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/// This file declares a class to represent arbitrary precision floating point
11/// values and provide a variety of arithmetic operations on them.
12///
13//===----------------------------------------------------------------------===//
14
15#ifndef LLVM_ADT_APFLOAT_H
16#define LLVM_ADT_APFLOAT_H
17
18#include "llvm/ADT/APInt.h"
19#include "llvm/ADT/ArrayRef.h"
20#include "llvm/ADT/FloatingPointMode.h"
21#include "llvm/Support/ErrorHandling.h"
22#include <memory>
23
24#define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL) \
25 do { \
26 if (usesLayout<IEEEFloat>(getSemantics())) \
27 return U.IEEE.METHOD_CALL; \
28 if (usesLayout<DoubleAPFloat>(getSemantics())) \
29 return U.Double.METHOD_CALL; \
30 llvm_unreachable("Unexpected semantics"); \
31 } while (false)
32
33namespace llvm {
34
35struct fltSemantics;
36class APSInt;
37class StringRef;
38class APFloat;
39class raw_ostream;
40
41template <typename T> class Expected;
42template <typename T> class SmallVectorImpl;
43
44/// Enum that represents what fraction of the LSB truncated bits of an fp number
45/// represent.
46///
47/// This essentially combines the roles of guard and sticky bits.
48enum lostFraction { // Example of truncated bits:
49 lfExactlyZero, // 000000
50 lfLessThanHalf, // 0xxxxx x's not all zero
51 lfExactlyHalf, // 100000
52 lfMoreThanHalf // 1xxxxx x's not all zero
53};
54
55/// A self-contained host- and target-independent arbitrary-precision
56/// floating-point software implementation.
57///
58/// APFloat uses bignum integer arithmetic as provided by static functions in
59/// the APInt class. The library will work with bignum integers whose parts are
60/// any unsigned type at least 16 bits wide, but 64 bits is recommended.
61///
62/// Written for clarity rather than speed, in particular with a view to use in
63/// the front-end of a cross compiler so that target arithmetic can be correctly
64/// performed on the host. Performance should nonetheless be reasonable,
65/// particularly for its intended use. It may be useful as a base
66/// implementation for a run-time library during development of a faster
67/// target-specific one.
68///
69/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
70/// implemented operations. Currently implemented operations are add, subtract,
71/// multiply, divide, fused-multiply-add, conversion-to-float,
72/// conversion-to-integer and conversion-from-integer. New rounding modes
73/// (e.g. away from zero) can be added with three or four lines of code.
74///
75/// Four formats are built-in: IEEE single precision, double precision,
76/// quadruple precision, and x87 80-bit extended double (when operating with
77/// full extended precision). Adding a new format that obeys IEEE semantics
78/// only requires adding two lines of code: a declaration and definition of the
79/// format.
80///
81/// All operations return the status of that operation as an exception bit-mask,
82/// so multiple operations can be done consecutively with their results or-ed
83/// together. The returned status can be useful for compiler diagnostics; e.g.,
84/// inexact, underflow and overflow can be easily diagnosed on constant folding,
85/// and compiler optimizers can determine what exceptions would be raised by
86/// folding operations and optimize, or perhaps not optimize, accordingly.
87///
88/// At present, underflow tininess is detected after rounding; it should be
89/// straight forward to add support for the before-rounding case too.
90///
91/// The library reads hexadecimal floating point numbers as per C99, and
92/// correctly rounds if necessary according to the specified rounding mode.
93/// Syntax is required to have been validated by the caller. It also converts
94/// floating point numbers to hexadecimal text as per the C99 %a and %A
95/// conversions. The output precision (or alternatively the natural minimal
96/// precision) can be specified; if the requested precision is less than the
97/// natural precision the output is correctly rounded for the specified rounding
98/// mode.
99///
100/// It also reads decimal floating point numbers and correctly rounds according
101/// to the specified rounding mode.
102///
103/// Conversion to decimal text is not currently implemented.
104///
105/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
106/// signed exponent, and the significand as an array of integer parts. After
107/// normalization of a number of precision P the exponent is within the range of
108/// the format, and if the number is not denormal the P-th bit of the
109/// significand is set as an explicit integer bit. For denormals the most
110/// significant bit is shifted right so that the exponent is maintained at the
111/// format's minimum, so that the smallest denormal has just the least
112/// significant bit of the significand set. The sign of zeroes and infinities
113/// is significant; the exponent and significand of such numbers is not stored,
114/// but has a known implicit (deterministic) value: 0 for the significands, 0
115/// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
116/// significand are deterministic, although not really meaningful, and preserved
117/// in non-conversion operations. The exponent is implicitly all 1 bits.
118///
119/// APFloat does not provide any exception handling beyond default exception
120/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
121/// by encoding Signaling NaNs with the first bit of its trailing significand as
122/// 0.
123///
124/// TODO
125/// ====
126///
127/// Some features that may or may not be worth adding:
128///
129/// Binary to decimal conversion (hard).
130///
131/// Optional ability to detect underflow tininess before rounding.
132///
133/// New formats: x87 in single and double precision mode (IEEE apart from
134/// extended exponent range) (hard).
135///
136/// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
137///
138
139// This is the common type definitions shared by APFloat and its internal
140// implementation classes. This struct should not define any non-static data
141// members.
142struct APFloatBase {
143 typedef APInt::WordType integerPart;
144 static constexpr unsigned integerPartWidth = APInt::APINT_BITS_PER_WORD;
145
146 /// A signed type to represent a floating point numbers unbiased exponent.
147 typedef int32_t ExponentType;
148
149 /// \name Floating Point Semantics.
150 /// @{
151 enum Semantics {
152 S_IEEEhalf,
153 S_BFloat,
154 S_IEEEsingle,
155 S_IEEEdouble,
156 S_IEEEquad,
157 S_PPCDoubleDouble,
158 // 8-bit floating point number following IEEE-754 conventions with bit
159 // layout S1E5M2 as described in https://arxiv.org/abs/2209.05433.
160 S_Float8E5M2,
161 // 8-bit floating point number mostly following IEEE-754 conventions
162 // and bit layout S1E5M2 described in https://arxiv.org/abs/2206.02915,
163 // with expanded range and with no infinity or signed zero.
164 // NaN is represented as negative zero. (FN -> Finite, UZ -> unsigned zero).
165 // This format's exponent bias is 16, instead of the 15 (2 ** (5 - 1) - 1)
166 // that IEEE precedent would imply.
167 S_Float8E5M2FNUZ,
168 // 8-bit floating point number mostly following IEEE-754 conventions with
169 // bit layout S1E4M3 as described in https://arxiv.org/abs/2209.05433.
170 // Unlike IEEE-754 types, there are no infinity values, and NaN is
171 // represented with the exponent and mantissa bits set to all 1s.
172 S_Float8E4M3FN,
173 // 8-bit floating point number mostly following IEEE-754 conventions
174 // and bit layout S1E4M3 described in https://arxiv.org/abs/2206.02915,
175 // with expanded range and with no infinity or signed zero.
176 // NaN is represented as negative zero. (FN -> Finite, UZ -> unsigned zero).
177 // This format's exponent bias is 8, instead of the 7 (2 ** (4 - 1) - 1)
178 // that IEEE precedent would imply.
179 S_Float8E4M3FNUZ,
180 // 8-bit floating point number mostly following IEEE-754 conventions
181 // and bit layout S1E4M3 with expanded range and with no infinity or signed
182 // zero.
183 // NaN is represented as negative zero. (FN -> Finite, UZ -> unsigned zero).
184 // This format's exponent bias is 11, instead of the 7 (2 ** (4 - 1) - 1)
185 // that IEEE precedent would imply.
186 S_Float8E4M3B11FNUZ,
187 // Floating point number that occupies 32 bits or less of storage, providing
188 // improved range compared to half (16-bit) formats, at (potentially)
189 // greater throughput than single precision (32-bit) formats.
190 S_FloatTF32,
191
192 S_x87DoubleExtended,
193 S_MaxSemantics = S_x87DoubleExtended,
194 };
195
196 static const llvm::fltSemantics &EnumToSemantics(Semantics S);
197 static Semantics SemanticsToEnum(const llvm::fltSemantics &Sem);
198
199 static const fltSemantics &IEEEhalf() LLVM_READNONE;
200 static const fltSemantics &BFloat() LLVM_READNONE;
201 static const fltSemantics &IEEEsingle() LLVM_READNONE;
202 static const fltSemantics &IEEEdouble() LLVM_READNONE;
203 static const fltSemantics &IEEEquad() LLVM_READNONE;
204 static const fltSemantics &PPCDoubleDouble() LLVM_READNONE;
205 static const fltSemantics &Float8E5M2() LLVM_READNONE;
206 static const fltSemantics &Float8E5M2FNUZ() LLVM_READNONE;
207 static const fltSemantics &Float8E4M3FN() LLVM_READNONE;
208 static const fltSemantics &Float8E4M3FNUZ() LLVM_READNONE;
209 static const fltSemantics &Float8E4M3B11FNUZ() LLVM_READNONE;
210 static const fltSemantics &FloatTF32() LLVM_READNONE;
211 static const fltSemantics &x87DoubleExtended() LLVM_READNONE;
212
213 /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
214 /// anything real.
215 static const fltSemantics &Bogus() LLVM_READNONE;
216
217 /// @}
218
219 /// IEEE-754R 5.11: Floating Point Comparison Relations.
220 enum cmpResult {
221 cmpLessThan,
222 cmpEqual,
223 cmpGreaterThan,
224 cmpUnordered
225 };
226
227 /// IEEE-754R 4.3: Rounding-direction attributes.
228 using roundingMode = llvm::RoundingMode;
229
230 static constexpr roundingMode rmNearestTiesToEven =
231 RoundingMode::NearestTiesToEven;
232 static constexpr roundingMode rmTowardPositive = RoundingMode::TowardPositive;
233 static constexpr roundingMode rmTowardNegative = RoundingMode::TowardNegative;
234 static constexpr roundingMode rmTowardZero = RoundingMode::TowardZero;
235 static constexpr roundingMode rmNearestTiesToAway =
236 RoundingMode::NearestTiesToAway;
237
238 /// IEEE-754R 7: Default exception handling.
239 ///
240 /// opUnderflow or opOverflow are always returned or-ed with opInexact.
241 ///
242 /// APFloat models this behavior specified by IEEE-754:
243 /// "For operations producing results in floating-point format, the default
244 /// result of an operation that signals the invalid operation exception
245 /// shall be a quiet NaN."
246 enum opStatus {
247 opOK = 0x00,
248 opInvalidOp = 0x01,
249 opDivByZero = 0x02,
250 opOverflow = 0x04,
251 opUnderflow = 0x08,
252 opInexact = 0x10
253 };
254
255 /// Category of internally-represented number.
256 enum fltCategory {
257 fcInfinity,
258 fcNaN,
259 fcNormal,
260 fcZero
261 };
262
263 /// Convenience enum used to construct an uninitialized APFloat.
264 enum uninitializedTag {
265 uninitialized
266 };
267
268 /// Enumeration of \c ilogb error results.
269 enum IlogbErrorKinds {
270 IEK_Zero = INT_MIN + 1,
271 IEK_NaN = INT_MIN,
272 IEK_Inf = INT_MAX
273 };
274
275 static unsigned int semanticsPrecision(const fltSemantics &);
276 static ExponentType semanticsMinExponent(const fltSemantics &);
277 static ExponentType semanticsMaxExponent(const fltSemantics &);
278 static unsigned int semanticsSizeInBits(const fltSemantics &);
279 static unsigned int semanticsIntSizeInBits(const fltSemantics&, bool);
280
281 // Returns true if any number described by \p Src can be precisely represented
282 // by a normal (not subnormal) value in \p Dst.
283 static bool isRepresentableAsNormalIn(const fltSemantics &Src,
284 const fltSemantics &Dst);
285
286 /// Returns the size of the floating point number (in bits) in the given
287 /// semantics.
288 static unsigned getSizeInBits(const fltSemantics &Sem);
289};
290
291namespace detail {
292
293class IEEEFloat final : public APFloatBase {
294public:
295 /// \name Constructors
296 /// @{
297
298 IEEEFloat(const fltSemantics &); // Default construct to +0.0
299 IEEEFloat(const fltSemantics &, integerPart);
300 IEEEFloat(const fltSemantics &, uninitializedTag);
301 IEEEFloat(const fltSemantics &, const APInt &);
302 explicit IEEEFloat(double d);
303 explicit IEEEFloat(float f);
304 IEEEFloat(const IEEEFloat &);
305 IEEEFloat(IEEEFloat &&);
306 ~IEEEFloat();
307
308 /// @}
309
310 /// Returns whether this instance allocated memory.
311 bool needsCleanup() const { return partCount() > 1; }
312
313 /// \name Convenience "constructors"
314 /// @{
315
316 /// @}
317
318 /// \name Arithmetic
319 /// @{
320
321 opStatus add(const IEEEFloat &, roundingMode);
322 opStatus subtract(const IEEEFloat &, roundingMode);
323 opStatus multiply(const IEEEFloat &, roundingMode);
324 opStatus divide(const IEEEFloat &, roundingMode);
325 /// IEEE remainder.
326 opStatus remainder(const IEEEFloat &);
327 /// C fmod, or llvm frem.
328 opStatus mod(const IEEEFloat &);
329 opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);
330 opStatus roundToIntegral(roundingMode);
331 /// IEEE-754R 5.3.1: nextUp/nextDown.
332 opStatus next(bool nextDown);
333
334 /// @}
335
336 /// \name Sign operations.
337 /// @{
338
339 void changeSign();
340
341 /// @}
342
343 /// \name Conversions
344 /// @{
345
346 opStatus convert(const fltSemantics &, roundingMode, bool *);
347 opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,
348 roundingMode, bool *) const;
349 opStatus convertFromAPInt(const APInt &, bool, roundingMode);
350 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
351 bool, roundingMode);
352 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
353 bool, roundingMode);
354 Expected<opStatus> convertFromString(StringRef, roundingMode);
355 APInt bitcastToAPInt() const;
356 double convertToDouble() const;
357 float convertToFloat() const;
358
359 /// @}
360
361 /// The definition of equality is not straightforward for floating point, so
362 /// we won't use operator==. Use one of the following, or write whatever it
363 /// is you really mean.
364 bool operator==(const IEEEFloat &) const = delete;
365
366 /// IEEE comparison with another floating point number (NaNs compare
367 /// unordered, 0==-0).
368 cmpResult compare(const IEEEFloat &) const;
369
370 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
371 bool bitwiseIsEqual(const IEEEFloat &) const;
372
373 /// Write out a hexadecimal representation of the floating point value to DST,
374 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
375 /// Return the number of characters written, excluding the terminating NUL.
376 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
377 bool upperCase, roundingMode) const;
378
379 /// \name IEEE-754R 5.7.2 General operations.
380 /// @{
381
382 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
383 /// negative.
384 ///
385 /// This applies to zeros and NaNs as well.
386 bool isNegative() const { return sign; }
387
388 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
389 ///
390 /// This implies that the current value of the float is not zero, subnormal,
391 /// infinite, or NaN following the definition of normality from IEEE-754R.
392 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
393
394 /// Returns true if and only if the current value is zero, subnormal, or
395 /// normal.
396 ///
397 /// This means that the value is not infinite or NaN.
398 bool isFinite() const { return !isNaN() && !isInfinity(); }
399
400 /// Returns true if and only if the float is plus or minus zero.
401 bool isZero() const { return category == fcZero; }
402
403 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
404 /// denormal.
405 bool isDenormal() const;
406
407 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
408 bool isInfinity() const { return category == fcInfinity; }
409
410 /// Returns true if and only if the float is a quiet or signaling NaN.
411 bool isNaN() const { return category == fcNaN; }
412
413 /// Returns true if and only if the float is a signaling NaN.
414 bool isSignaling() const;
415
416 /// @}
417
418 /// \name Simple Queries
419 /// @{
420
421 fltCategory getCategory() const { return category; }
422 const fltSemantics &getSemantics() const { return *semantics; }
423 bool isNonZero() const { return category != fcZero; }
424 bool isFiniteNonZero() const { return isFinite() && !isZero(); }
425 bool isPosZero() const { return isZero() && !isNegative(); }
426 bool isNegZero() const { return isZero() && isNegative(); }
427
428 /// Returns true if and only if the number has the smallest possible non-zero
429 /// magnitude in the current semantics.
430 bool isSmallest() const;
431
432 /// Returns true if this is the smallest (by magnitude) normalized finite
433 /// number in the given semantics.
434 bool isSmallestNormalized() const;
435
436 /// Returns true if and only if the number has the largest possible finite
437 /// magnitude in the current semantics.
438 bool isLargest() const;
439
440 /// Returns true if and only if the number is an exact integer.
441 bool isInteger() const;
442
443 /// @}
444
445 IEEEFloat &operator=(const IEEEFloat &);
446 IEEEFloat &operator=(IEEEFloat &&);
447
448 /// Overload to compute a hash code for an APFloat value.
449 ///
450 /// Note that the use of hash codes for floating point values is in general
451 /// frought with peril. Equality is hard to define for these values. For
452 /// example, should negative and positive zero hash to different codes? Are
453 /// they equal or not? This hash value implementation specifically
454 /// emphasizes producing different codes for different inputs in order to
455 /// be used in canonicalization and memoization. As such, equality is
456 /// bitwiseIsEqual, and 0 != -0.
457 friend hash_code hash_value(const IEEEFloat &Arg);
458
459 /// Converts this value into a decimal string.
460 ///
461 /// \param FormatPrecision The maximum number of digits of
462 /// precision to output. If there are fewer digits available,
463 /// zero padding will not be used unless the value is
464 /// integral and small enough to be expressed in
465 /// FormatPrecision digits. 0 means to use the natural
466 /// precision of the number.
467 /// \param FormatMaxPadding The maximum number of zeros to
468 /// consider inserting before falling back to scientific
469 /// notation. 0 means to always use scientific notation.
470 ///
471 /// \param TruncateZero Indicate whether to remove the trailing zero in
472 /// fraction part or not. Also setting this parameter to false forcing
473 /// producing of output more similar to default printf behavior.
474 /// Specifically the lower e is used as exponent delimiter and exponent
475 /// always contains no less than two digits.
476 ///
477 /// Number Precision MaxPadding Result
478 /// ------ --------- ---------- ------
479 /// 1.01E+4 5 2 10100
480 /// 1.01E+4 4 2 1.01E+4
481 /// 1.01E+4 5 1 1.01E+4
482 /// 1.01E-2 5 2 0.0101
483 /// 1.01E-2 4 2 0.0101
484 /// 1.01E-2 4 1 1.01E-2
485 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
486 unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;
487
488 /// If this value has an exact multiplicative inverse, store it in inv and
489 /// return true.
490 bool getExactInverse(APFloat *inv) const;
491
492 /// Returns the exponent of the internal representation of the APFloat.
493 ///
494 /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
495 /// For special APFloat values, this returns special error codes:
496 ///
497 /// NaN -> \c IEK_NaN
498 /// 0 -> \c IEK_Zero
499 /// Inf -> \c IEK_Inf
500 ///
501 friend int ilogb(const IEEEFloat &Arg);
502
503 /// Returns: X * 2^Exp for integral exponents.
504 friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);
505
506 friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);
507
508 /// \name Special value setters.
509 /// @{
510
511 void makeLargest(bool Neg = false);
512 void makeSmallest(bool Neg = false);
513 void makeNaN(bool SNaN = false, bool Neg = false,
514 const APInt *fill = nullptr);
515 void makeInf(bool Neg = false);
516 void makeZero(bool Neg = false);
517 void makeQuiet();
518
519 /// Returns the smallest (by magnitude) normalized finite number in the given
520 /// semantics.
521 ///
522 /// \param Negative - True iff the number should be negative
523 void makeSmallestNormalized(bool Negative = false);
524
525 /// @}
526
527 cmpResult compareAbsoluteValue(const IEEEFloat &) const;
528
529private:
530 /// \name Simple Queries
531 /// @{
532
533 integerPart *significandParts();
534 const integerPart *significandParts() const;
535 unsigned int partCount() const;
536
537 /// @}
538
539 /// \name Significand operations.
540 /// @{
541
542 integerPart addSignificand(const IEEEFloat &);
543 integerPart subtractSignificand(const IEEEFloat &, integerPart);
544 lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
545 lostFraction multiplySignificand(const IEEEFloat &, IEEEFloat);
546 lostFraction multiplySignificand(const IEEEFloat&);
547 lostFraction divideSignificand(const IEEEFloat &);
548 void incrementSignificand();
549 void initialize(const fltSemantics *);
550 void shiftSignificandLeft(unsigned int);
551 lostFraction shiftSignificandRight(unsigned int);
552 unsigned int significandLSB() const;
553 unsigned int significandMSB() const;
554 void zeroSignificand();
555 /// Return true if the significand excluding the integral bit is all ones.
556 bool isSignificandAllOnes() const;
557 bool isSignificandAllOnesExceptLSB() const;
558 /// Return true if the significand excluding the integral bit is all zeros.
559 bool isSignificandAllZeros() const;
560 bool isSignificandAllZerosExceptMSB() const;
561
562 /// @}
563
564 /// \name Arithmetic on special values.
565 /// @{
566
567 opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);
568 opStatus divideSpecials(const IEEEFloat &);
569 opStatus multiplySpecials(const IEEEFloat &);
570 opStatus modSpecials(const IEEEFloat &);
571 opStatus remainderSpecials(const IEEEFloat&);
572
573 /// @}
574
575 /// \name Miscellany
576 /// @{
577
578 bool convertFromStringSpecials(StringRef str);
579 opStatus normalize(roundingMode, lostFraction);
580 opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);
581 opStatus handleOverflow(roundingMode);
582 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
583 opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,
584 unsigned int, bool, roundingMode,
585 bool *) const;
586 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
587 roundingMode);
588 Expected<opStatus> convertFromHexadecimalString(StringRef, roundingMode);
589 Expected<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 ExponentType exponentNaN() const;
595 ExponentType exponentInf() const;
596 ExponentType exponentZero() const;
597
598 /// @}
599
600 template <const fltSemantics &S> APInt convertIEEEFloatToAPInt() const;
601 APInt convertHalfAPFloatToAPInt() const;
602 APInt convertBFloatAPFloatToAPInt() const;
603 APInt convertFloatAPFloatToAPInt() const;
604 APInt convertDoubleAPFloatToAPInt() const;
605 APInt convertQuadrupleAPFloatToAPInt() const;
606 APInt convertF80LongDoubleAPFloatToAPInt() const;
607 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
608 APInt convertFloat8E5M2APFloatToAPInt() const;
609 APInt convertFloat8E5M2FNUZAPFloatToAPInt() const;
610 APInt convertFloat8E4M3FNAPFloatToAPInt() const;
611 APInt convertFloat8E4M3FNUZAPFloatToAPInt() const;
612 APInt convertFloat8E4M3B11FNUZAPFloatToAPInt() const;
613 APInt convertFloatTF32APFloatToAPInt() const;
614 void initFromAPInt(const fltSemantics *Sem, const APInt &api);
615 template <const fltSemantics &S> void initFromIEEEAPInt(const APInt &api);
616 void initFromHalfAPInt(const APInt &api);
617 void initFromBFloatAPInt(const APInt &api);
618 void initFromFloatAPInt(const APInt &api);
619 void initFromDoubleAPInt(const APInt &api);
620 void initFromQuadrupleAPInt(const APInt &api);
621 void initFromF80LongDoubleAPInt(const APInt &api);
622 void initFromPPCDoubleDoubleAPInt(const APInt &api);
623 void initFromFloat8E5M2APInt(const APInt &api);
624 void initFromFloat8E5M2FNUZAPInt(const APInt &api);
625 void initFromFloat8E4M3FNAPInt(const APInt &api);
626 void initFromFloat8E4M3FNUZAPInt(const APInt &api);
627 void initFromFloat8E4M3B11FNUZAPInt(const APInt &api);
628 void initFromFloatTF32APInt(const APInt &api);
629
630 void assign(const IEEEFloat &);
631 void copySignificand(const IEEEFloat &);
632 void freeSignificand();
633
634 /// Note: this must be the first data member.
635 /// The semantics that this value obeys.
636 const fltSemantics *semantics;
637
638 /// A binary fraction with an explicit integer bit.
639 ///
640 /// The significand must be at least one bit wider than the target precision.
641 union Significand {
642 integerPart part;
643 integerPart *parts;
644 } significand;
645
646 /// The signed unbiased exponent of the value.
647 ExponentType exponent;
648
649 /// What kind of floating point number this is.
650 ///
651 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
652 /// Using the extra bit keeps it from failing under VisualStudio.
653 fltCategory category : 3;
654
655 /// Sign bit of the number.
656 unsigned int sign : 1;
657};
658
659hash_code hash_value(const IEEEFloat &Arg);
660int ilogb(const IEEEFloat &Arg);
661IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode);
662IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);
663
664// This mode implements more precise float in terms of two APFloats.
665// The interface and layout is designed for arbitrary underlying semantics,
666// though currently only PPCDoubleDouble semantics are supported, whose
667// corresponding underlying semantics are IEEEdouble.
668class DoubleAPFloat final : public APFloatBase {
669 // Note: this must be the first data member.
670 const fltSemantics *Semantics;
671 std::unique_ptr<APFloat[]> Floats;
672
673 opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,
674 const APFloat &cc, roundingMode RM);
675
676 opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,
677 DoubleAPFloat &Out, roundingMode RM);
678
679public:
680 DoubleAPFloat(const fltSemantics &S);
681 DoubleAPFloat(const fltSemantics &S, uninitializedTag);
682 DoubleAPFloat(const fltSemantics &S, integerPart);
683 DoubleAPFloat(const fltSemantics &S, const APInt &I);
684 DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);
685 DoubleAPFloat(const DoubleAPFloat &RHS);
686 DoubleAPFloat(DoubleAPFloat &&RHS);
687
688 DoubleAPFloat &operator=(const DoubleAPFloat &RHS);
689 inline DoubleAPFloat &operator=(DoubleAPFloat &&RHS);
690
691 bool needsCleanup() const { return Floats != nullptr; }
692
693 inline APFloat &getFirst();
694 inline const APFloat &getFirst() const;
695 inline APFloat &getSecond();
696 inline const APFloat &getSecond() const;
697
698 opStatus add(const DoubleAPFloat &RHS, roundingMode RM);
699 opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);
700 opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);
701 opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);
702 opStatus remainder(const DoubleAPFloat &RHS);
703 opStatus mod(const DoubleAPFloat &RHS);
704 opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
705 const DoubleAPFloat &Addend, roundingMode RM);
706 opStatus roundToIntegral(roundingMode RM);
707 void changeSign();
708 cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;
709
710 fltCategory getCategory() const;
711 bool isNegative() const;
712
713 void makeInf(bool Neg);
714 void makeZero(bool Neg);
715 void makeLargest(bool Neg);
716 void makeSmallest(bool Neg);
717 void makeSmallestNormalized(bool Neg);
718 void makeNaN(bool SNaN, bool Neg, const APInt *fill);
719
720 cmpResult compare(const DoubleAPFloat &RHS) const;
721 bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;
722 APInt bitcastToAPInt() const;
723 Expected<opStatus> convertFromString(StringRef, roundingMode);
724 opStatus next(bool nextDown);
725
726 opStatus convertToInteger(MutableArrayRef<integerPart> Input,
727 unsigned int Width, bool IsSigned, roundingMode RM,
728 bool *IsExact) const;
729 opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);
730 opStatus convertFromSignExtendedInteger(const integerPart *Input,
731 unsigned int InputSize, bool IsSigned,
732 roundingMode RM);
733 opStatus convertFromZeroExtendedInteger(const integerPart *Input,
734 unsigned int InputSize, bool IsSigned,
735 roundingMode RM);
736 unsigned int convertToHexString(char *DST, unsigned int HexDigits,
737 bool UpperCase, roundingMode RM) const;
738
739 bool isDenormal() const;
740 bool isSmallest() const;
741 bool isSmallestNormalized() const;
742 bool isLargest() const;
743 bool isInteger() const;
744
745 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
746 unsigned FormatMaxPadding, bool TruncateZero = true) const;
747
748 bool getExactInverse(APFloat *inv) const;
749
750 friend DoubleAPFloat scalbn(const DoubleAPFloat &X, int Exp, roundingMode);
751 friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);
752 friend hash_code hash_value(const DoubleAPFloat &Arg);
753};
754
755hash_code hash_value(const DoubleAPFloat &Arg);
756
757} // End detail namespace
758
759// This is a interface class that is currently forwarding functionalities from
760// detail::IEEEFloat.
761class APFloat : public APFloatBase {
762 typedef detail::IEEEFloat IEEEFloat;
763 typedef detail::DoubleAPFloat DoubleAPFloat;
764
765 static_assert(std::is_standard_layout<IEEEFloat>::value);
766
767 union Storage {
768 const fltSemantics *semantics;
769 IEEEFloat IEEE;
770 DoubleAPFloat Double;
771
772 explicit Storage(IEEEFloat F, const fltSemantics &S);
773 explicit Storage(DoubleAPFloat F, const fltSemantics &S)
774 : Double(std::move(F)) {
775 assert(&S == &PPCDoubleDouble());
776 }
777
778 template <typename... ArgTypes>
779 Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {
780 if (usesLayout<IEEEFloat>(Semantics)) {
781 new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);
782 return;
783 }
784 if (usesLayout<DoubleAPFloat>(Semantics)) {
785 new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);
786 return;
787 }
788 llvm_unreachable("Unexpected semantics");
789 }
790
791 ~Storage() {
792 if (usesLayout<IEEEFloat>(Semantics: *semantics)) {
793 IEEE.~IEEEFloat();
794 return;
795 }
796 if (usesLayout<DoubleAPFloat>(Semantics: *semantics)) {
797 Double.~DoubleAPFloat();
798 return;
799 }
800 llvm_unreachable("Unexpected semantics");
801 }
802
803 Storage(const Storage &RHS) {
804 if (usesLayout<IEEEFloat>(Semantics: *RHS.semantics)) {
805 new (this) IEEEFloat(RHS.IEEE);
806 return;
807 }
808 if (usesLayout<DoubleAPFloat>(Semantics: *RHS.semantics)) {
809 new (this) DoubleAPFloat(RHS.Double);
810 return;
811 }
812 llvm_unreachable("Unexpected semantics");
813 }
814
815 Storage(Storage &&RHS) {
816 if (usesLayout<IEEEFloat>(Semantics: *RHS.semantics)) {
817 new (this) IEEEFloat(std::move(RHS.IEEE));
818 return;
819 }
820 if (usesLayout<DoubleAPFloat>(Semantics: *RHS.semantics)) {
821 new (this) DoubleAPFloat(std::move(RHS.Double));
822 return;
823 }
824 llvm_unreachable("Unexpected semantics");
825 }
826
827 Storage &operator=(const Storage &RHS) {
828 if (usesLayout<IEEEFloat>(Semantics: *semantics) &&
829 usesLayout<IEEEFloat>(Semantics: *RHS.semantics)) {
830 IEEE = RHS.IEEE;
831 } else if (usesLayout<DoubleAPFloat>(Semantics: *semantics) &&
832 usesLayout<DoubleAPFloat>(Semantics: *RHS.semantics)) {
833 Double = RHS.Double;
834 } else if (this != &RHS) {
835 this->~Storage();
836 new (this) Storage(RHS);
837 }
838 return *this;
839 }
840
841 Storage &operator=(Storage &&RHS) {
842 if (usesLayout<IEEEFloat>(Semantics: *semantics) &&
843 usesLayout<IEEEFloat>(Semantics: *RHS.semantics)) {
844 IEEE = std::move(RHS.IEEE);
845 } else if (usesLayout<DoubleAPFloat>(Semantics: *semantics) &&
846 usesLayout<DoubleAPFloat>(Semantics: *RHS.semantics)) {
847 Double = std::move(RHS.Double);
848 } else if (this != &RHS) {
849 this->~Storage();
850 new (this) Storage(std::move(RHS));
851 }
852 return *this;
853 }
854 } U;
855
856 template <typename T> static bool usesLayout(const fltSemantics &Semantics) {
857 static_assert(std::is_same<T, IEEEFloat>::value ||
858 std::is_same<T, DoubleAPFloat>::value);
859 if (std::is_same<T, DoubleAPFloat>::value) {
860 return &Semantics == &PPCDoubleDouble();
861 }
862 return &Semantics != &PPCDoubleDouble();
863 }
864
865 IEEEFloat &getIEEE() {
866 if (usesLayout<IEEEFloat>(Semantics: *U.semantics))
867 return U.IEEE;
868 if (usesLayout<DoubleAPFloat>(Semantics: *U.semantics))
869 return U.Double.getFirst().U.IEEE;
870 llvm_unreachable("Unexpected semantics");
871 }
872
873 const IEEEFloat &getIEEE() const {
874 if (usesLayout<IEEEFloat>(Semantics: *U.semantics))
875 return U.IEEE;
876 if (usesLayout<DoubleAPFloat>(Semantics: *U.semantics))
877 return U.Double.getFirst().U.IEEE;
878 llvm_unreachable("Unexpected semantics");
879 }
880
881 void makeZero(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeZero(Neg)); }
882
883 void makeInf(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeInf(Neg)); }
884
885 void makeNaN(bool SNaN, bool Neg, const APInt *fill) {
886 APFLOAT_DISPATCH_ON_SEMANTICS(makeNaN(SNaN, Neg, fill));
887 }
888
889 void makeLargest(bool Neg) {
890 APFLOAT_DISPATCH_ON_SEMANTICS(makeLargest(Neg));
891 }
892
893 void makeSmallest(bool Neg) {
894 APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallest(Neg));
895 }
896
897 void makeSmallestNormalized(bool Neg) {
898 APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallestNormalized(Neg));
899 }
900
901 explicit APFloat(IEEEFloat F, const fltSemantics &S) : U(std::move(F), S) {}
902 explicit APFloat(DoubleAPFloat F, const fltSemantics &S)
903 : U(std::move(F), S) {}
904
905 cmpResult compareAbsoluteValue(const APFloat &RHS) const {
906 assert(&getSemantics() == &RHS.getSemantics() &&
907 "Should only compare APFloats with the same semantics");
908 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
909 return U.IEEE.compareAbsoluteValue(RHS.U.IEEE);
910 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
911 return U.Double.compareAbsoluteValue(RHS: RHS.U.Double);
912 llvm_unreachable("Unexpected semantics");
913 }
914
915public:
916 APFloat(const fltSemantics &Semantics) : U(Semantics) {}
917 APFloat(const fltSemantics &Semantics, StringRef S);
918 APFloat(const fltSemantics &Semantics, integerPart I) : U(Semantics, I) {}
919 template <typename T,
920 typename = std::enable_if_t<std::is_floating_point<T>::value>>
921 APFloat(const fltSemantics &Semantics, T V) = delete;
922 // TODO: Remove this constructor. This isn't faster than the first one.
923 APFloat(const fltSemantics &Semantics, uninitializedTag)
924 : U(Semantics, uninitialized) {}
925 APFloat(const fltSemantics &Semantics, const APInt &I) : U(Semantics, I) {}
926 explicit APFloat(double d) : U(IEEEFloat(d), IEEEdouble()) {}
927 explicit APFloat(float f) : U(IEEEFloat(f), IEEEsingle()) {}
928 APFloat(const APFloat &RHS) = default;
929 APFloat(APFloat &&RHS) = default;
930
931 ~APFloat() = default;
932
933 bool needsCleanup() const { APFLOAT_DISPATCH_ON_SEMANTICS(needsCleanup()); }
934
935 /// Factory for Positive and Negative Zero.
936 ///
937 /// \param Negative True iff the number should be negative.
938 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
939 APFloat Val(Sem, uninitialized);
940 Val.makeZero(Neg: Negative);
941 return Val;
942 }
943
944 /// Factory for Positive and Negative Infinity.
945 ///
946 /// \param Negative True iff the number should be negative.
947 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
948 APFloat Val(Sem, uninitialized);
949 Val.makeInf(Neg: Negative);
950 return Val;
951 }
952
953 /// Factory for NaN values.
954 ///
955 /// \param Negative - True iff the NaN generated should be negative.
956 /// \param payload - The unspecified fill bits for creating the NaN, 0 by
957 /// default. The value is truncated as necessary.
958 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
959 uint64_t payload = 0) {
960 if (payload) {
961 APInt intPayload(64, payload);
962 return getQNaN(Sem, Negative, payload: &intPayload);
963 } else {
964 return getQNaN(Sem, Negative, payload: nullptr);
965 }
966 }
967
968 /// Factory for QNaN values.
969 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
970 const APInt *payload = nullptr) {
971 APFloat Val(Sem, uninitialized);
972 Val.makeNaN(SNaN: false, Neg: Negative, fill: payload);
973 return Val;
974 }
975
976 /// Factory for SNaN values.
977 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
978 const APInt *payload = nullptr) {
979 APFloat Val(Sem, uninitialized);
980 Val.makeNaN(SNaN: true, Neg: Negative, fill: payload);
981 return Val;
982 }
983
984 /// Returns the largest finite number in the given semantics.
985 ///
986 /// \param Negative - True iff the number should be negative
987 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false) {
988 APFloat Val(Sem, uninitialized);
989 Val.makeLargest(Neg: Negative);
990 return Val;
991 }
992
993 /// Returns the smallest (by magnitude) finite number in the given semantics.
994 /// Might be denormalized, which implies a relative loss of precision.
995 ///
996 /// \param Negative - True iff the number should be negative
997 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false) {
998 APFloat Val(Sem, uninitialized);
999 Val.makeSmallest(Neg: Negative);
1000 return Val;
1001 }
1002
1003 /// Returns the smallest (by magnitude) normalized finite number in the given
1004 /// semantics.
1005 ///
1006 /// \param Negative - True iff the number should be negative
1007 static APFloat getSmallestNormalized(const fltSemantics &Sem,
1008 bool Negative = false) {
1009 APFloat Val(Sem, uninitialized);
1010 Val.makeSmallestNormalized(Neg: Negative);
1011 return Val;
1012 }
1013
1014 /// Returns a float which is bitcasted from an all one value int.
1015 ///
1016 /// \param Semantics - type float semantics
1017 static APFloat getAllOnesValue(const fltSemantics &Semantics);
1018
1019 /// Used to insert APFloat objects, or objects that contain APFloat objects,
1020 /// into FoldingSets.
1021 void Profile(FoldingSetNodeID &NID) const;
1022
1023 opStatus add(const APFloat &RHS, roundingMode RM) {
1024 assert(&getSemantics() == &RHS.getSemantics() &&
1025 "Should only call on two APFloats with the same semantics");
1026 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1027 return U.IEEE.add(RHS.U.IEEE, RM);
1028 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1029 return U.Double.add(RHS: RHS.U.Double, RM);
1030 llvm_unreachable("Unexpected semantics");
1031 }
1032 opStatus subtract(const APFloat &RHS, roundingMode RM) {
1033 assert(&getSemantics() == &RHS.getSemantics() &&
1034 "Should only call on two APFloats with the same semantics");
1035 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1036 return U.IEEE.subtract(RHS.U.IEEE, RM);
1037 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1038 return U.Double.subtract(RHS: RHS.U.Double, RM);
1039 llvm_unreachable("Unexpected semantics");
1040 }
1041 opStatus multiply(const APFloat &RHS, roundingMode RM) {
1042 assert(&getSemantics() == &RHS.getSemantics() &&
1043 "Should only call on two APFloats with the same semantics");
1044 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1045 return U.IEEE.multiply(RHS.U.IEEE, RM);
1046 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1047 return U.Double.multiply(RHS: RHS.U.Double, RM);
1048 llvm_unreachable("Unexpected semantics");
1049 }
1050 opStatus divide(const APFloat &RHS, roundingMode RM) {
1051 assert(&getSemantics() == &RHS.getSemantics() &&
1052 "Should only call on two APFloats with the same semantics");
1053 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1054 return U.IEEE.divide(RHS.U.IEEE, RM);
1055 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1056 return U.Double.divide(RHS: RHS.U.Double, RM);
1057 llvm_unreachable("Unexpected semantics");
1058 }
1059 opStatus remainder(const APFloat &RHS) {
1060 assert(&getSemantics() == &RHS.getSemantics() &&
1061 "Should only call on two APFloats with the same semantics");
1062 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1063 return U.IEEE.remainder(RHS.U.IEEE);
1064 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1065 return U.Double.remainder(RHS: RHS.U.Double);
1066 llvm_unreachable("Unexpected semantics");
1067 }
1068 opStatus mod(const APFloat &RHS) {
1069 assert(&getSemantics() == &RHS.getSemantics() &&
1070 "Should only call on two APFloats with the same semantics");
1071 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1072 return U.IEEE.mod(RHS.U.IEEE);
1073 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1074 return U.Double.mod(RHS: RHS.U.Double);
1075 llvm_unreachable("Unexpected semantics");
1076 }
1077 opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend,
1078 roundingMode RM) {
1079 assert(&getSemantics() == &Multiplicand.getSemantics() &&
1080 "Should only call on APFloats with the same semantics");
1081 assert(&getSemantics() == &Addend.getSemantics() &&
1082 "Should only call on APFloats with the same semantics");
1083 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1084 return U.IEEE.fusedMultiplyAdd(Multiplicand.U.IEEE, Addend.U.IEEE, RM);
1085 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1086 return U.Double.fusedMultiplyAdd(Multiplicand: Multiplicand.U.Double, Addend: Addend.U.Double,
1087 RM);
1088 llvm_unreachable("Unexpected semantics");
1089 }
1090 opStatus roundToIntegral(roundingMode RM) {
1091 APFLOAT_DISPATCH_ON_SEMANTICS(roundToIntegral(RM));
1092 }
1093
1094 // TODO: bool parameters are not readable and a source of bugs.
1095 // Do something.
1096 opStatus next(bool nextDown) {
1097 APFLOAT_DISPATCH_ON_SEMANTICS(next(nextDown));
1098 }
1099
1100 /// Negate an APFloat.
1101 APFloat operator-() const {
1102 APFloat Result(*this);
1103 Result.changeSign();
1104 return Result;
1105 }
1106
1107 /// Add two APFloats, rounding ties to the nearest even.
1108 /// No error checking.
1109 APFloat operator+(const APFloat &RHS) const {
1110 APFloat Result(*this);
1111 (void)Result.add(RHS, RM: rmNearestTiesToEven);
1112 return Result;
1113 }
1114
1115 /// Subtract two APFloats, rounding ties to the nearest even.
1116 /// No error checking.
1117 APFloat operator-(const APFloat &RHS) const {
1118 APFloat Result(*this);
1119 (void)Result.subtract(RHS, RM: rmNearestTiesToEven);
1120 return Result;
1121 }
1122
1123 /// Multiply two APFloats, rounding ties to the nearest even.
1124 /// No error checking.
1125 APFloat operator*(const APFloat &RHS) const {
1126 APFloat Result(*this);
1127 (void)Result.multiply(RHS, RM: rmNearestTiesToEven);
1128 return Result;
1129 }
1130
1131 /// Divide the first APFloat by the second, rounding ties to the nearest even.
1132 /// No error checking.
1133 APFloat operator/(const APFloat &RHS) const {
1134 APFloat Result(*this);
1135 (void)Result.divide(RHS, RM: rmNearestTiesToEven);
1136 return Result;
1137 }
1138
1139 void changeSign() { APFLOAT_DISPATCH_ON_SEMANTICS(changeSign()); }
1140 void clearSign() {
1141 if (isNegative())
1142 changeSign();
1143 }
1144 void copySign(const APFloat &RHS) {
1145 if (isNegative() != RHS.isNegative())
1146 changeSign();
1147 }
1148
1149 /// A static helper to produce a copy of an APFloat value with its sign
1150 /// copied from some other APFloat.
1151 static APFloat copySign(APFloat Value, const APFloat &Sign) {
1152 Value.copySign(RHS: Sign);
1153 return Value;
1154 }
1155
1156 /// Assuming this is an IEEE-754 NaN value, quiet its signaling bit.
1157 /// This preserves the sign and payload bits.
1158 APFloat makeQuiet() const {
1159 APFloat Result(*this);
1160 Result.getIEEE().makeQuiet();
1161 return Result;
1162 }
1163
1164 opStatus convert(const fltSemantics &ToSemantics, roundingMode RM,
1165 bool *losesInfo);
1166 opStatus convertToInteger(MutableArrayRef<integerPart> Input,
1167 unsigned int Width, bool IsSigned, roundingMode RM,
1168 bool *IsExact) const {
1169 APFLOAT_DISPATCH_ON_SEMANTICS(
1170 convertToInteger(Input, Width, IsSigned, RM, IsExact));
1171 }
1172 opStatus convertToInteger(APSInt &Result, roundingMode RM,
1173 bool *IsExact) const;
1174 opStatus convertFromAPInt(const APInt &Input, bool IsSigned,
1175 roundingMode RM) {
1176 APFLOAT_DISPATCH_ON_SEMANTICS(convertFromAPInt(Input, IsSigned, RM));
1177 }
1178 opStatus convertFromSignExtendedInteger(const integerPart *Input,
1179 unsigned int InputSize, bool IsSigned,
1180 roundingMode RM) {
1181 APFLOAT_DISPATCH_ON_SEMANTICS(
1182 convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM));
1183 }
1184 opStatus convertFromZeroExtendedInteger(const integerPart *Input,
1185 unsigned int InputSize, bool IsSigned,
1186 roundingMode RM) {
1187 APFLOAT_DISPATCH_ON_SEMANTICS(
1188 convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM));
1189 }
1190 Expected<opStatus> convertFromString(StringRef, roundingMode);
1191 APInt bitcastToAPInt() const {
1192 APFLOAT_DISPATCH_ON_SEMANTICS(bitcastToAPInt());
1193 }
1194
1195 /// Converts this APFloat to host double value.
1196 ///
1197 /// \pre The APFloat must be built using semantics, that can be represented by
1198 /// the host double type without loss of precision. It can be IEEEdouble and
1199 /// shorter semantics, like IEEEsingle and others.
1200 double convertToDouble() const;
1201
1202 /// Converts this APFloat to host float value.
1203 ///
1204 /// \pre The APFloat must be built using semantics, that can be represented by
1205 /// the host float type without loss of precision. It can be IEEEsingle and
1206 /// shorter semantics, like IEEEhalf.
1207 float convertToFloat() const;
1208
1209 bool operator==(const APFloat &RHS) const { return compare(RHS) == cmpEqual; }
1210
1211 bool operator!=(const APFloat &RHS) const { return compare(RHS) != cmpEqual; }
1212
1213 bool operator<(const APFloat &RHS) const {
1214 return compare(RHS) == cmpLessThan;
1215 }
1216
1217 bool operator>(const APFloat &RHS) const {
1218 return compare(RHS) == cmpGreaterThan;
1219 }
1220
1221 bool operator<=(const APFloat &RHS) const {
1222 cmpResult Res = compare(RHS);
1223 return Res == cmpLessThan || Res == cmpEqual;
1224 }
1225
1226 bool operator>=(const APFloat &RHS) const {
1227 cmpResult Res = compare(RHS);
1228 return Res == cmpGreaterThan || Res == cmpEqual;
1229 }
1230
1231 cmpResult compare(const APFloat &RHS) const {
1232 assert(&getSemantics() == &RHS.getSemantics() &&
1233 "Should only compare APFloats with the same semantics");
1234 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1235 return U.IEEE.compare(RHS.U.IEEE);
1236 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1237 return U.Double.compare(RHS: RHS.U.Double);
1238 llvm_unreachable("Unexpected semantics");
1239 }
1240
1241 bool bitwiseIsEqual(const APFloat &RHS) const {
1242 if (&getSemantics() != &RHS.getSemantics())
1243 return false;
1244 if (usesLayout<IEEEFloat>(Semantics: getSemantics()))
1245 return U.IEEE.bitwiseIsEqual(RHS.U.IEEE);
1246 if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()))
1247 return U.Double.bitwiseIsEqual(RHS: RHS.U.Double);
1248 llvm_unreachable("Unexpected semantics");
1249 }
1250
1251 /// We don't rely on operator== working on double values, as
1252 /// it returns true for things that are clearly not equal, like -0.0 and 0.0.
1253 /// As such, this method can be used to do an exact bit-for-bit comparison of
1254 /// two floating point values.
1255 ///
1256 /// We leave the version with the double argument here because it's just so
1257 /// convenient to write "2.0" and the like. Without this function we'd
1258 /// have to duplicate its logic everywhere it's called.
1259 bool isExactlyValue(double V) const {
1260 bool ignored;
1261 APFloat Tmp(V);
1262 Tmp.convert(ToSemantics: getSemantics(), RM: APFloat::rmNearestTiesToEven, losesInfo: &ignored);
1263 return bitwiseIsEqual(RHS: Tmp);
1264 }
1265
1266 unsigned int convertToHexString(char *DST, unsigned int HexDigits,
1267 bool UpperCase, roundingMode RM) const {
1268 APFLOAT_DISPATCH_ON_SEMANTICS(
1269 convertToHexString(DST, HexDigits, UpperCase, RM));
1270 }
1271
1272 bool isZero() const { return getCategory() == fcZero; }
1273 bool isInfinity() const { return getCategory() == fcInfinity; }
1274 bool isNaN() const { return getCategory() == fcNaN; }
1275
1276 bool isNegative() const { return getIEEE().isNegative(); }
1277 bool isDenormal() const { APFLOAT_DISPATCH_ON_SEMANTICS(isDenormal()); }
1278 bool isSignaling() const { return getIEEE().isSignaling(); }
1279
1280 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
1281 bool isFinite() const { return !isNaN() && !isInfinity(); }
1282
1283 fltCategory getCategory() const { return getIEEE().getCategory(); }
1284 const fltSemantics &getSemantics() const { return *U.semantics; }
1285 bool isNonZero() const { return !isZero(); }
1286 bool isFiniteNonZero() const { return isFinite() && !isZero(); }
1287 bool isPosZero() const { return isZero() && !isNegative(); }
1288 bool isNegZero() const { return isZero() && isNegative(); }
1289 bool isPosInfinity() const { return isInfinity() && !isNegative(); }
1290 bool isNegInfinity() const { return isInfinity() && isNegative(); }
1291 bool isSmallest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isSmallest()); }
1292 bool isLargest() const { APFLOAT_DISPATCH_ON_SEMANTICS(isLargest()); }
1293 bool isInteger() const { APFLOAT_DISPATCH_ON_SEMANTICS(isInteger()); }
1294 bool isIEEE() const { return usesLayout<IEEEFloat>(Semantics: getSemantics()); }
1295
1296 bool isSmallestNormalized() const {
1297 APFLOAT_DISPATCH_ON_SEMANTICS(isSmallestNormalized());
1298 }
1299
1300 /// Return the FPClassTest which will return true for the value.
1301 FPClassTest classify() const;
1302
1303 APFloat &operator=(const APFloat &RHS) = default;
1304 APFloat &operator=(APFloat &&RHS) = default;
1305
1306 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
1307 unsigned FormatMaxPadding = 3, bool TruncateZero = true) const {
1308 APFLOAT_DISPATCH_ON_SEMANTICS(
1309 toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero));
1310 }
1311
1312 void print(raw_ostream &) const;
1313 void dump() const;
1314
1315 bool getExactInverse(APFloat *inv) const {
1316 APFLOAT_DISPATCH_ON_SEMANTICS(getExactInverse(inv));
1317 }
1318
1319 friend hash_code hash_value(const APFloat &Arg);
1320 friend int ilogb(const APFloat &Arg) { return ilogb(Arg: Arg.getIEEE()); }
1321 friend APFloat scalbn(APFloat X, int Exp, roundingMode RM);
1322 friend APFloat frexp(const APFloat &X, int &Exp, roundingMode RM);
1323 friend IEEEFloat;
1324 friend DoubleAPFloat;
1325};
1326
1327/// See friend declarations above.
1328///
1329/// These additional declarations are required in order to compile LLVM with IBM
1330/// xlC compiler.
1331hash_code hash_value(const APFloat &Arg);
1332inline APFloat scalbn(APFloat X, int Exp, APFloat::roundingMode RM) {
1333 if (APFloat::usesLayout<detail::IEEEFloat>(Semantics: X.getSemantics()))
1334 return APFloat(scalbn(X: X.U.IEEE, Exp, RM), X.getSemantics());
1335 if (APFloat::usesLayout<detail::DoubleAPFloat>(Semantics: X.getSemantics()))
1336 return APFloat(scalbn(X: X.U.Double, Exp, RM), X.getSemantics());
1337 llvm_unreachable("Unexpected semantics");
1338}
1339
1340/// Equivalent of C standard library function.
1341///
1342/// While the C standard says Exp is an unspecified value for infinity and nan,
1343/// this returns INT_MAX for infinities, and INT_MIN for NaNs.
1344inline APFloat frexp(const APFloat &X, int &Exp, APFloat::roundingMode RM) {
1345 if (APFloat::usesLayout<detail::IEEEFloat>(Semantics: X.getSemantics()))
1346 return APFloat(frexp(Val: X.U.IEEE, Exp, RM), X.getSemantics());
1347 if (APFloat::usesLayout<detail::DoubleAPFloat>(Semantics: X.getSemantics()))
1348 return APFloat(frexp(X: X.U.Double, Exp, RM), X.getSemantics());
1349 llvm_unreachable("Unexpected semantics");
1350}
1351/// Returns the absolute value of the argument.
1352inline APFloat abs(APFloat X) {
1353 X.clearSign();
1354 return X;
1355}
1356
1357/// Returns the negated value of the argument.
1358inline APFloat neg(APFloat X) {
1359 X.changeSign();
1360 return X;
1361}
1362
1363/// Implements IEEE minNum semantics. Returns the smaller of the 2 arguments if
1364/// both are not NaN. If either argument is a NaN, returns the other argument.
1365LLVM_READONLY
1366inline APFloat minnum(const APFloat &A, const APFloat &B) {
1367 if (A.isNaN())
1368 return B;
1369 if (B.isNaN())
1370 return A;
1371 return B < A ? B : A;
1372}
1373
1374/// Implements IEEE maxNum semantics. Returns the larger of the 2 arguments if
1375/// both are not NaN. If either argument is a NaN, returns the other argument.
1376LLVM_READONLY
1377inline APFloat maxnum(const APFloat &A, const APFloat &B) {
1378 if (A.isNaN())
1379 return B;
1380 if (B.isNaN())
1381 return A;
1382 return A < B ? B : A;
1383}
1384
1385/// Implements IEEE 754-2018 minimum semantics. Returns the smaller of 2
1386/// arguments, propagating NaNs and treating -0 as less than +0.
1387LLVM_READONLY
1388inline APFloat minimum(const APFloat &A, const APFloat &B) {
1389 if (A.isNaN())
1390 return A;
1391 if (B.isNaN())
1392 return B;
1393 if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1394 return A.isNegative() ? A : B;
1395 return B < A ? B : A;
1396}
1397
1398/// Implements IEEE 754-2018 maximum semantics. Returns the larger of 2
1399/// arguments, propagating NaNs and treating -0 as less than +0.
1400LLVM_READONLY
1401inline APFloat maximum(const APFloat &A, const APFloat &B) {
1402 if (A.isNaN())
1403 return A;
1404 if (B.isNaN())
1405 return B;
1406 if (A.isZero() && B.isZero() && (A.isNegative() != B.isNegative()))
1407 return A.isNegative() ? B : A;
1408 return A < B ? B : A;
1409}
1410
1411// We want the following functions to be available in the header for inlining.
1412// We cannot define them inline in the class definition of `DoubleAPFloat`
1413// because doing so would instantiate `std::unique_ptr<APFloat[]>` before
1414// `APFloat` is defined, and that would be undefined behavior.
1415namespace detail {
1416
1417DoubleAPFloat &DoubleAPFloat::operator=(DoubleAPFloat &&RHS) {
1418 if (this != &RHS) {
1419 this->~DoubleAPFloat();
1420 new (this) DoubleAPFloat(std::move(RHS));
1421 }
1422 return *this;
1423}
1424
1425APFloat &DoubleAPFloat::getFirst() { return Floats[0]; }
1426const APFloat &DoubleAPFloat::getFirst() const { return Floats[0]; }
1427APFloat &DoubleAPFloat::getSecond() { return Floats[1]; }
1428const APFloat &DoubleAPFloat::getSecond() const { return Floats[1]; }
1429
1430} // namespace detail
1431
1432} // namespace llvm
1433
1434#undef APFLOAT_DISPATCH_ON_SEMANTICS
1435#endif // LLVM_ADT_APFLOAT_H
1436

source code of include/llvm-17/llvm/ADT/APFloat.h