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 };
 159
 160
 161 /* The target format used for each floating point mode.
 162    Float modes are followed by decimal float modes, with entries for
 163    float modes indexed by (MODE - first float mode), and entries for
 164    decimal float modes indexed by (MODE - first decimal float mode) +
 165    the number of float modes.  */
 166 extern const struct real_format *
 167   real_format_for_mode[MAX_MODE_FLOAT - MIN_MODE_FLOAT + 1
 168                        + MAX_MODE_DECIMAL_FLOAT - MIN_MODE_DECIMAL_FLOAT + 1];
 169
 170 #define REAL_MODE_FORMAT(MODE)                                          \
 171   (real_format_for_mode[DECIMAL_FLOAT_MODE_P (MODE)                     \
 172                         ? (((MODE) - MIN_MODE_DECIMAL_FLOAT)            \
 173                            + (MAX_MODE_FLOAT - MIN_MODE_FLOAT + 1))     \
 174                         : ((MODE) - MIN_MODE_FLOAT)])
 175
 176 #define FLOAT_MODE_FORMAT(MODE) \
 177   (REAL_MODE_FORMAT (SCALAR_FLOAT_MODE_P (MODE)? (MODE) \
 178                                                : GET_MODE_INNER (MODE)))
 179
 180 /* The following macro determines whether the floating point format is
 181    composite, i.e. may contain non-consecutive mantissa bits, in which
 182    case compile-time FP overflow may not model run-time overflow.  */
 183 #define MODE_COMPOSITE_P(MODE) \
 184   (FLOAT_MODE_P (MODE) \
 185    && FLOAT_MODE_FORMAT (MODE)->pnan < FLOAT_MODE_FORMAT (MODE)->p)
 186
 187 /* Accessor macros for format properties.  */
 188 #define MODE_HAS_NANS(MODE) \
 189   (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_nans)
 190 #define MODE_HAS_INFINITIES(MODE) \
 191   (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_inf)
 192 #define MODE_HAS_SIGNED_ZEROS(MODE) \
 193   (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_signed_zero)
 194 #define MODE_HAS_SIGN_DEPENDENT_ROUNDING(MODE) \
 195   (FLOAT_MODE_P (MODE) \
 196    && FLOAT_MODE_FORMAT (MODE)->has_sign_dependent_rounding)
 197
 198 /* Declare functions in real.c.  */
 199
 200 /* True if the given mode has a NaN representation and the treatment of
 201    NaN operands is important.  Certain optimizations, such as folding
 202    x * 0 into 0, are not correct for NaN operands, and are normally
 203    disabled for modes with NaNs.  The user can ask for them to be
 204    done anyway using the -funsafe-math-optimizations switch.  */
 205 extern bool HONOR_NANS (machine_mode);
 206 extern bool HONOR_NANS (const_tree);
 207 extern bool HONOR_NANS (const_rtx);
 208
 209 /* Like HONOR_NANs, but true if we honor signaling NaNs (or sNaNs).  */
 210 extern bool HONOR_SNANS (machine_mode);
 211 extern bool HONOR_SNANS (const_tree);
 212 extern bool HONOR_SNANS (const_rtx);
 213
 214 /* As for HONOR_NANS, but true if the mode can represent infinity and
 215    the treatment of infinite values is important.  */
 216 extern bool HONOR_INFINITIES (machine_mode);
 217 extern bool HONOR_INFINITIES (const_tree);
 218 extern bool HONOR_INFINITIES (const_rtx);
 219
 220 /* Like HONOR_NANS, but true if the given mode distinguishes between
 221    positive and negative zero, and the sign of zero is important.  */
 222 extern bool HONOR_SIGNED_ZEROS (machine_mode);
 223 extern bool HONOR_SIGNED_ZEROS (const_tree);
 224 extern bool HONOR_SIGNED_ZEROS (const_rtx);
 225
 226 /* Like HONOR_NANS, but true if given mode supports sign-dependent rounding,
 227    and the rounding mode is important.  */
 228 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (machine_mode);
 229 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_tree);
 230 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_rtx);
 231
 232 /* Binary or unary arithmetic on tree_code.  */
 233 extern bool real_arithmetic (REAL_VALUE_TYPE *, int, const REAL_VALUE_TYPE *,
 234                              const REAL_VALUE_TYPE *);
 235
 236 /* Compare reals by tree_code.  */
 237 extern bool real_compare (int, const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
 238
 239 /* Determine whether a floating-point value X is infinite.  */
 240 extern bool real_isinf (const REAL_VALUE_TYPE *);
 241
 242 /* Determine whether a floating-point value X is a NaN.  */
 243 extern bool real_isnan (const REAL_VALUE_TYPE *);
 244
 245 /* Determine whether a floating-point value X is finite.  */
 246 extern bool real_isfinite (const REAL_VALUE_TYPE *);
 247
 248 /* Determine whether a floating-point value X is negative.  */
 249 extern bool real_isneg (const REAL_VALUE_TYPE *);
 250
 251 /* Determine whether a floating-point value X is minus zero.  */
 252 extern bool real_isnegzero (const REAL_VALUE_TYPE *);
 253
 254 /* Compare two floating-point objects for bitwise identity.  */
 255 extern bool real_identical (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
 256
 257 /* Extend or truncate to a new mode.  */
 258 extern void real_convert (REAL_VALUE_TYPE *, machine_mode,
 259                           const REAL_VALUE_TYPE *);
 260
 261 /* Return true if truncating to NEW is exact.  */
 262 extern bool exact_real_truncate (machine_mode, const REAL_VALUE_TYPE *);
 263
 264 /* Render R as a decimal floating point constant.  */
 265 extern void real_to_decimal (char *, const REAL_VALUE_TYPE *, size_t,
 266                              size_t, int);
 267
 268 /* Render R as a decimal floating point constant, rounded so as to be
 269    parsed back to the same value when interpreted in mode MODE.  */
 270 extern void real_to_decimal_for_mode (char *, const REAL_VALUE_TYPE *, size_t,
 271                                       size_t, int, machine_mode);
 272
 273 /* Render R as a hexadecimal floating point constant.  */
 274 extern void real_to_hexadecimal (char *, const REAL_VALUE_TYPE *,
 275                                  size_t, size_t, int);
 276
 277 /* Render R as an integer.  */
 278 extern HOST_WIDE_INT real_to_integer (const REAL_VALUE_TYPE *);
 279
 280 /* Initialize R from a decimal or hexadecimal string.  Return -1 if
 281    the value underflows, +1 if overflows, and 0 otherwise.  */
 282 extern int real_from_string (REAL_VALUE_TYPE *, const char *);
 283 /* Wrapper to allow different internal representation for decimal floats. */
 284 extern void real_from_string3 (REAL_VALUE_TYPE *, const char *, machine_mode);
 285
 286 extern long real_to_target_fmt (long *, const REAL_VALUE_TYPE *,
 287                                 const struct real_format *);
 288 extern long real_to_target (long *, const REAL_VALUE_TYPE *, machine_mode);
 289
 290 extern void real_from_target_fmt (REAL_VALUE_TYPE *, const long *,
 291                                   const struct real_format *);
 292 extern void real_from_target (REAL_VALUE_TYPE *, const long *,
 293                               machine_mode);
 294
 295 extern void real_inf (REAL_VALUE_TYPE *);
 296
 297 extern bool real_nan (REAL_VALUE_TYPE *, const char *, int, machine_mode);
 298
 299 extern void real_maxval (REAL_VALUE_TYPE *, int, machine_mode);
 300
 301 extern void real_2expN (REAL_VALUE_TYPE *, int, machine_mode);
 302
 303 extern unsigned int real_hash (const REAL_VALUE_TYPE *);
 304
 305
 306 /* Target formats defined in real.c.  */
 307 extern const struct real_format ieee_single_format;
 308 extern const struct real_format mips_single_format;
 309 extern const struct real_format motorola_single_format;
 310 extern const struct real_format spu_single_format;
 311 extern const struct real_format ieee_double_format;
 312 extern const struct real_format mips_double_format;
 313 extern const struct real_format motorola_double_format;
 314 extern const struct real_format ieee_extended_motorola_format;
 315 extern const struct real_format ieee_extended_intel_96_format;
 316 extern const struct real_format ieee_extended_intel_96_round_53_format;
 317 extern const struct real_format ieee_extended_intel_128_format;
 318 extern const struct real_format ibm_extended_format;
 319 extern const struct real_format mips_extended_format;
 320 extern const struct real_format ieee_quad_format;
 321 extern const struct real_format mips_quad_format;
 322 extern const struct real_format vax_f_format;
 323 extern const struct real_format vax_d_format;
 324 extern const struct real_format vax_g_format;
 325 extern const struct real_format real_internal_format;
 326 extern const struct real_format decimal_single_format;
 327 extern const struct real_format decimal_double_format;
 328 extern const struct real_format decimal_quad_format;
 329 extern const struct real_format ieee_half_format;
 330 extern const struct real_format arm_half_format;
 331
 332
 333 /* ====================================================================== */
 334 /* Crap.  */
 335
 336 #define REAL_ARITHMETIC(value, code, d1, d2) \
 337   real_arithmetic (&(value), code, &(d1), &(d2))
 338
 339 #define REAL_VALUES_IDENTICAL(x, y)     real_identical (&(x), &(y))
 340 #define REAL_VALUES_EQUAL(x, y)         real_compare (EQ_EXPR, &(x), &(y))
 341 #define REAL_VALUES_LESS(x, y)          real_compare (LT_EXPR, &(x), &(y))
 342
 343 /* Determine whether a floating-point value X is infinite.  */
 344 #define REAL_VALUE_ISINF(x)             real_isinf (&(x))
 345
 346 /* Determine whether a floating-point value X is a NaN.  */
 347 #define REAL_VALUE_ISNAN(x)             real_isnan (&(x))
 348
 349 /* Determine whether a floating-point value X is negative.  */
 350 #define REAL_VALUE_NEGATIVE(x)          real_isneg (&(x))
 351
 352 /* Determine whether a floating-point value X is minus zero.  */
 353 #define REAL_VALUE_MINUS_ZERO(x)        real_isnegzero (&(x))
 354
 355 /* IN is a REAL_VALUE_TYPE.  OUT is an array of longs.  */
 356 #define REAL_VALUE_TO_TARGET_LONG_DOUBLE(IN, OUT)                       \
 357   real_to_target (OUT, &(IN),                                           \
 358                   mode_for_size (LONG_DOUBLE_TYPE_SIZE, MODE_FLOAT, 0))
 359
 360 #define REAL_VALUE_TO_TARGET_DOUBLE(IN, OUT) \
 361   real_to_target (OUT, &(IN), mode_for_size (64, MODE_FLOAT, 0))
 362
 363 /* IN is a REAL_VALUE_TYPE.  OUT is a long.  */
 364 #define REAL_VALUE_TO_TARGET_SINGLE(IN, OUT) \
 365   ((OUT) = real_to_target (NULL, &(IN), mode_for_size (32, MODE_FLOAT, 0)))
 366
 367 /* Real values to IEEE 754 decimal floats.  */
 368
 369 /* IN is a REAL_VALUE_TYPE.  OUT is an array of longs.  */
 370 #define REAL_VALUE_TO_TARGET_DECIMAL128(IN, OUT) \
 371   real_to_target (OUT, &(IN), mode_for_size (128, MODE_DECIMAL_FLOAT, 0))
 372
 373 #define REAL_VALUE_TO_TARGET_DECIMAL64(IN, OUT) \
 374   real_to_target (OUT, &(IN), mode_for_size (64, MODE_DECIMAL_FLOAT, 0))
 375
 376 /* IN is a REAL_VALUE_TYPE.  OUT is a long.  */
 377 #define REAL_VALUE_TO_TARGET_DECIMAL32(IN, OUT) \
 378   ((OUT) = real_to_target (NULL, &(IN), mode_for_size (32, MODE_DECIMAL_FLOAT, 0)))
 379
 380 extern REAL_VALUE_TYPE real_value_truncate (machine_mode,
 381                                             REAL_VALUE_TYPE);
 382
 383 extern REAL_VALUE_TYPE real_value_negate (const REAL_VALUE_TYPE *);
 384 extern REAL_VALUE_TYPE real_value_abs (const REAL_VALUE_TYPE *);
 385
 386 extern int significand_size (machine_mode);
 387
 388 extern REAL_VALUE_TYPE real_from_string2 (const char *, machine_mode);
 389
 390 #define REAL_VALUE_ATOF(s, m) \
 391   real_from_string2 (s, m)
 392
 393 #define CONST_DOUBLE_ATOF(s, m) \
 394   CONST_DOUBLE_FROM_REAL_VALUE (real_from_string2 (s, m), m)
 395
 396 #define REAL_VALUE_FIX(r) \
 397   real_to_integer (&(r))
 398
 399 /* ??? Not quite right.  */
 400 #define REAL_VALUE_UNSIGNED_FIX(r) \
 401   real_to_integer (&(r))
 402
 403 /* ??? These were added for Paranoia support.  */
 404
 405 /* Return floor log2(R).  */
 406 extern int real_exponent (const REAL_VALUE_TYPE *);
 407
 408 /* R = A * 2**EXP.  */
 409 extern void real_ldexp (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, int);
 410
 411 /* **** End of software floating point emulator interface macros **** */
 412 \f
 413 /* Constant real values 0, 1, 2, -1 and 0.5.  */
 414
 415 extern REAL_VALUE_TYPE dconst0;
 416 extern REAL_VALUE_TYPE dconst1;
 417 extern REAL_VALUE_TYPE dconst2;
 418 extern REAL_VALUE_TYPE dconstm1;
 419 extern REAL_VALUE_TYPE dconsthalf;
 420
 421 #define dconst_e()  (*dconst_e_ptr ())
 422 #define dconst_third()  (*dconst_third_ptr ())
 423 #define dconst_sqrt2()  (*dconst_sqrt2_ptr ())
 424
 425 /* Function to return the real value special constant 'e'.  */
 426 extern const REAL_VALUE_TYPE * dconst_e_ptr (void);
 427
 428 /* Returns the special REAL_VALUE_TYPE corresponding to 1/3.  */
 429 extern const REAL_VALUE_TYPE * dconst_third_ptr (void);
 430
 431 /* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2).  */
 432 extern const REAL_VALUE_TYPE * dconst_sqrt2_ptr (void);
 433
 434 /* Function to return a real value (not a tree node)
 435    from a given integer constant.  */
 436 REAL_VALUE_TYPE real_value_from_int_cst (const_tree, const_tree);
 437
 438 /* Given a CONST_DOUBLE in FROM, store into TO the value it represents.  */
 439 #define REAL_VALUE_FROM_CONST_DOUBLE(to, from) \
 440   ((to) = *CONST_DOUBLE_REAL_VALUE (from))
 441
 442 /* Return a CONST_DOUBLE with value R and mode M.  */
 443 #define CONST_DOUBLE_FROM_REAL_VALUE(r, m) \
 444   const_double_from_real_value (r, m)
 445 extern rtx const_double_from_real_value (REAL_VALUE_TYPE, machine_mode);
 446
 447 /* Replace R by 1/R in the given machine mode, if the result is exact.  */
 448 extern bool exact_real_inverse (machine_mode, REAL_VALUE_TYPE *);
 449
 450 /* Return true if arithmetic on values in IMODE that were promoted
 451    from values in TMODE is equivalent to direct arithmetic on values
 452    in TMODE.  */
 453 bool real_can_shorten_arithmetic (machine_mode, machine_mode);
 454
 455 /* In tree.c: wrap up a REAL_VALUE_TYPE in a tree node.  */
 456 extern tree build_real (tree, REAL_VALUE_TYPE);
 457
 458 /* Calculate R as X raised to the integer exponent N in mode MODE.  */
 459 extern bool real_powi (REAL_VALUE_TYPE *, machine_mode,
 460                        const REAL_VALUE_TYPE *, HOST_WIDE_INT);
 461
 462 /* Standard round to integer value functions.  */
 463 extern void real_trunc (REAL_VALUE_TYPE *, machine_mode,
 464                         const REAL_VALUE_TYPE *);
 465 extern void real_floor (REAL_VALUE_TYPE *, machine_mode,
 466                         const REAL_VALUE_TYPE *);
 467 extern void real_ceil (REAL_VALUE_TYPE *, machine_mode,
 468                        const REAL_VALUE_TYPE *);
 469 extern void real_round (REAL_VALUE_TYPE *, machine_mode,
 470                         const REAL_VALUE_TYPE *);
 471
 472 /* Set the sign of R to the sign of X.  */
 473 extern void real_copysign (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
 474
 475 /* Check whether the real constant value given is an integer.  */
 476 extern bool real_isinteger (const REAL_VALUE_TYPE *c, machine_mode mode);
 477
 478 /* Write into BUF the maximum representable finite floating-point
 479    number, (1 - b**-p) * b**emax for a given FP format FMT as a hex
 480    float string.  BUF must be large enough to contain the result.  */
 481 extern void get_max_float (const struct real_format *, char *, size_t);
 482
 483 #ifndef GENERATOR_FILE
 484 /* real related routines.  */
 485 extern wide_int real_to_integer (const REAL_VALUE_TYPE *, bool *, int);
 486 extern void real_from_integer (REAL_VALUE_TYPE *, machine_mode,
 487                                const wide_int_ref &, signop);
 488 #endif
 489
 490 #endif /* ! GCC_REAL_H */