1 /* Definitions of floating-point access for GNU compiler.
2 Copyright (C) 1989-2022 Free Software Foundation, Inc.
4 This file is part of GCC.
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
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
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/>. */
23 /* An expanded form of the represented number. */
25 /* Enumerate the special cases of numbers that we encounter. */
26 enum real_value_class
{
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))
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
43 unsigned int /* ENUM_BITFIELD (real_value_class) */ cl
: 2;
44 /* 1 if number is decimal floating point. */
45 unsigned int decimal
: 1;
46 /* 1 if number is negative. */
47 unsigned int sign
: 1;
48 /* 1 if number is signalling. */
49 unsigned int signalling
: 1;
50 /* 1 if number is canonical
51 All are generally used for handling cases in real.cc. */
52 unsigned int canonical
: 1;
53 /* unbiased exponent of the number. */
54 unsigned int uexp
: EXP_BITS
;
55 /* significand of the number. */
56 unsigned long sig
[SIGSZ
];
59 #define REAL_EXP(REAL) \
60 ((int)((REAL)->uexp ^ (unsigned int)(1 << (EXP_BITS - 1))) \
61 - (1 << (EXP_BITS - 1)))
62 #define SET_REAL_EXP(REAL, EXP) \
63 ((REAL)->uexp = ((unsigned int)(EXP) & (unsigned int)((1 << EXP_BITS) - 1)))
65 /* Various headers condition prototypes on #ifdef REAL_VALUE_TYPE, so it
66 needs to be a macro. We do need to continue to have a structure tag
67 so that other headers can forward declare it. */
68 #define REAL_VALUE_TYPE struct real_value
70 /* We store a REAL_VALUE_TYPE into an rtx, and we do this by putting it in
71 consecutive "w" slots. Moreover, we've got to compute the number of "w"
72 slots at preprocessor time, which means we can't use sizeof. Guess. */
74 #define REAL_VALUE_TYPE_SIZE (SIGNIFICAND_BITS + 32)
76 (REAL_VALUE_TYPE_SIZE/HOST_BITS_PER_WIDE_INT \
77 + (REAL_VALUE_TYPE_SIZE%HOST_BITS_PER_WIDE_INT ? 1 : 0)) /* round up */
82 // #define REAL_WIDTH 2
84 /* Verify the guess. */
85 extern char test_real_width
86 [sizeof (REAL_VALUE_TYPE
) <= REAL_WIDTH
* sizeof (HOST_WIDE_INT
) ? 1 : -1];
88 /* Calculate the format for CONST_DOUBLE. We need as many slots as
89 are necessary to overlay a REAL_VALUE_TYPE on them. This could be
90 as many as four (32-bit HOST_WIDE_INT, 128-bit REAL_VALUE_TYPE).
92 A number of places assume that there are always at least two 'w'
93 slots in a CONST_DOUBLE, so we provide them even if one would suffice. */
96 # define CONST_DOUBLE_FORMAT "ww"
99 # define CONST_DOUBLE_FORMAT "ww"
102 # define CONST_DOUBLE_FORMAT "www"
105 # define CONST_DOUBLE_FORMAT "wwww"
108 # define CONST_DOUBLE_FORMAT "wwwww"
111 # define CONST_DOUBLE_FORMAT "wwwwww"
113 #error "REAL_WIDTH > 6 not supported"
122 /* Describes the properties of the specific target format in use. */
125 /* Move to and from the target bytes. */
126 void (*encode
) (const struct real_format
*, long *,
127 const REAL_VALUE_TYPE
*);
128 void (*decode
) (const struct real_format
*, REAL_VALUE_TYPE
*,
131 /* The radix of the exponent and digits of the significand. */
134 /* Size of the significand in digits of radix B. */
137 /* Size of the significant of a NaN, in digits of radix B. */
140 /* The minimum negative integer, x, such that b**(x-1) is normalized. */
143 /* The maximum integer, x, such that b**(x-1) is representable. */
146 /* The bit position of the sign bit, for determining whether a value
147 is positive/negative, or -1 for a complex encoding. */
150 /* The bit position of the sign bit, for changing the sign of a number,
151 or -1 for a complex encoding. */
154 /* If this is an IEEE interchange format, the number of bits in the
155 format; otherwise, if it is an IEEE extended format, one more
156 than the greatest number of bits in an interchange format it
157 extends; otherwise 0. Formats need not follow the IEEE 754-2008
158 recommended practice regarding how signaling NaNs are identified,
159 and may vary in the choice of default NaN, but must follow other
160 IEEE practice regarding having NaNs, infinities and subnormal
161 values, and the relation of minimum and maximum exponents, and,
162 for interchange formats, the details of the encoding. */
165 /* Default rounding mode for operations on this format. */
166 bool round_towards_zero
;
167 bool has_sign_dependent_rounding
;
169 /* Properties of the format. */
173 bool has_signed_zero
;
175 bool canonical_nan_lsbs_set
;
180 /* The target format used for each floating point mode.
181 Float modes are followed by decimal float modes, with entries for
182 float modes indexed by (MODE - first float mode), and entries for
183 decimal float modes indexed by (MODE - first decimal float mode) +
184 the number of float modes. */
185 extern const struct real_format
*
186 real_format_for_mode
[NUM_MODE_FLOAT
+ NUM_MODE_DECIMAL_FLOAT
];
188 #define REAL_MODE_FORMAT(MODE) \
189 (real_format_for_mode[DECIMAL_FLOAT_MODE_P (MODE) \
190 ? (((MODE) - MIN_MODE_DECIMAL_FLOAT) \
192 : GET_MODE_CLASS (MODE) == MODE_FLOAT \
193 ? ((MODE) - MIN_MODE_FLOAT) \
194 : (gcc_unreachable (), 0)])
196 #define FLOAT_MODE_FORMAT(MODE) \
197 (REAL_MODE_FORMAT (as_a <scalar_float_mode> (GET_MODE_INNER (MODE))))
199 /* The following macro determines whether the floating point format is
200 composite, i.e. may contain non-consecutive mantissa bits, in which
201 case compile-time FP overflow may not model run-time overflow. */
202 #define MODE_COMPOSITE_P(MODE) \
203 (FLOAT_MODE_P (MODE) \
204 && FLOAT_MODE_FORMAT (MODE)->pnan < FLOAT_MODE_FORMAT (MODE)->p)
206 /* Accessor macros for format properties. */
207 #define MODE_HAS_NANS(MODE) \
208 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_nans)
209 #define MODE_HAS_INFINITIES(MODE) \
210 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_inf)
211 #define MODE_HAS_SIGNED_ZEROS(MODE) \
212 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_signed_zero)
213 #define MODE_HAS_SIGN_DEPENDENT_ROUNDING(MODE) \
214 (FLOAT_MODE_P (MODE) \
215 && FLOAT_MODE_FORMAT (MODE)->has_sign_dependent_rounding)
217 /* This class allows functions in this file to accept a floating-point
218 format as either a mode or an explicit real_format pointer. In the
219 former case the mode must be VOIDmode (which means "no particular
220 format") or must satisfy SCALAR_FLOAT_MODE_P. */
224 format_helper (const real_format
*format
) : m_format (format
) {}
225 template<typename T
> format_helper (const T
&);
226 const real_format
*operator-> () const { return m_format
; }
227 operator const real_format
*() const { return m_format
; }
229 bool decimal_p () const { return m_format
&& m_format
->b
== 10; }
230 bool can_represent_integral_type_p (tree type
) const;
233 const real_format
*m_format
;
237 inline format_helper::format_helper (const T
&m
)
238 : m_format (m
== VOIDmode
? 0 : REAL_MODE_FORMAT (m
))
241 /* Declare functions in real.cc. */
243 /* True if the given mode has a NaN representation and the treatment of
244 NaN operands is important. Certain optimizations, such as folding
245 x * 0 into 0, are not correct for NaN operands, and are normally
246 disabled for modes with NaNs. The user can ask for them to be
247 done anyway using the -funsafe-math-optimizations switch. */
248 extern bool HONOR_NANS (machine_mode
);
249 extern bool HONOR_NANS (const_tree
);
250 extern bool HONOR_NANS (const_rtx
);
252 /* Like HONOR_NANs, but true if we honor signaling NaNs (or sNaNs). */
253 extern bool HONOR_SNANS (machine_mode
);
254 extern bool HONOR_SNANS (const_tree
);
255 extern bool HONOR_SNANS (const_rtx
);
257 /* As for HONOR_NANS, but true if the mode can represent infinity and
258 the treatment of infinite values is important. */
259 extern bool HONOR_INFINITIES (machine_mode
);
260 extern bool HONOR_INFINITIES (const_tree
);
261 extern bool HONOR_INFINITIES (const_rtx
);
263 /* Like HONOR_NANS, but true if the given mode distinguishes between
264 positive and negative zero, and the sign of zero is important. */
265 extern bool HONOR_SIGNED_ZEROS (machine_mode
);
266 extern bool HONOR_SIGNED_ZEROS (const_tree
);
267 extern bool HONOR_SIGNED_ZEROS (const_rtx
);
269 /* Like HONOR_NANS, but true if given mode supports sign-dependent rounding,
270 and the rounding mode is important. */
271 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (machine_mode
);
272 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_tree
);
273 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_rtx
);
275 /* Binary or unary arithmetic on tree_code. */
276 extern bool real_arithmetic (REAL_VALUE_TYPE
*, int, const REAL_VALUE_TYPE
*,
277 const REAL_VALUE_TYPE
*);
279 /* Compare reals by tree_code. */
280 extern bool real_compare (int, const REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*);
282 /* Determine whether a floating-point value X is infinite. */
283 extern bool real_isinf (const REAL_VALUE_TYPE
*);
285 /* Determine whether a floating-point value X is a NaN. */
286 extern bool real_isnan (const REAL_VALUE_TYPE
*);
288 /* Determine whether a floating-point value X is a signaling NaN. */
289 extern bool real_issignaling_nan (const REAL_VALUE_TYPE
*);
291 /* Determine whether a floating-point value X is finite. */
292 extern bool real_isfinite (const REAL_VALUE_TYPE
*);
294 /* Determine whether a floating-point value X is negative. */
295 extern bool real_isneg (const REAL_VALUE_TYPE
*);
297 /* Determine whether a floating-point value X is minus zero. */
298 extern bool real_isnegzero (const REAL_VALUE_TYPE
*);
300 /* Test relationships between reals. */
301 extern bool real_identical (const REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*);
302 extern bool real_equal (const REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*);
303 extern bool real_less (const REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*);
305 /* Extend or truncate to a new format. */
306 extern void real_convert (REAL_VALUE_TYPE
*, format_helper
,
307 const REAL_VALUE_TYPE
*);
309 /* Return true if truncating to NEW is exact. */
310 extern bool exact_real_truncate (format_helper
, const REAL_VALUE_TYPE
*);
312 /* Render R as a decimal floating point constant. */
313 extern void real_to_decimal (char *, const REAL_VALUE_TYPE
*, size_t,
316 /* Render R as a decimal floating point constant, rounded so as to be
317 parsed back to the same value when interpreted in mode MODE. */
318 extern void real_to_decimal_for_mode (char *, const REAL_VALUE_TYPE
*, size_t,
319 size_t, int, machine_mode
);
321 /* Render R as a hexadecimal floating point constant. */
322 extern void real_to_hexadecimal (char *, const REAL_VALUE_TYPE
*,
323 size_t, size_t, int);
325 /* Render R as an integer. */
326 extern HOST_WIDE_INT
real_to_integer (const REAL_VALUE_TYPE
*);
328 /* Initialize R from a decimal or hexadecimal string. Return -1 if
329 the value underflows, +1 if overflows, and 0 otherwise. */
330 extern int real_from_string (REAL_VALUE_TYPE
*, const char *);
331 /* Wrapper to allow different internal representation for decimal floats. */
332 extern void real_from_string3 (REAL_VALUE_TYPE
*, const char *, format_helper
);
334 extern long real_to_target (long *, const REAL_VALUE_TYPE
*, format_helper
);
336 extern void real_from_target (REAL_VALUE_TYPE
*, const long *,
339 extern void real_inf (REAL_VALUE_TYPE
*);
341 extern bool real_nan (REAL_VALUE_TYPE
*, const char *, int, format_helper
);
343 extern void real_maxval (REAL_VALUE_TYPE
*, int, machine_mode
);
345 extern void real_2expN (REAL_VALUE_TYPE
*, int, format_helper
);
347 extern unsigned int real_hash (const REAL_VALUE_TYPE
*);
350 /* Target formats defined in real.cc. */
351 extern const struct real_format ieee_single_format
;
352 extern const struct real_format mips_single_format
;
353 extern const struct real_format motorola_single_format
;
354 extern const struct real_format spu_single_format
;
355 extern const struct real_format ieee_double_format
;
356 extern const struct real_format mips_double_format
;
357 extern const struct real_format motorola_double_format
;
358 extern const struct real_format ieee_extended_motorola_format
;
359 extern const struct real_format ieee_extended_intel_96_format
;
360 extern const struct real_format ieee_extended_intel_96_round_53_format
;
361 extern const struct real_format ieee_extended_intel_128_format
;
362 extern const struct real_format ibm_extended_format
;
363 extern const struct real_format mips_extended_format
;
364 extern const struct real_format ieee_quad_format
;
365 extern const struct real_format mips_quad_format
;
366 extern const struct real_format vax_f_format
;
367 extern const struct real_format vax_d_format
;
368 extern const struct real_format vax_g_format
;
369 extern const struct real_format real_internal_format
;
370 extern const struct real_format decimal_single_format
;
371 extern const struct real_format decimal_double_format
;
372 extern const struct real_format decimal_quad_format
;
373 extern const struct real_format ieee_half_format
;
374 extern const struct real_format arm_half_format
;
375 extern const struct real_format arm_bfloat_half_format
;
378 /* ====================================================================== */
381 /* Determine whether a floating-point value X is infinite. */
382 #define REAL_VALUE_ISINF(x) real_isinf (&(x))
384 /* Determine whether a floating-point value X is a NaN. */
385 #define REAL_VALUE_ISNAN(x) real_isnan (&(x))
387 /* Determine whether a floating-point value X is a signaling NaN. */
388 #define REAL_VALUE_ISSIGNALING_NAN(x) real_issignaling_nan (&(x))
390 /* Determine whether a floating-point value X is negative. */
391 #define REAL_VALUE_NEGATIVE(x) real_isneg (&(x))
393 /* Determine whether a floating-point value X is minus zero. */
394 #define REAL_VALUE_MINUS_ZERO(x) real_isnegzero (&(x))
396 /* IN is a REAL_VALUE_TYPE. OUT is an array of longs. */
397 #define REAL_VALUE_TO_TARGET_LONG_DOUBLE(IN, OUT) \
398 real_to_target (OUT, &(IN), \
399 float_mode_for_size (LONG_DOUBLE_TYPE_SIZE).require ())
401 #define REAL_VALUE_TO_TARGET_DOUBLE(IN, OUT) \
402 real_to_target (OUT, &(IN), float_mode_for_size (64).require ())
404 /* IN is a REAL_VALUE_TYPE. OUT is a long. */
405 #define REAL_VALUE_TO_TARGET_SINGLE(IN, OUT) \
406 ((OUT) = real_to_target (NULL, &(IN), float_mode_for_size (32).require ()))
408 /* Real values to IEEE 754 decimal floats. */
410 /* IN is a REAL_VALUE_TYPE. OUT is an array of longs. */
411 #define REAL_VALUE_TO_TARGET_DECIMAL128(IN, OUT) \
412 real_to_target (OUT, &(IN), decimal_float_mode_for_size (128).require ())
414 #define REAL_VALUE_TO_TARGET_DECIMAL64(IN, OUT) \
415 real_to_target (OUT, &(IN), decimal_float_mode_for_size (64).require ())
417 /* IN is a REAL_VALUE_TYPE. OUT is a long. */
418 #define REAL_VALUE_TO_TARGET_DECIMAL32(IN, OUT) \
419 ((OUT) = real_to_target (NULL, &(IN), \
420 decimal_float_mode_for_size (32).require ()))
422 extern REAL_VALUE_TYPE
real_value_truncate (format_helper
, REAL_VALUE_TYPE
);
424 extern REAL_VALUE_TYPE
real_value_negate (const REAL_VALUE_TYPE
*);
425 extern REAL_VALUE_TYPE
real_value_abs (const REAL_VALUE_TYPE
*);
427 extern int significand_size (format_helper
);
429 extern REAL_VALUE_TYPE
real_from_string2 (const char *, format_helper
);
431 #define REAL_VALUE_ATOF(s, m) \
432 real_from_string2 (s, m)
434 #define CONST_DOUBLE_ATOF(s, m) \
435 const_double_from_real_value (real_from_string2 (s, m), m)
437 #define REAL_VALUE_FIX(r) \
438 real_to_integer (&(r))
440 /* ??? Not quite right. */
441 #define REAL_VALUE_UNSIGNED_FIX(r) \
442 real_to_integer (&(r))
444 /* ??? These were added for Paranoia support. */
446 /* Return floor log2(R). */
447 extern int real_exponent (const REAL_VALUE_TYPE
*);
449 /* R = A * 2**EXP. */
450 extern void real_ldexp (REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*, int);
452 /* **** End of software floating point emulator interface macros **** */
454 /* Constant real values 0, 1, 2, -1 and 0.5. */
456 extern REAL_VALUE_TYPE dconst0
;
457 extern REAL_VALUE_TYPE dconst1
;
458 extern REAL_VALUE_TYPE dconst2
;
459 extern REAL_VALUE_TYPE dconstm1
;
460 extern REAL_VALUE_TYPE dconsthalf
;
462 #define dconst_e() (*dconst_e_ptr ())
463 #define dconst_third() (*dconst_third_ptr ())
464 #define dconst_quarter() (*dconst_quarter_ptr ())
465 #define dconst_sixth() (*dconst_sixth_ptr ())
466 #define dconst_ninth() (*dconst_ninth_ptr ())
467 #define dconst_sqrt2() (*dconst_sqrt2_ptr ())
469 /* Function to return the real value special constant 'e'. */
470 extern const REAL_VALUE_TYPE
* dconst_e_ptr (void);
472 /* Returns a cached REAL_VALUE_TYPE corresponding to 1/n, for various n. */
473 extern const REAL_VALUE_TYPE
*dconst_third_ptr (void);
474 extern const REAL_VALUE_TYPE
*dconst_quarter_ptr (void);
475 extern const REAL_VALUE_TYPE
*dconst_sixth_ptr (void);
476 extern const REAL_VALUE_TYPE
*dconst_ninth_ptr (void);
478 /* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2). */
479 extern const REAL_VALUE_TYPE
* dconst_sqrt2_ptr (void);
481 /* Function to return a real value (not a tree node)
482 from a given integer constant. */
483 REAL_VALUE_TYPE
real_value_from_int_cst (const_tree
, const_tree
);
485 /* Return a CONST_DOUBLE with value R and mode M. */
486 extern rtx
const_double_from_real_value (REAL_VALUE_TYPE
, machine_mode
);
488 /* Replace R by 1/R in the given format, if the result is exact. */
489 extern bool exact_real_inverse (format_helper
, REAL_VALUE_TYPE
*);
491 /* Return true if arithmetic on values in IMODE that were promoted
492 from values in TMODE is equivalent to direct arithmetic on values
494 bool real_can_shorten_arithmetic (machine_mode
, machine_mode
);
496 /* In tree.cc: wrap up a REAL_VALUE_TYPE in a tree node. */
497 extern tree
build_real (tree
, REAL_VALUE_TYPE
);
499 /* Likewise, but first truncate the value to the type. */
500 extern tree
build_real_truncate (tree
, REAL_VALUE_TYPE
);
502 /* Calculate R as X raised to the integer exponent N in format FMT. */
503 extern bool real_powi (REAL_VALUE_TYPE
*, format_helper
,
504 const REAL_VALUE_TYPE
*, HOST_WIDE_INT
);
506 /* Standard round to integer value functions. */
507 extern void real_trunc (REAL_VALUE_TYPE
*, format_helper
,
508 const REAL_VALUE_TYPE
*);
509 extern void real_floor (REAL_VALUE_TYPE
*, format_helper
,
510 const REAL_VALUE_TYPE
*);
511 extern void real_ceil (REAL_VALUE_TYPE
*, format_helper
,
512 const REAL_VALUE_TYPE
*);
513 extern void real_round (REAL_VALUE_TYPE
*, format_helper
,
514 const REAL_VALUE_TYPE
*);
515 extern void real_roundeven (REAL_VALUE_TYPE
*, format_helper
,
516 const REAL_VALUE_TYPE
*);
518 /* Set the sign of R to the sign of X. */
519 extern void real_copysign (REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*);
521 /* Check whether the real constant value given is an integer. */
522 extern bool real_isinteger (const REAL_VALUE_TYPE
*, format_helper
);
523 extern bool real_isinteger (const REAL_VALUE_TYPE
*, HOST_WIDE_INT
*);
525 /* Calculate nextafter (X, Y) in format FMT. */
526 extern bool real_nextafter (REAL_VALUE_TYPE
*, format_helper
,
527 const REAL_VALUE_TYPE
*, const REAL_VALUE_TYPE
*);
529 /* Write into BUF the maximum representable finite floating-point
530 number, (1 - b**-p) * b**emax for a given FP format FMT as a hex
531 float string. BUF must be large enough to contain the result. */
532 extern void get_max_float (const struct real_format
*, char *, size_t, bool);
534 #if 0 // sdcpp ndef GENERATOR_FILE
535 /* real related routines. */
536 extern wide_int
real_to_integer (const REAL_VALUE_TYPE
*, bool *, int);
537 extern void real_from_integer (REAL_VALUE_TYPE
*, format_helper
,
538 const wide_int_ref
&, signop
);
541 /* Fills r with the largest value such that 1 + r*r won't overflow.
542 This is used in both sin (atan (x)) and cos (atan(x)) optimizations. */
543 extern void build_sinatan_real (REAL_VALUE_TYPE
*, tree
);
545 #endif /* ! GCC_REAL_H */