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 static ExponentType semanticsMinExponent(const fltSemantics &); 146 static ExponentType semanticsMaxExponent(const fltSemantics &); 147 static unsigned int semanticsSizeInBits(const fltSemantics &); 148 149 /// IEEE-754R 5.11: Floating Point Comparison Relations. 150 enum cmpResult { 151 cmpLessThan, 152 cmpEqual, 153 cmpGreaterThan, 154 cmpUnordered 155 }; 156 157 /// IEEE-754R 4.3: Rounding-direction attributes. 158 enum roundingMode { 159 rmNearestTiesToEven, 160 rmTowardPositive, 161 rmTowardNegative, 162 rmTowardZero, 163 rmNearestTiesToAway 164 }; 165 166 /// IEEE-754R 7: Default exception handling. 167 /// 168 /// opUnderflow or opOverflow are always returned or-ed with opInexact. 169 enum opStatus { 170 opOK = 0x00, 171 opInvalidOp = 0x01, 172 opDivByZero = 0x02, 173 opOverflow = 0x04, 174 opUnderflow = 0x08, 175 opInexact = 0x10 176 }; 177 178 /// Category of internally-represented number. 179 enum fltCategory { 180 fcInfinity, 181 fcNaN, 182 fcNormal, 183 fcZero 184 }; 185 186 /// Convenience enum used to construct an uninitialized APFloat. 187 enum uninitializedTag { 188 uninitialized 189 }; 190 191 /// \name Constructors 192 /// @{ 193 194 APFloat(const fltSemantics &); // Default construct to 0.0 195 APFloat(const fltSemantics &, StringRef); 196 APFloat(const fltSemantics &, integerPart); 197 APFloat(const fltSemantics &, uninitializedTag); 198 APFloat(const fltSemantics &, const APInt &); 199 explicit APFloat(double d); 200 explicit APFloat(float f); 201 APFloat(const APFloat &); 202 APFloat(APFloat &&); 203 ~APFloat(); 204 205 /// @} 206 207 /// \brief Returns whether this instance allocated memory. 208 bool needsCleanup() const { return partCount() > 1; } 209 210 /// \name Convenience "constructors" 211 /// @{ 212 213 /// Factory for Positive and Negative Zero. 214 /// 215 /// \param Negative True iff the number should be negative. 216 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) { 217 APFloat Val(Sem, uninitialized); 218 Val.makeZero(Negative); 219 return Val; 220 } 221 222 /// Factory for Positive and Negative Infinity. 223 /// 224 /// \param Negative True iff the number should be negative. 225 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) { 226 APFloat Val(Sem, uninitialized); 227 Val.makeInf(Negative); 228 return Val; 229 } 230 231 /// Factory for QNaN values. 232 /// 233 /// \param Negative - True iff the NaN generated should be negative. 234 /// \param type - The unspecified fill bits for creating the NaN, 0 by 235 /// default. The value is truncated as necessary. 236 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false, 237 unsigned type = 0) { 238 if (type) { 239 APInt fill(64, type); 240 return getQNaN(Sem, Negative, &fill); 241 } else { 242 return getQNaN(Sem, Negative, nullptr); 243 } 244 } 245 246 /// Factory for QNaN values. 247 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false, 248 const APInt *payload = nullptr) { 249 return makeNaN(Sem, false, Negative, payload); 250 } 251 252 /// Factory for SNaN values. 253 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false, 254 const APInt *payload = nullptr) { 255 return makeNaN(Sem, true, Negative, payload); 256 } 257 258 /// Returns the largest finite number in the given semantics. 259 /// 260 /// \param Negative - True iff the number should be negative 261 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false); 262 263 /// Returns the smallest (by magnitude) finite number in the given semantics. 264 /// Might be denormalized, which implies a relative loss of precision. 265 /// 266 /// \param Negative - True iff the number should be negative 267 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false); 268 269 /// Returns the smallest (by magnitude) normalized finite number in the given 270 /// semantics. 271 /// 272 /// \param Negative - True iff the number should be negative 273 static APFloat getSmallestNormalized(const fltSemantics &Sem, 274 bool Negative = false); 275 276 /// Returns a float which is bitcasted from an all one value int. 277 /// 278 /// \param BitWidth - Select float type 279 /// \param isIEEE - If 128 bit number, select between PPC and IEEE 280 static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false); 281 282 /// Returns the size of the floating point number (in bits) in the given 283 /// semantics. 284 static unsigned getSizeInBits(const fltSemantics &Sem); 285 286 /// @} 287 288 /// Used to insert APFloat objects, or objects that contain APFloat objects, 289 /// into FoldingSets. 290 void Profile(FoldingSetNodeID &NID) const; 291 292 /// \name Arithmetic 293 /// @{ 294 295 opStatus add(const APFloat &, roundingMode); 296 opStatus subtract(const APFloat &, roundingMode); 297 opStatus multiply(const APFloat &, roundingMode); 298 opStatus divide(const APFloat &, roundingMode); 299 /// IEEE remainder. 300 opStatus remainder(const APFloat &); 301 /// C fmod, or llvm frem. 302 opStatus mod(const APFloat &); 303 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode); 304 opStatus roundToIntegral(roundingMode); 305 /// IEEE-754R 5.3.1: nextUp/nextDown. 306 opStatus next(bool nextDown); 307 308 /// \brief Operator+ overload which provides the default 309 /// \c nmNearestTiesToEven rounding mode and *no* error checking. 310 APFloat operator+(const APFloat &RHS) const { 311 APFloat Result = *this; 312 Result.add(RHS, rmNearestTiesToEven); 313 return Result; 314 } 315 316 /// \brief Operator- overload which provides the default 317 /// \c nmNearestTiesToEven rounding mode and *no* error checking. 318 APFloat operator-(const APFloat &RHS) const { 319 APFloat Result = *this; 320 Result.subtract(RHS, rmNearestTiesToEven); 321 return Result; 322 } 323 324 /// \brief Operator* overload which provides the default 325 /// \c nmNearestTiesToEven rounding mode and *no* error checking. 326 APFloat operator*(const APFloat &RHS) const { 327 APFloat Result = *this; 328 Result.multiply(RHS, rmNearestTiesToEven); 329 return Result; 330 } 331 332 /// \brief Operator/ overload which provides the default 333 /// \c nmNearestTiesToEven rounding mode and *no* error checking. 334 APFloat operator/(const APFloat &RHS) const { 335 APFloat Result = *this; 336 Result.divide(RHS, rmNearestTiesToEven); 337 return Result; 338 } 339 340 /// @} 341 342 /// \name Sign operations. 343 /// @{ 344 345 void changeSign(); 346 void clearSign(); 347 void copySign(const APFloat &); 348 349 /// \brief A static helper to produce a copy of an APFloat value with its sign 350 /// copied from some other APFloat. 351 static APFloat copySign(APFloat Value, const APFloat &Sign) { 352 Value.copySign(Sign); 353 return Value; 354 } 355 356 /// @} 357 358 /// \name Conversions 359 /// @{ 360 361 opStatus convert(const fltSemantics &, roundingMode, bool *); 362 opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode, 363 bool *) const; 364 opStatus convertToInteger(APSInt &, roundingMode, bool *) const; 365 opStatus convertFromAPInt(const APInt &, bool, roundingMode); 366 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int, 367 bool, roundingMode); 368 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int, 369 bool, roundingMode); 370 opStatus convertFromString(StringRef, roundingMode); 371 APInt bitcastToAPInt() const; 372 double convertToDouble() const; 373 float convertToFloat() const; 374 375 /// @} 376 377 /// The definition of equality is not straightforward for floating point, so 378 /// we won't use operator==. Use one of the following, or write whatever it 379 /// is you really mean. 380 bool operator==(const APFloat &) const = delete; 381 382 /// IEEE comparison with another floating point number (NaNs compare 383 /// unordered, 0==-0). 384 cmpResult compare(const APFloat &) const; 385 386 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0). 387 bool bitwiseIsEqual(const APFloat &) const; 388 389 /// Write out a hexadecimal representation of the floating point value to DST, 390 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d. 391 /// Return the number of characters written, excluding the terminating NUL. 392 unsigned int convertToHexString(char *dst, unsigned int hexDigits, 393 bool upperCase, roundingMode) const; 394 395 /// \name IEEE-754R 5.7.2 General operations. 396 /// @{ 397 398 /// IEEE-754R isSignMinus: Returns true if and only if the current value is 399 /// negative. 400 /// 401 /// This applies to zeros and NaNs as well. 402 bool isNegative() const { return sign; } 403 404 /// IEEE-754R isNormal: Returns true if and only if the current value is normal. 405 /// 406 /// This implies that the current value of the float is not zero, subnormal, 407 /// infinite, or NaN following the definition of normality from IEEE-754R. 408 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); } 409 410 /// Returns true if and only if the current value is zero, subnormal, or 411 /// normal. 412 /// 413 /// This means that the value is not infinite or NaN. 414 bool isFinite() const { return !isNaN() && !isInfinity(); } 415 416 /// Returns true if and only if the float is plus or minus zero. 417 bool isZero() const { return category == fcZero; } 418 419 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a 420 /// denormal. 421 bool isDenormal() const; 422 423 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity. 424 bool isInfinity() const { return category == fcInfinity; } 425 426 /// Returns true if and only if the float is a quiet or signaling NaN. 427 bool isNaN() const { return category == fcNaN; } 428 429 /// Returns true if and only if the float is a signaling NaN. 430 bool isSignaling() const; 431 432 /// @} 433 434 /// \name Simple Queries 435 /// @{ 436 437 fltCategory getCategory() const { return category; } 438 const fltSemantics &getSemantics() const { return *semantics; } 439 bool isNonZero() const { return category != fcZero; } 440 bool isFiniteNonZero() const { return isFinite() && !isZero(); } 441 bool isPosZero() const { return isZero() && !isNegative(); } 442 bool isNegZero() const { return isZero() && isNegative(); } 443 444 /// Returns true if and only if the number has the smallest possible non-zero 445 /// magnitude in the current semantics. 446 bool isSmallest() const; 447 448 /// Returns true if and only if the number has the largest possible finite 449 /// magnitude in the current semantics. 450 bool isLargest() const; 451 452 /// Returns true if and only if the number is an exact integer. 453 bool isInteger() const; 454 455 /// @} 456 457 APFloat &operator=(const APFloat &); 458 APFloat &operator=(APFloat &&); 459 460 /// \brief Overload to compute a hash code for an APFloat value. 461 /// 462 /// Note that the use of hash codes for floating point values is in general 463 /// frought with peril. Equality is hard to define for these values. For 464 /// example, should negative and positive zero hash to different codes? Are 465 /// they equal or not? This hash value implementation specifically 466 /// emphasizes producing different codes for different inputs in order to 467 /// be used in canonicalization and memoization. As such, equality is 468 /// bitwiseIsEqual, and 0 != -0. 469 friend hash_code hash_value(const APFloat &Arg); 470 471 /// Converts this value into a decimal string. 472 /// 473 /// \param FormatPrecision The maximum number of digits of 474 /// precision to output. If there are fewer digits available, 475 /// zero padding will not be used unless the value is 476 /// integral and small enough to be expressed in 477 /// FormatPrecision digits. 0 means to use the natural 478 /// precision of the number. 479 /// \param FormatMaxPadding The maximum number of zeros to 480 /// consider inserting before falling back to scientific 481 /// notation. 0 means to always use scientific notation. 482 /// 483 /// Number Precision MaxPadding Result 484 /// ------ --------- ---------- ------ 485 /// 1.01E+4 5 2 10100 486 /// 1.01E+4 4 2 1.01E+4 487 /// 1.01E+4 5 1 1.01E+4 488 /// 1.01E-2 5 2 0.0101 489 /// 1.01E-2 4 2 0.0101 490 /// 1.01E-2 4 1 1.01E-2 491 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0, 492 unsigned FormatMaxPadding = 3) const; 493 494 /// If this value has an exact multiplicative inverse, store it in inv and 495 /// return true. 496 bool getExactInverse(APFloat *inv) const; 497 498 /// \brief Enumeration of \c ilogb error results. 499 enum IlogbErrorKinds { 500 IEK_Zero = INT_MIN+1, 501 IEK_NaN = INT_MIN, 502 IEK_Inf = INT_MAX 503 }; 504 505 /// \brief Returns the exponent of the internal representation of the APFloat. 506 /// 507 /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)). 508 /// For special APFloat values, this returns special error codes: 509 /// 510 /// NaN -> \c IEK_NaN 511 /// 0 -> \c IEK_Zero 512 /// Inf -> \c IEK_Inf 513 /// 514 friend int ilogb(const APFloat &Arg) { 515 if (Arg.isNaN()) 516 return IEK_NaN; 517 if (Arg.isZero()) 518 return IEK_Zero; 519 if (Arg.isInfinity()) 520 return IEK_Inf; 521 522 return Arg.exponent; 523 } 524 525 /// \brief Returns: X * 2^Exp for integral exponents. 526 friend APFloat scalbn(APFloat X, int Exp); 527 528 private: 529 530 /// \name Simple Queries 531 /// @{ 532 533 integerPart *significandParts(); 534 const integerPart *significandParts() const; 535 unsigned int partCount() const; 536 537 /// @} 538 539 /// \name Significand operations. 540 /// @{ 541 542 integerPart addSignificand(const APFloat &); 543 integerPart subtractSignificand(const APFloat &, integerPart); 544 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract); 545 lostFraction multiplySignificand(const APFloat &, const APFloat *); 546 lostFraction divideSignificand(const APFloat &); 547 void incrementSignificand(); 548 void initialize(const fltSemantics *); 549 void shiftSignificandLeft(unsigned int); 550 lostFraction shiftSignificandRight(unsigned int); 551 unsigned int significandLSB() const; 552 unsigned int significandMSB() const; 553 void zeroSignificand(); 554 /// Return true if the significand excluding the integral bit is all ones. 555 bool isSignificandAllOnes() const; 556 /// Return true if the significand excluding the integral bit is all zeros. 557 bool isSignificandAllZeros() const; 558 559 /// @} 560 561 /// \name Arithmetic on special values. 562 /// @{ 563 564 opStatus addOrSubtractSpecials(const APFloat &, bool subtract); 565 opStatus divideSpecials(const APFloat &); 566 opStatus multiplySpecials(const APFloat &); 567 opStatus modSpecials(const APFloat &); 568 569 /// @} 570 571 /// \name Special value setters. 572 /// @{ 573 574 void makeLargest(bool Neg = false); 575 void makeSmallest(bool Neg = false); 576 void makeNaN(bool SNaN = false, bool Neg = false, 577 const APInt *fill = nullptr); 578 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative, 579 const APInt *fill); 580 void makeInf(bool Neg = false); 581 void makeZero(bool Neg = false); 582 583 /// @} 584 585 /// \name Miscellany 586 /// @{ 587 588 bool convertFromStringSpecials(StringRef str); 589 opStatus normalize(roundingMode, lostFraction); 590 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract); 591 cmpResult compareAbsoluteValue(const APFloat &) const; 592 opStatus handleOverflow(roundingMode); 593 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const; 594 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool, 595 roundingMode, bool *) const; 596 opStatus convertFromUnsignedParts(const integerPart *, unsigned int, 597 roundingMode); 598 opStatus convertFromHexadecimalString(StringRef, roundingMode); 599 opStatus convertFromDecimalString(StringRef, roundingMode); 600 char *convertNormalToHexString(char *, unsigned int, bool, 601 roundingMode) const; 602 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int, 603 roundingMode); 604 605 /// @} 606 607 APInt convertHalfAPFloatToAPInt() const; 608 APInt convertFloatAPFloatToAPInt() const; 609 APInt convertDoubleAPFloatToAPInt() const; 610 APInt convertQuadrupleAPFloatToAPInt() const; 611 APInt convertF80LongDoubleAPFloatToAPInt() const; 612 APInt convertPPCDoubleDoubleAPFloatToAPInt() const; 613 void initFromAPInt(const fltSemantics *Sem, const APInt &api); 614 void initFromHalfAPInt(const APInt &api); 615 void initFromFloatAPInt(const APInt &api); 616 void initFromDoubleAPInt(const APInt &api); 617 void initFromQuadrupleAPInt(const APInt &api); 618 void initFromF80LongDoubleAPInt(const APInt &api); 619 void initFromPPCDoubleDoubleAPInt(const APInt &api); 620 621 void assign(const APFloat &); 622 void copySignificand(const APFloat &); 623 void freeSignificand(); 624 625 /// The semantics that this value obeys. 626 const fltSemantics *semantics; 627 628 /// A binary fraction with an explicit integer bit. 629 /// 630 /// The significand must be at least one bit wider than the target precision. 631 union Significand { 632 integerPart part; 633 integerPart *parts; 634 } significand; 635 636 /// The signed unbiased exponent of the value. 637 ExponentType exponent; 638 639 /// What kind of floating point number this is. 640 /// 641 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it. 642 /// Using the extra bit keeps it from failing under VisualStudio. 643 fltCategory category : 3; 644 645 /// Sign bit of the number. 646 unsigned int sign : 1; 647 }; 648 649 /// See friend declarations above. 650 /// 651 /// These additional declarations are required in order to compile LLVM with IBM 652 /// xlC compiler. 653 hash_code hash_value(const APFloat &Arg); 654 APFloat scalbn(APFloat X, int Exp); 655 656 /// \brief Returns the absolute value of the argument. 657 inline APFloat abs(APFloat X) { 658 X.clearSign(); 659 return X; 660 } 661 662 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if 663 /// both are not NaN. If either argument is a NaN, returns the other argument. 664 LLVM_READONLY 665 inline APFloat minnum(const APFloat &A, const APFloat &B) { 666 if (A.isNaN()) 667 return B; 668 if (B.isNaN()) 669 return A; 670 return (B.compare(A) == APFloat::cmpLessThan) ? B : A; 671 } 672 673 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if 674 /// both are not NaN. If either argument is a NaN, returns the other argument. 675 LLVM_READONLY 676 inline APFloat maxnum(const APFloat &A, const APFloat &B) { 677 if (A.isNaN()) 678 return B; 679 if (B.isNaN()) 680 return A; 681 return (A.compare(B) == APFloat::cmpLessThan) ? B : A; 682 } 683 684 } // namespace llvm 685 686 #endif // LLVM_ADT_APFLOAT_H 687
