gcc/real.h

   1 /* Definitions of floating-point access for GNU compiler.
   2    Copyright (C) 1989-2015 Free Software Foundation, Inc.
   3
   4    This file is part of GCC.
   5
   6    GCC is free software; you can redistribute it and/or modify it under
   7    the terms of the GNU General Public License as published by the Free
   8    Software Foundation; either version 3, or (at your option) any later
   9    version.
  10
  11    GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  12    WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14    for more details.
  15
  16    You should have received a copy of the GNU General Public License
  17    along with GCC; see the file COPYING3.  If not see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #ifndef GCC_REAL_H
  21 #define GCC_REAL_H
  22
  23 #include "machmode.h"
  24 #include "signop.h"
  25 #include "wide-int.h"
  26 #include "insn-modes.h"
  27
  28 /* An expanded form of the represented number.  */
  29
  30 /* Enumerate the special cases of numbers that we encounter.  */
  31 enum real_value_class {
  32   rvc_zero,
  33   rvc_normal,
  34   rvc_inf,
  35   rvc_nan
  36 };
  37
  38 #define SIGNIFICAND_BITS        (128 + HOST_BITS_PER_LONG)
  39 #define EXP_BITS                (32 - 6)
  40 #define MAX_EXP                 ((1 << (EXP_BITS - 1)) - 1)
  41 #define SIGSZ                   (SIGNIFICAND_BITS / HOST_BITS_PER_LONG)
  42 #define SIG_MSB                 ((unsigned long)1 << (HOST_BITS_PER_LONG - 1))
  43
  44 struct GTY(()) real_value {
  45   /* Use the same underlying type for all bit-fields, so as to make
  46      sure they're packed together, otherwise REAL_VALUE_TYPE_SIZE will
  47      be miscomputed.  */
  48   unsigned int /* ENUM_BITFIELD (real_value_class) */ cl : 2;
  49   unsigned int decimal : 1;
  50   unsigned int sign : 1;
  51   unsigned int signalling : 1;
  52   unsigned int canonical : 1;
  53   unsigned int uexp : EXP_BITS;
  54   unsigned long sig[SIGSZ];
  55 };
  56
  57 #define REAL_EXP(REAL) \
  58   ((int)((REAL)->uexp ^ (unsigned int)(1 << (EXP_BITS - 1))) \
  59    - (1 << (EXP_BITS - 1)))
  60 #define SET_REAL_EXP(REAL, EXP) \
  61   ((REAL)->uexp = ((unsigned int)(EXP) & (unsigned int)((1 << EXP_BITS) - 1)))
  62
  63 /* Various headers condition prototypes on #ifdef REAL_VALUE_TYPE, so it
  64    needs to be a macro.  We do need to continue to have a structure tag
  65    so that other headers can forward declare it.  */
  66 #define REAL_VALUE_TYPE struct real_value
  67
  68 /* We store a REAL_VALUE_TYPE into an rtx, and we do this by putting it in
  69    consecutive "w" slots.  Moreover, we've got to compute the number of "w"
  70    slots at preprocessor time, which means we can't use sizeof.  Guess.  */
  71
  72 #define REAL_VALUE_TYPE_SIZE (SIGNIFICAND_BITS + 32)
  73 #define REAL_WIDTH \
  74   (REAL_VALUE_TYPE_SIZE/HOST_BITS_PER_WIDE_INT \
  75    + (REAL_VALUE_TYPE_SIZE%HOST_BITS_PER_WIDE_INT ? 1 : 0)) /* round up */
  76
  77 /* Verify the guess.  */
  78 extern char test_real_width
  79   [sizeof (REAL_VALUE_TYPE) <= REAL_WIDTH * sizeof (HOST_WIDE_INT) ? 1 : -1];
  80
  81 /* Calculate the format for CONST_DOUBLE.  We need as many slots as
  82    are necessary to overlay a REAL_VALUE_TYPE on them.  This could be
  83    as many as four (32-bit HOST_WIDE_INT, 128-bit REAL_VALUE_TYPE).
  84
  85    A number of places assume that there are always at least two 'w'
  86    slots in a CONST_DOUBLE, so we provide them even if one would suffice.  */
  87
  88 #if REAL_WIDTH == 1
  89 # define CONST_DOUBLE_FORMAT     "ww"
  90 #else
  91 # if REAL_WIDTH == 2
  92 #  define CONST_DOUBLE_FORMAT    "ww"
  93 # else
  94 #  if REAL_WIDTH == 3
  95 #   define CONST_DOUBLE_FORMAT   "www"
  96 #  else
  97 #   if REAL_WIDTH == 4
  98 #    define CONST_DOUBLE_FORMAT  "wwww"
  99 #   else
 100 #    if REAL_WIDTH == 5
 101 #     define CONST_DOUBLE_FORMAT "wwwww"
 102 #    else
 103 #     if REAL_WIDTH == 6
 104 #      define CONST_DOUBLE_FORMAT "wwwwww"
 105 #     else
 106        #error "REAL_WIDTH > 6 not supported"
 107 #     endif
 108 #    endif
 109 #   endif
 110 #  endif
 111 # endif
 112 #endif
 113
 114
 115 /* Describes the properties of the specific target format in use.  */
 116 struct real_format
 117 {
 118   /* Move to and from the target bytes.  */
 119   void (*encode) (const struct real_format *, long *,
 120                   const REAL_VALUE_TYPE *);
 121   void (*decode) (const struct real_format *, REAL_VALUE_TYPE *,
 122                   const long *);
 123
 124   /* The radix of the exponent and digits of the significand.  */
 125   int b;
 126
 127   /* Size of the significand in digits of radix B.  */
 128   int p;
 129
 130   /* Size of the significant of a NaN, in digits of radix B.  */
 131   int pnan;
 132
 133   /* The minimum negative integer, x, such that b**(x-1) is normalized.  */
 134   int emin;
 135
 136   /* The maximum integer, x, such that b**(x-1) is representable.  */
 137   int emax;
 138
 139   /* The bit position of the sign bit, for determining whether a value
 140      is positive/negative, or -1 for a complex encoding.  */
 141   int signbit_ro;
 142
 143   /* The bit position of the sign bit, for changing the sign of a number,
 144      or -1 for a complex encoding.  */
 145   int signbit_rw;
 146
 147   /* Default rounding mode for operations on this format.  */
 148   bool round_towards_zero;
 149   bool has_sign_dependent_rounding;
 150
 151   /* Properties of the format.  */
 152   bool has_nans;
 153   bool has_inf;
 154   bool has_denorm;
 155   bool has_signed_zero;
 156   bool qnan_msb_set;
 157   bool canonical_nan_lsbs_set;
 158   const char *name;
 159 };
 160
 161
 162 /* The target format used for each floating point mode.
 163    Float modes are followed by decimal float modes, with entries for
 164    float modes indexed by (MODE - first float mode), and entries for
 165    decimal float modes indexed by (MODE - first decimal float mode) +
 166    the number of float modes.  */
 167 extern const struct real_format *
 168   real_format_for_mode[MAX_MODE_FLOAT - MIN_MODE_FLOAT + 1
 169                        + MAX_MODE_DECIMAL_FLOAT - MIN_MODE_DECIMAL_FLOAT + 1];
 170
 171 #define REAL_MODE_FORMAT(MODE)                                          \
 172   (real_format_for_mode[DECIMAL_FLOAT_MODE_P (MODE)                     \
 173                         ? (((MODE) - MIN_MODE_DECIMAL_FLOAT)            \
 174                            + (MAX_MODE_FLOAT - MIN_MODE_FLOAT + 1))     \
 175                         : ((MODE) - MIN_MODE_FLOAT)])
 176
 177 #define FLOAT_MODE_FORMAT(MODE) \
 178   (REAL_MODE_FORMAT (SCALAR_FLOAT_MODE_P (MODE)? (MODE) \
 179                                                : GET_MODE_INNER (MODE)))
 180
 181 /* The following macro determines whether the floating point format is
 182    composite, i.e. may contain non-consecutive mantissa bits, in which
 183    case compile-time FP overflow may not model run-time overflow.  */
 184 #define MODE_COMPOSITE_P(MODE) \
 185   (FLOAT_MODE_P (MODE) \
 186    && FLOAT_MODE_FORMAT (MODE)->pnan < FLOAT_MODE_FORMAT (MODE)->p)
 187
 188 /* Accessor macros for format properties.  */
 189 #define MODE_HAS_NANS(MODE) \
 190   (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_nans)
 191 #define MODE_HAS_INFINITIES(MODE) \
 192   (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_inf)
 193 #define MODE_HAS_SIGNED_ZEROS(MODE) \
 194   (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_signed_zero)
 195 #define MODE_HAS_SIGN_DEPENDENT_ROUNDING(MODE) \
 196   (FLOAT_MODE_P (MODE) \
 197    && FLOAT_MODE_FORMAT (MODE)->has_sign_dependent_rounding)
 198
 199 /* Declare functions in real.c.  */
 200
 201 /* True if the given mode has a NaN representation and the treatment of
 202    NaN operands is important.  Certain optimizations, such as folding
 203    x * 0 into 0, are not correct for NaN operands, and are normally
 204    disabled for modes with NaNs.  The user can ask for them to be
 205    done anyway using the -funsafe-math-optimizations switch.  */
 206 extern bool HONOR_NANS (machine_mode);
 207 extern bool HONOR_NANS (const_tree);
 208 extern bool HONOR_NANS (const_rtx);
 209
 210 /* Like HONOR_NANs, but true if we honor signaling NaNs (or sNaNs).  */
 211 extern bool HONOR_SNANS (machine_mode);
 212 extern bool HONOR_SNANS (const_tree);
 213 extern bool HONOR_SNANS (const_rtx);
 214
 215 /* As for HONOR_NANS, but true if the mode can represent infinity and
 216    the treatment of infinite values is important.  */
 217 extern bool HONOR_INFINITIES (machine_mode);
 218 extern bool HONOR_INFINITIES (const_tree);
 219 extern bool HONOR_INFINITIES (const_rtx);
 220
 221 /* Like HONOR_NANS, but true if the given mode distinguishes between
 222    positive and negative zero, and the sign of zero is important.  */
 223 extern bool HONOR_SIGNED_ZEROS (machine_mode);
 224 extern bool HONOR_SIGNED_ZEROS (const_tree);
 225 extern bool HONOR_SIGNED_ZEROS (const_rtx);
 226
 227 /* Like HONOR_NANS, but true if given mode supports sign-dependent rounding,
 228    and the rounding mode is important.  */
 229 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (machine_mode);
 230 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_tree);
 231 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_rtx);
 232
 233 /* Binary or unary arithmetic on tree_code.  */
 234 extern bool real_arithmetic (REAL_VALUE_TYPE *, int, const REAL_VALUE_TYPE *,
 235                              const REAL_VALUE_TYPE *);
 236
 237 /* Compare reals by tree_code.  */
 238 extern bool real_compare (int, const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
 239
 240 /* Determine whether a floating-point value X is infinite.  */
 241 extern bool real_isinf (const REAL_VALUE_TYPE *);
 242
 243 /* Determine whether a floating-point value X is a NaN.  */
 244 extern bool real_isnan (const REAL_VALUE_TYPE *);
 245
 246 /* Determine whether a floating-point value X is finite.  */
 247 extern bool real_isfinite (const REAL_VALUE_TYPE *);
 248
 249 /* Determine whether a floating-point value X is negative.  */
 250 extern bool real_isneg (const REAL_VALUE_TYPE *);
 251
 252 /* Determine whether a floating-point value X is minus zero.  */
 253 extern bool real_isnegzero (const REAL_VALUE_TYPE *);
 254
 255 /* Compare two floating-point objects for bitwise identity.  */
 256 extern bool real_identical (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
 257
 258 /* Extend or truncate to a new mode.  */
 259 extern void real_convert (REAL_VALUE_TYPE *, machine_mode,
 260                           const REAL_VALUE_TYPE *);
 261
 262 /* Return true if truncating to NEW is exact.  */
 263 extern bool exact_real_truncate (machine_mode, const REAL_VALUE_TYPE *);
 264
 265 /* Render R as a decimal floating point constant.  */
 266 extern void real_to_decimal (char *, const REAL_VALUE_TYPE *, size_t,
 267                              size_t, int);
 268
 269 /* Render R as a decimal floating point constant, rounded so as to be
 270    parsed back to the same value when interpreted in mode MODE.  */
 271 extern void real_to_decimal_for_mode (char *, const REAL_VALUE_TYPE *, size_t,
 272                                       size_t, int, machine_mode);
 273
 274 /* Render R as a hexadecimal floating point constant.  */
 275 extern void real_to_hexadecimal (char *, const REAL_VALUE_TYPE *,
 276                                  size_t, size_t, int);
 277
 278 /* Render R as an integer.  */
 279 extern HOST_WIDE_INT real_to_integer (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 *, machine_mode);
 286
 287 extern long real_to_target_fmt (long *, const REAL_VALUE_TYPE *,
 288                                 const struct real_format *);
 289 extern long real_to_target (long *, const REAL_VALUE_TYPE *, machine_mode);
 290
 291 extern void real_from_target_fmt (REAL_VALUE_TYPE *, const long *,
 292                                   const struct real_format *);
 293 extern void real_from_target (REAL_VALUE_TYPE *, const long *,
 294                               machine_mode);
 295
 296 extern void real_inf (REAL_VALUE_TYPE *);
 297
 298 extern bool real_nan (REAL_VALUE_TYPE *, const char *, int, machine_mode);
 299
 300 extern void real_maxval (REAL_VALUE_TYPE *, int, machine_mode);
 301
 302 extern void real_2expN (REAL_VALUE_TYPE *, int, machine_mode);
 303
 304 extern unsigned int real_hash (const REAL_VALUE_TYPE *);
 305
 306
 307 /* Target formats defined in real.c.  */
 308 extern const struct real_format ieee_single_format;
 309 extern const struct real_format mips_single_format;
 310 extern const struct real_format motorola_single_format;
 311 extern const struct real_format spu_single_format;
 312 extern const struct real_format ieee_double_format;
 313 extern const struct real_format mips_double_format;
 314 extern const struct real_format motorola_double_format;
 315 extern const struct real_format ieee_extended_motorola_format;
 316 extern const struct real_format ieee_extended_intel_96_format;
 317 extern const struct real_format ieee_extended_intel_96_round_53_format;
 318 extern const struct real_format ieee_extended_intel_128_format;
 319 extern const struct real_format ibm_extended_format;
 320 extern const struct real_format mips_extended_format;
 321 extern const struct real_format ieee_quad_format;
 322 extern const struct real_format mips_quad_format;
 323 extern const struct real_format vax_f_format;
 324 extern const struct real_format vax_d_format;
 325 extern const struct real_format vax_g_format;
 326 extern const struct real_format real_internal_format;
 327 extern const struct real_format decimal_single_format;
 328 extern const struct real_format decimal_double_format;
 329 extern const struct real_format decimal_quad_format;
 330 extern const struct real_format ieee_half_format;
 331 extern const struct real_format arm_half_format;
 332
 333
 334 /* ====================================================================== */
 335 /* Crap.  */
 336
 337 #define REAL_ARITHMETIC(value, code, d1, d2) \
 338   real_arithmetic (&(value), code, &(d1), &(d2))
 339
 340 #define REAL_VALUES_IDENTICAL(x, y)     real_identical (&(x), &(y))
 341 #define REAL_VALUES_EQUAL(x, y)         real_compare (EQ_EXPR, &(x), &(y))
 342 #define REAL_VALUES_LESS(x, y)          real_compare (LT_EXPR, &(x), &(y))
 343
 344 /* Determine whether a floating-point value X is infinite.  */
 345 #define REAL_VALUE_ISINF(x)             real_isinf (&(x))
 346
 347 /* Determine whether a floating-point value X is a NaN.  */
 348 #define REAL_VALUE_ISNAN(x)             real_isnan (&(x))
 349
 350 /* Determine whether a floating-point value X is negative.  */
 351 #define REAL_VALUE_NEGATIVE(x)          real_isneg (&(x))
 352
 353 /* Determine whether a floating-point value X is minus zero.  */
 354 #define REAL_VALUE_MINUS_ZERO(x)        real_isnegzero (&(x))
 355
 356 /* IN is a REAL_VALUE_TYPE.  OUT is an array of longs.  */
 357 #define REAL_VALUE_TO_TARGET_LONG_DOUBLE(IN, OUT)                       \
 358   real_to_target (OUT, &(IN),                                           \
 359                   mode_for_size (LONG_DOUBLE_TYPE_SIZE, MODE_FLOAT, 0))
 360
 361 #define REAL_VALUE_TO_TARGET_DOUBLE(IN, OUT) \
 362   real_to_target (OUT, &(IN), mode_for_size (64, MODE_FLOAT, 0))
 363
 364 /* IN is a REAL_VALUE_TYPE.  OUT is a long.  */
 365 #define REAL_VALUE_TO_TARGET_SINGLE(IN, OUT) \
 366   ((OUT) = real_to_target (NULL, &(IN), mode_for_size (32, MODE_FLOAT, 0)))
 367
 368 /* Real values to IEEE 754 decimal floats.  */
 369
 370 /* IN is a REAL_VALUE_TYPE.  OUT is an array of longs.  */
 371 #define REAL_VALUE_TO_TARGET_DECIMAL128(IN, OUT) \
 372   real_to_target (OUT, &(IN), mode_for_size (128, MODE_DECIMAL_FLOAT, 0))
 373
 374 #define REAL_VALUE_TO_TARGET_DECIMAL64(IN, OUT) \
 375   real_to_target (OUT, &(IN), mode_for_size (64, MODE_DECIMAL_FLOAT, 0))
 376
 377 /* IN is a REAL_VALUE_TYPE.  OUT is a long.  */
 378 #define REAL_VALUE_TO_TARGET_DECIMAL32(IN, OUT) \
 379   ((OUT) = real_to_target (NULL, &(IN), mode_for_size (32, MODE_DECIMAL_FLOAT, 0)))
 380
 381 extern REAL_VALUE_TYPE real_value_truncate (machine_mode,
 382                                             REAL_VALUE_TYPE);
 383
 384 extern REAL_VALUE_TYPE real_value_negate (const REAL_VALUE_TYPE *);
 385 extern REAL_VALUE_TYPE real_value_abs (const REAL_VALUE_TYPE *);
 386
 387 extern int significand_size (machine_mode);
 388
 389 extern REAL_VALUE_TYPE real_from_string2 (const char *, machine_mode);
 390
 391 #define REAL_VALUE_ATOF(s, m) \
 392   real_from_string2 (s, m)
 393
 394 #define CONST_DOUBLE_ATOF(s, m) \
 395   CONST_DOUBLE_FROM_REAL_VALUE (real_from_string2 (s, m), m)
 396
 397 #define REAL_VALUE_FIX(r) \
 398   real_to_integer (&(r))
 399
 400 /* ??? Not quite right.  */
 401 #define REAL_VALUE_UNSIGNED_FIX(r) \
 402   real_to_integer (&(r))
 403
 404 /* ??? These were added for Paranoia support.  */
 405
 406 /* Return floor log2(R).  */
 407 extern int real_exponent (const REAL_VALUE_TYPE *);
 408
 409 /* R = A * 2**EXP.  */
 410 extern void real_ldexp (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, int);
 411
 412 /* **** End of software floating point emulator interface macros **** */
 413 \f
 414 /* Constant real values 0, 1, 2, -1 and 0.5.  */
 415
 416 extern REAL_VALUE_TYPE dconst0;
 417 extern REAL_VALUE_TYPE dconst1;
 418 extern REAL_VALUE_TYPE dconst2;
 419 extern REAL_VALUE_TYPE dconstm1;
 420 extern REAL_VALUE_TYPE dconsthalf;
 421
 422 #define dconst_e()  (*dconst_e_ptr ())
 423 #define dconst_third()  (*dconst_third_ptr ())
 424 #define dconst_sqrt2()  (*dconst_sqrt2_ptr ())
 425
 426 /* Function to return the real value special constant 'e'.  */
 427 extern const REAL_VALUE_TYPE * dconst_e_ptr (void);
 428
 429 /* Returns the special REAL_VALUE_TYPE corresponding to 1/3.  */
 430 extern const REAL_VALUE_TYPE * dconst_third_ptr (void);
 431
 432 /* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2).  */
 433 extern const REAL_VALUE_TYPE * dconst_sqrt2_ptr (void);
 434
 435 /* Function to return a real value (not a tree node)
 436    from a given integer constant.  */
 437 REAL_VALUE_TYPE real_value_from_int_cst (const_tree, const_tree);
 438
 439 /* Given a CONST_DOUBLE in FROM, store into TO the value it represents.  */
 440 #define REAL_VALUE_FROM_CONST_DOUBLE(to, from) \
 441   ((to) = *CONST_DOUBLE_REAL_VALUE (from))
 442
 443 /* Return a CONST_DOUBLE with value R and mode M.  */
 444 #define CONST_DOUBLE_FROM_REAL_VALUE(r, m) \
 445   const_double_from_real_value (r, m)
 446 extern rtx const_double_from_real_value (REAL_VALUE_TYPE, machine_mode);
 447
 448 /* Replace R by 1/R in the given machine mode, if the result is exact.  */
 449 extern bool exact_real_inverse (machine_mode, REAL_VALUE_TYPE *);
 450
 451 /* Return true if arithmetic on values in IMODE that were promoted
 452    from values in TMODE is equivalent to direct arithmetic on values
 453    in TMODE.  */
 454 bool real_can_shorten_arithmetic (machine_mode, machine_mode);
 455
 456 /* In tree.c: wrap up a REAL_VALUE_TYPE in a tree node.  */
 457 extern tree build_real (tree, REAL_VALUE_TYPE);
 458
 459 /* Calculate R as X raised to the integer exponent N in mode MODE.  */
 460 extern bool real_powi (REAL_VALUE_TYPE *, machine_mode,
 461                        const REAL_VALUE_TYPE *, HOST_WIDE_INT);
 462
 463 /* Standard round to integer value functions.  */
 464 extern void real_trunc (REAL_VALUE_TYPE *, machine_mode,
 465                         const REAL_VALUE_TYPE *);
 466 extern void real_floor (REAL_VALUE_TYPE *, machine_mode,
 467                         const REAL_VALUE_TYPE *);
 468 extern void real_ceil (REAL_VALUE_TYPE *, machine_mode,
 469                        const REAL_VALUE_TYPE *);
 470 extern void real_round (REAL_VALUE_TYPE *, machine_mode,
 471                         const REAL_VALUE_TYPE *);
 472
 473 /* Set the sign of R to the sign of X.  */
 474 extern void real_copysign (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
 475
 476 /* Check whether the real constant value given is an integer.  */
 477 extern bool real_isinteger (const REAL_VALUE_TYPE *c, machine_mode mode);
 478
 479 /* Write into BUF the maximum representable finite floating-point
 480    number, (1 - b**-p) * b**emax for a given FP format FMT as a hex
 481    float string.  BUF must be large enough to contain the result.  */
 482 extern void get_max_float (const struct real_format *, char *, size_t);
 483
 484 #ifndef GENERATOR_FILE
 485 /* real related routines.  */
 486 extern wide_int real_to_integer (const REAL_VALUE_TYPE *, bool *, int);
 487 extern void real_from_integer (REAL_VALUE_TYPE *, machine_mode,
 488                                const wide_int_ref &, signop);
 489 #endif
 490
 491 #endif /* ! GCC_REAL_H */