1 //===- llvm/ADT/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 &);
145 static ExponentType semanticsMinExponent(const fltSemantics &);
146 static ExponentType semanticsMaxExponent(const fltSemantics &);
147 static unsigned int semanticsSizeInBits(const fltSemantics &);
149 /// IEEE-754R 5.11: Floating Point Comparison Relations.
157 /// IEEE-754R 4.3: Rounding-direction attributes.
166 /// IEEE-754R 7: Default exception handling.
168 /// opUnderflow or opOverflow are always returned or-ed with opInexact.
178 /// Category of internally-represented number.
186 /// Convenience enum used to construct an uninitialized APFloat.
187 enum uninitializedTag {
191 /// \name Constructors
194 APFloat(const fltSemantics &); // Default construct to 0.0
195 APFloat(const fltSemantics &, StringRef);
196 APFloat(const fltSemantics &, integerPart);
197 APFloat(const fltSemantics &, uninitializedTag);
198 APFloat(const fltSemantics &, const APInt &);
199 explicit APFloat(double d);
200 explicit APFloat(float f);
201 APFloat(const APFloat &);
207 /// \brief Returns whether this instance allocated memory.
208 bool needsCleanup() const { return partCount() > 1; }
210 /// \name Convenience "constructors"
213 /// Factory for Positive and Negative Zero.
215 /// \param Negative True iff the number should be negative.
216 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
217 APFloat Val(Sem, uninitialized);
218 Val.makeZero(Negative);
222 /// Factory for Positive and Negative Infinity.
224 /// \param Negative True iff the number should be negative.
225 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
226 APFloat Val(Sem, uninitialized);
227 Val.makeInf(Negative);
231 /// Factory for QNaN values.
233 /// \param Negative - True iff the NaN generated should be negative.
234 /// \param type - The unspecified fill bits for creating the NaN, 0 by
235 /// default. The value is truncated as necessary.
236 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
239 APInt fill(64, type);
240 return getQNaN(Sem, Negative, &fill);
242 return getQNaN(Sem, Negative, nullptr);
246 /// Factory for QNaN values.
247 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
248 const APInt *payload = nullptr) {
249 return makeNaN(Sem, false, Negative, payload);
252 /// Factory for SNaN values.
253 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
254 const APInt *payload = nullptr) {
255 return makeNaN(Sem, true, Negative, payload);
258 /// Returns the largest finite number in the given semantics.
260 /// \param Negative - True iff the number should be negative
261 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
263 /// Returns the smallest (by magnitude) finite number in the given semantics.
264 /// Might be denormalized, which implies a relative loss of precision.
266 /// \param Negative - True iff the number should be negative
267 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
269 /// Returns the smallest (by magnitude) normalized finite number in the given
272 /// \param Negative - True iff the number should be negative
273 static APFloat getSmallestNormalized(const fltSemantics &Sem,
274 bool Negative = false);
276 /// Returns a float which is bitcasted from an all one value int.
278 /// \param BitWidth - Select float type
279 /// \param isIEEE - If 128 bit number, select between PPC and IEEE
280 static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
282 /// Returns the size of the floating point number (in bits) in the given
284 static unsigned getSizeInBits(const fltSemantics &Sem);
288 /// Used to insert APFloat objects, or objects that contain APFloat objects,
289 /// into FoldingSets.
290 void Profile(FoldingSetNodeID &NID) const;
295 opStatus add(const APFloat &, roundingMode);
296 opStatus subtract(const APFloat &, roundingMode);
297 opStatus multiply(const APFloat &, roundingMode);
298 opStatus divide(const APFloat &, roundingMode);
300 opStatus remainder(const APFloat &);
301 /// C fmod, or llvm frem.
302 opStatus mod(const APFloat &);
303 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
304 opStatus roundToIntegral(roundingMode);
305 /// IEEE-754R 5.3.1: nextUp/nextDown.
306 opStatus next(bool nextDown);
308 /// \brief Operator+ overload which provides the default
309 /// \c nmNearestTiesToEven rounding mode and *no* error checking.
310 APFloat operator+(const APFloat &RHS) const {
311 APFloat Result = *this;
312 Result.add(RHS, rmNearestTiesToEven);
316 /// \brief Operator- overload which provides the default
317 /// \c nmNearestTiesToEven rounding mode and *no* error checking.
318 APFloat operator-(const APFloat &RHS) const {
319 APFloat Result = *this;
320 Result.subtract(RHS, rmNearestTiesToEven);
324 /// \brief Operator* overload which provides the default
325 /// \c nmNearestTiesToEven rounding mode and *no* error checking.
326 APFloat operator*(const APFloat &RHS) const {
327 APFloat Result = *this;
328 Result.multiply(RHS, rmNearestTiesToEven);
332 /// \brief Operator/ overload which provides the default
333 /// \c nmNearestTiesToEven rounding mode and *no* error checking.
334 APFloat operator/(const APFloat &RHS) const {
335 APFloat Result = *this;
336 Result.divide(RHS, rmNearestTiesToEven);
342 /// \name Sign operations.
347 void copySign(const APFloat &);
349 /// \brief A static helper to produce a copy of an APFloat value with its sign
350 /// copied from some other APFloat.
351 static APFloat copySign(APFloat Value, const APFloat &Sign) {
352 Value.copySign(Sign);
358 /// \name Conversions
361 opStatus convert(const fltSemantics &, roundingMode, bool *);
362 opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
364 opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
365 opStatus convertFromAPInt(const APInt &, bool, roundingMode);
366 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
368 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
370 opStatus convertFromString(StringRef, roundingMode);
371 APInt bitcastToAPInt() const;
372 double convertToDouble() const;
373 float convertToFloat() const;
377 /// The definition of equality is not straightforward for floating point, so
378 /// we won't use operator==. Use one of the following, or write whatever it
379 /// is you really mean.
380 bool operator==(const APFloat &) const = delete;
382 /// IEEE comparison with another floating point number (NaNs compare
383 /// unordered, 0==-0).
384 cmpResult compare(const APFloat &) const;
386 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
387 bool bitwiseIsEqual(const APFloat &) const;
389 /// Write out a hexadecimal representation of the floating point value to DST,
390 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
391 /// Return the number of characters written, excluding the terminating NUL.
392 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
393 bool upperCase, roundingMode) const;
395 /// \name IEEE-754R 5.7.2 General operations.
398 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
401 /// This applies to zeros and NaNs as well.
402 bool isNegative() const { return sign; }
404 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
406 /// This implies that the current value of the float is not zero, subnormal,
407 /// infinite, or NaN following the definition of normality from IEEE-754R.
408 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
410 /// Returns true if and only if the current value is zero, subnormal, or
413 /// This means that the value is not infinite or NaN.
414 bool isFinite() const { return !isNaN() && !isInfinity(); }
416 /// Returns true if and only if the float is plus or minus zero.
417 bool isZero() const { return category == fcZero; }
419 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
421 bool isDenormal() const;
423 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
424 bool isInfinity() const { return category == fcInfinity; }
426 /// Returns true if and only if the float is a quiet or signaling NaN.
427 bool isNaN() const { return category == fcNaN; }
429 /// Returns true if and only if the float is a signaling NaN.
430 bool isSignaling() const;
434 /// \name Simple Queries
437 fltCategory getCategory() const { return category; }
438 const fltSemantics &getSemantics() const { return *semantics; }
439 bool isNonZero() const { return category != fcZero; }
440 bool isFiniteNonZero() const { return isFinite() && !isZero(); }
441 bool isPosZero() const { return isZero() && !isNegative(); }
442 bool isNegZero() const { return isZero() && isNegative(); }
444 /// Returns true if and only if the number has the smallest possible non-zero
445 /// magnitude in the current semantics.
446 bool isSmallest() const;
448 /// Returns true if and only if the number has the largest possible finite
449 /// magnitude in the current semantics.
450 bool isLargest() const;
452 /// Returns true if and only if the number is an exact integer.
453 bool isInteger() const;
457 APFloat &operator=(const APFloat &);
458 APFloat &operator=(APFloat &&);
460 /// \brief Overload to compute a hash code for an APFloat value.
462 /// Note that the use of hash codes for floating point values is in general
463 /// frought with peril. Equality is hard to define for these values. For
464 /// example, should negative and positive zero hash to different codes? Are
465 /// they equal or not? This hash value implementation specifically
466 /// emphasizes producing different codes for different inputs in order to
467 /// be used in canonicalization and memoization. As such, equality is
468 /// bitwiseIsEqual, and 0 != -0.
469 friend hash_code hash_value(const APFloat &Arg);
471 /// Converts this value into a decimal string.
473 /// \param FormatPrecision The maximum number of digits of
474 /// precision to output. If there are fewer digits available,
475 /// zero padding will not be used unless the value is
476 /// integral and small enough to be expressed in
477 /// FormatPrecision digits. 0 means to use the natural
478 /// precision of the number.
479 /// \param FormatMaxPadding The maximum number of zeros to
480 /// consider inserting before falling back to scientific
481 /// notation. 0 means to always use scientific notation.
483 /// Number Precision MaxPadding Result
484 /// ------ --------- ---------- ------
485 /// 1.01E+4 5 2 10100
486 /// 1.01E+4 4 2 1.01E+4
487 /// 1.01E+4 5 1 1.01E+4
488 /// 1.01E-2 5 2 0.0101
489 /// 1.01E-2 4 2 0.0101
490 /// 1.01E-2 4 1 1.01E-2
491 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
492 unsigned FormatMaxPadding = 3) const;
494 /// If this value has an exact multiplicative inverse, store it in inv and
496 bool getExactInverse(APFloat *inv) const;
498 /// \brief Enumeration of \c ilogb error results.
499 enum IlogbErrorKinds {
500 IEK_Zero = INT_MIN+1,
505 /// \brief Returns the exponent of the internal representation of the APFloat.
507 /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
508 /// For special APFloat values, this returns special error codes:
510 /// NaN -> \c IEK_NaN
512 /// Inf -> \c IEK_Inf
514 friend int ilogb(const APFloat &Arg) {
519 if (Arg.isInfinity())
525 /// \brief Returns: X * 2^Exp for integral exponents.
526 friend APFloat scalbn(APFloat X, int Exp);
530 /// \name Simple Queries
533 integerPart *significandParts();
534 const integerPart *significandParts() const;
535 unsigned int partCount() const;
539 /// \name Significand operations.
542 integerPart addSignificand(const APFloat &);
543 integerPart subtractSignificand(const APFloat &, integerPart);
544 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
545 lostFraction multiplySignificand(const APFloat &, const APFloat *);
546 lostFraction divideSignificand(const APFloat &);
547 void incrementSignificand();
548 void initialize(const fltSemantics *);
549 void shiftSignificandLeft(unsigned int);
550 lostFraction shiftSignificandRight(unsigned int);
551 unsigned int significandLSB() const;
552 unsigned int significandMSB() const;
553 void zeroSignificand();
554 /// Return true if the significand excluding the integral bit is all ones.
555 bool isSignificandAllOnes() const;
556 /// Return true if the significand excluding the integral bit is all zeros.
557 bool isSignificandAllZeros() const;
561 /// \name Arithmetic on special values.
564 opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
565 opStatus divideSpecials(const APFloat &);
566 opStatus multiplySpecials(const APFloat &);
567 opStatus modSpecials(const APFloat &);
571 /// \name Special value setters.
574 void makeLargest(bool Neg = false);
575 void makeSmallest(bool Neg = false);
576 void makeNaN(bool SNaN = false, bool Neg = false,
577 const APInt *fill = nullptr);
578 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
580 void makeInf(bool Neg = false);
581 void makeZero(bool Neg = false);
588 bool convertFromStringSpecials(StringRef str);
589 opStatus normalize(roundingMode, lostFraction);
590 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
591 cmpResult compareAbsoluteValue(const APFloat &) const;
592 opStatus handleOverflow(roundingMode);
593 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
594 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
595 roundingMode, bool *) const;
596 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
598 opStatus convertFromHexadecimalString(StringRef, roundingMode);
599 opStatus convertFromDecimalString(StringRef, roundingMode);
600 char *convertNormalToHexString(char *, unsigned int, bool,
602 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
607 APInt convertHalfAPFloatToAPInt() const;
608 APInt convertFloatAPFloatToAPInt() const;
609 APInt convertDoubleAPFloatToAPInt() const;
610 APInt convertQuadrupleAPFloatToAPInt() const;
611 APInt convertF80LongDoubleAPFloatToAPInt() const;
612 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
613 void initFromAPInt(const fltSemantics *Sem, const APInt &api);
614 void initFromHalfAPInt(const APInt &api);
615 void initFromFloatAPInt(const APInt &api);
616 void initFromDoubleAPInt(const APInt &api);
617 void initFromQuadrupleAPInt(const APInt &api);
618 void initFromF80LongDoubleAPInt(const APInt &api);
619 void initFromPPCDoubleDoubleAPInt(const APInt &api);
621 void assign(const APFloat &);
622 void copySignificand(const APFloat &);
623 void freeSignificand();
625 /// The semantics that this value obeys.
626 const fltSemantics *semantics;
628 /// A binary fraction with an explicit integer bit.
630 /// The significand must be at least one bit wider than the target precision.
636 /// The signed unbiased exponent of the value.
637 ExponentType exponent;
639 /// What kind of floating point number this is.
641 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
642 /// Using the extra bit keeps it from failing under VisualStudio.
643 fltCategory category : 3;
645 /// Sign bit of the number.
646 unsigned int sign : 1;
649 /// See friend declarations above.
651 /// These additional declarations are required in order to compile LLVM with IBM
653 hash_code hash_value(const APFloat &Arg);
654 APFloat scalbn(APFloat X, int Exp);
656 /// \brief Returns the absolute value of the argument.
657 inline APFloat abs(APFloat X) {
662 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
663 /// both are not NaN. If either argument is a NaN, returns the other argument.
665 inline APFloat minnum(const APFloat &A, const APFloat &B) {
670 return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
673 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
674 /// both are not NaN. If either argument is a NaN, returns the other argument.
676 inline APFloat maxnum(const APFloat &A, const APFloat &B) {
681 return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
686 #endif // LLVM_ADT_APFLOAT_H