1 /* Definitions of floating-point access for GNU compiler.
2 Copyright (C) 1989-2018 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 /* If this is an IEEE interchange format, the number of bits in the
143 format; otherwise, if it is an IEEE extended format, one more
144 than the greatest number of bits in an interchange format it
145 extends; otherwise 0. Formats need not follow the IEEE 754-2008
146 recommended practice regarding how signaling NaNs are identified,
147 and may vary in the choice of default NaN, but must follow other
148 IEEE practice regarding having NaNs, infinities and subnormal
149 values, and the relation of minimum and maximum exponents, and,
150 for interchange formats, the details of the encoding. */
151 int ieee_bits;
152
153 /* Default rounding mode for operations on this format. */
154 bool round_towards_zero;
155 bool has_sign_dependent_rounding;
156
157 /* Properties of the format. */
158 bool has_nans;
159 bool has_inf;
160 bool has_denorm;
161 bool has_signed_zero;
162 bool qnan_msb_set;
163 bool canonical_nan_lsbs_set;
164 const char *name;
165 };
166
167
168 /* The target format used for each floating point mode.
169 Float modes are followed by decimal float modes, with entries for
170 float modes indexed by (MODE - first float mode), and entries for
171 decimal float modes indexed by (MODE - first decimal float mode) +
172 the number of float modes. */
173 extern const struct real_format *
174 real_format_for_mode[MAX_MODE_FLOAT - MIN_MODE_FLOAT + 1
175 + MAX_MODE_DECIMAL_FLOAT - MIN_MODE_DECIMAL_FLOAT + 1];
176
177 #define REAL_MODE_FORMAT(MODE) \
178 (real_format_for_mode[DECIMAL_FLOAT_MODE_P (MODE) \
179 ? (((MODE) - MIN_MODE_DECIMAL_FLOAT) \
180 + (MAX_MODE_FLOAT - MIN_MODE_FLOAT + 1)) \
181 : GET_MODE_CLASS (MODE) == MODE_FLOAT \
182 ? ((MODE) - MIN_MODE_FLOAT) \
183 : (gcc_unreachable (), 0)])
184
185 #define FLOAT_MODE_FORMAT(MODE) \
186 (REAL_MODE_FORMAT (as_a <scalar_float_mode> (GET_MODE_INNER (MODE))))
187
188 /* The following macro determines whether the floating point format is
189 composite, i.e. may contain non-consecutive mantissa bits, in which
190 case compile-time FP overflow may not model run-time overflow. */
191 #define MODE_COMPOSITE_P(MODE) \
192 (FLOAT_MODE_P (MODE) \
193 && FLOAT_MODE_FORMAT (MODE)->pnan < FLOAT_MODE_FORMAT (MODE)->p)
194
195 /* Accessor macros for format properties. */
196 #define MODE_HAS_NANS(MODE) \
197 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_nans)
198 #define MODE_HAS_INFINITIES(MODE) \
199 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_inf)
200 #define MODE_HAS_SIGNED_ZEROS(MODE) \
201 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_signed_zero)
202 #define MODE_HAS_SIGN_DEPENDENT_ROUNDING(MODE) \
203 (FLOAT_MODE_P (MODE) \
204 && FLOAT_MODE_FORMAT (MODE)->has_sign_dependent_rounding)
205
206 /* This class allows functions in this file to accept a floating-point
207 format as either a mode or an explicit real_format pointer. In the
208 former case the mode must be VOIDmode (which means "no particular
209 format") or must satisfy SCALAR_FLOAT_MODE_P. */
210 class format_helper
211 {
212 public:
format_helper(const real_format * format)213 format_helper (const real_format *format) : m_format (format) {}
214 template<typename T> format_helper (const T &);
215 const real_format *operator-> () const { return m_format; }
216 operator const real_format *() const { return m_format; }
217
decimal_p()218 bool decimal_p () const { return m_format && m_format->b == 10; }
219
220 private:
221 const real_format *m_format;
222 };
223
224 template<typename T>
format_helper(const T & m)225 inline format_helper::format_helper (const T &m)
226 : m_format (m == VOIDmode ? 0 : REAL_MODE_FORMAT (m))
227 {}
228
229 /* Declare functions in real.c. */
230
231 /* True if the given mode has a NaN representation and the treatment of
232 NaN operands is important. Certain optimizations, such as folding
233 x * 0 into 0, are not correct for NaN operands, and are normally
234 disabled for modes with NaNs. The user can ask for them to be
235 done anyway using the -funsafe-math-optimizations switch. */
236 extern bool HONOR_NANS (machine_mode);
237 extern bool HONOR_NANS (const_tree);
238 extern bool HONOR_NANS (const_rtx);
239
240 /* Like HONOR_NANs, but true if we honor signaling NaNs (or sNaNs). */
241 extern bool HONOR_SNANS (machine_mode);
242 extern bool HONOR_SNANS (const_tree);
243 extern bool HONOR_SNANS (const_rtx);
244
245 /* As for HONOR_NANS, but true if the mode can represent infinity and
246 the treatment of infinite values is important. */
247 extern bool HONOR_INFINITIES (machine_mode);
248 extern bool HONOR_INFINITIES (const_tree);
249 extern bool HONOR_INFINITIES (const_rtx);
250
251 /* Like HONOR_NANS, but true if the given mode distinguishes between
252 positive and negative zero, and the sign of zero is important. */
253 extern bool HONOR_SIGNED_ZEROS (machine_mode);
254 extern bool HONOR_SIGNED_ZEROS (const_tree);
255 extern bool HONOR_SIGNED_ZEROS (const_rtx);
256
257 /* Like HONOR_NANS, but true if given mode supports sign-dependent rounding,
258 and the rounding mode is important. */
259 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (machine_mode);
260 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_tree);
261 extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_rtx);
262
263 /* Binary or unary arithmetic on tree_code. */
264 extern bool real_arithmetic (REAL_VALUE_TYPE *, int, const REAL_VALUE_TYPE *,
265 const REAL_VALUE_TYPE *);
266
267 /* Compare reals by tree_code. */
268 extern bool real_compare (int, const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
269
270 /* Determine whether a floating-point value X is infinite. */
271 extern bool real_isinf (const REAL_VALUE_TYPE *);
272
273 /* Determine whether a floating-point value X is a NaN. */
274 extern bool real_isnan (const REAL_VALUE_TYPE *);
275
276 /* Determine whether a floating-point value X is a signaling NaN. */
277 extern bool real_issignaling_nan (const REAL_VALUE_TYPE *);
278
279 /* Determine whether a floating-point value X is finite. */
280 extern bool real_isfinite (const REAL_VALUE_TYPE *);
281
282 /* Determine whether a floating-point value X is negative. */
283 extern bool real_isneg (const REAL_VALUE_TYPE *);
284
285 /* Determine whether a floating-point value X is minus zero. */
286 extern bool real_isnegzero (const REAL_VALUE_TYPE *);
287
288 /* Test relationships between reals. */
289 extern bool real_identical (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
290 extern bool real_equal (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
291 extern bool real_less (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
292
293 /* Extend or truncate to a new format. */
294 extern void real_convert (REAL_VALUE_TYPE *, format_helper,
295 const REAL_VALUE_TYPE *);
296
297 /* Return true if truncating to NEW is exact. */
298 extern bool exact_real_truncate (format_helper, const REAL_VALUE_TYPE *);
299
300 /* Render R as a decimal floating point constant. */
301 extern void real_to_decimal (char *, const REAL_VALUE_TYPE *, size_t,
302 size_t, int);
303
304 /* Render R as a decimal floating point constant, rounded so as to be
305 parsed back to the same value when interpreted in mode MODE. */
306 extern void real_to_decimal_for_mode (char *, const REAL_VALUE_TYPE *, size_t,
307 size_t, int, machine_mode);
308
309 /* Render R as a hexadecimal floating point constant. */
310 extern void real_to_hexadecimal (char *, const REAL_VALUE_TYPE *,
311 size_t, size_t, int);
312
313 /* Render R as an integer. */
314 extern HOST_WIDE_INT real_to_integer (const REAL_VALUE_TYPE *);
315
316 /* Initialize R from a decimal or hexadecimal string. Return -1 if
317 the value underflows, +1 if overflows, and 0 otherwise. */
318 extern int real_from_string (REAL_VALUE_TYPE *, const char *);
319 /* Wrapper to allow different internal representation for decimal floats. */
320 extern void real_from_string3 (REAL_VALUE_TYPE *, const char *, format_helper);
321
322 extern long real_to_target (long *, const REAL_VALUE_TYPE *, format_helper);
323
324 extern void real_from_target (REAL_VALUE_TYPE *, const long *,
325 format_helper);
326
327 extern void real_inf (REAL_VALUE_TYPE *);
328
329 extern bool real_nan (REAL_VALUE_TYPE *, const char *, int, format_helper);
330
331 extern void real_maxval (REAL_VALUE_TYPE *, int, machine_mode);
332
333 extern void real_2expN (REAL_VALUE_TYPE *, int, format_helper);
334
335 extern unsigned int real_hash (const REAL_VALUE_TYPE *);
336
337
338 /* Target formats defined in real.c. */
339 extern const struct real_format ieee_single_format;
340 extern const struct real_format mips_single_format;
341 extern const struct real_format motorola_single_format;
342 extern const struct real_format spu_single_format;
343 extern const struct real_format ieee_double_format;
344 extern const struct real_format mips_double_format;
345 extern const struct real_format motorola_double_format;
346 extern const struct real_format ieee_extended_motorola_format;
347 extern const struct real_format ieee_extended_intel_96_format;
348 extern const struct real_format ieee_extended_intel_96_round_53_format;
349 extern const struct real_format ieee_extended_intel_128_format;
350 extern const struct real_format ibm_extended_format;
351 extern const struct real_format mips_extended_format;
352 extern const struct real_format ieee_quad_format;
353 extern const struct real_format mips_quad_format;
354 extern const struct real_format vax_f_format;
355 extern const struct real_format vax_d_format;
356 extern const struct real_format vax_g_format;
357 extern const struct real_format real_internal_format;
358 extern const struct real_format decimal_single_format;
359 extern const struct real_format decimal_double_format;
360 extern const struct real_format decimal_quad_format;
361 extern const struct real_format ieee_half_format;
362 extern const struct real_format arm_half_format;
363
364
365 /* ====================================================================== */
366 /* Crap. */
367
368 /* Determine whether a floating-point value X is infinite. */
369 #define REAL_VALUE_ISINF(x) real_isinf (&(x))
370
371 /* Determine whether a floating-point value X is a NaN. */
372 #define REAL_VALUE_ISNAN(x) real_isnan (&(x))
373
374 /* Determine whether a floating-point value X is a signaling NaN. */
375 #define REAL_VALUE_ISSIGNALING_NAN(x) real_issignaling_nan (&(x))
376
377 /* Determine whether a floating-point value X is negative. */
378 #define REAL_VALUE_NEGATIVE(x) real_isneg (&(x))
379
380 /* Determine whether a floating-point value X is minus zero. */
381 #define REAL_VALUE_MINUS_ZERO(x) real_isnegzero (&(x))
382
383 /* IN is a REAL_VALUE_TYPE. OUT is an array of longs. */
384 #define REAL_VALUE_TO_TARGET_LONG_DOUBLE(IN, OUT) \
385 real_to_target (OUT, &(IN), \
386 float_mode_for_size (LONG_DOUBLE_TYPE_SIZE).require ())
387
388 #define REAL_VALUE_TO_TARGET_DOUBLE(IN, OUT) \
389 real_to_target (OUT, &(IN), float_mode_for_size (64).require ())
390
391 /* IN is a REAL_VALUE_TYPE. OUT is a long. */
392 #define REAL_VALUE_TO_TARGET_SINGLE(IN, OUT) \
393 ((OUT) = real_to_target (NULL, &(IN), float_mode_for_size (32).require ()))
394
395 /* Real values to IEEE 754 decimal floats. */
396
397 /* IN is a REAL_VALUE_TYPE. OUT is an array of longs. */
398 #define REAL_VALUE_TO_TARGET_DECIMAL128(IN, OUT) \
399 real_to_target (OUT, &(IN), decimal_float_mode_for_size (128).require ())
400
401 #define REAL_VALUE_TO_TARGET_DECIMAL64(IN, OUT) \
402 real_to_target (OUT, &(IN), decimal_float_mode_for_size (64).require ())
403
404 /* IN is a REAL_VALUE_TYPE. OUT is a long. */
405 #define REAL_VALUE_TO_TARGET_DECIMAL32(IN, OUT) \
406 ((OUT) = real_to_target (NULL, &(IN), \
407 decimal_float_mode_for_size (32).require ()))
408
409 extern REAL_VALUE_TYPE real_value_truncate (format_helper, REAL_VALUE_TYPE);
410
411 extern REAL_VALUE_TYPE real_value_negate (const REAL_VALUE_TYPE *);
412 extern REAL_VALUE_TYPE real_value_abs (const REAL_VALUE_TYPE *);
413
414 extern int significand_size (format_helper);
415
416 extern REAL_VALUE_TYPE real_from_string2 (const char *, format_helper);
417
418 #define REAL_VALUE_ATOF(s, m) \
419 real_from_string2 (s, m)
420
421 #define CONST_DOUBLE_ATOF(s, m) \
422 const_double_from_real_value (real_from_string2 (s, m), m)
423
424 #define REAL_VALUE_FIX(r) \
425 real_to_integer (&(r))
426
427 /* ??? Not quite right. */
428 #define REAL_VALUE_UNSIGNED_FIX(r) \
429 real_to_integer (&(r))
430
431 /* ??? These were added for Paranoia support. */
432
433 /* Return floor log2(R). */
434 extern int real_exponent (const REAL_VALUE_TYPE *);
435
436 /* R = A * 2**EXP. */
437 extern void real_ldexp (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, int);
438
439 /* **** End of software floating point emulator interface macros **** */
440
441 /* Constant real values 0, 1, 2, -1 and 0.5. */
442
443 extern REAL_VALUE_TYPE dconst0;
444 extern REAL_VALUE_TYPE dconst1;
445 extern REAL_VALUE_TYPE dconst2;
446 extern REAL_VALUE_TYPE dconstm1;
447 extern REAL_VALUE_TYPE dconsthalf;
448
449 #define dconst_e() (*dconst_e_ptr ())
450 #define dconst_third() (*dconst_third_ptr ())
451 #define dconst_quarter() (*dconst_quarter_ptr ())
452 #define dconst_sixth() (*dconst_sixth_ptr ())
453 #define dconst_ninth() (*dconst_ninth_ptr ())
454 #define dconst_sqrt2() (*dconst_sqrt2_ptr ())
455
456 /* Function to return the real value special constant 'e'. */
457 extern const REAL_VALUE_TYPE * dconst_e_ptr (void);
458
459 /* Returns a cached REAL_VALUE_TYPE corresponding to 1/n, for various n. */
460 extern const REAL_VALUE_TYPE *dconst_third_ptr (void);
461 extern const REAL_VALUE_TYPE *dconst_quarter_ptr (void);
462 extern const REAL_VALUE_TYPE *dconst_sixth_ptr (void);
463 extern const REAL_VALUE_TYPE *dconst_ninth_ptr (void);
464
465 /* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2). */
466 extern const REAL_VALUE_TYPE * dconst_sqrt2_ptr (void);
467
468 /* Function to return a real value (not a tree node)
469 from a given integer constant. */
470 REAL_VALUE_TYPE real_value_from_int_cst (const_tree, const_tree);
471
472 /* Return a CONST_DOUBLE with value R and mode M. */
473 extern rtx const_double_from_real_value (REAL_VALUE_TYPE, machine_mode);
474
475 /* Replace R by 1/R in the given format, if the result is exact. */
476 extern bool exact_real_inverse (format_helper, REAL_VALUE_TYPE *);
477
478 /* Return true if arithmetic on values in IMODE that were promoted
479 from values in TMODE is equivalent to direct arithmetic on values
480 in TMODE. */
481 bool real_can_shorten_arithmetic (machine_mode, machine_mode);
482
483 /* In tree.c: wrap up a REAL_VALUE_TYPE in a tree node. */
484 extern tree build_real (tree, REAL_VALUE_TYPE);
485
486 /* Likewise, but first truncate the value to the type. */
487 extern tree build_real_truncate (tree, REAL_VALUE_TYPE);
488
489 /* Calculate R as X raised to the integer exponent N in format FMT. */
490 extern bool real_powi (REAL_VALUE_TYPE *, format_helper,
491 const REAL_VALUE_TYPE *, HOST_WIDE_INT);
492
493 /* Standard round to integer value functions. */
494 extern void real_trunc (REAL_VALUE_TYPE *, format_helper,
495 const REAL_VALUE_TYPE *);
496 extern void real_floor (REAL_VALUE_TYPE *, format_helper,
497 const REAL_VALUE_TYPE *);
498 extern void real_ceil (REAL_VALUE_TYPE *, format_helper,
499 const REAL_VALUE_TYPE *);
500 extern void real_round (REAL_VALUE_TYPE *, format_helper,
501 const REAL_VALUE_TYPE *);
502
503 /* Set the sign of R to the sign of X. */
504 extern void real_copysign (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
505
506 /* Check whether the real constant value given is an integer. */
507 extern bool real_isinteger (const REAL_VALUE_TYPE *, format_helper);
508 extern bool real_isinteger (const REAL_VALUE_TYPE *, HOST_WIDE_INT *);
509
510 /* Write into BUF the maximum representable finite floating-point
511 number, (1 - b**-p) * b**emax for a given FP format FMT as a hex
512 float string. BUF must be large enough to contain the result. */
513 extern void get_max_float (const struct real_format *, char *, size_t);
514
515 #ifndef GENERATOR_FILE
516 /* real related routines. */
517 extern wide_int real_to_integer (const REAL_VALUE_TYPE *, bool *, int);
518 extern void real_from_integer (REAL_VALUE_TYPE *, format_helper,
519 const wide_int_ref &, signop);
520 #endif
521
522 #endif /* ! GCC_REAL_H */
523