1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/random.h Thu Jan 03 11:13:29 2008 +0100
1.3 @@ -0,0 +1,872 @@
1.4 +/* -*- C++ -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library
1.7 + *
1.8 + * Copyright (C) 2003-2007
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +/*
1.23 + * This file contains the reimplemented version of the Mersenne Twister
1.24 + * Generator of Matsumoto and Nishimura.
1.25 + *
1.26 + * See the appropriate copyright notice below.
1.27 + *
1.28 + * Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
1.29 + * All rights reserved.
1.30 + *
1.31 + * Redistribution and use in source and binary forms, with or without
1.32 + * modification, are permitted provided that the following conditions
1.33 + * are met:
1.34 + *
1.35 + * 1. Redistributions of source code must retain the above copyright
1.36 + * notice, this list of conditions and the following disclaimer.
1.37 + *
1.38 + * 2. Redistributions in binary form must reproduce the above copyright
1.39 + * notice, this list of conditions and the following disclaimer in the
1.40 + * documentation and/or other materials provided with the distribution.
1.41 + *
1.42 + * 3. The names of its contributors may not be used to endorse or promote
1.43 + * products derived from this software without specific prior written
1.44 + * permission.
1.45 + *
1.46 + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
1.47 + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
1.48 + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
1.49 + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
1.50 + * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
1.51 + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
1.52 + * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
1.53 + * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
1.54 + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
1.55 + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
1.56 + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
1.57 + * OF THE POSSIBILITY OF SUCH DAMAGE.
1.58 + *
1.59 + *
1.60 + * Any feedback is very welcome.
1.61 + * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
1.62 + * email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
1.63 + */
1.64 +
1.65 +#ifndef LEMON_RANDOM_H
1.66 +#define LEMON_RANDOM_H
1.67 +
1.68 +#include <algorithm>
1.69 +#include <iterator>
1.70 +#include <vector>
1.71 +
1.72 +#include <ctime>
1.73 +#include <cmath>
1.74 +
1.75 +#include <lemon/dim2.h>
1.76 +///\ingroup misc
1.77 +///\file
1.78 +///\brief Mersenne Twister random number generator
1.79 +
1.80 +namespace lemon {
1.81 +
1.82 + namespace _random_bits {
1.83 +
1.84 + template <typename _Word, int _bits = std::numeric_limits<_Word>::digits>
1.85 + struct RandomTraits {};
1.86 +
1.87 + template <typename _Word>
1.88 + struct RandomTraits<_Word, 32> {
1.89 +
1.90 + typedef _Word Word;
1.91 + static const int bits = 32;
1.92 +
1.93 + static const int length = 624;
1.94 + static const int shift = 397;
1.95 +
1.96 + static const Word mul = 0x6c078965u;
1.97 + static const Word arrayInit = 0x012BD6AAu;
1.98 + static const Word arrayMul1 = 0x0019660Du;
1.99 + static const Word arrayMul2 = 0x5D588B65u;
1.100 +
1.101 + static const Word mask = 0x9908B0DFu;
1.102 + static const Word loMask = (1u << 31) - 1;
1.103 + static const Word hiMask = ~loMask;
1.104 +
1.105 +
1.106 + static Word tempering(Word rnd) {
1.107 + rnd ^= (rnd >> 11);
1.108 + rnd ^= (rnd << 7) & 0x9D2C5680u;
1.109 + rnd ^= (rnd << 15) & 0xEFC60000u;
1.110 + rnd ^= (rnd >> 18);
1.111 + return rnd;
1.112 + }
1.113 +
1.114 + };
1.115 +
1.116 + template <typename _Word>
1.117 + struct RandomTraits<_Word, 64> {
1.118 +
1.119 + typedef _Word Word;
1.120 + static const int bits = 64;
1.121 +
1.122 + static const int length = 312;
1.123 + static const int shift = 156;
1.124 +
1.125 + static const Word mul = Word(0x5851F42Du) << 32 | Word(0x4C957F2Du);
1.126 + static const Word arrayInit = Word(0x00000000u) << 32 |Word(0x012BD6AAu);
1.127 + static const Word arrayMul1 = Word(0x369DEA0Fu) << 32 |Word(0x31A53F85u);
1.128 + static const Word arrayMul2 = Word(0x27BB2EE6u) << 32 |Word(0x87B0B0FDu);
1.129 +
1.130 + static const Word mask = Word(0xB5026F5Au) << 32 | Word(0xA96619E9u);
1.131 + static const Word loMask = (Word(1u) << 31) - 1;
1.132 + static const Word hiMask = ~loMask;
1.133 +
1.134 + static Word tempering(Word rnd) {
1.135 + rnd ^= (rnd >> 29) & (Word(0x55555555u) << 32 | Word(0x55555555u));
1.136 + rnd ^= (rnd << 17) & (Word(0x71D67FFFu) << 32 | Word(0xEDA60000u));
1.137 + rnd ^= (rnd << 37) & (Word(0xFFF7EEE0u) << 32 | Word(0x00000000u));
1.138 + rnd ^= (rnd >> 43);
1.139 + return rnd;
1.140 + }
1.141 +
1.142 + };
1.143 +
1.144 + template <typename _Word>
1.145 + class RandomCore {
1.146 + public:
1.147 +
1.148 + typedef _Word Word;
1.149 +
1.150 + private:
1.151 +
1.152 + static const int bits = RandomTraits<Word>::bits;
1.153 +
1.154 + static const int length = RandomTraits<Word>::length;
1.155 + static const int shift = RandomTraits<Word>::shift;
1.156 +
1.157 + public:
1.158 +
1.159 + void initState() {
1.160 + static const Word seedArray[4] = {
1.161 + 0x12345u, 0x23456u, 0x34567u, 0x45678u
1.162 + };
1.163 +
1.164 + initState(seedArray, seedArray + 4);
1.165 + }
1.166 +
1.167 + void initState(Word seed) {
1.168 +
1.169 + static const Word mul = RandomTraits<Word>::mul;
1.170 +
1.171 + current = state;
1.172 +
1.173 + Word *curr = state + length - 1;
1.174 + curr[0] = seed; --curr;
1.175 + for (int i = 1; i < length; ++i) {
1.176 + curr[0] = (mul * ( curr[1] ^ (curr[1] >> (bits - 2)) ) + i);
1.177 + --curr;
1.178 + }
1.179 + }
1.180 +
1.181 + template <typename Iterator>
1.182 + void initState(Iterator begin, Iterator end) {
1.183 +
1.184 + static const Word init = RandomTraits<Word>::arrayInit;
1.185 + static const Word mul1 = RandomTraits<Word>::arrayMul1;
1.186 + static const Word mul2 = RandomTraits<Word>::arrayMul2;
1.187 +
1.188 +
1.189 + Word *curr = state + length - 1; --curr;
1.190 + Iterator it = begin; int cnt = 0;
1.191 + int num;
1.192 +
1.193 + initState(init);
1.194 +
1.195 + num = length > end - begin ? length : end - begin;
1.196 + while (num--) {
1.197 + curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul1))
1.198 + + *it + cnt;
1.199 + ++it; ++cnt;
1.200 + if (it == end) {
1.201 + it = begin; cnt = 0;
1.202 + }
1.203 + if (curr == state) {
1.204 + curr = state + length - 1; curr[0] = state[0];
1.205 + }
1.206 + --curr;
1.207 + }
1.208 +
1.209 + num = length - 1; cnt = length - (curr - state) - 1;
1.210 + while (num--) {
1.211 + curr[0] = (curr[0] ^ ((curr[1] ^ (curr[1] >> (bits - 2))) * mul2))
1.212 + - cnt;
1.213 + --curr; ++cnt;
1.214 + if (curr == state) {
1.215 + curr = state + length - 1; curr[0] = state[0]; --curr;
1.216 + cnt = 1;
1.217 + }
1.218 + }
1.219 +
1.220 + state[length - 1] = Word(1) << (bits - 1);
1.221 + }
1.222 +
1.223 + void copyState(const RandomCore& other) {
1.224 + std::copy(other.state, other.state + length, state);
1.225 + current = state + (other.current - other.state);
1.226 + }
1.227 +
1.228 + Word operator()() {
1.229 + if (current == state) fillState();
1.230 + --current;
1.231 + Word rnd = *current;
1.232 + return RandomTraits<Word>::tempering(rnd);
1.233 + }
1.234 +
1.235 + private:
1.236 +
1.237 +
1.238 + void fillState() {
1.239 + static const Word mask[2] = { 0x0ul, RandomTraits<Word>::mask };
1.240 + static const Word loMask = RandomTraits<Word>::loMask;
1.241 + static const Word hiMask = RandomTraits<Word>::hiMask;
1.242 +
1.243 + current = state + length;
1.244 +
1.245 + register Word *curr = state + length - 1;
1.246 + register long num;
1.247 +
1.248 + num = length - shift;
1.249 + while (num--) {
1.250 + curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
1.251 + curr[- shift] ^ mask[curr[-1] & 1ul];
1.252 + --curr;
1.253 + }
1.254 + num = shift - 1;
1.255 + while (num--) {
1.256 + curr[0] = (((curr[0] & hiMask) | (curr[-1] & loMask)) >> 1) ^
1.257 + curr[length - shift] ^ mask[curr[-1] & 1ul];
1.258 + --curr;
1.259 + }
1.260 + curr[0] = (((curr[0] & hiMask) | (curr[length - 1] & loMask)) >> 1) ^
1.261 + curr[length - shift] ^ mask[curr[length - 1] & 1ul];
1.262 +
1.263 + }
1.264 +
1.265 +
1.266 + Word *current;
1.267 + Word state[length];
1.268 +
1.269 + };
1.270 +
1.271 +
1.272 + template <typename Result,
1.273 + int shift = (std::numeric_limits<Result>::digits + 1) / 2>
1.274 + struct Masker {
1.275 + static Result mask(const Result& result) {
1.276 + return Masker<Result, (shift + 1) / 2>::
1.277 + mask(static_cast<Result>(result | (result >> shift)));
1.278 + }
1.279 + };
1.280 +
1.281 + template <typename Result>
1.282 + struct Masker<Result, 1> {
1.283 + static Result mask(const Result& result) {
1.284 + return static_cast<Result>(result | (result >> 1));
1.285 + }
1.286 + };
1.287 +
1.288 + template <typename Result, typename Word,
1.289 + int rest = std::numeric_limits<Result>::digits, int shift = 0,
1.290 + bool last = rest <= std::numeric_limits<Word>::digits>
1.291 + struct IntConversion {
1.292 + static const int bits = std::numeric_limits<Word>::digits;
1.293 +
1.294 + static Result convert(RandomCore<Word>& rnd) {
1.295 + return static_cast<Result>(rnd() >> (bits - rest)) << shift;
1.296 + }
1.297 +
1.298 + };
1.299 +
1.300 + template <typename Result, typename Word, int rest, int shift>
1.301 + struct IntConversion<Result, Word, rest, shift, false> {
1.302 + static const int bits = std::numeric_limits<Word>::digits;
1.303 +
1.304 + static Result convert(RandomCore<Word>& rnd) {
1.305 + return (static_cast<Result>(rnd()) << shift) |
1.306 + IntConversion<Result, Word, rest - bits, shift + bits>::convert(rnd);
1.307 + }
1.308 + };
1.309 +
1.310 +
1.311 + template <typename Result, typename Word,
1.312 + bool one_word = (std::numeric_limits<Word>::digits <
1.313 + std::numeric_limits<Result>::digits) >
1.314 + struct Mapping {
1.315 + static Result map(RandomCore<Word>& rnd, const Result& bound) {
1.316 + Word max = Word(bound - 1);
1.317 + Result mask = Masker<Result>::mask(bound - 1);
1.318 + Result num;
1.319 + do {
1.320 + num = IntConversion<Result, Word>::convert(rnd) & mask;
1.321 + } while (num > max);
1.322 + return num;
1.323 + }
1.324 + };
1.325 +
1.326 + template <typename Result, typename Word>
1.327 + struct Mapping<Result, Word, false> {
1.328 + static Result map(RandomCore<Word>& rnd, const Result& bound) {
1.329 + Word max = Word(bound - 1);
1.330 + Word mask = Masker<Word, (std::numeric_limits<Result>::digits + 1) / 2>
1.331 + ::mask(max);
1.332 + Word num;
1.333 + do {
1.334 + num = rnd() & mask;
1.335 + } while (num > max);
1.336 + return num;
1.337 + }
1.338 + };
1.339 +
1.340 + template <typename Result, int exp, bool pos = (exp >= 0)>
1.341 + struct ShiftMultiplier {
1.342 + static const Result multiplier() {
1.343 + Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
1.344 + res *= res;
1.345 + if ((exp & 1) == 1) res *= static_cast<Result>(2.0);
1.346 + return res;
1.347 + }
1.348 + };
1.349 +
1.350 + template <typename Result, int exp>
1.351 + struct ShiftMultiplier<Result, exp, false> {
1.352 + static const Result multiplier() {
1.353 + Result res = ShiftMultiplier<Result, exp / 2>::multiplier();
1.354 + res *= res;
1.355 + if ((exp & 1) == 1) res *= static_cast<Result>(0.5);
1.356 + return res;
1.357 + }
1.358 + };
1.359 +
1.360 + template <typename Result>
1.361 + struct ShiftMultiplier<Result, 0, true> {
1.362 + static const Result multiplier() {
1.363 + return static_cast<Result>(1.0);
1.364 + }
1.365 + };
1.366 +
1.367 + template <typename Result>
1.368 + struct ShiftMultiplier<Result, -20, true> {
1.369 + static const Result multiplier() {
1.370 + return static_cast<Result>(1.0/1048576.0);
1.371 + }
1.372 + };
1.373 +
1.374 + template <typename Result>
1.375 + struct ShiftMultiplier<Result, -32, true> {
1.376 + static const Result multiplier() {
1.377 + return static_cast<Result>(1.0/424967296.0);
1.378 + }
1.379 + };
1.380 +
1.381 + template <typename Result>
1.382 + struct ShiftMultiplier<Result, -53, true> {
1.383 + static const Result multiplier() {
1.384 + return static_cast<Result>(1.0/9007199254740992.0);
1.385 + }
1.386 + };
1.387 +
1.388 + template <typename Result>
1.389 + struct ShiftMultiplier<Result, -64, true> {
1.390 + static const Result multiplier() {
1.391 + return static_cast<Result>(1.0/18446744073709551616.0);
1.392 + }
1.393 + };
1.394 +
1.395 + template <typename Result, int exp>
1.396 + struct Shifting {
1.397 + static Result shift(const Result& result) {
1.398 + return result * ShiftMultiplier<Result, exp>::multiplier();
1.399 + }
1.400 + };
1.401 +
1.402 + template <typename Result, typename Word,
1.403 + int rest = std::numeric_limits<Result>::digits, int shift = 0,
1.404 + bool last = rest <= std::numeric_limits<Word>::digits>
1.405 + struct RealConversion{
1.406 + static const int bits = std::numeric_limits<Word>::digits;
1.407 +
1.408 + static Result convert(RandomCore<Word>& rnd) {
1.409 + return Shifting<Result, - shift - rest>::
1.410 + shift(static_cast<Result>(rnd() >> (bits - rest)));
1.411 + }
1.412 + };
1.413 +
1.414 + template <typename Result, typename Word, int rest, int shift>
1.415 + struct RealConversion<Result, Word, rest, shift, false> {
1.416 + static const int bits = std::numeric_limits<Word>::digits;
1.417 +
1.418 + static Result convert(RandomCore<Word>& rnd) {
1.419 + return Shifting<Result, - shift - bits>::
1.420 + shift(static_cast<Result>(rnd())) +
1.421 + RealConversion<Result, Word, rest-bits, shift + bits>::
1.422 + convert(rnd);
1.423 + }
1.424 + };
1.425 +
1.426 + template <typename Result, typename Word>
1.427 + struct Initializer {
1.428 +
1.429 + template <typename Iterator>
1.430 + static void init(RandomCore<Word>& rnd, Iterator begin, Iterator end) {
1.431 + std::vector<Word> ws;
1.432 + for (Iterator it = begin; it != end; ++it) {
1.433 + ws.push_back(Word(*it));
1.434 + }
1.435 + rnd.initState(ws.begin(), ws.end());
1.436 + }
1.437 +
1.438 + static void init(RandomCore<Word>& rnd, Result seed) {
1.439 + rnd.initState(seed);
1.440 + }
1.441 + };
1.442 +
1.443 + template <typename Word>
1.444 + struct BoolConversion {
1.445 + static bool convert(RandomCore<Word>& rnd) {
1.446 + return (rnd() & 1) == 1;
1.447 + }
1.448 + };
1.449 +
1.450 + template <typename Word>
1.451 + struct BoolProducer {
1.452 + Word buffer;
1.453 + int num;
1.454 +
1.455 + BoolProducer() : num(0) {}
1.456 +
1.457 + bool convert(RandomCore<Word>& rnd) {
1.458 + if (num == 0) {
1.459 + buffer = rnd();
1.460 + num = RandomTraits<Word>::bits;
1.461 + }
1.462 + bool r = (buffer & 1);
1.463 + buffer >>= 1;
1.464 + --num;
1.465 + return r;
1.466 + }
1.467 + };
1.468 +
1.469 + }
1.470 +
1.471 + /// \ingroup misc
1.472 + ///
1.473 + /// \brief Mersenne Twister random number generator
1.474 + ///
1.475 + /// The Mersenne Twister is a twisted generalized feedback
1.476 + /// shift-register generator of Matsumoto and Nishimura. The period
1.477 + /// of this generator is \f$ 2^{19937} - 1 \f$ and it is
1.478 + /// equi-distributed in 623 dimensions for 32-bit numbers. The time
1.479 + /// performance of this generator is comparable to the commonly used
1.480 + /// generators.
1.481 + ///
1.482 + /// This implementation is specialized for both 32-bit and 64-bit
1.483 + /// architectures. The generators differ sligthly in the
1.484 + /// initialization and generation phase so they produce two
1.485 + /// completly different sequences.
1.486 + ///
1.487 + /// The generator gives back random numbers of serveral types. To
1.488 + /// get a random number from a range of a floating point type you
1.489 + /// can use one form of the \c operator() or the \c real() member
1.490 + /// function. If you want to get random number from the {0, 1, ...,
1.491 + /// n-1} integer range use the \c operator[] or the \c integer()
1.492 + /// method. And to get random number from the whole range of an
1.493 + /// integer type you can use the argumentless \c integer() or \c
1.494 + /// uinteger() functions. After all you can get random bool with
1.495 + /// equal chance of true and false or given probability of true
1.496 + /// result with the \c boolean() member functions.
1.497 + ///
1.498 + ///\code
1.499 + /// // The commented code is identical to the other
1.500 + /// double a = rnd(); // [0.0, 1.0)
1.501 + /// // double a = rnd.real(); // [0.0, 1.0)
1.502 + /// double b = rnd(100.0); // [0.0, 100.0)
1.503 + /// // double b = rnd.real(100.0); // [0.0, 100.0)
1.504 + /// double c = rnd(1.0, 2.0); // [1.0, 2.0)
1.505 + /// // double c = rnd.real(1.0, 2.0); // [1.0, 2.0)
1.506 + /// int d = rnd[100000]; // 0..99999
1.507 + /// // int d = rnd.integer(100000); // 0..99999
1.508 + /// int e = rnd[6] + 1; // 1..6
1.509 + /// // int e = rnd.integer(1, 1 + 6); // 1..6
1.510 + /// int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1
1.511 + /// int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1
1.512 + /// bool g = rnd.boolean(); // P(g = true) = 0.5
1.513 + /// bool h = rnd.boolean(0.8); // P(h = true) = 0.8
1.514 + ///\endcode
1.515 + ///
1.516 + /// The lemon provides a global instance of the random number
1.517 + /// generator which name is \ref lemon::rnd "rnd". Usually it is a
1.518 + /// good programming convenience to use this global generator to get
1.519 + /// random numbers.
1.520 + class Random {
1.521 + private:
1.522 +
1.523 + // Architecture word
1.524 + typedef unsigned long Word;
1.525 +
1.526 + _random_bits::RandomCore<Word> core;
1.527 + _random_bits::BoolProducer<Word> bool_producer;
1.528 +
1.529 +
1.530 + public:
1.531 +
1.532 + /// \brief Constructor
1.533 + ///
1.534 + /// Constructor with constant seeding.
1.535 + Random() { core.initState(); }
1.536 +
1.537 + /// \brief Constructor
1.538 + ///
1.539 + /// Constructor with seed. The current number type will be converted
1.540 + /// to the architecture word type.
1.541 + template <typename Number>
1.542 + Random(Number seed) {
1.543 + _random_bits::Initializer<Number, Word>::init(core, seed);
1.544 + }
1.545 +
1.546 + /// \brief Constructor
1.547 + ///
1.548 + /// Constructor with array seeding. The given range should contain
1.549 + /// any number type and the numbers will be converted to the
1.550 + /// architecture word type.
1.551 + template <typename Iterator>
1.552 + Random(Iterator begin, Iterator end) {
1.553 + typedef typename std::iterator_traits<Iterator>::value_type Number;
1.554 + _random_bits::Initializer<Number, Word>::init(core, begin, end);
1.555 + }
1.556 +
1.557 + /// \brief Copy constructor
1.558 + ///
1.559 + /// Copy constructor. The generated sequence will be identical to
1.560 + /// the other sequence. It can be used to save the current state
1.561 + /// of the generator and later use it to generate the same
1.562 + /// sequence.
1.563 + Random(const Random& other) {
1.564 + core.copyState(other.core);
1.565 + }
1.566 +
1.567 + /// \brief Assign operator
1.568 + ///
1.569 + /// Assign operator. The generated sequence will be identical to
1.570 + /// the other sequence. It can be used to save the current state
1.571 + /// of the generator and later use it to generate the same
1.572 + /// sequence.
1.573 + Random& operator=(const Random& other) {
1.574 + if (&other != this) {
1.575 + core.copyState(other.core);
1.576 + }
1.577 + return *this;
1.578 + }
1.579 +
1.580 + /// \brief Returns a random real number from the range [0, 1)
1.581 + ///
1.582 + /// It returns a random real number from the range [0, 1). The
1.583 + /// default Number type is double.
1.584 + template <typename Number>
1.585 + Number real() {
1.586 + return _random_bits::RealConversion<Number, Word>::convert(core);
1.587 + }
1.588 +
1.589 + double real() {
1.590 + return real<double>();
1.591 + }
1.592 +
1.593 + /// \brief Returns a random real number the range [0, b)
1.594 + ///
1.595 + /// It returns a random real number from the range [0, b).
1.596 + template <typename Number>
1.597 + Number real(Number b) {
1.598 + return real<Number>() * b;
1.599 + }
1.600 +
1.601 + /// \brief Returns a random real number from the range [a, b)
1.602 + ///
1.603 + /// It returns a random real number from the range [a, b).
1.604 + template <typename Number>
1.605 + Number real(Number a, Number b) {
1.606 + return real<Number>() * (b - a) + a;
1.607 + }
1.608 +
1.609 + /// \brief Returns a random real number from the range [0, 1)
1.610 + ///
1.611 + /// It returns a random double from the range [0, 1).
1.612 + double operator()() {
1.613 + return real<double>();
1.614 + }
1.615 +
1.616 + /// \brief Returns a random real number from the range [0, b)
1.617 + ///
1.618 + /// It returns a random real number from the range [0, b).
1.619 + template <typename Number>
1.620 + Number operator()(Number b) {
1.621 + return real<Number>() * b;
1.622 + }
1.623 +
1.624 + /// \brief Returns a random real number from the range [a, b)
1.625 + ///
1.626 + /// It returns a random real number from the range [a, b).
1.627 + template <typename Number>
1.628 + Number operator()(Number a, Number b) {
1.629 + return real<Number>() * (b - a) + a;
1.630 + }
1.631 +
1.632 + /// \brief Returns a random integer from a range
1.633 + ///
1.634 + /// It returns a random integer from the range {0, 1, ..., b - 1}.
1.635 + template <typename Number>
1.636 + Number integer(Number b) {
1.637 + return _random_bits::Mapping<Number, Word>::map(core, b);
1.638 + }
1.639 +
1.640 + /// \brief Returns a random integer from a range
1.641 + ///
1.642 + /// It returns a random integer from the range {a, a + 1, ..., b - 1}.
1.643 + template <typename Number>
1.644 + Number integer(Number a, Number b) {
1.645 + return _random_bits::Mapping<Number, Word>::map(core, b - a) + a;
1.646 + }
1.647 +
1.648 + /// \brief Returns a random integer from a range
1.649 + ///
1.650 + /// It returns a random integer from the range {0, 1, ..., b - 1}.
1.651 + template <typename Number>
1.652 + Number operator[](Number b) {
1.653 + return _random_bits::Mapping<Number, Word>::map(core, b);
1.654 + }
1.655 +
1.656 + /// \brief Returns a random non-negative integer
1.657 + ///
1.658 + /// It returns a random non-negative integer uniformly from the
1.659 + /// whole range of the current \c Number type. The default result
1.660 + /// type of this function is unsigned int.
1.661 + template <typename Number>
1.662 + Number uinteger() {
1.663 + return _random_bits::IntConversion<Number, Word>::convert(core);
1.664 + }
1.665 +
1.666 + unsigned int uinteger() {
1.667 + return uinteger<unsigned int>();
1.668 + }
1.669 +
1.670 + /// \brief Returns a random integer
1.671 + ///
1.672 + /// It returns a random integer uniformly from the whole range of
1.673 + /// the current \c Number type. The default result type of this
1.674 + /// function is int.
1.675 + template <typename Number>
1.676 + Number integer() {
1.677 + static const int nb = std::numeric_limits<Number>::digits +
1.678 + (std::numeric_limits<Number>::is_signed ? 1 : 0);
1.679 + return _random_bits::IntConversion<Number, Word, nb>::convert(core);
1.680 + }
1.681 +
1.682 + int integer() {
1.683 + return integer<int>();
1.684 + }
1.685 +
1.686 + /// \brief Returns a random bool
1.687 + ///
1.688 + /// It returns a random bool. The generator holds a buffer for
1.689 + /// random bits. Every time when it become empty the generator makes
1.690 + /// a new random word and fill the buffer up.
1.691 + bool boolean() {
1.692 + return bool_producer.convert(core);
1.693 + }
1.694 +
1.695 + ///\name Nonuniform distributions
1.696 + ///
1.697 +
1.698 + ///@{
1.699 +
1.700 + /// \brief Returns a random bool
1.701 + ///
1.702 + /// It returns a random bool with given probability of true result
1.703 + bool boolean(double p) {
1.704 + return operator()() < p;
1.705 + }
1.706 +
1.707 + /// Standard Gauss distribution
1.708 +
1.709 + /// Standard Gauss distribution.
1.710 + /// \note The Cartesian form of the Box-Muller
1.711 + /// transformation is used to generate a random normal distribution.
1.712 + /// \todo Consider using the "ziggurat" method instead.
1.713 + double gauss()
1.714 + {
1.715 + double V1,V2,S;
1.716 + do {
1.717 + V1=2*real<double>()-1;
1.718 + V2=2*real<double>()-1;
1.719 + S=V1*V1+V2*V2;
1.720 + } while(S>=1);
1.721 + return std::sqrt(-2*std::log(S)/S)*V1;
1.722 + }
1.723 + /// Gauss distribution with given mean and standard deviation
1.724 +
1.725 + /// Gauss distribution with given mean and standard deviation
1.726 + /// \sa gauss()
1.727 + double gauss(double mean,double std_dev)
1.728 + {
1.729 + return gauss()*std_dev+mean;
1.730 + }
1.731 +
1.732 + /// Exponential distribution with given mean
1.733 +
1.734 + /// This function generates an exponential distribution random number
1.735 + /// with mean <tt>1/lambda</tt>.
1.736 + ///
1.737 + double exponential(double lambda=1.0)
1.738 + {
1.739 + return -std::log(1.0-real<double>())/lambda;
1.740 + }
1.741 +
1.742 + /// Gamma distribution with given integer shape
1.743 +
1.744 + /// This function generates a gamma distribution random number.
1.745 + ///
1.746 + ///\param k shape parameter (<tt>k>0</tt> integer)
1.747 + double gamma(int k)
1.748 + {
1.749 + double s = 0;
1.750 + for(int i=0;i<k;i++) s-=std::log(1.0-real<double>());
1.751 + return s;
1.752 + }
1.753 +
1.754 + /// Gamma distribution with given shape and scale parameter
1.755 +
1.756 + /// This function generates a gamma distribution random number.
1.757 + ///
1.758 + ///\param k shape parameter (<tt>k>0</tt>)
1.759 + ///\param theta scale parameter
1.760 + ///
1.761 + double gamma(double k,double theta=1.0)
1.762 + {
1.763 + double xi,nu;
1.764 + const double delta = k-std::floor(k);
1.765 + const double v0=M_E/(M_E-delta);
1.766 + do {
1.767 + double V0=1.0-real<double>();
1.768 + double V1=1.0-real<double>();
1.769 + double V2=1.0-real<double>();
1.770 + if(V2<=v0)
1.771 + {
1.772 + xi=std::pow(V1,1.0/delta);
1.773 + nu=V0*std::pow(xi,delta-1.0);
1.774 + }
1.775 + else
1.776 + {
1.777 + xi=1.0-std::log(V1);
1.778 + nu=V0*std::exp(-xi);
1.779 + }
1.780 + } while(nu>std::pow(xi,delta-1.0)*std::exp(-xi));
1.781 + return theta*(xi-gamma(int(std::floor(k))));
1.782 + }
1.783 +
1.784 + /// Weibull distribution
1.785 +
1.786 + /// This function generates a Weibull distribution random number.
1.787 + ///
1.788 + ///\param k shape parameter (<tt>k>0</tt>)
1.789 + ///\param lambda scale parameter (<tt>lambda>0</tt>)
1.790 + ///
1.791 + double weibull(double k,double lambda)
1.792 + {
1.793 + return lambda*pow(-std::log(1.0-real<double>()),1.0/k);
1.794 + }
1.795 +
1.796 + /// Pareto distribution
1.797 +
1.798 + /// This function generates a Pareto distribution random number.
1.799 + ///
1.800 + ///\param k shape parameter (<tt>k>0</tt>)
1.801 + ///\param x_min location parameter (<tt>x_min>0</tt>)
1.802 + ///
1.803 + double pareto(double k,double x_min)
1.804 + {
1.805 + return exponential(gamma(k,1.0/x_min));
1.806 + }
1.807 +
1.808 + ///@}
1.809 +
1.810 + ///\name Two dimensional distributions
1.811 + ///
1.812 +
1.813 + ///@{
1.814 +
1.815 + /// Uniform distribution on the full unit circle.
1.816 +
1.817 + /// Uniform distribution on the full unit circle.
1.818 + ///
1.819 + dim2::Point<double> disc()
1.820 + {
1.821 + double V1,V2;
1.822 + do {
1.823 + V1=2*real<double>()-1;
1.824 + V2=2*real<double>()-1;
1.825 +
1.826 + } while(V1*V1+V2*V2>=1);
1.827 + return dim2::Point<double>(V1,V2);
1.828 + }
1.829 + /// A kind of two dimensional Gauss distribution
1.830 +
1.831 + /// This function provides a turning symmetric two-dimensional distribution.
1.832 + /// Both coordinates are of standard normal distribution, but they are not
1.833 + /// independent.
1.834 + ///
1.835 + /// \note The coordinates are the two random variables provided by
1.836 + /// the Box-Muller method.
1.837 + dim2::Point<double> gauss2()
1.838 + {
1.839 + double V1,V2,S;
1.840 + do {
1.841 + V1=2*real<double>()-1;
1.842 + V2=2*real<double>()-1;
1.843 + S=V1*V1+V2*V2;
1.844 + } while(S>=1);
1.845 + double W=std::sqrt(-2*std::log(S)/S);
1.846 + return dim2::Point<double>(W*V1,W*V2);
1.847 + }
1.848 + /// A kind of two dimensional exponential distribution
1.849 +
1.850 + /// This function provides a turning symmetric two-dimensional distribution.
1.851 + /// The x-coordinate is of conditionally exponential distribution
1.852 + /// with the condition that x is positive and y=0. If x is negative and
1.853 + /// y=0 then, -x is of exponential distribution. The same is true for the
1.854 + /// y-coordinate.
1.855 + dim2::Point<double> exponential2()
1.856 + {
1.857 + double V1,V2,S;
1.858 + do {
1.859 + V1=2*real<double>()-1;
1.860 + V2=2*real<double>()-1;
1.861 + S=V1*V1+V2*V2;
1.862 + } while(S>=1);
1.863 + double W=-std::log(S)/S;
1.864 + return dim2::Point<double>(W*V1,W*V2);
1.865 + }
1.866 +
1.867 + ///@}
1.868 + };
1.869 +
1.870 +
1.871 + extern Random rnd;
1.872 +
1.873 +}
1.874 +
1.875 +#endif