text: /* Copyright 2012-2021, The Tor Project, Inc
   * See LICENSE for licensing information */
  
  /** prob_distr_mpfr_ref.c
   *
   * Example reference file for GNU MPFR vectors tested in test_prob_distr.c .
   * Code by Riastradh.
   */
  
  #include <complex.h>
  #include <float.h>
  #include <math.h>
  #include <stdio.h>
  
  /* Must come after <stdio.h> so we get mpfr_printf.  */
  #include <mpfr.h>
  
  /*  gcc -o mpfr prob_distr_mpfr_ref.c -lmpfr -lm */
  
  /* Computes logit(p) for p = .49999 */
  int
  main(void)
  {
    mpfr_t p, q, r;
    mpfr_init(p);
    mpfr_set_prec(p, 200);
    mpfr_init(q);
    mpfr_set_prec(q, 200);
    mpfr_init(r);
    mpfr_set_prec(r, 200);
    mpfr_set_d(p, .49999, MPFR_RNDN);
    mpfr_set_d(q, 1, MPFR_RNDN);
    /* r := q - p = 1 - p */
    mpfr_sub(r, q, p, MPFR_RNDN);
    /* q := p/r = p/(1 - p) */
    mpfr_div(q, p, r, MPFR_RNDN);
    /* r := log(q) = log(p/(1 - p)) */
    mpfr_log(r, q, MPFR_RNDN);
    mpfr_printf("mpfr 200-bit\t%.128Rg\n", r);
  
    /*
     * Print a double approximation to logit three different ways.  All
     * three agree bit for bit on the libms I tried, with the nextafter
     * adjustment (which is well within the 10 eps relative error bound
     * advertised).  Apparently I must have used the Goldberg expression
     * for what I wrote down in the test case.
     */
    printf("mpfr 53-bit\t%.17g\n", nextafter(mpfr_get_d(r, MPFR_RNDN), 0), 0);
    volatile double p0 = .49999;
    printf("log1p\t\t%.17g\n", nextafter(-log1p((1 - 2*p0)/p0), 0));
    volatile double x = (1 - 2*p0)/p0;
    volatile double xp1 = x + 1;
    printf("Goldberg\t%.17g\n", -x*log(xp1)/(xp1 - 1));
  
    /*
     * Print a bad approximation, using the naive expression, to see a
     * lot of wrong digits, far beyond the 10 eps relative error attained
     * by -log1p((1 - 2*p)/p).
     */
    printf("naive\t\t%.17g\n", log(p0/(1 - p0)));
  
    fflush(stdout);
    return ferror(stdout);
  }
  