1 //== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file declares a class to represent arbitrary precision floating
11 // point values and provide a variety of arithmetic operations on them.
13 //===----------------------------------------------------------------------===//
15 /* A self-contained host- and target-independent arbitrary-precision
16 floating-point software implementation. It uses bignum integer
17 arithmetic as provided by static functions in the APInt class.
18 The library will work with bignum integers whose parts are any
19 unsigned type at least 16 bits wide, but 64 bits is recommended.
21 Written for clarity rather than speed, in particular with a view
22 to use in the front-end of a cross compiler so that target
23 arithmetic can be correctly performed on the host. Performance
24 should nonetheless be reasonable, particularly for its intended
25 use. It may be useful as a base implementation for a run-time
26 library during development of a faster target-specific one.
28 All 5 rounding modes in the IEEE-754R draft are handled correctly
29 for all implemented operations. Currently implemented operations
30 are add, subtract, multiply, divide, fused-multiply-add,
31 conversion-to-float, conversion-to-integer and
32 conversion-from-integer. New rounding modes (e.g. away from zero)
33 can be added with three or four lines of code.
35 Four formats are built-in: IEEE single precision, double
36 precision, quadruple precision, and x87 80-bit extended double
37 (when operating with full extended precision). Adding a new
38 format that obeys IEEE semantics only requires adding two lines of
39 code: a declaration and definition of the format.
41 All operations return the status of that operation as an exception
42 bit-mask, so multiple operations can be done consecutively with
43 their results or-ed together. The returned status can be useful
44 for compiler diagnostics; e.g., inexact, underflow and overflow
45 can be easily diagnosed on constant folding, and compiler
46 optimizers can determine what exceptions would be raised by
47 folding operations and optimize, or perhaps not optimize,
50 At present, underflow tininess is detected after rounding; it
51 should be straight forward to add support for the before-rounding
54 The library reads hexadecimal floating point numbers as per C99,
55 and correctly rounds if necessary according to the specified
56 rounding mode. Syntax is required to have been validated by the
57 caller. It also converts floating point numbers to hexadecimal
58 text as per the C99 %a and %A conversions. The output precision
59 (or alternatively the natural minimal precision) can be specified;
60 if the requested precision is less than the natural precision the
61 output is correctly rounded for the specified rounding mode.
63 It also reads decimal floating point numbers and correctly rounds
64 according to the specified rounding mode.
66 Conversion to decimal text is not currently implemented.
68 Non-zero finite numbers are represented internally as a sign bit,
69 a 16-bit signed exponent, and the significand as an array of
70 integer parts. After normalization of a number of precision P the
71 exponent is within the range of the format, and if the number is
72 not denormal the P-th bit of the significand is set as an explicit
73 integer bit. For denormals the most significant bit is shifted
74 right so that the exponent is maintained at the format's minimum,
75 so that the smallest denormal has just the least significant bit
76 of the significand set. The sign of zeroes and infinities is
77 significant; the exponent and significand of such numbers is not
78 stored, but has a known implicit (deterministic) value: 0 for the
79 significands, 0 for zero exponent, all 1 bits for infinity
80 exponent. For NaNs the sign and significand are deterministic,
81 although not really meaningful, and preserved in non-conversion
82 operations. The exponent is implicitly all 1 bits.
87 Some features that may or may not be worth adding:
89 Binary to decimal conversion (hard).
91 Optional ability to detect underflow tininess before rounding.
93 New formats: x87 in single and double precision mode (IEEE apart
94 from extended exponent range) (hard).
96 New operations: sqrt, IEEE remainder, C90 fmod, nextafter,
100 #ifndef LLVM_ADT_APFLOAT_H
101 #define LLVM_ADT_APFLOAT_H
103 // APInt contains static functions implementing bignum arithmetic.
104 #include "llvm/ADT/APInt.h"
108 /* Exponents are stored as signed numbers. */
109 typedef signed short exponent_t;
115 /* When bits of a floating point number are truncated, this enum is
116 used to indicate what fraction of the LSB those bits represented.
117 It essentially combines the roles of guard and sticky bits. */
118 enum lostFraction { // Example of truncated bits:
119 lfExactlyZero, // 000000
120 lfLessThanHalf, // 0xxxxx x's not all zero
121 lfExactlyHalf, // 100000
122 lfMoreThanHalf // 1xxxxx x's not all zero
128 /* We support the following floating point semantics. */
129 static const fltSemantics IEEEhalf;
130 static const fltSemantics IEEEsingle;
131 static const fltSemantics IEEEdouble;
132 static const fltSemantics IEEEquad;
133 static const fltSemantics PPCDoubleDouble;
134 static const fltSemantics x87DoubleExtended;
135 /* And this pseudo, used to construct APFloats that cannot
136 conflict with anything real. */
137 static const fltSemantics Bogus;
139 static unsigned int semanticsPrecision(const fltSemantics &);
141 /* Floating point numbers have a four-state comparison relation. */
149 /* IEEE-754R gives five rounding modes. */
158 // Operation status. opUnderflow or opOverflow are always returned
159 // or-ed with opInexact.
169 // Category of internally-represented number.
177 enum uninitializedTag {
182 APFloat(const fltSemantics &); // Default construct to 0.0
183 APFloat(const fltSemantics &, StringRef);
184 APFloat(const fltSemantics &, integerPart);
185 APFloat(const fltSemantics &, fltCategory, bool negative);
186 APFloat(const fltSemantics &, uninitializedTag);
187 APFloat(const fltSemantics &, const APInt &);
188 explicit APFloat(double d);
189 explicit APFloat(float f);
190 APFloat(const APFloat &);
193 // Convenience "constructors"
194 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
195 return APFloat(Sem, fcZero, Negative);
197 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
198 return APFloat(Sem, fcInfinity, Negative);
201 /// getNaN - Factory for QNaN values.
203 /// \param Negative - True iff the NaN generated should be negative.
204 /// \param type - The unspecified fill bits for creating the NaN, 0 by
205 /// default. The value is truncated as necessary.
206 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
209 APInt fill(64, type);
210 return getQNaN(Sem, Negative, &fill);
212 return getQNaN(Sem, Negative, 0);
216 /// getQNan - Factory for QNaN values.
217 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
218 const APInt *payload = 0) {
219 return makeNaN(Sem, false, Negative, payload);
222 /// getSNan - Factory for SNaN values.
223 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
224 const APInt *payload = 0) {
225 return makeNaN(Sem, true, Negative, payload);
228 /// getLargest - Returns the largest finite number in the given
231 /// \param Negative - True iff the number should be negative
232 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
234 /// getSmallest - Returns the smallest (by magnitude) finite number
235 /// in the given semantics. Might be denormalized, which implies a
236 /// relative loss of precision.
238 /// \param Negative - True iff the number should be negative
239 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
241 /// getSmallestNormalized - Returns the smallest (by magnitude)
242 /// normalized finite number in the given semantics.
244 /// \param Negative - True iff the number should be negative
245 static APFloat getSmallestNormalized(const fltSemantics &Sem,
246 bool Negative = false);
248 /// getAllOnesValue - Returns a float which is bitcasted from
249 /// an all one value int.
251 /// \param BitWidth - Select float type
252 /// \param isIEEE - If 128 bit number, select between PPC and IEEE
253 static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
255 /// Profile - Used to insert APFloat objects, or objects that contain
256 /// APFloat objects, into FoldingSets.
257 void Profile(FoldingSetNodeID &NID) const;
259 /// @brief Used by the Bitcode serializer to emit APInts to Bitcode.
260 void Emit(Serializer &S) const;
262 /// @brief Used by the Bitcode deserializer to deserialize APInts.
263 static APFloat ReadVal(Deserializer &D);
266 opStatus add(const APFloat &, roundingMode);
267 opStatus subtract(const APFloat &, roundingMode);
268 opStatus multiply(const APFloat &, roundingMode);
269 opStatus divide(const APFloat &, roundingMode);
270 /* IEEE remainder. */
271 opStatus remainder(const APFloat &);
272 /* C fmod, or llvm frem. */
273 opStatus mod(const APFloat &, roundingMode);
274 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
275 opStatus roundToIntegral(roundingMode);
277 /* Sign operations. */
280 void copySign(const APFloat &);
283 opStatus convert(const fltSemantics &, roundingMode, bool *);
284 opStatus convertToInteger(integerPart *, unsigned int, bool, roundingMode,
286 opStatus convertToInteger(APSInt &, roundingMode, bool *) const;
287 opStatus convertFromAPInt(const APInt &, bool, roundingMode);
288 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
290 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
292 opStatus convertFromString(StringRef, roundingMode);
293 APInt bitcastToAPInt() const;
294 double convertToDouble() const;
295 float convertToFloat() const;
297 /* The definition of equality is not straightforward for floating point,
298 so we won't use operator==. Use one of the following, or write
299 whatever it is you really mean. */
300 bool operator==(const APFloat &) const LLVM_DELETED_FUNCTION;
302 /* IEEE comparison with another floating point number (NaNs
303 compare unordered, 0==-0). */
304 cmpResult compare(const APFloat &) const;
306 /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
307 bool bitwiseIsEqual(const APFloat &) const;
309 /* Write out a hexadecimal representation of the floating point
310 value to DST, which must be of sufficient size, in the C99 form
311 [-]0xh.hhhhp[+-]d. Return the number of characters written,
312 excluding the terminating NUL. */
313 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
314 bool upperCase, roundingMode) const;
316 /* Simple queries. */
317 fltCategory getCategory() const { return category; }
318 const fltSemantics &getSemantics() const { return *semantics; }
319 bool isZero() const { return category == fcZero; }
320 bool isNonZero() const { return category != fcZero; }
321 bool isNormal() const { return category == fcNormal; }
322 bool isNaN() const { return category == fcNaN; }
323 bool isInfinity() const { return category == fcInfinity; }
324 bool isNegative() const { return sign; }
325 bool isPosZero() const { return isZero() && !isNegative(); }
326 bool isNegZero() const { return isZero() && isNegative(); }
327 bool isDenormal() const;
329 APFloat &operator=(const APFloat &);
331 /// \brief Overload to compute a hash code for an APFloat value.
333 /// Note that the use of hash codes for floating point values is in general
334 /// frought with peril. Equality is hard to define for these values. For
335 /// example, should negative and positive zero hash to different codes? Are
336 /// they equal or not? This hash value implementation specifically
337 /// emphasizes producing different codes for different inputs in order to
338 /// be used in canonicalization and memoization. As such, equality is
339 /// bitwiseIsEqual, and 0 != -0.
340 friend hash_code hash_value(const APFloat &Arg);
342 /// Converts this value into a decimal string.
344 /// \param FormatPrecision The maximum number of digits of
345 /// precision to output. If there are fewer digits available,
346 /// zero padding will not be used unless the value is
347 /// integral and small enough to be expressed in
348 /// FormatPrecision digits. 0 means to use the natural
349 /// precision of the number.
350 /// \param FormatMaxPadding The maximum number of zeros to
351 /// consider inserting before falling back to scientific
352 /// notation. 0 means to always use scientific notation.
354 /// Number Precision MaxPadding Result
355 /// ------ --------- ---------- ------
356 /// 1.01E+4 5 2 10100
357 /// 1.01E+4 4 2 1.01E+4
358 /// 1.01E+4 5 1 1.01E+4
359 /// 1.01E-2 5 2 0.0101
360 /// 1.01E-2 4 2 0.0101
361 /// 1.01E-2 4 1 1.01E-2
362 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
363 unsigned FormatMaxPadding = 3) const;
365 /// getExactInverse - If this value has an exact multiplicative inverse,
366 /// store it in inv and return true.
367 bool getExactInverse(APFloat *inv) const;
371 /* Trivial queries. */
372 integerPart *significandParts();
373 const integerPart *significandParts() const;
374 unsigned int partCount() const;
376 /* Significand operations. */
377 integerPart addSignificand(const APFloat &);
378 integerPart subtractSignificand(const APFloat &, integerPart);
379 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
380 lostFraction multiplySignificand(const APFloat &, const APFloat *);
381 lostFraction divideSignificand(const APFloat &);
382 void incrementSignificand();
383 void initialize(const fltSemantics *);
384 void shiftSignificandLeft(unsigned int);
385 lostFraction shiftSignificandRight(unsigned int);
386 unsigned int significandLSB() const;
387 unsigned int significandMSB() const;
388 void zeroSignificand();
390 /* Arithmetic on special values. */
391 opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
392 opStatus divideSpecials(const APFloat &);
393 opStatus multiplySpecials(const APFloat &);
394 opStatus modSpecials(const APFloat &);
397 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
399 void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
400 opStatus normalize(roundingMode, lostFraction);
401 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
402 cmpResult compareAbsoluteValue(const APFloat &) const;
403 opStatus handleOverflow(roundingMode);
404 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
405 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
406 roundingMode, bool *) const;
407 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
409 opStatus convertFromHexadecimalString(StringRef, roundingMode);
410 opStatus convertFromDecimalString(StringRef, roundingMode);
411 char *convertNormalToHexString(char *, unsigned int, bool,
413 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
416 APInt convertHalfAPFloatToAPInt() const;
417 APInt convertFloatAPFloatToAPInt() const;
418 APInt convertDoubleAPFloatToAPInt() const;
419 APInt convertQuadrupleAPFloatToAPInt() const;
420 APInt convertF80LongDoubleAPFloatToAPInt() const;
421 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
422 void initFromAPInt(const fltSemantics *Sem, const APInt &api);
423 void initFromHalfAPInt(const APInt &api);
424 void initFromFloatAPInt(const APInt &api);
425 void initFromDoubleAPInt(const APInt &api);
426 void initFromQuadrupleAPInt(const APInt &api);
427 void initFromF80LongDoubleAPInt(const APInt &api);
428 void initFromPPCDoubleDoubleAPInt(const APInt &api);
430 void assign(const APFloat &);
431 void copySignificand(const APFloat &);
432 void freeSignificand();
434 /* What kind of semantics does this value obey? */
435 const fltSemantics *semantics;
437 /* Significand - the fraction with an explicit integer bit. Must be
438 at least one bit wider than the target precision. */
444 /* The exponent - a signed number. */
447 /* What kind of floating point number this is. */
448 /* Only 2 bits are required, but VisualStudio incorrectly sign extends
449 it. Using the extra bit keeps it from failing under VisualStudio */
450 fltCategory category : 3;
452 /* The sign bit of this number. */
453 unsigned int sign : 1;
456 // See friend declaration above. This additional declaration is required in
457 // order to compile LLVM with IBM xlC compiler.
458 hash_code hash_value(const APFloat &Arg);
459 } /* namespace llvm */
461 #endif /* LLVM_ADT_APFLOAT_H */