1// Definition of numeric_limits replacement traits P1841R1 -*- C++ -*-
2
3// Copyright (C) 2020-2021 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library. This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25#include <type_traits>
26
27namespace std {
28
29template <template <typename> class _Trait, typename _Tp, typename = void>
30 struct __value_exists_impl : false_type {};
31
32template <template <typename> class _Trait, typename _Tp>
33 struct __value_exists_impl<_Trait, _Tp, void_t<decltype(_Trait<_Tp>::value)>>
34 : true_type {};
35
36template <typename _Tp, bool = is_arithmetic_v<_Tp>>
37 struct __digits_impl {};
38
39template <typename _Tp>
40 struct __digits_impl<_Tp, true>
41 {
42 static inline constexpr int value
43 = sizeof(_Tp) * __CHAR_BIT__ - is_signed_v<_Tp>;
44 };
45
46template <>
47 struct __digits_impl<float, true>
48 { static inline constexpr int value = __FLT_MANT_DIG__; };
49
50template <>
51 struct __digits_impl<double, true>
52 { static inline constexpr int value = __DBL_MANT_DIG__; };
53
54template <>
55 struct __digits_impl<long double, true>
56 { static inline constexpr int value = __LDBL_MANT_DIG__; };
57
58template <typename _Tp, bool = is_arithmetic_v<_Tp>>
59 struct __digits10_impl {};
60
61template <typename _Tp>
62 struct __digits10_impl<_Tp, true>
63 {
64 // The fraction 643/2136 approximates log10(2) to 7 significant digits.
65 static inline constexpr int value = __digits_impl<_Tp>::value * 643L / 2136;
66 };
67
68template <>
69 struct __digits10_impl<float, true>
70 { static inline constexpr int value = __FLT_DIG__; };
71
72template <>
73 struct __digits10_impl<double, true>
74 { static inline constexpr int value = __DBL_DIG__; };
75
76template <>
77 struct __digits10_impl<long double, true>
78 { static inline constexpr int value = __LDBL_DIG__; };
79
80template <typename _Tp, bool = is_arithmetic_v<_Tp>>
81 struct __max_digits10_impl {};
82
83template <typename _Tp>
84 struct __max_digits10_impl<_Tp, true>
85 {
86 static inline constexpr int value
87 = is_floating_point_v<_Tp> ? 2 + __digits_impl<_Tp>::value * 643L / 2136
88 : __digits10_impl<_Tp>::value + 1;
89 };
90
91template <typename _Tp>
92 struct __max_exponent_impl {};
93
94template <>
95 struct __max_exponent_impl<float>
96 { static inline constexpr int value = __FLT_MAX_EXP__; };
97
98template <>
99 struct __max_exponent_impl<double>
100 { static inline constexpr int value = __DBL_MAX_EXP__; };
101
102template <>
103 struct __max_exponent_impl<long double>
104 { static inline constexpr int value = __LDBL_MAX_EXP__; };
105
106template <typename _Tp>
107 struct __max_exponent10_impl {};
108
109template <>
110 struct __max_exponent10_impl<float>
111 { static inline constexpr int value = __FLT_MAX_10_EXP__; };
112
113template <>
114 struct __max_exponent10_impl<double>
115 { static inline constexpr int value = __DBL_MAX_10_EXP__; };
116
117template <>
118 struct __max_exponent10_impl<long double>
119 { static inline constexpr int value = __LDBL_MAX_10_EXP__; };
120
121template <typename _Tp>
122 struct __min_exponent_impl {};
123
124template <>
125 struct __min_exponent_impl<float>
126 { static inline constexpr int value = __FLT_MIN_EXP__; };
127
128template <>
129 struct __min_exponent_impl<double>
130 { static inline constexpr int value = __DBL_MIN_EXP__; };
131
132template <>
133 struct __min_exponent_impl<long double>
134 { static inline constexpr int value = __LDBL_MIN_EXP__; };
135
136template <typename _Tp>
137 struct __min_exponent10_impl {};
138
139template <>
140 struct __min_exponent10_impl<float>
141 { static inline constexpr int value = __FLT_MIN_10_EXP__; };
142
143template <>
144 struct __min_exponent10_impl<double>
145 { static inline constexpr int value = __DBL_MIN_10_EXP__; };
146
147template <>
148 struct __min_exponent10_impl<long double>
149 { static inline constexpr int value = __LDBL_MIN_10_EXP__; };
150
151template <typename _Tp, bool = is_arithmetic_v<_Tp>>
152 struct __radix_impl {};
153
154template <typename _Tp>
155 struct __radix_impl<_Tp, true>
156 {
157 static inline constexpr int value
158 = is_floating_point_v<_Tp> ? __FLT_RADIX__ : 2;
159 };
160
161// [num.traits.util], numeric utility traits
162template <template <typename> class _Trait, typename _Tp>
163 struct __value_exists : __value_exists_impl<_Trait, _Tp> {};
164
165template <template <typename> class _Trait, typename _Tp>
166 inline constexpr bool __value_exists_v = __value_exists<_Trait, _Tp>::value;
167
168template <template <typename> class _Trait, typename _Tp, typename _Up = _Tp>
169 inline constexpr _Up
170 __value_or(_Up __def = _Up()) noexcept
171 {
172 if constexpr (__value_exists_v<_Trait, _Tp>)
173 return static_cast<_Up>(_Trait<_Tp>::value);
174 else
175 return __def;
176 }
177
178template <typename _Tp, bool = is_arithmetic_v<_Tp>>
179 struct __norm_min_impl {};
180
181template <typename _Tp>
182 struct __norm_min_impl<_Tp, true>
183 { static inline constexpr _Tp value = 1; };
184
185template <>
186 struct __norm_min_impl<float, true>
187 { static inline constexpr float value = __FLT_MIN__; };
188
189template <>
190 struct __norm_min_impl<double, true>
191 { static inline constexpr double value = __DBL_MIN__; };
192
193template <>
194 struct __norm_min_impl<long double, true>
195 { static inline constexpr long double value = __LDBL_MIN__; };
196
197template <typename _Tp>
198 struct __denorm_min_impl : __norm_min_impl<_Tp> {};
199
200#if __FLT_HAS_DENORM__
201template <>
202 struct __denorm_min_impl<float>
203 { static inline constexpr float value = __FLT_DENORM_MIN__; };
204#endif
205
206#if __DBL_HAS_DENORM__
207template <>
208 struct __denorm_min_impl<double>
209 { static inline constexpr double value = __DBL_DENORM_MIN__; };
210#endif
211
212#if __LDBL_HAS_DENORM__
213template <>
214 struct __denorm_min_impl<long double>
215 { static inline constexpr long double value = __LDBL_DENORM_MIN__; };
216#endif
217
218template <typename _Tp>
219 struct __epsilon_impl {};
220
221template <>
222 struct __epsilon_impl<float>
223 { static inline constexpr float value = __FLT_EPSILON__; };
224
225template <>
226 struct __epsilon_impl<double>
227 { static inline constexpr double value = __DBL_EPSILON__; };
228
229template <>
230 struct __epsilon_impl<long double>
231 { static inline constexpr long double value = __LDBL_EPSILON__; };
232
233template <typename _Tp, bool = is_arithmetic_v<_Tp>>
234 struct __finite_min_impl {};
235
236template <typename _Tp>
237 struct __finite_min_impl<_Tp, true>
238 {
239 static inline constexpr _Tp value
240 = is_unsigned_v<_Tp> ? _Tp()
241 : -2 * (_Tp(1) << __digits_impl<_Tp>::value - 1);
242 };
243
244template <>
245 struct __finite_min_impl<float, true>
246 { static inline constexpr float value = -__FLT_MAX__; };
247
248template <>
249 struct __finite_min_impl<double, true>
250 { static inline constexpr double value = -__DBL_MAX__; };
251
252template <>
253 struct __finite_min_impl<long double, true>
254 { static inline constexpr long double value = -__LDBL_MAX__; };
255
256template <typename _Tp, bool = is_arithmetic_v<_Tp>>
257 struct __finite_max_impl {};
258
259template <typename _Tp>
260 struct __finite_max_impl<_Tp, true>
261 { static inline constexpr _Tp value = ~__finite_min_impl<_Tp>::value; };
262
263template <>
264 struct __finite_max_impl<float, true>
265 { static inline constexpr float value = __FLT_MAX__; };
266
267template <>
268 struct __finite_max_impl<double, true>
269 { static inline constexpr double value = __DBL_MAX__; };
270
271template <>
272 struct __finite_max_impl<long double, true>
273 { static inline constexpr long double value = __LDBL_MAX__; };
274
275template <typename _Tp>
276 struct __infinity_impl {};
277
278#if __FLT_HAS_INFINITY__
279template <>
280 struct __infinity_impl<float>
281 { static inline constexpr float value = __builtin_inff(); };
282#endif
283
284#if __DBL_HAS_INFINITY__
285template <>
286 struct __infinity_impl<double>
287 { static inline constexpr double value = __builtin_inf(); };
288#endif
289
290#if __LDBL_HAS_INFINITY__
291template <>
292 struct __infinity_impl<long double>
293 { static inline constexpr long double value = __builtin_infl(); };
294#endif
295
296template <typename _Tp>
297 struct __quiet_NaN_impl {};
298
299#if __FLT_HAS_QUIET_NAN__
300template <>
301 struct __quiet_NaN_impl<float>
302 { static inline constexpr float value = __builtin_nanf(""); };
303#endif
304
305#if __DBL_HAS_QUIET_NAN__
306template <>
307 struct __quiet_NaN_impl<double>
308 { static inline constexpr double value = __builtin_nan(""); };
309#endif
310
311#if __LDBL_HAS_QUIET_NAN__
312template <>
313 struct __quiet_NaN_impl<long double>
314 { static inline constexpr long double value = __builtin_nanl(""); };
315#endif
316
317template <typename _Tp, bool = is_floating_point_v<_Tp>>
318 struct __reciprocal_overflow_threshold_impl {};
319
320template <typename _Tp>
321 struct __reciprocal_overflow_threshold_impl<_Tp, true>
322 {
323 // This typically yields a subnormal value. Is this incorrect for
324 // flush-to-zero configurations?
325 static constexpr _Tp _S_search(_Tp __ok, _Tp __overflows)
326 {
327 const _Tp __mid = (__ok + __overflows) / 2;
328 // 1/__mid without -ffast-math is not a constant expression if it
329 // overflows. Therefore divide 1 by the radix before division.
330 // Consequently finite_max (the threshold) must be scaled by the
331 // same value.
332 if (__mid == __ok || __mid == __overflows)
333 return __ok;
334 else if (_Tp(1) / (__radix_impl<_Tp>::value * __mid)
335 <= __finite_max_impl<_Tp>::value / __radix_impl<_Tp>::value)
336 return _S_search(ok: __mid, __overflows);
337 else
338 return _S_search(__ok, overflows: __mid);
339 }
340
341 static inline constexpr _Tp value
342 = _S_search(ok: _Tp(1.01) / __finite_max_impl<_Tp>::value,
343 overflows: _Tp(0.99) / __finite_max_impl<_Tp>::value);
344 };
345
346template <typename _Tp, bool = is_floating_point_v<_Tp>>
347 struct __round_error_impl {};
348
349template <typename _Tp>
350 struct __round_error_impl<_Tp, true>
351 { static inline constexpr _Tp value = 0.5; };
352
353template <typename _Tp>
354 struct __signaling_NaN_impl {};
355
356#if __FLT_HAS_QUIET_NAN__
357template <>
358 struct __signaling_NaN_impl<float>
359 { static inline constexpr float value = __builtin_nansf(""); };
360#endif
361
362#if __DBL_HAS_QUIET_NAN__
363template <>
364 struct __signaling_NaN_impl<double>
365 { static inline constexpr double value = __builtin_nans(""); };
366#endif
367
368#if __LDBL_HAS_QUIET_NAN__
369template <>
370 struct __signaling_NaN_impl<long double>
371 { static inline constexpr long double value = __builtin_nansl(""); };
372#endif
373
374// [num.traits.val], numeric distinguished value traits
375template <typename _Tp>
376 struct __denorm_min : __denorm_min_impl<remove_cv_t<_Tp>> {};
377
378template <typename _Tp>
379 struct __epsilon : __epsilon_impl<remove_cv_t<_Tp>> {};
380
381template <typename _Tp>
382 struct __finite_max : __finite_max_impl<remove_cv_t<_Tp>> {};
383
384template <typename _Tp>
385 struct __finite_min : __finite_min_impl<remove_cv_t<_Tp>> {};
386
387template <typename _Tp>
388 struct __infinity : __infinity_impl<remove_cv_t<_Tp>> {};
389
390template <typename _Tp>
391 struct __norm_min : __norm_min_impl<remove_cv_t<_Tp>> {};
392
393template <typename _Tp>
394 struct __quiet_NaN : __quiet_NaN_impl<remove_cv_t<_Tp>> {};
395
396template <typename _Tp>
397 struct __reciprocal_overflow_threshold
398 : __reciprocal_overflow_threshold_impl<remove_cv_t<_Tp>> {};
399
400template <typename _Tp>
401 struct __round_error : __round_error_impl<remove_cv_t<_Tp>> {};
402
403template <typename _Tp>
404 struct __signaling_NaN : __signaling_NaN_impl<remove_cv_t<_Tp>> {};
405
406template <typename _Tp>
407 inline constexpr auto __denorm_min_v = __denorm_min<_Tp>::value;
408
409template <typename _Tp>
410 inline constexpr auto __epsilon_v = __epsilon<_Tp>::value;
411
412template <typename _Tp>
413 inline constexpr auto __finite_max_v = __finite_max<_Tp>::value;
414
415template <typename _Tp>
416 inline constexpr auto __finite_min_v = __finite_min<_Tp>::value;
417
418template <typename _Tp>
419 inline constexpr auto __infinity_v = __infinity<_Tp>::value;
420
421template <typename _Tp>
422 inline constexpr auto __norm_min_v = __norm_min<_Tp>::value;
423
424template <typename _Tp>
425 inline constexpr auto __quiet_NaN_v = __quiet_NaN<_Tp>::value;
426
427template <typename _Tp>
428 inline constexpr auto __reciprocal_overflow_threshold_v
429 = __reciprocal_overflow_threshold<_Tp>::value;
430
431template <typename _Tp>
432 inline constexpr auto __round_error_v = __round_error<_Tp>::value;
433
434template <typename _Tp>
435 inline constexpr auto __signaling_NaN_v = __signaling_NaN<_Tp>::value;
436
437// [num.traits.char], numeric characteristics traits
438template <typename _Tp>
439 struct __digits : __digits_impl<remove_cv_t<_Tp>> {};
440
441template <typename _Tp>
442 struct __digits10 : __digits10_impl<remove_cv_t<_Tp>> {};
443
444template <typename _Tp>
445 struct __max_digits10 : __max_digits10_impl<remove_cv_t<_Tp>> {};
446
447template <typename _Tp>
448 struct __max_exponent : __max_exponent_impl<remove_cv_t<_Tp>> {};
449
450template <typename _Tp>
451 struct __max_exponent10 : __max_exponent10_impl<remove_cv_t<_Tp>> {};
452
453template <typename _Tp>
454 struct __min_exponent : __min_exponent_impl<remove_cv_t<_Tp>> {};
455
456template <typename _Tp>
457 struct __min_exponent10 : __min_exponent10_impl<remove_cv_t<_Tp>> {};
458
459template <typename _Tp>
460 struct __radix : __radix_impl<remove_cv_t<_Tp>> {};
461
462template <typename _Tp>
463 inline constexpr auto __digits_v = __digits<_Tp>::value;
464
465template <typename _Tp>
466 inline constexpr auto __digits10_v = __digits10<_Tp>::value;
467
468template <typename _Tp>
469 inline constexpr auto __max_digits10_v = __max_digits10<_Tp>::value;
470
471template <typename _Tp>
472 inline constexpr auto __max_exponent_v = __max_exponent<_Tp>::value;
473
474template <typename _Tp>
475 inline constexpr auto __max_exponent10_v = __max_exponent10<_Tp>::value;
476
477template <typename _Tp>
478 inline constexpr auto __min_exponent_v = __min_exponent<_Tp>::value;
479
480template <typename _Tp>
481 inline constexpr auto __min_exponent10_v = __min_exponent10<_Tp>::value;
482
483template <typename _Tp>
484 inline constexpr auto __radix_v = __radix<_Tp>::value;
485
486// mkretz's extensions
487// TODO: does GCC tell me? __GCC_IEC_559 >= 2 is not the right answer
488template <typename _Tp>
489 struct __has_iec559_storage_format : true_type {};
490
491template <typename _Tp>
492 inline constexpr bool __has_iec559_storage_format_v
493 = __has_iec559_storage_format<_Tp>::value;
494
495/* To propose:
496 If __has_iec559_behavior<__quiet_NaN, T> is true the following holds:
497 - nan == nan is false
498 - isnan(nan) is true
499 - isnan(nan + x) is true
500 - isnan(inf/inf) is true
501 - isnan(0/0) is true
502 - isunordered(nan, x) is true
503
504 If __has_iec559_behavior<__infinity, T> is true the following holds (x is
505 neither nan nor inf):
506 - isinf(inf) is true
507 - isinf(inf + x) is true
508 - isinf(1/0) is true
509 */
510template <template <typename> class _Trait, typename _Tp>
511 struct __has_iec559_behavior : false_type {};
512
513template <template <typename> class _Trait, typename _Tp>
514 inline constexpr bool __has_iec559_behavior_v
515 = __has_iec559_behavior<_Trait, _Tp>::value;
516
517#if !__FINITE_MATH_ONLY__
518#if __FLT_HAS_QUIET_NAN__
519template <>
520 struct __has_iec559_behavior<__quiet_NaN, float> : true_type {};
521#endif
522
523#if __DBL_HAS_QUIET_NAN__
524template <>
525 struct __has_iec559_behavior<__quiet_NaN, double> : true_type {};
526#endif
527
528#if __LDBL_HAS_QUIET_NAN__
529template <>
530 struct __has_iec559_behavior<__quiet_NaN, long double> : true_type {};
531#endif
532
533#if __FLT_HAS_INFINITY__
534template <>
535 struct __has_iec559_behavior<__infinity, float> : true_type {};
536#endif
537
538#if __DBL_HAS_INFINITY__
539template <>
540 struct __has_iec559_behavior<__infinity, double> : true_type {};
541#endif
542
543#if __LDBL_HAS_INFINITY__
544template <>
545 struct __has_iec559_behavior<__infinity, long double> : true_type {};
546#endif
547
548#ifdef __SUPPORT_SNAN__
549#if __FLT_HAS_QUIET_NAN__
550template <>
551 struct __has_iec559_behavior<__signaling_NaN, float> : true_type {};
552#endif
553
554#if __DBL_HAS_QUIET_NAN__
555template <>
556 struct __has_iec559_behavior<__signaling_NaN, double> : true_type {};
557#endif
558
559#if __LDBL_HAS_QUIET_NAN__
560template <>
561 struct __has_iec559_behavior<__signaling_NaN, long double> : true_type {};
562#endif
563
564#endif
565#endif // __FINITE_MATH_ONLY__
566
567} // namespace std
568

source code of include/c++/11/experimental/bits/numeric_traits.h