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 /// \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.
copySign(APFloat Value,const APFloat & Sign)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.
isNegative()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.
isNormal()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.
isFinite()407 bool isFinite() const { return !isNaN() && !isInfinity(); }
408
409 /// Returns true if and only if the float is plus or minus zero.
isZero()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.
isInfinity()417 bool isInfinity() const { return category == fcInfinity; }
418
419 /// Returns true if and only if the float is a quiet or signaling NaN.
isNaN()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
getCategory()430 fltCategory getCategory() const { return category; }
getSemantics()431 const fltSemantics &getSemantics() const { return *semantics; }
isNonZero()432 bool isNonZero() const { return category != fcZero; }
isFiniteNonZero()433 bool isFiniteNonZero() const { return isFinite() && !isZero(); }
isPosZero()434 bool isPosZero() const { return isZero() && !isNegative(); }
isNegZero()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 ///
ilogb(const APFloat & Arg)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.
abs(APFloat X)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
minnum(const APFloat & A,const APFloat & B)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
maxnum(const APFloat & A,const APFloat & B)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