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. 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 /// \name Arithmetic 286 /// @{ 287 288 opStatus add(const APFloat &, roundingMode); 289 opStatus subtract(const APFloat &, roundingMode); 290 opStatus multiply(const APFloat &, roundingMode); 291 opStatus divide(const APFloat &, roundingMode); 292 /// IEEE remainder. 293 opStatus remainder(const APFloat &); 294 /// C fmod, or llvm frem. 295 opStatus mod(const APFloat &, roundingMode); 296 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode); 297 opStatus roundToIntegral(roundingMode); 298 /// IEEE-754R 5.3.1: nextUp/nextDown. 299 opStatus next(bool nextDown); 300 301 /// \brief Operator+ overload which provides the default 302 /// \c nmNearestTiesToEven rounding mode and *no* error checking. 303 APFloat operator+(const APFloat &RHS) const { 304 APFloat Result = *this; 305 Result.add(RHS, rmNearestTiesToEven); 306 return Result; 307 } 308 309 /// \brief Operator- overload which provides the default 310 /// \c nmNearestTiesToEven rounding mode and *no* error checking. 311 APFloat operator-(const APFloat &RHS) const { 312 APFloat Result = *this; 313 Result.subtract(RHS, rmNearestTiesToEven); 314 return Result; 315 } 316 317 /// \brief Operator* overload which provides the default 318 /// \c nmNearestTiesToEven rounding mode and *no* error checking. 319 APFloat operator*(const APFloat &RHS) const { 320 APFloat Result = *this; 321 Result.multiply(RHS, rmNearestTiesToEven); 322 return Result; 323 } 324 325 /// \brief Operator/ overload which provides the default 326 /// \c nmNearestTiesToEven rounding mode and *no* error checking. 327 APFloat operator/(const APFloat &RHS) const { 328 APFloat Result = *this; 329 Result.divide(RHS, rmNearestTiesToEven); 330 return Result; 331 } 332 333 /// @} 334 335 /// \name Sign operations. 336 /// @{ 337 338 void changeSign(); 339 void clearSign(); 340 void copySign(const APFloat &); 341 342 /// \brief A static helper to produce a copy of an APFloat value with its sign 343 /// copied from some other APFloat. 344 static APFloat copySign(APFloat Value, const APFloat &Sign) { 345 Value.copySign(Sign); 346 return std::move(Value); 347 } 348 349 /// @} 350 351 /// \name Conversions 352 /// @{ 353 354 opStatus convert(const fltSemantics &, roundingMode, bool *); 355 opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode, 356 bool *) const; 357 opStatus convertToInteger(APSInt &, roundingMode, bool *) const; 358 opStatus convertFromAPInt(const APInt &, bool, roundingMode); 359 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int, 360 bool, roundingMode); 361 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int, 362 bool, roundingMode); 363 opStatus convertFromString(StringRef, roundingMode); 364 APInt bitcastToAPInt() const; 365 double convertToDouble() const; 366 float convertToFloat() const; 367 368 /// @} 369 370 /// The definition of equality is not straightforward for floating point, so 371 /// we won't use operator==. Use one of the following, or write whatever it 372 /// is you really mean. 373 bool operator==(const APFloat &) const = delete; 374 375 /// IEEE comparison with another floating point number (NaNs compare 376 /// unordered, 0==-0). 377 cmpResult compare(const APFloat &) const; 378 379 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0). 380 bool bitwiseIsEqual(const APFloat &) const; 381 382 /// Write out a hexadecimal representation of the floating point value to DST, 383 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d. 384 /// Return the number of characters written, excluding the terminating NUL. 385 unsigned int convertToHexString(char *dst, unsigned int hexDigits, 386 bool upperCase, roundingMode) const; 387 388 /// \name IEEE-754R 5.7.2 General operations. 389 /// @{ 390 391 /// IEEE-754R isSignMinus: Returns true if and only if the current value is 392 /// negative. 393 /// 394 /// This applies to zeros and NaNs as well. 395 bool isNegative() const { return sign; } 396 397 /// IEEE-754R isNormal: Returns true if and only if the current value is normal. 398 /// 399 /// This implies that the current value of the float is not zero, subnormal, 400 /// infinite, or NaN following the definition of normality from IEEE-754R. 401 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); } 402 403 /// Returns true if and only if the current value is zero, subnormal, or 404 /// normal. 405 /// 406 /// This means that the value is not infinite or NaN. 407 bool isFinite() const { return !isNaN() && !isInfinity(); } 408 409 /// Returns true if and only if the float is plus or minus zero. 410 bool isZero() const { return category == fcZero; } 411 412 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a 413 /// denormal. 414 bool isDenormal() const; 415 416 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity. 417 bool isInfinity() const { return category == fcInfinity; } 418 419 /// Returns true if and only if the float is a quiet or signaling NaN. 420 bool isNaN() const { return category == fcNaN; } 421 422 /// Returns true if and only if the float is a signaling NaN. 423 bool isSignaling() const; 424 425 /// @} 426 427 /// \name Simple Queries 428 /// @{ 429 430 fltCategory getCategory() const { return category; } 431 const fltSemantics &getSemantics() const { return *semantics; } 432 bool isNonZero() const { return category != fcZero; } 433 bool isFiniteNonZero() const { return isFinite() && !isZero(); } 434 bool isPosZero() const { return isZero() && !isNegative(); } 435 bool isNegZero() const { return isZero() && isNegative(); } 436 437 /// Returns true if and only if the number has the smallest possible non-zero 438 /// magnitude in the current semantics. 439 bool isSmallest() const; 440 441 /// Returns true if and only if the number has the largest possible finite 442 /// magnitude in the current semantics. 443 bool isLargest() const; 444 445 /// @} 446 447 APFloat &operator=(const APFloat &); 448 APFloat &operator=(APFloat &&); 449 450 /// \brief Overload to compute a hash code for an APFloat value. 451 /// 452 /// Note that the use of hash codes for floating point values is in general 453 /// frought with peril. Equality is hard to define for these values. For 454 /// example, should negative and positive zero hash to different codes? Are 455 /// they equal or not? This hash value implementation specifically 456 /// emphasizes producing different codes for different inputs in order to 457 /// be used in canonicalization and memoization. As such, equality is 458 /// bitwiseIsEqual, and 0 != -0. 459 friend hash_code hash_value(const APFloat &Arg); 460 461 /// Converts this value into a decimal string. 462 /// 463 /// \param FormatPrecision The maximum number of digits of 464 /// precision to output. If there are fewer digits available, 465 /// zero padding will not be used unless the value is 466 /// integral and small enough to be expressed in 467 /// FormatPrecision digits. 0 means to use the natural 468 /// precision of the number. 469 /// \param FormatMaxPadding The maximum number of zeros to 470 /// consider inserting before falling back to scientific 471 /// notation. 0 means to always use scientific notation. 472 /// 473 /// Number Precision MaxPadding Result 474 /// ------ --------- ---------- ------ 475 /// 1.01E+4 5 2 10100 476 /// 1.01E+4 4 2 1.01E+4 477 /// 1.01E+4 5 1 1.01E+4 478 /// 1.01E-2 5 2 0.0101 479 /// 1.01E-2 4 2 0.0101 480 /// 1.01E-2 4 1 1.01E-2 481 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0, 482 unsigned FormatMaxPadding = 3) const; 483 484 /// If this value has an exact multiplicative inverse, store it in inv and 485 /// return true. 486 bool getExactInverse(APFloat *inv) const; 487 488 /// \brief Enumeration of \c ilogb error results. 489 enum IlogbErrorKinds { 490 IEK_Zero = INT_MIN+1, 491 IEK_NaN = INT_MIN, 492 IEK_Inf = INT_MAX 493 }; 494 495 /// \brief Returns the exponent of the internal representation of the APFloat. 496 /// 497 /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)). 498 /// For special APFloat values, this returns special error codes: 499 /// 500 /// NaN -> \c IEK_NaN 501 /// 0 -> \c IEK_Zero 502 /// Inf -> \c IEK_Inf 503 /// 504 friend int ilogb(const APFloat &Arg) { 505 if (Arg.isNaN()) 506 return IEK_NaN; 507 if (Arg.isZero()) 508 return IEK_Zero; 509 if (Arg.isInfinity()) 510 return IEK_Inf; 511 512 return Arg.exponent; 513 } 514 515 /// \brief Returns: X * 2^Exp for integral exponents. 516 friend APFloat scalbn(APFloat X, int Exp); 517 518 private: 519 520 /// \name Simple Queries 521 /// @{ 522 523 integerPart *significandParts(); 524 const integerPart *significandParts() const; 525 unsigned int partCount() const; 526 527 /// @} 528 529 /// \name Significand operations. 530 /// @{ 531 532 integerPart addSignificand(const APFloat &); 533 integerPart subtractSignificand(const APFloat &, integerPart); 534 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract); 535 lostFraction multiplySignificand(const APFloat &, const APFloat *); 536 lostFraction divideSignificand(const APFloat &); 537 void incrementSignificand(); 538 void initialize(const fltSemantics *); 539 void shiftSignificandLeft(unsigned int); 540 lostFraction shiftSignificandRight(unsigned int); 541 unsigned int significandLSB() const; 542 unsigned int significandMSB() const; 543 void zeroSignificand(); 544 /// Return true if the significand excluding the integral bit is all ones. 545 bool isSignificandAllOnes() const; 546 /// Return true if the significand excluding the integral bit is all zeros. 547 bool isSignificandAllZeros() const; 548 549 /// @} 550 551 /// \name Arithmetic on special values. 552 /// @{ 553 554 opStatus addOrSubtractSpecials(const APFloat &, bool subtract); 555 opStatus divideSpecials(const APFloat &); 556 opStatus multiplySpecials(const APFloat &); 557 opStatus modSpecials(const APFloat &); 558 559 /// @} 560 561 /// \name Special value setters. 562 /// @{ 563 564 void makeLargest(bool Neg = false); 565 void makeSmallest(bool Neg = false); 566 void makeNaN(bool SNaN = false, bool Neg = false, 567 const APInt *fill = nullptr); 568 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative, 569 const APInt *fill); 570 void makeInf(bool Neg = false); 571 void makeZero(bool Neg = false); 572 573 /// @} 574 575 /// \name Miscellany 576 /// @{ 577 578 bool convertFromStringSpecials(StringRef str); 579 opStatus normalize(roundingMode, lostFraction); 580 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract); 581 cmpResult compareAbsoluteValue(const APFloat &) const; 582 opStatus handleOverflow(roundingMode); 583 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const; 584 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool, 585 roundingMode, bool *) const; 586 opStatus convertFromUnsignedParts(const integerPart *, unsigned int, 587 roundingMode); 588 opStatus convertFromHexadecimalString(StringRef, roundingMode); 589 opStatus convertFromDecimalString(StringRef, roundingMode); 590 char *convertNormalToHexString(char *, unsigned int, bool, 591 roundingMode) const; 592 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int, 593 roundingMode); 594 595 /// @} 596 597 APInt convertHalfAPFloatToAPInt() const; 598 APInt convertFloatAPFloatToAPInt() const; 599 APInt convertDoubleAPFloatToAPInt() const; 600 APInt convertQuadrupleAPFloatToAPInt() const; 601 APInt convertF80LongDoubleAPFloatToAPInt() const; 602 APInt convertPPCDoubleDoubleAPFloatToAPInt() const; 603 void initFromAPInt(const fltSemantics *Sem, const APInt &api); 604 void initFromHalfAPInt(const APInt &api); 605 void initFromFloatAPInt(const APInt &api); 606 void initFromDoubleAPInt(const APInt &api); 607 void initFromQuadrupleAPInt(const APInt &api); 608 void initFromF80LongDoubleAPInt(const APInt &api); 609 void initFromPPCDoubleDoubleAPInt(const APInt &api); 610 611 void assign(const APFloat &); 612 void copySignificand(const APFloat &); 613 void freeSignificand(); 614 615 /// The semantics that this value obeys. 616 const fltSemantics *semantics; 617 618 /// A binary fraction with an explicit integer bit. 619 /// 620 /// The significand must be at least one bit wider than the target precision. 621 union Significand { 622 integerPart part; 623 integerPart *parts; 624 } significand; 625 626 /// The signed unbiased exponent of the value. 627 ExponentType exponent; 628 629 /// What kind of floating point number this is. 630 /// 631 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it. 632 /// Using the extra bit keeps it from failing under VisualStudio. 633 fltCategory category : 3; 634 635 /// Sign bit of the number. 636 unsigned int sign : 1; 637 }; 638 639 /// See friend declarations above. 640 /// 641 /// These additional declarations are required in order to compile LLVM with IBM 642 /// xlC compiler. 643 hash_code hash_value(const APFloat &Arg); 644 APFloat scalbn(APFloat X, int Exp); 645 646 /// \brief Returns the absolute value of the argument. 647 inline APFloat abs(APFloat X) { 648 X.clearSign(); 649 return X; 650 } 651 652 /// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if 653 /// both are not NaN. If either argument is a NaN, returns the other argument. 654 LLVM_READONLY 655 inline APFloat minnum(const APFloat &A, const APFloat &B) { 656 if (A.isNaN()) 657 return B; 658 if (B.isNaN()) 659 return A; 660 return (B.compare(A) == APFloat::cmpLessThan) ? B : A; 661 } 662 663 /// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if 664 /// both are not NaN. If either argument is a NaN, returns the other argument. 665 LLVM_READONLY 666 inline APFloat maxnum(const APFloat &A, const APFloat &B) { 667 if (A.isNaN()) 668 return B; 669 if (B.isNaN()) 670 return A; 671 return (A.compare(B) == APFloat::cmpLessThan) ? B : A; 672 } 673 674 } // namespace llvm 675 676 #endif // LLVM_ADT_APFLOAT_H 677
