-//== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==//
+//===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//
//
// The LLVM Compiler Infrastructure
//
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
-//
-// This file declares a class to represent arbitrary precision floating
-// point values and provide a variety of arithmetic operations on them.
-//
+///
+/// \file
+/// \brief
+/// This file declares a class to represent arbitrary precision floating point
+/// values and provide a variety of arithmetic operations on them.
+///
//===----------------------------------------------------------------------===//
-/* A self-contained host- and target-independent arbitrary-precision
- floating-point software implementation. It 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.
-
- 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, nextafter,
- nexttoward.
-*/
-
-#ifndef LLVM_FLOAT_H
-#define LLVM_FLOAT_H
-
-// APInt contains static functions implementing bignum arithmetic.
+#ifndef LLVM_ADT_APFLOAT_H
+#define LLVM_ADT_APFLOAT_H
+
#include "llvm/ADT/APInt.h"
namespace llvm {
- /* Exponents are stored as signed numbers. */
- typedef signed short exponent_t;
+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
+ };
- struct fltSemantics;
+ /// IEEE-754R 4.3: Rounding-direction attributes.
+ enum roundingMode {
+ rmNearestTiesToEven,
+ rmTowardPositive,
+ rmTowardNegative,
+ rmTowardZero,
+ rmNearestTiesToAway
+ };
- /* When bits of a floating point number are truncated, this enum is
- used to indicate what fraction of the LSB those bits represented.
- It 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
+ /// 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
};
- class APFloat {
- public:
-
- /* We support the following floating point semantics. */
- static const fltSemantics IEEEsingle;
- static const fltSemantics IEEEdouble;
- static const fltSemantics IEEEquad;
- static const fltSemantics PPCDoubleDouble;
- static const fltSemantics x87DoubleExtended;
- /* And this pseudo, used to construct APFloats that cannot
- conflict with anything real. */
- static const fltSemantics Bogus;
-
- static unsigned int semanticsPrecision(const fltSemantics &);
-
- /* Floating point numbers have a four-state comparison relation. */
- enum cmpResult {
- cmpLessThan,
- cmpEqual,
- cmpGreaterThan,
- cmpUnordered
- };
-
- /* IEEE-754R gives five rounding modes. */
- enum roundingMode {
- rmNearestTiesToEven,
- rmTowardPositive,
- rmTowardNegative,
- rmTowardZero,
- rmNearestTiesToAway
- };
-
- // Operation status. 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
- };
-
- // Constructors.
- APFloat(const fltSemantics &, const char *);
- APFloat(const fltSemantics &, integerPart);
- APFloat(const fltSemantics &, fltCategory, bool negative);
- explicit APFloat(double d);
- explicit APFloat(float f);
- explicit APFloat(const APInt &, bool isIEEE = false);
- APFloat(const APFloat &);
- ~APFloat();
-
- // Convenience "constructors"
- static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
- return APFloat(Sem, fcZero, Negative);
- }
- static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
- return APFloat(Sem, fcInfinity, Negative);
- }
- static APFloat getNaN(const fltSemantics &Sem, bool Negative = false) {
- return APFloat(Sem, fcNaN, Negative);
- }
+ /// Category of internally-represented number.
+ enum fltCategory {
+ fcInfinity,
+ fcNaN,
+ fcNormal,
+ fcZero
+ };
- /// Profile - 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);
-
- /* 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);
-
- /* Sign operations. */
- void changeSign();
- void clearSign();
- void copySign(const APFloat &);
-
- /* Conversions. */
- opStatus convert(const fltSemantics &, roundingMode, bool *);
- opStatus convertToInteger(integerPart *, unsigned int, bool,
- 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(const char *, 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; // DO NOT IMPLEMENT
-
- /* 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;
-
- /* Simple queries. */
- fltCategory getCategory() const { return category; }
- const fltSemantics &getSemantics() const { return *semantics; }
- bool isZero() const { return category == fcZero; }
- bool isNonZero() const { return category != fcZero; }
- bool isNaN() const { return category == fcNaN; }
- bool isInfinity() const { return category == fcInfinity; }
- bool isNegative() const { return sign; }
- bool isPosZero() const { return isZero() && !isNegative(); }
- bool isNegZero() const { return isZero() && isNegative(); }
-
- APFloat& operator=(const APFloat &);
-
- /* Return an arbitrary integer value usable for hashing. */
- uint32_t getHashValue() const;
-
- private:
-
- /* Trivial queries. */
- integerPart *significandParts();
- const integerPart *significandParts() const;
- unsigned int partCount() const;
-
- /* 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();
-
- /* Arithmetic on special values. */
- opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
- opStatus divideSpecials(const APFloat &);
- opStatus multiplySpecials(const APFloat &);
-
- /* Miscellany. */
- void makeNaN(void);
- 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(const char *, roundingMode);
- opStatus convertFromDecimalString (const char *, roundingMode);
- char *convertNormalToHexString(char *, unsigned int, bool,
- roundingMode) const;
- opStatus roundSignificandWithExponent(const integerPart *, unsigned int,
- int, roundingMode);
-
- APInt convertFloatAPFloatToAPInt() const;
- APInt convertDoubleAPFloatToAPInt() const;
- APInt convertF80LongDoubleAPFloatToAPInt() const;
- APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
- void initFromAPInt(const APInt& api, bool isIEEE = false);
- void initFromFloatAPInt(const APInt& api);
- void initFromDoubleAPInt(const APInt& api);
- void initFromF80LongDoubleAPInt(const APInt& api);
- void initFromPPCDoubleDoubleAPInt(const APInt& api);
-
- void assign(const APFloat &);
- void copySignificand(const APFloat &);
- void freeSignificand();
-
- /* What kind of semantics does this value obey? */
- const fltSemantics *semantics;
-
- /* Significand - the fraction with an explicit integer bit. Must be
- at least one bit wider than the target precision. */
- union Significand
- {
- integerPart part;
- integerPart *parts;
- } significand;
-
- /* The exponent - a signed number. */
- exponent_t 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;
-
- /* The sign bit of this number. */
- unsigned int sign: 1;
-
- /* For PPCDoubleDouble, we have a second exponent and sign (the second
- significand is appended to the first one, although it would be wrong to
- regard these as a single number for arithmetic purposes). These fields
- are not meaningful for any other type. */
- exponent_t exponent2 : 11;
- unsigned int sign2: 1;
+ /// 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(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, nullptr);
+ }
+ }
+
+ /// Factory for QNaN values.
+ static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
+ const APInt *payload = nullptr) {
+ return makeNaN(Sem, false, Negative, payload);
+ }
+
+ /// Factory for SNaN values.
+ static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
+ const APInt *payload = nullptr) {
+ 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;
+
+ /// \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);
+
+ /// \brief Operator+ overload which provides the default
+ /// \c nmNearestTiesToEven rounding mode and *no* error checking.
+ APFloat operator+(const APFloat &RHS) const {
+ APFloat Result = *this;
+ Result.add(RHS, rmNearestTiesToEven);
+ return Result;
+ }
+
+ /// \brief Operator- overload which provides the default
+ /// \c nmNearestTiesToEven rounding mode and *no* error checking.
+ APFloat operator-(const APFloat &RHS) const {
+ APFloat Result = *this;
+ Result.subtract(RHS, rmNearestTiesToEven);
+ return Result;
+ }
+
+ /// \brief Operator* overload which provides the default
+ /// \c nmNearestTiesToEven rounding mode and *no* error checking.
+ APFloat operator*(const APFloat &RHS) const {
+ APFloat Result = *this;
+ Result.multiply(RHS, rmNearestTiesToEven);
+ return Result;
+ }
+
+ /// \brief Operator/ overload which provides the default
+ /// \c nmNearestTiesToEven rounding mode and *no* error checking.
+ APFloat operator/(const APFloat &RHS) const {
+ APFloat Result = *this;
+ Result.divide(RHS, rmNearestTiesToEven);
+ return Result;
+ }
+
+ /// @}
+
+ /// \name Sign operations.
+ /// @{
+
+ void changeSign();
+ void clearSign();
+ void copySign(const APFloat &);
+
+ /// \brief A static helper to produce a copy of an APFloat value with its sign
+ /// copied from some other APFloat.
+ static APFloat copySign(APFloat Value, const APFloat &Sign) {
+ Value.copySign(Sign);
+ return Value;
+ }
+
+ /// @}
+
+ /// \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 = delete;
+
+ /// 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 &);
+ APFloat &operator=(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;
+
+ /// \brief Enumeration of \c ilogb error results.
+ enum IlogbErrorKinds {
+ IEK_Zero = INT_MIN+1,
+ IEK_NaN = INT_MIN,
+ IEK_Inf = INT_MAX
};
-} /* namespace llvm */
-#endif /* LLVM_FLOAT_H */
+ /// \brief Returns the exponent of the internal representation of the APFloat.
+ ///
+ /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
+ /// For special APFloat values, this returns special error codes:
+ ///
+ /// NaN -> \c IEK_NaN
+ /// 0 -> \c IEK_Zero
+ /// Inf -> \c IEK_Inf
+ ///
+ friend int ilogb(const APFloat &Arg) {
+ if (Arg.isNaN())
+ return IEK_NaN;
+ if (Arg.isZero())
+ return IEK_Zero;
+ if (Arg.isInfinity())
+ return IEK_Inf;
+
+ return Arg.exponent;
+ }
+
+ /// \brief Returns: X * 2^Exp for integral exponents.
+ friend APFloat scalbn(APFloat X, int Exp);
+
+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 = nullptr);
+ 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 declarations above.
+///
+/// These additional declarations are required in order to compile LLVM with IBM
+/// xlC compiler.
+hash_code hash_value(const APFloat &Arg);
+APFloat scalbn(APFloat X, int Exp);
+
+/// \brief Returns the absolute value of the argument.
+inline APFloat abs(APFloat X) {
+ X.clearSign();
+ return X;
+}
+
+/// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
+/// both are not NaN. If either argument is a NaN, returns the other argument.
+LLVM_READONLY
+inline APFloat minnum(const APFloat &A, const APFloat &B) {
+ if (A.isNaN())
+ return B;
+ if (B.isNaN())
+ return A;
+ return (B.compare(A) == APFloat::cmpLessThan) ? B : A;
+}
+
+/// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
+/// both are not NaN. If either argument is a NaN, returns the other argument.
+LLVM_READONLY
+inline APFloat maxnum(const APFloat &A, const APFloat &B) {
+ if (A.isNaN())
+ return B;
+ if (B.isNaN())
+ return A;
+ return (A.compare(B) == APFloat::cmpLessThan) ? B : A;
+}
+
+} // namespace llvm
+
+#endif // LLVM_ADT_APFLOAT_H
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