1 // random number generation (out of line) -*- C++ -*-
3 // Copyright (C) 2009-2020 Free Software Foundation, Inc.
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)
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.
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.
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/>.
25 /** @file bits/random.tcc
26 * This is an internal header file, included by other library headers.
27 * Do not attempt to use it directly. @headername{random}
33 #include <numeric> // std::accumulate and std::partial_sum
35 namespace std _GLIBCXX_VISIBILITY(default)
37 _GLIBCXX_BEGIN_NAMESPACE_VERSION
40 * (Further) implementation-space details.
44 // General case for x = (ax + c) mod m -- use Schrage's algorithm
45 // to avoid integer overflow.
47 // Preconditions: a > 0, m > 0.
49 // Note: only works correctly for __m % __a < __m / __a.
50 template<typename _Tp, _Tp __m, _Tp __a, _Tp __c>
52 _Mod<_Tp, __m, __a, __c, false, true>::
59 static const _Tp __q = __m / __a;
60 static const _Tp __r = __m % __a;
62 _Tp __t1 = __a * (__x % __q);
63 _Tp __t2 = __r * (__x / __q);
67 __x = __m - __t2 + __t1;
72 const _Tp __d = __m - __x;
81 template<typename _InputIterator, typename _OutputIterator,
84 __normalize(_InputIterator __first, _InputIterator __last,
85 _OutputIterator __result, const _Tp& __factor)
87 for (; __first != __last; ++__first, ++__result)
88 *__result = *__first / __factor;
92 } // namespace __detail
94 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
96 linear_congruential_engine<_UIntType, __a, __c, __m>::multiplier;
98 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
100 linear_congruential_engine<_UIntType, __a, __c, __m>::increment;
102 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
104 linear_congruential_engine<_UIntType, __a, __c, __m>::modulus;
106 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
108 linear_congruential_engine<_UIntType, __a, __c, __m>::default_seed;
111 * Seeds the LCR with integral value @p __s, adjusted so that the
112 * ring identity is never a member of the convergence set.
114 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
116 linear_congruential_engine<_UIntType, __a, __c, __m>::
117 seed(result_type __s)
119 if ((__detail::__mod<_UIntType, __m>(__c) == 0)
120 && (__detail::__mod<_UIntType, __m>(__s) == 0))
123 _M_x = __detail::__mod<_UIntType, __m>(__s);
127 * Seeds the LCR engine with a value generated by @p __q.
129 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
130 template<typename _Sseq>
132 linear_congruential_engine<_UIntType, __a, __c, __m>::
134 -> _If_seed_seq<_Sseq>
136 const _UIntType __k0 = __m == 0 ? std::numeric_limits<_UIntType>::digits
138 const _UIntType __k = (__k0 + 31) / 32;
139 uint_least32_t __arr[__k + 3];
140 __q.generate(__arr + 0, __arr + __k + 3);
141 _UIntType __factor = 1u;
142 _UIntType __sum = 0u;
143 for (size_t __j = 0; __j < __k; ++__j)
145 __sum += __arr[__j + 3] * __factor;
146 __factor *= __detail::_Shift<_UIntType, 32>::__value;
151 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
152 typename _CharT, typename _Traits>
153 std::basic_ostream<_CharT, _Traits>&
154 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
155 const linear_congruential_engine<_UIntType,
156 __a, __c, __m>& __lcr)
158 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
159 typedef typename __ostream_type::ios_base __ios_base;
161 const typename __ios_base::fmtflags __flags = __os.flags();
162 const _CharT __fill = __os.fill();
163 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
164 __os.fill(__os.widen(' '));
173 template<typename _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
174 typename _CharT, typename _Traits>
175 std::basic_istream<_CharT, _Traits>&
176 operator>>(std::basic_istream<_CharT, _Traits>& __is,
177 linear_congruential_engine<_UIntType, __a, __c, __m>& __lcr)
179 typedef std::basic_istream<_CharT, _Traits> __istream_type;
180 typedef typename __istream_type::ios_base __ios_base;
182 const typename __ios_base::fmtflags __flags = __is.flags();
183 __is.flags(__ios_base::dec);
192 template<typename _UIntType,
193 size_t __w, size_t __n, size_t __m, size_t __r,
194 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
195 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
198 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
199 __s, __b, __t, __c, __l, __f>::word_size;
201 template<typename _UIntType,
202 size_t __w, size_t __n, size_t __m, size_t __r,
203 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
204 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
207 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
208 __s, __b, __t, __c, __l, __f>::state_size;
210 template<typename _UIntType,
211 size_t __w, size_t __n, size_t __m, size_t __r,
212 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
213 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
216 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
217 __s, __b, __t, __c, __l, __f>::shift_size;
219 template<typename _UIntType,
220 size_t __w, size_t __n, size_t __m, size_t __r,
221 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
222 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
225 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
226 __s, __b, __t, __c, __l, __f>::mask_bits;
228 template<typename _UIntType,
229 size_t __w, size_t __n, size_t __m, size_t __r,
230 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
231 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
234 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
235 __s, __b, __t, __c, __l, __f>::xor_mask;
237 template<typename _UIntType,
238 size_t __w, size_t __n, size_t __m, size_t __r,
239 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
240 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
243 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
244 __s, __b, __t, __c, __l, __f>::tempering_u;
246 template<typename _UIntType,
247 size_t __w, size_t __n, size_t __m, size_t __r,
248 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
249 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
252 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
253 __s, __b, __t, __c, __l, __f>::tempering_d;
255 template<typename _UIntType,
256 size_t __w, size_t __n, size_t __m, size_t __r,
257 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
258 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
261 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
262 __s, __b, __t, __c, __l, __f>::tempering_s;
264 template<typename _UIntType,
265 size_t __w, size_t __n, size_t __m, size_t __r,
266 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
267 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
270 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
271 __s, __b, __t, __c, __l, __f>::tempering_b;
273 template<typename _UIntType,
274 size_t __w, size_t __n, size_t __m, size_t __r,
275 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
276 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
279 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
280 __s, __b, __t, __c, __l, __f>::tempering_t;
282 template<typename _UIntType,
283 size_t __w, size_t __n, size_t __m, size_t __r,
284 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
285 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
288 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
289 __s, __b, __t, __c, __l, __f>::tempering_c;
291 template<typename _UIntType,
292 size_t __w, size_t __n, size_t __m, size_t __r,
293 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
294 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
297 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
298 __s, __b, __t, __c, __l, __f>::tempering_l;
300 template<typename _UIntType,
301 size_t __w, size_t __n, size_t __m, size_t __r,
302 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
303 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
306 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
307 __s, __b, __t, __c, __l, __f>::
308 initialization_multiplier;
310 template<typename _UIntType,
311 size_t __w, size_t __n, size_t __m, size_t __r,
312 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
313 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
316 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
317 __s, __b, __t, __c, __l, __f>::default_seed;
319 template<typename _UIntType,
320 size_t __w, size_t __n, size_t __m, size_t __r,
321 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
322 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
325 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
326 __s, __b, __t, __c, __l, __f>::
327 seed(result_type __sd)
329 _M_x[0] = __detail::__mod<_UIntType,
330 __detail::_Shift<_UIntType, __w>::__value>(__sd);
332 for (size_t __i = 1; __i < state_size; ++__i)
334 _UIntType __x = _M_x[__i - 1];
335 __x ^= __x >> (__w - 2);
337 __x += __detail::__mod<_UIntType, __n>(__i);
338 _M_x[__i] = __detail::__mod<_UIntType,
339 __detail::_Shift<_UIntType, __w>::__value>(__x);
344 template<typename _UIntType,
345 size_t __w, size_t __n, size_t __m, size_t __r,
346 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
347 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
349 template<typename _Sseq>
351 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
352 __s, __b, __t, __c, __l, __f>::
354 -> _If_seed_seq<_Sseq>
356 const _UIntType __upper_mask = (~_UIntType()) << __r;
357 const size_t __k = (__w + 31) / 32;
358 uint_least32_t __arr[__n * __k];
359 __q.generate(__arr + 0, __arr + __n * __k);
362 for (size_t __i = 0; __i < state_size; ++__i)
364 _UIntType __factor = 1u;
365 _UIntType __sum = 0u;
366 for (size_t __j = 0; __j < __k; ++__j)
368 __sum += __arr[__k * __i + __j] * __factor;
369 __factor *= __detail::_Shift<_UIntType, 32>::__value;
371 _M_x[__i] = __detail::__mod<_UIntType,
372 __detail::_Shift<_UIntType, __w>::__value>(__sum);
378 if ((_M_x[0] & __upper_mask) != 0u)
381 else if (_M_x[__i] != 0u)
386 _M_x[0] = __detail::_Shift<_UIntType, __w - 1>::__value;
390 template<typename _UIntType, size_t __w,
391 size_t __n, size_t __m, size_t __r,
392 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
393 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
396 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
397 __s, __b, __t, __c, __l, __f>::
400 const _UIntType __upper_mask = (~_UIntType()) << __r;
401 const _UIntType __lower_mask = ~__upper_mask;
403 for (size_t __k = 0; __k < (__n - __m); ++__k)
405 _UIntType __y = ((_M_x[__k] & __upper_mask)
406 | (_M_x[__k + 1] & __lower_mask));
407 _M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1)
408 ^ ((__y & 0x01) ? __a : 0));
411 for (size_t __k = (__n - __m); __k < (__n - 1); ++__k)
413 _UIntType __y = ((_M_x[__k] & __upper_mask)
414 | (_M_x[__k + 1] & __lower_mask));
415 _M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1)
416 ^ ((__y & 0x01) ? __a : 0));
419 _UIntType __y = ((_M_x[__n - 1] & __upper_mask)
420 | (_M_x[0] & __lower_mask));
421 _M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1)
422 ^ ((__y & 0x01) ? __a : 0));
426 template<typename _UIntType, size_t __w,
427 size_t __n, size_t __m, size_t __r,
428 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
429 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
432 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
433 __s, __b, __t, __c, __l, __f>::
434 discard(unsigned long long __z)
436 while (__z > state_size - _M_p)
438 __z -= state_size - _M_p;
444 template<typename _UIntType, size_t __w,
445 size_t __n, size_t __m, size_t __r,
446 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
447 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
450 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
451 __s, __b, __t, __c, __l, __f>::result_type
452 mersenne_twister_engine<_UIntType, __w, __n, __m, __r, __a, __u, __d,
453 __s, __b, __t, __c, __l, __f>::
456 // Reload the vector - cost is O(n) amortized over n calls.
457 if (_M_p >= state_size)
460 // Calculate o(x(i)).
461 result_type __z = _M_x[_M_p++];
462 __z ^= (__z >> __u) & __d;
463 __z ^= (__z << __s) & __b;
464 __z ^= (__z << __t) & __c;
470 template<typename _UIntType, size_t __w,
471 size_t __n, size_t __m, size_t __r,
472 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
473 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
474 _UIntType __f, typename _CharT, typename _Traits>
475 std::basic_ostream<_CharT, _Traits>&
476 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
477 const mersenne_twister_engine<_UIntType, __w, __n, __m,
478 __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
480 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
481 typedef typename __ostream_type::ios_base __ios_base;
483 const typename __ios_base::fmtflags __flags = __os.flags();
484 const _CharT __fill = __os.fill();
485 const _CharT __space = __os.widen(' ');
486 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
489 for (size_t __i = 0; __i < __n; ++__i)
490 __os << __x._M_x[__i] << __space;
498 template<typename _UIntType, size_t __w,
499 size_t __n, size_t __m, size_t __r,
500 _UIntType __a, size_t __u, _UIntType __d, size_t __s,
501 _UIntType __b, size_t __t, _UIntType __c, size_t __l,
502 _UIntType __f, typename _CharT, typename _Traits>
503 std::basic_istream<_CharT, _Traits>&
504 operator>>(std::basic_istream<_CharT, _Traits>& __is,
505 mersenne_twister_engine<_UIntType, __w, __n, __m,
506 __r, __a, __u, __d, __s, __b, __t, __c, __l, __f>& __x)
508 typedef std::basic_istream<_CharT, _Traits> __istream_type;
509 typedef typename __istream_type::ios_base __ios_base;
511 const typename __ios_base::fmtflags __flags = __is.flags();
512 __is.flags(__ios_base::dec | __ios_base::skipws);
514 for (size_t __i = 0; __i < __n; ++__i)
515 __is >> __x._M_x[__i];
523 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
525 subtract_with_carry_engine<_UIntType, __w, __s, __r>::word_size;
527 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
529 subtract_with_carry_engine<_UIntType, __w, __s, __r>::short_lag;
531 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
533 subtract_with_carry_engine<_UIntType, __w, __s, __r>::long_lag;
535 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
537 subtract_with_carry_engine<_UIntType, __w, __s, __r>::default_seed;
539 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
541 subtract_with_carry_engine<_UIntType, __w, __s, __r>::
542 seed(result_type __value)
544 std::linear_congruential_engine<result_type, 40014u, 0u, 2147483563u>
545 __lcg(__value == 0u ? default_seed : __value);
547 const size_t __n = (__w + 31) / 32;
549 for (size_t __i = 0; __i < long_lag; ++__i)
551 _UIntType __sum = 0u;
552 _UIntType __factor = 1u;
553 for (size_t __j = 0; __j < __n; ++__j)
555 __sum += __detail::__mod<uint_least32_t,
556 __detail::_Shift<uint_least32_t, 32>::__value>
557 (__lcg()) * __factor;
558 __factor *= __detail::_Shift<_UIntType, 32>::__value;
560 _M_x[__i] = __detail::__mod<_UIntType,
561 __detail::_Shift<_UIntType, __w>::__value>(__sum);
563 _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
567 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
568 template<typename _Sseq>
570 subtract_with_carry_engine<_UIntType, __w, __s, __r>::
572 -> _If_seed_seq<_Sseq>
574 const size_t __k = (__w + 31) / 32;
575 uint_least32_t __arr[__r * __k];
576 __q.generate(__arr + 0, __arr + __r * __k);
578 for (size_t __i = 0; __i < long_lag; ++__i)
580 _UIntType __sum = 0u;
581 _UIntType __factor = 1u;
582 for (size_t __j = 0; __j < __k; ++__j)
584 __sum += __arr[__k * __i + __j] * __factor;
585 __factor *= __detail::_Shift<_UIntType, 32>::__value;
587 _M_x[__i] = __detail::__mod<_UIntType,
588 __detail::_Shift<_UIntType, __w>::__value>(__sum);
590 _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
594 template<typename _UIntType, size_t __w, size_t __s, size_t __r>
595 typename subtract_with_carry_engine<_UIntType, __w, __s, __r>::
597 subtract_with_carry_engine<_UIntType, __w, __s, __r>::
600 // Derive short lag index from current index.
601 long __ps = _M_p - short_lag;
605 // Calculate new x(i) without overflow or division.
606 // NB: Thanks to the requirements for _UIntType, _M_x[_M_p] + _M_carry
609 if (_M_x[__ps] >= _M_x[_M_p] + _M_carry)
611 __xi = _M_x[__ps] - _M_x[_M_p] - _M_carry;
616 __xi = (__detail::_Shift<_UIntType, __w>::__value
617 - _M_x[_M_p] - _M_carry + _M_x[__ps]);
622 // Adjust current index to loop around in ring buffer.
623 if (++_M_p >= long_lag)
629 template<typename _UIntType, size_t __w, size_t __s, size_t __r,
630 typename _CharT, typename _Traits>
631 std::basic_ostream<_CharT, _Traits>&
632 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
633 const subtract_with_carry_engine<_UIntType,
636 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
637 typedef typename __ostream_type::ios_base __ios_base;
639 const typename __ios_base::fmtflags __flags = __os.flags();
640 const _CharT __fill = __os.fill();
641 const _CharT __space = __os.widen(' ');
642 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
645 for (size_t __i = 0; __i < __r; ++__i)
646 __os << __x._M_x[__i] << __space;
647 __os << __x._M_carry << __space << __x._M_p;
654 template<typename _UIntType, size_t __w, size_t __s, size_t __r,
655 typename _CharT, typename _Traits>
656 std::basic_istream<_CharT, _Traits>&
657 operator>>(std::basic_istream<_CharT, _Traits>& __is,
658 subtract_with_carry_engine<_UIntType, __w, __s, __r>& __x)
660 typedef std::basic_ostream<_CharT, _Traits> __istream_type;
661 typedef typename __istream_type::ios_base __ios_base;
663 const typename __ios_base::fmtflags __flags = __is.flags();
664 __is.flags(__ios_base::dec | __ios_base::skipws);
666 for (size_t __i = 0; __i < __r; ++__i)
667 __is >> __x._M_x[__i];
668 __is >> __x._M_carry;
676 template<typename _RandomNumberEngine, size_t __p, size_t __r>
678 discard_block_engine<_RandomNumberEngine, __p, __r>::block_size;
680 template<typename _RandomNumberEngine, size_t __p, size_t __r>
682 discard_block_engine<_RandomNumberEngine, __p, __r>::used_block;
684 template<typename _RandomNumberEngine, size_t __p, size_t __r>
685 typename discard_block_engine<_RandomNumberEngine,
686 __p, __r>::result_type
687 discard_block_engine<_RandomNumberEngine, __p, __r>::
690 if (_M_n >= used_block)
692 _M_b.discard(block_size - _M_n);
699 template<typename _RandomNumberEngine, size_t __p, size_t __r,
700 typename _CharT, typename _Traits>
701 std::basic_ostream<_CharT, _Traits>&
702 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
703 const discard_block_engine<_RandomNumberEngine,
706 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
707 typedef typename __ostream_type::ios_base __ios_base;
709 const typename __ios_base::fmtflags __flags = __os.flags();
710 const _CharT __fill = __os.fill();
711 const _CharT __space = __os.widen(' ');
712 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
715 __os << __x.base() << __space << __x._M_n;
722 template<typename _RandomNumberEngine, size_t __p, size_t __r,
723 typename _CharT, typename _Traits>
724 std::basic_istream<_CharT, _Traits>&
725 operator>>(std::basic_istream<_CharT, _Traits>& __is,
726 discard_block_engine<_RandomNumberEngine, __p, __r>& __x)
728 typedef std::basic_istream<_CharT, _Traits> __istream_type;
729 typedef typename __istream_type::ios_base __ios_base;
731 const typename __ios_base::fmtflags __flags = __is.flags();
732 __is.flags(__ios_base::dec | __ios_base::skipws);
734 __is >> __x._M_b >> __x._M_n;
741 template<typename _RandomNumberEngine, size_t __w, typename _UIntType>
742 typename independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
744 independent_bits_engine<_RandomNumberEngine, __w, _UIntType>::
747 typedef typename _RandomNumberEngine::result_type _Eresult_type;
748 const _Eresult_type __r
749 = (_M_b.max() - _M_b.min() < std::numeric_limits<_Eresult_type>::max()
750 ? _M_b.max() - _M_b.min() + 1 : 0);
751 const unsigned __edig = std::numeric_limits<_Eresult_type>::digits;
752 const unsigned __m = __r ? std::__lg(__r) : __edig;
754 typedef typename std::common_type<_Eresult_type, result_type>::type
756 const unsigned __cdig = std::numeric_limits<__ctype>::digits;
759 __ctype __s0, __s1, __y0, __y1;
761 for (size_t __i = 0; __i < 2; ++__i)
763 __n = (__w + __m - 1) / __m + __i;
764 __n0 = __n - __w % __n;
765 const unsigned __w0 = __w / __n; // __w0 <= __m
771 __s0 = __ctype(1) << __w0;
779 __y0 = __s0 * (__r / __s0);
781 __y1 = __s1 * (__r / __s1);
783 if (__r - __y0 <= __y0 / __n)
790 result_type __sum = 0;
791 for (size_t __k = 0; __k < __n0; ++__k)
795 __u = _M_b() - _M_b.min();
796 while (__y0 && __u >= __y0);
797 __sum = __s0 * __sum + (__s0 ? __u % __s0 : __u);
799 for (size_t __k = __n0; __k < __n; ++__k)
803 __u = _M_b() - _M_b.min();
804 while (__y1 && __u >= __y1);
805 __sum = __s1 * __sum + (__s1 ? __u % __s1 : __u);
811 template<typename _RandomNumberEngine, size_t __k>
813 shuffle_order_engine<_RandomNumberEngine, __k>::table_size;
815 template<typename _RandomNumberEngine, size_t __k>
816 typename shuffle_order_engine<_RandomNumberEngine, __k>::result_type
817 shuffle_order_engine<_RandomNumberEngine, __k>::
820 size_t __j = __k * ((_M_y - _M_b.min())
821 / (_M_b.max() - _M_b.min() + 1.0L));
828 template<typename _RandomNumberEngine, size_t __k,
829 typename _CharT, typename _Traits>
830 std::basic_ostream<_CharT, _Traits>&
831 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
832 const shuffle_order_engine<_RandomNumberEngine, __k>& __x)
834 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
835 typedef typename __ostream_type::ios_base __ios_base;
837 const typename __ios_base::fmtflags __flags = __os.flags();
838 const _CharT __fill = __os.fill();
839 const _CharT __space = __os.widen(' ');
840 __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
844 for (size_t __i = 0; __i < __k; ++__i)
845 __os << __space << __x._M_v[__i];
846 __os << __space << __x._M_y;
853 template<typename _RandomNumberEngine, size_t __k,
854 typename _CharT, typename _Traits>
855 std::basic_istream<_CharT, _Traits>&
856 operator>>(std::basic_istream<_CharT, _Traits>& __is,
857 shuffle_order_engine<_RandomNumberEngine, __k>& __x)
859 typedef std::basic_istream<_CharT, _Traits> __istream_type;
860 typedef typename __istream_type::ios_base __ios_base;
862 const typename __ios_base::fmtflags __flags = __is.flags();
863 __is.flags(__ios_base::dec | __ios_base::skipws);
866 for (size_t __i = 0; __i < __k; ++__i)
867 __is >> __x._M_v[__i];
875 template<typename _IntType, typename _CharT, typename _Traits>
876 std::basic_ostream<_CharT, _Traits>&
877 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
878 const uniform_int_distribution<_IntType>& __x)
880 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
881 typedef typename __ostream_type::ios_base __ios_base;
883 const typename __ios_base::fmtflags __flags = __os.flags();
884 const _CharT __fill = __os.fill();
885 const _CharT __space = __os.widen(' ');
886 __os.flags(__ios_base::scientific | __ios_base::left);
889 __os << __x.a() << __space << __x.b();
896 template<typename _IntType, typename _CharT, typename _Traits>
897 std::basic_istream<_CharT, _Traits>&
898 operator>>(std::basic_istream<_CharT, _Traits>& __is,
899 uniform_int_distribution<_IntType>& __x)
901 typedef std::basic_istream<_CharT, _Traits> __istream_type;
902 typedef typename __istream_type::ios_base __ios_base;
904 const typename __ios_base::fmtflags __flags = __is.flags();
905 __is.flags(__ios_base::dec | __ios_base::skipws);
909 __x.param(typename uniform_int_distribution<_IntType>::
910 param_type(__a, __b));
917 template<typename _RealType>
918 template<typename _ForwardIterator,
919 typename _UniformRandomNumberGenerator>
921 uniform_real_distribution<_RealType>::
922 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
923 _UniformRandomNumberGenerator& __urng,
924 const param_type& __p)
926 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
927 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
929 auto __range = __p.b() - __p.a();
931 *__f++ = __aurng() * __range + __p.a();
934 template<typename _RealType, typename _CharT, typename _Traits>
935 std::basic_ostream<_CharT, _Traits>&
936 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
937 const uniform_real_distribution<_RealType>& __x)
939 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
940 typedef typename __ostream_type::ios_base __ios_base;
942 const typename __ios_base::fmtflags __flags = __os.flags();
943 const _CharT __fill = __os.fill();
944 const std::streamsize __precision = __os.precision();
945 const _CharT __space = __os.widen(' ');
946 __os.flags(__ios_base::scientific | __ios_base::left);
948 __os.precision(std::numeric_limits<_RealType>::max_digits10);
950 __os << __x.a() << __space << __x.b();
954 __os.precision(__precision);
958 template<typename _RealType, typename _CharT, typename _Traits>
959 std::basic_istream<_CharT, _Traits>&
960 operator>>(std::basic_istream<_CharT, _Traits>& __is,
961 uniform_real_distribution<_RealType>& __x)
963 typedef std::basic_istream<_CharT, _Traits> __istream_type;
964 typedef typename __istream_type::ios_base __ios_base;
966 const typename __ios_base::fmtflags __flags = __is.flags();
967 __is.flags(__ios_base::skipws);
971 __x.param(typename uniform_real_distribution<_RealType>::
972 param_type(__a, __b));
979 template<typename _ForwardIterator,
980 typename _UniformRandomNumberGenerator>
982 std::bernoulli_distribution::
983 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
984 _UniformRandomNumberGenerator& __urng,
985 const param_type& __p)
987 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
988 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
990 auto __limit = __p.p() * (__aurng.max() - __aurng.min());
993 *__f++ = (__aurng() - __aurng.min()) < __limit;
996 template<typename _CharT, typename _Traits>
997 std::basic_ostream<_CharT, _Traits>&
998 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
999 const bernoulli_distribution& __x)
1001 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
1002 typedef typename __ostream_type::ios_base __ios_base;
1004 const typename __ios_base::fmtflags __flags = __os.flags();
1005 const _CharT __fill = __os.fill();
1006 const std::streamsize __precision = __os.precision();
1007 __os.flags(__ios_base::scientific | __ios_base::left);
1008 __os.fill(__os.widen(' '));
1009 __os.precision(std::numeric_limits<double>::max_digits10);
1013 __os.flags(__flags);
1015 __os.precision(__precision);
1020 template<typename _IntType>
1021 template<typename _UniformRandomNumberGenerator>
1022 typename geometric_distribution<_IntType>::result_type
1023 geometric_distribution<_IntType>::
1024 operator()(_UniformRandomNumberGenerator& __urng,
1025 const param_type& __param)
1027 // About the epsilon thing see this thread:
1028 // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
1029 const double __naf =
1030 (1 - std::numeric_limits<double>::epsilon()) / 2;
1031 // The largest _RealType convertible to _IntType.
1032 const double __thr =
1033 std::numeric_limits<_IntType>::max() + __naf;
1034 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1039 __cand = std::floor(std::log(1.0 - __aurng()) / __param._M_log_1_p);
1040 while (__cand >= __thr);
1042 return result_type(__cand + __naf);
1045 template<typename _IntType>
1046 template<typename _ForwardIterator,
1047 typename _UniformRandomNumberGenerator>
1049 geometric_distribution<_IntType>::
1050 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1051 _UniformRandomNumberGenerator& __urng,
1052 const param_type& __param)
1054 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1055 // About the epsilon thing see this thread:
1056 // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
1057 const double __naf =
1058 (1 - std::numeric_limits<double>::epsilon()) / 2;
1059 // The largest _RealType convertible to _IntType.
1060 const double __thr =
1061 std::numeric_limits<_IntType>::max() + __naf;
1062 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1069 __cand = std::floor(std::log(1.0 - __aurng())
1070 / __param._M_log_1_p);
1071 while (__cand >= __thr);
1073 *__f++ = __cand + __naf;
1077 template<typename _IntType,
1078 typename _CharT, typename _Traits>
1079 std::basic_ostream<_CharT, _Traits>&
1080 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1081 const geometric_distribution<_IntType>& __x)
1083 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
1084 typedef typename __ostream_type::ios_base __ios_base;
1086 const typename __ios_base::fmtflags __flags = __os.flags();
1087 const _CharT __fill = __os.fill();
1088 const std::streamsize __precision = __os.precision();
1089 __os.flags(__ios_base::scientific | __ios_base::left);
1090 __os.fill(__os.widen(' '));
1091 __os.precision(std::numeric_limits<double>::max_digits10);
1095 __os.flags(__flags);
1097 __os.precision(__precision);
1101 template<typename _IntType,
1102 typename _CharT, typename _Traits>
1103 std::basic_istream<_CharT, _Traits>&
1104 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1105 geometric_distribution<_IntType>& __x)
1107 typedef std::basic_istream<_CharT, _Traits> __istream_type;
1108 typedef typename __istream_type::ios_base __ios_base;
1110 const typename __ios_base::fmtflags __flags = __is.flags();
1111 __is.flags(__ios_base::skipws);
1115 __x.param(typename geometric_distribution<_IntType>::param_type(__p));
1117 __is.flags(__flags);
1121 // This is Leger's algorithm, also in Devroye, Ch. X, Example 1.5.
1122 template<typename _IntType>
1123 template<typename _UniformRandomNumberGenerator>
1124 typename negative_binomial_distribution<_IntType>::result_type
1125 negative_binomial_distribution<_IntType>::
1126 operator()(_UniformRandomNumberGenerator& __urng)
1128 const double __y = _M_gd(__urng);
1130 // XXX Is the constructor too slow?
1131 std::poisson_distribution<result_type> __poisson(__y);
1132 return __poisson(__urng);
1135 template<typename _IntType>
1136 template<typename _UniformRandomNumberGenerator>
1137 typename negative_binomial_distribution<_IntType>::result_type
1138 negative_binomial_distribution<_IntType>::
1139 operator()(_UniformRandomNumberGenerator& __urng,
1140 const param_type& __p)
1142 typedef typename std::gamma_distribution<double>::param_type
1146 _M_gd(__urng, param_type(__p.k(), (1.0 - __p.p()) / __p.p()));
1148 std::poisson_distribution<result_type> __poisson(__y);
1149 return __poisson(__urng);
1152 template<typename _IntType>
1153 template<typename _ForwardIterator,
1154 typename _UniformRandomNumberGenerator>
1156 negative_binomial_distribution<_IntType>::
1157 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1158 _UniformRandomNumberGenerator& __urng)
1160 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1163 const double __y = _M_gd(__urng);
1165 // XXX Is the constructor too slow?
1166 std::poisson_distribution<result_type> __poisson(__y);
1167 *__f++ = __poisson(__urng);
1171 template<typename _IntType>
1172 template<typename _ForwardIterator,
1173 typename _UniformRandomNumberGenerator>
1175 negative_binomial_distribution<_IntType>::
1176 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1177 _UniformRandomNumberGenerator& __urng,
1178 const param_type& __p)
1180 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1181 typename std::gamma_distribution<result_type>::param_type
1182 __p2(__p.k(), (1.0 - __p.p()) / __p.p());
1186 const double __y = _M_gd(__urng, __p2);
1188 std::poisson_distribution<result_type> __poisson(__y);
1189 *__f++ = __poisson(__urng);
1193 template<typename _IntType, typename _CharT, typename _Traits>
1194 std::basic_ostream<_CharT, _Traits>&
1195 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1196 const negative_binomial_distribution<_IntType>& __x)
1198 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
1199 typedef typename __ostream_type::ios_base __ios_base;
1201 const typename __ios_base::fmtflags __flags = __os.flags();
1202 const _CharT __fill = __os.fill();
1203 const std::streamsize __precision = __os.precision();
1204 const _CharT __space = __os.widen(' ');
1205 __os.flags(__ios_base::scientific | __ios_base::left);
1206 __os.fill(__os.widen(' '));
1207 __os.precision(std::numeric_limits<double>::max_digits10);
1209 __os << __x.k() << __space << __x.p()
1210 << __space << __x._M_gd;
1212 __os.flags(__flags);
1214 __os.precision(__precision);
1218 template<typename _IntType, typename _CharT, typename _Traits>
1219 std::basic_istream<_CharT, _Traits>&
1220 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1221 negative_binomial_distribution<_IntType>& __x)
1223 typedef std::basic_istream<_CharT, _Traits> __istream_type;
1224 typedef typename __istream_type::ios_base __ios_base;
1226 const typename __ios_base::fmtflags __flags = __is.flags();
1227 __is.flags(__ios_base::skipws);
1231 __is >> __k >> __p >> __x._M_gd;
1232 __x.param(typename negative_binomial_distribution<_IntType>::
1233 param_type(__k, __p));
1235 __is.flags(__flags);
1240 template<typename _IntType>
1242 poisson_distribution<_IntType>::param_type::
1245 #if _GLIBCXX_USE_C99_MATH_TR1
1248 const double __m = std::floor(_M_mean);
1249 _M_lm_thr = std::log(_M_mean);
1250 _M_lfm = std::lgamma(__m + 1);
1251 _M_sm = std::sqrt(__m);
1253 const double __pi_4 = 0.7853981633974483096156608458198757L;
1254 const double __dx = std::sqrt(2 * __m * std::log(32 * __m
1256 _M_d = std::round(std::max<double>(6.0, std::min(__m, __dx)));
1257 const double __cx = 2 * __m + _M_d;
1258 _M_scx = std::sqrt(__cx / 2);
1261 _M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx);
1262 _M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2))
1267 _M_lm_thr = std::exp(-_M_mean);
1271 * A rejection algorithm when mean >= 12 and a simple method based
1272 * upon the multiplication of uniform random variates otherwise.
1273 * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1277 * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1278 * New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).
1280 template<typename _IntType>
1281 template<typename _UniformRandomNumberGenerator>
1282 typename poisson_distribution<_IntType>::result_type
1283 poisson_distribution<_IntType>::
1284 operator()(_UniformRandomNumberGenerator& __urng,
1285 const param_type& __param)
1287 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1289 #if _GLIBCXX_USE_C99_MATH_TR1
1290 if (__param.mean() >= 12)
1294 // See comments above...
1295 const double __naf =
1296 (1 - std::numeric_limits<double>::epsilon()) / 2;
1297 const double __thr =
1298 std::numeric_limits<_IntType>::max() + __naf;
1300 const double __m = std::floor(__param.mean());
1302 const double __spi_2 = 1.2533141373155002512078826424055226L;
1303 const double __c1 = __param._M_sm * __spi_2;
1304 const double __c2 = __param._M_c2b + __c1;
1305 const double __c3 = __c2 + 1;
1306 const double __c4 = __c3 + 1;
1308 const double __178 = 0.0128205128205128205128205128205128L;
1310 const double __e178 = 1.0129030479320018583185514777512983L;
1311 const double __c5 = __c4 + __e178;
1312 const double __c = __param._M_cb + __c5;
1313 const double __2cx = 2 * (2 * __m + __param._M_d);
1315 bool __reject = true;
1318 const double __u = __c * __aurng();
1319 const double __e = -std::log(1.0 - __aurng());
1325 const double __n = _M_nd(__urng);
1326 const double __y = -std::abs(__n) * __param._M_sm - 1;
1327 __x = std::floor(__y);
1328 __w = -__n * __n / 2;
1332 else if (__u <= __c2)
1334 const double __n = _M_nd(__urng);
1335 const double __y = 1 + std::abs(__n) * __param._M_scx;
1336 __x = std::ceil(__y);
1337 __w = __y * (2 - __y) * __param._M_1cx;
1338 if (__x > __param._M_d)
1341 else if (__u <= __c3)
1342 // NB: This case not in the book, nor in the Errata,
1343 // but should be ok...
1345 else if (__u <= __c4)
1347 else if (__u <= __c5)
1350 // Only in the Errata, see libstdc++/83237.
1355 const double __v = -std::log(1.0 - __aurng());
1356 const double __y = __param._M_d
1357 + __v * __2cx / __param._M_d;
1358 __x = std::ceil(__y);
1359 __w = -__param._M_d * __param._M_1cx * (1 + __y / 2);
1362 __reject = (__w - __e - __x * __param._M_lm_thr
1363 > __param._M_lfm - std::lgamma(__x + __m + 1));
1365 __reject |= __x + __m >= __thr;
1369 return result_type(__x + __m + __naf);
1375 double __prod = 1.0;
1379 __prod *= __aurng();
1382 while (__prod > __param._M_lm_thr);
1388 template<typename _IntType>
1389 template<typename _ForwardIterator,
1390 typename _UniformRandomNumberGenerator>
1392 poisson_distribution<_IntType>::
1393 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1394 _UniformRandomNumberGenerator& __urng,
1395 const param_type& __param)
1397 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1398 // We could duplicate everything from operator()...
1400 *__f++ = this->operator()(__urng, __param);
1403 template<typename _IntType,
1404 typename _CharT, typename _Traits>
1405 std::basic_ostream<_CharT, _Traits>&
1406 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1407 const poisson_distribution<_IntType>& __x)
1409 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
1410 typedef typename __ostream_type::ios_base __ios_base;
1412 const typename __ios_base::fmtflags __flags = __os.flags();
1413 const _CharT __fill = __os.fill();
1414 const std::streamsize __precision = __os.precision();
1415 const _CharT __space = __os.widen(' ');
1416 __os.flags(__ios_base::scientific | __ios_base::left);
1418 __os.precision(std::numeric_limits<double>::max_digits10);
1420 __os << __x.mean() << __space << __x._M_nd;
1422 __os.flags(__flags);
1424 __os.precision(__precision);
1428 template<typename _IntType,
1429 typename _CharT, typename _Traits>
1430 std::basic_istream<_CharT, _Traits>&
1431 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1432 poisson_distribution<_IntType>& __x)
1434 typedef std::basic_istream<_CharT, _Traits> __istream_type;
1435 typedef typename __istream_type::ios_base __ios_base;
1437 const typename __ios_base::fmtflags __flags = __is.flags();
1438 __is.flags(__ios_base::skipws);
1441 __is >> __mean >> __x._M_nd;
1442 __x.param(typename poisson_distribution<_IntType>::param_type(__mean));
1444 __is.flags(__flags);
1449 template<typename _IntType>
1451 binomial_distribution<_IntType>::param_type::
1454 const double __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
1458 #if _GLIBCXX_USE_C99_MATH_TR1
1459 if (_M_t * __p12 >= 8)
1462 const double __np = std::floor(_M_t * __p12);
1463 const double __pa = __np / _M_t;
1464 const double __1p = 1 - __pa;
1466 const double __pi_4 = 0.7853981633974483096156608458198757L;
1467 const double __d1x =
1468 std::sqrt(__np * __1p * std::log(32 * __np
1469 / (81 * __pi_4 * __1p)));
1470 _M_d1 = std::round(std::max<double>(1.0, __d1x));
1471 const double __d2x =
1472 std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
1473 / (__pi_4 * __pa)));
1474 _M_d2 = std::round(std::max<double>(1.0, __d2x));
1477 const double __spi_2 = 1.2533141373155002512078826424055226L;
1478 _M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np));
1479 _M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * _M_t * __1p));
1480 _M_c = 2 * _M_d1 / __np;
1481 _M_a1 = std::exp(_M_c) * _M_s1 * __spi_2;
1482 const double __a12 = _M_a1 + _M_s2 * __spi_2;
1483 const double __s1s = _M_s1 * _M_s1;
1484 _M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p))
1486 * std::exp(-_M_d1 * _M_d1 / (2 * __s1s)));
1487 const double __s2s = _M_s2 * _M_s2;
1488 _M_s = (_M_a123 + 2 * __s2s / _M_d2
1489 * std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
1490 _M_lf = (std::lgamma(__np + 1)
1491 + std::lgamma(_M_t - __np + 1));
1492 _M_lp1p = std::log(__pa / __1p);
1494 _M_q = -std::log(1 - (__p12 - __pa) / __1p);
1498 _M_q = -std::log(1 - __p12);
1501 template<typename _IntType>
1502 template<typename _UniformRandomNumberGenerator>
1503 typename binomial_distribution<_IntType>::result_type
1504 binomial_distribution<_IntType>::
1505 _M_waiting(_UniformRandomNumberGenerator& __urng,
1506 _IntType __t, double __q)
1510 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1517 const double __e = -std::log(1.0 - __aurng());
1518 __sum += __e / (__t - __x);
1521 while (__sum <= __q);
1527 * A rejection algorithm when t * p >= 8 and a simple waiting time
1528 * method - the second in the referenced book - otherwise.
1529 * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1533 * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1534 * New York, 1986, Ch. X, Sect. 4 (+ Errata!).
1536 template<typename _IntType>
1537 template<typename _UniformRandomNumberGenerator>
1538 typename binomial_distribution<_IntType>::result_type
1539 binomial_distribution<_IntType>::
1540 operator()(_UniformRandomNumberGenerator& __urng,
1541 const param_type& __param)
1544 const _IntType __t = __param.t();
1545 const double __p = __param.p();
1546 const double __p12 = __p <= 0.5 ? __p : 1.0 - __p;
1547 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
1550 #if _GLIBCXX_USE_C99_MATH_TR1
1551 if (!__param._M_easy)
1555 // See comments above...
1556 const double __naf =
1557 (1 - std::numeric_limits<double>::epsilon()) / 2;
1558 const double __thr =
1559 std::numeric_limits<_IntType>::max() + __naf;
1561 const double __np = std::floor(__t * __p12);
1564 const double __spi_2 = 1.2533141373155002512078826424055226L;
1565 const double __a1 = __param._M_a1;
1566 const double __a12 = __a1 + __param._M_s2 * __spi_2;
1567 const double __a123 = __param._M_a123;
1568 const double __s1s = __param._M_s1 * __param._M_s1;
1569 const double __s2s = __param._M_s2 * __param._M_s2;
1574 const double __u = __param._M_s * __aurng();
1580 const double __n = _M_nd(__urng);
1581 const double __y = __param._M_s1 * std::abs(__n);
1582 __reject = __y >= __param._M_d1;
1585 const double __e = -std::log(1.0 - __aurng());
1586 __x = std::floor(__y);
1587 __v = -__e - __n * __n / 2 + __param._M_c;
1590 else if (__u <= __a12)
1592 const double __n = _M_nd(__urng);
1593 const double __y = __param._M_s2 * std::abs(__n);
1594 __reject = __y >= __param._M_d2;
1597 const double __e = -std::log(1.0 - __aurng());
1598 __x = std::floor(-__y);
1599 __v = -__e - __n * __n / 2;
1602 else if (__u <= __a123)
1604 const double __e1 = -std::log(1.0 - __aurng());
1605 const double __e2 = -std::log(1.0 - __aurng());
1607 const double __y = __param._M_d1
1608 + 2 * __s1s * __e1 / __param._M_d1;
1609 __x = std::floor(__y);
1610 __v = (-__e2 + __param._M_d1 * (1 / (__t - __np)
1611 -__y / (2 * __s1s)));
1616 const double __e1 = -std::log(1.0 - __aurng());
1617 const double __e2 = -std::log(1.0 - __aurng());
1619 const double __y = __param._M_d2
1620 + 2 * __s2s * __e1 / __param._M_d2;
1621 __x = std::floor(-__y);
1622 __v = -__e2 - __param._M_d2 * __y / (2 * __s2s);
1626 __reject = __reject || __x < -__np || __x > __t - __np;
1629 const double __lfx =
1630 std::lgamma(__np + __x + 1)
1631 + std::lgamma(__t - (__np + __x) + 1);
1632 __reject = __v > __param._M_lf - __lfx
1633 + __x * __param._M_lp1p;
1636 __reject |= __x + __np >= __thr;
1640 __x += __np + __naf;
1642 const _IntType __z = _M_waiting(__urng, __t - _IntType(__x),
1644 __ret = _IntType(__x) + __z;
1648 __ret = _M_waiting(__urng, __t, __param._M_q);
1651 __ret = __t - __ret;
1655 template<typename _IntType>
1656 template<typename _ForwardIterator,
1657 typename _UniformRandomNumberGenerator>
1659 binomial_distribution<_IntType>::
1660 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1661 _UniformRandomNumberGenerator& __urng,
1662 const param_type& __param)
1664 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1665 // We could duplicate everything from operator()...
1667 *__f++ = this->operator()(__urng, __param);
1670 template<typename _IntType,
1671 typename _CharT, typename _Traits>
1672 std::basic_ostream<_CharT, _Traits>&
1673 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1674 const binomial_distribution<_IntType>& __x)
1676 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
1677 typedef typename __ostream_type::ios_base __ios_base;
1679 const typename __ios_base::fmtflags __flags = __os.flags();
1680 const _CharT __fill = __os.fill();
1681 const std::streamsize __precision = __os.precision();
1682 const _CharT __space = __os.widen(' ');
1683 __os.flags(__ios_base::scientific | __ios_base::left);
1685 __os.precision(std::numeric_limits<double>::max_digits10);
1687 __os << __x.t() << __space << __x.p()
1688 << __space << __x._M_nd;
1690 __os.flags(__flags);
1692 __os.precision(__precision);
1696 template<typename _IntType,
1697 typename _CharT, typename _Traits>
1698 std::basic_istream<_CharT, _Traits>&
1699 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1700 binomial_distribution<_IntType>& __x)
1702 typedef std::basic_istream<_CharT, _Traits> __istream_type;
1703 typedef typename __istream_type::ios_base __ios_base;
1705 const typename __ios_base::fmtflags __flags = __is.flags();
1706 __is.flags(__ios_base::dec | __ios_base::skipws);
1710 __is >> __t >> __p >> __x._M_nd;
1711 __x.param(typename binomial_distribution<_IntType>::
1712 param_type(__t, __p));
1714 __is.flags(__flags);
1719 template<typename _RealType>
1720 template<typename _ForwardIterator,
1721 typename _UniformRandomNumberGenerator>
1723 std::exponential_distribution<_RealType>::
1724 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1725 _UniformRandomNumberGenerator& __urng,
1726 const param_type& __p)
1728 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1729 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1732 *__f++ = -std::log(result_type(1) - __aurng()) / __p.lambda();
1735 template<typename _RealType, typename _CharT, typename _Traits>
1736 std::basic_ostream<_CharT, _Traits>&
1737 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1738 const exponential_distribution<_RealType>& __x)
1740 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
1741 typedef typename __ostream_type::ios_base __ios_base;
1743 const typename __ios_base::fmtflags __flags = __os.flags();
1744 const _CharT __fill = __os.fill();
1745 const std::streamsize __precision = __os.precision();
1746 __os.flags(__ios_base::scientific | __ios_base::left);
1747 __os.fill(__os.widen(' '));
1748 __os.precision(std::numeric_limits<_RealType>::max_digits10);
1750 __os << __x.lambda();
1752 __os.flags(__flags);
1754 __os.precision(__precision);
1758 template<typename _RealType, typename _CharT, typename _Traits>
1759 std::basic_istream<_CharT, _Traits>&
1760 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1761 exponential_distribution<_RealType>& __x)
1763 typedef std::basic_istream<_CharT, _Traits> __istream_type;
1764 typedef typename __istream_type::ios_base __ios_base;
1766 const typename __ios_base::fmtflags __flags = __is.flags();
1767 __is.flags(__ios_base::dec | __ios_base::skipws);
1771 __x.param(typename exponential_distribution<_RealType>::
1772 param_type(__lambda));
1774 __is.flags(__flags);
1780 * Polar method due to Marsaglia.
1782 * Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag,
1783 * New York, 1986, Ch. V, Sect. 4.4.
1785 template<typename _RealType>
1786 template<typename _UniformRandomNumberGenerator>
1787 typename normal_distribution<_RealType>::result_type
1788 normal_distribution<_RealType>::
1789 operator()(_UniformRandomNumberGenerator& __urng,
1790 const param_type& __param)
1793 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1796 if (_M_saved_available)
1798 _M_saved_available = false;
1803 result_type __x, __y, __r2;
1806 __x = result_type(2.0) * __aurng() - 1.0;
1807 __y = result_type(2.0) * __aurng() - 1.0;
1808 __r2 = __x * __x + __y * __y;
1810 while (__r2 > 1.0 || __r2 == 0.0);
1812 const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1813 _M_saved = __x * __mult;
1814 _M_saved_available = true;
1815 __ret = __y * __mult;
1818 __ret = __ret * __param.stddev() + __param.mean();
1822 template<typename _RealType>
1823 template<typename _ForwardIterator,
1824 typename _UniformRandomNumberGenerator>
1826 normal_distribution<_RealType>::
1827 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1828 _UniformRandomNumberGenerator& __urng,
1829 const param_type& __param)
1831 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1836 if (_M_saved_available)
1838 _M_saved_available = false;
1839 *__f++ = _M_saved * __param.stddev() + __param.mean();
1845 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
1848 while (__f + 1 < __t)
1850 result_type __x, __y, __r2;
1853 __x = result_type(2.0) * __aurng() - 1.0;
1854 __y = result_type(2.0) * __aurng() - 1.0;
1855 __r2 = __x * __x + __y * __y;
1857 while (__r2 > 1.0 || __r2 == 0.0);
1859 const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1860 *__f++ = __y * __mult * __param.stddev() + __param.mean();
1861 *__f++ = __x * __mult * __param.stddev() + __param.mean();
1866 result_type __x, __y, __r2;
1869 __x = result_type(2.0) * __aurng() - 1.0;
1870 __y = result_type(2.0) * __aurng() - 1.0;
1871 __r2 = __x * __x + __y * __y;
1873 while (__r2 > 1.0 || __r2 == 0.0);
1875 const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1876 _M_saved = __x * __mult;
1877 _M_saved_available = true;
1878 *__f = __y * __mult * __param.stddev() + __param.mean();
1882 template<typename _RealType>
1884 operator==(const std::normal_distribution<_RealType>& __d1,
1885 const std::normal_distribution<_RealType>& __d2)
1887 if (__d1._M_param == __d2._M_param
1888 && __d1._M_saved_available == __d2._M_saved_available)
1890 if (__d1._M_saved_available
1891 && __d1._M_saved == __d2._M_saved)
1893 else if(!__d1._M_saved_available)
1902 template<typename _RealType, typename _CharT, typename _Traits>
1903 std::basic_ostream<_CharT, _Traits>&
1904 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1905 const normal_distribution<_RealType>& __x)
1907 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
1908 typedef typename __ostream_type::ios_base __ios_base;
1910 const typename __ios_base::fmtflags __flags = __os.flags();
1911 const _CharT __fill = __os.fill();
1912 const std::streamsize __precision = __os.precision();
1913 const _CharT __space = __os.widen(' ');
1914 __os.flags(__ios_base::scientific | __ios_base::left);
1916 __os.precision(std::numeric_limits<_RealType>::max_digits10);
1918 __os << __x.mean() << __space << __x.stddev()
1919 << __space << __x._M_saved_available;
1920 if (__x._M_saved_available)
1921 __os << __space << __x._M_saved;
1923 __os.flags(__flags);
1925 __os.precision(__precision);
1929 template<typename _RealType, typename _CharT, typename _Traits>
1930 std::basic_istream<_CharT, _Traits>&
1931 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1932 normal_distribution<_RealType>& __x)
1934 typedef std::basic_istream<_CharT, _Traits> __istream_type;
1935 typedef typename __istream_type::ios_base __ios_base;
1937 const typename __ios_base::fmtflags __flags = __is.flags();
1938 __is.flags(__ios_base::dec | __ios_base::skipws);
1940 double __mean, __stddev;
1941 __is >> __mean >> __stddev
1942 >> __x._M_saved_available;
1943 if (__x._M_saved_available)
1944 __is >> __x._M_saved;
1945 __x.param(typename normal_distribution<_RealType>::
1946 param_type(__mean, __stddev));
1948 __is.flags(__flags);
1953 template<typename _RealType>
1954 template<typename _ForwardIterator,
1955 typename _UniformRandomNumberGenerator>
1957 lognormal_distribution<_RealType>::
1958 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
1959 _UniformRandomNumberGenerator& __urng,
1960 const param_type& __p)
1962 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
1964 *__f++ = std::exp(__p.s() * _M_nd(__urng) + __p.m());
1967 template<typename _RealType, typename _CharT, typename _Traits>
1968 std::basic_ostream<_CharT, _Traits>&
1969 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1970 const lognormal_distribution<_RealType>& __x)
1972 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
1973 typedef typename __ostream_type::ios_base __ios_base;
1975 const typename __ios_base::fmtflags __flags = __os.flags();
1976 const _CharT __fill = __os.fill();
1977 const std::streamsize __precision = __os.precision();
1978 const _CharT __space = __os.widen(' ');
1979 __os.flags(__ios_base::scientific | __ios_base::left);
1981 __os.precision(std::numeric_limits<_RealType>::max_digits10);
1983 __os << __x.m() << __space << __x.s()
1984 << __space << __x._M_nd;
1986 __os.flags(__flags);
1988 __os.precision(__precision);
1992 template<typename _RealType, typename _CharT, typename _Traits>
1993 std::basic_istream<_CharT, _Traits>&
1994 operator>>(std::basic_istream<_CharT, _Traits>& __is,
1995 lognormal_distribution<_RealType>& __x)
1997 typedef std::basic_istream<_CharT, _Traits> __istream_type;
1998 typedef typename __istream_type::ios_base __ios_base;
2000 const typename __ios_base::fmtflags __flags = __is.flags();
2001 __is.flags(__ios_base::dec | __ios_base::skipws);
2004 __is >> __m >> __s >> __x._M_nd;
2005 __x.param(typename lognormal_distribution<_RealType>::
2006 param_type(__m, __s));
2008 __is.flags(__flags);
2012 template<typename _RealType>
2013 template<typename _ForwardIterator,
2014 typename _UniformRandomNumberGenerator>
2016 std::chi_squared_distribution<_RealType>::
2017 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2018 _UniformRandomNumberGenerator& __urng)
2020 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2022 *__f++ = 2 * _M_gd(__urng);
2025 template<typename _RealType>
2026 template<typename _ForwardIterator,
2027 typename _UniformRandomNumberGenerator>
2029 std::chi_squared_distribution<_RealType>::
2030 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2031 _UniformRandomNumberGenerator& __urng,
2033 std::gamma_distribution<result_type>::param_type& __p)
2035 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2037 *__f++ = 2 * _M_gd(__urng, __p);
2040 template<typename _RealType, typename _CharT, typename _Traits>
2041 std::basic_ostream<_CharT, _Traits>&
2042 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2043 const chi_squared_distribution<_RealType>& __x)
2045 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2046 typedef typename __ostream_type::ios_base __ios_base;
2048 const typename __ios_base::fmtflags __flags = __os.flags();
2049 const _CharT __fill = __os.fill();
2050 const std::streamsize __precision = __os.precision();
2051 const _CharT __space = __os.widen(' ');
2052 __os.flags(__ios_base::scientific | __ios_base::left);
2054 __os.precision(std::numeric_limits<_RealType>::max_digits10);
2056 __os << __x.n() << __space << __x._M_gd;
2058 __os.flags(__flags);
2060 __os.precision(__precision);
2064 template<typename _RealType, typename _CharT, typename _Traits>
2065 std::basic_istream<_CharT, _Traits>&
2066 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2067 chi_squared_distribution<_RealType>& __x)
2069 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2070 typedef typename __istream_type::ios_base __ios_base;
2072 const typename __ios_base::fmtflags __flags = __is.flags();
2073 __is.flags(__ios_base::dec | __ios_base::skipws);
2076 __is >> __n >> __x._M_gd;
2077 __x.param(typename chi_squared_distribution<_RealType>::
2080 __is.flags(__flags);
2085 template<typename _RealType>
2086 template<typename _UniformRandomNumberGenerator>
2087 typename cauchy_distribution<_RealType>::result_type
2088 cauchy_distribution<_RealType>::
2089 operator()(_UniformRandomNumberGenerator& __urng,
2090 const param_type& __p)
2092 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2099 const _RealType __pi = 3.1415926535897932384626433832795029L;
2100 return __p.a() + __p.b() * std::tan(__pi * __u);
2103 template<typename _RealType>
2104 template<typename _ForwardIterator,
2105 typename _UniformRandomNumberGenerator>
2107 cauchy_distribution<_RealType>::
2108 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2109 _UniformRandomNumberGenerator& __urng,
2110 const param_type& __p)
2112 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2113 const _RealType __pi = 3.1415926535897932384626433832795029L;
2114 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2123 *__f++ = __p.a() + __p.b() * std::tan(__pi * __u);
2127 template<typename _RealType, typename _CharT, typename _Traits>
2128 std::basic_ostream<_CharT, _Traits>&
2129 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2130 const cauchy_distribution<_RealType>& __x)
2132 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2133 typedef typename __ostream_type::ios_base __ios_base;
2135 const typename __ios_base::fmtflags __flags = __os.flags();
2136 const _CharT __fill = __os.fill();
2137 const std::streamsize __precision = __os.precision();
2138 const _CharT __space = __os.widen(' ');
2139 __os.flags(__ios_base::scientific | __ios_base::left);
2141 __os.precision(std::numeric_limits<_RealType>::max_digits10);
2143 __os << __x.a() << __space << __x.b();
2145 __os.flags(__flags);
2147 __os.precision(__precision);
2151 template<typename _RealType, typename _CharT, typename _Traits>
2152 std::basic_istream<_CharT, _Traits>&
2153 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2154 cauchy_distribution<_RealType>& __x)
2156 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2157 typedef typename __istream_type::ios_base __ios_base;
2159 const typename __ios_base::fmtflags __flags = __is.flags();
2160 __is.flags(__ios_base::dec | __ios_base::skipws);
2164 __x.param(typename cauchy_distribution<_RealType>::
2165 param_type(__a, __b));
2167 __is.flags(__flags);
2172 template<typename _RealType>
2173 template<typename _ForwardIterator,
2174 typename _UniformRandomNumberGenerator>
2176 std::fisher_f_distribution<_RealType>::
2177 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2178 _UniformRandomNumberGenerator& __urng)
2180 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2182 *__f++ = ((_M_gd_x(__urng) * n()) / (_M_gd_y(__urng) * m()));
2185 template<typename _RealType>
2186 template<typename _ForwardIterator,
2187 typename _UniformRandomNumberGenerator>
2189 std::fisher_f_distribution<_RealType>::
2190 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2191 _UniformRandomNumberGenerator& __urng,
2192 const param_type& __p)
2194 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2195 typedef typename std::gamma_distribution<result_type>::param_type
2197 param_type __p1(__p.m() / 2);
2198 param_type __p2(__p.n() / 2);
2200 *__f++ = ((_M_gd_x(__urng, __p1) * n())
2201 / (_M_gd_y(__urng, __p2) * m()));
2204 template<typename _RealType, typename _CharT, typename _Traits>
2205 std::basic_ostream<_CharT, _Traits>&
2206 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2207 const fisher_f_distribution<_RealType>& __x)
2209 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2210 typedef typename __ostream_type::ios_base __ios_base;
2212 const typename __ios_base::fmtflags __flags = __os.flags();
2213 const _CharT __fill = __os.fill();
2214 const std::streamsize __precision = __os.precision();
2215 const _CharT __space = __os.widen(' ');
2216 __os.flags(__ios_base::scientific | __ios_base::left);
2218 __os.precision(std::numeric_limits<_RealType>::max_digits10);
2220 __os << __x.m() << __space << __x.n()
2221 << __space << __x._M_gd_x << __space << __x._M_gd_y;
2223 __os.flags(__flags);
2225 __os.precision(__precision);
2229 template<typename _RealType, typename _CharT, typename _Traits>
2230 std::basic_istream<_CharT, _Traits>&
2231 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2232 fisher_f_distribution<_RealType>& __x)
2234 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2235 typedef typename __istream_type::ios_base __ios_base;
2237 const typename __ios_base::fmtflags __flags = __is.flags();
2238 __is.flags(__ios_base::dec | __ios_base::skipws);
2241 __is >> __m >> __n >> __x._M_gd_x >> __x._M_gd_y;
2242 __x.param(typename fisher_f_distribution<_RealType>::
2243 param_type(__m, __n));
2245 __is.flags(__flags);
2250 template<typename _RealType>
2251 template<typename _ForwardIterator,
2252 typename _UniformRandomNumberGenerator>
2254 std::student_t_distribution<_RealType>::
2255 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2256 _UniformRandomNumberGenerator& __urng)
2258 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2260 *__f++ = _M_nd(__urng) * std::sqrt(n() / _M_gd(__urng));
2263 template<typename _RealType>
2264 template<typename _ForwardIterator,
2265 typename _UniformRandomNumberGenerator>
2267 std::student_t_distribution<_RealType>::
2268 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2269 _UniformRandomNumberGenerator& __urng,
2270 const param_type& __p)
2272 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2273 typename std::gamma_distribution<result_type>::param_type
2274 __p2(__p.n() / 2, 2);
2276 *__f++ = _M_nd(__urng) * std::sqrt(__p.n() / _M_gd(__urng, __p2));
2279 template<typename _RealType, typename _CharT, typename _Traits>
2280 std::basic_ostream<_CharT, _Traits>&
2281 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2282 const student_t_distribution<_RealType>& __x)
2284 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2285 typedef typename __ostream_type::ios_base __ios_base;
2287 const typename __ios_base::fmtflags __flags = __os.flags();
2288 const _CharT __fill = __os.fill();
2289 const std::streamsize __precision = __os.precision();
2290 const _CharT __space = __os.widen(' ');
2291 __os.flags(__ios_base::scientific | __ios_base::left);
2293 __os.precision(std::numeric_limits<_RealType>::max_digits10);
2295 __os << __x.n() << __space << __x._M_nd << __space << __x._M_gd;
2297 __os.flags(__flags);
2299 __os.precision(__precision);
2303 template<typename _RealType, typename _CharT, typename _Traits>
2304 std::basic_istream<_CharT, _Traits>&
2305 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2306 student_t_distribution<_RealType>& __x)
2308 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2309 typedef typename __istream_type::ios_base __ios_base;
2311 const typename __ios_base::fmtflags __flags = __is.flags();
2312 __is.flags(__ios_base::dec | __ios_base::skipws);
2315 __is >> __n >> __x._M_nd >> __x._M_gd;
2316 __x.param(typename student_t_distribution<_RealType>::param_type(__n));
2318 __is.flags(__flags);
2323 template<typename _RealType>
2325 gamma_distribution<_RealType>::param_type::
2328 _M_malpha = _M_alpha < 1.0 ? _M_alpha + _RealType(1.0) : _M_alpha;
2330 const _RealType __a1 = _M_malpha - _RealType(1.0) / _RealType(3.0);
2331 _M_a2 = _RealType(1.0) / std::sqrt(_RealType(9.0) * __a1);
2335 * Marsaglia, G. and Tsang, W. W.
2336 * "A Simple Method for Generating Gamma Variables"
2337 * ACM Transactions on Mathematical Software, 26, 3, 363-372, 2000.
2339 template<typename _RealType>
2340 template<typename _UniformRandomNumberGenerator>
2341 typename gamma_distribution<_RealType>::result_type
2342 gamma_distribution<_RealType>::
2343 operator()(_UniformRandomNumberGenerator& __urng,
2344 const param_type& __param)
2346 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2349 result_type __u, __v, __n;
2350 const result_type __a1 = (__param._M_malpha
2351 - _RealType(1.0) / _RealType(3.0));
2357 __n = _M_nd(__urng);
2358 __v = result_type(1.0) + __param._M_a2 * __n;
2362 __v = __v * __v * __v;
2365 while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2366 && (std::log(__u) > (0.5 * __n * __n + __a1
2367 * (1.0 - __v + std::log(__v)))));
2369 if (__param.alpha() == __param._M_malpha)
2370 return __a1 * __v * __param.beta();
2377 return (std::pow(__u, result_type(1.0) / __param.alpha())
2378 * __a1 * __v * __param.beta());
2382 template<typename _RealType>
2383 template<typename _ForwardIterator,
2384 typename _UniformRandomNumberGenerator>
2386 gamma_distribution<_RealType>::
2387 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2388 _UniformRandomNumberGenerator& __urng,
2389 const param_type& __param)
2391 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2392 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2395 result_type __u, __v, __n;
2396 const result_type __a1 = (__param._M_malpha
2397 - _RealType(1.0) / _RealType(3.0));
2399 if (__param.alpha() == __param._M_malpha)
2406 __n = _M_nd(__urng);
2407 __v = result_type(1.0) + __param._M_a2 * __n;
2411 __v = __v * __v * __v;
2414 while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2415 && (std::log(__u) > (0.5 * __n * __n + __a1
2416 * (1.0 - __v + std::log(__v)))));
2418 *__f++ = __a1 * __v * __param.beta();
2427 __n = _M_nd(__urng);
2428 __v = result_type(1.0) + __param._M_a2 * __n;
2432 __v = __v * __v * __v;
2435 while (__u > result_type(1.0) - 0.0331 * __n * __n * __n * __n
2436 && (std::log(__u) > (0.5 * __n * __n + __a1
2437 * (1.0 - __v + std::log(__v)))));
2443 *__f++ = (std::pow(__u, result_type(1.0) / __param.alpha())
2444 * __a1 * __v * __param.beta());
2448 template<typename _RealType, typename _CharT, typename _Traits>
2449 std::basic_ostream<_CharT, _Traits>&
2450 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2451 const gamma_distribution<_RealType>& __x)
2453 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2454 typedef typename __ostream_type::ios_base __ios_base;
2456 const typename __ios_base::fmtflags __flags = __os.flags();
2457 const _CharT __fill = __os.fill();
2458 const std::streamsize __precision = __os.precision();
2459 const _CharT __space = __os.widen(' ');
2460 __os.flags(__ios_base::scientific | __ios_base::left);
2462 __os.precision(std::numeric_limits<_RealType>::max_digits10);
2464 __os << __x.alpha() << __space << __x.beta()
2465 << __space << __x._M_nd;
2467 __os.flags(__flags);
2469 __os.precision(__precision);
2473 template<typename _RealType, typename _CharT, typename _Traits>
2474 std::basic_istream<_CharT, _Traits>&
2475 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2476 gamma_distribution<_RealType>& __x)
2478 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2479 typedef typename __istream_type::ios_base __ios_base;
2481 const typename __ios_base::fmtflags __flags = __is.flags();
2482 __is.flags(__ios_base::dec | __ios_base::skipws);
2484 _RealType __alpha_val, __beta_val;
2485 __is >> __alpha_val >> __beta_val >> __x._M_nd;
2486 __x.param(typename gamma_distribution<_RealType>::
2487 param_type(__alpha_val, __beta_val));
2489 __is.flags(__flags);
2494 template<typename _RealType>
2495 template<typename _UniformRandomNumberGenerator>
2496 typename weibull_distribution<_RealType>::result_type
2497 weibull_distribution<_RealType>::
2498 operator()(_UniformRandomNumberGenerator& __urng,
2499 const param_type& __p)
2501 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2503 return __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
2504 result_type(1) / __p.a());
2507 template<typename _RealType>
2508 template<typename _ForwardIterator,
2509 typename _UniformRandomNumberGenerator>
2511 weibull_distribution<_RealType>::
2512 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2513 _UniformRandomNumberGenerator& __urng,
2514 const param_type& __p)
2516 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2517 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2519 auto __inv_a = result_type(1) / __p.a();
2522 *__f++ = __p.b() * std::pow(-std::log(result_type(1) - __aurng()),
2526 template<typename _RealType, typename _CharT, typename _Traits>
2527 std::basic_ostream<_CharT, _Traits>&
2528 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2529 const weibull_distribution<_RealType>& __x)
2531 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2532 typedef typename __ostream_type::ios_base __ios_base;
2534 const typename __ios_base::fmtflags __flags = __os.flags();
2535 const _CharT __fill = __os.fill();
2536 const std::streamsize __precision = __os.precision();
2537 const _CharT __space = __os.widen(' ');
2538 __os.flags(__ios_base::scientific | __ios_base::left);
2540 __os.precision(std::numeric_limits<_RealType>::max_digits10);
2542 __os << __x.a() << __space << __x.b();
2544 __os.flags(__flags);
2546 __os.precision(__precision);
2550 template<typename _RealType, typename _CharT, typename _Traits>
2551 std::basic_istream<_CharT, _Traits>&
2552 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2553 weibull_distribution<_RealType>& __x)
2555 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2556 typedef typename __istream_type::ios_base __ios_base;
2558 const typename __ios_base::fmtflags __flags = __is.flags();
2559 __is.flags(__ios_base::dec | __ios_base::skipws);
2563 __x.param(typename weibull_distribution<_RealType>::
2564 param_type(__a, __b));
2566 __is.flags(__flags);
2571 template<typename _RealType>
2572 template<typename _UniformRandomNumberGenerator>
2573 typename extreme_value_distribution<_RealType>::result_type
2574 extreme_value_distribution<_RealType>::
2575 operator()(_UniformRandomNumberGenerator& __urng,
2576 const param_type& __p)
2578 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2580 return __p.a() - __p.b() * std::log(-std::log(result_type(1)
2584 template<typename _RealType>
2585 template<typename _ForwardIterator,
2586 typename _UniformRandomNumberGenerator>
2588 extreme_value_distribution<_RealType>::
2589 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2590 _UniformRandomNumberGenerator& __urng,
2591 const param_type& __p)
2593 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2594 __detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
2598 *__f++ = __p.a() - __p.b() * std::log(-std::log(result_type(1)
2602 template<typename _RealType, typename _CharT, typename _Traits>
2603 std::basic_ostream<_CharT, _Traits>&
2604 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2605 const extreme_value_distribution<_RealType>& __x)
2607 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2608 typedef typename __ostream_type::ios_base __ios_base;
2610 const typename __ios_base::fmtflags __flags = __os.flags();
2611 const _CharT __fill = __os.fill();
2612 const std::streamsize __precision = __os.precision();
2613 const _CharT __space = __os.widen(' ');
2614 __os.flags(__ios_base::scientific | __ios_base::left);
2616 __os.precision(std::numeric_limits<_RealType>::max_digits10);
2618 __os << __x.a() << __space << __x.b();
2620 __os.flags(__flags);
2622 __os.precision(__precision);
2626 template<typename _RealType, typename _CharT, typename _Traits>
2627 std::basic_istream<_CharT, _Traits>&
2628 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2629 extreme_value_distribution<_RealType>& __x)
2631 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2632 typedef typename __istream_type::ios_base __ios_base;
2634 const typename __ios_base::fmtflags __flags = __is.flags();
2635 __is.flags(__ios_base::dec | __ios_base::skipws);
2639 __x.param(typename extreme_value_distribution<_RealType>::
2640 param_type(__a, __b));
2642 __is.flags(__flags);
2647 template<typename _IntType>
2649 discrete_distribution<_IntType>::param_type::
2652 if (_M_prob.size() < 2)
2658 const double __sum = std::accumulate(_M_prob.begin(),
2659 _M_prob.end(), 0.0);
2660 // Now normalize the probabilites.
2661 __detail::__normalize(_M_prob.begin(), _M_prob.end(), _M_prob.begin(),
2663 // Accumulate partial sums.
2664 _M_cp.reserve(_M_prob.size());
2665 std::partial_sum(_M_prob.begin(), _M_prob.end(),
2666 std::back_inserter(_M_cp));
2667 // Make sure the last cumulative probability is one.
2668 _M_cp[_M_cp.size() - 1] = 1.0;
2671 template<typename _IntType>
2672 template<typename _Func>
2673 discrete_distribution<_IntType>::param_type::
2674 param_type(size_t __nw, double __xmin, double __xmax, _Func __fw)
2675 : _M_prob(), _M_cp()
2677 const size_t __n = __nw == 0 ? 1 : __nw;
2678 const double __delta = (__xmax - __xmin) / __n;
2680 _M_prob.reserve(__n);
2681 for (size_t __k = 0; __k < __nw; ++__k)
2682 _M_prob.push_back(__fw(__xmin + __k * __delta + 0.5 * __delta));
2687 template<typename _IntType>
2688 template<typename _UniformRandomNumberGenerator>
2689 typename discrete_distribution<_IntType>::result_type
2690 discrete_distribution<_IntType>::
2691 operator()(_UniformRandomNumberGenerator& __urng,
2692 const param_type& __param)
2694 if (__param._M_cp.empty())
2695 return result_type(0);
2697 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2700 const double __p = __aurng();
2701 auto __pos = std::lower_bound(__param._M_cp.begin(),
2702 __param._M_cp.end(), __p);
2704 return __pos - __param._M_cp.begin();
2707 template<typename _IntType>
2708 template<typename _ForwardIterator,
2709 typename _UniformRandomNumberGenerator>
2711 discrete_distribution<_IntType>::
2712 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2713 _UniformRandomNumberGenerator& __urng,
2714 const param_type& __param)
2716 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2718 if (__param._M_cp.empty())
2721 *__f++ = result_type(0);
2725 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2730 const double __p = __aurng();
2731 auto __pos = std::lower_bound(__param._M_cp.begin(),
2732 __param._M_cp.end(), __p);
2734 *__f++ = __pos - __param._M_cp.begin();
2738 template<typename _IntType, typename _CharT, typename _Traits>
2739 std::basic_ostream<_CharT, _Traits>&
2740 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2741 const discrete_distribution<_IntType>& __x)
2743 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2744 typedef typename __ostream_type::ios_base __ios_base;
2746 const typename __ios_base::fmtflags __flags = __os.flags();
2747 const _CharT __fill = __os.fill();
2748 const std::streamsize __precision = __os.precision();
2749 const _CharT __space = __os.widen(' ');
2750 __os.flags(__ios_base::scientific | __ios_base::left);
2752 __os.precision(std::numeric_limits<double>::max_digits10);
2754 std::vector<double> __prob = __x.probabilities();
2755 __os << __prob.size();
2756 for (auto __dit = __prob.begin(); __dit != __prob.end(); ++__dit)
2757 __os << __space << *__dit;
2759 __os.flags(__flags);
2761 __os.precision(__precision);
2765 template<typename _IntType, typename _CharT, typename _Traits>
2766 std::basic_istream<_CharT, _Traits>&
2767 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2768 discrete_distribution<_IntType>& __x)
2770 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2771 typedef typename __istream_type::ios_base __ios_base;
2773 const typename __ios_base::fmtflags __flags = __is.flags();
2774 __is.flags(__ios_base::dec | __ios_base::skipws);
2779 std::vector<double> __prob_vec;
2780 __prob_vec.reserve(__n);
2781 for (; __n != 0; --__n)
2785 __prob_vec.push_back(__prob);
2788 __x.param(typename discrete_distribution<_IntType>::
2789 param_type(__prob_vec.begin(), __prob_vec.end()));
2791 __is.flags(__flags);
2796 template<typename _RealType>
2798 piecewise_constant_distribution<_RealType>::param_type::
2801 if (_M_int.size() < 2
2802 || (_M_int.size() == 2
2803 && _M_int[0] == _RealType(0)
2804 && _M_int[1] == _RealType(1)))
2811 const double __sum = std::accumulate(_M_den.begin(),
2814 __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
2817 _M_cp.reserve(_M_den.size());
2818 std::partial_sum(_M_den.begin(), _M_den.end(),
2819 std::back_inserter(_M_cp));
2821 // Make sure the last cumulative probability is one.
2822 _M_cp[_M_cp.size() - 1] = 1.0;
2824 for (size_t __k = 0; __k < _M_den.size(); ++__k)
2825 _M_den[__k] /= _M_int[__k + 1] - _M_int[__k];
2828 template<typename _RealType>
2829 template<typename _InputIteratorB, typename _InputIteratorW>
2830 piecewise_constant_distribution<_RealType>::param_type::
2831 param_type(_InputIteratorB __bbegin,
2832 _InputIteratorB __bend,
2833 _InputIteratorW __wbegin)
2834 : _M_int(), _M_den(), _M_cp()
2836 if (__bbegin != __bend)
2840 _M_int.push_back(*__bbegin);
2842 if (__bbegin == __bend)
2845 _M_den.push_back(*__wbegin);
2853 template<typename _RealType>
2854 template<typename _Func>
2855 piecewise_constant_distribution<_RealType>::param_type::
2856 param_type(initializer_list<_RealType> __bl, _Func __fw)
2857 : _M_int(), _M_den(), _M_cp()
2859 _M_int.reserve(__bl.size());
2860 for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
2861 _M_int.push_back(*__biter);
2863 _M_den.reserve(_M_int.size() - 1);
2864 for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
2865 _M_den.push_back(__fw(0.5 * (_M_int[__k + 1] + _M_int[__k])));
2870 template<typename _RealType>
2871 template<typename _Func>
2872 piecewise_constant_distribution<_RealType>::param_type::
2873 param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
2874 : _M_int(), _M_den(), _M_cp()
2876 const size_t __n = __nw == 0 ? 1 : __nw;
2877 const _RealType __delta = (__xmax - __xmin) / __n;
2879 _M_int.reserve(__n + 1);
2880 for (size_t __k = 0; __k <= __nw; ++__k)
2881 _M_int.push_back(__xmin + __k * __delta);
2883 _M_den.reserve(__n);
2884 for (size_t __k = 0; __k < __nw; ++__k)
2885 _M_den.push_back(__fw(_M_int[__k] + 0.5 * __delta));
2890 template<typename _RealType>
2891 template<typename _UniformRandomNumberGenerator>
2892 typename piecewise_constant_distribution<_RealType>::result_type
2893 piecewise_constant_distribution<_RealType>::
2894 operator()(_UniformRandomNumberGenerator& __urng,
2895 const param_type& __param)
2897 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2900 const double __p = __aurng();
2901 if (__param._M_cp.empty())
2904 auto __pos = std::lower_bound(__param._M_cp.begin(),
2905 __param._M_cp.end(), __p);
2906 const size_t __i = __pos - __param._M_cp.begin();
2908 const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
2910 return __param._M_int[__i] + (__p - __pref) / __param._M_den[__i];
2913 template<typename _RealType>
2914 template<typename _ForwardIterator,
2915 typename _UniformRandomNumberGenerator>
2917 piecewise_constant_distribution<_RealType>::
2918 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
2919 _UniformRandomNumberGenerator& __urng,
2920 const param_type& __param)
2922 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
2923 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
2926 if (__param._M_cp.empty())
2935 const double __p = __aurng();
2937 auto __pos = std::lower_bound(__param._M_cp.begin(),
2938 __param._M_cp.end(), __p);
2939 const size_t __i = __pos - __param._M_cp.begin();
2941 const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
2943 *__f++ = (__param._M_int[__i]
2944 + (__p - __pref) / __param._M_den[__i]);
2948 template<typename _RealType, typename _CharT, typename _Traits>
2949 std::basic_ostream<_CharT, _Traits>&
2950 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
2951 const piecewise_constant_distribution<_RealType>& __x)
2953 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
2954 typedef typename __ostream_type::ios_base __ios_base;
2956 const typename __ios_base::fmtflags __flags = __os.flags();
2957 const _CharT __fill = __os.fill();
2958 const std::streamsize __precision = __os.precision();
2959 const _CharT __space = __os.widen(' ');
2960 __os.flags(__ios_base::scientific | __ios_base::left);
2962 __os.precision(std::numeric_limits<_RealType>::max_digits10);
2964 std::vector<_RealType> __int = __x.intervals();
2965 __os << __int.size() - 1;
2967 for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
2968 __os << __space << *__xit;
2970 std::vector<double> __den = __x.densities();
2971 for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
2972 __os << __space << *__dit;
2974 __os.flags(__flags);
2976 __os.precision(__precision);
2980 template<typename _RealType, typename _CharT, typename _Traits>
2981 std::basic_istream<_CharT, _Traits>&
2982 operator>>(std::basic_istream<_CharT, _Traits>& __is,
2983 piecewise_constant_distribution<_RealType>& __x)
2985 typedef std::basic_istream<_CharT, _Traits> __istream_type;
2986 typedef typename __istream_type::ios_base __ios_base;
2988 const typename __ios_base::fmtflags __flags = __is.flags();
2989 __is.flags(__ios_base::dec | __ios_base::skipws);
2994 std::vector<_RealType> __int_vec;
2995 __int_vec.reserve(__n + 1);
2996 for (size_t __i = 0; __i <= __n; ++__i)
3000 __int_vec.push_back(__int);
3003 std::vector<double> __den_vec;
3004 __den_vec.reserve(__n);
3005 for (size_t __i = 0; __i < __n; ++__i)
3009 __den_vec.push_back(__den);
3012 __x.param(typename piecewise_constant_distribution<_RealType>::
3013 param_type(__int_vec.begin(), __int_vec.end(), __den_vec.begin()));
3015 __is.flags(__flags);
3020 template<typename _RealType>
3022 piecewise_linear_distribution<_RealType>::param_type::
3025 if (_M_int.size() < 2
3026 || (_M_int.size() == 2
3027 && _M_int[0] == _RealType(0)
3028 && _M_int[1] == _RealType(1)
3029 && _M_den[0] == _M_den[1]))
3037 _M_cp.reserve(_M_int.size() - 1);
3038 _M_m.reserve(_M_int.size() - 1);
3039 for (size_t __k = 0; __k < _M_int.size() - 1; ++__k)
3041 const _RealType __delta = _M_int[__k + 1] - _M_int[__k];
3042 __sum += 0.5 * (_M_den[__k + 1] + _M_den[__k]) * __delta;
3043 _M_cp.push_back(__sum);
3044 _M_m.push_back((_M_den[__k + 1] - _M_den[__k]) / __delta);
3047 // Now normalize the densities...
3048 __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
3050 // ... and partial sums...
3051 __detail::__normalize(_M_cp.begin(), _M_cp.end(), _M_cp.begin(), __sum);
3053 __detail::__normalize(_M_m.begin(), _M_m.end(), _M_m.begin(), __sum);
3055 // Make sure the last cumulative probablility is one.
3056 _M_cp[_M_cp.size() - 1] = 1.0;
3059 template<typename _RealType>
3060 template<typename _InputIteratorB, typename _InputIteratorW>
3061 piecewise_linear_distribution<_RealType>::param_type::
3062 param_type(_InputIteratorB __bbegin,
3063 _InputIteratorB __bend,
3064 _InputIteratorW __wbegin)
3065 : _M_int(), _M_den(), _M_cp(), _M_m()
3067 for (; __bbegin != __bend; ++__bbegin, ++__wbegin)
3069 _M_int.push_back(*__bbegin);
3070 _M_den.push_back(*__wbegin);
3076 template<typename _RealType>
3077 template<typename _Func>
3078 piecewise_linear_distribution<_RealType>::param_type::
3079 param_type(initializer_list<_RealType> __bl, _Func __fw)
3080 : _M_int(), _M_den(), _M_cp(), _M_m()
3082 _M_int.reserve(__bl.size());
3083 _M_den.reserve(__bl.size());
3084 for (auto __biter = __bl.begin(); __biter != __bl.end(); ++__biter)
3086 _M_int.push_back(*__biter);
3087 _M_den.push_back(__fw(*__biter));
3093 template<typename _RealType>
3094 template<typename _Func>
3095 piecewise_linear_distribution<_RealType>::param_type::
3096 param_type(size_t __nw, _RealType __xmin, _RealType __xmax, _Func __fw)
3097 : _M_int(), _M_den(), _M_cp(), _M_m()
3099 const size_t __n = __nw == 0 ? 1 : __nw;
3100 const _RealType __delta = (__xmax - __xmin) / __n;
3102 _M_int.reserve(__n + 1);
3103 _M_den.reserve(__n + 1);
3104 for (size_t __k = 0; __k <= __nw; ++__k)
3106 _M_int.push_back(__xmin + __k * __delta);
3107 _M_den.push_back(__fw(_M_int[__k] + __delta));
3113 template<typename _RealType>
3114 template<typename _UniformRandomNumberGenerator>
3115 typename piecewise_linear_distribution<_RealType>::result_type
3116 piecewise_linear_distribution<_RealType>::
3117 operator()(_UniformRandomNumberGenerator& __urng,
3118 const param_type& __param)
3120 __detail::_Adaptor<_UniformRandomNumberGenerator, double>
3123 const double __p = __aurng();
3124 if (__param._M_cp.empty())
3127 auto __pos = std::lower_bound(__param._M_cp.begin(),
3128 __param._M_cp.end(), __p);
3129 const size_t __i = __pos - __param._M_cp.begin();
3131 const double __pref = __i > 0 ? __param._M_cp[__i - 1] : 0.0;
3133 const double __a = 0.5 * __param._M_m[__i];
3134 const double __b = __param._M_den[__i];
3135 const double __cm = __p - __pref;
3137 _RealType __x = __param._M_int[__i];
3142 const double __d = __b * __b + 4.0 * __a * __cm;
3143 __x += 0.5 * (std::sqrt(__d) - __b) / __a;
3149 template<typename _RealType>
3150 template<typename _ForwardIterator,
3151 typename _UniformRandomNumberGenerator>
3153 piecewise_linear_distribution<_RealType>::
3154 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
3155 _UniformRandomNumberGenerator& __urng,
3156 const param_type& __param)
3158 __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
3159 // We could duplicate everything from operator()...
3161 *__f++ = this->operator()(__urng, __param);
3164 template<typename _RealType, typename _CharT, typename _Traits>
3165 std::basic_ostream<_CharT, _Traits>&
3166 operator<<(std::basic_ostream<_CharT, _Traits>& __os,
3167 const piecewise_linear_distribution<_RealType>& __x)
3169 typedef std::basic_ostream<_CharT, _Traits> __ostream_type;
3170 typedef typename __ostream_type::ios_base __ios_base;
3172 const typename __ios_base::fmtflags __flags = __os.flags();
3173 const _CharT __fill = __os.fill();
3174 const std::streamsize __precision = __os.precision();
3175 const _CharT __space = __os.widen(' ');
3176 __os.flags(__ios_base::scientific | __ios_base::left);
3178 __os.precision(std::numeric_limits<_RealType>::max_digits10);
3180 std::vector<_RealType> __int = __x.intervals();
3181 __os << __int.size() - 1;
3183 for (auto __xit = __int.begin(); __xit != __int.end(); ++__xit)
3184 __os << __space << *__xit;
3186 std::vector<double> __den = __x.densities();
3187 for (auto __dit = __den.begin(); __dit != __den.end(); ++__dit)
3188 __os << __space << *__dit;
3190 __os.flags(__flags);
3192 __os.precision(__precision);
3196 template<typename _RealType, typename _CharT, typename _Traits>
3197 std::basic_istream<_CharT, _Traits>&
3198 operator>>(std::basic_istream<_CharT, _Traits>& __is,
3199 piecewise_linear_distribution<_RealType>& __x)
3201 typedef std::basic_istream<_CharT, _Traits> __istream_type;
3202 typedef typename __istream_type::ios_base __ios_base;
3204 const typename __ios_base::fmtflags __flags = __is.flags();
3205 __is.flags(__ios_base::dec | __ios_base::skipws);
3210 std::vector<_RealType> __int_vec;
3211 __int_vec.reserve(__n + 1);
3212 for (size_t __i = 0; __i <= __n; ++__i)
3216 __int_vec.push_back(__int);
3219 std::vector<double> __den_vec;
3220 __den_vec.reserve(__n + 1);
3221 for (size_t __i = 0; __i <= __n; ++__i)
3225 __den_vec.push_back(__den);
3228 __x.param(typename piecewise_linear_distribution<_RealType>::
3229 param_type(__int_vec.begin(), __int_vec.end(), __den_vec.begin()));
3231 __is.flags(__flags);
3236 template<typename _IntType>
3237 seed_seq::seed_seq(std::initializer_list<_IntType> __il)
3239 for (auto __iter = __il.begin(); __iter != __il.end(); ++__iter)
3240 _M_v.push_back(__detail::__mod<result_type,
3241 __detail::_Shift<result_type, 32>::__value>(*__iter));
3244 template<typename _InputIterator>
3245 seed_seq::seed_seq(_InputIterator __begin, _InputIterator __end)
3247 for (_InputIterator __iter = __begin; __iter != __end; ++__iter)
3248 _M_v.push_back(__detail::__mod<result_type,
3249 __detail::_Shift<result_type, 32>::__value>(*__iter));
3252 template<typename _RandomAccessIterator>
3254 seed_seq::generate(_RandomAccessIterator __begin,
3255 _RandomAccessIterator __end)
3257 typedef typename iterator_traits<_RandomAccessIterator>::value_type
3260 if (__begin == __end)
3263 std::fill(__begin, __end, _Type(0x8b8b8b8bu));
3265 const size_t __n = __end - __begin;
3266 const size_t __s = _M_v.size();
3267 const size_t __t = (__n >= 623) ? 11
3272 const size_t __p = (__n - __t) / 2;
3273 const size_t __q = __p + __t;
3274 const size_t __m = std::max(size_t(__s + 1), __n);
3276 for (size_t __k = 0; __k < __m; ++__k)
3278 _Type __arg = (__begin[__k % __n]
3279 ^ __begin[(__k + __p) % __n]
3280 ^ __begin[(__k - 1) % __n]);
3281 _Type __r1 = __arg ^ (__arg >> 27);
3282 __r1 = __detail::__mod<_Type,
3283 __detail::_Shift<_Type, 32>::__value>(1664525u * __r1);
3287 else if (__k <= __s)
3288 __r2 += __k % __n + _M_v[__k - 1];
3291 __r2 = __detail::__mod<_Type,
3292 __detail::_Shift<_Type, 32>::__value>(__r2);
3293 __begin[(__k + __p) % __n] += __r1;
3294 __begin[(__k + __q) % __n] += __r2;
3295 __begin[__k % __n] = __r2;
3298 for (size_t __k = __m; __k < __m + __n; ++__k)
3300 _Type __arg = (__begin[__k % __n]
3301 + __begin[(__k + __p) % __n]
3302 + __begin[(__k - 1) % __n]);
3303 _Type __r3 = __arg ^ (__arg >> 27);
3304 __r3 = __detail::__mod<_Type,
3305 __detail::_Shift<_Type, 32>::__value>(1566083941u * __r3);
3306 _Type __r4 = __r3 - __k % __n;
3307 __r4 = __detail::__mod<_Type,
3308 __detail::_Shift<_Type, 32>::__value>(__r4);
3309 __begin[(__k + __p) % __n] ^= __r3;
3310 __begin[(__k + __q) % __n] ^= __r4;
3311 __begin[__k % __n] = __r4;
3315 template<typename _RealType, size_t __bits,
3316 typename _UniformRandomNumberGenerator>
3318 generate_canonical(_UniformRandomNumberGenerator& __urng)
3320 static_assert(std::is_floating_point<_RealType>::value,
3321 "template argument must be a floating point type");
3324 = std::min(static_cast<size_t>(std::numeric_limits<_RealType>::digits),
3326 const long double __r = static_cast<long double>(__urng.max())
3327 - static_cast<long double>(__urng.min()) + 1.0L;
3328 const size_t __log2r = std::log(__r) / std::log(2.0L);
3329 const size_t __m = std::max<size_t>(1UL,
3330 (__b + __log2r - 1UL) / __log2r);
3332 _RealType __sum = _RealType(0);
3333 _RealType __tmp = _RealType(1);
3334 for (size_t __k = __m; __k != 0; --__k)
3336 __sum += _RealType(__urng() - __urng.min()) * __tmp;
3339 __ret = __sum / __tmp;
3340 if (__builtin_expect(__ret >= _RealType(1), 0))
3342 #if _GLIBCXX_USE_C99_MATH_TR1
3343 __ret = std::nextafter(_RealType(1), _RealType(0));
3345 __ret = _RealType(1)
3346 - std::numeric_limits<_RealType>::epsilon() / _RealType(2);
3352 _GLIBCXX_END_NAMESPACE_VERSION