1/* Definitions of floating-point access for GNU compiler.
2 Copyright (C) 1989-2022 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. */
26enum 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
39struct 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 /* 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];
57};
58
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)))
64
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
69
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. */
73
74#define REAL_VALUE_TYPE_SIZE (SIGNIFICAND_BITS + 32)
75#define REAL_WIDTH \
76 (REAL_VALUE_TYPE_SIZE/HOST_BITS_PER_WIDE_INT \
77 + (REAL_VALUE_TYPE_SIZE%HOST_BITS_PER_WIDE_INT ? 1 : 0)) /* round up */
78
79/* Verify the guess. */
80extern char test_real_width
81 [sizeof (REAL_VALUE_TYPE) <= REAL_WIDTH * sizeof (HOST_WIDE_INT) ? 1 : -1];
82
83/* Calculate the format for CONST_DOUBLE. We need as many slots as
84 are necessary to overlay a REAL_VALUE_TYPE on them. This could be
85 as many as four (32-bit HOST_WIDE_INT, 128-bit REAL_VALUE_TYPE).
86
87 A number of places assume that there are always at least two 'w'
88 slots in a CONST_DOUBLE, so we provide them even if one would suffice. */
89
90#if REAL_WIDTH == 1
91# define CONST_DOUBLE_FORMAT "ww"
92#else
93# if REAL_WIDTH == 2
94# define CONST_DOUBLE_FORMAT "ww"
95# else
96# if REAL_WIDTH == 3
97# define CONST_DOUBLE_FORMAT "www"
98# else
99# if REAL_WIDTH == 4
100# define CONST_DOUBLE_FORMAT "wwww"
101# else
102# if REAL_WIDTH == 5
103# define CONST_DOUBLE_FORMAT "wwwww"
104# else
105# if REAL_WIDTH == 6
106# define CONST_DOUBLE_FORMAT "wwwwww"
107# else
108 #error "REAL_WIDTH > 6 not supported"
109# endif
110# endif
111# endif
112# endif
113# endif
114#endif
115
116
117/* Describes the properties of the specific target format in use. */
118struct real_format
119{
120 /* Move to and from the target bytes. */
121 void (*encode) (const struct real_format *, long *,
122 const REAL_VALUE_TYPE *);
123 void (*decode) (const struct real_format *, REAL_VALUE_TYPE *,
124 const long *);
125
126 /* The radix of the exponent and digits of the significand. */
127 int b;
128
129 /* Size of the significand in digits of radix B. */
130 int p;
131
132 /* Size of the significant of a NaN, in digits of radix B. */
133 int pnan;
134
135 /* The minimum negative integer, x, such that b**(x-1) is normalized. */
136 int emin;
137
138 /* The maximum integer, x, such that b**(x-1) is representable. */
139 int emax;
140
141 /* The bit position of the sign bit, for determining whether a value
142 is positive/negative, or -1 for a complex encoding. */
143 int signbit_ro;
144
145 /* The bit position of the sign bit, for changing the sign of a number,
146 or -1 for a complex encoding. */
147 int signbit_rw;
148
149 /* If this is an IEEE interchange format, the number of bits in the
150 format; otherwise, if it is an IEEE extended format, one more
151 than the greatest number of bits in an interchange format it
152 extends; otherwise 0. Formats need not follow the IEEE 754-2008
153 recommended practice regarding how signaling NaNs are identified,
154 and may vary in the choice of default NaN, but must follow other
155 IEEE practice regarding having NaNs, infinities and subnormal
156 values, and the relation of minimum and maximum exponents, and,
157 for interchange formats, the details of the encoding. */
158 int ieee_bits;
159
160 /* Default rounding mode for operations on this format. */
161 bool round_towards_zero;
162 bool has_sign_dependent_rounding;
163
164 /* Properties of the format. */
165 bool has_nans;
166 bool has_inf;
167 bool has_denorm;
168 bool has_signed_zero;
169 bool qnan_msb_set;
170 bool canonical_nan_lsbs_set;
171 const char *name;
172};
173
174
175/* The target format used for each floating point mode.
176 Float modes are followed by decimal float modes, with entries for
177 float modes indexed by (MODE - first float mode), and entries for
178 decimal float modes indexed by (MODE - first decimal float mode) +
179 the number of float modes. */
180extern const struct real_format *
181 real_format_for_mode[NUM_MODE_FLOAT + NUM_MODE_DECIMAL_FLOAT];
182
183#define REAL_MODE_FORMAT(MODE) \
184 (real_format_for_mode[DECIMAL_FLOAT_MODE_P (MODE) \
185 ? (((MODE) - MIN_MODE_DECIMAL_FLOAT) \
186 + NUM_MODE_FLOAT) \
187 : GET_MODE_CLASS (MODE) == MODE_FLOAT \
188 ? ((MODE) - MIN_MODE_FLOAT) \
189 : (gcc_unreachable (), 0)])
190
191#define FLOAT_MODE_FORMAT(MODE) \
192 (REAL_MODE_FORMAT (as_a <scalar_float_mode> (GET_MODE_INNER (MODE))))
193
194/* The following macro determines whether the floating point format is
195 composite, i.e. may contain non-consecutive mantissa bits, in which
196 case compile-time FP overflow may not model run-time overflow. */
197#define MODE_COMPOSITE_P(MODE) \
198 (FLOAT_MODE_P (MODE) \
199 && FLOAT_MODE_FORMAT (MODE)->pnan < FLOAT_MODE_FORMAT (MODE)->p)
200
201/* Accessor macros for format properties. */
202#define MODE_HAS_NANS(MODE) \
203 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_nans)
204#define MODE_HAS_INFINITIES(MODE) \
205 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_inf)
206#define MODE_HAS_SIGNED_ZEROS(MODE) \
207 (FLOAT_MODE_P (MODE) && FLOAT_MODE_FORMAT (MODE)->has_signed_zero)
208#define MODE_HAS_SIGN_DEPENDENT_ROUNDING(MODE) \
209 (FLOAT_MODE_P (MODE) \
210 && FLOAT_MODE_FORMAT (MODE)->has_sign_dependent_rounding)
211
212/* This class allows functions in this file to accept a floating-point
213 format as either a mode or an explicit real_format pointer. In the
214 former case the mode must be VOIDmode (which means "no particular
215 format") or must satisfy SCALAR_FLOAT_MODE_P. */
216class format_helper
217{
218public:
219 format_helper (const real_format *format) : m_format (format) {}
220 template<typename T> format_helper (const T &);
221 const real_format *operator-> () const { return m_format; }
222 operator const real_format *() const { return m_format; }
223
224 bool decimal_p () const { return m_format && m_format->b == 10; }
225 bool can_represent_integral_type_p (tree type) const;
226
227private:
228 const real_format *m_format;
229};
230
231template<typename T>
232inline format_helper::format_helper (const T &m)
233 : m_format (m == VOIDmode ? 0 : REAL_MODE_FORMAT (m))
234{}
235
236/* Declare functions in real.cc. */
237
238/* True if the given mode has a NaN representation and the treatment of
239 NaN operands is important. Certain optimizations, such as folding
240 x * 0 into 0, are not correct for NaN operands, and are normally
241 disabled for modes with NaNs. The user can ask for them to be
242 done anyway using the -funsafe-math-optimizations switch. */
243extern bool HONOR_NANS (machine_mode);
244extern bool HONOR_NANS (const_tree);
245extern bool HONOR_NANS (const_rtx);
246
247/* Like HONOR_NANs, but true if we honor signaling NaNs (or sNaNs). */
248extern bool HONOR_SNANS (machine_mode);
249extern bool HONOR_SNANS (const_tree);
250extern bool HONOR_SNANS (const_rtx);
251
252/* As for HONOR_NANS, but true if the mode can represent infinity and
253 the treatment of infinite values is important. */
254extern bool HONOR_INFINITIES (machine_mode);
255extern bool HONOR_INFINITIES (const_tree);
256extern bool HONOR_INFINITIES (const_rtx);
257
258/* Like HONOR_NANS, but true if the given mode distinguishes between
259 positive and negative zero, and the sign of zero is important. */
260extern bool HONOR_SIGNED_ZEROS (machine_mode);
261extern bool HONOR_SIGNED_ZEROS (const_tree);
262extern bool HONOR_SIGNED_ZEROS (const_rtx);
263
264/* Like HONOR_NANS, but true if given mode supports sign-dependent rounding,
265 and the rounding mode is important. */
266extern bool HONOR_SIGN_DEPENDENT_ROUNDING (machine_mode);
267extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_tree);
268extern bool HONOR_SIGN_DEPENDENT_ROUNDING (const_rtx);
269
270/* Binary or unary arithmetic on tree_code. */
271extern bool real_arithmetic (REAL_VALUE_TYPE *, int, const REAL_VALUE_TYPE *,
272 const REAL_VALUE_TYPE *);
273
274/* Compare reals by tree_code. */
275extern bool real_compare (int, const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
276
277/* Determine whether a floating-point value X is infinite. */
278extern bool real_isinf (const REAL_VALUE_TYPE *);
279
280/* Determine whether a floating-point value X is a NaN. */
281extern bool real_isnan (const REAL_VALUE_TYPE *);
282
283/* Determine whether a floating-point value X is a signaling NaN. */
284extern bool real_issignaling_nan (const REAL_VALUE_TYPE *);
285
286/* Determine whether a floating-point value X is finite. */
287extern bool real_isfinite (const REAL_VALUE_TYPE *);
288
289/* Determine whether a floating-point value X is negative. */
290extern bool real_isneg (const REAL_VALUE_TYPE *);
291
292/* Determine whether a floating-point value X is minus zero. */
293extern bool real_isnegzero (const REAL_VALUE_TYPE *);
294
295/* Test relationships between reals. */
296extern bool real_identical (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
297extern bool real_equal (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
298extern bool real_less (const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
299
300/* Extend or truncate to a new format. */
301extern void real_convert (REAL_VALUE_TYPE *, format_helper,
302 const REAL_VALUE_TYPE *);
303
304/* Return true if truncating to NEW is exact. */
305extern bool exact_real_truncate (format_helper, const REAL_VALUE_TYPE *);
306
307/* Render R as a decimal floating point constant. */
308extern void real_to_decimal (char *, const REAL_VALUE_TYPE *, size_t,
309 size_t, int);
310
311/* Render R as a decimal floating point constant, rounded so as to be
312 parsed back to the same value when interpreted in mode MODE. */
313extern void real_to_decimal_for_mode (char *, const REAL_VALUE_TYPE *, size_t,
314 size_t, int, machine_mode);
315
316/* Render R as a hexadecimal floating point constant. */
317extern void real_to_hexadecimal (char *, const REAL_VALUE_TYPE *,
318 size_t, size_t, int);
319
320/* Render R as an integer. */
321extern HOST_WIDE_INT real_to_integer (const REAL_VALUE_TYPE *);
322
323/* Initialize R from a decimal or hexadecimal string. Return -1 if
324 the value underflows, +1 if overflows, and 0 otherwise. */
325extern int real_from_string (REAL_VALUE_TYPE *, const char *);
326/* Wrapper to allow different internal representation for decimal floats. */
327extern void real_from_string3 (REAL_VALUE_TYPE *, const char *, format_helper);
328
329extern long real_to_target (long *, const REAL_VALUE_TYPE *, format_helper);
330
331extern void real_from_target (REAL_VALUE_TYPE *, const long *,
332 format_helper);
333
334extern void real_inf (REAL_VALUE_TYPE *);
335
336extern bool real_nan (REAL_VALUE_TYPE *, const char *, int, format_helper);
337
338extern void real_maxval (REAL_VALUE_TYPE *, int, machine_mode);
339
340extern void real_2expN (REAL_VALUE_TYPE *, int, format_helper);
341
342extern unsigned int real_hash (const REAL_VALUE_TYPE *);
343
344
345/* Target formats defined in real.cc. */
346extern const struct real_format ieee_single_format;
347extern const struct real_format mips_single_format;
348extern const struct real_format motorola_single_format;
349extern const struct real_format spu_single_format;
350extern const struct real_format ieee_double_format;
351extern const struct real_format mips_double_format;
352extern const struct real_format motorola_double_format;
353extern const struct real_format ieee_extended_motorola_format;
354extern const struct real_format ieee_extended_intel_96_format;
355extern const struct real_format ieee_extended_intel_96_round_53_format;
356extern const struct real_format ieee_extended_intel_128_format;
357extern const struct real_format ibm_extended_format;
358extern const struct real_format mips_extended_format;
359extern const struct real_format ieee_quad_format;
360extern const struct real_format mips_quad_format;
361extern const struct real_format vax_f_format;
362extern const struct real_format vax_d_format;
363extern const struct real_format vax_g_format;
364extern const struct real_format real_internal_format;
365extern const struct real_format decimal_single_format;
366extern const struct real_format decimal_double_format;
367extern const struct real_format decimal_quad_format;
368extern const struct real_format ieee_half_format;
369extern const struct real_format arm_half_format;
370extern const struct real_format arm_bfloat_half_format;
371
372
373/* ====================================================================== */
374/* Crap. */
375
376/* Determine whether a floating-point value X is infinite. */
377#define REAL_VALUE_ISINF(x) real_isinf (&(x))
378
379/* Determine whether a floating-point value X is a NaN. */
380#define REAL_VALUE_ISNAN(x) real_isnan (&(x))
381
382/* Determine whether a floating-point value X is a signaling NaN. */
383#define REAL_VALUE_ISSIGNALING_NAN(x) real_issignaling_nan (&(x))
384
385/* Determine whether a floating-point value X is negative. */
386#define REAL_VALUE_NEGATIVE(x) real_isneg (&(x))
387
388/* Determine whether a floating-point value X is minus zero. */
389#define REAL_VALUE_MINUS_ZERO(x) real_isnegzero (&(x))
390
391/* IN is a REAL_VALUE_TYPE. OUT is an array of longs. */
392#define REAL_VALUE_TO_TARGET_LONG_DOUBLE(IN, OUT) \
393 real_to_target (OUT, &(IN), \
394 float_mode_for_size (LONG_DOUBLE_TYPE_SIZE).require ())
395
396#define REAL_VALUE_TO_TARGET_DOUBLE(IN, OUT) \
397 real_to_target (OUT, &(IN), float_mode_for_size (64).require ())
398
399/* IN is a REAL_VALUE_TYPE. OUT is a long. */
400#define REAL_VALUE_TO_TARGET_SINGLE(IN, OUT) \
401 ((OUT) = real_to_target (NULL, &(IN), float_mode_for_size (32).require ()))
402
403/* Real values to IEEE 754 decimal floats. */
404
405/* IN is a REAL_VALUE_TYPE. OUT is an array of longs. */
406#define REAL_VALUE_TO_TARGET_DECIMAL128(IN, OUT) \
407 real_to_target (OUT, &(IN), decimal_float_mode_for_size (128).require ())
408
409#define REAL_VALUE_TO_TARGET_DECIMAL64(IN, OUT) \
410 real_to_target (OUT, &(IN), decimal_float_mode_for_size (64).require ())
411
412/* IN is a REAL_VALUE_TYPE. OUT is a long. */
413#define REAL_VALUE_TO_TARGET_DECIMAL32(IN, OUT) \
414 ((OUT) = real_to_target (NULL, &(IN), \
415 decimal_float_mode_for_size (32).require ()))
416
417extern REAL_VALUE_TYPE real_value_truncate (format_helper, REAL_VALUE_TYPE);
418
419extern REAL_VALUE_TYPE real_value_negate (const REAL_VALUE_TYPE *);
420extern REAL_VALUE_TYPE real_value_abs (const REAL_VALUE_TYPE *);
421
422extern int significand_size (format_helper);
423
424extern REAL_VALUE_TYPE real_from_string2 (const char *, format_helper);
425
426#define REAL_VALUE_ATOF(s, m) \
427 real_from_string2 (s, m)
428
429#define CONST_DOUBLE_ATOF(s, m) \
430 const_double_from_real_value (real_from_string2 (s, m), m)
431
432#define REAL_VALUE_FIX(r) \
433 real_to_integer (&(r))
434
435/* ??? Not quite right. */
436#define REAL_VALUE_UNSIGNED_FIX(r) \
437 real_to_integer (&(r))
438
439/* ??? These were added for Paranoia support. */
440
441/* Return floor log2(R). */
442extern int real_exponent (const REAL_VALUE_TYPE *);
443
444/* R = A * 2**EXP. */
445extern void real_ldexp (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *, int);
446
447/* **** End of software floating point emulator interface macros **** */
448
449/* Constant real values 0, 1, 2, -1 and 0.5. */
450
451extern REAL_VALUE_TYPE dconst0;
452extern REAL_VALUE_TYPE dconst1;
453extern REAL_VALUE_TYPE dconst2;
454extern REAL_VALUE_TYPE dconstm1;
455extern REAL_VALUE_TYPE dconsthalf;
456
457#define dconst_e() (*dconst_e_ptr ())
458#define dconst_third() (*dconst_third_ptr ())
459#define dconst_quarter() (*dconst_quarter_ptr ())
460#define dconst_sixth() (*dconst_sixth_ptr ())
461#define dconst_ninth() (*dconst_ninth_ptr ())
462#define dconst_sqrt2() (*dconst_sqrt2_ptr ())
463
464/* Function to return the real value special constant 'e'. */
465extern const REAL_VALUE_TYPE * dconst_e_ptr (void);
466
467/* Returns a cached REAL_VALUE_TYPE corresponding to 1/n, for various n. */
468extern const REAL_VALUE_TYPE *dconst_third_ptr (void);
469extern const REAL_VALUE_TYPE *dconst_quarter_ptr (void);
470extern const REAL_VALUE_TYPE *dconst_sixth_ptr (void);
471extern const REAL_VALUE_TYPE *dconst_ninth_ptr (void);
472
473/* Returns the special REAL_VALUE_TYPE corresponding to sqrt(2). */
474extern const REAL_VALUE_TYPE * dconst_sqrt2_ptr (void);
475
476/* Function to return a real value (not a tree node)
477 from a given integer constant. */
478REAL_VALUE_TYPE real_value_from_int_cst (const_tree, const_tree);
479
480/* Return a CONST_DOUBLE with value R and mode M. */
481extern rtx const_double_from_real_value (REAL_VALUE_TYPE, machine_mode);
482
483/* Replace R by 1/R in the given format, if the result is exact. */
484extern bool exact_real_inverse (format_helper, REAL_VALUE_TYPE *);
485
486/* Return true if arithmetic on values in IMODE that were promoted
487 from values in TMODE is equivalent to direct arithmetic on values
488 in TMODE. */
489bool real_can_shorten_arithmetic (machine_mode, machine_mode);
490
491/* In tree.cc: wrap up a REAL_VALUE_TYPE in a tree node. */
492extern tree build_real (tree, REAL_VALUE_TYPE);
493
494/* Likewise, but first truncate the value to the type. */
495extern tree build_real_truncate (tree, REAL_VALUE_TYPE);
496
497/* Calculate R as X raised to the integer exponent N in format FMT. */
498extern bool real_powi (REAL_VALUE_TYPE *, format_helper,
499 const REAL_VALUE_TYPE *, HOST_WIDE_INT);
500
501/* Standard round to integer value functions. */
502extern void real_trunc (REAL_VALUE_TYPE *, format_helper,
503 const REAL_VALUE_TYPE *);
504extern void real_floor (REAL_VALUE_TYPE *, format_helper,
505 const REAL_VALUE_TYPE *);
506extern void real_ceil (REAL_VALUE_TYPE *, format_helper,
507 const REAL_VALUE_TYPE *);
508extern void real_round (REAL_VALUE_TYPE *, format_helper,
509 const REAL_VALUE_TYPE *);
510extern void real_roundeven (REAL_VALUE_TYPE *, format_helper,
511 const REAL_VALUE_TYPE *);
512
513/* Set the sign of R to the sign of X. */
514extern void real_copysign (REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
515
516/* Check whether the real constant value given is an integer. */
517extern bool real_isinteger (const REAL_VALUE_TYPE *, format_helper);
518extern bool real_isinteger (const REAL_VALUE_TYPE *, HOST_WIDE_INT *);
519
520/* Calculate nextafter (X, Y) in format FMT. */
521extern bool real_nextafter (REAL_VALUE_TYPE *, format_helper,
522 const REAL_VALUE_TYPE *, const REAL_VALUE_TYPE *);
523
524/* Write into BUF the maximum representable finite floating-point
525 number, (1 - b**-p) * b**emax for a given FP format FMT as a hex
526 float string. BUF must be large enough to contain the result. */
527extern void get_max_float (const struct real_format *, char *, size_t, bool);
528
529#ifndef GENERATOR_FILE
530/* real related routines. */
531extern wide_int real_to_integer (const REAL_VALUE_TYPE *, bool *, int);
532extern void real_from_integer (REAL_VALUE_TYPE *, format_helper,
533 const wide_int_ref &, signop);
534#endif
535
536/* Fills r with the largest value such that 1 + r*r won't overflow.
537 This is used in both sin (atan (x)) and cos (atan(x)) optimizations. */
538extern void build_sinatan_real (REAL_VALUE_TYPE *, tree);
539
540#endif /* ! GCC_REAL_H */
541

source code of gcc/real.h