servatrice/common/rng_sfmt.cpp

#include "rng_sfmt.h"

#include <QDateTime>
#include <algorithm>
#include <climits>
#include <stdexcept>

// This is from gcc sources, namely from fixincludes/inclhack.def
// On C++11 systems, <cstdint> could be included instead.
#ifndef UINT64_MAX
#define UINT64_MAX (~(uint64_t)0)
#endif

RNG_SFMT::RNG_SFMT(QObject *parent) : RNG_Abstract(parent)
{
    // initialize the random number generator with a 32bit integer seed (timestamp)
    sfmt_init_gen_rand(&sfmt, QDateTime::currentDateTime().toSecsSinceEpoch());
}

/**
 * This method is the rand() equivalent which calls the cdf with proper bounds.
 *
 * It is possible to generate random numbers from [-min, +/-max] though the RNG uses
 * unsigned numbers only, so this wrapper handles some special cases for min and max.
 *
 * It is only necessary that the upper bound is larger or equal to the lower bound - with the exception
 * that someone wants something like rand() % -foo.
 */
unsigned int RNG_SFMT::rand(int min, int max)
{
    /* If min is negative, it would be possible to calculate
     * cdf(0, max - min) + min
     * There has been no use for negative random numbers with rand() though, so it's treated as error.
     */
    if (min < 0) {
        throw std::invalid_argument(
            QString("Invalid bounds for RNG: Got min " + QString::number(min) + " < 0!\n").toStdString());
        // at this point, the method exits. No return value is needed, because
        // basically the exception itself is returned.
    }

    // For complete fairness and equal timing, this should be a roll, but let's skip it anyway
    if (min == max)
        return max;

    // This is actually not used in Cockatrice:
    // Someone wants rand() % -foo, so we compute -rand(0, +foo)
    // This is the only time where min > max is (sort of) legal.
    // Not handling this will cause the application to crash.
    if (min == 0 && max < 0) {
        return -cdf(0, -max);
    }

    // No special cases are left, except !(min > max) which is caught in the cdf itself.
    return cdf(min, max);
}

/**
 * Much thought went into this, please read this comment before you modify the code.
 * Let SFMT() be an alias for sfmt_genrand_uint64() aka SFMT's rand() function.
 *
 * SMFT() returns a uniformly distributed pseudorandom number from 0 to UINT64_MAX.
 * As SFMT() operates on a limited integer range, it is a _discrete_ function.
 *
 * We want a random number from a given interval [min, max] though, so we need to
 * implement the (discrete) cumulative distribution function SFMT(min, max), which
 * returns a random number X from [min, max].
 *
 * This CDF is by formal definition:
 * SFMT(X; min, max) = (floor(X) - min + 1) / (max - min + 1)
 *
 * To get out the random variable, solve for X:
 * floor(X) = SFMT(X; min, max) * (max - min + 1) + min - 1
 * So this is, what rand(min, max) should look like.
 * Problem: SFMT(X; min, max) * (max - min + 1) could produce an integer overflow,
 * so it is not safe.
 *
 * One solution is to divide the universe into buckets of equal size depending on the
 * range [min, max] and assign X to the bucket that contains the number generated
 * by SFMT(). This equals to modulo computation and is not satisfying:
 * If the buckets don't divide the universe equally, because the bucket size is not
 * a divisor of 2, there will be a range in the universe that is biased because one
 * bucket is too small thus will be chosen less equally!
 *
 * This is solved by rejection sampling:
 * As SFMT() is assumed to be unbiased, we are allowed to ignore those random numbers
 * from SFMT() that would force us to have an unequal bucket and generate new random
 * numbers until one number fits into one of the other buckets.
 * This can be compared to an ideal six sided die that is rolled until only sides
 * 1-5 show up, while 6 represents something that you don't want. So you basically roll
 * a five sided die.
 *
 * Note: If you replace the SFMT RNG with some other rand() function in the future,
 * then you _need_ to change the UINT64_MAX constant to the largest possible random
 * number which can be created by the new rand() function. This value is often defined
 * in a RAND_MAX constant.
 * Otherwise you will probably skew the outcome of the rand() method or worsen the
 * performance of the application.
 */
unsigned int RNG_SFMT::cdf(unsigned int min, unsigned int max)
{
    // This all makes no sense if min > max, which should never happen.
    if (min > max) {
        throw std::invalid_argument(QString("Invalid bounds for RNG: min > max! Values were: min = " +
                                            QString::number(min) + ", max = " + QString::number(max))
                                        .toStdString());
        // at this point, the method exits. No return value is needed, because
        // basically the exception itself is returned.
    }

    // First compute the diameter (aka size, length) of the [min, max] interval
    const unsigned int diameter = max - min + 1;

    // Compute how many buckets (each in size of the diameter) will fit into the
    // universe.
    // If the division has a remainder, the result is floored automatically.
    const uint64_t buckets = UINT64_MAX / diameter;

    // Compute the last valid random number. All numbers beyond have to be ignored.
    // If there was no remainder in the previous step, limit is equal to UINT64_MAX.
    const uint64_t limit = diameter * buckets;

    uint64_t rand;
    // To make the random number generation thread-safe, a mutex is created around
    // the generation. Outside of the loop of course, to avoid lock/unlock overhead.
    mutex.lock();
    do {
        rand = sfmt_genrand_uint64(&sfmt);
    } while (rand >= limit);
    mutex.unlock();

    // Now determine the bucket containing the SFMT() random number and after adding
    // the lower bound, a random number from [min, max] can be returned.
    return (unsigned int)(rand / buckets + min);
}