1 //== llvm/Support/APFloat.h - Arbitrary Precision Floating Point -*- C++ -*-==//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by Neil Booth and is distributed under the
6 // University of Illinois Open Source 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 Conversion to and from decimal text is not currently implemented.
65 Non-zero finite numbers are represented internally as a sign bit,
66 a 16-bit signed exponent, and the significand as an array of
67 integer parts. After normalization of a number of precision P the
68 exponent is within the range of the format, and if the number is
69 not denormal the P-th bit of the significand is set as an explicit
70 integer bit. For denormals the most significant bit is shifted
71 right so that the exponent is maintained at the format's minimum,
72 so that the smallest denormal has just the least significant bit
73 of the significand set. The sign of zeroes and infinities is
74 significant; the exponent and significand of such numbers is not
75 stored, but has a known implicit (deterministic) value: 0 for the
76 significands, 0 for zero exponent, all 1 bits for infinity
77 exponent. For NaNs the sign and significand are deterministic,
78 although not really meaningful, and preserved in non-conversion
79 operations. The exponent is implicitly all 1 bits.
84 Some features that may or may not be worth adding:
86 Conversions to and from decimal strings (hard).
88 Optional ability to detect underflow tininess before rounding.
90 New formats: x87 in single and double precision mode (IEEE apart
91 from extended exponent range) and IBM two-double extended
94 New operations: sqrt, IEEE remainder, C90 fmod, nextafter,
101 // APInt contains static functions implementing bignum arithmetic.
102 #include "llvm/ADT/APInt.h"
103 #include "llvm/CodeGen/ValueTypes.h"
107 /* Exponents are stored as signed numbers. */
108 typedef signed short exponent_t;
112 /* When bits of a floating point number are truncated, this enum is
113 used to indicate what fraction of the LSB those bits represented.
114 It essentially combines the roles of guard and sticky bits. */
115 enum lostFraction { // Example of truncated bits:
116 lfExactlyZero, // 000000
117 lfLessThanHalf, // 0xxxxx x's not all zero
118 lfExactlyHalf, // 100000
119 lfMoreThanHalf // 1xxxxx x's not all zero
125 /* We support the following floating point semantics. */
126 static const fltSemantics IEEEsingle;
127 static const fltSemantics IEEEdouble;
128 static const fltSemantics IEEEquad;
129 static const fltSemantics x87DoubleExtended;
130 /* And this psuedo, used to construct APFloats that cannot
131 conflict with anything real. */
132 static const fltSemantics Bogus;
134 static unsigned int semanticsPrecision(const fltSemantics &);
136 /* Floating point numbers have a four-state comparison relation. */
144 /* IEEE-754R gives five rounding modes. */
153 /* Operation status. opUnderflow or opOverflow are always returned
154 or-ed with opInexact. */
164 /* Category of internally-represented number. */
173 APFloat(const fltSemantics &, const char *);
174 APFloat(const fltSemantics &, integerPart);
175 APFloat(const fltSemantics &, fltCategory, bool negative);
176 explicit APFloat(double d);
177 explicit APFloat(float f);
178 explicit APFloat(const APInt &);
179 APFloat(const APFloat &);
183 opStatus add(const APFloat &, roundingMode);
184 opStatus subtract(const APFloat &, roundingMode);
185 opStatus multiply(const APFloat &, roundingMode);
186 opStatus divide(const APFloat &, roundingMode);
187 opStatus mod(const APFloat &, roundingMode);
188 void copySign(const APFloat &);
189 opStatus fusedMultiplyAdd(const APFloat &, const APFloat &, roundingMode);
190 void changeSign(); // neg
191 void clearSign(); // abs
194 opStatus convert(const fltSemantics &, roundingMode);
195 opStatus convertToInteger(integerPart *, unsigned int, bool,
197 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
199 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
201 opStatus convertFromString(const char *, roundingMode);
202 APInt convertToAPInt() const;
203 double convertToDouble() const;
204 float convertToFloat() const;
206 /* The definition of equality is not straightforward for floating point,
207 so we won't use operator==. Use one of the following, or write
208 whatever it is you really mean. */
209 // bool operator==(const APFloat &) const; // DO NOT IMPLEMENT
211 /* IEEE comparison with another floating point number (NaNs
212 compare unordered, 0==-0). */
213 cmpResult compare(const APFloat &) const;
215 /* Write out a hexadecimal representation of the floating point
216 value to DST, which must be of sufficient size, in the C99 form
217 [-]0xh.hhhhp[+-]d. Return the number of characters written,
218 excluding the terminating NUL. */
219 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
220 bool upperCase, roundingMode) const;
222 /* Bitwise comparison for equality (QNaNs compare equal, 0!=-0). */
223 bool bitwiseIsEqual(const APFloat &) const;
225 /* Simple queries. */
226 fltCategory getCategory() const { return category; }
227 const fltSemantics &getSemantics() const { return *semantics; }
228 bool isZero() const { return category == fcZero; }
229 bool isNonZero() const { return category != fcZero; }
230 bool isNegative() const { return sign; }
231 bool isPosZero() const { return isZero() && !isNegative(); }
232 bool isNegZero() const { return isZero() && isNegative(); }
234 APFloat& operator=(const APFloat &);
236 /* Return an arbitrary integer value usable for hashing. */
237 uint32_t getHashValue() const;
241 /* Trivial queries. */
242 integerPart *significandParts();
243 const integerPart *significandParts() const;
244 unsigned int partCount() const;
246 /* Significand operations. */
247 integerPart addSignificand(const APFloat &);
248 integerPart subtractSignificand(const APFloat &, integerPart);
249 lostFraction addOrSubtractSignificand(const APFloat &, bool subtract);
250 lostFraction multiplySignificand(const APFloat &, const APFloat *);
251 lostFraction divideSignificand(const APFloat &);
252 void incrementSignificand();
253 void initialize(const fltSemantics *);
254 void shiftSignificandLeft(unsigned int);
255 lostFraction shiftSignificandRight(unsigned int);
256 unsigned int significandLSB() const;
257 unsigned int significandMSB() const;
258 void zeroSignificand();
260 /* Arithmetic on special values. */
261 opStatus addOrSubtractSpecials(const APFloat &, bool subtract);
262 opStatus divideSpecials(const APFloat &);
263 opStatus multiplySpecials(const APFloat &);
266 opStatus normalize(roundingMode, lostFraction);
267 opStatus addOrSubtract(const APFloat &, roundingMode, bool subtract);
268 cmpResult compareAbsoluteValue(const APFloat &) const;
269 opStatus handleOverflow(roundingMode);
270 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
271 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
273 opStatus convertFromHexadecimalString(const char *, roundingMode);
274 char *convertNormalToHexString(char *, unsigned int, bool,
276 APInt convertFloatAPFloatToAPInt() const;
277 APInt convertDoubleAPFloatToAPInt() const;
278 APInt convertF80LongDoubleAPFloatToAPInt() const;
279 void initFromAPInt(const APInt& api);
280 void initFromFloatAPInt(const APInt& api);
281 void initFromDoubleAPInt(const APInt& api);
282 void initFromF80LongDoubleAPInt(const APInt& api);
284 void assign(const APFloat &);
285 void copySignificand(const APFloat &);
286 void freeSignificand();
288 /* What kind of semantics does this value obey? */
289 const fltSemantics *semantics;
291 /* Significand - the fraction with an explicit integer bit. Must be
292 at least one bit wider than the target precision. */
299 /* The exponent - a signed number. */
302 /* What kind of floating point number this is. */
303 /* Only 2 bits are required, but VisualStudio incorrectly sign extends
304 it. Using the extra bit keeps it from failing under VisualStudio */
305 fltCategory category: 3;
307 /* The sign bit of this number. */
308 unsigned int sign: 1;
310 } /* namespace llvm */
312 #endif /* LLVM_FLOAT_H */