real.h revision 1.1 1 /* Definitions of floating-point access for GNU compiler.
2 Copyright (C) 1989, 1991, 1994, 1996, 1997, 1998, 1999,
3 2000, 2002, 2003, 2004, 2005, 2007, 2008, 2009, 2010
4 Free Software Foundation, Inc.
5
6 This file is part of GCC.
7
8 GCC is free software; you can redistribute it and/or modify it under
9 the terms of the GNU General Public License as published by the Free
10 Software Foundation; either version 3, or (at your option) any later
11 version.
12
13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
14 WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
16 for more details.
17
18 You should have received a copy of the GNU General Public License
19 along with GCC; see the file COPYING3. If not see
20 <http://www.gnu.org/licenses/>. */
21
22 #ifndef GCC_REAL_H
23 #define GCC_REAL_H
24
25 #ifndef GENERATOR_FILE
26 #include <gmp.h>
27 #include <mpfr.h>
28 #include <mpc.h>
29 extern tree do_mpc_arg2 (tree, tree, tree, int, int (*)(mpc_ptr, mpc_srcptr, mpc_srcptr, mpc_rnd_t));
30 #endif
31 #include "machmode.h"
32
33 /* An expanded form of the represented number. */
34
35 /* Enumerate the special cases of numbers that we encounter. */
36 enum real_value_class {
37 rvc_zero,
38 rvc_normal,
39 rvc_inf,
40 rvc_nan
41 };
42
43 #define SIGNIFICAND_BITS (128 + HOST_BITS_PER_LONG)
44 #define EXP_BITS (32 - 6)
45 #define MAX_EXP ((1 << (EXP_BITS - 1)) - 1)
46 #define SIGSZ (SIGNIFICAND_BITS / HOST_BITS_PER_LONG)
47 #define SIG_MSB ((unsigned long)1 << (HOST_BITS_PER_LONG - 1))
48
49 struct GTY(()) real_value {
50 /* Use the same underlying type for all bit-fields, so as to make
51 sure they're packed together, otherwise REAL_VALUE_TYPE_SIZE will
52 be miscomputed. */
53 unsigned int /* ENUM_BITFIELD (real_value_class) */ cl : 2;
54 unsigned int decimal : 1;
55 unsigned int sign : 1;
56 unsigned int signalling : 1;
57 unsigned int canonical : 1;
58 unsigned int uexp : EXP_BITS;
59 unsigned long sig[SIGSZ];
60 };
61
62 #define REAL_EXP(REAL) \
63 ((int)((REAL)->uexp ^ (unsigned int)(1 << (EXP_BITS - 1))) \
64 - (1 << (EXP_BITS - 1)))
65 #define SET_REAL_EXP(REAL, EXP) \
66 ((REAL)->uexp = ((unsigned int)(EXP) & (unsigned int)((1 << EXP_BITS) - 1)))
67
68 /* Various headers condition prototypes on #ifdef REAL_VALUE_TYPE, so it
69 needs to be a macro. We do need to continue to have a structure tag
70 so that other headers can forward declare it. */
71 #define REAL_VALUE_TYPE struct real_value
72
73 /* We store a REAL_VALUE_TYPE into an rtx, and we do this by putting it in
74 consecutive "w" slots. Moreover, we've got to compute the number of "w"
75 slots at preprocessor time, which means we can't use sizeof. Guess. */
76
77 #define REAL_VALUE_TYPE_SIZE (SIGNIFICAND_BITS + 32)
78 #define REAL_WIDTH \
79 (REAL_VALUE_TYPE_SIZE/HOST_BITS_PER_WIDE_INT \
80 + (REAL_VALUE_TYPE_SIZE%HOST_BITS_PER_WIDE_INT ? 1 : 0)) /* round up */
81
82 /* Verify the guess. */
83 extern char test_real_width
84 [sizeof(REAL_VALUE_TYPE) <= REAL_WIDTH*sizeof(HOST_WIDE_INT) ? 1 : -1];
85
86 /* Calculate the format for CONST_DOUBLE. We need as many slots as
87 are necessary to overlay a REAL_VALUE_TYPE on them. This could be
88 as many as four (32-bit HOST_WIDE_INT, 128-bit REAL_VALUE_TYPE).
89
90 A number of places assume that there are always at least two 'w'
91 slots in a CONST_DOUBLE, so we provide them even if one would suffice. */
92
93 #if REAL_WIDTH == 1
94 # define CONST_DOUBLE_FORMAT "ww"
95 #else
96 # if REAL_WIDTH == 2
97 # define CONST_DOUBLE_FORMAT "ww"
98 # else
99 # if REAL_WIDTH == 3
100 # define CONST_DOUBLE_FORMAT "www"
101 # else
102 # if REAL_WIDTH == 4
103 # define CONST_DOUBLE_FORMAT "wwww"
104 # else
105 # if REAL_WIDTH == 5
106 # define CONST_DOUBLE_FORMAT "wwwww"
107 # else
108 # if REAL_WIDTH == 6
109 # define CONST_DOUBLE_FORMAT "wwwwww"
110 # else
111 #error "REAL_WIDTH > 6 not supported"
112 # endif
113 # endif
114 # endif
115 # endif
116 # endif
117 #endif
118
119
120 /* Describes the properties of the specific target format in use. */
121 struct real_format
122 {
123 /* Move to and from the target bytes. */
124 void (*encode) (const struct real_format *, long *,
125 const REAL_VALUE_TYPE *);
126 void (*decode) (const struct real_format *, REAL_VALUE_TYPE *,
127 const long *);
128
129 /* The radix of the exponent and digits of the significand. */
130 int b;
131
132 /* Size of the significand in digits of radix B. */
133 int p;
134
135 /* Size of the significant of a NaN, in digits of radix B. */
136 int pnan;
137
138 /* The minimum negative integer, x, such that b**(x-1) is normalized. */
139 int emin;
140
141 /* The maximum integer, x, such that b**(x-1) is representable. */
142 int emax;
143
144 /* The bit position of the sign bit, for determining whether a value
145 is positive/negative, or -1 for a complex encoding. */
146 int signbit_ro;
147
148 /* The bit position of the sign bit, for changing the sign of a number,
149 or -1 for a complex encoding. */
150 int signbit_rw;
151
152 /* Default rounding mode for operations on this format. */
153 bool round_towards_zero;
154 bool has_sign_dependent_rounding;
155
156 /* Properties of the format. */
157 bool has_nans;
158 bool has_inf;
159 bool has_denorm;
160 bool has_signed_zero;
161 bool qnan_msb_set;
162 bool canonical_nan_lsbs_set;
163 };
164
165
166 /* The target format used for each floating point mode.
167 Float modes are followed by decimal float modes, with entries for
168 float modes indexed by (MODE - first float mode), and entries for
169 decimal float modes indexed by (MODE - first decimal float mode) +
170 the number of float modes. */
171 extern const struct real_format *
172 real_format_for_mode[MAX_MODE_FLOAT - MIN_MODE_FLOAT + 1
173 + MAX_MODE_DECIMAL_FLOAT - MIN_MODE_DECIMAL_FLOAT + 1];
174
175 #define REAL_MODE_FORMAT(MODE) \
176 (real_format_for_mode[DECIMAL_FLOAT_MODE_P (MODE) \
177 ? (((MODE) - MIN_MODE_DECIMAL_FLOAT) \
178 + (MAX_MODE_FLOAT - MIN_MODE_FLOAT + 1)) \
179 : ((MODE) - MIN_MODE_FLOAT)])
180
181 #define FLOAT_MODE_FORMAT(MODE) \
182 (REAL_MODE_FORMAT (SCALAR_FLOAT_MODE_P (MODE)? (MODE) \
183 : GET_MODE_INNER (MODE)))
184
185 /* The following macro determines whether the floating point format is
186 composite, i.e. may contain non-consecutive mantissa bits, in which
187 case compile-time FP overflow may not model run-time overflow. */
188 #define MODE_COMPOSITE_P(MODE) \
189 (FLOAT_MODE_P (MODE) \
190 && FLOAT_MODE_FORMAT (MODE)->pnan < FLOAT_MODE_FORMAT (MODE)->p)
191
192 /* Accessor macros for format properties. */
193 #define MODE_HAS_NANS(MODE) \
194 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_nans)
195 #define MODE_HAS_INFINITIES(MODE) \
196 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_inf)
197 #define MODE_HAS_SIGNED_ZEROS(MODE) \
198 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_signed_zero)
199 #define MODE_HAS_SIGN_DEPENDENT_ROUNDING(MODE) \
200 (FLOAT_MODE_P (MODE) \
201 && FLOAT_MODE_FORMAT (MODE)->has_sign_dependent_rounding)
202
203 /* True if the given mode has a NaN representation and the treatment of
204 NaN operands is important. Certain optimizations, such as folding
205 x * 0 into 0, are not correct for NaN operands, and are normally
206 disabled for modes with NaNs. The user can ask for them to be
207 done anyway using the -funsafe-math-optimizations switch. */
208 #define HONOR_NANS(MODE) \
209 (MODE_HAS_NANS (MODE) && !flag_finite_math_only)
210
211 /* Like HONOR_NANs, but true if we honor signaling NaNs (or sNaNs). */
212 #define HONOR_SNANS(MODE) (flag_signaling_nans && HONOR_NANS (MODE))
213
214 /* As for HONOR_NANS, but true if the mode can represent infinity and
215 the treatment of infinite values is important. */
216 #define HONOR_INFINITIES(MODE) \
217 (MODE_HAS_INFINITIES (MODE) && !flag_finite_math_only)
218
219 /* Like HONOR_NANS, but true if the given mode distinguishes between
220 positive and negative zero, and the sign of zero is important. */
221 #define HONOR_SIGNED_ZEROS(MODE) \
222 (MODE_HAS_SIGNED_ZEROS (MODE) && flag_signed_zeros)
223
224 /* Like HONOR_NANS, but true if given mode supports sign-dependent rounding,
225 and the rounding mode is important. */
226 #define HONOR_SIGN_DEPENDENT_ROUNDING(MODE) \
227 (MODE_HAS_SIGN_DEPENDENT_ROUNDING (MODE) && flag_rounding_math)
228
229 /* Declare functions in real.c. */
230
231 /* Binary or unary arithmetic on tree_code. */
232 extern bool real_arithmetic (REAL_VALUE_TYPE *, int, const REAL_VALUE_TYPE *,
233 const REAL_VALUE_TYPE *);
234
235 /* Compare reals by tree_code. */
236 extern bool real_compare (int, const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
237
238 /* Determine whether a floating-point value X is infinite. */
239 extern bool real_isinf (const REAL_VALUE_TYPE *);
240
241 /* Determine whether a floating-point value X is a NaN. */
242 extern bool real_isnan (const REAL_VALUE_TYPE *);
243
244 /* Determine whether a floating-point value X is finite. */
245 extern bool real_isfinite (const REAL_VALUE_TYPE *);
246
247 /* Determine whether a floating-point value X is negative. */
248 extern bool real_isneg (const REAL_VALUE_TYPE *);
249
250 /* Determine whether a floating-point value X is minus zero. */
251 extern bool real_isnegzero (const REAL_VALUE_TYPE *);
252
253 /* Compare two floating-point objects for bitwise identity. */
254 extern bool real_identical (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
255
256 /* Extend or truncate to a new mode. */
257 extern void real_convert (REAL_VALUE_TYPE *, enum machine_mode,
258 const REAL_VALUE_TYPE *);
259
260 /* Return true if truncating to NEW is exact. */
261 extern bool exact_real_truncate (enum machine_mode, const REAL_VALUE_TYPE *);
262
263 /* Render R as a decimal floating point constant. */
264 extern void real_to_decimal (char *, const REAL_VALUE_TYPE *, size_t,
265 size_t, int);
266
267 /* Render R as a decimal floating point constant, rounded so as to be
268 parsed back to the same value when interpreted in mode MODE. */
269 extern void real_to_decimal_for_mode (char *, const REAL_VALUE_TYPE *, size_t,
270 size_t, int, enum machine_mode);
271
272 /* Render R as a hexadecimal floating point constant. */
273 extern void real_to_hexadecimal (char *, const REAL_VALUE_TYPE *,
274 size_t, size_t, int);
275
276 /* Render R as an integer. */
277 extern HOST_WIDE_INT real_to_integer (const REAL_VALUE_TYPE *);
278 extern void real_to_integer2 (HOST_WIDE_INT *, HOST_WIDE_INT *,
279 const REAL_VALUE_TYPE *);
280
281 /* Initialize R from a decimal or hexadecimal string. Return -1 if
282 the value underflows, +1 if overflows, and 0 otherwise. */
283 extern int real_from_string (REAL_VALUE_TYPE *, const char *);
284 /* Wrapper to allow different internal representation for decimal floats. */
285 extern void real_from_string3 (REAL_VALUE_TYPE *, const char *, enum machine_mode);
286
287 /* Initialize R from an integer pair HIGH/LOW. */
288 extern void real_from_integer (REAL_VALUE_TYPE *, enum machine_mode,
289 unsigned HOST_WIDE_INT, HOST_WIDE_INT, int);
290
291 extern long real_to_target_fmt (long *, const REAL_VALUE_TYPE *,
292 const struct real_format *);
293 extern long real_to_target (long *, const REAL_VALUE_TYPE *, enum machine_mode);
294
295 extern void real_from_target_fmt (REAL_VALUE_TYPE *, const long *,
296 const struct real_format *);
297 extern void real_from_target (REAL_VALUE_TYPE *, const long *,
298 enum machine_mode);
299
300 extern void real_inf (REAL_VALUE_TYPE *);
301
302 extern bool real_nan (REAL_VALUE_TYPE *, const char *, int, enum machine_mode);
303
304 extern void real_maxval (REAL_VALUE_TYPE *, int, enum machine_mode);
305
306 extern void real_2expN (REAL_VALUE_TYPE *, int, enum machine_mode);
307
308 extern unsigned int real_hash (const REAL_VALUE_TYPE *);
309
310
311 /* Target formats defined in real.c. */
312 extern const struct real_format ieee_single_format;
313 extern const struct real_format mips_single_format;
314 extern const struct real_format motorola_single_format;
315 extern const struct real_format spu_single_format;
316 extern const struct real_format ieee_double_format;
317 extern const struct real_format mips_double_format;
318 extern const struct real_format motorola_double_format;
319 extern const struct real_format ieee_extended_motorola_format;
320 extern const struct real_format ieee_extended_intel_96_format;
321 extern const struct real_format ieee_extended_intel_96_round_53_format;
322 extern const struct real_format ieee_extended_intel_128_format;
323 extern const struct real_format ibm_extended_format;
324 extern const struct real_format mips_extended_format;
325 extern const struct real_format ieee_quad_format;
326 extern const struct real_format mips_quad_format;
327 extern const struct real_format vax_f_format;
328 extern const struct real_format vax_d_format;
329 extern const struct real_format vax_g_format;
330 extern const struct real_format real_internal_format;
331 extern const struct real_format decimal_single_format;
332 extern const struct real_format decimal_double_format;
333 extern const struct real_format decimal_quad_format;
334 extern const struct real_format ieee_half_format;
335 extern const struct real_format arm_half_format;
336
337
338 /* ====================================================================== */
339 /* Crap. */
340
341 #define REAL_ARITHMETIC(value, code, d1, d2) \
342 real_arithmetic (&(value), code, &(d1), &(d2))
343
344 #define REAL_VALUES_IDENTICAL(x, y) real_identical (&(x), &(y))
345 #define REAL_VALUES_EQUAL(x, y) real_compare (EQ_EXPR, &(x), &(y))
346 #define REAL_VALUES_LESS(x, y) real_compare (LT_EXPR, &(x), &(y))
347
348 /* Determine whether a floating-point value X is infinite. */
349 #define REAL_VALUE_ISINF(x) real_isinf (&(x))
350
351 /* Determine whether a floating-point value X is a NaN. */
352 #define REAL_VALUE_ISNAN(x) real_isnan (&(x))
353
354 /* Determine whether a floating-point value X is negative. */
355 #define REAL_VALUE_NEGATIVE(x) real_isneg (&(x))
356
357 /* Determine whether a floating-point value X is minus zero. */
358 #define REAL_VALUE_MINUS_ZERO(x) real_isnegzero (&(x))
359
360 /* IN is a REAL_VALUE_TYPE. OUT is an array of longs. */
361 #define REAL_VALUE_TO_TARGET_LONG_DOUBLE(IN, OUT) \
362 real_to_target (OUT, &(IN), \
363 mode_for_size (LONG_DOUBLE_TYPE_SIZE, MODE_FLOAT, 0))
364
365 #define REAL_VALUE_TO_TARGET_DOUBLE(IN, OUT) \
366 real_to_target (OUT, &(IN), mode_for_size (64, MODE_FLOAT, 0))
367
368 /* IN is a REAL_VALUE_TYPE. OUT is a long. */
369 #define REAL_VALUE_TO_TARGET_SINGLE(IN, OUT) \
370 ((OUT) = real_to_target (NULL, &(IN), mode_for_size (32, MODE_FLOAT, 0)))
371
372 #define REAL_VALUE_FROM_INT(r, lo, hi, mode) \
373 real_from_integer (&(r), mode, lo, hi, 0)
374
375 #define REAL_VALUE_FROM_UNSIGNED_INT(r, lo, hi, mode) \
376 real_from_integer (&(r), mode, lo, hi, 1)
377
378 /* Real values to IEEE 754 decimal floats. */
379
380 /* IN is a REAL_VALUE_TYPE. OUT is an array of longs. */
381 #define REAL_VALUE_TO_TARGET_DECIMAL128(IN, OUT) \
382 real_to_target (OUT, &(IN), mode_for_size (128, MODE_DECIMAL_FLOAT, 0))
383
384 #define REAL_VALUE_TO_TARGET_DECIMAL64(IN, OUT) \
385 real_to_target (OUT, &(IN), mode_for_size (64, MODE_DECIMAL_FLOAT, 0))
386
387 /* IN is a REAL_VALUE_TYPE. OUT is a long. */
388 #define REAL_VALUE_TO_TARGET_DECIMAL32(IN, OUT) \
389 ((OUT) = real_to_target (NULL, &(IN), mode_for_size (32, MODE_DECIMAL_FLOAT, 0)))
390
391 extern REAL_VALUE_TYPE real_value_truncate (enum machine_mode,
392 REAL_VALUE_TYPE);
393
394 #define REAL_VALUE_TO_INT(plow, phigh, r) \
395 real_to_integer2 (plow, phigh, &(r))
396
397 extern REAL_VALUE_TYPE real_arithmetic2 (int, const REAL_VALUE_TYPE *,
398 const REAL_VALUE_TYPE *);
399
400 #define REAL_VALUE_NEGATE(X) \
401 real_arithmetic2 (NEGATE_EXPR, &(X), NULL)
402
403 #define REAL_VALUE_ABS(X) \
404 real_arithmetic2 (ABS_EXPR, &(X), NULL)
405
406 extern int significand_size (enum machine_mode);
407
408 extern REAL_VALUE_TYPE real_from_string2 (const char *, enum machine_mode);
409
410 #define REAL_VALUE_ATOF(s, m) \
411 real_from_string2 (s, m)
412
413 #define CONST_DOUBLE_ATOF(s, m) \
414 CONST_DOUBLE_FROM_REAL_VALUE (real_from_string2 (s, m), m)
415
416 #define REAL_VALUE_FIX(r) \
417 real_to_integer (&(r))
418
419 /* ??? Not quite right. */
420 #define REAL_VALUE_UNSIGNED_FIX(r) \
421 real_to_integer (&(r))
422
423 /* ??? These were added for Paranoia support. */
424
425 /* Return floor log2(R). */
426 extern int real_exponent (const REAL_VALUE_TYPE *);
427
428 /* R = A * 2**EXP. */
429 extern void real_ldexp (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, int);
430
431 /* **** End of software floating point emulator interface macros **** */
432
433 /* Constant real values 0, 1, 2, -1 and 0.5. */
435
436 extern REAL_VALUE_TYPE dconst0;
437 extern REAL_VALUE_TYPE dconst1;
438 extern REAL_VALUE_TYPE dconst2;
439 extern REAL_VALUE_TYPE dconstm1;
440 extern REAL_VALUE_TYPE dconsthalf;
441
442 #define dconst_e() (*dconst_e_ptr ())
443 #define dconst_third() (*dconst_third_ptr ())
444 #define dconst_sqrt2() (*dconst_sqrt2_ptr ())
445
446 /* Function to return the real value special constant 'e'. */
447 extern const REAL_VALUE_TYPE * dconst_e_ptr (void);
448
449 /* Returns the special REAL_VALUE_TYPE corresponding to 1/3. */
450 extern const REAL_VALUE_TYPE * dconst_third_ptr (void);
451
452 /* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2). */
453 extern const REAL_VALUE_TYPE * dconst_sqrt2_ptr (void);
454
455 /* Function to return a real value (not a tree node)
456 from a given integer constant. */
457 REAL_VALUE_TYPE real_value_from_int_cst (const_tree, const_tree);
458
459 /* Given a CONST_DOUBLE in FROM, store into TO the value it represents. */
460 #define REAL_VALUE_FROM_CONST_DOUBLE(to, from) \
461 ((to) = *CONST_DOUBLE_REAL_VALUE (from))
462
463 /* Return a CONST_DOUBLE with value R and mode M. */
464 #define CONST_DOUBLE_FROM_REAL_VALUE(r, m) \
465 const_double_from_real_value (r, m)
466 extern rtx const_double_from_real_value (REAL_VALUE_TYPE, enum machine_mode);
467
468 /* Replace R by 1/R in the given machine mode, if the result is exact. */
469 extern bool exact_real_inverse (enum machine_mode, REAL_VALUE_TYPE *);
470
471 /* Return true if arithmetic on values in IMODE that were promoted
472 from values in TMODE is equivalent to direct arithmetic on values
473 in TMODE. */
474 bool real_can_shorten_arithmetic (enum machine_mode, enum machine_mode);
475
476 /* In tree.c: wrap up a REAL_VALUE_TYPE in a tree node. */
477 extern tree build_real (tree, REAL_VALUE_TYPE);
478
479 /* Calculate R as the square root of X in the given machine mode. */
480 extern bool real_sqrt (REAL_VALUE_TYPE *, enum machine_mode,
481 const REAL_VALUE_TYPE *);
482
483 /* Calculate R as X raised to the integer exponent N in mode MODE. */
484 extern bool real_powi (REAL_VALUE_TYPE *, enum machine_mode,
485 const REAL_VALUE_TYPE *, HOST_WIDE_INT);
486
487 /* Standard round to integer value functions. */
488 extern void real_trunc (REAL_VALUE_TYPE *, enum machine_mode,
489 const REAL_VALUE_TYPE *);
490 extern void real_floor (REAL_VALUE_TYPE *, enum machine_mode,
491 const REAL_VALUE_TYPE *);
492 extern void real_ceil (REAL_VALUE_TYPE *, enum machine_mode,
493 const REAL_VALUE_TYPE *);
494 extern void real_round (REAL_VALUE_TYPE *, enum machine_mode,
495 const REAL_VALUE_TYPE *);
496
497 /* Set the sign of R to the sign of X. */
498 extern void real_copysign (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
499
500 #ifndef GENERATOR_FILE
501 /* Convert between MPFR and REAL_VALUE_TYPE. The caller is
502 responsible for initializing and clearing the MPFR parameter. */
503
504 extern void real_from_mpfr (REAL_VALUE_TYPE *, mpfr_srcptr, tree, mp_rnd_t);
505 extern void mpfr_from_real (mpfr_ptr, const REAL_VALUE_TYPE *, mp_rnd_t);
506 #endif
507
508 /* Check whether the real constant value given is an integer. */
509 extern bool real_isinteger (const REAL_VALUE_TYPE *c, enum machine_mode mode);
510
511 /* Write into BUF the maximum representable finite floating-point
512 number, (1 - b**-p) * b**emax for a given FP format FMT as a hex
513 float string. BUF must be large enough to contain the result. */
514 extern void get_max_float (const struct real_format *, char *, size_t);
515 #endif /* ! GCC_REAL_H */
516