1 //===- llvm/ADT/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 /// \file 11 /// \brief 12 /// This file declares a class to represent arbitrary precision floating point 13 /// values and provide a variety of arithmetic operations on them. 14 /// 15 //===----------------------------------------------------------------------===// 16 17 #ifndef LLVM_ADT_APFLOAT_H 18 #define LLVM_ADT_APFLOAT_H 19 20 #include "llvm/ADT/APInt.h" 21 22 namespace llvm { 23 24 struct fltSemantics; 25 class APSInt; 26 class StringRef; 27 28 /// Enum that represents what fraction of the LSB truncated bits of an fp number 29 /// represent. 30 /// 31 /// This essentially combines the roles of guard and sticky bits. 32 enum lostFraction { // Example of truncated bits: 33 lfExactlyZero, // 000000 34 lfLessThanHalf, // 0xxxxx x's not all zero 35 lfExactlyHalf, // 100000 36 lfMoreThanHalf // 1xxxxx x's not all zero 37 }; 38 39 /// \brief A self-contained host- and target-independent arbitrary-precision 40 /// floating-point software implementation. 41 /// 42 /// APFloat uses bignum integer arithmetic as provided by static functions in 43 /// the APInt class. The library will work with bignum integers whose parts are 44 /// any unsigned type at least 16 bits wide, but 64 bits is recommended. 45 /// 46 /// Written for clarity rather than speed, in particular with a view to use in 47 /// the front-end of a cross compiler so that target arithmetic can be correctly 48 /// performed on the host. Performance should nonetheless be reasonable, 49 /// particularly for its intended use. It may be useful as a base 50 /// implementation for a run-time library during development of a faster 51 /// target-specific one. 52 /// 53 /// All 5 rounding modes in the IEEE-754R draft are handled correctly for all 54 /// implemented operations. Currently implemented operations are add, subtract, 55 /// multiply, divide, fused-multiply-add, conversion-to-float, 56 /// conversion-to-integer and conversion-from-integer. New rounding modes 57 /// (e.g. away from zero) can be added with three or four lines of code. 58 /// 59 /// Four formats are built-in: IEEE single precision, double precision, 60 /// quadruple precision, and x87 80-bit extended double (when operating with 61 /// full extended precision). Adding a new format that obeys IEEE semantics 62 /// only requires adding two lines of code: a declaration and definition of the 63 /// format. 64 /// 65 /// All operations return the status of that operation as an exception bit-mask, 66 /// so multiple operations can be done consecutively with their results or-ed 67 /// together. The returned status can be useful for compiler diagnostics; e.g., 68 /// inexact, underflow and overflow can be easily diagnosed on constant folding, 69 /// and compiler optimizers can determine what exceptions would be raised by 70 /// folding operations and optimize, or perhaps not optimize, accordingly. 71 /// 72 /// At present, underflow tininess is detected after rounding; it should be 73 /// straight forward to add support for the before-rounding case too. 74 /// 75 /// The library reads hexadecimal floating point numbers as per C99, and 76 /// correctly rounds if necessary according to the specified rounding mode. 77 /// Syntax is required to have been validated by the caller. It also converts 78 /// floating point numbers to hexadecimal text as per the C99 %a and %A 79 /// conversions. The output precision (or alternatively the natural minimal 80 /// precision) can be specified; if the requested precision is less than the 81 /// natural precision the output is correctly rounded for the specified rounding 82 /// mode. 83 /// 84 /// It also reads decimal floating point numbers and correctly rounds according 85 /// to the specified rounding mode. 86 /// 87 /// Conversion to decimal text is not currently implemented. 88 /// 89 /// Non-zero finite numbers are represented internally as a sign bit, a 16-bit 90 /// signed exponent, and the significand as an array of integer parts. After 91 /// normalization of a number of precision P the exponent is within the range of 92 /// the format, and if the number is not denormal the P-th bit of the 93 /// significand is set as an explicit integer bit. For denormals the most 94 /// significant bit is shifted right so that the exponent is maintained at the 95 /// format's minimum, so that the smallest denormal has just the least 96 /// significant bit of the significand set. The sign of zeroes and infinities 97 /// is significant; the exponent and significand of such numbers is not stored, 98 /// but has a known implicit (deterministic) value: 0 for the significands, 0 99 /// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and 100 /// significand are deterministic, although not really meaningful, and preserved 101 /// in non-conversion operations. The exponent is implicitly all 1 bits. 102 /// 103 /// APFloat does not provide any exception handling beyond default exception 104 /// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause 105 /// by encoding Signaling NaNs with the first bit of its trailing significand as 106 /// 0. 107 /// 108 /// TODO 109 /// ==== 110 /// 111 /// Some features that may or may not be worth adding: 112 /// 113 /// Binary to decimal conversion (hard). 114 /// 115 /// Optional ability to detect underflow tininess before rounding. 116 /// 117 /// New formats: x87 in single and double precision mode (IEEE apart from 118 /// extended exponent range) (hard). 119 /// 120 /// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward. 121 /// 122 class APFloat { 123 public: 124 125 /// A signed type to represent a floating point numbers unbiased exponent. 126 typedef signed short ExponentType; 127 128 /// \name Floating Point Semantics. 129 /// @{ 130 131 static const fltSemantics IEEEhalf; 132 static const fltSemantics IEEEsingle; 133 static const fltSemantics IEEEdouble; 134 static const fltSemantics IEEEquad; 135 static const fltSemantics PPCDoubleDouble; 136 static const fltSemantics x87DoubleExtended; 137 138 /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with 139 /// anything real. 140 static const fltSemantics Bogus; 141 142 /// @} 143 144 static unsigned int semanticsPrecision(const fltSemantics &); 145 146 /// IEEE-754R 5.11: Floating Point Comparison Relations. 147 enum cmpResult { 148 cmpLessThan, 149 cmpEqual, 150 cmpGreaterThan, 151 cmpUnordered 152 }; 153 154 /// IEEE-754R 4.3: Rounding-direction attributes. 155 enum roundingMode { 156 rmNearestTiesToEven, 157 rmTowardPositive, 158 rmTowardNegative, 159 rmTowardZero, 160 rmNearestTiesToAway 161 }; 162 163 /// IEEE-754R 7: Default exception handling. 164 /// 165 /// opUnderflow or opOverflow are always returned or-ed with opInexact. 166 enum opStatus { 167 opOK = 0x00, 168 opInvalidOp = 0x01, 169 opDivByZero = 0x02, 170 opOverflow = 0x04, 171 opUnderflow = 0x08, 172 opInexact = 0x10 173 }; 174 175 /// Category of internally-represented number. 176 enum fltCategory { 177 fcInfinity, 178 fcNaN, 179 fcNormal, 180 fcZero 181 }; 182 183 /// Convenience enum used to construct an uninitialized APFloat. 184 enum uninitializedTag { 185 uninitialized 186 }; 187 188 /// \name Constructors 189 /// @{ 190 191 APFloat(const fltSemantics &); // Default construct to 0.0 192 APFloat(const fltSemantics &, StringRef); 193 APFloat(const fltSemantics &, integerPart); 194 APFloat(const fltSemantics &, uninitializedTag); 195 APFloat(const fltSemantics &, const APInt &); 196 explicit APFloat(double d); 197 explicit APFloat(float f); 198 APFloat(const APFloat &); 199 APFloat(APFloat &&); 200 ~APFloat(); 201 202 /// @} 203 204 /// \brief Returns whether this instance allocated memory. needsCleanup()205 bool needsCleanup() const { return partCount() > 1; } 206 207 /// \name Convenience "constructors" 208 /// @{ 209 210 /// Factory for Positive and Negative Zero. 211 /// 212 /// \param Negative True iff the number should be negative. 213 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) { 214 APFloat Val(Sem, uninitialized); 215 Val.makeZero(Negative); 216 return Val; 217 } 218 219 /// Factory for Positive and Negative Infinity. 220 /// 221 /// \param Negative True iff the number should be negative. 222 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) { 223 APFloat Val(Sem, uninitialized); 224 Val.makeInf(Negative); 225 return Val; 226 } 227 228 /// Factory for QNaN values. 229 /// 230 /// \param Negative - True iff the NaN generated should be negative. 231 /// \param type - The unspecified fill bits for creating the NaN, 0 by 232 /// default. The value is truncated as necessary. 233 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false, 234 unsigned type = 0) { 235 if (type) { 236 APInt fill(64, type); 237 return getQNaN(Sem, Negative, &fill); 238 } else { 239 return getQNaN(Sem, Negative, nullptr); 240 } 241 } 242 243 /// Factory for QNaN values. 244 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false, 245 const APInt *payload = nullptr) { 246 return makeNaN(Sem, false, Negative, payload); 247 } 248 249 /// Factory for SNaN values. 250 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false, 251 const APInt *payload = nullptr) { 252 return makeNaN(Sem, true, Negative, payload); 253 } 254 255 /// Returns the largest finite number in the given semantics. 256 /// 257 /// \param Negative - True iff the number should be negative 258 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false); 259 260 /// Returns the smallest (by magnitude) finite number in the given semantics. 261 /// Might be denormalized, which implies a relative loss of precision. 262 /// 263 /// \param Negative - True iff the number should be negative 264 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false); 265 266 /// Returns the smallest (by magnitude) normalized finite number in the given 267 /// semantics. 268 /// 269 /// \param Negative - True iff the number should be negative 270 static APFloat getSmallestNormalized(const fltSemantics &Sem, 271 bool Negative = false); 272 273 /// Returns a float which is bitcasted from an all one value int. 274 /// 275 /// \param BitWidth - Select float type 276 /// \param isIEEE - If 128 bit number, select between PPC and IEEE 277 static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false); 278 279 /// @} 280 281 /// Used to insert APFloat objects, or objects that contain APFloat objects, 282 /// into FoldingSets. 283 void Profile(FoldingSetNodeID &NID) const; 284 285 /// \brief Used by the Bitcode serializer to emit APInts to Bitcode. 286 void Emit(Serializer &S) const; 287 288 /// \brief Used by the Bitcode deserializer to deserialize APInts. 289 static APFloat ReadVal(Deserializer &D); 290 291 /// \name Arithmetic 292 /// @{ 293 294 opStatus add(const APFloat &, roundingMode); 295 opStatus subtract(const APFloat &, roundingMode); 296 opStatus multiply(const APFloat &, roundingMode); 297 opStatus divide(const APFloat &, roundingMode); 298 /// IEEE remainder. 299 opStatus remainder(const APFloat &); 300 /// C fmod, or llvm frem. 301 opStatus mod(const APFloat &, roundingMode); 302 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode); 303 opStatus roundToIntegral(roundingMode); 304 /// IEEE-754R 5.3.1: nextUp/nextDown. 305 opStatus next(bool nextDown); 306 307 /// @} 308 309 /// \name Sign operations. 310 /// @{ 311 312 void changeSign(); 313 void clearSign(); 314 void copySign(const APFloat &); 315 316 /// @} 317 318 /// \name Conversions 319 /// @{ 320 321 opStatus convert(const fltSemantics &, roundingMode, bool *); 322 opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode, 323 bool *) const; 324 opStatus convertToInteger(APSInt &, roundingMode, bool *) const; 325 opStatus convertFromAPInt(const APInt &, bool, roundingMode); 326 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int, 327 bool, roundingMode); 328 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int, 329 bool, roundingMode); 330 opStatus convertFromString(StringRef, roundingMode); 331 APInt bitcastToAPInt() const; 332 double convertToDouble() const; 333 float convertToFloat() const; 334 335 /// @} 336 337 /// The definition of equality is not straightforward for floating point, so 338 /// we won't use operator==. Use one of the following, or write whatever it 339 /// is you really mean. 340 bool operator==(const APFloat &) const LLVM_DELETED_FUNCTION; 341 342 /// IEEE comparison with another floating point number (NaNs compare 343 /// unordered, 0==-0). 344 cmpResult compare(const APFloat &) const; 345 346 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0). 347 bool bitwiseIsEqual(const APFloat &) const; 348 349 /// Write out a hexadecimal representation of the floating point value to DST, 350 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d. 351 /// Return the number of characters written, excluding the terminating NUL. 352 unsigned int convertToHexString(char *dst, unsigned int hexDigits, 353 bool upperCase, roundingMode) const; 354 355 /// \name IEEE-754R 5.7.2 General operations. 356 /// @{ 357 358 /// IEEE-754R isSignMinus: Returns true if and only if the current value is 359 /// negative. 360 /// 361 /// This applies to zeros and NaNs as well. isNegative()362 bool isNegative() const { return sign; } 363 364 /// IEEE-754R isNormal: Returns true if and only if the current value is normal. 365 /// 366 /// This implies that the current value of the float is not zero, subnormal, 367 /// infinite, or NaN following the definition of normality from IEEE-754R. isNormal()368 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); } 369 370 /// Returns true if and only if the current value is zero, subnormal, or 371 /// normal. 372 /// 373 /// This means that the value is not infinite or NaN. isFinite()374 bool isFinite() const { return !isNaN() && !isInfinity(); } 375 376 /// Returns true if and only if the float is plus or minus zero. isZero()377 bool isZero() const { return category == fcZero; } 378 379 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a 380 /// denormal. 381 bool isDenormal() const; 382 383 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity. isInfinity()384 bool isInfinity() const { return category == fcInfinity; } 385 386 /// Returns true if and only if the float is a quiet or signaling NaN. isNaN()387 bool isNaN() const { return category == fcNaN; } 388 389 /// Returns true if and only if the float is a signaling NaN. 390 bool isSignaling() const; 391 392 /// @} 393 394 /// \name Simple Queries 395 /// @{ 396 getCategory()397 fltCategory getCategory() const { return category; } getSemantics()398 const fltSemantics &getSemantics() const { return *semantics; } isNonZero()399 bool isNonZero() const { return category != fcZero; } isFiniteNonZero()400 bool isFiniteNonZero() const { return isFinite() && !isZero(); } isPosZero()401 bool isPosZero() const { return isZero() && !isNegative(); } isNegZero()402 bool isNegZero() const { return isZero() && isNegative(); } 403 404 /// Returns true if and only if the number has the smallest possible non-zero 405 /// magnitude in the current semantics. 406 bool isSmallest() const; 407 408 /// Returns true if and only if the number has the largest possible finite 409 /// magnitude in the current semantics. 410 bool isLargest() const; 411 412 /// @} 413 414 APFloat &operator=(const APFloat &); 415 APFloat &operator=(APFloat &&); 416 417 /// \brief Overload to compute a hash code for an APFloat value. 418 /// 419 /// Note that the use of hash codes for floating point values is in general 420 /// frought with peril. Equality is hard to define for these values. For 421 /// example, should negative and positive zero hash to different codes? Are 422 /// they equal or not? This hash value implementation specifically 423 /// emphasizes producing different codes for different inputs in order to 424 /// be used in canonicalization and memoization. As such, equality is 425 /// bitwiseIsEqual, and 0 != -0. 426 friend hash_code hash_value(const APFloat &Arg); 427 428 /// Converts this value into a decimal string. 429 /// 430 /// \param FormatPrecision The maximum number of digits of 431 /// precision to output. If there are fewer digits available, 432 /// zero padding will not be used unless the value is 433 /// integral and small enough to be expressed in 434 /// FormatPrecision digits. 0 means to use the natural 435 /// precision of the number. 436 /// \param FormatMaxPadding The maximum number of zeros to 437 /// consider inserting before falling back to scientific 438 /// notation. 0 means to always use scientific notation. 439 /// 440 /// Number Precision MaxPadding Result 441 /// ------ --------- ---------- ------ 442 /// 1.01E+4 5 2 10100 443 /// 1.01E+4 4 2 1.01E+4 444 /// 1.01E+4 5 1 1.01E+4 445 /// 1.01E-2 5 2 0.0101 446 /// 1.01E-2 4 2 0.0101 447 /// 1.01E-2 4 1 1.01E-2 448 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0, 449 unsigned FormatMaxPadding = 3) const; 450 451 /// If this value has an exact multiplicative inverse, store it in inv and 452 /// return true. 453 bool getExactInverse(APFloat *inv) const; 454 455 private: 456 457 /// \name Simple Queries 458 /// @{ 459 460 integerPart *significandParts(); 461 const integerPart *significandParts() const; 462 unsigned int partCount() const; 463 464 /// @} 465 466 /// \name Significand operations. 467 /// @{ 468 469 integerPart addSignificand(const APFloat &); 470 integerPart subtractSignificand(const APFloat &, integerPart); 471 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract); 472 lostFraction multiplySignificand(const APFloat &, const APFloat *); 473 lostFraction divideSignificand(const APFloat &); 474 void incrementSignificand(); 475 void initialize(const fltSemantics *); 476 void shiftSignificandLeft(unsigned int); 477 lostFraction shiftSignificandRight(unsigned int); 478 unsigned int significandLSB() const; 479 unsigned int significandMSB() const; 480 void zeroSignificand(); 481 /// Return true if the significand excluding the integral bit is all ones. 482 bool isSignificandAllOnes() const; 483 /// Return true if the significand excluding the integral bit is all zeros. 484 bool isSignificandAllZeros() const; 485 486 /// @} 487 488 /// \name Arithmetic on special values. 489 /// @{ 490 491 opStatus addOrSubtractSpecials(const APFloat &, bool subtract); 492 opStatus divideSpecials(const APFloat &); 493 opStatus multiplySpecials(const APFloat &); 494 opStatus modSpecials(const APFloat &); 495 496 /// @} 497 498 /// \name Special value setters. 499 /// @{ 500 501 void makeLargest(bool Neg = false); 502 void makeSmallest(bool Neg = false); 503 void makeNaN(bool SNaN = false, bool Neg = false, 504 const APInt *fill = nullptr); 505 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative, 506 const APInt *fill); 507 void makeInf(bool Neg = false); 508 void makeZero(bool Neg = false); 509 510 /// @} 511 512 /// \name Miscellany 513 /// @{ 514 515 bool convertFromStringSpecials(StringRef str); 516 opStatus normalize(roundingMode, lostFraction); 517 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract); 518 cmpResult compareAbsoluteValue(const APFloat &) const; 519 opStatus handleOverflow(roundingMode); 520 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const; 521 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool, 522 roundingMode, bool *) const; 523 opStatus convertFromUnsignedParts(const integerPart *, unsigned int, 524 roundingMode); 525 opStatus convertFromHexadecimalString(StringRef, roundingMode); 526 opStatus convertFromDecimalString(StringRef, roundingMode); 527 char *convertNormalToHexString(char *, unsigned int, bool, 528 roundingMode) const; 529 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int, 530 roundingMode); 531 532 /// @} 533 534 APInt convertHalfAPFloatToAPInt() const; 535 APInt convertFloatAPFloatToAPInt() const; 536 APInt convertDoubleAPFloatToAPInt() const; 537 APInt convertQuadrupleAPFloatToAPInt() const; 538 APInt convertF80LongDoubleAPFloatToAPInt() const; 539 APInt convertPPCDoubleDoubleAPFloatToAPInt() const; 540 void initFromAPInt(const fltSemantics *Sem, const APInt &api); 541 void initFromHalfAPInt(const APInt &api); 542 void initFromFloatAPInt(const APInt &api); 543 void initFromDoubleAPInt(const APInt &api); 544 void initFromQuadrupleAPInt(const APInt &api); 545 void initFromF80LongDoubleAPInt(const APInt &api); 546 void initFromPPCDoubleDoubleAPInt(const APInt &api); 547 548 void assign(const APFloat &); 549 void copySignificand(const APFloat &); 550 void freeSignificand(); 551 552 /// The semantics that this value obeys. 553 const fltSemantics *semantics; 554 555 /// A binary fraction with an explicit integer bit. 556 /// 557 /// The significand must be at least one bit wider than the target precision. 558 union Significand { 559 integerPart part; 560 integerPart *parts; 561 } significand; 562 563 /// The signed unbiased exponent of the value. 564 ExponentType exponent; 565 566 /// What kind of floating point number this is. 567 /// 568 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it. 569 /// Using the extra bit keeps it from failing under VisualStudio. 570 fltCategory category : 3; 571 572 /// Sign bit of the number. 573 unsigned int sign : 1; 574 }; 575 576 /// See friend declaration above. 577 /// 578 /// This additional declaration is required in order to compile LLVM with IBM 579 /// xlC compiler. 580 hash_code hash_value(const APFloat &Arg); 581 } // namespace llvm 582 583 #endif // LLVM_ADT_APFLOAT_H 584