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,
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 explicit APFloat(double d);
188 explicit APFloat(float f);
189 explicit APFloat(const APInt &, bool isIEEE = false);
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,
218 bool Negative = false,
219 const APInt *payload = 0) {
220 return makeNaN(Sem, false, Negative, payload);
223 /// getSNan - Factory for SNaN values.
224 static APFloat getSNaN(const fltSemantics &Sem,
225 bool Negative = false,
226 const APInt *payload = 0) {
227 return makeNaN(Sem, true, Negative, payload);
230 /// getLargest - Returns the largest finite number in the given
233 /// \param Negative - True iff the number should be negative
234 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
236 /// getSmallest - Returns the smallest (by magnitude) finite number
237 /// in the given semantics. Might be denormalized, which implies a
238 /// relative loss of precision.
240 /// \param Negative - True iff the number should be negative
241 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
243 /// getSmallestNormalized - Returns the smallest (by magnitude)
244 /// normalized finite number in the given semantics.
246 /// \param Negative - True iff the number should be negative
247 static APFloat getSmallestNormalized(const fltSemantics &Sem,
248 bool Negative = false);
250 /// getAllOnesValue - Returns a float which is bitcasted from
251 /// an all one value int.
253 /// \param BitWidth - Select float type
254 /// \param isIEEE - If 128 bit number, select between PPC and IEEE
255 static APFloat getAllOnesValue(unsigned BitWidth, bool isIEEE = false);
257 /// Profile - Used to insert APFloat objects, or objects that contain
258 /// APFloat objects, into FoldingSets.
259 void Profile(FoldingSetNodeID& NID) const;
261 /// @brief Used by the Bitcode serializer to emit APInts to Bitcode.
262 void Emit(Serializer& S) const;
264 /// @brief Used by the Bitcode deserializer to deserialize APInts.
265 static APFloat ReadVal(Deserializer& D);
268 opStatus add(const APFloat &, roundingMode);
269 opStatus subtract(const APFloat &, roundingMode);
270 opStatus multiply(const APFloat &, roundingMode);
271 opStatus divide(const APFloat &, roundingMode);
272 /* IEEE remainder. */
273 opStatus remainder(const APFloat &);
274 /* C fmod, or llvm frem. */
275 opStatus mod(const APFloat &, roundingMode);
276 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
278 /* Sign operations. */
281 void copySign(const APFloat &);
284 opStatus convert(const fltSemantics &, roundingMode, bool *);
285 opStatus convertToInteger(integerPart *, unsigned int, bool,
286 roundingMode, bool *) const;
287 opStatus convertToInteger(APSInt&, roundingMode, bool *) const;
288 opStatus convertFromAPInt(const APInt &,
290 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
292 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
294 opStatus convertFromString(StringRef, roundingMode);
295 APInt bitcastToAPInt() const;
296 double convertToDouble() const;
297 float convertToFloat() const;
299 /* The definition of equality is not straightforward for floating point,
300 so we won't use operator==. Use one of the following, or write
301 whatever it is you really mean. */
302 // bool operator==(const APFloat &) const; // DO NOT IMPLEMENT
304 /* IEEE comparison with another floating point number (NaNs
305 compare unordered, 0==-0). */
306 cmpResult compare(const APFloat &) const;
308 /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
309 bool bitwiseIsEqual(const APFloat &) const;
311 /* Write out a hexadecimal representation of the floating point
312 value to DST, which must be of sufficient size, in the C99 form
313 [-]0xh.hhhhp[+-]d. Return the number of characters written,
314 excluding the terminating NUL. */
315 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
316 bool upperCase, roundingMode) const;
318 /* Simple queries. */
319 fltCategory getCategory() const { return category; }
320 const fltSemantics &getSemantics() const { return *semantics; }
321 bool isZero() const { return category == fcZero; }
322 bool isNonZero() const { return category != fcZero; }
323 bool isNormal() const { return category == fcNormal; }
324 bool isNaN() const { return category == fcNaN; }
325 bool isInfinity() const { return category == fcInfinity; }
326 bool isNegative() const { return sign; }
327 bool isPosZero() const { return isZero() && !isNegative(); }
328 bool isNegZero() const { return isZero() && isNegative(); }
330 APFloat& operator=(const APFloat &);
332 /// \brief Overload to compute a hash code for an APFloat value.
334 /// Note that the use of hash codes for floating point values is in general
335 /// frought with peril. Equality is hard to define for these values. For
336 /// example, should negative and positive zero hash to different codes? Are
337 /// they equal or not? This hash value implementation specifically
338 /// emphasizes producing different codes for different inputs in order to
339 /// be used in canonicalization and memoization. As such, equality is
340 /// bitwiseIsEqual, and 0 != -0.
341 friend hash_code hash_value(const APFloat &Arg);
343 /// Converts this value into a decimal string.
345 /// \param FormatPrecision The maximum number of digits of
346 /// precision to output. If there are fewer digits available,
347 /// zero padding will not be used unless the value is
348 /// integral and small enough to be expressed in
349 /// FormatPrecision digits. 0 means to use the natural
350 /// precision of the number.
351 /// \param FormatMaxPadding The maximum number of zeros to
352 /// consider inserting before falling back to scientific
353 /// notation. 0 means to always use scientific notation.
355 /// Number Precision MaxPadding Result
356 /// ------ --------- ---------- ------
357 /// 1.01E+4 5 2 10100
358 /// 1.01E+4 4 2 1.01E+4
359 /// 1.01E+4 5 1 1.01E+4
360 /// 1.01E-2 5 2 0.0101
361 /// 1.01E-2 4 2 0.0101
362 /// 1.01E-2 4 1 1.01E-2
363 void toString(SmallVectorImpl<char> &Str,
364 unsigned FormatPrecision = 0,
365 unsigned FormatMaxPadding = 3) const;
367 /// getExactInverse - If this value has an exact multiplicative inverse,
368 /// store it in inv and return true.
369 bool getExactInverse(APFloat *inv) const;
373 /* Trivial queries. */
374 integerPart *significandParts();
375 const integerPart *significandParts() const;
376 unsigned int partCount() const;
378 /* Significand operations. */
379 integerPart addSignificand(const APFloat &);
380 integerPart subtractSignificand(const APFloat &, integerPart);
381 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
382 lostFraction multiplySignificand(const APFloat &, const APFloat *);
383 lostFraction divideSignificand(const APFloat &);
384 void incrementSignificand();
385 void initialize(const fltSemantics *);
386 void shiftSignificandLeft(unsigned int);
387 lostFraction shiftSignificandRight(unsigned int);
388 unsigned int significandLSB() const;
389 unsigned int significandMSB() const;
390 void zeroSignificand();
392 /* Arithmetic on special values. */
393 opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
394 opStatus divideSpecials(const APFloat &);
395 opStatus multiplySpecials(const APFloat &);
396 opStatus modSpecials(const APFloat &);
399 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
401 void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
402 opStatus normalize(roundingMode, lostFraction);
403 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
404 cmpResult compareAbsoluteValue(const APFloat &) const;
405 opStatus handleOverflow(roundingMode);
406 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
407 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
408 roundingMode, bool *) const;
409 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
411 opStatus convertFromHexadecimalString(StringRef, roundingMode);
412 opStatus convertFromDecimalString(StringRef, roundingMode);
413 char *convertNormalToHexString(char *, unsigned int, bool,
415 opStatus roundSignificandWithExponent(const integerPart *, unsigned int,
418 APInt convertHalfAPFloatToAPInt() const;
419 APInt convertFloatAPFloatToAPInt() const;
420 APInt convertDoubleAPFloatToAPInt() const;
421 APInt convertQuadrupleAPFloatToAPInt() const;
422 APInt convertF80LongDoubleAPFloatToAPInt() const;
423 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
424 void initFromAPInt(const APInt& api, bool isIEEE = false);
425 void initFromHalfAPInt(const APInt& api);
426 void initFromFloatAPInt(const APInt& api);
427 void initFromDoubleAPInt(const APInt& api);
428 void initFromQuadrupleAPInt(const APInt &api);
429 void initFromF80LongDoubleAPInt(const APInt& api);
430 void initFromPPCDoubleDoubleAPInt(const APInt& api);
432 void assign(const APFloat &);
433 void copySignificand(const APFloat &);
434 void freeSignificand();
436 /* What kind of semantics does this value obey? */
437 const fltSemantics *semantics;
439 /* Significand - the fraction with an explicit integer bit. Must be
440 at least one bit wider than the target precision. */
447 /* The exponent - a signed number. */
450 /* What kind of floating point number this is. */
451 /* Only 2 bits are required, but VisualStudio incorrectly sign extends
452 it. Using the extra bit keeps it from failing under VisualStudio */
453 fltCategory category: 3;
455 /* The sign bit of this number. */
456 unsigned int sign: 1;
458 /* For PPCDoubleDouble, we have a second exponent and sign (the second
459 significand is appended to the first one, although it would be wrong to
460 regard these as a single number for arithmetic purposes). These fields
461 are not meaningful for any other type. */
462 exponent_t exponent2 : 11;
463 unsigned int sign2: 1;
465 } /* namespace llvm */
467 #endif /* LLVM_FLOAT_H */