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/* Copyright 2012-2020, 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);
}
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