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65 lines
1.8 KiB
C
65 lines
1.8 KiB
C
/* Copyright 2012-2020, The Tor Project, Inc
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* See LICENSE for licensing information */
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/** prob_distr_mpfr_ref.c
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*
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* Example reference file for GNU MPFR vectors tested in test_prob_distr.c .
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* Code by Riastradh.
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*/
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#include <complex.h>
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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/* Must come after <stdio.h> so we get mpfr_printf. */
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#include <mpfr.h>
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/* gcc -o mpfr prob_distr_mpfr_ref.c -lmpfr -lm */
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/* Computes logit(p) for p = .49999 */
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int
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main(void)
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{
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mpfr_t p, q, r;
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mpfr_init(p);
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mpfr_set_prec(p, 200);
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mpfr_init(q);
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mpfr_set_prec(q, 200);
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mpfr_init(r);
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mpfr_set_prec(r, 200);
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mpfr_set_d(p, .49999, MPFR_RNDN);
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mpfr_set_d(q, 1, MPFR_RNDN);
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/* r := q - p = 1 - p */
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mpfr_sub(r, q, p, MPFR_RNDN);
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/* q := p/r = p/(1 - p) */
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mpfr_div(q, p, r, MPFR_RNDN);
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/* r := log(q) = log(p/(1 - p)) */
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mpfr_log(r, q, MPFR_RNDN);
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mpfr_printf("mpfr 200-bit\t%.128Rg\n", r);
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/*
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* Print a double approximation to logit three different ways. All
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* three agree bit for bit on the libms I tried, with the nextafter
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* adjustment (which is well within the 10 eps relative error bound
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* advertised). Apparently I must have used the Goldberg expression
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* for what I wrote down in the test case.
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*/
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printf("mpfr 53-bit\t%.17g\n", nextafter(mpfr_get_d(r, MPFR_RNDN), 0), 0);
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volatile double p0 = .49999;
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printf("log1p\t\t%.17g\n", nextafter(-log1p((1 - 2*p0)/p0), 0));
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volatile double x = (1 - 2*p0)/p0;
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volatile double xp1 = x + 1;
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printf("Goldberg\t%.17g\n", -x*log(xp1)/(xp1 - 1));
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/*
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* Print a bad approximation, using the naive expression, to see a
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* lot of wrong digits, far beyond the 10 eps relative error attained
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* by -log1p((1 - 2*p)/p).
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*/
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printf("naive\t\t%.17g\n", log(p0/(1 - p0)));
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fflush(stdout);
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return ferror(stdout);
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}
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