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 
27 namespace std {
28 
29 template <template <typename> class _Trait, typename _Tp, typename = void>
30   struct __value_exists_impl : false_type {};
31 
32 template <template <typename> class _Trait, typename _Tp>
33   struct __value_exists_impl<_Trait, _Tp, void_t<decltype(_Trait<_Tp>::value)>>
34   : true_type {};
35 
36 template <typename _Tp, bool = is_arithmetic_v<_Tp>>
37   struct __digits_impl {};
38 
39 template <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 
46 template <>
47   struct __digits_impl<float, true>
48   { static inline constexpr int value = __FLT_MANT_DIG__; };
49 
50 template <>
51   struct __digits_impl<double, true>
52   { static inline constexpr int value = __DBL_MANT_DIG__; };
53 
54 template <>
55   struct __digits_impl<long double, true>
56   { static inline constexpr int value = __LDBL_MANT_DIG__; };
57 
58 template <typename _Tp, bool = is_arithmetic_v<_Tp>>
59   struct __digits10_impl {};
60 
61 template <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 
68 template <>
69   struct __digits10_impl<float, true>
70   { static inline constexpr int value = __FLT_DIG__; };
71 
72 template <>
73   struct __digits10_impl<double, true>
74   { static inline constexpr int value = __DBL_DIG__; };
75 
76 template <>
77   struct __digits10_impl<long double, true>
78   { static inline constexpr int value = __LDBL_DIG__; };
79 
80 template <typename _Tp, bool = is_arithmetic_v<_Tp>>
81   struct __max_digits10_impl {};
82 
83 template <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 
91 template <typename _Tp>
92   struct __max_exponent_impl {};
93 
94 template <>
95   struct __max_exponent_impl<float>
96   { static inline constexpr int value = __FLT_MAX_EXP__; };
97 
98 template <>
99   struct __max_exponent_impl<double>
100   { static inline constexpr int value = __DBL_MAX_EXP__; };
101 
102 template <>
103   struct __max_exponent_impl<long double>
104   { static inline constexpr int value = __LDBL_MAX_EXP__; };
105 
106 template <typename _Tp>
107   struct __max_exponent10_impl {};
108 
109 template <>
110   struct __max_exponent10_impl<float>
111   { static inline constexpr int value = __FLT_MAX_10_EXP__; };
112 
113 template <>
114   struct __max_exponent10_impl<double>
115   { static inline constexpr int value = __DBL_MAX_10_EXP__; };
116 
117 template <>
118   struct __max_exponent10_impl<long double>
119   { static inline constexpr int value = __LDBL_MAX_10_EXP__; };
120 
121 template <typename _Tp>
122   struct __min_exponent_impl {};
123 
124 template <>
125   struct __min_exponent_impl<float>
126   { static inline constexpr int value = __FLT_MIN_EXP__; };
127 
128 template <>
129   struct __min_exponent_impl<double>
130   { static inline constexpr int value = __DBL_MIN_EXP__; };
131 
132 template <>
133   struct __min_exponent_impl<long double>
134   { static inline constexpr int value = __LDBL_MIN_EXP__; };
135 
136 template <typename _Tp>
137   struct __min_exponent10_impl {};
138 
139 template <>
140   struct __min_exponent10_impl<float>
141   { static inline constexpr int value = __FLT_MIN_10_EXP__; };
142 
143 template <>
144   struct __min_exponent10_impl<double>
145   { static inline constexpr int value = __DBL_MIN_10_EXP__; };
146 
147 template <>
148   struct __min_exponent10_impl<long double>
149   { static inline constexpr int value = __LDBL_MIN_10_EXP__; };
150 
151 template <typename _Tp, bool = is_arithmetic_v<_Tp>>
152   struct __radix_impl {};
153 
154 template <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
162 template <template <typename> class _Trait, typename _Tp>
163   struct __value_exists : __value_exists_impl<_Trait, _Tp> {};
164 
165 template <template <typename> class _Trait, typename _Tp>
166   inline constexpr bool __value_exists_v = __value_exists<_Trait, _Tp>::value;
167 
168 template <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 
178 template <typename _Tp, bool = is_arithmetic_v<_Tp>>
179   struct __norm_min_impl {};
180 
181 template <typename _Tp>
182   struct __norm_min_impl<_Tp, true>
183   { static inline constexpr _Tp value = 1; };
184 
185 template <>
186   struct __norm_min_impl<float, true>
187   { static inline constexpr float value = __FLT_MIN__; };
188 
189 template <>
190   struct __norm_min_impl<double, true>
191   { static inline constexpr double value = __DBL_MIN__; };
192 
193 template <>
194   struct __norm_min_impl<long double, true>
195   { static inline constexpr long double value = __LDBL_MIN__; };
196 
197 template <typename _Tp>
198   struct __denorm_min_impl : __norm_min_impl<_Tp> {};
199 
200 #if __FLT_HAS_DENORM__
201 template <>
202   struct __denorm_min_impl<float>
203   { static inline constexpr float value = __FLT_DENORM_MIN__; };
204 #endif
205 
206 #if __DBL_HAS_DENORM__
207 template <>
208   struct __denorm_min_impl<double>
209   { static inline constexpr double value = __DBL_DENORM_MIN__; };
210 #endif
211 
212 #if __LDBL_HAS_DENORM__
213 template <>
214   struct __denorm_min_impl<long double>
215   { static inline constexpr long double value = __LDBL_DENORM_MIN__; };
216 #endif
217 
218 template <typename _Tp>
219   struct __epsilon_impl {};
220 
221 template <>
222   struct __epsilon_impl<float>
223   { static inline constexpr float value = __FLT_EPSILON__; };
224 
225 template <>
226   struct __epsilon_impl<double>
227   { static inline constexpr double value = __DBL_EPSILON__; };
228 
229 template <>
230   struct __epsilon_impl<long double>
231   { static inline constexpr long double value = __LDBL_EPSILON__; };
232 
233 template <typename _Tp, bool = is_arithmetic_v<_Tp>>
234   struct __finite_min_impl {};
235 
236 template <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 
244 template <>
245   struct __finite_min_impl<float, true>
246   { static inline constexpr float value = -__FLT_MAX__; };
247 
248 template <>
249   struct __finite_min_impl<double, true>
250   { static inline constexpr double value = -__DBL_MAX__; };
251 
252 template <>
253   struct __finite_min_impl<long double, true>
254   { static inline constexpr long double value = -__LDBL_MAX__; };
255 
256 template <typename _Tp, bool = is_arithmetic_v<_Tp>>
257   struct __finite_max_impl {};
258 
259 template <typename _Tp>
260   struct __finite_max_impl<_Tp, true>
261   { static inline constexpr _Tp value = ~__finite_min_impl<_Tp>::value; };
262 
263 template <>
264   struct __finite_max_impl<float, true>
265   { static inline constexpr float value = __FLT_MAX__; };
266 
267 template <>
268   struct __finite_max_impl<double, true>
269   { static inline constexpr double value = __DBL_MAX__; };
270 
271 template <>
272   struct __finite_max_impl<long double, true>
273   { static inline constexpr long double value = __LDBL_MAX__; };
274 
275 template <typename _Tp>
276   struct __infinity_impl {};
277 
278 #if __FLT_HAS_INFINITY__
279 template <>
280   struct __infinity_impl<float>
281   { static inline constexpr float value = __builtin_inff(); };
282 #endif
283 
284 #if __DBL_HAS_INFINITY__
285 template <>
286   struct __infinity_impl<double>
287   { static inline constexpr double value = __builtin_inf(); };
288 #endif
289 
290 #if __LDBL_HAS_INFINITY__
291 template <>
292   struct __infinity_impl<long double>
293   { static inline constexpr long double value = __builtin_infl(); };
294 #endif
295 
296 template <typename _Tp>
297   struct __quiet_NaN_impl {};
298 
299 #if __FLT_HAS_QUIET_NAN__
300 template <>
301   struct __quiet_NaN_impl<float>
302   { static inline constexpr float value = __builtin_nanf(""); };
303 #endif
304 
305 #if __DBL_HAS_QUIET_NAN__
306 template <>
307   struct __quiet_NaN_impl<double>
308   { static inline constexpr double value = __builtin_nan(""); };
309 #endif
310 
311 #if __LDBL_HAS_QUIET_NAN__
312 template <>
313   struct __quiet_NaN_impl<long double>
314   { static inline constexpr long double value = __builtin_nanl(""); };
315 #endif
316 
317 template <typename _Tp, bool = is_floating_point_v<_Tp>>
318   struct __reciprocal_overflow_threshold_impl {};
319 
320 template <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(__mid, __overflows);
337       else
338 	return _S_search(__ok, __mid);
339     }
340 
341     static inline constexpr _Tp value
342       = _S_search(_Tp(1.01) / __finite_max_impl<_Tp>::value,
343 		  _Tp(0.99) / __finite_max_impl<_Tp>::value);
344   };
345 
346 template <typename _Tp, bool = is_floating_point_v<_Tp>>
347   struct __round_error_impl {};
348 
349 template <typename _Tp>
350   struct __round_error_impl<_Tp, true>
351   { static inline constexpr _Tp value = 0.5; };
352 
353 template <typename _Tp>
354   struct __signaling_NaN_impl {};
355 
356 #if __FLT_HAS_QUIET_NAN__
357 template <>
358   struct __signaling_NaN_impl<float>
359   { static inline constexpr float value = __builtin_nansf(""); };
360 #endif
361 
362 #if __DBL_HAS_QUIET_NAN__
363 template <>
364   struct __signaling_NaN_impl<double>
365   { static inline constexpr double value = __builtin_nans(""); };
366 #endif
367 
368 #if __LDBL_HAS_QUIET_NAN__
369 template <>
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
375 template <typename _Tp>
376   struct __denorm_min : __denorm_min_impl<remove_cv_t<_Tp>> {};
377 
378 template <typename _Tp>
379   struct __epsilon : __epsilon_impl<remove_cv_t<_Tp>> {};
380 
381 template <typename _Tp>
382   struct __finite_max : __finite_max_impl<remove_cv_t<_Tp>> {};
383 
384 template <typename _Tp>
385   struct __finite_min : __finite_min_impl<remove_cv_t<_Tp>> {};
386 
387 template <typename _Tp>
388   struct __infinity : __infinity_impl<remove_cv_t<_Tp>> {};
389 
390 template <typename _Tp>
391   struct __norm_min : __norm_min_impl<remove_cv_t<_Tp>> {};
392 
393 template <typename _Tp>
394   struct __quiet_NaN : __quiet_NaN_impl<remove_cv_t<_Tp>> {};
395 
396 template <typename _Tp>
397   struct __reciprocal_overflow_threshold
398   : __reciprocal_overflow_threshold_impl<remove_cv_t<_Tp>> {};
399 
400 template <typename _Tp>
401   struct __round_error : __round_error_impl<remove_cv_t<_Tp>> {};
402 
403 template <typename _Tp>
404   struct __signaling_NaN : __signaling_NaN_impl<remove_cv_t<_Tp>> {};
405 
406 template <typename _Tp>
407   inline constexpr auto __denorm_min_v = __denorm_min<_Tp>::value;
408 
409 template <typename _Tp>
410   inline constexpr auto __epsilon_v = __epsilon<_Tp>::value;
411 
412 template <typename _Tp>
413   inline constexpr auto __finite_max_v = __finite_max<_Tp>::value;
414 
415 template <typename _Tp>
416   inline constexpr auto __finite_min_v = __finite_min<_Tp>::value;
417 
418 template <typename _Tp>
419   inline constexpr auto __infinity_v = __infinity<_Tp>::value;
420 
421 template <typename _Tp>
422   inline constexpr auto __norm_min_v = __norm_min<_Tp>::value;
423 
424 template <typename _Tp>
425   inline constexpr auto __quiet_NaN_v = __quiet_NaN<_Tp>::value;
426 
427 template <typename _Tp>
428   inline constexpr auto __reciprocal_overflow_threshold_v
429     = __reciprocal_overflow_threshold<_Tp>::value;
430 
431 template <typename _Tp>
432   inline constexpr auto __round_error_v = __round_error<_Tp>::value;
433 
434 template <typename _Tp>
435   inline constexpr auto __signaling_NaN_v = __signaling_NaN<_Tp>::value;
436 
437 // [num.traits.char], numeric characteristics traits
438 template <typename _Tp>
439   struct __digits : __digits_impl<remove_cv_t<_Tp>> {};
440 
441 template <typename _Tp>
442   struct __digits10 : __digits10_impl<remove_cv_t<_Tp>> {};
443 
444 template <typename _Tp>
445   struct __max_digits10 : __max_digits10_impl<remove_cv_t<_Tp>> {};
446 
447 template <typename _Tp>
448   struct __max_exponent : __max_exponent_impl<remove_cv_t<_Tp>> {};
449 
450 template <typename _Tp>
451   struct __max_exponent10 : __max_exponent10_impl<remove_cv_t<_Tp>> {};
452 
453 template <typename _Tp>
454   struct __min_exponent : __min_exponent_impl<remove_cv_t<_Tp>> {};
455 
456 template <typename _Tp>
457   struct __min_exponent10 : __min_exponent10_impl<remove_cv_t<_Tp>> {};
458 
459 template <typename _Tp>
460   struct __radix : __radix_impl<remove_cv_t<_Tp>> {};
461 
462 template <typename _Tp>
463   inline constexpr auto __digits_v = __digits<_Tp>::value;
464 
465 template <typename _Tp>
466   inline constexpr auto __digits10_v = __digits10<_Tp>::value;
467 
468 template <typename _Tp>
469   inline constexpr auto __max_digits10_v = __max_digits10<_Tp>::value;
470 
471 template <typename _Tp>
472   inline constexpr auto __max_exponent_v = __max_exponent<_Tp>::value;
473 
474 template <typename _Tp>
475   inline constexpr auto __max_exponent10_v = __max_exponent10<_Tp>::value;
476 
477 template <typename _Tp>
478   inline constexpr auto __min_exponent_v = __min_exponent<_Tp>::value;
479 
480 template <typename _Tp>
481   inline constexpr auto __min_exponent10_v = __min_exponent10<_Tp>::value;
482 
483 template <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
488 template <typename _Tp>
489   struct __has_iec559_storage_format : true_type {};
490 
491 template <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  */
510 template <template <typename> class _Trait, typename _Tp>
511   struct __has_iec559_behavior : false_type {};
512 
513 template <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__
519 template <>
520   struct __has_iec559_behavior<__quiet_NaN, float> : true_type {};
521 #endif
522 
523 #if __DBL_HAS_QUIET_NAN__
524 template <>
525   struct __has_iec559_behavior<__quiet_NaN, double> : true_type {};
526 #endif
527 
528 #if __LDBL_HAS_QUIET_NAN__
529 template <>
530   struct __has_iec559_behavior<__quiet_NaN, long double> : true_type {};
531 #endif
532 
533 #if __FLT_HAS_INFINITY__
534 template <>
535   struct __has_iec559_behavior<__infinity, float> : true_type {};
536 #endif
537 
538 #if __DBL_HAS_INFINITY__
539 template <>
540   struct __has_iec559_behavior<__infinity, double> : true_type {};
541 #endif
542 
543 #if __LDBL_HAS_INFINITY__
544 template <>
545   struct __has_iec559_behavior<__infinity, long double> : true_type {};
546 #endif
547 
548 #ifdef __SUPPORT_SNAN__
549 #if __FLT_HAS_QUIET_NAN__
550 template <>
551   struct __has_iec559_behavior<__signaling_NaN, float> : true_type {};
552 #endif
553 
554 #if __DBL_HAS_QUIET_NAN__
555 template <>
556   struct __has_iec559_behavior<__signaling_NaN, double> : true_type {};
557 #endif
558 
559 #if __LDBL_HAS_QUIET_NAN__
560 template <>
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