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"
28 /// Enum that represents what fraction of the LSB truncated bits of an fp number
31 /// This essentially combines the roles of guard and sticky bits.
32 enum lostFraction { // Example of truncated bits:
33 lfExactlyZero, // 000000
34 lfLessThanHalf, // 0xxxxx x's not all zero
35 lfExactlyHalf, // 100000
36 lfMoreThanHalf // 1xxxxx x's not all zero
39 /// \brief A self-contained host- and target-independent arbitrary-precision
40 /// floating-point software implementation.
42 /// APFloat uses bignum integer arithmetic as provided by static functions in
43 /// the APInt class. The library will work with bignum integers whose parts are
44 /// any unsigned type at least 16 bits wide, but 64 bits is recommended.
46 /// Written for clarity rather than speed, in particular with a view to use in
47 /// the front-end of a cross compiler so that target arithmetic can be correctly
48 /// performed on the host. Performance should nonetheless be reasonable,
49 /// particularly for its intended use. It may be useful as a base
50 /// implementation for a run-time library during development of a faster
51 /// target-specific one.
53 /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
54 /// implemented operations. Currently implemented operations are add, subtract,
55 /// multiply, divide, fused-multiply-add, conversion-to-float,
56 /// conversion-to-integer and conversion-from-integer. New rounding modes
57 /// (e.g. away from zero) can be added with three or four lines of code.
59 /// Four formats are built-in: IEEE single precision, double precision,
60 /// quadruple precision, and x87 80-bit extended double (when operating with
61 /// full extended precision). Adding a new format that obeys IEEE semantics
62 /// only requires adding two lines of code: a declaration and definition of the
65 /// All operations return the status of that operation as an exception bit-mask,
66 /// so multiple operations can be done consecutively with their results or-ed
67 /// together. The returned status can be useful for compiler diagnostics; e.g.,
68 /// inexact, underflow and overflow can be easily diagnosed on constant folding,
69 /// and compiler optimizers can determine what exceptions would be raised by
70 /// folding operations and optimize, or perhaps not optimize, accordingly.
72 /// At present, underflow tininess is detected after rounding; it should be
73 /// straight forward to add support for the before-rounding case too.
75 /// The library reads hexadecimal floating point numbers as per C99, and
76 /// correctly rounds if necessary according to the specified rounding mode.
77 /// Syntax is required to have been validated by the caller. It also converts
78 /// floating point numbers to hexadecimal text as per the C99 %a and %A
79 /// conversions. The output precision (or alternatively the natural minimal
80 /// precision) can be specified; if the requested precision is less than the
81 /// natural precision the output is correctly rounded for the specified rounding
84 /// It also reads decimal floating point numbers and correctly rounds according
85 /// to the specified rounding mode.
87 /// Conversion to decimal text is not currently implemented.
89 /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
90 /// signed exponent, and the significand as an array of integer parts. After
91 /// normalization of a number of precision P the exponent is within the range of
92 /// the format, and if the number is not denormal the P-th bit of the
93 /// significand is set as an explicit integer bit. For denormals the most
94 /// significant bit is shifted right so that the exponent is maintained at the
95 /// format's minimum, so that the smallest denormal has just the least
96 /// significant bit of the significand set. The sign of zeroes and infinities
97 /// is significant; the exponent and significand of such numbers is not stored,
98 /// but has a known implicit (deterministic) value: 0 for the significands, 0
99 /// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
100 /// significand are deterministic, although not really meaningful, and preserved
101 /// in non-conversion operations. The exponent is implicitly all 1 bits.
103 /// APFloat does not provide any exception handling beyond default exception
104 /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
105 /// by encoding Signaling NaNs with the first bit of its trailing significand as
111 /// Some features that may or may not be worth adding:
113 /// Binary to decimal conversion (hard).
115 /// Optional ability to detect underflow tininess before rounding.
117 /// New formats: x87 in single and double precision mode (IEEE apart from
118 /// extended exponent range) (hard).
120 /// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
125 /// A signed type to represent a floating point numbers unbiased exponent.
126 typedef signed short ExponentType;
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 &, uninitializedTag);
195 APFloat(const fltSemantics &, const APInt &);
196 explicit APFloat(double d);
197 explicit APFloat(float f);
198 APFloat(const APFloat &);
203 /// \brief Returns whether this instance allocated memory.
204 bool needsCleanup() const { return partCount() > 1; }
206 /// \name Convenience "constructors"
209 /// Factory for Positive and Negative Zero.
211 /// \param Negative True iff the number should be negative.
212 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
213 APFloat Val(Sem, uninitialized);
214 Val.makeZero(Negative);
218 /// Factory for Positive and Negative Infinity.
220 /// \param Negative True iff the number should be negative.
221 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
222 APFloat Val(Sem, uninitialized);
223 Val.makeInf(Negative);
227 /// Factory for QNaN values.
229 /// \param Negative - True iff the NaN generated should be negative.
230 /// \param type - The unspecified fill bits for creating the NaN, 0 by
231 /// default. The value is truncated as necessary.
232 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
235 APInt fill(64, type);
236 return getQNaN(Sem, Negative, &fill);
238 return getQNaN(Sem, Negative, 0);
242 /// Factory for QNaN values.
243 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
244 const APInt *payload = 0) {
245 return makeNaN(Sem, false, Negative, payload);
248 /// Factory for SNaN values.
249 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
250 const APInt *payload = 0) {
251 return makeNaN(Sem, true, Negative, payload);
254 /// Returns the largest finite number in the given semantics.
256 /// \param Negative - True iff the number should be negative
257 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
259 /// Returns the smallest (by magnitude) finite number in the given semantics.
260 /// Might be denormalized, which implies a relative loss of precision.
262 /// \param Negative - True iff the number should be negative
263 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
265 /// Returns the smallest (by magnitude) normalized finite number in the given
268 /// \param Negative - True iff the number should be negative
269 static APFloat getSmallestNormalized(const fltSemantics &Sem,
270 bool Negative = false);
272 /// Returns a float which is bitcasted from an all one value int.
274 /// \param BitWidth - Select float type
275 /// \param isIEEE - If 128 bit number, select between PPC and IEEE
276 static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
280 /// Used to insert APFloat objects, or objects that contain APFloat objects,
281 /// into FoldingSets.
282 void Profile(FoldingSetNodeID &NID) const;
284 /// \brief Used by the Bitcode serializer to emit APInts to Bitcode.
285 void Emit(Serializer &S) const;
287 /// \brief Used by the Bitcode deserializer to deserialize APInts.
288 static APFloat ReadVal(Deserializer &D);
293 opStatus add(const APFloat &, roundingMode);
294 opStatus subtract(const APFloat &, roundingMode);
295 opStatus multiply(const APFloat &, roundingMode);
296 opStatus divide(const APFloat &, roundingMode);
298 opStatus remainder(const APFloat &);
299 /// C fmod, or llvm frem.
300 opStatus mod(const APFloat &, roundingMode);
301 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
302 opStatus roundToIntegral(roundingMode);
303 /// IEEE-754R 5.3.1: nextUp/nextDown.
304 opStatus next(bool nextDown);
308 /// \name Sign operations.
313 void copySign(const APFloat &);
317 /// \name Conversions
320 opStatus convert(const fltSemantics &, roundingMode, bool *);
321 opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
323 opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
324 opStatus convertFromAPInt(const APInt &, bool, roundingMode);
325 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
327 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
329 opStatus convertFromString(StringRef, roundingMode);
330 APInt bitcastToAPInt() const;
331 double convertToDouble() const;
332 float convertToFloat() const;
336 /// The definition of equality is not straightforward for floating point, so
337 /// we won't use operator==. Use one of the following, or write whatever it
338 /// is you really mean.
339 bool operator==(const APFloat &) const LLVM_DELETED_FUNCTION;
341 /// IEEE comparison with another floating point number (NaNs compare
342 /// unordered, 0==-0).
343 cmpResult compare(const APFloat &) const;
345 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
346 bool bitwiseIsEqual(const APFloat &) const;
348 /// Write out a hexadecimal representation of the floating point value to DST,
349 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
350 /// Return the number of characters written, excluding the terminating NUL.
351 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
352 bool upperCase, roundingMode) const;
354 /// \name IEEE-754R 5.7.2 General operations.
357 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
360 /// This applies to zeros and NaNs as well.
361 bool isNegative() const { return sign; }
363 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
365 /// This implies that the current value of the float is not zero, subnormal,
366 /// infinite, or NaN following the definition of normality from IEEE-754R.
367 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
369 /// Returns true if and only if the current value is zero, subnormal, or
372 /// This means that the value is not infinite or NaN.
373 bool isFinite() const { return !isNaN() && !isInfinity(); }
375 /// Returns true if and only if the float is plus or minus zero.
376 bool isZero() const { return category == fcZero; }
378 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
380 bool isDenormal() const;
382 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
383 bool isInfinity() const { return category == fcInfinity; }
385 /// Returns true if and only if the float is a quiet or signaling NaN.
386 bool isNaN() const { return category == fcNaN; }
388 /// Returns true if and only if the float is a signaling NaN.
389 bool isSignaling() const;
393 /// \name Simple Queries
396 fltCategory getCategory() const { return category; }
397 const fltSemantics &getSemantics() const { return *semantics; }
398 bool isNonZero() const { return category != fcZero; }
399 bool isFiniteNonZero() const { return isFinite() && !isZero(); }
400 bool isPosZero() const { return isZero() && !isNegative(); }
401 bool isNegZero() const { return isZero() && isNegative(); }
403 /// Returns true if and only if the number has the smallest possible non-zero
404 /// magnitude in the current semantics.
405 bool isSmallest() const;
407 /// Returns true if and only if the number has the largest possible finite
408 /// magnitude in the current semantics.
409 bool isLargest() const;
413 APFloat &operator=(const APFloat &);
415 /// \brief Overload to compute a hash code for an APFloat value.
417 /// Note that the use of hash codes for floating point values is in general
418 /// frought with peril. Equality is hard to define for these values. For
419 /// example, should negative and positive zero hash to different codes? Are
420 /// they equal or not? This hash value implementation specifically
421 /// emphasizes producing different codes for different inputs in order to
422 /// be used in canonicalization and memoization. As such, equality is
423 /// bitwiseIsEqual, and 0 != -0.
424 friend hash_code hash_value(const APFloat &Arg);
426 /// Converts this value into a decimal string.
428 /// \param FormatPrecision The maximum number of digits of
429 /// precision to output. If there are fewer digits available,
430 /// zero padding will not be used unless the value is
431 /// integral and small enough to be expressed in
432 /// FormatPrecision digits. 0 means to use the natural
433 /// precision of the number.
434 /// \param FormatMaxPadding The maximum number of zeros to
435 /// consider inserting before falling back to scientific
436 /// notation. 0 means to always use scientific notation.
438 /// Number Precision MaxPadding Result
439 /// ------ --------- ---------- ------
440 /// 1.01E+4 5 2 10100
441 /// 1.01E+4 4 2 1.01E+4
442 /// 1.01E+4 5 1 1.01E+4
443 /// 1.01E-2 5 2 0.0101
444 /// 1.01E-2 4 2 0.0101
445 /// 1.01E-2 4 1 1.01E-2
446 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
447 unsigned FormatMaxPadding = 3) const;
449 /// If this value has an exact multiplicative inverse, store it in inv and
451 bool getExactInverse(APFloat *inv) const;
455 /// \name Simple Queries
458 integerPart *significandParts();
459 const integerPart *significandParts() const;
460 unsigned int partCount() const;
464 /// \name Significand operations.
467 integerPart addSignificand(const APFloat &);
468 integerPart subtractSignificand(const APFloat &, integerPart);
469 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
470 lostFraction multiplySignificand(const APFloat &, const APFloat *);
471 lostFraction divideSignificand(const APFloat &);
472 void incrementSignificand();
473 void initialize(const fltSemantics *);
474 void shiftSignificandLeft(unsigned int);
475 lostFraction shiftSignificandRight(unsigned int);
476 unsigned int significandLSB() const;
477 unsigned int significandMSB() const;
478 void zeroSignificand();
479 /// Return true if the significand excluding the integral bit is all ones.
480 bool isSignificandAllOnes() const;
481 /// Return true if the significand excluding the integral bit is all zeros.
482 bool isSignificandAllZeros() const;
486 /// \name Arithmetic on special values.
489 opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
490 opStatus divideSpecials(const APFloat &);
491 opStatus multiplySpecials(const APFloat &);
492 opStatus modSpecials(const APFloat &);
496 /// \name Special value setters.
499 void makeLargest(bool Neg = false);
500 void makeSmallest(bool Neg = false);
501 void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
502 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
504 void makeInf(bool Neg = false);
505 void makeZero(bool Neg = false);
512 bool convertFromStringSpecials(StringRef str);
513 opStatus normalize(roundingMode, lostFraction);
514 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
515 cmpResult compareAbsoluteValue(const APFloat &) const;
516 opStatus handleOverflow(roundingMode);
517 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
518 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
519 roundingMode, bool *) const;
520 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
522 opStatus convertFromHexadecimalString(StringRef, roundingMode);
523 opStatus convertFromDecimalString(StringRef, roundingMode);
524 char *convertNormalToHexString(char *, unsigned int, bool,
526 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
531 APInt convertHalfAPFloatToAPInt() const;
532 APInt convertFloatAPFloatToAPInt() const;
533 APInt convertDoubleAPFloatToAPInt() const;
534 APInt convertQuadrupleAPFloatToAPInt() const;
535 APInt convertF80LongDoubleAPFloatToAPInt() const;
536 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
537 void initFromAPInt(const fltSemantics *Sem, const APInt &api);
538 void initFromHalfAPInt(const APInt &api);
539 void initFromFloatAPInt(const APInt &api);
540 void initFromDoubleAPInt(const APInt &api);
541 void initFromQuadrupleAPInt(const APInt &api);
542 void initFromF80LongDoubleAPInt(const APInt &api);
543 void initFromPPCDoubleDoubleAPInt(const APInt &api);
545 void assign(const APFloat &);
546 void copySignificand(const APFloat &);
547 void freeSignificand();
549 /// The semantics that this value obeys.
550 const fltSemantics *semantics;
552 /// A binary fraction with an explicit integer bit.
554 /// The significand must be at least one bit wider than the target precision.
560 /// The signed unbiased exponent of the value.
561 ExponentType exponent;
563 /// What kind of floating point number this is.
565 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
566 /// Using the extra bit keeps it from failing under VisualStudio.
567 fltCategory category : 3;
569 /// Sign bit of the number.
570 unsigned int sign : 1;
573 /// See friend declaration above.
575 /// This additional declaration is required in order to compile LLVM with IBM
577 hash_code hash_value(const APFloat &Arg);
580 #endif // LLVM_ADT_APFLOAT_H