1 files changed, 64 insertions, 0 deletions
diff --git a/src/test/prob_distr_mpfr_ref.c b/src/test/prob_distr_mpfr_ref.c
new file mode 100644
index 0000000000..de4179c4e0
--- /dev/null
+++ b/src/test/prob_distr_mpfr_ref.c
@@ -0,0 +1,64 @@
+/* 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);
+}