/3rd_party/llvm/include/llvm/ADT/APFloat.h
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- //== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==//
- //
- // The LLVM Compiler Infrastructure
- //
- // This file is distributed under the University of Illinois Open Source
- // License. See LICENSE.TXT for details.
- //
- //===----------------------------------------------------------------------===//
- ///
- /// \file
- /// \brief
- /// This file declares a class to represent arbitrary precision floating point
- /// values and provide a variety of arithmetic operations on them.
- ///
- //===----------------------------------------------------------------------===//
- #ifndef LLVM_ADT_APFLOAT_H
- #define LLVM_ADT_APFLOAT_H
- #include "llvm/ADT/APInt.h"
- namespace llvm {
- struct fltSemantics;
- class APSInt;
- class StringRef;
- /// Enum that represents what fraction of the LSB truncated bits of an fp number
- /// represent.
- ///
- /// This essentially combines the roles of guard and sticky bits.
- enum lostFraction { // Example of truncated bits:
- lfExactlyZero, // 000000
- lfLessThanHalf, // 0xxxxx x's not all zero
- lfExactlyHalf, // 100000
- lfMoreThanHalf // 1xxxxx x's not all zero
- };
- /// \brief A self-contained host- and target-independent arbitrary-precision
- /// floating-point software implementation.
- ///
- /// APFloat uses bignum integer arithmetic as provided by static functions in
- /// the APInt class. The library will work with bignum integers whose parts are
- /// any unsigned type at least 16 bits wide, but 64 bits is recommended.
- ///
- /// Written for clarity rather than speed, in particular with a view to use in
- /// the front-end of a cross compiler so that target arithmetic can be correctly
- /// performed on the host. Performance should nonetheless be reasonable,
- /// particularly for its intended use. It may be useful as a base
- /// implementation for a run-time library during development of a faster
- /// target-specific one.
- ///
- /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
- /// implemented operations. Currently implemented operations are add, subtract,
- /// multiply, divide, fused-multiply-add, conversion-to-float,
- /// conversion-to-integer and conversion-from-integer. New rounding modes
- /// (e.g. away from zero) can be added with three or four lines of code.
- ///
- /// Four formats are built-in: IEEE single precision, double precision,
- /// quadruple precision, and x87 80-bit extended double (when operating with
- /// full extended precision). Adding a new format that obeys IEEE semantics
- /// only requires adding two lines of code: a declaration and definition of the
- /// format.
- ///
- /// All operations return the status of that operation as an exception bit-mask,
- /// so multiple operations can be done consecutively with their results or-ed
- /// together. The returned status can be useful for compiler diagnostics; e.g.,
- /// inexact, underflow and overflow can be easily diagnosed on constant folding,
- /// and compiler optimizers can determine what exceptions would be raised by
- /// folding operations and optimize, or perhaps not optimize, accordingly.
- ///
- /// At present, underflow tininess is detected after rounding; it should be
- /// straight forward to add support for the before-rounding case too.
- ///
- /// The library reads hexadecimal floating point numbers as per C99, and
- /// correctly rounds if necessary according to the specified rounding mode.
- /// Syntax is required to have been validated by the caller. It also converts
- /// floating point numbers to hexadecimal text as per the C99 %a and %A
- /// conversions. The output precision (or alternatively the natural minimal
- /// precision) can be specified; if the requested precision is less than the
- /// natural precision the output is correctly rounded for the specified rounding
- /// mode.
- ///
- /// It also reads decimal floating point numbers and correctly rounds according
- /// to the specified rounding mode.
- ///
- /// Conversion to decimal text is not currently implemented.
- ///
- /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
- /// signed exponent, and the significand as an array of integer parts. After
- /// normalization of a number of precision P the exponent is within the range of
- /// the format, and if the number is not denormal the P-th bit of the
- /// significand is set as an explicit integer bit. For denormals the most
- /// significant bit is shifted right so that the exponent is maintained at the
- /// format's minimum, so that the smallest denormal has just the least
- /// significant bit of the significand set. The sign of zeroes and infinities
- /// is significant; the exponent and significand of such numbers is not stored,
- /// but has a known implicit (deterministic) value: 0 for the significands, 0
- /// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
- /// significand are deterministic, although not really meaningful, and preserved
- /// in non-conversion operations. The exponent is implicitly all 1 bits.
- ///
- /// APFloat does not provide any exception handling beyond default exception
- /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
- /// by encoding Signaling NaNs with the first bit of its trailing significand as
- /// 0.
- ///
- /// TODO
- /// ====
- ///
- /// Some features that may or may not be worth adding:
- ///
- /// Binary to decimal conversion (hard).
- ///
- /// Optional ability to detect underflow tininess before rounding.
- ///
- /// New formats: x87 in single and double precision mode (IEEE apart from
- /// extended exponent range) (hard).
- ///
- /// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
- ///
- class APFloat {
- public:
- /// A signed type to represent a floating point numbers unbiased exponent.
- typedef signed short ExponentType;
- /// \name Floating Point Semantics.
- /// @{
- static const fltSemantics IEEEhalf;
- static const fltSemantics IEEEsingle;
- static const fltSemantics IEEEdouble;
- static const fltSemantics IEEEquad;
- static const fltSemantics PPCDoubleDouble;
- static const fltSemantics x87DoubleExtended;
- /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
- /// anything real.
- static const fltSemantics Bogus;
- /// @}
- static unsigned int semanticsPrecision(const fltSemantics &);
- /// IEEE-754R 5.11: Floating Point Comparison Relations.
- enum cmpResult {
- cmpLessThan,
- cmpEqual,
- cmpGreaterThan,
- cmpUnordered
- };
- /// IEEE-754R 4.3: Rounding-direction attributes.
- enum roundingMode {
- rmNearestTiesToEven,
- rmTowardPositive,
- rmTowardNegative,
- rmTowardZero,
- rmNearestTiesToAway
- };
- /// IEEE-754R 7: Default exception handling.
- ///
- /// opUnderflow or opOverflow are always returned or-ed with opInexact.
- enum opStatus {
- opOK = 0x00,
- opInvalidOp = 0x01,
- opDivByZero = 0x02,
- opOverflow = 0x04,
- opUnderflow = 0x08,
- opInexact = 0x10
- };
- /// Category of internally-represented number.
- enum fltCategory {
- fcInfinity,
- fcNaN,
- fcNormal,
- fcZero
- };
- /// Convenience enum used to construct an uninitialized APFloat.
- enum uninitializedTag {
- uninitialized
- };
- /// \name Constructors
- /// @{
- APFloat(const fltSemantics &); // Default construct to 0.0
- APFloat(const fltSemantics &, StringRef);
- APFloat(const fltSemantics &, integerPart);
- APFloat(const fltSemantics &, uninitializedTag);
- APFloat(const fltSemantics &, const APInt &);
- explicit APFloat(double d);
- explicit APFloat(float f);
- APFloat(const APFloat &);
- ~APFloat();
- /// @}
- /// \brief Returns whether this instance allocated memory.
- bool needsCleanup() const { return partCount() > 1; }
- /// \name Convenience "constructors"
- /// @{
- /// Factory for Positive and Negative Zero.
- ///
- /// \param Negative True iff the number should be negative.
- static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
- APFloat Val(Sem, uninitialized);
- Val.makeZero(Negative);
- return Val;
- }
- /// Factory for Positive and Negative Infinity.
- ///
- /// \param Negative True iff the number should be negative.
- static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
- APFloat Val(Sem, uninitialized);
- Val.makeInf(Negative);
- return Val;
- }
- /// Factory for QNaN values.
- ///
- /// \param Negative - True iff the NaN generated should be negative.
- /// \param type - The unspecified fill bits for creating the NaN, 0 by
- /// default. The value is truncated as necessary.
- static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
- unsigned type = 0) {
- if (type) {
- APInt fill(64, type);
- return getQNaN(Sem, Negative, &fill);
- } else {
- return getQNaN(Sem, Negative, 0);
- }
- }
- /// Factory for QNaN values.
- static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
- const APInt *payload = 0) {
- return makeNaN(Sem, false, Negative, payload);
- }
- /// Factory for SNaN values.
- static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
- const APInt *payload = 0) {
- return makeNaN(Sem, true, Negative, payload);
- }
- /// Returns the largest finite number in the given semantics.
- ///
- /// \param Negative - True iff the number should be negative
- static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
- /// Returns the smallest (by magnitude) finite number in the given semantics.
- /// Might be denormalized, which implies a relative loss of precision.
- ///
- /// \param Negative - True iff the number should be negative
- static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
- /// Returns the smallest (by magnitude) normalized finite number in the given
- /// semantics.
- ///
- /// \param Negative - True iff the number should be negative
- static APFloat getSmallestNormalized(const fltSemantics &Sem,
- bool Negative = false);
- /// Returns a float which is bitcasted from an all one value int.
- ///
- /// \param BitWidth - Select float type
- /// \param isIEEE - If 128 bit number, select between PPC and IEEE
- static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
- /// @}
- /// Used to insert APFloat objects, or objects that contain APFloat objects,
- /// into FoldingSets.
- void Profile(FoldingSetNodeID &NID) const;
- /// \brief Used by the Bitcode serializer to emit APInts to Bitcode.
- void Emit(Serializer &S) const;
- /// \brief Used by the Bitcode deserializer to deserialize APInts.
- static APFloat ReadVal(Deserializer &D);
- /// \name Arithmetic
- /// @{
- opStatus add(const APFloat &, roundingMode);
- opStatus subtract(const APFloat &, roundingMode);
- opStatus multiply(const APFloat &, roundingMode);
- opStatus divide(const APFloat &, roundingMode);
- /// IEEE remainder.
- opStatus remainder(const APFloat &);
- /// C fmod, or llvm frem.
- opStatus mod(const APFloat &, roundingMode);
- opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
- opStatus roundToIntegral(roundingMode);
- /// IEEE-754R 5.3.1: nextUp/nextDown.
- opStatus next(bool nextDown);
- /// @}
- /// \name Sign operations.
- /// @{
- void changeSign();
- void clearSign();
- void copySign(const APFloat &);
- /// @}
- /// \name Conversions
- /// @{
- opStatus convert(const fltSemantics &, roundingMode, bool *);
- opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
- bool *) const;
- opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
- opStatus convertFromAPInt(const APInt &, bool, roundingMode);
- opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
- bool, roundingMode);
- opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
- bool, roundingMode);
- opStatus convertFromString(StringRef, roundingMode);
- APInt bitcastToAPInt() const;
- double convertToDouble() const;
- float convertToFloat() const;
- /// @}
- /// The definition of equality is not straightforward for floating point, so
- /// we won't use operator==. Use one of the following, or write whatever it
- /// is you really mean.
- bool operator==(const APFloat &) const LLVM_DELETED_FUNCTION;
- /// IEEE comparison with another floating point number (NaNs compare
- /// unordered, 0==-0).
- cmpResult compare(const APFloat &) const;
- /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
- bool bitwiseIsEqual(const APFloat &) const;
- /// Write out a hexadecimal representation of the floating point value to DST,
- /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
- /// Return the number of characters written, excluding the terminating NUL.
- unsigned int convertToHexString(char *dst, unsigned int hexDigits,
- bool upperCase, roundingMode) const;
- /// \name IEEE-754R 5.7.2 General operations.
- /// @{
- /// IEEE-754R isSignMinus: Returns true if and only if the current value is
- /// negative.
- ///
- /// This applies to zeros and NaNs as well.
- bool isNegative() const { return sign; }
- /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
- ///
- /// This implies that the current value of the float is not zero, subnormal,
- /// infinite, or NaN following the definition of normality from IEEE-754R.
- bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
- /// Returns true if and only if the current value is zero, subnormal, or
- /// normal.
- ///
- /// This means that the value is not infinite or NaN.
- bool isFinite() const { return !isNaN() && !isInfinity(); }
- /// Returns true if and only if the float is plus or minus zero.
- bool isZero() const { return category == fcZero; }
- /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
- /// denormal.
- bool isDenormal() const;
- /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
- bool isInfinity() const { return category == fcInfinity; }
- /// Returns true if and only if the float is a quiet or signaling NaN.
- bool isNaN() const { return category == fcNaN; }
- /// Returns true if and only if the float is a signaling NaN.
- bool isSignaling() const;
- /// @}
- /// \name Simple Queries
- /// @{
- fltCategory getCategory() const { return category; }
- const fltSemantics &getSemantics() const { return *semantics; }
- bool isNonZero() const { return category != fcZero; }
- bool isFiniteNonZero() const { return isFinite() && !isZero(); }
- bool isPosZero() const { return isZero() && !isNegative(); }
- bool isNegZero() const { return isZero() && isNegative(); }
- /// Returns true if and only if the number has the smallest possible non-zero
- /// magnitude in the current semantics.
- bool isSmallest() const;
- /// Returns true if and only if the number has the largest possible finite
- /// magnitude in the current semantics.
- bool isLargest() const;
- /// @}
- APFloat &operator=(const APFloat &);
- /// \brief Overload to compute a hash code for an APFloat value.
- ///
- /// Note that the use of hash codes for floating point values is in general
- /// frought with peril. Equality is hard to define for these values. For
- /// example, should negative and positive zero hash to different codes? Are
- /// they equal or not? This hash value implementation specifically
- /// emphasizes producing different codes for different inputs in order to
- /// be used in canonicalization and memoization. As such, equality is
- /// bitwiseIsEqual, and 0 != -0.
- friend hash_code hash_value(const APFloat &Arg);
- /// Converts this value into a decimal string.
- ///
- /// \param FormatPrecision The maximum number of digits of
- /// precision to output. If there are fewer digits available,
- /// zero padding will not be used unless the value is
- /// integral and small enough to be expressed in
- /// FormatPrecision digits. 0 means to use the natural
- /// precision of the number.
- /// \param FormatMaxPadding The maximum number of zeros to
- /// consider inserting before falling back to scientific
- /// notation. 0 means to always use scientific notation.
- ///
- /// Number Precision MaxPadding Result
- /// ------ --------- ---------- ------
- /// 1.01E+4 5 2 10100
- /// 1.01E+4 4 2 1.01E+4
- /// 1.01E+4 5 1 1.01E+4
- /// 1.01E-2 5 2 0.0101
- /// 1.01E-2 4 2 0.0101
- /// 1.01E-2 4 1 1.01E-2
- void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
- unsigned FormatMaxPadding = 3) const;
- /// If this value has an exact multiplicative inverse, store it in inv and
- /// return true.
- bool getExactInverse(APFloat *inv) const;
- private:
- /// \name Simple Queries
- /// @{
- integerPart *significandParts();
- const integerPart *significandParts() const;
- unsigned int partCount() const;
- /// @}
- /// \name Significand operations.
- /// @{
- integerPart addSignificand(const APFloat &);
- integerPart subtractSignificand(const APFloat &, integerPart);
- lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
- lostFraction multiplySignificand(const APFloat &, const APFloat *);
- lostFraction divideSignificand(const APFloat &);
- void incrementSignificand();
- void initialize(const fltSemantics *);
- void shiftSignificandLeft(unsigned int);
- lostFraction shiftSignificandRight(unsigned int);
- unsigned int significandLSB() const;
- unsigned int significandMSB() const;
- void zeroSignificand();
- /// Return true if the significand excluding the integral bit is all ones.
- bool isSignificandAllOnes() const;
- /// Return true if the significand excluding the integral bit is all zeros.
- bool isSignificandAllZeros() const;
- /// @}
- /// \name Arithmetic on special values.
- /// @{
- opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
- opStatus divideSpecials(const APFloat &);
- opStatus multiplySpecials(const APFloat &);
- opStatus modSpecials(const APFloat &);
- /// @}
- /// \name Special value setters.
- /// @{
- void makeLargest(bool Neg = false);
- void makeSmallest(bool Neg = false);
- void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
- static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
- const APInt *fill);
- void makeInf(bool Neg = false);
- void makeZero(bool Neg = false);
- /// @}
- /// \name Miscellany
- /// @{
- bool convertFromStringSpecials(StringRef str);
- opStatus normalize(roundingMode, lostFraction);
- opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
- cmpResult compareAbsoluteValue(const APFloat &) const;
- opStatus handleOverflow(roundingMode);
- bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
- opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
- roundingMode, bool *) const;
- opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
- roundingMode);
- opStatus convertFromHexadecimalString(StringRef, roundingMode);
- opStatus convertFromDecimalString(StringRef, roundingMode);
- char *convertNormalToHexString(char *, unsigned int, bool,
- roundingMode) const;
- opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
- roundingMode);
- /// @}
- APInt convertHalfAPFloatToAPInt() const;
- APInt convertFloatAPFloatToAPInt() const;
- APInt convertDoubleAPFloatToAPInt() const;
- APInt convertQuadrupleAPFloatToAPInt() const;
- APInt convertF80LongDoubleAPFloatToAPInt() const;
- APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
- void initFromAPInt(const fltSemantics *Sem, const APInt &api);
- void initFromHalfAPInt(const APInt &api);
- void initFromFloatAPInt(const APInt &api);
- void initFromDoubleAPInt(const APInt &api);
- void initFromQuadrupleAPInt(const APInt &api);
- void initFromF80LongDoubleAPInt(const APInt &api);
- void initFromPPCDoubleDoubleAPInt(const APInt &api);
- void assign(const APFloat &);
- void copySignificand(const APFloat &);
- void freeSignificand();
- /// The semantics that this value obeys.
- const fltSemantics *semantics;
- /// A binary fraction with an explicit integer bit.
- ///
- /// The significand must be at least one bit wider than the target precision.
- union Significand {
- integerPart part;
- integerPart *parts;
- } significand;
- /// The signed unbiased exponent of the value.
- ExponentType exponent;
- /// What kind of floating point number this is.
- ///
- /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
- /// Using the extra bit keeps it from failing under VisualStudio.
- fltCategory category : 3;
- /// Sign bit of the number.
- unsigned int sign : 1;
- };
- /// See friend declaration above.
- ///
- /// This additional declaration is required in order to compile LLVM with IBM
- /// xlC compiler.
- hash_code hash_value(const APFloat &Arg);
- } // namespace llvm
- #endif // LLVM_ADT_APFLOAT_H