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