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;
113 /* When bits of a floating point number are truncated, this enum is
114 used to indicate what fraction of the LSB those bits represented.
115 It essentially combines the roles of guard and sticky bits. */
116 enum lostFraction { // Example of truncated bits:
117 lfExactlyZero, // 000000
118 lfLessThanHalf, // 0xxxxx x's not all zero
119 lfExactlyHalf, // 100000
120 lfMoreThanHalf // 1xxxxx x's not all zero
126 /* We support the following floating point semantics. */
127 static const fltSemantics IEEEsingle;
128 static const fltSemantics IEEEdouble;
129 static const fltSemantics IEEEquad;
130 static const fltSemantics PPCDoubleDouble;
131 static const fltSemantics x87DoubleExtended;
132 /* And this pseudo, used to construct APFloats that cannot
133 conflict with anything real. */
134 static const fltSemantics Bogus;
136 static unsigned int semanticsPrecision(const fltSemantics &);
138 /* Floating point numbers have a four-state comparison relation. */
146 /* IEEE-754R gives five rounding modes. */
155 // Operation status. opUnderflow or opOverflow are always returned
156 // or-ed with opInexact.
166 // Category of internally-represented number.
175 APFloat(const fltSemantics &, const char *);
176 APFloat(const fltSemantics &, integerPart);
177 APFloat(const fltSemantics &, fltCategory, bool negative);
178 explicit APFloat(double d);
179 explicit APFloat(float f);
180 explicit APFloat(const APInt &, bool isIEEE = false);
181 APFloat(const APFloat &);
184 // Convenience "constructors"
185 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
186 return APFloat(Sem, fcZero, Negative);
188 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
189 return APFloat(Sem, fcInfinity, Negative);
191 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false) {
192 return APFloat(Sem, fcNaN, Negative);
195 /// Profile - Used to insert APFloat objects, or objects that contain
196 /// APFloat objects, into FoldingSets.
197 void Profile(FoldingSetNodeID& NID) const;
199 /// @brief Used by the Bitcode serializer to emit APInts to Bitcode.
200 void Emit(Serializer& S) const;
202 /// @brief Used by the Bitcode deserializer to deserialize APInts.
203 static APFloat ReadVal(Deserializer& D);
206 opStatus add(const APFloat &, roundingMode);
207 opStatus subtract(const APFloat &, roundingMode);
208 opStatus multiply(const APFloat &, roundingMode);
209 opStatus divide(const APFloat &, roundingMode);
210 /* IEEE remainder. */
211 opStatus remainder(const APFloat &);
212 /* C fmod, or llvm frem. */
213 opStatus mod(const APFloat &, roundingMode);
214 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
216 /* Sign operations. */
219 void copySign(const APFloat &);
222 opStatus convert(const fltSemantics &, roundingMode, bool *);
223 opStatus convertToInteger(integerPart *, unsigned int, bool,
224 roundingMode, bool *) const;
225 opStatus convertFromAPInt(const APInt &,
227 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
229 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
231 opStatus convertFromString(const char *, roundingMode);
232 APInt bitcastToAPInt() const;
233 double convertToDouble() const;
234 float convertToFloat() const;
236 /* The definition of equality is not straightforward for floating point,
237 so we won't use operator==. Use one of the following, or write
238 whatever it is you really mean. */
239 // bool operator==(const APFloat &) const; // DO NOT IMPLEMENT
241 /* IEEE comparison with another floating point number (NaNs
242 compare unordered, 0==-0). */
243 cmpResult compare(const APFloat &) const;
245 /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
246 bool bitwiseIsEqual(const APFloat &) const;
248 /* Write out a hexadecimal representation of the floating point
249 value to DST, which must be of sufficient size, in the C99 form
250 [-]0xh.hhhhp[+-]d. Return the number of characters written,
251 excluding the terminating NUL. */
252 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
253 bool upperCase, roundingMode) const;
255 /* Simple queries. */
256 fltCategory getCategory() const { return category; }
257 const fltSemantics &getSemantics() const { return *semantics; }
258 bool isZero() const { return category == fcZero; }
259 bool isNonZero() const { return category != fcZero; }
260 bool isNaN() const { return category == fcNaN; }
261 bool isInfinity() const { return category == fcInfinity; }
262 bool isNegative() const { return sign; }
263 bool isPosZero() const { return isZero() && !isNegative(); }
264 bool isNegZero() const { return isZero() && isNegative(); }
266 APFloat& operator=(const APFloat &);
268 /* Return an arbitrary integer value usable for hashing. */
269 uint32_t getHashValue() const;
273 /* Trivial queries. */
274 integerPart *significandParts();
275 const integerPart *significandParts() const;
276 unsigned int partCount() const;
278 /* Significand operations. */
279 integerPart addSignificand(const APFloat &);
280 integerPart subtractSignificand(const APFloat &, integerPart);
281 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
282 lostFraction multiplySignificand(const APFloat &, const APFloat *);
283 lostFraction divideSignificand(const APFloat &);
284 void incrementSignificand();
285 void initialize(const fltSemantics *);
286 void shiftSignificandLeft(unsigned int);
287 lostFraction shiftSignificandRight(unsigned int);
288 unsigned int significandLSB() const;
289 unsigned int significandMSB() const;
290 void zeroSignificand();
292 /* Arithmetic on special values. */
293 opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
294 opStatus divideSpecials(const APFloat &);
295 opStatus multiplySpecials(const APFloat &);
296 opStatus modSpecials(const APFloat &);
300 opStatus normalize(roundingMode, lostFraction);
301 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
302 cmpResult compareAbsoluteValue(const APFloat &) const;
303 opStatus handleOverflow(roundingMode);
304 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
305 opStatus convertToSignExtendedInteger(integerPart *, unsigned int, bool,
306 roundingMode, bool *) const;
307 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
309 opStatus convertFromHexadecimalString(const char *, roundingMode);
310 opStatus convertFromDecimalString (const char *, roundingMode);
311 char *convertNormalToHexString(char *, unsigned int, bool,
313 opStatus roundSignificandWithExponent(const integerPart *, unsigned int,
316 APInt convertFloatAPFloatToAPInt() const;
317 APInt convertDoubleAPFloatToAPInt() const;
318 APInt convertF80LongDoubleAPFloatToAPInt() const;
319 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
320 void initFromAPInt(const APInt& api, bool isIEEE = false);
321 void initFromFloatAPInt(const APInt& api);
322 void initFromDoubleAPInt(const APInt& api);
323 void initFromF80LongDoubleAPInt(const APInt& api);
324 void initFromPPCDoubleDoubleAPInt(const APInt& api);
326 void assign(const APFloat &);
327 void copySignificand(const APFloat &);
328 void freeSignificand();
330 /* What kind of semantics does this value obey? */
331 const fltSemantics *semantics;
333 /* Significand - the fraction with an explicit integer bit. Must be
334 at least one bit wider than the target precision. */
341 /* The exponent - a signed number. */
344 /* What kind of floating point number this is. */
345 /* Only 2 bits are required, but VisualStudio incorrectly sign extends
346 it. Using the extra bit keeps it from failing under VisualStudio */
347 fltCategory category: 3;
349 /* The sign bit of this number. */
350 unsigned int sign: 1;
352 /* For PPCDoubleDouble, we have a second exponent and sign (the second
353 significand is appended to the first one, although it would be wrong to
354 regard these as a single number for arithmetic purposes). These fields
355 are not meaningful for any other type. */
356 exponent_t exponent2 : 11;
357 unsigned int sign2: 1;
359 } /* namespace llvm */
361 #endif /* LLVM_FLOAT_H */