//== 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. // //===----------------------------------------------------------------------===// // // 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. #include "llvm/ADT/APInt.h" namespace llvm { /* Exponents are stored as signed numbers. */ typedef signed short exponent_t; struct fltSemantics; class APSInt; class StringRef; /* 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 }; class APFloat { public: /* We support the following 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; /* 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 }; enum uninitializedTag { uninitialized }; // Constructors. APFloat(const fltSemantics &); // Default construct to 0.0 APFloat(const fltSemantics &, StringRef); APFloat(const fltSemantics &, integerPart); APFloat(const fltSemantics &, fltCategory, bool negative); APFloat(const fltSemantics &, uninitializedTag); 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); } /// getNaN - 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); } } /// getQNan - Factory for QNaN values. static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false, const APInt *payload = 0) { return makeNaN(Sem, false, Negative, payload); } /// getSNan - Factory for SNaN values. static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false, const APInt *payload = 0) { return makeNaN(Sem, true, Negative, payload); } /// getLargest - 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); /// getSmallest - 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); /// getSmallestNormalized - 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); /// getAllOnesValue - 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); /// 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 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; // 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; /// 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; /// getExactInverse - If this value has an exact multiplicative inverse, /// store it in inv and return true. bool getExactInverse(APFloat *inv) 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 &); opStatus modSpecials(const APFloat &); /* Miscellany. */ static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative, const APInt *fill); void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0); 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 APInt& api, bool isIEEE = false); 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(); /* 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; }; } /* namespace llvm */ #endif /* LLVM_FLOAT_H */