Bug fixes in the ReferenceMap concept.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
20 * This file contains the reimplemented version of the Mersenne Twister
21 * Generator of Matsumoto and Nishimura.
23 * See the appropriate copyright notice below.
25 * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
26 * All rights reserved.
28 * Redistribution and use in source and binary forms, with or without
29 * modification, are permitted provided that the following conditions
32 * 1. Redistributions of source code must retain the above copyright
33 * notice, this list of conditions and the following disclaimer.
35 * 2. Redistributions in binary form must reproduce the above copyright
36 * notice, this list of conditions and the following disclaimer in the
37 * documentation and/or other materials provided with the distribution.
39 * 3. The names of its contributors may not be used to endorse or promote
40 * products derived from this software without specific prior written
43 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
44 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
45 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
46 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
47 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
48 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
49 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
50 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
51 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
52 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
53 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
54 * OF THE POSSIBILITY OF SUCH DAMAGE.
57 * Any feedback is very welcome.
58 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
59 * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
62 #ifndef LEMON_RANDOM_H
63 #define LEMON_RANDOM_H
72 #include <lemon/dim2.h>
75 ///\brief Mersenne Twister random number generator
79 namespace _random_bits {
81 template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
82 struct RandomTraits {};
84 template <typename _Word>
85 struct RandomTraits<_Word, 32> {
88 static const int bits = 32;
90 static const int length = 624;
91 static const int shift = 397;
93 static const Word mul = 0x6c078965u;
94 static const Word arrayInit = 0x012BD6AAu;
95 static const Word arrayMul1 = 0x0019660Du;
96 static const Word arrayMul2 = 0x5D588B65u;
98 static const Word mask = 0x9908B0DFu;
99 static const Word loMask = (1u << 31) - 1;
100 static const Word hiMask = ~loMask;
103 static Word tempering(Word rnd) {
105 rnd ^= (rnd << 7) & 0x9D2C5680u;
106 rnd ^= (rnd << 15) & 0xEFC60000u;
113 template <typename _Word>
114 struct RandomTraits<_Word, 64> {
117 static const int bits = 64;
119 static const int length = 312;
120 static const int shift = 156;
122 static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
123 static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
124 static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
125 static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
127 static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
128 static const Word loMask = (Word(1u) << 31) - 1;
129 static const Word hiMask = ~loMask;
131 static Word tempering(Word rnd) {
132 rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
133 rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
134 rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
141 template <typename _Word>
149 static const int bits = RandomTraits<Word>::bits;
151 static const int length = RandomTraits<Word>::length;
152 static const int shift = RandomTraits<Word>::shift;
157 static const Word seedArray[4] = {
158 0x12345u, 0x23456u, 0x34567u, 0x45678u
161 initState(seedArray, seedArray + 4);
164 void initState(Word seed) {
166 static const Word mul = RandomTraits<Word>::mul;
170 Word *curr = state + length - 1;
171 curr[0] = seed; --curr;
172 for (int i = 1; i < length; ++i) {
173 curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
178 template <typename Iterator>
179 void initState(Iterator begin, Iterator end) {
181 static const Word init = RandomTraits<Word>::arrayInit;
182 static const Word mul1 = RandomTraits<Word>::arrayMul1;
183 static const Word mul2 = RandomTraits<Word>::arrayMul2;
186 Word *curr = state + length - 1; --curr;
187 Iterator it = begin; int cnt = 0;
192 num = length > end - begin ? length : end - begin;
194 curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
201 curr = state + length - 1; curr[0] = state[0];
206 num = length - 1; cnt = length - (curr - state) - 1;
208 curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
212 curr = state + length - 1; curr[0] = state[0]; --curr;
217 state[length - 1] = Word(1) << (bits - 1);
220 void copyState(const RandomCore& other) {
221 std::copy(other.state, other.state + length, state);
222 current = state + (other.current - other.state);
226 if (current == state) fillState();
229 return RandomTraits<Word>::tempering(rnd);
236 static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
237 static const Word loMask = RandomTraits<Word>::loMask;
238 static const Word hiMask = RandomTraits<Word>::hiMask;
240 current = state + length;
242 register Word *curr = state + length - 1;
245 num = length - shift;
247 curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
248 curr[- shift] ^ mask[curr[-1] & 1ul];
253 curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
254 curr[length - shift] ^ mask[curr[-1] & 1ul];
257 state[0] = (((state[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
258 curr[length - shift] ^ mask[curr[length - 1] & 1ul];
269 template <typename Result,
270 int shift = (std::numeric_limits<Result>::digits + 1) / 2>
272 static Result mask(const Result& result) {
273 return Masker<Result, (shift + 1) / 2>::
274 mask(static_cast<Result>(result | (result >> shift)));
278 template <typename Result>
279 struct Masker<Result, 1> {
280 static Result mask(const Result& result) {
281 return static_cast<Result>(result | (result >> 1));
285 template <typename Result, typename Word,
286 int rest = std::numeric_limits<Result>::digits, int shift = 0,
287 bool last = rest <= std::numeric_limits<Word>::digits>
288 struct IntConversion {
289 static const int bits = std::numeric_limits<Word>::digits;
291 static Result convert(RandomCore<Word>& rnd) {
292 return static_cast<Result>(rnd() >> (bits - rest)) << shift;
297 template <typename Result, typename Word, int rest, int shift>
298 struct IntConversion<Result, Word, rest, shift, false> {
299 static const int bits = std::numeric_limits<Word>::digits;
301 static Result convert(RandomCore<Word>& rnd) {
302 return (static_cast<Result>(rnd()) << shift) |
303 IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
308 template <typename Result, typename Word,
309 bool one_word = (std::numeric_limits<Word>::digits <
310 std::numeric_limits<Result>::digits) >
312 static Result map(RandomCore<Word>& rnd, const Result& bound) {
313 Word max = Word(bound - 1);
314 Result mask = Masker<Result>::mask(bound - 1);
317 num = IntConversion<Result, Word>::convert(rnd) & mask;
323 template <typename Result, typename Word>
324 struct Mapping<Result, Word, false> {
325 static Result map(RandomCore<Word>& rnd, const Result& bound) {
326 Word max = Word(bound - 1);
327 Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
337 template <typename Result, int exp, bool pos = (exp >= 0)>
338 struct ShiftMultiplier {
339 static const Result multiplier() {
340 Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
342 if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
347 template <typename Result, int exp>
348 struct ShiftMultiplier<Result, exp, false> {
349 static const Result multiplier() {
350 Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
352 if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
357 template <typename Result>
358 struct ShiftMultiplier<Result, 0, true> {
359 static const Result multiplier() {
360 return static_cast<Result>(1.0);
364 template <typename Result>
365 struct ShiftMultiplier<Result, -20, true> {
366 static const Result multiplier() {
367 return static_cast<Result>(1.0/1048576.0);
371 template <typename Result>
372 struct ShiftMultiplier<Result, -32, true> {
373 static const Result multiplier() {
374 return static_cast<Result>(1.0/424967296.0);
378 template <typename Result>
379 struct ShiftMultiplier<Result, -53, true> {
380 static const Result multiplier() {
381 return static_cast<Result>(1.0/9007199254740992.0);
385 template <typename Result>
386 struct ShiftMultiplier<Result, -64, true> {
387 static const Result multiplier() {
388 return static_cast<Result>(1.0/18446744073709551616.0);
392 template <typename Result, int exp>
394 static Result shift(const Result& result) {
395 return result * ShiftMultiplier<Result, exp>::multiplier();
399 template <typename Result, typename Word,
400 int rest = std::numeric_limits<Result>::digits, int shift = 0,
401 bool last = rest <= std::numeric_limits<Word>::digits>
402 struct RealConversion{
403 static const int bits = std::numeric_limits<Word>::digits;
405 static Result convert(RandomCore<Word>& rnd) {
406 return Shifting<Result, - shift - rest>::
407 shift(static_cast<Result>(rnd() >> (bits - rest)));
411 template <typename Result, typename Word, int rest, int shift>
412 struct RealConversion<Result, Word, rest, shift, false> {
413 static const int bits = std::numeric_limits<Word>::digits;
415 static Result convert(RandomCore<Word>& rnd) {
416 return Shifting<Result, - shift - bits>::
417 shift(static_cast<Result>(rnd())) +
418 RealConversion<Result, Word, rest-bits, shift + bits>::
423 template <typename Result, typename Word>
426 template <typename Iterator>
427 static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
428 std::vector<Word> ws;
429 for (Iterator it = begin; it != end; ++it) {
430 ws.push_back(Word(*it));
432 rnd.initState(ws.begin(), ws.end());
435 static void init(RandomCore<Word>& rnd, Result seed) {
440 template <typename Word>
441 struct BoolConversion {
442 static bool convert(RandomCore<Word>& rnd) {
443 return (rnd() & 1) == 1;
447 template <typename Word>
448 struct BoolProducer {
452 BoolProducer() : num(0) {}
454 bool convert(RandomCore<Word>& rnd) {
457 num = RandomTraits<Word>::bits;
459 bool r = (buffer & 1);
470 /// \brief Mersenne Twister random number generator
472 /// The Mersenne Twister is a twisted generalized feedback
473 /// shift-register generator of Matsumoto and Nishimura. The period
474 /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
475 /// equi-distributed in 623 dimensions for 32-bit numbers. The time
476 /// performance of this generator is comparable to the commonly used
479 /// This implementation is specialized for both 32-bit and 64-bit
480 /// architectures. The generators differ sligthly in the
481 /// initialization and generation phase so they produce two
482 /// completly different sequences.
484 /// The generator gives back random numbers of serveral types. To
485 /// get a random number from a range of a floating point type you
486 /// can use one form of the \c operator() or the \c real() member
487 /// function. If you want to get random number from the {0, 1, ...,
488 /// n-1} integer range use the \c operator[] or the \c integer()
489 /// method. And to get random number from the whole range of an
490 /// integer type you can use the argumentless \c integer() or \c
491 /// uinteger() functions. After all you can get random bool with
492 /// equal chance of true and false or given probability of true
493 /// result with the \c boolean() member functions.
496 /// // The commented code is identical to the other
497 /// double a = rnd(); // [0.0, 1.0)
498 /// // double a = rnd.real(); // [0.0, 1.0)
499 /// double b = rnd(100.0); // [0.0, 100.0)
500 /// // double b = rnd.real(100.0); // [0.0, 100.0)
501 /// double c = rnd(1.0, 2.0); // [1.0, 2.0)
502 /// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0)
503 /// int d = rnd[100000]; // 0..99999
504 /// // int d = rnd.integer(100000); // 0..99999
505 /// int e = rnd[6] + 1; // 1..6
506 /// // int e = rnd.integer(1, 1 + 6); // 1..6
507 /// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1
508 /// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1
509 /// bool g = rnd.boolean(); // P(g = true) = 0.5
510 /// bool h = rnd.boolean(0.8); // P(h = true) = 0.8
513 /// LEMON provides a global instance of the random number
514 /// generator which name is \ref lemon::rnd "rnd". Usually it is a
515 /// good programming convenience to use this global generator to get
521 typedef unsigned long Word;
523 _random_bits::RandomCore<Word> core;
524 _random_bits::BoolProducer<Word> bool_producer;
529 /// \brief Default constructor
531 /// Constructor with constant seeding.
532 Random() { core.initState(); }
534 /// \brief Constructor with seed
536 /// Constructor with seed. The current number type will be converted
537 /// to the architecture word type.
538 template <typename Number>
539 Random(Number seed) {
540 _random_bits::Initializer<Number, Word>::init(core, seed);
543 /// \brief Constructor with array seeding
545 /// Constructor with array seeding. The given range should contain
546 /// any number type and the numbers will be converted to the
547 /// architecture word type.
548 template <typename Iterator>
549 Random(Iterator begin, Iterator end) {
550 typedef typename std::iterator_traits<Iterator>::value_type Number;
551 _random_bits::Initializer<Number, Word>::init(core, begin, end);
554 /// \brief Copy constructor
556 /// Copy constructor. The generated sequence will be identical to
557 /// the other sequence. It can be used to save the current state
558 /// of the generator and later use it to generate the same
560 Random(const Random& other) {
561 core.copyState(other.core);
564 /// \brief Assign operator
566 /// Assign operator. The generated sequence will be identical to
567 /// the other sequence. It can be used to save the current state
568 /// of the generator and later use it to generate the same
570 Random& operator=(const Random& other) {
571 if (&other != this) {
572 core.copyState(other.core);
577 /// \brief Returns a random real number from the range [0, 1)
579 /// It returns a random real number from the range [0, 1). The
580 /// default Number type is \c double.
581 template <typename Number>
583 return _random_bits::RealConversion<Number, Word>::convert(core);
587 return real<double>();
590 /// \brief Returns a random real number the range [0, b)
592 /// It returns a random real number from the range [0, b).
593 template <typename Number>
594 Number real(Number b) {
595 return real<Number>() * b;
598 /// \brief Returns a random real number from the range [a, b)
600 /// It returns a random real number from the range [a, b).
601 template <typename Number>
602 Number real(Number a, Number b) {
603 return real<Number>() * (b - a) + a;
606 /// \brief Returns a random real number from the range [0, 1)
608 /// It returns a random double from the range [0, 1).
609 double operator()() {
610 return real<double>();
613 /// \brief Returns a random real number from the range [0, b)
615 /// It returns a random real number from the range [0, b).
616 template <typename Number>
617 Number operator()(Number b) {
618 return real<Number>() * b;
621 /// \brief Returns a random real number from the range [a, b)
623 /// It returns a random real number from the range [a, b).
624 template <typename Number>
625 Number operator()(Number a, Number b) {
626 return real<Number>() * (b - a) + a;
629 /// \brief Returns a random integer from a range
631 /// It returns a random integer from the range {0, 1, ..., b - 1}.
632 template <typename Number>
633 Number integer(Number b) {
634 return _random_bits::Mapping<Number, Word>::map(core, b);
637 /// \brief Returns a random integer from a range
639 /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
640 template <typename Number>
641 Number integer(Number a, Number b) {
642 return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
645 /// \brief Returns a random integer from a range
647 /// It returns a random integer from the range {0, 1, ..., b - 1}.
648 template <typename Number>
649 Number operator[](Number b) {
650 return _random_bits::Mapping<Number, Word>::map(core, b);
653 /// \brief Returns a random non-negative integer
655 /// It returns a random non-negative integer uniformly from the
656 /// whole range of the current \c Number type. The default result
657 /// type of this function is <tt>unsigned int</tt>.
658 template <typename Number>
660 return _random_bits::IntConversion<Number, Word>::convert(core);
663 unsigned int uinteger() {
664 return uinteger<unsigned int>();
667 /// \brief Returns a random integer
669 /// It returns a random integer uniformly from the whole range of
670 /// the current \c Number type. The default result type of this
671 /// function is \c int.
672 template <typename Number>
674 static const int nb = std::numeric_limits<Number>::digits +
675 (std::numeric_limits<Number>::is_signed ? 1 : 0);
676 return _random_bits::IntConversion<Number, Word, nb>::convert(core);
680 return integer<int>();
683 /// \brief Returns a random bool
685 /// It returns a random bool. The generator holds a buffer for
686 /// random bits. Every time when it become empty the generator makes
687 /// a new random word and fill the buffer up.
689 return bool_producer.convert(core);
692 ///\name Non-uniform distributions
697 /// \brief Returns a random bool
699 /// It returns a random bool with given probability of true result.
700 bool boolean(double p) {
701 return operator()() < p;
704 /// Standard Gauss distribution
706 /// Standard Gauss distribution.
707 /// \note The Cartesian form of the Box-Muller
708 /// transformation is used to generate a random normal distribution.
709 /// \todo Consider using the "ziggurat" method instead.
714 V1=2*real<double>()-1;
715 V2=2*real<double>()-1;
718 return std::sqrt(-2*std::log(S)/S)*V1;
720 /// Gauss distribution with given mean and standard deviation
722 /// Gauss distribution with given mean and standard deviation.
724 double gauss(double mean,double std_dev)
726 return gauss()*std_dev+mean;
729 /// Exponential distribution with given mean
731 /// This function generates an exponential distribution random number
732 /// with mean <tt>1/lambda</tt>.
734 double exponential(double lambda=1.0)
736 return -std::log(1.0-real<double>())/lambda;
739 /// Gamma distribution with given integer shape
741 /// This function generates a gamma distribution random number.
743 ///\param k shape parameter (<tt>k>0</tt> integer)
747 for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
751 /// Gamma distribution with given shape and scale parameter
753 /// This function generates a gamma distribution random number.
755 ///\param k shape parameter (<tt>k>0</tt>)
756 ///\param theta scale parameter
758 double gamma(double k,double theta=1.0)
761 const double delta = k-std::floor(k);
762 const double v0=M_E/(M_E-delta);
764 double V0=1.0-real<double>();
765 double V1=1.0-real<double>();
766 double V2=1.0-real<double>();
769 xi=std::pow(V1,1.0/delta);
770 nu=V0*std::pow(xi,delta-1.0);
777 } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
778 return theta*(xi-gamma(int(std::floor(k))));
781 /// Weibull distribution
783 /// This function generates a Weibull distribution random number.
785 ///\param k shape parameter (<tt>k>0</tt>)
786 ///\param lambda scale parameter (<tt>lambda>0</tt>)
788 double weibull(double k,double lambda)
790 return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
793 /// Pareto distribution
795 /// This function generates a Pareto distribution random number.
797 ///\param k shape parameter (<tt>k>0</tt>)
798 ///\param x_min location parameter (<tt>x_min>0</tt>)
800 double pareto(double k,double x_min)
802 return exponential(gamma(k,1.0/x_min));
807 ///\name Two dimensional distributions
812 /// Uniform distribution on the full unit circle
814 /// Uniform distribution on the full unit circle.
816 dim2::Point<double> disc()
820 V1=2*real<double>()-1;
821 V2=2*real<double>()-1;
823 } while(V1*V1+V2*V2>=1);
824 return dim2::Point<double>(V1,V2);
826 /// A kind of two dimensional Gauss distribution
828 /// This function provides a turning symmetric two-dimensional distribution.
829 /// Both coordinates are of standard normal distribution, but they are not
832 /// \note The coordinates are the two random variables provided by
833 /// the Box-Muller method.
834 dim2::Point<double> gauss2()
838 V1=2*real<double>()-1;
839 V2=2*real<double>()-1;
842 double W=std::sqrt(-2*std::log(S)/S);
843 return dim2::Point<double>(W*V1,W*V2);
845 /// A kind of two dimensional exponential distribution
847 /// This function provides a turning symmetric two-dimensional distribution.
848 /// The x-coordinate is of conditionally exponential distribution
849 /// with the condition that x is positive and y=0. If x is negative and
850 /// y=0 then, -x is of exponential distribution. The same is true for the
852 dim2::Point<double> exponential2()
856 V1=2*real<double>()-1;
857 V2=2*real<double>()-1;
860 double W=-std::log(S)/S;
861 return dim2::Point<double>(W*V1,W*V2);