFromString(StringRef, roundingMode);
322 APInt bitcastToAPInt() const;
323 double convertToDouble() const;
324 float convertToFloat() const;
328 /// The definition of equality is not straightforward for floating point, so
329 /// we won't use operator==. Use one of the following, or write whatever it
330 /// is you really mean.
331 bool operator==(const APFloat &) const LLVM_DELETED_FUNCTION;
333 /// IEEE comparison with another floating point number (NaNs compare
334 /// unordered, 0==-0).
335 cmpResult compare(const APFloat &) const;
337 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
338 bool bitwiseIsEqual(const APFloat &) const;
340 /// Write out a hexadecimal representation of the floating point value to DST,
341 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
342 /// Return the number of characters written, excluding the terminating NUL.
343 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
344 bool upperCase, roundingMode) const;
346 /// \name Simple Queries
349 fltCategory getCategory() const { return category; }
350 const fltSemantics &getSemantics() const { return *semantics; }
351 bool isZero() const { return category == fcZero; }
352 bool isNonZero() const { return category != fcZero; }
353 bool isNormal() const { return category == fcNormal; }
354 bool isNaN() const { return category == fcNaN; }
355 bool isInfinity() const { return category == fcInfinity; }
356 bool isNegative() const { return sign; }
357 bool isPosZero() const { return isZero() && !isNegative(); }
358 bool isNegZero() const { return isZero() && isNegative(); }
359 bool isDenormal() const;
360 /// IEEE-754R 5.7.2: isSignaling. Returns true if this is a signaling NaN.
361 bool isSignaling() const;
365 APFloat &operator=(const APFloat &);
367 /// \brief Overload to compute a hash code for an APFloat value.
369 /// Note that the use of hash codes for floating point values is in general
370 /// frought with peril. Equality is hard to define for these values. For
371 /// example, should negative and positive zero hash to different codes? Are
372 /// they equal or not? This hash value implementation specifically
373 /// emphasizes producing different codes for different inputs in order to
374 /// be used in canonicalization and memoization. As such, equality is
375 /// bitwiseIsEqual, and 0 != -0.
376 friend hash_code hash_value(const APFloat &Arg);
378 /// Converts this value into a decimal string.
380 /// \param FormatPrecision The maximum number of digits of
381 /// precision to output. If there are fewer digits available,
382 /// zero padding will not be used unless the value is
383 /// integral and small enough to be expressed in
384 /// FormatPrecision digits. 0 means to use the natural
385 /// precision of the number.
386 /// \param FormatMaxPadding The maximum number of zeros to
387 /// consider inserting before falling back to scientific
388 /// notation. 0 means to always use scientific notation.
390 /// Number Precision MaxPadding Result
391 /// ------ --------- ---------- ------
392 /// 1.01E+4 5 2 10100
393 /// 1.01E+4 4 2 1.01E+4
394 /// 1.01E+4 5 1 1.01E+4
395 /// 1.01E-2 5 2 0.0101
396 /// 1.01E-2 4 2 0.0101
397 /// 1.01E-2 4 1 1.01E-2
398 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
399 unsigned FormatMaxPadding = 3) const;
401 /// If this value has an exact multiplicative inverse, store it in inv and
403 bool getExactInverse(APFloat *inv) const;
407 /// \name Simple Queries
410 integerPart *significandParts();
411 const integerPart *significandParts() const;
412 unsigned int partCount() const;
416 /// \name Significand operations.
419 integerPart addSignificand(const APFloat &);
420 integerPart subtractSignificand(const APFloat &, integerPart);
421 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
422 lostFraction multiplySignificand(const APFloat &, const APFloat *);
423 lostFraction divideSignificand(const APFloat &);
424 void incrementSignificand();
425 void initialize(const fltSemantics *);
426 void shiftSignificandLeft(unsigned int);
427 lostFraction shiftSignificandRight(unsigned int);
428 unsigned int significandLSB() const;
429 unsigned int significandMSB() const;
430 void zeroSignificand();
431 /// Return true if the significand excluding the integral bit is all ones.
432 bool isSignificandAllOnes() const;
433 /// Return true if the significand excluding the integral bit is all zeros.
434 bool isSignificandAllZeros() const;
438 /// \name Arithmetic on special values.
441 opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
442 opStatus divideSpecials(const APFloat &);
443 opStatus multiplySpecials(const APFloat &);
444 opStatus modSpecials(const APFloat &);
448 /// \name Special value setters.
451 void makeLargest(bool Neg = false);
452 void makeSmallest(bool Neg = false);
453 void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
454 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
459 /// \name Special value queries only useful internally to APFloat
462 /// Returns true if and only if the number has the smallest possible non-zero
463 /// magnitude in the current semantics.
464 bool isSmallest() const;
465 /// Returns true if and only if the number has the largest possible finite
466 /// magnitude in the current semantics.
467 bool isLargest() const;
474 opStatus normalize(roundingMode, lostFraction);
475 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
476 cmpResult compareAbsoluteValue(const APFloat &) const;
477 opStatus handleOverflow(roundingMode);
478 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
479 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
480 roundingMode, bool *) const;
481 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
483 opStatus convertFromHexadecimalString(StringRef, roundingMode);
484 opStatus convertFromDecimalString(StringRef, roundingMode);
485 char *convertNormalToHexString(char *, unsigned int, bool,
487 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
492 APInt convertHalfAPFloatToAPInt() const;
493 APInt convertFloatAPFloatToAPInt() const;
494 APInt convertDoubleAPFloatToAPInt() const;
495 APInt convertQuadrupleAPFloatToAPInt() const;
496 APInt convertF80LongDoubleAPFloatToAPInt() const;
497 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
498 void initFromAPInt(const fltSemantics *Sem, const APInt &api);
499 void initFromHalfAPInt(const APInt &api);
500 void initFromFloatAPInt(const APInt &api);
501 void initFromDoubleAPInt(const APInt &api);
502 void initFromQuadrupleAPInt(const APInt &api);
503 void initFromF80LongDoubleAPInt(const APInt &api);
504 void initFromPPCDoubleDoubleAPInt(const APInt &api);
506 void assign(const APFloat &);
507 void copySignificand(const APFloat &);
508 void freeSignificand();
510 /// The semantics that this value obeys.
511 const fltSemantics *semantics;
513 /// A binary fraction with an explicit integer bit.
515 /// The significand must be at least one bit wider than the target precision.
521 /// The signed unbiased exponent of the value.
524 /// What kind of floating point number this is.
526 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
527 /// Using the extra bit keeps it from failing under VisualStudio.
528 fltCategory category : 3;
530 /// Sign bit of the number.
531 unsigned int sign : 1;
534 /// See friend declaration above.
536 /// This additional declaration is required in order to compile LLVM with IBM
538 hash_code hash_value(const APFloat &Arg);
541 #endif // LLVM_ADT_APFLOAT_H