mirror of
https://github.com/RobTillaart/Arduino.git
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313 lines
6.3 KiB
C++
313 lines
6.3 KiB
C++
//
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// FILE: Prandom.cpp
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// AUTHOR: Rob dot Tillaart at gmail dot com
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// VERSION: 0.1.3
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// PURPOSE: Arduino library for random number generation with Python random interface
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// URL: https://github.com/RobTillaart/Prandom
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//
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// HISTORY:
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// 0.1.0 2020-05-13 complete redo based upon python random interface
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// https://docs.python.org/3/library/random.html
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// 0.1.1 renamed all to Prandom
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// 0.1.2 2020-06-19 fix library.json
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// 0.1.3 2021-01-06 arduino-CI + unit test
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// code based upon Python implementation although some small
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// optimizations and tweaks were needed to get it working.
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#include "Prandom.h"
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Prandom::Prandom()
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{
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seed();
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}
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Prandom::Prandom(uint32_t s)
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{
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seed(s);
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}
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void Prandom::seed()
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{
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// no argument ==> time based.
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seed(_rndTime());
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}
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void Prandom::seed(uint32_t s, uint32_t t)
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{
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// set marsaglia constants, prevent 0 as value
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if (s == 0) s = 1;
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if (t == 0) t = 2;
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_m_w = s;
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_m_z = t;
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}
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uint32_t Prandom::getrandbits(uint8_t n)
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{
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uint8_t shift = min(31, n - 1);
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return _rnd(1UL << shift);
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}
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uint32_t Prandom::randrange(uint32_t stop)
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{
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return _rnd(stop);
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}
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uint32_t Prandom::randrange(uint32_t start, uint32_t stop, uint32_t step)
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{
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if (step == 1) return start + _rnd(stop - start);
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return start + step * _rnd((stop - start + step - 1) / step);
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}
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// returns value between 0 and top which defaults to 1.0
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// the parameter does not exist in Python
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// note: not all possible (0xFFFFFFFF) values are used
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// function has an uniform distribution.
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float Prandom::random(const float top)
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{
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if (top == 0) return 0;
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float f = (top * __random()) / 0xFFFFFFFF;
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return f;
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}
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float Prandom::uniform(float lo, float hi)
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{
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if (lo == hi) return lo;
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return lo + random(hi - lo);
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}
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float Prandom::triangular(float lo, float hi, float mid)
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{
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if (lo == hi) return lo;
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float val = random();
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if (val > mid)
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{
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val = 1 - val;
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mid = 1 - mid;
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float t = hi;
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hi = lo;
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lo = t;
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}
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return lo + (hi - lo) * sqrt(val * mid);
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}
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// minor optimization.
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float Prandom::normalvariate(float mu, float sigma)
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{
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// const float NV_MAGICCONST = 4 * exp(-0.5)/sqrt(2.0);
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const float NV_MAGICCONST = 2 * exp(-0.5)/sqrt(2.0);
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float u1, u2, z;
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while (true)
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{
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u1 = random();
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u2 = 1 - random();
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z = NV_MAGICCONST * (u1 - 0.5) / u2 ;
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// if ((z * z / 4) <= -log(u2)) break;
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if ((z * z) <= -log(u2)) break;
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}
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return z * sigma + mu;
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}
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float Prandom::lognormvariate(float mu, float sigma)
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{
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return exp(normalvariate(mu, sigma));
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}
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// implemented slightly differently
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float Prandom::gauss(float mu, float sigma)
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{
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static bool generate = false;
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static float next = 0;
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float z = 0;
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generate = !generate;
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if (generate == false)
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{
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z = next;
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}
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else
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{
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float x2pi = random(TWO_PI);
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float g2rad = sqrt( -2.0 * log(1.0 - random()));
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z = cos(x2pi) * g2rad;
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next = sin(x2pi) * g2rad;
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}
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return z * sigma + mu;
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};
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float Prandom::expovariate(float lambda)
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{
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return -log(1.0 - random()) / lambda;
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}
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// alpha & beta > 0
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float Prandom::gammavariate(float alpha, float beta)
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{
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const float LOG4 = log(4);
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const float SG_MAGICCONST = 1.0 + log(4.5);
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if (alpha > 1.0)
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{
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// # Uses R.C.H. Cheng, "The generation of Gamma
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// # variables with non-integral shape parameters",
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// # Applied Statistics, (1977), 26, No. 1, p71-74
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float ainv = sqrt(2.0 * alpha - 1.0);
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float bbb = alpha - LOG4;
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float ccc = alpha + ainv;
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float u1, u2, v, x, z, r;
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while (true)
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{
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u1 = random();
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if (u1 < 1e-7) continue;
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if (u1 > 0.9999999) continue; // needed?
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u2 = 1.0 - random();
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v = log(u1 / (1.0 - u1)) / ainv;
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x = alpha * exp(v);
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z = u1 * u1 * u2;
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r = bbb + ccc * v - x;
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if ( ( (r + SG_MAGICCONST - 4.5 * z) >= 0.0) ||
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(r >= log(z)) )
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{
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return x * beta;
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}
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}
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}
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else if (alpha == 1.0)
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{
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return -log(1.0 - random()) * beta;
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}
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else // alpha in 0..1
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{
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// # Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
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float u, b, p, x, u1;
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while (true)
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{
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u = random();
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b = (EULER + alpha)/ EULER;
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p = b * u;
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if ( p <= 1.0) x = pow(p, (1.0 / alpha));
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else x = -log((b - p) / alpha);
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u1 = random();
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if (p > 1.0)
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{
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if (u1 <= pow(x, (alpha - 1.0))) break;
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}
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else
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{
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if (u1 <= exp(-x)) break;
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}
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}
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return x * beta;
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}
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}
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float Prandom::betavariate(float alpha, float beta)
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{
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float y = gammavariate(alpha, 1.0);
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if (y == 0) return 0.0;
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return y / (y + gammavariate(beta, 1.0));
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};
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float Prandom::paretovariate(float alpha)
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{
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float u = 1 - random();
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return pow(u, (-1.0 / alpha));
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}
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float Prandom::weibullvariate(float alpha, float beta)
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{
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float u = 1 - random();
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return alpha * pow(-log(u), 1.0/beta);
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}
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float Prandom::vonmisesvariate(float mu, float kappa)
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{
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if (kappa <= 1e-6) return TWO_PI * random();
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float s = 0.5 / kappa;
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float r = s + sqrt(1.0 + s * s);
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float u1, u2, u3, z, d, q, f, theta;
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do
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{
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u1 = random();
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z = cos(PI * u1);
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d = z / (r + z);
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u2 = random();
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} while ( ( u2 >= 1.0 - d * d ) && (u2 > (1.0 - d) * exp(d)) );
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q = 1.0 / r;
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f = (q + z) / (1.0 + q * z);
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u3 = random();
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if (u3 > 0.5) theta = mu + acos(f);
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else theta = mu - acos(f);
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while (theta < 0) theta += TWO_PI;
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while (theta > TWO_PI) theta -= TWO_PI;
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return theta;
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}
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////////////////////////////////////////////////////////////////////////////
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//
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// PRIVATE
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//
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uint32_t Prandom::_rndTime()
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{
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return (micros() + (micros() >> 2) ) ^ (millis());
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}
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// TODO how to guarantee it uniform between 0 .. n-1
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uint32_t Prandom::_rnd(uint32_t n)
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{
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// float formula works fastest but it looses precision for large values of n
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// as floats have only 23 bit mantissa
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uint32_t val = __random();
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if (n > 0x003FFFFF) return val % n; // distribution will fail here
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return (n * 1.0 * val) / 0xFFFFFFFF;
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}
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// An example of a simple pseudo-random number generator is the
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// Multiply-with-carry method invented by George Marsaglia.
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// two initializers (not null)
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uint32_t Prandom::__random()
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{
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_m_z = 36969L * (_m_z & 65535L) + (_m_z >> 16);
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_m_w = 18000L * (_m_w & 65535L) + (_m_w >> 16);
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return (_m_z << 16) + _m_w; /* 32-bit result */
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}
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// -- END OF FILE --
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