1//===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8///
9/// \file
10/// \brief
11/// This file declares a class to represent arbitrary precision floating point
12/// values and provide a variety of arithmetic operations on them.
13///
14//===----------------------------------------------------------------------===//
15
16#ifndef LLVM_ADT_APFLOAT_H
17#define LLVM_ADT_APFLOAT_H
18
19#include "llvm/ADT/APInt.h"
20#include "llvm/ADT/ArrayRef.h"
21#include "llvm/ADT/FloatingPointMode.h"
22#include "llvm/Support/ErrorHandling.h"
23#include <memory>
24
25#define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL) \
26 do { \
27 if (usesLayout<IEEEFloat>(getSemantics())) \
28 return U.IEEE.METHOD_CALL; \
29 if (usesLayout<DoubleAPFloat>(getSemantics())) \
30 return U.Double.METHOD_CALL; \
31 llvm_unreachable("Unexpected semantics"); \
32 } while (false)
33
34namespace llvm {
35
36struct fltSemantics;
37class APSInt;
38class StringRef;
39class APFloat;
40class raw_ostream;
41
42template <typename T> class Expected;
43template <typename T> class SmallVectorImpl;
44
45/// Enum that represents what fraction of the LSB truncated bits of an fp number
46/// represent.
47///
48/// This essentially combines the roles of guard and sticky bits.
49enum lostFraction { // Example of truncated bits:
50 lfExactlyZero, // 000000
51 lfLessThanHalf, // 0xxxxx x's not all zero
52 lfExactlyHalf, // 100000
53 lfMoreThanHalf // 1xxxxx x's not all zero
54};
55
56/// A self-contained host- and target-independent arbitrary-precision
57/// floating-point software implementation.
58///
59/// APFloat uses bignum integer arithmetic as provided by static functions in
60/// the APInt class. The library will work with bignum integers whose parts are
61/// any unsigned type at least 16 bits wide, but 64 bits is recommended.
62///
63/// Written for clarity rather than speed, in particular with a view to use in
64/// the front-end of a cross compiler so that target arithmetic can be correctly
65/// performed on the host. Performance should nonetheless be reasonable,
66/// particularly for its intended use. It may be useful as a base
67/// implementation for a run-time library during development of a faster
68/// target-specific one.
69///
70/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
71/// implemented operations. Currently implemented operations are add, subtract,
72/// multiply, divide, fused-multiply-add, conversion-to-float,
73/// conversion-to-integer and conversion-from-integer. New rounding modes
74/// (e.g. away from zero) can be added with three or four lines of code.
75///
76/// Four formats are built-in: IEEE single precision, double precision,
77/// quadruple precision, and x87 80-bit extended double (when operating with
78/// full extended precision). Adding a new format that obeys IEEE semantics
79/// only requires adding two lines of code: a declaration and definition of the
80/// format.
81///
82/// All operations return the status of that operation as an exception bit-mask,
83/// so multiple operations can be done consecutively with their results or-ed
84/// together. The returned status can be useful for compiler diagnostics; e.g.,
85/// inexact, underflow and overflow can be easily diagnosed on constant folding,
86/// and compiler optimizers can determine what exceptions would be raised by
87/// folding operations and optimize, or perhaps not optimize, accordingly.
88///
89/// At present, underflow tininess is detected after rounding; it should be
90/// straight forward to add support for the before-rounding case too.
91///
92/// The library reads hexadecimal floating point numbers as per C99, and
93/// correctly rounds if necessary according to the specified rounding mode.
94/// Syntax is required to have been validated by the caller. It also converts
95/// floating point numbers to hexadecimal text as per the C99 %a and %A
96/// conversions. The output precision (or alternatively the natural minimal
97/// precision) can be specified; if the requested precision is less than the
98/// natural precision the output is correctly rounded for the specified rounding
99/// mode.
100///
101/// It also reads decimal floating point numbers and correctly rounds according
102/// to the specified rounding mode.
103///
104/// Conversion to decimal text is not currently implemented.
105///
106/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
107/// signed exponent, and the significand as an array of integer parts. After
108/// normalization of a number of precision P the exponent is within the range of
109/// the format, and if the number is not denormal the P-th bit of the
110/// significand is set as an explicit integer bit. For denormals the most
111/// significant bit is shifted right so that the exponent is maintained at the
112/// format's minimum, so that the smallest denormal has just the least
113/// significant bit of the significand set. The sign of zeroes and infinities
114/// is significant; the exponent and significand of such numbers is not stored,
115/// but has a known implicit (deterministic) value: 0 for the significands, 0
116/// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
117/// significand are deterministic, although not really meaningful, and preserved
118/// in non-conversion operations. The exponent is implicitly all 1 bits.
119///
120/// APFloat does not provide any exception handling beyond default exception
121/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
122/// by encoding Signaling NaNs with the first bit of its trailing significand as
123/// 0.
124///
125/// TODO
126/// ====
127///
128/// Some features that may or may not be worth adding:
129///
130/// Binary to decimal conversion (hard).
131///
132/// Optional ability to detect underflow tininess before rounding.
133///
134/// New formats: x87 in single and double precision mode (IEEE apart from
135/// extended exponent range) (hard).
136///
137/// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
138///
139
140// This is the common type definitions shared by APFloat and its internal
141// implementation classes. This struct should not define any non-static data
142// members.
143struct APFloatBase {
144 typedef APInt::WordType integerPart;
145 static constexpr unsigned integerPartWidth = APInt::APINT_BITS_PER_WORD;
146
147 /// A signed type to represent a floating point numbers unbiased exponent.
148 typedef int32_t ExponentType;
149
150 /// \name Floating Point Semantics.
151 /// @{
152 enum Semantics {
153 S_IEEEhalf,
154 S_BFloat,
155 S_IEEEsingle,
156 S_IEEEdouble,
157 S_x87DoubleExtended,
158 S_IEEEquad,
159 S_PPCDoubleDouble
160 };
161
162 static const llvm::fltSemantics &EnumToSemantics(Semantics S);
163 static Semantics SemanticsToEnum(const llvm::fltSemantics &Sem);
164
165 static const fltSemantics &IEEEhalf() LLVM_READNONE;
166 static const fltSemantics &BFloat() LLVM_READNONE;
167 static const fltSemantics &IEEEsingle() LLVM_READNONE;
168 static const fltSemantics &IEEEdouble() LLVM_READNONE;
169 static const fltSemantics &IEEEquad() LLVM_READNONE;
170 static const fltSemantics &PPCDoubleDouble() LLVM_READNONE;
171 static const fltSemantics &x87DoubleExtended() LLVM_READNONE;
172
173 /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
174 /// anything real.
175 static const fltSemantics &Bogus() LLVM_READNONE;
176
177 /// @}
178
179 /// IEEE-754R 5.11: Floating Point Comparison Relations.
180 enum cmpResult {
181 cmpLessThan,
182 cmpEqual,
183 cmpGreaterThan,
184 cmpUnordered
185 };
186
187 /// IEEE-754R 4.3: Rounding-direction attributes.
188 using roundingMode = llvm::RoundingMode;
189
190 static constexpr roundingMode rmNearestTiesToEven =
191 RoundingMode::NearestTiesToEven;
192 static constexpr roundingMode rmTowardPositive = RoundingMode::TowardPositive;
193 static constexpr roundingMode rmTowardNegative = RoundingMode::TowardNegative;
194 static constexpr roundingMode rmTowardZero = RoundingMode::TowardZero;
195 static constexpr roundingMode rmNearestTiesToAway =
196 RoundingMode::NearestTiesToAway;
197
198 /// IEEE-754R 7: Default exception handling.
199 ///
200 /// opUnderflow or opOverflow are always returned or-ed with opInexact.
201 ///
202 /// APFloat models this behavior specified by IEEE-754:
203 /// "For operations producing results in floating-point format, the default
204 /// result of an operation that signals the invalid operation exception
205 /// shall be a quiet NaN."
206 enum opStatus {
207 opOK = 0x00,
208 opInvalidOp = 0x01,
209 opDivByZero = 0x02,
210 opOverflow = 0x04,
211 opUnderflow = 0x08,
212 opInexact = 0x10
213 };
214
215 /// Category of internally-represented number.
216 enum fltCategory {
217 fcInfinity,
218 fcNaN,
219 fcNormal,
220 fcZero
221 };
222
223 /// Convenience enum used to construct an uninitialized APFloat.
224 enum uninitializedTag {
225 uninitialized
226 };
227
228 /// Enumeration of \c ilogb error results.
229 enum IlogbErrorKinds {
230 IEK_Zero = INT_MIN + 1,
231 IEK_NaN = INT_MIN,
232 IEK_Inf = INT_MAX
233 };
234
235 static unsigned int semanticsPrecision(const fltSemantics &);
236 static ExponentType semanticsMinExponent(const fltSemantics &);
237 static ExponentType semanticsMaxExponent(const fltSemantics &);
238 static unsigned int semanticsSizeInBits(const fltSemantics &);
239
240 /// Returns the size of the floating point number (in bits) in the given
241 /// semantics.
242 static unsigned getSizeInBits(const fltSemantics &Sem);
243};
244
245namespace detail {
246
247class IEEEFloat final : public APFloatBase {
248public:
249 /// \name Constructors
250 /// @{
251
252 IEEEFloat(const fltSemantics &); // Default construct to +0.0
253 IEEEFloat(const fltSemantics &, integerPart);
254 IEEEFloat(const fltSemantics &, uninitializedTag);
255 IEEEFloat(const fltSemantics &, const APInt &);
256 explicit IEEEFloat(double d);
257 explicit IEEEFloat(float f);
258 IEEEFloat(const IEEEFloat &);
259 IEEEFloat(IEEEFloat &&);
260 ~IEEEFloat();
261
262 /// @}
263
264 /// Returns whether this instance allocated memory.
265 bool needsCleanup() const { return partCount() > 1; }
266
267 /// \name Convenience "constructors"
268 /// @{
269
270 /// @}
271
272 /// \name Arithmetic
273 /// @{
274
275 opStatus add(const IEEEFloat &, roundingMode);
276 opStatus subtract(const IEEEFloat &, roundingMode);
277 opStatus multiply(const IEEEFloat &, roundingMode);
278 opStatus divide(const IEEEFloat &, roundingMode);
279 /// IEEE remainder.
280 opStatus remainder(const IEEEFloat &);
281 /// C fmod, or llvm frem.
282 opStatus mod(const IEEEFloat &);
283 opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);
284 opStatus roundToIntegral(roundingMode);
285 /// IEEE-754R 5.3.1: nextUp/nextDown.
286 opStatus next(bool nextDown);
287
288 /// @}
289
290 /// \name Sign operations.
291 /// @{
292
293 void changeSign();
294
295 /// @}
296
297 /// \name Conversions
298 /// @{
299
300 opStatus convert(const fltSemantics &, roundingMode, bool *);
301 opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,
302 roundingMode, bool *) const;
303 opStatus convertFromAPInt(const APInt &, bool, roundingMode);
304 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
305 bool, roundingMode);
306 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
307 bool, roundingMode);
308 Expected<opStatus> convertFromString(StringRef, roundingMode);
309 APInt bitcastToAPInt() const;
310 double convertToDouble() const;
311 float convertToFloat() const;
312
313 /// @}
314
315 /// The definition of equality is not straightforward for floating point, so
316 /// we won't use operator==. Use one of the following, or write whatever it
317 /// is you really mean.
318 bool operator==(const IEEEFloat &) const = delete;
319
320 /// IEEE comparison with another floating point number (NaNs compare
321 /// unordered, 0==-0).
322 cmpResult compare(const IEEEFloat &) const;
323
324 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
325 bool bitwiseIsEqual(const IEEEFloat &) const;
326
327 /// Write out a hexadecimal representation of the floating point value to DST,
328 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
329 /// Return the number of characters written, excluding the terminating NUL.
330 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
331 bool upperCase, roundingMode) const;
332
333 /// \name IEEE-754R 5.7.2 General operations.
334 /// @{
335
336 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
337 /// negative.
338 ///
339 /// This applies to zeros and NaNs as well.
340 bool isNegative() const { return sign; }
341
342 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
343 ///
344 /// This implies that the current value of the float is not zero, subnormal,
345 /// infinite, or NaN following the definition of normality from IEEE-754R.
346 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
347
348 /// Returns true if and only if the current value is zero, subnormal, or
349 /// normal.
350 ///
351 /// This means that the value is not infinite or NaN.
352 bool isFinite() const { return !isNaN() && !isInfinity(); }
353
354 /// Returns true if and only if the float is plus or minus zero.
355 bool isZero() const { return category == fcZero; }
356
357 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
358 /// denormal.
359 bool isDenormal() const;
360
361 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
362 bool isInfinity() const { return category == fcInfinity; }
363
364 /// Returns true if and only if the float is a quiet or signaling NaN.
365 bool isNaN() const { return category == fcNaN; }
366
367 /// Returns true if and only if the float is a signaling NaN.
368 bool isSignaling() const;
369
370 /// @}
371
372 /// \name Simple Queries
373 /// @{
374
375 fltCategory getCategory() const { return category; }
376 const fltSemantics &getSemantics() const { return *semantics; }
377 bool isNonZero() const { return category != fcZero; }
378 bool isFiniteNonZero() const { return isFinite() && !isZero(); }
379 bool isPosZero() const { return isZero() && !isNegative(); }
380 bool isNegZero() const { return isZero() && isNegative(); }
381
382 /// Returns true if and only if the number has the smallest possible non-zero
383 /// magnitude in the current semantics.
384 bool isSmallest() const;
385
386 /// Returns true if and only if the number has the largest possible finite
387 /// magnitude in the current semantics.
388 bool isLargest() const;
389
390 /// Returns true if and only if the number is an exact integer.
391 bool isInteger() const;
392
393 /// @}
394
395 IEEEFloat &operator=(const IEEEFloat &);
396 IEEEFloat &operator=(IEEEFloat &&);
397
398 /// Overload to compute a hash code for an APFloat value.
399 ///
400 /// Note that the use of hash codes for floating point values is in general
401 /// frought with peril. Equality is hard to define for these values. For
402 /// example, should negative and positive zero hash to different codes? Are
403 /// they equal or not? This hash value implementation specifically
404 /// emphasizes producing different codes for different inputs in order to
405 /// be used in canonicalization and memoization. As such, equality is
406 /// bitwiseIsEqual, and 0 != -0.
407 friend hash_code hash_value(const IEEEFloat &Arg);
408
409 /// Converts this value into a decimal string.
410 ///
411 /// \param FormatPrecision The maximum number of digits of
412 /// precision to output. If there are fewer digits available,
413 /// zero padding will not be used unless the value is
414 /// integral and small enough to be expressed in
415 /// FormatPrecision digits. 0 means to use the natural
416 /// precision of the number.
417 /// \param FormatMaxPadding The maximum number of zeros to
418 /// consider inserting before falling back to scientific
419 /// notation. 0 means to always use scientific notation.
420 ///
421 /// \param TruncateZero Indicate whether to remove the trailing zero in
422 /// fraction part or not. Also setting this parameter to false forcing
423 /// producing of output more similar to default printf behavior.
424 /// Specifically the lower e is used as exponent delimiter and exponent
425 /// always contains no less than two digits.
426 ///
427 /// Number Precision MaxPadding Result
428 /// ------ --------- ---------- ------
429 /// 1.01E+4 5 2 10100
430 /// 1.01E+4 4 2 1.01E+4
431 /// 1.01E+4 5 1 1.01E+4
432 /// 1.01E-2 5 2 0.0101
433 /// 1.01E-2 4 2 0.0101
434 /// 1.01E-2 4 1 1.01E-2
435 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
436 unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;
437
438 /// If this value has an exact multiplicative inverse, store it in inv and
439 /// return true.
440 bool getExactInverse(APFloat *inv) const;
441
442 /// Returns the exponent of the internal representation of the APFloat.
443 ///
444 /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
445 /// For special APFloat values, this returns special error codes:
446 ///
447 /// NaN -> \c IEK_NaN
448 /// 0 -> \c IEK_Zero
449 /// Inf -> \c IEK_Inf
450 ///
451 friend int ilogb(const IEEEFloat &Arg);
452
453 /// Returns: X * 2^Exp for integral exponents.
454 friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);
455
456 friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);
457
458 /// \name Special value setters.
459 /// @{
460
461 void makeLargest(bool Neg = false);
462 void makeSmallest(bool Neg = false);
463 void makeNaN(bool SNaN = false, bool Neg = false,
464 const APInt *fill = nullptr);
465 void makeInf(bool Neg = false);
466 void makeZero(bool Neg = false);
467 void makeQuiet();
468
469 /// Returns the smallest (by magnitude) normalized finite number in the given
470 /// semantics.
471 ///
472 /// \param Negative - True iff the number should be negative
473 void makeSmallestNormalized(bool Negative = false);
474
475 /// @}
476
477 cmpResult compareAbsoluteValue(const IEEEFloat &) const;
478
479private:
480 /// \name Simple Queries
481 /// @{
482
483 integerPart *significandParts();
484 const integerPart *significandParts() const;
485 unsigned int partCount() const;
486
487 /// @}
488
489 /// \name Significand operations.
490 /// @{
491
492 integerPart addSignificand(const IEEEFloat &);
493 integerPart subtractSignificand(const IEEEFloat &, integerPart);
494 lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
495 lostFraction multiplySignificand(const IEEEFloat &, IEEEFloat);
496 lostFraction multiplySignificand(const IEEEFloat&);
497 lostFraction divideSignificand(const IEEEFloat &);
498 void incrementSignificand();
499 void initialize(const fltSemantics *);
500 void shiftSignificandLeft(unsigned int);
501 lostFraction shiftSignificandRight(unsigned int);
502 unsigned int significandLSB() const;
503 unsigned int significandMSB() const;
504 void zeroSignificand();
505 /// Return true if the significand excluding the integral bit is all ones.
506 bool isSignificandAllOnes() const;
507 /// Return true if the significand excluding the integral bit is all zeros.
508 bool isSignificandAllZeros() const;
509
510 /// @}
511
512 /// \name Arithmetic on special values.
513 /// @{
514
515 opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);
516 opStatus divideSpecials(const IEEEFloat &);
517 opStatus multiplySpecials(const IEEEFloat &);
518 opStatus modSpecials(const IEEEFloat &);
519 opStatus remainderSpecials(const IEEEFloat&);
520
521 /// @}
522
523 /// \name Miscellany
524 /// @{
525
526 bool convertFromStringSpecials(StringRef str);
527 opStatus normalize(roundingMode, lostFraction);
528 opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);
529 opStatus handleOverflow(roundingMode);
530 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
531 opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,
532 unsigned int, bool, roundingMode,
533 bool *) const;
534 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
535 roundingMode);
536 Expected<opStatus> convertFromHexadecimalString(StringRef, roundingMode);
537 Expected<opStatus> convertFromDecimalString(StringRef, roundingMode);
538 char *convertNormalToHexString(char *, unsigned int, bool,
539 roundingMode) const;
540 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
541 roundingMode);
542 ExponentType exponentNaN() const;
543 ExponentType exponentInf() const;
544 ExponentType exponentZero() const;
545
546 /// @}
547
548 APInt convertHalfAPFloatToAPInt() const;
549 APInt convertBFloatAPFloatToAPInt() const;
550 APInt convertFloatAPFloatToAPInt() const;
551 APInt convertDoubleAPFloatToAPInt() const;
552 APInt convertQuadrupleAPFloatToAPInt() const;
553 APInt convertF80LongDoubleAPFloatToAPInt() const;
554 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
555 void initFromAPInt(const fltSemantics *Sem, const APInt &api);
556 void initFromHalfAPInt(const APInt &api);
557 void initFromBFloatAPInt(const APInt &api);
558 void initFromFloatAPInt(const APInt &api);
559 void initFromDoubleAPInt(const APInt &api);
560 void initFromQuadrupleAPInt(const APInt &api);
561 void initFromF80LongDoubleAPInt(const APInt &api);
562 void initFromPPCDoubleDoubleAPInt(const APInt &api);
563
564 void assign(const IEEEFloat &);
565 void copySignificand(const IEEEFloat &);
566 void freeSignificand();
567
568 /// Note: this must be the first data member.
569 /// The semantics that this value obeys.
570 const fltSemantics *semantics;
571
572 /// A binary fraction with an explicit integer bit.
573 ///
574 /// The significand must be at least one bit wider than the target precision.
575 union Significand {
576 integerPart part;
577 integerPart *parts;
578 } significand;
579
580 /// The signed unbiased exponent of the value.
581 ExponentType exponent;
582
583 /// What kind of floating point number this is.
584 ///
585 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
586 /// Using the extra bit keeps it from failing under VisualStudio.
587 fltCategory category : 3;
588
589 /// Sign bit of the number.
590 unsigned int sign : 1;
591};
592
593hash_code hash_value(const IEEEFloat &Arg);
594int ilogb(const IEEEFloat &Arg);
595IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode);
596IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);
597
598// This mode implements more precise float in terms of two APFloats.
599// The interface and layout is designed for arbitrary underlying semantics,
600// though currently only PPCDoubleDouble semantics are supported, whose
601// corresponding underlying semantics are IEEEdouble.
602class DoubleAPFloat final : public APFloatBase {
603 // Note: this must be the first data member.
604 const fltSemantics *Semantics;
605 std::unique_ptr<APFloat[]> Floats;
606
607 opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,
608 const APFloat &cc, roundingMode RM);
609
610 opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,
611 DoubleAPFloat &Out, roundingMode RM);
612
613public:
614 DoubleAPFloat(const fltSemantics &S);
615 DoubleAPFloat(const fltSemantics &S, uninitializedTag);
616 DoubleAPFloat(const fltSemantics &S, integerPart);
617 DoubleAPFloat(const fltSemantics &S, const APInt &I);
618 DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);
619 DoubleAPFloat(const DoubleAPFloat &RHS);
620 DoubleAPFloat(DoubleAPFloat &&RHS);
621
622 DoubleAPFloat &operator=(const DoubleAPFloat &RHS);
623
624 DoubleAPFloat &operator=(DoubleAPFloat &&RHS) {
625 if (this != &RHS) {
626 this->~DoubleAPFloat();
627 new (this) DoubleAPFloat(std::move(RHS));
628 }
629 return *this;
630 }
631
632 bool needsCleanup() const { return Floats != nullptr; }
633
634 APFloat &getFirst() { return Floats[0]; }
635 const APFloat &getFirst() const { return Floats[0]; }
636 APFloat &getSecond() { return Floats[1]; }
637 const APFloat &getSecond() const { return Floats[1]; }
638
639 opStatus add(const DoubleAPFloat &RHS, roundingMode RM);
640 opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);
641 opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);
642 opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);
643 opStatus remainder(const DoubleAPFloat &RHS);
644 opStatus mod(const DoubleAPFloat &RHS);
645 opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
646 const DoubleAPFloat &Addend, roundingMode RM);
647 opStatus roundToIntegral(roundingMode RM);
648 void changeSign();
649 cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;
650
651 fltCategory getCategory() const;
652 bool isNegative() const;
653
654 void makeInf(bool Neg);
655 void makeZero(bool Neg);
656 void makeLargest(bool Neg);
657 void makeSmallest(bool Neg);
658 void makeSmallestNormalized(bool Neg);
659 void makeNaN(bool SNaN, bool Neg, const APInt *fill);
660
661 cmpResult compare(const DoubleAPFloat &RHS) const;
662 bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;
663 APInt bitcastToAPInt() const;
664 Expected<opStatus> convertFromString(StringRef, roundingMode);
665 opStatus next(bool nextDown);
666
667 opStatus convertToInteger(MutableArrayRef<integerPart> Input,
668 unsigned int Width, bool IsSigned, roundingMode RM,
669 bool *IsExact) const;
670 opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);
671 opStatus convertFromSignExtendedInteger(const integerPart *Input,
672 unsigned int InputSize, bool IsSigned,
673 roundingMode RM);
674 opStatus convertFromZeroExtendedInteger(const integerPart *Input,
675 unsigned int InputSize, bool IsSigned,
676 roundingMode RM);
677 unsigned int convertToHexString(char *DST, unsigned int HexDigits,
678 bool UpperCase, roundingMode RM) const;
679
680 bool isDenormal() const;
681 bool isSmallest() const;
682 bool isLargest() const;
683 bool isInteger() const;
684
685 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
686 unsigned FormatMaxPadding, bool TruncateZero = true) const;
687
688 bool getExactInverse(APFloat *inv) const;
689
690 friend DoubleAPFloat scalbn(const DoubleAPFloat &X, int Exp, roundingMode);
691 friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);
692 friend hash_code hash_value(const DoubleAPFloat &Arg);
693};
694
695hash_code hash_value(const DoubleAPFloat &Arg);
696
697} // End detail namespace
698
699// This is a interface class that is currently forwarding functionalities from
700// detail::IEEEFloat.
701class APFloat : public APFloatBase {
702 typedef detail::IEEEFloat IEEEFloat;
703 typedef detail::DoubleAPFloat DoubleAPFloat;
704
705 static_assert(std::is_standard_layout<IEEEFloat>::value, "");
706
707 union Storage {
708 const fltSemantics *semantics;
709 IEEEFloat IEEE;
710 DoubleAPFloat Double;
711
712 explicit Storage(IEEEFloat F, const fltSemantics &S);
713 explicit Storage(DoubleAPFloat F, const fltSemantics &S)
714 : Double(std::move(F)) {
715 assert(&S == &PPCDoubleDouble());
716 }
717
718 template <typename... ArgTypes>
719 Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {
720 if (usesLayout<IEEEFloat>(Semantics)) {
721 new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);
722 return;
723 }
724 if (usesLayout<DoubleAPFloat>(Semantics)) {
725 new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);
726 return;
727 }
728 llvm_unreachable("Unexpected semantics");
729 }
730
731 ~Storage() {
732 if (usesLayout<IEEEFloat>(*semantics)) {
733 IEEE.~IEEEFloat();
734 return;
735 }
736 if (usesLayout<DoubleAPFloat>(*semantics)) {
737 Double.~DoubleAPFloat();
738 return;
739 }
740 llvm_unreachable("Unexpected semantics");
741 }
742
743 Storage(const Storage &RHS) {
744 if (usesLayout<IEEEFloat>(*RHS.semantics)) {
745 new (this) IEEEFloat(RHS.IEEE);
746 return;
747 }
748 if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
749 new (this) DoubleAPFloat(RHS.Double);
750 return;
751 }
752 llvm_unreachable("Unexpected semantics");
753 }
754
755 Storage(Storage &&RHS) {
756 if (usesLayout<IEEEFloat>(*RHS.semantics)) {
757 new (this) IEEEFloat(std::move(RHS.IEEE));
758 return;
759 }
760 if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
761 new (this) DoubleAPFloat(std::move(RHS.Double));
762 return;
763 }
764 llvm_unreachable("Unexpected semantics");
765 }
766
767 Storage &operator=(const Storage &RHS) {
768 if (usesLayout<IEEEFloat>(*semantics) &&
769 usesLayout<IEEEFloat>(*RHS.semantics)) {
770 IEEE = RHS.IEEE;
771 } else if (usesLayout<DoubleAPFloat>(*semantics) &&
772 usesLayout<DoubleAPFloat>(*RHS.semantics)) {
773 Double = RHS.Double;
774 } else if (this != &RHS) {
775 this->~Storage();
776 new (this) Storage(RHS);
777 }
778 return *this;
779 }
780
781 Storage &operator=(Storage &&RHS) {
782 if (usesLayout<IEEEFloat>(*semantics) &&
783 usesLayout<IEEEFloat>(*RHS.semantics)) {
784 IEEE = std::move(RHS.IEEE);
785 } else if (usesLayout<DoubleAPFloat>(*semantics) &&
786 usesLayout<DoubleAPFloat>(*RHS.semantics)) {
787 Double = std::move(RHS.Double);
788 } else if (this != &RHS) {
789 this->~Storage();
790 new (this) Storage(std::move(RHS));
791 }
792 return *this;
793 }
794 } U;
795
796 template <typename T> static bool usesLayout(const fltSemantics &Semantics) {
797 static_assert(std::is_same<T, IEEEFloat>::value ||
798 std::is_same<T, DoubleAPFloat>::value, "");
799 if (std::is_same<T, DoubleAPFloat>::value) {
800 return &Semantics == &PPCDoubleDouble();
801 }
802 return &Semantics != &PPCDoubleDouble();
803 }
804
805 IEEEFloat &getIEEE() {
806 if (usesLayout<IEEEFloat>(*U.semantics))
807 return U.IEEE;
808 if (usesLayout<DoubleAPFloat>(*U.semantics))
809 return U.Double.getFirst().U.IEEE;
810 llvm_unreachable("Unexpected semantics");
811 }
812
813 const IEEEFloat &getIEEE() const {
814 if (usesLayout<IEEEFloat>(*U.semantics))
815 return U.IEEE;
816 if (usesLayout<DoubleAPFloat>(*U.semantics))
817 return U.Double.getFirst().U.IEEE;
818 llvm_unreachable("Unexpected semantics");
819 }
820
821 void makeZero(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeZero(Neg)); }
822
823 void makeInf(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeInf(Neg)); }
824
825 void makeNaN(bool SNaN, bool Neg, const APInt *fill) {
826 APFLOAT_DISPATCH_ON_SEMANTICS(makeNaN(SNaN, Neg, fill));
827 }
828
829 void makeLargest(bool Neg) {
830 APFLOAT_DISPATCH_ON_SEMANTICS(makeLargest(Neg));
831 }
832
833 void makeSmallest(bool Neg) {
834 APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallest(Neg));
835 }
836
837 void makeSmallestNormalized(bool Neg) {
838 APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallestNormalized(Neg));
839 }
840
841 // FIXME: This is due to clang 3.3 (or older version) always checks for the
842 // default constructor in an array aggregate initialization, even if no
843 // elements in the array is default initialized.
844 APFloat() : U(IEEEdouble()) {
845 llvm_unreachable("This is a workaround for old clang.");
846 }
847
848 explicit APFloat(IEEEFloat F, const fltSemantics &S) : U(std::move(F), S) {}
849 explicit APFloat(DoubleAPFloat F, const fltSemantics &S)
850 : U(std::move(F), S) {}
851
852 cmpResult compareAbsoluteValue(const APFloat &RHS) const {
853 assert(&getSemantics() == &RHS.getSemantics() &&
854 "Should only compare APFloats with the same semantics");
855 if (usesLayout<IEEEFloat>(getSemantics()))
856 return U.IEEE.compareAbsoluteValue(RHS.U.IEEE);
857 if (usesLayout<DoubleAPFloat>(getSemantics()))
858 return U.Double.compareAbsoluteValue(RHS.U.Double);
859 llvm_unreachable("Unexpected semantics");
860 }
861
862public:
863 APFloat(const fltSemantics &Semantics) : U(Semantics) {}
864 APFloat(const fltSemantics &Semantics, StringRef S);
865 APFloat(const fltSemantics &Semantics, integerPart I) : U(Semantics, I) {}
866 template <typename T,
867 typename = std::enable_if_t<std::is_floating_point<T>::value>>
868 APFloat(const fltSemantics &Semantics, T V) = delete;
869 // TODO: Remove this constructor. This isn't faster than the first one.
870 APFloat(const fltSemantics &Semantics, uninitializedTag)
871 : U(Semantics, uninitialized) {}
872 APFloat(const fltSemantics &Semantics, const APInt &I) : U(Semantics, I) {}
873 explicit APFloat(double d) : U(IEEEFloat(d), IEEEdouble()) {}
874 explicit APFloat(float f) : U(IEEEFloat(f), IEEEsingle()) {}
875 APFloat(const APFloat &RHS) = default;
876 APFloat(APFloat &&RHS) = default;
877
878 ~APFloat() = default;
879
880 bool needsCleanup() const { APFLOAT_DISPATCH_ON_SEMANTICS(needsCleanup()); }
881
882 /// Factory for Positive and Negative Zero.
883 ///
884 /// \param Negative True iff the number should be negative.
885 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
886 APFloat Val(Sem, uninitialized);
887 Val.makeZero(Negative);
888 return Val;
889 }
890
891 /// Factory for Positive and Negative Infinity.
892 ///
893 /// \param Negative True iff the number should be negative.
894 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
895 APFloat Val(Sem, uninitialized);
896 Val.makeInf(Negative);
897 return Val;
898 }
899
900 /// Factory for NaN values.
901 ///
902 /// \param Negative - True iff the NaN generated should be negative.
903 /// \param payload - The unspecified fill bits for creating the NaN, 0 by
904 /// default. The value is truncated as necessary.
905 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
906 uint64_t payload = 0) {
907 if (payload) {
908 APInt intPayload(64, payload);
909 return getQNaN(Sem, Negative, &intPayload);
910 } else {
911 return getQNaN(Sem, Negative, nullptr);
912 }
913 }
914
915 /// Factory for QNaN values.
916 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
917 const APInt *payload = nullptr) {
918 APFloat Val(Sem, uninitialized);
919 Val.makeNaN(false, Negative, payload);
920 return Val;
921 }
922
923 /// Factory for SNaN values.
924 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
925 const APInt *payload = nullptr) {
926 APFloat Val(Sem, uninitialized);
927 Val.makeNaN(true, Negative, payload);
928 return Val;
929 }
930
931 /// Returns the largest finite number in the given semantics.
932 ///
933 /// \param Negative - True iff the number should be negative
934 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false) {
935 APFloat Val(Sem, uninitialized);
936 Val.makeLargest(Negative);
937 return Val;
938 }
939
940 /// Returns the smallest (by magnitude) finite number in the given semantics.
941 /// Might be denormalized, which implies a relative loss of precision.
942 ///
943 /// \param Negative - True iff the number should be negative
944 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false) {
945 APFloat Val(Sem, uninitialized);
946 Val.makeSmallest(Negative);
947 return Val;
948 }
949
950 /// Returns the smallest (by magnitude) normalized finite number in the given
951 /// semantics.
952 ///
953 /// \param Negative - True iff the number should be negative
954 static APFloat getSmallestNormalized(const fltSemantics &Sem,
955 bool Negative = false) {
956 APFloat Val(Sem, uninitialized);
957 Val.makeSmallestNormalized(Negative);
958 return Val;
959 }
960
961 /// Returns a float which is bitcasted from an all one value int.
962 ///
963 /// \param Semantics - type float semantics
964 /// \param BitWidth - Select float type
965 static APFloat getAllOnesValue(const fltSemantics &Semantics,
966 unsigned BitWidth);
967
968 /// Used to insert APFloat objects, or objects that contain APFloat objects,
969 /// into FoldingSets.
970 void Profile(FoldingSetNodeID &NID) const;
971
972 opStatus add(const APFloat &RHS, roundingMode RM) {
973 assert(&getSemantics() == &RHS.getSemantics() &&
974 "Should only call on two APFloats with the same semantics");
975 if (usesLayout<IEEEFloat>(getSemantics()))
976 return U.IEEE.add(RHS.U.IEEE, RM);
977 if (usesLayout<DoubleAPFloat>(getSemantics()))
978 return U.Double.add(RHS.U.Double, RM);
979 llvm_unreachable("Unexpected semantics");
980 }
981 opStatus subtract(const APFloat &RHS, roundingMode RM) {
982 assert(&getSemantics() == &RHS.getSemantics() &&
983 "Should only call on two APFloats with the same semantics");
984 if (usesLayout<IEEEFloat>(getSemantics()))
985 return U.IEEE.subtract(RHS.U.IEEE, RM);
986 if (usesLayout<DoubleAPFloat>(getSemantics()))
987 return U.Double.subtract(RHS.U.Double, RM);
988 llvm_unreachable("Unexpected semantics");
989 }
990 opStatus multiply(const APFloat &RHS, roundingMode RM) {
991 assert(&getSemantics() == &RHS.getSemantics() &&
992 "Should only call on two APFloats with the same semantics");
993 if (usesLayout<IEEEFloat>(getSemantics()))
994 return U.IEEE.multiply(RHS.U.IEEE, RM);
995 if (usesLayout<DoubleAPFloat>(getSemantics()))
996 return U.Double.multiply(RHS.U.Double, RM);
997 llvm_unreachable("Unexpected semantics");
998 }
999 opStatus divide(const APFloat &RHS, roundingMode RM) {
1000 assert(&getSemantics() == &RHS.getSemantics() &&
1001 "Should only call on two APFloats with the same semantics");
1002 if (usesLayout<IEEEFloat>(getSemantics()))
1003 return U.IEEE.divide(RHS.U.IEEE, RM);
1004 if (usesLayout<DoubleAPFloat>(getSemantics()))
1005 return U.Double.divide(RHS.U.Double, RM);
1006 llvm_unreachable("Unexpected semantics");
1007 }
1008 opStatus remainder(const APFloat &RHS) {
1009 assert(&getSemantics() == &RHS.getSemantics() &&
1010 "Should only call on two APFloats with the same semantics");
1011 if (usesLayout<IEEEFloat>(getSemantics()))
1012 return U.IEEE.remainder(RHS.U.IEEE);
1013 if (usesLayout<DoubleAPFloat>(getSemantics()))
1014 return U.Double.remainder(RHS.U.Double);
1015 llvm_unreachable("Unexpected semantics");
1016 }
1017 opStatus mod(const APFloat &RHS) {
1018 assert(&getSemantics() == &RHS.getSemantics() &&
1019 "Should only call on two APFloats with the same semantics");
1020 if (usesLayout<IEEEFloat>(getSemantics()))
1021 return U.IEEE.mod(RHS.U.IEEE);
1022 if (usesLayout<DoubleAPFloat>(getSemantics()))
1023 return U.Double.mod(RHS.U.Double);
1024 llvm_unreachable("Unexpected semantics");
1025 }
1026 opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend,
1027 roundingMode RM) {
1028 assert(&getSemantics() == &Multiplicand.getSemantics() &&
1029 "Should only call on APFloats with the same semantics");
1030 assert(&getSemantics() == &Addend.getSemantics() &&
1031 "Should only call on APFloats with the same semantics");
1032 if (usesLayout<IEEEFloat>(getSemantics()))
1033 return U.IEEE.fusedMultiplyAdd(Multiplicand.U.IEEE, Addend.U.IEEE, RM);
1034 if (usesLayout<DoubleAPFloat>(getSemantics()))
1035 return U.Double.fusedMultiplyAdd(Multiplicand.U.Double, Addend.U.Double,
1036 RM);
1037 llvm_unreachable("Unexpected semantics");
1038 }
1039 opStatus roundToIntegral(roundingMode RM) {
1040 APFLOAT_DISPATCH_ON_SEMANTICS(roundToIntegral(RM));
1041 }
1042
1043 // TODO: bool parameters are not readable and a source of bugs.
1044 // Do something.
1045 opStatus next(bool nextDown) {
1046 APFLOAT_DISPATCH_ON_SEMANTICS(next(nextDown));
1047 }
1048
1049 /// Negate an APFloat.
1050 APFloat operator-() const {
1051 APFloat Result(*this);
1052 Result.changeSign();
1053 return Result;
1054 }
1055
1056 /// Add two APFloats, rounding ties to the nearest even.
1057 /// No error checking.
1058 APFloat operator+(const APFloat &RHS) const {
1059 APFloat Result(*this);
1060 (void)Result.add(RHS, rmNearestTiesToEven);
1061 return Result;
1062 }
1063
1064 /// Subtract two APFloats, rounding ties to the nearest even.
1065 /// No error checking.
1066 APFloat operator-(const APFloat &RHS) const {
1067 APFloat Result(*this);
1068 (void)Result.subtract(RHS, rmNearestTiesToEven);
1069 return Result;
1070 }
1071
1072 /// Multiply two APFloats, rounding ties to the nearest even.
1073 /// No error checking.
1074 APFloat operator*(const APFloat &RHS) const {
1075 APFloat Result(*this);
1076 (void)Result.multiply(RHS, rmNearestTiesToEven);
1077 return Result;
1078 }
1079
1080 /// Divide the first APFloat by the second, rounding ties to the nearest even.
1081 /// No error checking.
1082 APFloat operator/(const APFloat &RHS) const {
1083 APFloat Result(*this);
1084 (void)Result.divide(RHS, rmNearestTiesToEven);
1085 return Result;
1086 }
1087
1088 void changeSign() { APFLOAT_DISPATCH_ON_SEMANTICS(changeSign()); }
1089 void clearSign() {
1090 if (isNegative())
1091 changeSign();
1092 }
1093 void copySign(const APFloat &RHS) {
1094 if (isNegative() != RHS.isNegative())
1095 changeSign();
1096 }
1097
1098 /// A static helper to produce a copy of an APFloat value with its sign
1099 /// copied from some other APFloat.
1100 static APFloat copySign(APFloat Value, const APFloat &Sign) {
1101 Value.copySign(Sign);
1102 return Value;
1103 }
1104
1105 opStatus convert(const fltSemantics &ToSemantics, roundingMode RM,
1106 bool *losesInfo);
1107 opStatus convertToInteger(MutableArrayRef<integerPart> Input,
1108 unsigned int Width, bool IsSigned, roundingMode RM,
1109 bool *IsExact) const {
1110 APFLOAT_DISPATCH_ON_SEMANTICS(
1111 convertToInteger(Input, Width, IsSigned, RM, IsExact));
1112 }
1113 opStatus convertToInteger(APSInt &Result, roundingMode RM,
1114 bool *IsExact) const;
1115 opStatus convertFromAPInt(const APInt &Input, bool IsSigned,
1116 roundingMode RM) {
1117 APFLOAT_DISPATCH_ON_SEMANTICS(convertFromAPInt(Input, IsSigned, RM));
1118 }
1119 opStatus convertFromSignExtendedInteger(const integerPart *Input,
1120 unsigned int InputSize, bool IsSigned,
1121 roundingMode RM) {
1122 APFLOAT_DISPATCH_ON_SEMANTICS(
1123 convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM));
1124 }
1125 opStatus convertFromZeroExtendedInteger(const integerPart *Input,
1126 unsigned int InputSize, bool IsSigned,
1127 roundingMode RM) {
1128 APFLOAT_DISPATCH_ON_SEMANTICS(
1129 convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM));
1130 }
1131 Expected<opStatus> convertFromString(StringRef, roundingMode);
1132 APInt bitcastToAPInt() const {
1133 APFLOAT_DISPATCH_ON_SEMANTICS(bitcastToAPInt());
1134 }
1135 double convertToDouble() const { return getIEEE().convertToDouble(); }
1136 float convertToFloat() const { return getIEEE().convertToFloat(); }
1137
1138 bool operator==(const APFloat &RHS) const { return compare(RHS) == cmpEqual; }
1139
1140 bool operator!=(const APFloat &RHS) const { return compare(RHS) != cmpEqual; }
1141
1142 bool operator<(const APFloat &RHS) const {
1143 return compare(RHS) == cmpLessThan;
1144 }
1145
1146 bool operator>(const APFloat &RHS) const {
1147 return compare(RHS) == cmpGreaterThan;
1148 }
1149
1150 bool operator<=(const APFloat &RHS) const {
1151 cmpResult Res = compare(RHS);
1152 return Res == cmpLessThan || Res == cmpEqual;
1153 }
1154
1155 bool operator>=(const APFloat &RHS) const {
1156 cmpResult Res = compare(RHS);
1157 return Res == cmpGreaterThan || Res == cmpEqual;
1158 }
1159
1160 cmpResult compare(const APFloat &RHS) const {
1161 assert(&getSemantics() == &RHS.getSemantics() &&
1162 "Should only compare APFloats with the same semantics");
1163 if (usesLayout<IEEEFloat>(getSemantics()))
1164 return U.IEEE.compare(RHS.U.IEEE);
1165 if (usesLayout<DoubleAPFloat>(getSemantics()))
1166 return U.Double.compare(RHS.U.Double);
1167 llvm_unreachable("Unexpected semantics");
1168 }
1169
1170 bool bitwiseIsEqual(const APFloat &RHS) const {
1171 if (&getSemantics() != &RHS.getSemantics())
1172 return false;
1173 if (usesLayout<IEEEFloat>(getSemantics()))
1174 return U.IEEE.bitwiseIsEqual(RHS.U.IEEE);
1175 if (usesLayout<DoubleAPFloat>(getSemantics()))
1176 return U.Double.bitwiseIsEqual(RHS.U.Double);
1177 llvm_unreachable("Unexpected semantics");
1178 }
1179
1180 /// We don't rely on operator== working on double values, as
1181 /// it returns true for things that are clearly not equal, like -0.0 and 0.0.
1182 /// As such, this method can be used to do an exact bit-for-bit comparison of
1183 /// two floating point values.
1184 ///
1185 /// We leave the version with the double argument here because it's just so
1186 /// convenient to write "2.0" and the like. Without this function we'd
1187 /// have to duplicate its logic everywhere it's called.
1188 bool isExactlyValue(double V) const {
1189 bool ignored;
1190 APFloat Tmp(V);
1191 Tmp.convert(getSemantics(), APFloat::rmNearestTiesToEven, &ignored);
1192 return bitwiseIsEqual(Tmp);
1193 }
1194
1195 unsigned int convertToHexString(char *DST, unsigned int HexDigits,
1196 bool UpperCase, roundingMode RM) const {
1197 APFLOAT_DISPATCH_ON_SEMANTICS(
1198 convertToHexString(DST, HexDigits, UpperCase, RM));
1199 }
1200
1201 bool isZero() const { return getCategory() == fcZero; }
1202 bool isInfinity() const { return getCategory() == fcInfinity; }
1203 bool isNaN() const { return getCategory() == fcNaN; }
1204
1205 bool isNegative() const { return getIEEE().isNegative(); }
1206 bool isDenormal() const { APFLOAT_DISPATCH_ON_SEMANTICS(isDenormal()); }
1207 bool isSignaling() const { return getIEEE().isSignaling(); }
1208
1209 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
1210 bool isFinite() const { return !isNaN() && !isInfinity(); }
1211
1212 fltCategory getCategory() const { return getIEEE().getCategory(); }
1213 const fltSemantics &getSemantics() const { return *U.semantics; }
1214 bool isNonZero() const { return !isZero(); }
1215 bool isFiniteNonZero() const { return isFinite() && !isZero(); }
1216 bool isPosZero() const { return isZero() && !isNegative(); }
1217 bool isNegZero() const { return isZero() && isNegative(); }
1218 bool isSmallest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isSmallest()); }
1219 bool isLargest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isLargest()); }
1220 bool isInteger() const { APFLOAT_DISPATCH_ON_SEMANTICS(isInteger()); }
1221 bool isIEEE() const { return usesLayout<IEEEFloat>(getSemantics()); }
1222
1223 APFloat &operator=(const APFloat &RHS) = default;
1224 APFloat &operator=(APFloat &&RHS) = default;
1225
1226 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
1227 unsigned FormatMaxPadding = 3, bool TruncateZero = true) const {
1228 APFLOAT_DISPATCH_ON_SEMANTICS(
1229 toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero));
1230 }
1231
1232 void print(raw_ostream &) const;
1233 void dump() const;
1234
1235 bool getExactInverse(APFloat *inv) const {
1236 APFLOAT_DISPATCH_ON_SEMANTICS(getExactInverse(inv));
1237 }
1238
1239 friend hash_code hash_value(const APFloat &Arg);
1240 friend int ilogb(const APFloat &Arg) { return ilogb(Arg.getIEEE()); }
1241 friend APFloat scalbn(APFloat X, int Exp, roundingMode RM);
1242 friend APFloat frexp(const APFloat &X, int &Exp, roundingMode RM);
1243 friend IEEEFloat;
1244 friend DoubleAPFloat;
1245};
1246
1247/// See friend declarations above.
1248///
1249/// These additional declarations are required in order to compile LLVM with IBM
1250/// xlC compiler.
1251hash_code hash_value(const APFloat &Arg);
1252inline APFloat scalbn(APFloat X, int Exp, APFloat::roundingMode RM) {
1253 if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1254 return APFloat(scalbn(X.U.IEEE, Exp, RM), X.getSemantics());
1255 if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1256 return APFloat(scalbn(X.U.Double, Exp, RM), X.getSemantics());
1257 llvm_unreachable("Unexpected semantics");
1258}
1259
1260/// Equivalent of C standard library function.
1261///
1262/// While the C standard says Exp is an unspecified value for infinity and nan,
1263/// this returns INT_MAX for infinities, and INT_MIN for NaNs.
1264inline APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM) {
1265 if (APFloat::usesLayout<detail::IEEEFloat>(X.getSemantics()))
1266 return APFloat(frexp(X.U.IEEE, Exp, RM), X.getSemantics());
1267 if (APFloat::usesLayout<detail::DoubleAPFloat>(X.getSemantics()))
1268 return APFloat(frexp(X.U.Double, Exp, RM), X.getSemantics());
1269 llvm_unreachable("Unexpected semantics");
1270}
1271/// Returns the absolute value of the argument.
1272inline APFloat abs(APFloat X) {
1273 X.clearSign();
1274 return X;
1275}
1276
1277/// Returns the negated value of the argument.
1278inline APFloat neg(APFloat X) {
1279 X.changeSign();
1280 return X;
1281}
1282
1283/// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
1284/// both are not NaN. If either argument is a NaN, returns the other argument.
1285LLVM_READONLY
1286inline APFloat minnum(const APFloat &A, const APFloat &B) {
1287 if (A.isNaN())
1288 return B;
1289 if (B.isNaN())
1290 return A;
1291 return B < A ? B : A;
1292}
1293
1294/// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
1295/// both are not NaN. If either argument is a NaN, returns the other argument.
1296LLVM_READONLY
1297inline APFloat maxnum(const APFloat &A, const APFloat &B) {
1298 if (A.isNaN())
1299 return B;
1300 if (B.isNaN())
1301 return A;
1302 return A < B ? B : A;
1303}
1304
1305/// Implements IEEE 754-2018 minimum semantics. Returns the smaller of 2
1306/// arguments, propagating NaNs and treating -0 as less than +0.
1307LLVM_READONLY
1308inline APFloat minimum(const APFloat &A, const APFloat &B) {
1309 if (A.isNaN())
1310 return A;
1311 if (B.isNaN())
1312 return B;
1313 if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1314 return A.isNegative() ? A : B;
1315 return B < A ? B : A;
1316}
1317
1318/// Implements IEEE 754-2018 maximum semantics. Returns the larger of 2
1319/// arguments, propagating NaNs and treating -0 as less than +0.
1320LLVM_READONLY
1321inline APFloat maximum(const APFloat &A, const APFloat &B) {
1322 if (A.isNaN())
1323 return A;
1324 if (B.isNaN())
1325 return B;
1326 if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1327 return A.isNegative() ? B : A;
1328 return A < B ? B : A;
1329}
1330
1331} // namespace llvm
1332
1333#undef APFLOAT_DISPATCH_ON_SEMANTICS
1334#endif // LLVM_ADT_APFLOAT_H
1335