1 // Class template uniform_int_distribution -*- C++ -*-
2
3 // Copyright (C) 2009-2023 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 /**
26 * @file bits/uniform_int_dist.h
27 * This is an internal header file, included by other library headers.
28 * Do not attempt to use it directly. @headername{random}
29 */
30
31 #ifndef _GLIBCXX_BITS_UNIFORM_INT_DIST_H
32 #define _GLIBCXX_BITS_UNIFORM_INT_DIST_H
33
34 #include <type_traits>
35 #include <ext/numeric_traits.h>
36 #if __cplusplus > 201703L
37 # include <concepts>
38 #endif
39 #include <bits/concept_check.h> // __glibcxx_function_requires
40
41 namespace std _GLIBCXX_VISIBILITY(default)
42 {
43 _GLIBCXX_BEGIN_NAMESPACE_VERSION
44
45 #ifdef __cpp_lib_concepts
46 /// Requirements for a uniform random bit generator.
47 /**
48 * @ingroup random_distributions_uniform
49 * @headerfile random
50 * @since C++20
51 */
52 template<typename _Gen>
53 concept uniform_random_bit_generator
54 = invocable<_Gen&> && unsigned_integral<invoke_result_t<_Gen&>>
55 && requires
56 {
57 { _Gen::min() } -> same_as<invoke_result_t<_Gen&>>;
58 { _Gen::max() } -> same_as<invoke_result_t<_Gen&>>;
59 requires bool_constant<(_Gen::min() < _Gen::max())>::value;
60 };
61 #endif
62
63 /// @cond undocumented
64 namespace __detail
65 {
66 // Determine whether number is a power of two.
67 // This is true for zero, which is OK because we want _Power_of_2(n+1)
68 // to be true if n==numeric_limits<_Tp>::max() and so n+1 wraps around.
69 template<typename _Tp>
70 constexpr bool
71 _Power_of_2(_Tp __x)
72 {
73 return ((__x - 1) & __x) == 0;
74 }
75 }
76 /// @endcond
77
78 /**
79 * @brief Uniform discrete distribution for random numbers.
80 * A discrete random distribution on the range @f$[min, max]@f$ with equal
81 * probability throughout the range.
82 *
83 * @ingroup random_distributions_uniform
84 * @headerfile random
85 * @since C++11
86 */
87 template<typename _IntType = int>
88 class uniform_int_distribution
89 {
90 static_assert(std::is_integral<_IntType>::value,
91 "template argument must be an integral type");
92
93 public:
94 /** The type of the range of the distribution. */
95 typedef _IntType result_type;
96 /** Parameter type. */
97 struct param_type
98 {
99 typedef uniform_int_distribution<_IntType> distribution_type;
100
101 param_type() : param_type(0) { }
102
103 explicit
104 param_type(_IntType __a,
105 _IntType __b = __gnu_cxx::__int_traits<_IntType>::__max)
106 : _M_a(__a), _M_b(__b)
107 {
108 __glibcxx_assert(_M_a <= _M_b);
109 }
110
111 result_type
112 a() const
113 { return _M_a; }
114
115 result_type
116 b() const
117 { return _M_b; }
118
119 friend bool
120 operator==(const param_type& __p1, const param_type& __p2)
121 { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }
122
123 friend bool
124 operator!=(const param_type& __p1, const param_type& __p2)
125 { return !(__p1 == __p2); }
126
127 private:
128 _IntType _M_a;
129 _IntType _M_b;
130 };
131
132 public:
133 /**
134 * @brief Constructs a uniform distribution object.
135 */
136 uniform_int_distribution() : uniform_int_distribution(0) { }
137
138 /**
139 * @brief Constructs a uniform distribution object.
140 */
141 explicit
142 uniform_int_distribution(_IntType __a,
143 _IntType __b
144 = __gnu_cxx::__int_traits<_IntType>::__max)
145 : _M_param(__a, __b)
146 { }
147
148 explicit
149 uniform_int_distribution(const param_type& __p)
150 : _M_param(__p)
151 { }
152
153 /**
154 * @brief Resets the distribution state.
155 *
156 * Does nothing for the uniform integer distribution.
157 */
158 void
159 reset() { }
160
161 result_type
162 a() const
163 { return _M_param.a(); }
164
165 result_type
166 b() const
167 { return _M_param.b(); }
168
169 /**
170 * @brief Returns the parameter set of the distribution.
171 */
172 param_type
173 param() const
174 { return _M_param; }
175
176 /**
177 * @brief Sets the parameter set of the distribution.
178 * @param __param The new parameter set of the distribution.
179 */
180 void
181 param(const param_type& __param)
182 { _M_param = __param; }
183
184 /**
185 * @brief Returns the inclusive lower bound of the distribution range.
186 */
187 result_type
188 min() const
189 { return this->a(); }
190
191 /**
192 * @brief Returns the inclusive upper bound of the distribution range.
193 */
194 result_type
195 max() const
196 { return this->b(); }
197
198 /**
199 * @brief Generating functions.
200 */
201 template<typename _UniformRandomBitGenerator>
202 result_type
203 operator()(_UniformRandomBitGenerator& __urng)
204 { return this->operator()(__urng, _M_param); }
205
206 template<typename _UniformRandomBitGenerator>
207 result_type
208 operator()(_UniformRandomBitGenerator& __urng,
209 const param_type& __p);
210
211 template<typename _ForwardIterator,
212 typename _UniformRandomBitGenerator>
213 void
214 __generate(_ForwardIterator __f, _ForwardIterator __t,
215 _UniformRandomBitGenerator& __urng)
216 { this->__generate(__f, __t, __urng, _M_param); }
217
218 template<typename _ForwardIterator,
219 typename _UniformRandomBitGenerator>
220 void
221 __generate(_ForwardIterator __f, _ForwardIterator __t,
222 _UniformRandomBitGenerator& __urng,
223 const param_type& __p)
224 { this->__generate_impl(__f, __t, __urng, __p); }
225
226 template<typename _UniformRandomBitGenerator>
227 void
228 __generate(result_type* __f, result_type* __t,
229 _UniformRandomBitGenerator& __urng,
230 const param_type& __p)
231 { this->__generate_impl(__f, __t, __urng, __p); }
232
233 /**
234 * @brief Return true if two uniform integer distributions have
235 * the same parameters.
236 */
237 friend bool
238 operator==(const uniform_int_distribution& __d1,
239 const uniform_int_distribution& __d2)
240 { return __d1._M_param == __d2._M_param; }
241
242 private:
243 template<typename _ForwardIterator,
244 typename _UniformRandomBitGenerator>
245 void
246 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
247 _UniformRandomBitGenerator& __urng,
248 const param_type& __p);
249
250 param_type _M_param;
251
252 // Lemire's nearly divisionless algorithm.
253 // Returns an unbiased random number from __g downscaled to [0,__range)
254 // using an unsigned type _Wp twice as wide as unsigned type _Up.
255 template<typename _Wp, typename _Urbg, typename _Up>
256 static _Up
257 _S_nd(_Urbg& __g, _Up __range)
258 {
259 using _Up_traits = __gnu_cxx::__int_traits<_Up>;
260 using _Wp_traits = __gnu_cxx::__int_traits<_Wp>;
261 static_assert(!_Up_traits::__is_signed, "U must be unsigned");
262 static_assert(!_Wp_traits::__is_signed, "W must be unsigned");
263 static_assert(_Wp_traits::__digits == (2 * _Up_traits::__digits),
264 "W must be twice as wide as U");
265
266 // reference: Fast Random Integer Generation in an Interval
267 // ACM Transactions on Modeling and Computer Simulation 29 (1), 2019
268 // https://arxiv.org/abs/1805.10941
269 _Wp __product = _Wp(__g()) * _Wp(__range);
270 _Up __low = _Up(__product);
271 if (__low < __range)
272 {
273 _Up __threshold = -__range % __range;
274 while (__low < __threshold)
275 {
276 __product = _Wp(__g()) * _Wp(__range);
277 __low = _Up(__product);
278 }
279 }
280 return __product >> _Up_traits::__digits;
281 }
282 };
283
284 template<typename _IntType>
285 template<typename _UniformRandomBitGenerator>
286 typename uniform_int_distribution<_IntType>::result_type
287 uniform_int_distribution<_IntType>::
288 operator()(_UniformRandomBitGenerator& __urng,
289 const param_type& __param)
290 {
291 typedef typename _UniformRandomBitGenerator::result_type _Gresult_type;
292 typedef typename make_unsigned<result_type>::type __utype;
293 typedef typename common_type<_Gresult_type, __utype>::type __uctype;
294
295 constexpr __uctype __urngmin = _UniformRandomBitGenerator::min();
296 constexpr __uctype __urngmax = _UniformRandomBitGenerator::max();
297 static_assert( __urngmin < __urngmax,
298 "Uniform random bit generator must define min() < max()");
299 constexpr __uctype __urngrange = __urngmax - __urngmin;
300
301 const __uctype __urange
302 = __uctype(__param.b()) - __uctype(__param.a());
303
304 __uctype __ret;
305 if (__urngrange > __urange)
306 {
307 // downscaling
308
309 const __uctype __uerange = __urange + 1; // __urange can be zero
310
311 #if defined __UINT64_TYPE__ && defined __UINT32_TYPE__
312 #if __SIZEOF_INT128__
313 if _GLIBCXX17_CONSTEXPR (__urngrange == __UINT64_MAX__)
314 {
315 // __urng produces values that use exactly 64-bits,
316 // so use 128-bit integers to downscale to desired range.
317 __UINT64_TYPE__ __u64erange = __uerange;
318 __ret = __extension__ _S_nd<unsigned __int128>(__urng,
319 __u64erange);
320 }
321 else
322 #endif
323 if _GLIBCXX17_CONSTEXPR (__urngrange == __UINT32_MAX__)
324 {
325 // __urng produces values that use exactly 32-bits,
326 // so use 64-bit integers to downscale to desired range.
327 __UINT32_TYPE__ __u32erange = __uerange;
328 __ret = _S_nd<__UINT64_TYPE__>(__urng, __u32erange);
329 }
330 else
331 #endif
332 {
333 // fallback case (2 divisions)
334 const __uctype __scaling = __urngrange / __uerange;
335 const __uctype __past = __uerange * __scaling;
336 do
337 __ret = __uctype(__urng()) - __urngmin;
338 while (__ret >= __past);
339 __ret /= __scaling;
340 }
341 }
342 else if (__urngrange < __urange)
343 {
344 // upscaling
345 /*
346 Note that every value in [0, urange]
347 can be written uniquely as
348
349 (urngrange + 1) * high + low
350
351 where
352
353 high in [0, urange / (urngrange + 1)]
354
355 and
356
357 low in [0, urngrange].
358 */
359 __uctype __tmp; // wraparound control
360 do
361 {
362 const __uctype __uerngrange = __urngrange + 1;
363 __tmp = (__uerngrange * operator()
364 (__urng, param_type(0, __urange / __uerngrange)));
365 __ret = __tmp + (__uctype(__urng()) - __urngmin);
366 }
367 while (__ret > __urange || __ret < __tmp);
368 }
369 else
370 __ret = __uctype(__urng()) - __urngmin;
371
372 return __ret + __param.a();
373 }
374
375
376 template<typename _IntType>
377 template<typename _ForwardIterator,
378 typename _UniformRandomBitGenerator>
379 void
380 uniform_int_distribution<_IntType>::
381 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
382 _UniformRandomBitGenerator& __urng,
383 const param_type& __param)
384 {
385 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
386 typedef typename _UniformRandomBitGenerator::result_type _Gresult_type;
387 typedef typename make_unsigned<result_type>::type __utype;
388 typedef typename common_type<_Gresult_type, __utype>::type __uctype;
389
390 static_assert( __urng.min() < __urng.max(),
391 "Uniform random bit generator must define min() < max()");
392
393 constexpr __uctype __urngmin = __urng.min();
394 constexpr __uctype __urngmax = __urng.max();
395 constexpr __uctype __urngrange = __urngmax - __urngmin;
396 const __uctype __urange
397 = __uctype(__param.b()) - __uctype(__param.a());
398
399 __uctype __ret;
400
401 if (__urngrange > __urange)
402 {
403 if (__detail::_Power_of_2(__urngrange + 1)
404 && __detail::_Power_of_2(__urange + 1))
405 {
406 while (__f != __t)
407 {
408 __ret = __uctype(__urng()) - __urngmin;
409 *__f++ = (__ret & __urange) + __param.a();
410 }
411 }
412 else
413 {
414 // downscaling
415 const __uctype __uerange = __urange + 1; // __urange can be zero
416 const __uctype __scaling = __urngrange / __uerange;
417 const __uctype __past = __uerange * __scaling;
418 while (__f != __t)
419 {
420 do
421 __ret = __uctype(__urng()) - __urngmin;
422 while (__ret >= __past);
423 *__f++ = __ret / __scaling + __param.a();
424 }
425 }
426 }
427 else if (__urngrange < __urange)
428 {
429 // upscaling
430 /*
431 Note that every value in [0, urange]
432 can be written uniquely as
433
434 (urngrange + 1) * high + low
435
436 where
437
438 high in [0, urange / (urngrange + 1)]
439
440 and
441
442 low in [0, urngrange].
443 */
444 __uctype __tmp; // wraparound control
445 while (__f != __t)
446 {
447 do
448 {
449 constexpr __uctype __uerngrange = __urngrange + 1;
450 __tmp = (__uerngrange * operator()
451 (__urng, param_type(0, __urange / __uerngrange)));
452 __ret = __tmp + (__uctype(__urng()) - __urngmin);
453 }
454 while (__ret > __urange || __ret < __tmp);
455 *__f++ = __ret;
456 }
457 }
458 else
459 while (__f != __t)
460 *__f++ = __uctype(__urng()) - __urngmin + __param.a();
461 }
462
463 // operator!= and operator<< and operator>> are defined in <bits/random.h>
464
465 _GLIBCXX_END_NAMESPACE_VERSION
466 } // namespace std
467
468 #endif