1 // random number generation (out of line) -*- C++ -*-
2 
3 // Copyright (C) 2006, 2007 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 2, 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 // You should have received a copy of the GNU General Public License along
17 // with this library; see the file COPYING.  If not, write to the Free
18 // Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
19 // USA.
20 
21 // As a special exception, you may use this file as part of a free software
22 // library without restriction.  Specifically, if other files instantiate
23 // templates or use macros or inline functions from this file, or you compile
24 // this file and link it with other files to produce an executable, this
25 // file does not by itself cause the resulting executable to be covered by
26 // the GNU General Public License.  This exception does not however
27 // invalidate any other reasons why the executable file might be covered by
28 // the GNU General Public License.
29 
30 /** @file tr1/random.tcc
31  *  This is a TR1 C++ Library header.
32  */
33 
34 namespace std
35 {
36 _GLIBCXX_BEGIN_NAMESPACE(tr1)
37 
38   /*
39    * (Further) implementation-space details.
40    */
41   namespace __detail
42   {
43     // General case for x = (ax + c) mod m -- use Schrage's algorithm to avoid
44     // integer overflow.
45     //
46     // Because a and c are compile-time integral constants the compiler kindly
47     // elides any unreachable paths.
48     //
49     // Preconditions:  a > 0, m > 0.
50     //
51     template<typename _Tp, _Tp __a, _Tp __c, _Tp __m, bool>
52       struct _Mod
53       {
54 	static _Tp
55 	__calc(_Tp __x)
56 	{
57 	  if (__a == 1)
58 	    __x %= __m;
59 	  else
60 	    {
61 	      static const _Tp __q = __m / __a;
62 	      static const _Tp __r = __m % __a;
63 
64 	      _Tp __t1 = __a * (__x % __q);
65 	      _Tp __t2 = __r * (__x / __q);
66 	      if (__t1 >= __t2)
67 		__x = __t1 - __t2;
68 	      else
69 		__x = __m - __t2 + __t1;
70 	    }
71 
72 	  if (__c != 0)
73 	    {
74 	      const _Tp __d = __m - __x;
75 	      if (__d > __c)
76 		__x += __c;
77 	      else
78 		__x = __c - __d;
79 	    }
80 	  return __x;
81 	}
82       };
83 
84     // Special case for m == 0 -- use unsigned integer overflow as modulo
85     // operator.
86     template<typename _Tp, _Tp __a, _Tp __c, _Tp __m>
87       struct _Mod<_Tp, __a, __c, __m, true>
88       {
89 	static _Tp
90 	__calc(_Tp __x)
91 	{ return __a * __x + __c; }
92       };
93   } // namespace __detail
94 
95   /**
96    * Seeds the LCR with integral value @p __x0, adjusted so that the
97    * ring identity is never a member of the convergence set.
98    */
99   template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
100     void
101     linear_congruential<_UIntType, __a, __c, __m>::
102     seed(unsigned long __x0)
103     {
104       if ((__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0)
105 	  && (__detail::__mod<_UIntType, 1, 0, __m>(__x0) == 0))
106 	_M_x = __detail::__mod<_UIntType, 1, 0, __m>(1);
107       else
108 	_M_x = __detail::__mod<_UIntType, 1, 0, __m>(__x0);
109     }
110 
111   /**
112    * Seeds the LCR engine with a value generated by @p __g.
113    */
114   template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
115     template<class _Gen>
116       void
117       linear_congruential<_UIntType, __a, __c, __m>::
118       seed(_Gen& __g, false_type)
119       {
120 	_UIntType __x0 = __g();
121 	if ((__detail::__mod<_UIntType, 1, 0, __m>(__c) == 0)
122 	    && (__detail::__mod<_UIntType, 1, 0, __m>(__x0) == 0))
123 	  _M_x = __detail::__mod<_UIntType, 1, 0, __m>(1);
124 	else
125 	  _M_x = __detail::__mod<_UIntType, 1, 0, __m>(__x0);
126       }
127 
128   /**
129    * Gets the next generated value in sequence.
130    */
131   template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m>
132     typename linear_congruential<_UIntType, __a, __c, __m>::result_type
133     linear_congruential<_UIntType, __a, __c, __m>::
134     operator()()
135     {
136       _M_x = __detail::__mod<_UIntType, __a, __c, __m>(_M_x);
137       return _M_x;
138     }
139 
140   template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
141 	   typename _CharT, typename _Traits>
142     std::basic_ostream<_CharT, _Traits>&
143     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
144 	       const linear_congruential<_UIntType, __a, __c, __m>& __lcr)
145     {
146       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
147       typedef typename __ostream_type::ios_base    __ios_base;
148 
149       const typename __ios_base::fmtflags __flags = __os.flags();
150       const _CharT __fill = __os.fill();
151       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
152       __os.fill(__os.widen(' '));
153 
154       __os << __lcr._M_x;
155 
156       __os.flags(__flags);
157       __os.fill(__fill);
158       return __os;
159     }
160 
161   template<class _UIntType, _UIntType __a, _UIntType __c, _UIntType __m,
162 	   typename _CharT, typename _Traits>
163     std::basic_istream<_CharT, _Traits>&
164     operator>>(std::basic_istream<_CharT, _Traits>& __is,
165 	       linear_congruential<_UIntType, __a, __c, __m>& __lcr)
166     {
167       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
168       typedef typename __istream_type::ios_base    __ios_base;
169 
170       const typename __ios_base::fmtflags __flags = __is.flags();
171       __is.flags(__ios_base::dec);
172 
173       __is >> __lcr._M_x;
174 
175       __is.flags(__flags);
176       return __is;
177     }
178 
179 
180   template<class _UIntType, int __w, int __n, int __m, int __r,
181 	   _UIntType __a, int __u, int __s,
182 	   _UIntType __b, int __t, _UIntType __c, int __l>
183     void
184     mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
185 		     __b, __t, __c, __l>::
186     seed(unsigned long __value)
187     {
188       _M_x[0] = __detail::__mod<_UIntType, 1, 0,
189 	__detail::_Shift<_UIntType, __w>::__value>(__value);
190 
191       for (int __i = 1; __i < state_size; ++__i)
192 	{
193 	  _UIntType __x = _M_x[__i - 1];
194 	  __x ^= __x >> (__w - 2);
195 	  __x *= 1812433253ul;
196 	  __x += __i;
197 	  _M_x[__i] = __detail::__mod<_UIntType, 1, 0,
198 	    __detail::_Shift<_UIntType, __w>::__value>(__x);
199 	}
200       _M_p = state_size;
201     }
202 
203   template<class _UIntType, int __w, int __n, int __m, int __r,
204 	   _UIntType __a, int __u, int __s,
205 	   _UIntType __b, int __t, _UIntType __c, int __l>
206     template<class _Gen>
207       void
208       mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
209 		       __b, __t, __c, __l>::
210       seed(_Gen& __gen, false_type)
211       {
212 	for (int __i = 0; __i < state_size; ++__i)
213 	  _M_x[__i] = __detail::__mod<_UIntType, 1, 0,
214 	    __detail::_Shift<_UIntType, __w>::__value>(__gen());
215 	_M_p = state_size;
216       }
217 
218   template<class _UIntType, int __w, int __n, int __m, int __r,
219 	   _UIntType __a, int __u, int __s,
220 	   _UIntType __b, int __t, _UIntType __c, int __l>
221     typename
222     mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
223 		     __b, __t, __c, __l>::result_type
224     mersenne_twister<_UIntType, __w, __n, __m, __r, __a, __u, __s,
225 		     __b, __t, __c, __l>::
226     operator()()
227     {
228       // Reload the vector - cost is O(n) amortized over n calls.
229       if (_M_p >= state_size)
230 	{
231 	  const _UIntType __upper_mask = (~_UIntType()) << __r;
232 	  const _UIntType __lower_mask = ~__upper_mask;
233 
234 	  for (int __k = 0; __k < (__n - __m); ++__k)
235 	    {
236 	      _UIntType __y = ((_M_x[__k] & __upper_mask)
237 			       | (_M_x[__k + 1] & __lower_mask));
238 	      _M_x[__k] = (_M_x[__k + __m] ^ (__y >> 1)
239 			   ^ ((__y & 0x01) ? __a : 0));
240 	    }
241 
242 	  for (int __k = (__n - __m); __k < (__n - 1); ++__k)
243 	    {
244 	      _UIntType __y = ((_M_x[__k] & __upper_mask)
245 			       | (_M_x[__k + 1] & __lower_mask));
246 	      _M_x[__k] = (_M_x[__k + (__m - __n)] ^ (__y >> 1)
247 			   ^ ((__y & 0x01) ? __a : 0));
248 	    }
249 
250 	  _UIntType __y = ((_M_x[__n - 1] & __upper_mask)
251 			   | (_M_x[0] & __lower_mask));
252 	  _M_x[__n - 1] = (_M_x[__m - 1] ^ (__y >> 1)
253 			   ^ ((__y & 0x01) ? __a : 0));
254 	  _M_p = 0;
255 	}
256 
257       // Calculate o(x(i)).
258       result_type __z = _M_x[_M_p++];
259       __z ^= (__z >> __u);
260       __z ^= (__z << __s) & __b;
261       __z ^= (__z << __t) & __c;
262       __z ^= (__z >> __l);
263 
264       return __z;
265     }
266 
267   template<class _UIntType, int __w, int __n, int __m, int __r,
268 	   _UIntType __a, int __u, int __s, _UIntType __b, int __t,
269 	   _UIntType __c, int __l,
270 	   typename _CharT, typename _Traits>
271     std::basic_ostream<_CharT, _Traits>&
272     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
273 	       const mersenne_twister<_UIntType, __w, __n, __m,
274 	       __r, __a, __u, __s, __b, __t, __c, __l>& __x)
275     {
276       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
277       typedef typename __ostream_type::ios_base    __ios_base;
278 
279       const typename __ios_base::fmtflags __flags = __os.flags();
280       const _CharT __fill = __os.fill();
281       const _CharT __space = __os.widen(' ');
282       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
283       __os.fill(__space);
284 
285       for (int __i = 0; __i < __n - 1; ++__i)
286 	__os << __x._M_x[__i] << __space;
287       __os << __x._M_x[__n - 1];
288 
289       __os.flags(__flags);
290       __os.fill(__fill);
291       return __os;
292     }
293 
294   template<class _UIntType, int __w, int __n, int __m, int __r,
295 	   _UIntType __a, int __u, int __s, _UIntType __b, int __t,
296 	   _UIntType __c, int __l,
297 	   typename _CharT, typename _Traits>
298     std::basic_istream<_CharT, _Traits>&
299     operator>>(std::basic_istream<_CharT, _Traits>& __is,
300 	       mersenne_twister<_UIntType, __w, __n, __m,
301 	       __r, __a, __u, __s, __b, __t, __c, __l>& __x)
302     {
303       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
304       typedef typename __istream_type::ios_base    __ios_base;
305 
306       const typename __ios_base::fmtflags __flags = __is.flags();
307       __is.flags(__ios_base::dec | __ios_base::skipws);
308 
309       for (int __i = 0; __i < __n; ++__i)
310 	__is >> __x._M_x[__i];
311 
312       __is.flags(__flags);
313       return __is;
314     }
315 
316 
317   template<typename _IntType, _IntType __m, int __s, int __r>
318     void
319     subtract_with_carry<_IntType, __m, __s, __r>::
320     seed(unsigned long __value)
321     {
322       if (__value == 0)
323 	__value = 19780503;
324 
325       std::tr1::linear_congruential<unsigned long, 40014, 0, 2147483563>
326 	__lcg(__value);
327 
328       for (int __i = 0; __i < long_lag; ++__i)
329 	_M_x[__i] = __detail::__mod<_UIntType, 1, 0, modulus>(__lcg());
330 
331       _M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
332       _M_p = 0;
333     }
334 
335   template<typename _IntType, _IntType __m, int __s, int __r>
336     template<class _Gen>
337       void
338       subtract_with_carry<_IntType, __m, __s, __r>::
339       seed(_Gen& __gen, false_type)
340       {
341 	const int __n = (std::numeric_limits<_UIntType>::digits + 31) / 32;
342 
343 	for (int __i = 0; __i < long_lag; ++__i)
344 	  {
345 	    _UIntType __tmp = 0;
346 	    _UIntType __factor = 1;
347 	    for (int __j = 0; __j < __n; ++__j)
348 	      {
349 		__tmp += __detail::__mod<__detail::_UInt32Type, 1, 0, 0>
350 		         (__gen()) * __factor;
351 		__factor *= __detail::_Shift<_UIntType, 32>::__value;
352 	      }
353 	    _M_x[__i] = __detail::__mod<_UIntType, 1, 0, modulus>(__tmp);
354 	  }
355 	_M_carry = (_M_x[long_lag - 1] == 0) ? 1 : 0;
356 	_M_p = 0;
357       }
358 
359   template<typename _IntType, _IntType __m, int __s, int __r>
360     typename subtract_with_carry<_IntType, __m, __s, __r>::result_type
361     subtract_with_carry<_IntType, __m, __s, __r>::
362     operator()()
363     {
364       // Derive short lag index from current index.
365       int __ps = _M_p - short_lag;
366       if (__ps < 0)
367 	__ps += long_lag;
368 
369       // Calculate new x(i) without overflow or division.
370       // NB: Thanks to the requirements for _IntType, _M_x[_M_p] + _M_carry
371       // cannot overflow.
372       _UIntType __xi;
373       if (_M_x[__ps] >= _M_x[_M_p] + _M_carry)
374 	{
375 	  __xi = _M_x[__ps] - _M_x[_M_p] - _M_carry;
376 	  _M_carry = 0;
377 	}
378       else
379 	{
380 	  __xi = modulus - _M_x[_M_p] - _M_carry + _M_x[__ps];
381 	  _M_carry = 1;
382 	}
383       _M_x[_M_p] = __xi;
384 
385       // Adjust current index to loop around in ring buffer.
386       if (++_M_p >= long_lag)
387 	_M_p = 0;
388 
389       return __xi;
390     }
391 
392   template<typename _IntType, _IntType __m, int __s, int __r,
393 	   typename _CharT, typename _Traits>
394     std::basic_ostream<_CharT, _Traits>&
395     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
396 	       const subtract_with_carry<_IntType, __m, __s, __r>& __x)
397     {
398       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
399       typedef typename __ostream_type::ios_base    __ios_base;
400 
401       const typename __ios_base::fmtflags __flags = __os.flags();
402       const _CharT __fill = __os.fill();
403       const _CharT __space = __os.widen(' ');
404       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
405       __os.fill(__space);
406 
407       for (int __i = 0; __i < __r; ++__i)
408 	__os << __x._M_x[__i] << __space;
409       __os << __x._M_carry;
410 
411       __os.flags(__flags);
412       __os.fill(__fill);
413       return __os;
414     }
415 
416   template<typename _IntType, _IntType __m, int __s, int __r,
417 	   typename _CharT, typename _Traits>
418     std::basic_istream<_CharT, _Traits>&
419     operator>>(std::basic_istream<_CharT, _Traits>& __is,
420 	       subtract_with_carry<_IntType, __m, __s, __r>& __x)
421     {
422       typedef std::basic_ostream<_CharT, _Traits>  __istream_type;
423       typedef typename __istream_type::ios_base    __ios_base;
424 
425       const typename __ios_base::fmtflags __flags = __is.flags();
426       __is.flags(__ios_base::dec | __ios_base::skipws);
427 
428       for (int __i = 0; __i < __r; ++__i)
429 	__is >> __x._M_x[__i];
430       __is >> __x._M_carry;
431 
432       __is.flags(__flags);
433       return __is;
434     }
435 
436 
437   template<typename _RealType, int __w, int __s, int __r>
438     void
439     subtract_with_carry_01<_RealType, __w, __s, __r>::
440     _M_initialize_npows()
441     {
442       for (int __j = 0; __j < __n; ++__j)
443 #if _GLIBCXX_USE_C99_MATH_TR1
444 	_M_npows[__j] = std::tr1::ldexp(_RealType(1), -__w + __j * 32);
445 #else
446         _M_npows[__j] = std::pow(_RealType(2), -__w + __j * 32);
447 #endif
448     }
449 
450   template<typename _RealType, int __w, int __s, int __r>
451     void
452     subtract_with_carry_01<_RealType, __w, __s, __r>::
453     seed(unsigned long __value)
454     {
455       if (__value == 0)
456 	__value = 19780503;
457 
458       // _GLIBCXX_RESOLVE_LIB_DEFECTS
459       // 512. Seeding subtract_with_carry_01 from a single unsigned long.
460       std::tr1::linear_congruential<unsigned long, 40014, 0, 2147483563>
461 	__lcg(__value);
462 
463       this->seed(__lcg);
464     }
465 
466   template<typename _RealType, int __w, int __s, int __r>
467     template<class _Gen>
468       void
469       subtract_with_carry_01<_RealType, __w, __s, __r>::
470       seed(_Gen& __gen, false_type)
471       {
472 	for (int __i = 0; __i < long_lag; ++__i)
473 	  {
474 	    for (int __j = 0; __j < __n - 1; ++__j)
475 	      _M_x[__i][__j] = __detail::__mod<_UInt32Type, 1, 0, 0>(__gen());
476 	    _M_x[__i][__n - 1] = __detail::__mod<_UInt32Type, 1, 0,
477 	      __detail::_Shift<_UInt32Type, __w % 32>::__value>(__gen());
478 	  }
479 
480 	_M_carry = 1;
481 	for (int __j = 0; __j < __n; ++__j)
482 	  if (_M_x[long_lag - 1][__j] != 0)
483 	    {
484 	      _M_carry = 0;
485 	      break;
486 	    }
487 
488 	_M_p = 0;
489       }
490 
491   template<typename _RealType, int __w, int __s, int __r>
492     typename subtract_with_carry_01<_RealType, __w, __s, __r>::result_type
493     subtract_with_carry_01<_RealType, __w, __s, __r>::
494     operator()()
495     {
496       // Derive short lag index from current index.
497       int __ps = _M_p - short_lag;
498       if (__ps < 0)
499 	__ps += long_lag;
500 
501       _UInt32Type __new_carry;
502       for (int __j = 0; __j < __n - 1; ++__j)
503 	{
504 	  if (_M_x[__ps][__j] > _M_x[_M_p][__j]
505 	      || (_M_x[__ps][__j] == _M_x[_M_p][__j] && _M_carry == 0))
506 	    __new_carry = 0;
507 	  else
508 	    __new_carry = 1;
509 
510 	  _M_x[_M_p][__j] = _M_x[__ps][__j] - _M_x[_M_p][__j] - _M_carry;
511 	  _M_carry = __new_carry;
512 	}
513 
514       if (_M_x[__ps][__n - 1] > _M_x[_M_p][__n - 1]
515 	  || (_M_x[__ps][__n - 1] == _M_x[_M_p][__n - 1] && _M_carry == 0))
516 	__new_carry = 0;
517       else
518 	__new_carry = 1;
519 
520       _M_x[_M_p][__n - 1] = __detail::__mod<_UInt32Type, 1, 0,
521 	__detail::_Shift<_UInt32Type, __w % 32>::__value>
522 	(_M_x[__ps][__n - 1] - _M_x[_M_p][__n - 1] - _M_carry);
523       _M_carry = __new_carry;
524 
525       result_type __ret = 0.0;
526       for (int __j = 0; __j < __n; ++__j)
527 	__ret += _M_x[_M_p][__j] * _M_npows[__j];
528 
529       // Adjust current index to loop around in ring buffer.
530       if (++_M_p >= long_lag)
531 	_M_p = 0;
532 
533       return __ret;
534     }
535 
536   template<typename _RealType, int __w, int __s, int __r,
537 	   typename _CharT, typename _Traits>
538     std::basic_ostream<_CharT, _Traits>&
539     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
540 	       const subtract_with_carry_01<_RealType, __w, __s, __r>& __x)
541     {
542       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
543       typedef typename __ostream_type::ios_base    __ios_base;
544 
545       const typename __ios_base::fmtflags __flags = __os.flags();
546       const _CharT __fill = __os.fill();
547       const _CharT __space = __os.widen(' ');
548       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
549       __os.fill(__space);
550 
551       for (int __i = 0; __i < __r; ++__i)
552 	for (int __j = 0; __j < __x.__n; ++__j)
553 	  __os << __x._M_x[__i][__j] << __space;
554       __os << __x._M_carry;
555 
556       __os.flags(__flags);
557       __os.fill(__fill);
558       return __os;
559     }
560 
561   template<typename _RealType, int __w, int __s, int __r,
562 	   typename _CharT, typename _Traits>
563     std::basic_istream<_CharT, _Traits>&
564     operator>>(std::basic_istream<_CharT, _Traits>& __is,
565 	       subtract_with_carry_01<_RealType, __w, __s, __r>& __x)
566     {
567       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
568       typedef typename __istream_type::ios_base    __ios_base;
569 
570       const typename __ios_base::fmtflags __flags = __is.flags();
571       __is.flags(__ios_base::dec | __ios_base::skipws);
572 
573       for (int __i = 0; __i < __r; ++__i)
574 	for (int __j = 0; __j < __x.__n; ++__j)
575 	  __is >> __x._M_x[__i][__j];
576       __is >> __x._M_carry;
577 
578       __is.flags(__flags);
579       return __is;
580     }
581 
582 
583   template<class _UniformRandomNumberGenerator, int __p, int __r>
584     typename discard_block<_UniformRandomNumberGenerator,
585 			   __p, __r>::result_type
586     discard_block<_UniformRandomNumberGenerator, __p, __r>::
587     operator()()
588     {
589       if (_M_n >= used_block)
590 	{
591 	  while (_M_n < block_size)
592 	    {
593 	      _M_b();
594 	      ++_M_n;
595 	    }
596 	  _M_n = 0;
597 	}
598       ++_M_n;
599       return _M_b();
600     }
601 
602   template<class _UniformRandomNumberGenerator, int __p, int __r,
603 	   typename _CharT, typename _Traits>
604     std::basic_ostream<_CharT, _Traits>&
605     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
606 	       const discard_block<_UniformRandomNumberGenerator,
607 	       __p, __r>& __x)
608     {
609       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
610       typedef typename __ostream_type::ios_base    __ios_base;
611 
612       const typename __ios_base::fmtflags __flags = __os.flags();
613       const _CharT __fill = __os.fill();
614       const _CharT __space = __os.widen(' ');
615       __os.flags(__ios_base::dec | __ios_base::fixed
616 		 | __ios_base::left);
617       __os.fill(__space);
618 
619       __os << __x._M_b << __space << __x._M_n;
620 
621       __os.flags(__flags);
622       __os.fill(__fill);
623       return __os;
624     }
625 
626   template<class _UniformRandomNumberGenerator, int __p, int __r,
627 	   typename _CharT, typename _Traits>
628     std::basic_istream<_CharT, _Traits>&
629     operator>>(std::basic_istream<_CharT, _Traits>& __is,
630 	       discard_block<_UniformRandomNumberGenerator, __p, __r>& __x)
631     {
632       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
633       typedef typename __istream_type::ios_base    __ios_base;
634 
635       const typename __ios_base::fmtflags __flags = __is.flags();
636       __is.flags(__ios_base::dec | __ios_base::skipws);
637 
638       __is >> __x._M_b >> __x._M_n;
639 
640       __is.flags(__flags);
641       return __is;
642     }
643 
644 
645   template<class _UniformRandomNumberGenerator1, int __s1,
646 	   class _UniformRandomNumberGenerator2, int __s2>
647     void
648     xor_combine<_UniformRandomNumberGenerator1, __s1,
649 		_UniformRandomNumberGenerator2, __s2>::
650     _M_initialize_max()
651     {
652       const int __w = std::numeric_limits<result_type>::digits;
653 
654       const result_type __m1 =
655 	std::min(result_type(_M_b1.max() - _M_b1.min()),
656 		 __detail::_Shift<result_type, __w - __s1>::__value - 1);
657 
658       const result_type __m2 =
659 	std::min(result_type(_M_b2.max() - _M_b2.min()),
660 		 __detail::_Shift<result_type, __w - __s2>::__value - 1);
661 
662       // NB: In TR1 s1 is not required to be >= s2.
663       if (__s1 < __s2)
664 	_M_max = _M_initialize_max_aux(__m2, __m1, __s2 - __s1) << __s1;
665       else
666 	_M_max = _M_initialize_max_aux(__m1, __m2, __s1 - __s2) << __s2;
667     }
668 
669   template<class _UniformRandomNumberGenerator1, int __s1,
670 	   class _UniformRandomNumberGenerator2, int __s2>
671     typename xor_combine<_UniformRandomNumberGenerator1, __s1,
672 			 _UniformRandomNumberGenerator2, __s2>::result_type
673     xor_combine<_UniformRandomNumberGenerator1, __s1,
674 		_UniformRandomNumberGenerator2, __s2>::
675     _M_initialize_max_aux(result_type __a, result_type __b, int __d)
676     {
677       const result_type __two2d = result_type(1) << __d;
678       const result_type __c = __a * __two2d;
679 
680       if (__a == 0 || __b < __two2d)
681 	return __c + __b;
682 
683       const result_type __t = std::max(__c, __b);
684       const result_type __u = std::min(__c, __b);
685 
686       result_type __ub = __u;
687       result_type __p;
688       for (__p = 0; __ub != 1; __ub >>= 1)
689 	++__p;
690 
691       const result_type __two2p = result_type(1) << __p;
692       const result_type __k = __t / __two2p;
693 
694       if (__k & 1)
695 	return (__k + 1) * __two2p - 1;
696 
697       if (__c >= __b)
698 	return (__k + 1) * __two2p + _M_initialize_max_aux((__t % __two2p)
699 							   / __two2d,
700 							   __u % __two2p, __d);
701       else
702 	return (__k + 1) * __two2p + _M_initialize_max_aux((__u % __two2p)
703 							   / __two2d,
704 							   __t % __two2p, __d);
705     }
706 
707   template<class _UniformRandomNumberGenerator1, int __s1,
708 	   class _UniformRandomNumberGenerator2, int __s2,
709 	   typename _CharT, typename _Traits>
710     std::basic_ostream<_CharT, _Traits>&
711     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
712 	       const xor_combine<_UniformRandomNumberGenerator1, __s1,
713 	       _UniformRandomNumberGenerator2, __s2>& __x)
714     {
715       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
716       typedef typename __ostream_type::ios_base    __ios_base;
717 
718       const typename __ios_base::fmtflags __flags = __os.flags();
719       const _CharT __fill = __os.fill();
720       const _CharT __space = __os.widen(' ');
721       __os.flags(__ios_base::dec | __ios_base::fixed | __ios_base::left);
722       __os.fill(__space);
723 
724       __os << __x.base1() << __space << __x.base2();
725 
726       __os.flags(__flags);
727       __os.fill(__fill);
728       return __os;
729     }
730 
731   template<class _UniformRandomNumberGenerator1, int __s1,
732 	   class _UniformRandomNumberGenerator2, int __s2,
733 	   typename _CharT, typename _Traits>
734     std::basic_istream<_CharT, _Traits>&
735     operator>>(std::basic_istream<_CharT, _Traits>& __is,
736 	       xor_combine<_UniformRandomNumberGenerator1, __s1,
737 	       _UniformRandomNumberGenerator2, __s2>& __x)
738     {
739       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
740       typedef typename __istream_type::ios_base    __ios_base;
741 
742       const typename __ios_base::fmtflags __flags = __is.flags();
743       __is.flags(__ios_base::skipws);
744 
745       __is >> __x._M_b1 >> __x._M_b2;
746 
747       __is.flags(__flags);
748       return __is;
749     }
750 
751 
752   template<typename _IntType, typename _CharT, typename _Traits>
753     std::basic_ostream<_CharT, _Traits>&
754     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
755 	       const uniform_int<_IntType>& __x)
756     {
757       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
758       typedef typename __ostream_type::ios_base    __ios_base;
759 
760       const typename __ios_base::fmtflags __flags = __os.flags();
761       const _CharT __fill = __os.fill();
762       const _CharT __space = __os.widen(' ');
763       __os.flags(__ios_base::scientific | __ios_base::left);
764       __os.fill(__space);
765 
766       __os << __x.min() << __space << __x.max();
767 
768       __os.flags(__flags);
769       __os.fill(__fill);
770       return __os;
771     }
772 
773   template<typename _IntType, typename _CharT, typename _Traits>
774     std::basic_istream<_CharT, _Traits>&
775     operator>>(std::basic_istream<_CharT, _Traits>& __is,
776 	       uniform_int<_IntType>& __x)
777     {
778       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
779       typedef typename __istream_type::ios_base    __ios_base;
780 
781       const typename __ios_base::fmtflags __flags = __is.flags();
782       __is.flags(__ios_base::dec | __ios_base::skipws);
783 
784       __is >> __x._M_min >> __x._M_max;
785 
786       __is.flags(__flags);
787       return __is;
788     }
789 
790 
791   template<typename _CharT, typename _Traits>
792     std::basic_ostream<_CharT, _Traits>&
793     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
794 	       const bernoulli_distribution& __x)
795     {
796       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
797       typedef typename __ostream_type::ios_base    __ios_base;
798 
799       const typename __ios_base::fmtflags __flags = __os.flags();
800       const _CharT __fill = __os.fill();
801       const std::streamsize __precision = __os.precision();
802       __os.flags(__ios_base::scientific | __ios_base::left);
803       __os.fill(__os.widen(' '));
804       __os.precision(__gnu_cxx::__numeric_traits<double>::__max_digits10);
805 
806       __os << __x.p();
807 
808       __os.flags(__flags);
809       __os.fill(__fill);
810       __os.precision(__precision);
811       return __os;
812     }
813 
814 
815   template<typename _IntType, typename _RealType>
816     template<class _UniformRandomNumberGenerator>
817       typename geometric_distribution<_IntType, _RealType>::result_type
818       geometric_distribution<_IntType, _RealType>::
819       operator()(_UniformRandomNumberGenerator& __urng)
820       {
821 	// About the epsilon thing see this thread:
822         // http://gcc.gnu.org/ml/gcc-patches/2006-10/msg00971.html
823 	const _RealType __naf =
824 	  (1 - std::numeric_limits<_RealType>::epsilon()) / 2;
825 	// The largest _RealType convertible to _IntType.
826 	const _RealType __thr =
827 	  std::numeric_limits<_IntType>::max() + __naf;
828 
829 	_RealType __cand;
830 	do
831 	  __cand = std::ceil(std::log(__urng()) / _M_log_p);
832 	while (__cand >= __thr);
833 
834 	return result_type(__cand + __naf);
835       }
836 
837   template<typename _IntType, typename _RealType,
838 	   typename _CharT, typename _Traits>
839     std::basic_ostream<_CharT, _Traits>&
840     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
841 	       const geometric_distribution<_IntType, _RealType>& __x)
842     {
843       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
844       typedef typename __ostream_type::ios_base    __ios_base;
845 
846       const typename __ios_base::fmtflags __flags = __os.flags();
847       const _CharT __fill = __os.fill();
848       const std::streamsize __precision = __os.precision();
849       __os.flags(__ios_base::scientific | __ios_base::left);
850       __os.fill(__os.widen(' '));
851       __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
852 
853       __os << __x.p();
854 
855       __os.flags(__flags);
856       __os.fill(__fill);
857       __os.precision(__precision);
858       return __os;
859     }
860 
861 
862   template<typename _IntType, typename _RealType>
863     void
864     poisson_distribution<_IntType, _RealType>::
865     _M_initialize()
866     {
867 #if _GLIBCXX_USE_C99_MATH_TR1
868       if (_M_mean >= 12)
869 	{
870 	  const _RealType __m = std::floor(_M_mean);
871 	  _M_lm_thr = std::log(_M_mean);
872 	  _M_lfm = std::tr1::lgamma(__m + 1);
873 	  _M_sm = std::sqrt(__m);
874 
875 	  const _RealType __pi_4 = 0.7853981633974483096156608458198757L;
876 	  const _RealType __dx = std::sqrt(2 * __m * std::log(32 * __m
877 							      / __pi_4));
878 	  _M_d = std::tr1::round(std::max(_RealType(6),
879 					  std::min(__m, __dx)));
880 	  const _RealType __cx = 2 * __m + _M_d;
881 	  _M_scx = std::sqrt(__cx / 2);
882 	  _M_1cx = 1 / __cx;
883 
884 	  _M_c2b = std::sqrt(__pi_4 * __cx) * std::exp(_M_1cx);
885 	  _M_cb = 2 * __cx * std::exp(-_M_d * _M_1cx * (1 + _M_d / 2)) / _M_d;
886 	}
887       else
888 #endif
889 	_M_lm_thr = std::exp(-_M_mean);
890       }
891 
892   /**
893    * A rejection algorithm when mean >= 12 and a simple method based
894    * upon the multiplication of uniform random variates otherwise.
895    * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
896    * is defined.
897    *
898    * Reference:
899    * Devroye, L. "Non-Uniform Random Variates Generation." Springer-Verlag,
900    * New York, 1986, Ch. X, Sects. 3.3 & 3.4 (+ Errata!).
901    */
902   template<typename _IntType, typename _RealType>
903     template<class _UniformRandomNumberGenerator>
904       typename poisson_distribution<_IntType, _RealType>::result_type
905       poisson_distribution<_IntType, _RealType>::
906       operator()(_UniformRandomNumberGenerator& __urng)
907       {
908 #if _GLIBCXX_USE_C99_MATH_TR1
909 	if (_M_mean >= 12)
910 	  {
911 	    _RealType __x;
912 
913 	    // See comments above...
914 	    const _RealType __naf =
915 	      (1 - std::numeric_limits<_RealType>::epsilon()) / 2;
916 	    const _RealType __thr =
917 	      std::numeric_limits<_IntType>::max() + __naf;
918 
919 	    const _RealType __m = std::floor(_M_mean);
920 	    // sqrt(pi / 2)
921 	    const _RealType __spi_2 = 1.2533141373155002512078826424055226L;
922 	    const _RealType __c1 = _M_sm * __spi_2;
923 	    const _RealType __c2 = _M_c2b + __c1;
924 	    const _RealType __c3 = __c2 + 1;
925 	    const _RealType __c4 = __c3 + 1;
926 	    // e^(1 / 78)
927 	    const _RealType __e178 = 1.0129030479320018583185514777512983L;
928 	    const _RealType __c5 = __c4 + __e178;
929 	    const _RealType __c = _M_cb + __c5;
930 	    const _RealType __2cx = 2 * (2 * __m + _M_d);
931 
932 	    bool __reject = true;
933 	    do
934 	      {
935 		const _RealType __u = __c * __urng();
936 		const _RealType __e = -std::log(__urng());
937 
938 		_RealType __w = 0.0;
939 
940 		if (__u <= __c1)
941 		  {
942 		    const _RealType __n = _M_nd(__urng);
943 		    const _RealType __y = -std::abs(__n) * _M_sm - 1;
944 		    __x = std::floor(__y);
945 		    __w = -__n * __n / 2;
946 		    if (__x < -__m)
947 		      continue;
948 		  }
949 		else if (__u <= __c2)
950 		  {
951 		    const _RealType __n = _M_nd(__urng);
952 		    const _RealType __y = 1 + std::abs(__n) * _M_scx;
953 		    __x = std::ceil(__y);
954 		    __w = __y * (2 - __y) * _M_1cx;
955 		    if (__x > _M_d)
956 		      continue;
957 		  }
958 		else if (__u <= __c3)
959 		  // NB: This case not in the book, nor in the Errata,
960 		  // but should be ok...
961 		  __x = -1;
962 		else if (__u <= __c4)
963 		  __x = 0;
964 		else if (__u <= __c5)
965 		  __x = 1;
966 		else
967 		  {
968 		    const _RealType __v = -std::log(__urng());
969 		    const _RealType __y = _M_d + __v * __2cx / _M_d;
970 		    __x = std::ceil(__y);
971 		    __w = -_M_d * _M_1cx * (1 + __y / 2);
972 		  }
973 
974 		__reject = (__w - __e - __x * _M_lm_thr
975 			    > _M_lfm - std::tr1::lgamma(__x + __m + 1));
976 
977 		__reject |= __x + __m >= __thr;
978 
979 	      } while (__reject);
980 
981 	    return result_type(__x + __m + __naf);
982 	  }
983 	else
984 #endif
985 	  {
986 	    _IntType     __x = 0;
987 	    _RealType __prod = 1.0;
988 
989 	    do
990 	      {
991 		__prod *= __urng();
992 		__x += 1;
993 	      }
994 	    while (__prod > _M_lm_thr);
995 
996 	    return __x - 1;
997 	  }
998       }
999 
1000   template<typename _IntType, typename _RealType,
1001 	   typename _CharT, typename _Traits>
1002     std::basic_ostream<_CharT, _Traits>&
1003     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1004 	       const poisson_distribution<_IntType, _RealType>& __x)
1005     {
1006       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1007       typedef typename __ostream_type::ios_base    __ios_base;
1008 
1009       const typename __ios_base::fmtflags __flags = __os.flags();
1010       const _CharT __fill = __os.fill();
1011       const std::streamsize __precision = __os.precision();
1012       const _CharT __space = __os.widen(' ');
1013       __os.flags(__ios_base::scientific | __ios_base::left);
1014       __os.fill(__space);
1015       __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
1016 
1017       __os << __x.mean() << __space << __x._M_nd;
1018 
1019       __os.flags(__flags);
1020       __os.fill(__fill);
1021       __os.precision(__precision);
1022       return __os;
1023     }
1024 
1025   template<typename _IntType, typename _RealType,
1026 	   typename _CharT, typename _Traits>
1027     std::basic_istream<_CharT, _Traits>&
1028     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1029 	       poisson_distribution<_IntType, _RealType>& __x)
1030     {
1031       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1032       typedef typename __istream_type::ios_base    __ios_base;
1033 
1034       const typename __ios_base::fmtflags __flags = __is.flags();
1035       __is.flags(__ios_base::skipws);
1036 
1037       __is >> __x._M_mean >> __x._M_nd;
1038       __x._M_initialize();
1039 
1040       __is.flags(__flags);
1041       return __is;
1042     }
1043 
1044 
1045   template<typename _IntType, typename _RealType>
1046     void
1047     binomial_distribution<_IntType, _RealType>::
1048     _M_initialize()
1049     {
1050       const _RealType __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
1051 
1052       _M_easy = true;
1053 
1054 #if _GLIBCXX_USE_C99_MATH_TR1
1055       if (_M_t * __p12 >= 8)
1056 	{
1057 	  _M_easy = false;
1058 	  const _RealType __np = std::floor(_M_t * __p12);
1059 	  const _RealType __pa = __np / _M_t;
1060 	  const _RealType __1p = 1 - __pa;
1061 
1062 	  const _RealType __pi_4 = 0.7853981633974483096156608458198757L;
1063 	  const _RealType __d1x =
1064 	    std::sqrt(__np * __1p * std::log(32 * __np
1065 					     / (81 * __pi_4 * __1p)));
1066 	  _M_d1 = std::tr1::round(std::max(_RealType(1), __d1x));
1067 	  const _RealType __d2x =
1068 	    std::sqrt(__np * __1p * std::log(32 * _M_t * __1p
1069 					     / (__pi_4 * __pa)));
1070 	  _M_d2 = std::tr1::round(std::max(_RealType(1), __d2x));
1071 
1072 	  // sqrt(pi / 2)
1073 	  const _RealType __spi_2 = 1.2533141373155002512078826424055226L;
1074 	  _M_s1 = std::sqrt(__np * __1p) * (1 + _M_d1 / (4 * __np));
1075 	  _M_s2 = std::sqrt(__np * __1p) * (1 + _M_d2 / (4 * _M_t * __1p));
1076 	  _M_c = 2 * _M_d1 / __np;
1077 	  _M_a1 = std::exp(_M_c) * _M_s1 * __spi_2;
1078 	  const _RealType __a12 = _M_a1 + _M_s2 * __spi_2;
1079 	  const _RealType __s1s = _M_s1 * _M_s1;
1080 	  _M_a123 = __a12 + (std::exp(_M_d1 / (_M_t * __1p))
1081 			     * 2 * __s1s / _M_d1
1082 			     * std::exp(-_M_d1 * _M_d1 / (2 * __s1s)));
1083 	  const _RealType __s2s = _M_s2 * _M_s2;
1084 	  _M_s = (_M_a123 + 2 * __s2s / _M_d2
1085 		  * std::exp(-_M_d2 * _M_d2 / (2 * __s2s)));
1086 	  _M_lf = (std::tr1::lgamma(__np + 1)
1087 		   + std::tr1::lgamma(_M_t - __np + 1));
1088 	  _M_lp1p = std::log(__pa / __1p);
1089 
1090 	  _M_q = -std::log(1 - (__p12 - __pa) / __1p);
1091 	}
1092       else
1093 #endif
1094 	_M_q = -std::log(1 - __p12);
1095     }
1096 
1097   template<typename _IntType, typename _RealType>
1098     template<class _UniformRandomNumberGenerator>
1099       typename binomial_distribution<_IntType, _RealType>::result_type
1100       binomial_distribution<_IntType, _RealType>::
1101       _M_waiting(_UniformRandomNumberGenerator& __urng, _IntType __t)
1102       {
1103 	_IntType    __x = 0;
1104 	_RealType __sum = 0;
1105 
1106 	do
1107 	  {
1108 	    const _RealType __e = -std::log(__urng());
1109 	    __sum += __e / (__t - __x);
1110 	    __x += 1;
1111 	  }
1112 	while (__sum <= _M_q);
1113 
1114 	return __x - 1;
1115       }
1116 
1117   /**
1118    * A rejection algorithm when t * p >= 8 and a simple waiting time
1119    * method - the second in the referenced book - otherwise.
1120    * NB: The former is available only if _GLIBCXX_USE_C99_MATH_TR1
1121    * is defined.
1122    *
1123    * Reference:
1124    * Devroye, L. "Non-Uniform Random Variates Generation." Springer-Verlag,
1125    * New York, 1986, Ch. X, Sect. 4 (+ Errata!).
1126    */
1127   template<typename _IntType, typename _RealType>
1128     template<class _UniformRandomNumberGenerator>
1129       typename binomial_distribution<_IntType, _RealType>::result_type
1130       binomial_distribution<_IntType, _RealType>::
1131       operator()(_UniformRandomNumberGenerator& __urng)
1132       {
1133 	result_type __ret;
1134 	const _RealType __p12 = _M_p <= 0.5 ? _M_p : 1.0 - _M_p;
1135 
1136 #if _GLIBCXX_USE_C99_MATH_TR1
1137 	if (!_M_easy)
1138 	  {
1139 	    _RealType __x;
1140 
1141 	    // See comments above...
1142 	    const _RealType __naf =
1143 	      (1 - std::numeric_limits<_RealType>::epsilon()) / 2;
1144 	    const _RealType __thr =
1145 	      std::numeric_limits<_IntType>::max() + __naf;
1146 
1147 	    const _RealType __np = std::floor(_M_t * __p12);
1148 	    const _RealType __pa = __np / _M_t;
1149 
1150 	    // sqrt(pi / 2)
1151 	    const _RealType __spi_2 = 1.2533141373155002512078826424055226L;
1152 	    const _RealType __a1 = _M_a1;
1153 	    const _RealType __a12 = __a1 + _M_s2 * __spi_2;
1154 	    const _RealType __a123 = _M_a123;
1155 	    const _RealType __s1s = _M_s1 * _M_s1;
1156 	    const _RealType __s2s = _M_s2 * _M_s2;
1157 
1158 	    bool __reject;
1159 	    do
1160 	      {
1161 		const _RealType __u = _M_s * __urng();
1162 
1163 		_RealType __v;
1164 
1165 		if (__u <= __a1)
1166 		  {
1167 		    const _RealType __n = _M_nd(__urng);
1168 		    const _RealType __y = _M_s1 * std::abs(__n);
1169 		    __reject = __y >= _M_d1;
1170 		    if (!__reject)
1171 		      {
1172 			const _RealType __e = -std::log(__urng());
1173 			__x = std::floor(__y);
1174 			__v = -__e - __n * __n / 2 + _M_c;
1175 		      }
1176 		  }
1177 		else if (__u <= __a12)
1178 		  {
1179 		    const _RealType __n = _M_nd(__urng);
1180 		    const _RealType __y = _M_s2 * std::abs(__n);
1181 		    __reject = __y >= _M_d2;
1182 		    if (!__reject)
1183 		      {
1184 			const _RealType __e = -std::log(__urng());
1185 			__x = std::floor(-__y);
1186 			__v = -__e - __n * __n / 2;
1187 		      }
1188 		  }
1189 		else if (__u <= __a123)
1190 		  {
1191 		    const _RealType __e1 = -std::log(__urng());
1192 		    const _RealType __e2 = -std::log(__urng());
1193 
1194 		    const _RealType __y = _M_d1 + 2 * __s1s * __e1 / _M_d1;
1195 		    __x = std::floor(__y);
1196 		    __v = (-__e2 + _M_d1 * (1 / (_M_t - __np)
1197 					    -__y / (2 * __s1s)));
1198 		    __reject = false;
1199 		  }
1200 		else
1201 		  {
1202 		    const _RealType __e1 = -std::log(__urng());
1203 		    const _RealType __e2 = -std::log(__urng());
1204 
1205 		    const _RealType __y = _M_d2 + 2 * __s2s * __e1 / _M_d2;
1206 		    __x = std::floor(-__y);
1207 		    __v = -__e2 - _M_d2 * __y / (2 * __s2s);
1208 		    __reject = false;
1209 		  }
1210 
1211 		__reject = __reject || __x < -__np || __x > _M_t - __np;
1212 		if (!__reject)
1213 		  {
1214 		    const _RealType __lfx =
1215 		      std::tr1::lgamma(__np + __x + 1)
1216 		      + std::tr1::lgamma(_M_t - (__np + __x) + 1);
1217 		    __reject = __v > _M_lf - __lfx + __x * _M_lp1p;
1218 		  }
1219 
1220 		__reject |= __x + __np >= __thr;
1221 	      }
1222 	    while (__reject);
1223 
1224 	    __x += __np + __naf;
1225 
1226 	    const _IntType __z = _M_waiting(__urng, _M_t - _IntType(__x));
1227 	    __ret = _IntType(__x) + __z;
1228 	  }
1229 	else
1230 #endif
1231 	  __ret = _M_waiting(__urng, _M_t);
1232 
1233 	if (__p12 != _M_p)
1234 	  __ret = _M_t - __ret;
1235 	return __ret;
1236       }
1237 
1238   template<typename _IntType, typename _RealType,
1239 	   typename _CharT, typename _Traits>
1240     std::basic_ostream<_CharT, _Traits>&
1241     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1242 	       const binomial_distribution<_IntType, _RealType>& __x)
1243     {
1244       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1245       typedef typename __ostream_type::ios_base    __ios_base;
1246 
1247       const typename __ios_base::fmtflags __flags = __os.flags();
1248       const _CharT __fill = __os.fill();
1249       const std::streamsize __precision = __os.precision();
1250       const _CharT __space = __os.widen(' ');
1251       __os.flags(__ios_base::scientific | __ios_base::left);
1252       __os.fill(__space);
1253       __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
1254 
1255       __os << __x.t() << __space << __x.p()
1256 	   << __space << __x._M_nd;
1257 
1258       __os.flags(__flags);
1259       __os.fill(__fill);
1260       __os.precision(__precision);
1261       return __os;
1262     }
1263 
1264   template<typename _IntType, typename _RealType,
1265 	   typename _CharT, typename _Traits>
1266     std::basic_istream<_CharT, _Traits>&
1267     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1268 	       binomial_distribution<_IntType, _RealType>& __x)
1269     {
1270       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1271       typedef typename __istream_type::ios_base    __ios_base;
1272 
1273       const typename __ios_base::fmtflags __flags = __is.flags();
1274       __is.flags(__ios_base::dec | __ios_base::skipws);
1275 
1276       __is >> __x._M_t >> __x._M_p >> __x._M_nd;
1277       __x._M_initialize();
1278 
1279       __is.flags(__flags);
1280       return __is;
1281     }
1282 
1283 
1284   template<typename _RealType, typename _CharT, typename _Traits>
1285     std::basic_ostream<_CharT, _Traits>&
1286     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1287 	       const uniform_real<_RealType>& __x)
1288     {
1289       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1290       typedef typename __ostream_type::ios_base    __ios_base;
1291 
1292       const typename __ios_base::fmtflags __flags = __os.flags();
1293       const _CharT __fill = __os.fill();
1294       const std::streamsize __precision = __os.precision();
1295       const _CharT __space = __os.widen(' ');
1296       __os.flags(__ios_base::scientific | __ios_base::left);
1297       __os.fill(__space);
1298       __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
1299 
1300       __os << __x.min() << __space << __x.max();
1301 
1302       __os.flags(__flags);
1303       __os.fill(__fill);
1304       __os.precision(__precision);
1305       return __os;
1306     }
1307 
1308   template<typename _RealType, typename _CharT, typename _Traits>
1309     std::basic_istream<_CharT, _Traits>&
1310     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1311 	       uniform_real<_RealType>& __x)
1312     {
1313       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1314       typedef typename __istream_type::ios_base    __ios_base;
1315 
1316       const typename __ios_base::fmtflags __flags = __is.flags();
1317       __is.flags(__ios_base::skipws);
1318 
1319       __is >> __x._M_min >> __x._M_max;
1320 
1321       __is.flags(__flags);
1322       return __is;
1323     }
1324 
1325 
1326   template<typename _RealType, typename _CharT, typename _Traits>
1327     std::basic_ostream<_CharT, _Traits>&
1328     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1329 	       const exponential_distribution<_RealType>& __x)
1330     {
1331       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1332       typedef typename __ostream_type::ios_base    __ios_base;
1333 
1334       const typename __ios_base::fmtflags __flags = __os.flags();
1335       const _CharT __fill = __os.fill();
1336       const std::streamsize __precision = __os.precision();
1337       __os.flags(__ios_base::scientific | __ios_base::left);
1338       __os.fill(__os.widen(' '));
1339       __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
1340 
1341       __os << __x.lambda();
1342 
1343       __os.flags(__flags);
1344       __os.fill(__fill);
1345       __os.precision(__precision);
1346       return __os;
1347     }
1348 
1349 
1350   /**
1351    * Polar method due to Marsaglia.
1352    *
1353    * Devroye, L. "Non-Uniform Random Variates Generation." Springer-Verlag,
1354    * New York, 1986, Ch. V, Sect. 4.4.
1355    */
1356   template<typename _RealType>
1357     template<class _UniformRandomNumberGenerator>
1358       typename normal_distribution<_RealType>::result_type
1359       normal_distribution<_RealType>::
1360       operator()(_UniformRandomNumberGenerator& __urng)
1361       {
1362 	result_type __ret;
1363 
1364 	if (_M_saved_available)
1365 	  {
1366 	    _M_saved_available = false;
1367 	    __ret = _M_saved;
1368 	  }
1369 	else
1370 	  {
1371 	    result_type __x, __y, __r2;
1372 	    do
1373 	      {
1374 		__x = result_type(2.0) * __urng() - 1.0;
1375 		__y = result_type(2.0) * __urng() - 1.0;
1376 		__r2 = __x * __x + __y * __y;
1377 	      }
1378 	    while (__r2 > 1.0 || __r2 == 0.0);
1379 
1380 	    const result_type __mult = std::sqrt(-2 * std::log(__r2) / __r2);
1381 	    _M_saved = __x * __mult;
1382 	    _M_saved_available = true;
1383 	    __ret = __y * __mult;
1384 	  }
1385 
1386 	__ret = __ret * _M_sigma + _M_mean;
1387 	return __ret;
1388       }
1389 
1390   template<typename _RealType, typename _CharT, typename _Traits>
1391     std::basic_ostream<_CharT, _Traits>&
1392     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1393 	       const normal_distribution<_RealType>& __x)
1394     {
1395       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1396       typedef typename __ostream_type::ios_base    __ios_base;
1397 
1398       const typename __ios_base::fmtflags __flags = __os.flags();
1399       const _CharT __fill = __os.fill();
1400       const std::streamsize __precision = __os.precision();
1401       const _CharT __space = __os.widen(' ');
1402       __os.flags(__ios_base::scientific | __ios_base::left);
1403       __os.fill(__space);
1404       __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
1405 
1406       __os << __x._M_saved_available << __space
1407 	   << __x.mean() << __space
1408 	   << __x.sigma();
1409       if (__x._M_saved_available)
1410 	__os << __space << __x._M_saved;
1411 
1412       __os.flags(__flags);
1413       __os.fill(__fill);
1414       __os.precision(__precision);
1415       return __os;
1416     }
1417 
1418   template<typename _RealType, typename _CharT, typename _Traits>
1419     std::basic_istream<_CharT, _Traits>&
1420     operator>>(std::basic_istream<_CharT, _Traits>& __is,
1421 	       normal_distribution<_RealType>& __x)
1422     {
1423       typedef std::basic_istream<_CharT, _Traits>  __istream_type;
1424       typedef typename __istream_type::ios_base    __ios_base;
1425 
1426       const typename __ios_base::fmtflags __flags = __is.flags();
1427       __is.flags(__ios_base::dec | __ios_base::skipws);
1428 
1429       __is >> __x._M_saved_available >> __x._M_mean
1430 	   >> __x._M_sigma;
1431       if (__x._M_saved_available)
1432 	__is >> __x._M_saved;
1433 
1434       __is.flags(__flags);
1435       return __is;
1436     }
1437 
1438 
1439   template<typename _RealType>
1440     void
1441     gamma_distribution<_RealType>::
1442     _M_initialize()
1443     {
1444       if (_M_alpha >= 1)
1445 	_M_l_d = std::sqrt(2 * _M_alpha - 1);
1446       else
1447 	_M_l_d = (std::pow(_M_alpha, _M_alpha / (1 - _M_alpha))
1448 		  * (1 - _M_alpha));
1449     }
1450 
1451   /**
1452    * Cheng's rejection algorithm GB for alpha >= 1 and a modification
1453    * of Vaduva's rejection from Weibull algorithm due to Devroye for
1454    * alpha < 1.
1455    *
1456    * References:
1457    * Cheng, R. C. "The Generation of Gamma Random Variables with Non-integral
1458    * Shape Parameter." Applied Statistics, 26, 71-75, 1977.
1459    *
1460    * Vaduva, I. "Computer Generation of Gamma Gandom Variables by Rejection
1461    * and Composition Procedures." Math. Operationsforschung and Statistik,
1462    * Series in Statistics, 8, 545-576, 1977.
1463    *
1464    * Devroye, L. "Non-Uniform Random Variates Generation." Springer-Verlag,
1465    * New York, 1986, Ch. IX, Sect. 3.4 (+ Errata!).
1466    */
1467   template<typename _RealType>
1468     template<class _UniformRandomNumberGenerator>
1469       typename gamma_distribution<_RealType>::result_type
1470       gamma_distribution<_RealType>::
1471       operator()(_UniformRandomNumberGenerator& __urng)
1472       {
1473 	result_type __x;
1474 
1475 	bool __reject;
1476 	if (_M_alpha >= 1)
1477 	  {
1478 	    // alpha - log(4)
1479 	    const result_type __b = _M_alpha
1480 	      - result_type(1.3862943611198906188344642429163531L);
1481 	    const result_type __c = _M_alpha + _M_l_d;
1482 	    const result_type __1l = 1 / _M_l_d;
1483 
1484 	    // 1 + log(9 / 2)
1485 	    const result_type __k = 2.5040773967762740733732583523868748L;
1486 
1487 	    do
1488 	      {
1489 		const result_type __u = __urng();
1490 		const result_type __v = __urng();
1491 
1492 		const result_type __y = __1l * std::log(__v / (1 - __v));
1493 		__x = _M_alpha * std::exp(__y);
1494 
1495 		const result_type __z = __u * __v * __v;
1496 		const result_type __r = __b + __c * __y - __x;
1497 
1498 		__reject = __r < result_type(4.5) * __z - __k;
1499 		if (__reject)
1500 		  __reject = __r < std::log(__z);
1501 	      }
1502 	    while (__reject);
1503 	  }
1504 	else
1505 	  {
1506 	    const result_type __c = 1 / _M_alpha;
1507 
1508 	    do
1509 	      {
1510 		const result_type __z = -std::log(__urng());
1511 		const result_type __e = -std::log(__urng());
1512 
1513 		__x = std::pow(__z, __c);
1514 
1515 		__reject = __z + __e < _M_l_d + __x;
1516 	      }
1517 	    while (__reject);
1518 	  }
1519 
1520 	return __x;
1521       }
1522 
1523   template<typename _RealType, typename _CharT, typename _Traits>
1524     std::basic_ostream<_CharT, _Traits>&
1525     operator<<(std::basic_ostream<_CharT, _Traits>& __os,
1526 	       const gamma_distribution<_RealType>& __x)
1527     {
1528       typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
1529       typedef typename __ostream_type::ios_base    __ios_base;
1530 
1531       const typename __ios_base::fmtflags __flags = __os.flags();
1532       const _CharT __fill = __os.fill();
1533       const std::streamsize __precision = __os.precision();
1534       __os.flags(__ios_base::scientific | __ios_base::left);
1535       __os.fill(__os.widen(' '));
1536       __os.precision(__gnu_cxx::__numeric_traits<_RealType>::__max_digits10);
1537 
1538       __os << __x.alpha();
1539 
1540       __os.flags(__flags);
1541       __os.fill(__fill);
1542       __os.precision(__precision);
1543       return __os;
1544     }
1545 
1546 _GLIBCXX_END_NAMESPACE
1547 }
1548