al_Random.hpp

#ifndef INCLUDE_AL_UTIL_MATH_RANDOM_HPP
#define INCLUDE_AL_UTIL_MATH_RANDOM_HPP
 
/*  Allocore --
  Multimedia / virtual environment application class library
 
  Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.
  Copyright (C) 2012. The Regents of the University of California.
  All rights reserved.
 
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
 
    Redistributions of source code must retain the above copyright notice,
    this list of conditions and the following disclaimer.
 
    Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.
 
    Neither the name of the University of California nor the names of its
    contributors may be used to endorse or promote products derived from
    this software without specific prior written permission.
 
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
 
 
  File description:
  Various flavors of pseudo-random number generators and distributions
 
  File author(s):
  Lance Putnam, 2006, putnam.lance@gmail.com
*/
 
#include "al/math/al_StdRandom.hpp"
 
/* req'd for int to float conversion */
#include <time.h> /* req'd for time() */
 
#include <cmath>
#include <random>
 
#include "al/math/al_Constants.hpp"
#include "al/types/al_Conversion.hpp"
 
namespace al {
 
namespace rnd {
 
class LinCon;
class MulLinCon;
class Tausworthe;
template <class RNG>
class Random;
 
inline static uint32_t seed() {
  static uint32_t val = time(NULL);
  return val = val * 1664525UL + 1013904223UL;
}
 
template <class RNG = al::rnd::Tausworthe>
class Random {
 public:
  Random() {}
 
  Random(uint32_t seed) : mRNG(seed) {}
 
  Random& seed(uint32_t v) {
    mRNG.seed(v);
    return *this;
  }
 
  RNG& rng() { return mRNG; }
 
  float uniform() { return al::uintToUnit<float>(mRNG()); }
 
  template <class T>
  T uniform(const T& hi) {
    return hi * uniform();
  }
 
  template <class T>
  T uniform(const T& hi, const T& lo) {
    return T((hi - lo) * uniform()) + lo;
  }
 
  float uniformS() { return al::uintToUnitS<float>(mRNG()); }
 
  template <class T>
  T uniformS(const T& lim) {
    return lim * uniformS();
  }
 
 
  template <int N, class T>
  void ball(T* point);
 
  template <template <int, class> class VecType, int N, class T>
  void ball(VecType<N, T>& point) {
    ball<N>(&point[0]);
  }
 
  template <class VecType>
  VecType ball() {
    VecType v;
    ball(v);
    return v;
  }
 
  float normal() {
    float r;
    normal(r, r);
    return r;
  }
 
  template <class T>
  void normal(T& y1, T& y2);
 
  float triangle();
 
  template <class T>
  T triangle(const T& hi) {
    return hi * triangle();
  }
 
  float sign(float x = 1.f);
 
  bool prob() { return mRNG() & 0x80000000; }
 
  bool prob(float p) { return uniform() < p; }
 
  template <class T>
  void shuffle(T* arr, uint32_t len);
 
  // DEPRECATED:
  float gaussian() { return normal(); }
  template <class T>
  void gaussian(T& y1, T& y2) {
    normal(y1, y2);
  }
 
 protected:
  RNG mRNG;
};
 
 
class LinCon {
 public:
  LinCon() {
    seed(al::rnd::seed());
    type(0);
  }
 
  LinCon(uint32_t seed) : mVal(seed) { type(0); }
 
  uint32_t operator()() { return mVal = mVal * mMul + mAdd; }
 
  void seed(uint32_t v) { mVal = v; }
 
 
  void type(int v) {
    switch (v) {
      default:
      case 0:
        mMul = 1664525;
        mAdd = 1013904223;
        break;
      case 1:
        mMul = 2147001325;
        mAdd = 715136305;
        break;
    }
  }
 
 private:
  uint32_t mVal;
  uint32_t mMul, mAdd;
};
 
 
class MulLinCon {
 public:
  MulLinCon() {
    seed(al::rnd::seed());
    type(0);
  }
 
  MulLinCon(uint32_t seed) : mVal(seed) { type(0); }
 
  uint32_t operator()() { return mVal *= mMul; }
 
  void seed(uint32_t v) { mVal = v; }
 
 
  void type(int v) {
    switch (v) {
      default:
        mMul = 2891336453UL;
        break;  // L'Ecuyer M8
      case 1:
        mMul = 29943829UL;
        break;  // L'Ecuyer M16
      case 2:
        mMul = 32310901UL;
        break;  // L'Ecuyer M32
      case 3:
        mMul = 69069UL;
        break;  // Super-duper
    }
  }
 
 private:
  uint32_t mVal;
  uint32_t mMul;
};
 
 
class Tausworthe {
 public:
  Tausworthe();
 
  Tausworthe(uint32_t seed);
 
  uint32_t operator()();
 
  void seed(uint32_t v);
 
  void seed(uint32_t v1, uint32_t v2, uint32_t v3, uint32_t v4);
 
 private:
  uint32_t s1, s2, s3, s4;
  void iterate();
};
 
// Implementation_______________________________________________________________
 
inline Tausworthe::Tausworthe() { seed(al::rnd::seed()); }
inline Tausworthe::Tausworthe(uint32_t sd) { seed(sd); }
 
inline uint32_t Tausworthe::operator()() {
  iterate();
  return s1 ^ s2 ^ s3 ^ s4;
}
 
inline void Tausworthe::seed(uint32_t v) {
  al::rnd::LinCon g(v);
  g();
  seed(g(), g(), g(), g());
}
 
inline void Tausworthe::seed(uint32_t v1, uint32_t v2, uint32_t v3,
                             uint32_t v4) {
  // printf("%u %u %u %u\n", v1, v2, v3, v4);
  v1& 0xffffffe ? s1 = v1 : s1 = ~v1;
  v2& 0xffffff8 ? s2 = v2 : s2 = ~v2;
  v3& 0xffffff0 ? s3 = v3 : s3 = ~v3;
  v4& 0xfffff80 ? s4 = v4 : s4 = ~v4;
}
 
inline void Tausworthe::iterate() {
  s1 = ((s1 & 0xfffffffe) << 18) ^ (((s1 << 6) ^ s1) >> 13);
  s2 = ((s2 & 0xfffffff8) << 2) ^ (((s2 << 2) ^ s2) >> 27);
  s3 = ((s3 & 0xfffffff0) << 7) ^ (((s3 << 13) ^ s3) >> 21);
  s4 = ((s4 & 0xffffff80) << 13) ^ (((s4 << 3) ^ s4) >> 12);
}
 
template <class RNG>
template <int N, class T>
void Random<RNG>::ball(T* point) {
  T w;
  do {
    w = T(0);
    for (int i = 0; i < N; ++i) {
      float v = uniformS();
      point[i] = v;
      w += v * v;
    }
  } while (w >= T(1));  // if on or outside unit ball, try again
}
 
// Box-Muller transform
//    Box, G. and Muller, M. A note on the generation of normal deviates.
//    Ann. Math. Slat. 28, (1958).
//
// http://en.wikipedia.org/wiki/Box-Muller_transform
template <class RNG>
template <class T>
void Random<RNG>::normal(T& y1, T& y2) {
  float x1, x2, w;
 
  // Search for point within unit circle using sample-reject.
  // This will pass with probability pi/4 = ~0.785.
  do {
    x1 = uniformS();
    x2 = uniformS();
    w = x1 * x1 + x2 * x2;
  } while (w >= 1.f);
 
  // perform inverse Gaussian function mapping
  w = std::sqrt((-2.f * std::log(w)) / w);
  y1 = T(x1 * w);
  y2 = T(x2 * w);
}
 
template <class RNG>
inline float Random<RNG>::triangle() {
  union {
    float f;
    uint32_t i;
  } u, v;
  u.i = 0x3f800000 | (mRNG() >> 9);  // float in [1,2)
  v.i = 0x3f800000 | (mRNG() >> 9);  // float in [1,2)
  return u.f - v.f;
}
 
template <class RNG>
inline float Random<RNG>::sign(float x) {
  union {
    float f;
    uint32_t i;
  } u = {x};
  u.i |= mRNG() & 0x80000000;
  return u.f;
}
 
// Fisher-Yates shuffle
template <class RNG>
template <class T>
void Random<RNG>::shuffle(T* arr, uint32_t len) {
  for (uint32_t i = len - 1; i > 0; --i) {
    uint32_t j = uniform(i + 1);
    T t = arr[i];
    arr[i] = arr[j];
    arr[j] = t;
  }
}
 
}  // namespace rnd
 
// for using std random class with al_Random interface
 
class StdRnd {
 public:
  rand_uniformf mUniformf;
  rand_uniformi mUniformi;
 
  StdRnd() : mUniformf{} {}
  StdRnd(unsigned int seed) : mUniformf{seed}, mUniformi{seed} {}
 
  // [0, 1)
  float operator()() { return mUniformf(); }
  float operator()(float hi) { return mUniformf(0, hi); }
  float operator()(float lo, float hi) { return mUniformf(lo, hi); }
 
  void seed(unsigned int s) { mUniformf.seed(s); }
 
  int randi(int hi) { return mUniformi(0, hi); }
  int randi(int lo, int hi) { return mUniformi(lo, hi); }
 
  void seedi(unsigned int s) { mUniformi.seed(s); }
};
 
using StdRandom = al::rnd::Random<StdRnd>;
 
namespace rnd {
 
template <>
inline float StdRandom::uniform() {
  return mRNG();
}
 
template <>
template <typename T>
inline T StdRandom::uniform(T const& hi) {
  return static_cast<T>(mRNG(float(hi)));
}
 
template <>
template <typename T>
inline T StdRandom::uniform(T const& hi, T const& lo) {
  return static_cast<T>(mRNG(float(lo), float(hi)));
}
 
template <>
inline float StdRandom::uniformS() {
  return mRNG(-1.0f, 1.0f);
}
 
template <>
template <typename T>
inline T StdRandom::uniformS(T const& lim) {
  return static_cast<T>(mRNG(float(-lim), float(lim)));
}
 
template <>
inline float StdRandom::triangle() {
  return 0.5f * (uniformS() + uniformS());
}
 
template <>
inline float StdRandom::sign(float x) {
  static float arr[2] = {-1.0f, 1.0f};
  return x * arr[mRNG.randi(0, 1)];
}
 
template <>
template <class T>
inline void StdRandom::shuffle(T* arr, uint32_t len) {
  for (uint32_t i = len - 1; i > 0; i -= 1) {
    uint32_t j = mRNG.randi(i + 1);
    T t = arr[i];
    arr[i] = arr[j];
    arr[j] = t;
  }
}
 
}  // namespace rnd
 
}  // namespace al
 
#endif