/* mpfr_erandom (rop, state, rnd_mode) -- Generate an exponential deviate with
   mean 1 and round it to the precision of rop according to the given rounding
   mode.

Copyright 2013-2018 Free Software Foundation, Inc.
Contributed by Charles Karney <charles@karney.com>, SRI International.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */

/*
 * Sampling from the exponential distribution with unit mean using the method
 * given in John von Neumann, Various techniques used in connection with random
 * digits, in A. S. Householder, G. E. Forsythe, and H. H. Germond, editors,
 * "Monte Carlo Method", number 12 in Applied Mathematics Series, pp. 36-38
 * (NBS, Washington, DC, 1951), Proceedings of a symposium held June 29-July 1,
 * 1949, in Los Angeles.
 *
 * A modification to this algorithm is given in:
 *   Charles F. F. Karney,
 *   "Sampling exactly from the normal distribution",
 *   ACM Trans. Math. Software 42(1), 3:1-14 (Jan. 2016).
 *   https://dx.doi.org/10.1145/2710016
 *   http://arxiv.org/abs/1303.6257
 * Although this improves the bit efficiency, in practice, it results in
 * a slightly slower algorithm for MPFR. So here the original von Neumann
 * algorithm is used.
 *
 * There are a few "weasel words" regarding the accuracy of this
 * implementation.  The algorithm produces exactly rounded exponential deviates
 * provided that gmp's random number engine delivers truly random bits.  If it
 * did, the algorithm would be perfect; however, this implementation would have
 * problems, e.g., in that the integer part of the exponential deviate is
 * represented by an unsigned long, whereas in reality the integer part in
 * unbounded.  In this implementation, asserts catch overflow in the integer
 * part and similar (very, very) unlikely events.  In reality, of course, gmp's
 * random number engine has a finite internal state (19937 bits in the case of
 * the MT19937 method).  This means that these unlikely events in fact won't
 * occur.  If the asserts are triggered, then this is an indication that the
 * random number engine is defective.  (Even if a hardware random number
 * generator were used, the most likely explanation for the triggering of the
 * asserts would be that the hardware generator was broken.)
 */

#include "random_deviate.h"

/* true with prob exp(-x) */
static int
E (mpfr_random_deviate_t x, gmp_randstate_t r,
   mpfr_random_deviate_t p, mpfr_random_deviate_t q)
{
  /* p and q are temporaries */
  mpfr_random_deviate_reset (p);
  if (!mpfr_random_deviate_less (p, x, r))
    return 1;
  for (;;)
    {
      mpfr_random_deviate_reset (q);
      if (!mpfr_random_deviate_less (q, p, r))
        return 0;
      mpfr_random_deviate_reset (p);
      if (!mpfr_random_deviate_less (p, q, r))
        return 1;
    }
}

/* return an exponential random deviate with mean 1 as a MPFR  */
int
mpfr_erandom (mpfr_t z, gmp_randstate_t r, mpfr_rnd_t rnd)
{
  mpfr_random_deviate_t x, p, q;
  int inex;
  unsigned long k = 0;

  mpfr_random_deviate_init (x);
  mpfr_random_deviate_init (p);
  mpfr_random_deviate_init (q);
  while (!E(x, r, p, q))
    {
      ++k;
      /* Catch k wrapping around to 0; for a 32-bit unsigned long, the
       * probability of this is exp(-2^32)). */
      MPFR_ASSERTN (k != 0UL);
      mpfr_random_deviate_reset (x);
    }
  mpfr_random_deviate_clear (q);
  mpfr_random_deviate_clear (p);
  inex = mpfr_random_deviate_value (0, k, x, z, r, rnd);
  mpfr_random_deviate_clear (x);
  return inex;
}
