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;
114 /* When bits of a floating point number are truncated, this enum is
115 used to indicate what fraction of the LSB those bits represented.
116 It essentially combines the roles of guard and sticky bits. */
117 enum lostFraction { // Example of truncated bits:
118 lfExactlyZero, // 000000
119 lfLessThanHalf, // 0xxxxx x's not all zero
120 lfExactlyHalf, // 100000
121 lfMoreThanHalf // 1xxxxx x's not all zero
127 /* We support the following floating point semantics. */
128 static const fltSemantics IEEEhalf;
129 static const fltSemantics IEEEsingle;
130 static const fltSemantics IEEEdouble;
131 static const fltSemantics IEEEquad;
132 static const fltSemantics PPCDoubleDouble;
133 static const fltSemantics x87DoubleExtended;
134 /* And this pseudo, used to construct APFloats that cannot
135 conflict with anything real. */
136 static const fltSemantics Bogus;
138 static unsigned int semanticsPrecision(const fltSemantics &);
140 /* Floating point numbers have a four-state comparison relation. */
148 /* IEEE-754R gives five rounding modes. */
157 // Operation status. opUnderflow or opOverflow are always returned
158 // or-ed with opInexact.
168 // Category of internally-represented number.
176 enum uninitializedTag {
181 APFloat(const fltSemantics &); // Default construct to 0.0
182 APFloat(const fltSemantics &, StringRef);
183 APFloat(const fltSemantics &, integerPart);
184 APFloat(const fltSemantics &, fltCategory, bool negative);
185 APFloat(const fltSemantics &, uninitializedTag);
186 explicit APFloat(double d);
187 explicit APFloat(float f);
188 explicit APFloat(const APInt &, bool isIEEE = false);
189 APFloat(const APFloat &);
192 // Convenience "constructors"
193 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
194 return APFloat(Sem, fcZero, Negative);
196 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
197 return APFloat(Sem, fcInfinity, Negative);
200 /// getNaN - Factory for QNaN values.
202 /// \param Negative - True iff the NaN generated should be negative.
203 /// \param type - The unspecified fill bits for creating the NaN, 0 by
204 /// default. The value is truncated as necessary.
205 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
208 APInt fill(64, type);
209 return getQNaN(Sem, Negative, &fill);
211 return getQNaN(Sem, Negative, 0);
215 /// getQNan - Factory for QNaN values.
216 static APFloat getQNaN(const fltSemantics &Sem,
217 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,
224 bool Negative = false,
225 const APInt *payload = 0) {
226 return makeNaN(Sem, true, Negative, payload);
229 /// getLargest - Returns the largest finite number in the given
232 /// \param Negative - True iff the number should be negative
233 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false);
235 /// getSmallest - Returns the smallest (by magnitude) finite number
236 /// in the given semantics. Might be denormalized, which implies a
237 /// relative loss of precision.
239 /// \param Negative - True iff the number should be negative
240 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false);
242 /// getSmallestNormalized - Returns the smallest (by magnitude)
243 /// normalized finite number in the given semantics.
245 /// \param Negative - True iff the number should be negative
246 static APFloat getSmallestNormalized(const fltSemantics &Sem,
247 bool Negative = false);
249 /// Profile - Used to insert APFloat objects, or objects that contain
250 /// APFloat objects, into FoldingSets.
251 void Profile(FoldingSetNodeID& NID) const;
253 /// @brief Used by the Bitcode serializer to emit APInts to Bitcode.
254 void Emit(Serializer& S) const;
256 /// @brief Used by the Bitcode deserializer to deserialize APInts.
257 static APFloat ReadVal(Deserializer& D);
260 opStatus add(const APFloat &, roundingMode);
261 opStatus subtract(const APFloat &, roundingMode);
262 opStatus multiply(const APFloat &, roundingMode);
263 opStatus divide(const APFloat &, roundingMode);
264 /* IEEE remainder. */
265 opStatus remainder(const APFloat &);
266 /* C fmod, or llvm frem. */
267 opStatus mod(const APFloat &, roundingMode);
268 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
270 /* Sign operations. */
273 void copySign(const APFloat &);
276 opStatus convert(const fltSemantics &, roundingMode, bool *);
277 opStatus convertToInteger(integerPart *, unsigned int, bool,
278 roundingMode, bool *) const;
279 opStatus convertFromAPInt(const APInt &,
281 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
283 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
285 opStatus convertFromString(StringRef, roundingMode);
286 APInt bitcastToAPInt() const;
287 double convertToDouble() const;
288 float convertToFloat() const;
290 /* The definition of equality is not straightforward for floating point,
291 so we won't use operator==. Use one of the following, or write
292 whatever it is you really mean. */
293 // bool operator==(const APFloat &) const; // DO NOT IMPLEMENT
295 /* IEEE comparison with another floating point number (NaNs
296 compare unordered, 0==-0). */
297 cmpResult compare(const APFloat &) const;
299 /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
300 bool bitwiseIsEqual(const APFloat &) const;
302 /* Write out a hexadecimal representation of the floating point
303 value to DST, which must be of sufficient size, in the C99 form
304 [-]0xh.hhhhp[+-]d. Return the number of characters written,
305 excluding the terminating NUL. */
306 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
307 bool upperCase, roundingMode) const;
309 /* Simple queries. */
310 fltCategory getCategory() const { return category; }
311 const fltSemantics &getSemantics() const { return *semantics; }
312 bool isZero() const { return category == fcZero; }
313 bool isNonZero() const { return category != fcZero; }
314 bool isNaN() const { return category == fcNaN; }
315 bool isInfinity() const { return category == fcInfinity; }
316 bool isNegative() const { return sign; }
317 bool isPosZero() const { return isZero() && !isNegative(); }
318 bool isNegZero() const { return isZero() && isNegative(); }
320 APFloat& operator=(const APFloat &);
322 /* Return an arbitrary integer value usable for hashing. */
323 uint32_t getHashValue() const;
325 /// Converts this value into a decimal string.
327 /// \param FormatPrecision The maximum number of digits of
328 /// precision to output. If there are fewer digits available,
329 /// zero padding will not be used unless the value is
330 /// integral and small enough to be expressed in
331 /// FormatPrecision digits. 0 means to use the natural
332 /// precision of the number.
333 /// \param FormatMaxPadding The maximum number of zeros to
334 /// consider inserting before falling back to scientific
335 /// notation. 0 means to always use scientific notation.
337 /// Number Precision MaxPadding Result
338 /// ------ --------- ---------- ------
339 /// 1.01E+4 5 2 10100
340 /// 1.01E+4 4 2 1.01E+4
341 /// 1.01E+4 5 1 1.01E+4
342 /// 1.01E-2 5 2 0.0101
343 /// 1.01E-2 4 2 0.0101
344 /// 1.01E-2 4 1 1.01E-2
345 void toString(SmallVectorImpl<char> &Str,
346 unsigned FormatPrecision = 0,
347 unsigned FormatMaxPadding = 3) const;
351 /* Trivial queries. */
352 integerPart *significandParts();
353 const integerPart *significandParts() const;
354 unsigned int partCount() const;
356 /* Significand operations. */
357 integerPart addSignificand(const APFloat &);
358 integerPart subtractSignificand(const APFloat &, integerPart);
359 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
360 lostFraction multiplySignificand(const APFloat &, const APFloat *);
361 lostFraction divideSignificand(const APFloat &);
362 void incrementSignificand();
363 void initialize(const fltSemantics *);
364 void shiftSignificandLeft(unsigned int);
365 lostFraction shiftSignificandRight(unsigned int);
366 unsigned int significandLSB() const;
367 unsigned int significandMSB() const;
368 void zeroSignificand();
370 /* Arithmetic on special values. */
371 opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
372 opStatus divideSpecials(const APFloat &);
373 opStatus multiplySpecials(const APFloat &);
374 opStatus modSpecials(const APFloat &);
377 static APFloat makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
379 void makeNaN(bool SNaN = false, bool Neg = false, const APInt *fill = 0);
380 opStatus normalize(roundingMode, lostFraction);
381 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
382 cmpResult compareAbsoluteValue(const APFloat &) const;
383 opStatus handleOverflow(roundingMode);
384 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
385 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
386 roundingMode, bool *) const;
387 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
389 opStatus convertFromHexadecimalString(StringRef, roundingMode);
390 opStatus convertFromDecimalString(StringRef, roundingMode);
391 char *convertNormalToHexString(char *, unsigned int, bool,
393 opStatus roundSignificandWithExponent(const integerPart *, unsigned int,
396 APInt convertHalfAPFloatToAPInt() const;
397 APInt convertFloatAPFloatToAPInt() const;
398 APInt convertDoubleAPFloatToAPInt() const;
399 APInt convertQuadrupleAPFloatToAPInt() const;
400 APInt convertF80LongDoubleAPFloatToAPInt() const;
401 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
402 void initFromAPInt(const APInt& api, bool isIEEE = false);
403 void initFromHalfAPInt(const APInt& api);
404 void initFromFloatAPInt(const APInt& api);
405 void initFromDoubleAPInt(const APInt& api);
406 void initFromQuadrupleAPInt(const APInt &api);
407 void initFromF80LongDoubleAPInt(const APInt& api);
408 void initFromPPCDoubleDoubleAPInt(const APInt& api);
410 void assign(const APFloat &);
411 void copySignificand(const APFloat &);
412 void freeSignificand();
414 /* What kind of semantics does this value obey? */
415 const fltSemantics *semantics;
417 /* Significand - the fraction with an explicit integer bit. Must be
418 at least one bit wider than the target precision. */
425 /* The exponent - a signed number. */
428 /* What kind of floating point number this is. */
429 /* Only 2 bits are required, but VisualStudio incorrectly sign extends
430 it. Using the extra bit keeps it from failing under VisualStudio */
431 fltCategory category: 3;
433 /* The sign bit of this number. */
434 unsigned int sign: 1;
436 /* For PPCDoubleDouble, we have a second exponent and sign (the second
437 significand is appended to the first one, although it would be wrong to
438 regard these as a single number for arithmetic purposes). These fields
439 are not meaningful for any other type. */
440 exponent_t exponent2 : 11;
441 unsigned int sign2: 1;
443 } /* namespace llvm */
445 #endif /* LLVM_FLOAT_H */