1 //== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==// 2 // 3 // The LLVM Compiler Infrastructure 4 // 5 // This file is distributed under the University of Illinois Open Source 6 // License. See LICENSE.TXT for details. 7 // 8 //===----------------------------------------------------------------------===// 9 // 10 // This file declares a class to represent arbitrary precision floating 11 // point values and provide a variety of arithmetic operations on them. 12 // 13 //===----------------------------------------------------------------------===// 14 15 /* A self-contained host- and target-independent arbitrary-precision 16 floating-point software implementation. It uses bignum integer 17 arithmetic as provided by static functions in the APInt class. 18 The library will work with bignum integers whose parts are any 19 unsigned type at least 16 bits wide, but 64 bits is recommended. 20 21 Written for clarity rather than speed, in particular with a view 22 to use in the front-end of a cross compiler so that target 23 arithmetic can be correctly performed on the host. Performance 24 should nonetheless be reasonable, particularly for its intended 25 use. It may be useful as a base implementation for a run-time 26 library during development of a faster target-specific one. 27 28 All 5 rounding modes in the IEEE-754R draft are handled correctly 29 for all implemented operations. Currently implemented operations 30 are add, subtract, multiply, divide, fused-multiply-add, 31 conversion-to-float, conversion-to-integer and 32 conversion-from-integer. New rounding modes (e.g. away from zero) 33 can be added with three or four lines of code. 34 35 Four formats are built-in: IEEE single precision, double 36 precision, quadruple precision, and x87 80-bit extended double 37 (when operating with full extended precision). Adding a new 38 format that obeys IEEE semantics only requires adding two lines of 39 code: a declaration and definition of the format. 40 41 All operations return the status of that operation as an exception 42 bit-mask, so multiple operations can be done consecutively with 43 their results or-ed together. The returned status can be useful 44 for compiler diagnostics; e.g., inexact, underflow and overflow 45 can be easily diagnosed on constant folding, and compiler 46 optimizers can determine what exceptions would be raised by 47 folding operations and optimize, or perhaps not optimize, 48 accordingly. 49 50 At present, underflow tininess is detected after rounding; it 51 should be straight forward to add support for the before-rounding 52 case too. 53 54 The library reads hexadecimal floating point numbers as per C99, 55 and correctly rounds if necessary according to the specified 56 rounding mode. Syntax is required to have been validated by the 57 caller. It also converts floating point numbers to hexadecimal 58 text as per the C99 %a and %A conversions. The output precision 59 (or alternatively the natural minimal precision) can be specified; 60 if the requested precision is less than the natural precision the 61 output is correctly rounded for the specified rounding mode. 62 63 It also reads decimal floating point numbers and correctly rounds 64 according to the specified rounding mode. 65 66 Conversion to decimal text is not currently implemented. 67 68 Non-zero finite numbers are represented internally as a sign bit, 69 a 16-bit signed exponent, and the significand as an array of 70 integer parts. After normalization of a number of precision P the 71 exponent is within the range of the format, and if the number is 72 not denormal the P-th bit of the significand is set as an explicit 73 integer bit. For denormals the most significant bit is shifted 74 right so that the exponent is maintained at the format's minimum, 75 so that the smallest denormal has just the least significant bit 76 of the significand set. The sign of zeroes and infinities is 77 significant; the exponent and significand of such numbers is not 78 stored, but has a known implicit (deterministic) value: 0 for the 79 significands, 0 for zero exponent, all 1 bits for infinity 80 exponent. For NaNs the sign and significand are deterministic, 81 although not really meaningful, and preserved in non-conversion 82 operations. The exponent is implicitly all 1 bits. 83 84 TODO 85 ==== 86 87 Some features that may or may not be worth adding: 88 89 Binary to decimal conversion (hard). 90 91 Optional ability to detect underflow tininess before rounding. 92 93 New formats: x87 in single and double precision mode (IEEE apart 94 from extended exponent range) (hard). 95 96 New operations: sqrt, IEEE remainder, C90 fmod, nextafter, 97 nexttoward. 98 */ 99 100 #ifndef LLVM_FLOAT_H 101 #define LLVM_FLOAT_H 102 103 // APInt contains static functions implementing bignum arithmetic. 104 #include "llvm/ADT/APInt.h" 105 106 namespace llvm { 107 108 /* Exponents are stored as signed numbers. */ 109 typedef signed short exponent_t; 110 111 struct fltSemantics; 112 class APSInt; 113 class StringRef; 114 115 /* When bits of a floating point number are truncated, this enum is 116 used to indicate what fraction of the LSB those bits represented. 117 It essentially combines the roles of guard and sticky bits. */ 118 enum lostFraction { // Example of truncated bits: 119 lfExactlyZero, // 000000 120 lfLessThanHalf, // 0xxxxx x's not all zero 121 lfExactlyHalf, // 100000 122 lfMoreThanHalf // 1xxxxx x's not all zero 123 }; 124 125 class APFloat { 126 public: 127 128 /* We support the following floating point semantics. */ 129 static const fltSemantics IEEEhalf; 130 static const fltSemantics IEEEsingle; 131 static const fltSemantics IEEEdouble; 132 static const fltSemantics IEEEquad; 133 static const fltSemantics PPCDoubleDouble; 134 static const fltSemantics x87DoubleExtended; 135 /* And this pseudo, used to construct APFloats that cannot 136 conflict with anything real. */ 137 static const fltSemantics Bogus; 138 139 static unsigned int semanticsPrecision(const fltSemantics &); 140 141 /* Floating point numbers have a four-state comparison relation. */ 142 enum cmpResult { 143 cmpLessThan, 144 cmpEqual, 145 cmpGreaterThan, 146 cmpUnordered 147 }; 148 149 /* IEEE-754R gives five rounding modes. */ 150 enum roundingMode { 151 rmNearestTiesToEven, 152 rmTowardPositive, 153 rmTowardNegative, 154 rmTowardZero, 155 rmNearestTiesToAway 156 }; 157 158 // Operation status. opUnderflow or opOverflow are always returned 159 // or-ed with opInexact. 160 enum opStatus { 161 opOK = 0x00, 162 opInvalidOp = 0x01, 163 opDivByZero = 0x02, 164 opOverflow = 0x04, 165 opUnderflow = 0x08, 166 opInexact = 0x10 167 }; 168 169 // Category of internally-represented number. 170 enum fltCategory { 171 fcInfinity, 172 fcNaN, 173 fcNormal, 174 fcZero 175 }; 176 177 enum uninitializedTag { 178 uninitialized 179 }; 180 181 // Constructors. 182 APFloat(const fltSemantics &); // Default construct to 0.0 183 APFloat(const fltSemantics &, StringRef); 184 APFloat(const fltSemantics &, integerPart); 185 APFloat(const fltSemantics &, fltCategory, bool negative); 186 APFloat(const fltSemantics &, uninitializedTag); 187 explicit APFloat(double d); 188 explicit APFloat(float f); 189 explicit APFloat(const APInt &, bool isIEEE = false); 190 APFloat(const APFloat &); 191 ~APFloat(); 192 193 // Convenience "constructors" 194 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) { 195 return APFloat(Sem, fcZero, Negative); 196 } 197 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) { 198 return APFloat(Sem, fcInfinity, Negative); 199 } 200 201 /// getNaN - Factory for QNaN values. 202 /// 203 /// \param Negative - True iff the NaN generated should be negative. 204 /// \param type - The unspecified fill bits for creating the NaN, 0 by 205 /// default. The value is truncated as necessary. 206 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false, 207 unsigned type = 0) { 208 if (type) { 209 APInt fill(64, type); 210 return getQNaN(Sem, Negative, &fill); 211 } else { 212 return getQNaN(Sem, Negative, 0); 213 } 214 } 215 216 /// getQNan - Factory for QNaN values. 217 static APFloat getQNaN(const fltSemantics &Sem, 218 bool Negative = false, 219 const APInt *payload = 0) { 220 return makeNaN(Sem, false, Negative, payload); 221 } 222 223 /// getSNan - Factory for SNaN values. 224 static APFloat getSNaN(const fltSemantics &Sem, 225 bool Negative = false, 226 const APInt *payload = 0) { 227 return makeNaN(Sem, true, Negative, payload); 228 } 229 230 /// getLargest - Returns the largest finite number in the given 231 /// semantics. 232 /// 233 /// \param Negative - True iff the number should be negative 234 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false); 235 236 /// getSmallest - Returns the smallest (by magnitude) finite number 237 /// in the given semantics. Might be denormalized, which implies a 238 /// relative loss of precision. 239 /// 240 /// \param Negative - True iff the number should be negative 241 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false); 242 243 /// getSmallestNormalized - Returns the smallest (by magnitude) 244 /// normalized finite number in the given semantics. 245 /// 246 /// \param Negative - True iff the number should be negative 247 static APFloat getSmallestNormalized(const fltSemantics &Sem, 248 bool Negative = false); 249 250 /// getAllOnesValue - Returns a float which is bitcasted from 251 /// an all one value int. 252 /// 253 /// \param BitWidth - Select float type 254 /// \param isIEEE - If 128 bit number, select between PPC and IEEE 255 static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false); 256 257 /// Profile - Used to insert APFloat objects, or objects that contain 258 /// APFloat objects, into FoldingSets. 259 void Profile(FoldingSetNodeID& NID) const; 260 261 /// @brief Used by the Bitcode serializer to emit APInts to Bitcode. 262 void Emit(Serializer& S) const; 263 264 /// @brief Used by the Bitcode deserializer to deserialize APInts. 265 static APFloat ReadVal(Deserializer& D); 266 267 /* Arithmetic. */ 268 opStatus add(const APFloat &, roundingMode); 269 opStatus subtract(const APFloat &, roundingMode); 270 opStatus multiply(const APFloat &, roundingMode); 271 opStatus divide(const APFloat &, roundingMode); 272 /* IEEE remainder. */ 273 opStatus remainder(const APFloat &); 274 /* C fmod, or llvm frem. */ 275 opStatus mod(const APFloat &, roundingMode); 276 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode); 277 278 /* Sign operations. */ 279 void changeSign(); 280 void clearSign(); 281 void copySign(const APFloat &); 282 283 /* Conversions. */ 284 opStatus convert(const fltSemantics &, roundingMode, bool *); 285 opStatus convertToInteger(integerPart *, unsigned int, bool, 286 roundingMode, bool *) const; 287 opStatus convertToInteger(APSInt&, roundingMode, bool *) const; 288 opStatus convertFromAPInt(const APInt &, 289 bool, roundingMode); 290 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int, 291 bool, roundingMode); 292 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int, 293 bool, roundingMode); 294 opStatus convertFromString(StringRef, roundingMode); 295 APInt bitcastToAPInt() const; 296 double convertToDouble() const; 297 float convertToFloat() const; 298 299 /* The definition of equality is not straightforward for floating point, 300 so we won't use operator==. Use one of the following, or write 301 whatever it is you really mean. */ 302 // bool operator==(const APFloat &) const; // DO NOT IMPLEMENT 303 304 /* IEEE comparison with another floating point number (NaNs 305 compare unordered, 0==-0). */ 306 cmpResult compare(const APFloat &) const; 307 308 /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */ 309 bool bitwiseIsEqual(const APFloat &) const; 310 311 /* Write out a hexadecimal representation of the floating point 312 value to DST, which must be of sufficient size, in the C99 form 313 [-]0xh.hhhhp[+-]d. Return the number of characters written, 314 excluding the terminating NUL. */ 315 unsigned int convertToHexString(char *dst, unsigned int hexDigits, 316 bool upperCase, roundingMode) const; 317 318 /* Simple queries. */ getCategory()319 fltCategory getCategory() const { return category; } getSemantics()320 const fltSemantics &getSemantics() const { return *semantics; } isZero()321 bool isZero() const { return category == fcZero; } isNonZero()322 bool isNonZero() const { return category != fcZero; } isNormal()323 bool isNormal() const { return category == fcNormal; } isNaN()324 bool isNaN() const { return category == fcNaN; } isInfinity()325 bool isInfinity() const { return category == fcInfinity; } isNegative()326 bool isNegative() const { return sign; } isPosZero()327 bool isPosZero() const { return isZero() && !isNegative(); } isNegZero()328 bool isNegZero() const { return isZero() && isNegative(); } 329 330 APFloat& operator=(const APFloat &); 331 332 /// \brief Overload to compute a hash code for an APFloat value. 333 /// 334 /// Note that the use of hash codes for floating point values is in general 335 /// frought with peril. Equality is hard to define for these values. For 336 /// example, should negative and positive zero hash to different codes? Are 337 /// they equal or not? This hash value implementation specifically 338 /// emphasizes producing different codes for different inputs in order to 339 /// be used in canonicalization and memoization. As such, equality is 340 /// bitwiseIsEqual, and 0 != -0. 341 friend hash_code hash_value(const APFloat &Arg); 342 343 /// Converts this value into a decimal string. 344 /// 345 /// \param FormatPrecision The maximum number of digits of 346 /// precision to output. If there are fewer digits available, 347 /// zero padding will not be used unless the value is 348 /// integral and small enough to be expressed in 349 /// FormatPrecision digits. 0 means to use the natural 350 /// precision of the number. 351 /// \param FormatMaxPadding The maximum number of zeros to 352 /// consider inserting before falling back to scientific 353 /// notation. 0 means to always use scientific notation. 354 /// 355 /// Number Precision MaxPadding Result 356 /// ------ --------- ---------- ------ 357 /// 1.01E+4 5 2 10100 358 /// 1.01E+4 4 2 1.01E+4 359 /// 1.01E+4 5 1 1.01E+4 360 /// 1.01E-2 5 2 0.0101 361 /// 1.01E-2 4 2 0.0101 362 /// 1.01E-2 4 1 1.01E-2 363 void toString(SmallVectorImpl<char> &Str, 364 unsigned FormatPrecision = 0, 365 unsigned FormatMaxPadding = 3) const; 366 367 /// getExactInverse - If this value has an exact multiplicative inverse, 368 /// store it in inv and return true. 369 bool getExactInverse(APFloat *inv) const; 370 371 private: 372 373 /* Trivial queries. */ 374 integerPart *significandParts(); 375 const integerPart *significandParts() const; 376 unsigned int partCount() const; 377 378 /* Significand operations. */ 379 integerPart addSignificand(const APFloat &); 380 integerPart subtractSignificand(const APFloat &, integerPart); 381 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract); 382 lostFraction multiplySignificand(const APFloat &, const APFloat *); 383 lostFraction divideSignificand(const APFloat &); 384 void incrementSignificand(); 385 void initialize(const fltSemantics *); 386 void shiftSignificandLeft(unsigned int); 387 lostFraction shiftSignificandRight(unsigned int); 388 unsigned int significandLSB() const; 389 unsigned int significandMSB() const; 390 void zeroSignificand(); 391 392 /* Arithmetic on special values. */ 393 opStatus addOrSubtractSpecials(const APFloat &, bool subtract); 394 opStatus divideSpecials(const APFloat &); 395 opStatus multiplySpecials(const APFloat &); 396 opStatus modSpecials(const APFloat &); 397 398 /* Miscellany. */ 399 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative, 400 const APInt *fill); 401 void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0); 402 opStatus normalize(roundingMode, lostFraction); 403 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract); 404 cmpResult compareAbsoluteValue(const APFloat &) const; 405 opStatus handleOverflow(roundingMode); 406 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const; 407 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool, 408 roundingMode, bool *) const; 409 opStatus convertFromUnsignedParts(const integerPart *, unsigned int, 410 roundingMode); 411 opStatus convertFromHexadecimalString(StringRef, roundingMode); 412 opStatus convertFromDecimalString(StringRef, roundingMode); 413 char *convertNormalToHexString(char *, unsigned int, bool, 414 roundingMode) const; 415 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, 416 int, roundingMode); 417 418 APInt convertHalfAPFloatToAPInt() const; 419 APInt convertFloatAPFloatToAPInt() const; 420 APInt convertDoubleAPFloatToAPInt() const; 421 APInt convertQuadrupleAPFloatToAPInt() const; 422 APInt convertF80LongDoubleAPFloatToAPInt() const; 423 APInt convertPPCDoubleDoubleAPFloatToAPInt() const; 424 void initFromAPInt(const APInt& api, bool isIEEE = false); 425 void initFromHalfAPInt(const APInt& api); 426 void initFromFloatAPInt(const APInt& api); 427 void initFromDoubleAPInt(const APInt& api); 428 void initFromQuadrupleAPInt(const APInt &api); 429 void initFromF80LongDoubleAPInt(const APInt& api); 430 void initFromPPCDoubleDoubleAPInt(const APInt& api); 431 432 void assign(const APFloat &); 433 void copySignificand(const APFloat &); 434 void freeSignificand(); 435 436 /* What kind of semantics does this value obey? */ 437 const fltSemantics *semantics; 438 439 /* Significand - the fraction with an explicit integer bit. Must be 440 at least one bit wider than the target precision. */ 441 union Significand 442 { 443 integerPart part; 444 integerPart *parts; 445 } significand; 446 447 /* The exponent - a signed number. */ 448 exponent_t exponent; 449 450 /* What kind of floating point number this is. */ 451 /* Only 2 bits are required, but VisualStudio incorrectly sign extends 452 it. Using the extra bit keeps it from failing under VisualStudio */ 453 fltCategory category: 3; 454 455 /* The sign bit of this number. */ 456 unsigned int sign: 1; 457 458 /* For PPCDoubleDouble, we have a second exponent and sign (the second 459 significand is appended to the first one, although it would be wrong to 460 regard these as a single number for arithmetic purposes). These fields 461 are not meaningful for any other type. */ 462 exponent_t exponent2 : 11; 463 unsigned int sign2: 1; 464 }; 465 } /* namespace llvm */ 466 467 #endif /* LLVM_FLOAT_H */ 468