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 opStatus roundToIntegral(roundingMode); 278 279 /* Sign operations. */ 280 void changeSign(); 281 void clearSign(); 282 void copySign(const APFloat &); 283 284 /* Conversions. */ 285 opStatus convert(const fltSemantics &, roundingMode, bool *); 286 opStatus convertToInteger(integerPart *, unsigned int, bool, 287 roundingMode, bool *) const; 288 opStatus convertToInteger(APSInt&, roundingMode, bool *) const; 289 opStatus convertFromAPInt(const APInt &, 290 bool, roundingMode); 291 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int, 292 bool, roundingMode); 293 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int, 294 bool, roundingMode); 295 opStatus convertFromString(StringRef, roundingMode); 296 APInt bitcastToAPInt() const; 297 double convertToDouble() const; 298 float convertToFloat() const; 299 300 /* The definition of equality is not straightforward for floating point, 301 so we won't use operator==. Use one of the following, or write 302 whatever it is you really mean. */ 303 // bool operator==(const APFloat &) const; // DO NOT IMPLEMENT 304 305 /* IEEE comparison with another floating point number (NaNs 306 compare unordered, 0==-0). */ 307 cmpResult compare(const APFloat &) const; 308 309 /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */ 310 bool bitwiseIsEqual(const APFloat &) const; 311 312 /* Write out a hexadecimal representation of the floating point 313 value to DST, which must be of sufficient size, in the C99 form 314 [-]0xh.hhhhp[+-]d. Return the number of characters written, 315 excluding the terminating NUL. */ 316 unsigned int convertToHexString(char *dst, unsigned int hexDigits, 317 bool upperCase, roundingMode) const; 318 319 /* Simple queries. */ 320 fltCategory getCategory() const { return category; } 321 const fltSemantics &getSemantics() const { return *semantics; } 322 bool isZero() const { return category == fcZero; } 323 bool isNonZero() const { return category != fcZero; } 324 bool isNormal() const { return category == fcNormal; } 325 bool isNaN() const { return category == fcNaN; } 326 bool isInfinity() const { return category == fcInfinity; } 327 bool isNegative() const { return sign; } 328 bool isPosZero() const { return isZero() && !isNegative(); } 329 bool isNegZero() const { return isZero() && isNegative(); } 330 331 APFloat& operator=(const APFloat &); 332 333 /// \brief Overload to compute a hash code for an APFloat value. 334 /// 335 /// Note that the use of hash codes for floating point values is in general 336 /// frought with peril. Equality is hard to define for these values. For 337 /// example, should negative and positive zero hash to different codes? Are 338 /// they equal or not? This hash value implementation specifically 339 /// emphasizes producing different codes for different inputs in order to 340 /// be used in canonicalization and memoization. As such, equality is 341 /// bitwiseIsEqual, and 0 != -0. 342 friend hash_code hash_value(const APFloat &Arg); 343 344 /// Converts this value into a decimal string. 345 /// 346 /// \param FormatPrecision The maximum number of digits of 347 /// precision to output. If there are fewer digits available, 348 /// zero padding will not be used unless the value is 349 /// integral and small enough to be expressed in 350 /// FormatPrecision digits. 0 means to use the natural 351 /// precision of the number. 352 /// \param FormatMaxPadding The maximum number of zeros to 353 /// consider inserting before falling back to scientific 354 /// notation. 0 means to always use scientific notation. 355 /// 356 /// Number Precision MaxPadding Result 357 /// ------ --------- ---------- ------ 358 /// 1.01E+4 5 2 10100 359 /// 1.01E+4 4 2 1.01E+4 360 /// 1.01E+4 5 1 1.01E+4 361 /// 1.01E-2 5 2 0.0101 362 /// 1.01E-2 4 2 0.0101 363 /// 1.01E-2 4 1 1.01E-2 364 void toString(SmallVectorImpl<char> &Str, 365 unsigned FormatPrecision = 0, 366 unsigned FormatMaxPadding = 3) const; 367 368 /// getExactInverse - If this value has an exact multiplicative inverse, 369 /// store it in inv and return true. 370 bool getExactInverse(APFloat *inv) const; 371 372 private: 373 374 /* Trivial queries. */ 375 integerPart *significandParts(); 376 const integerPart *significandParts() const; 377 unsigned int partCount() const; 378 379 /* Significand operations. */ 380 integerPart addSignificand(const APFloat &); 381 integerPart subtractSignificand(const APFloat &, integerPart); 382 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract); 383 lostFraction multiplySignificand(const APFloat &, const APFloat *); 384 lostFraction divideSignificand(const APFloat &); 385 void incrementSignificand(); 386 void initialize(const fltSemantics *); 387 void shiftSignificandLeft(unsigned int); 388 lostFraction shiftSignificandRight(unsigned int); 389 unsigned int significandLSB() const; 390 unsigned int significandMSB() const; 391 void zeroSignificand(); 392 393 /* Arithmetic on special values. */ 394 opStatus addOrSubtractSpecials(const APFloat &, bool subtract); 395 opStatus divideSpecials(const APFloat &); 396 opStatus multiplySpecials(const APFloat &); 397 opStatus modSpecials(const APFloat &); 398 399 /* Miscellany. */ 400 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative, 401 const APInt *fill); 402 void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0); 403 opStatus normalize(roundingMode, lostFraction); 404 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract); 405 cmpResult compareAbsoluteValue(const APFloat &) const; 406 opStatus handleOverflow(roundingMode); 407 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const; 408 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool, 409 roundingMode, bool *) const; 410 opStatus convertFromUnsignedParts(const integerPart *, unsigned int, 411 roundingMode); 412 opStatus convertFromHexadecimalString(StringRef, roundingMode); 413 opStatus convertFromDecimalString(StringRef, roundingMode); 414 char *convertNormalToHexString(char *, unsigned int, bool, 415 roundingMode) const; 416 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, 417 int, roundingMode); 418 419 APInt convertHalfAPFloatToAPInt() const; 420 APInt convertFloatAPFloatToAPInt() const; 421 APInt convertDoubleAPFloatToAPInt() const; 422 APInt convertQuadrupleAPFloatToAPInt() const; 423 APInt convertF80LongDoubleAPFloatToAPInt() const; 424 APInt convertPPCDoubleDoubleAPFloatToAPInt() const; 425 void initFromAPInt(const APInt& api, bool isIEEE = false); 426 void initFromHalfAPInt(const APInt& api); 427 void initFromFloatAPInt(const APInt& api); 428 void initFromDoubleAPInt(const APInt& api); 429 void initFromQuadrupleAPInt(const APInt &api); 430 void initFromF80LongDoubleAPInt(const APInt& api); 431 void initFromPPCDoubleDoubleAPInt(const APInt& api); 432 433 void assign(const APFloat &); 434 void copySignificand(const APFloat &); 435 void freeSignificand(); 436 437 /* What kind of semantics does this value obey? */ 438 const fltSemantics *semantics; 439 440 /* Significand - the fraction with an explicit integer bit. Must be 441 at least one bit wider than the target precision. */ 442 union Significand 443 { 444 integerPart part; 445 integerPart *parts; 446 } significand; 447 448 /* The exponent - a signed number. */ 449 exponent_t exponent; 450 451 /* What kind of floating point number this is. */ 452 /* Only 2 bits are required, but VisualStudio incorrectly sign extends 453 it. Using the extra bit keeps it from failing under VisualStudio */ 454 fltCategory category: 3; 455 456 /* The sign bit of this number. */ 457 unsigned int sign: 1; 458 459 /* For PPCDoubleDouble, we have a second exponent and sign (the second 460 significand is appended to the first one, although it would be wrong to 461 regard these as a single number for arithmetic purposes). These fields 462 are not meaningful for any other type. */ 463 exponent_t exponent2 : 11; 464 unsigned int sign2: 1; 465 }; 466 } /* namespace llvm */ 467 468 #endif /* LLVM_FLOAT_H */ 469
