Add Chromium-only Blender WebEngine parity work

blender-5.2.0/extern/gmp-source/tests/rand/statlib.c

@@ -0,0 +1,836 @@
+/* statlib.c -- Statistical functions for testing the randomness of
+   number sequences. */
+
+/*
+Copyright 1999, 2000 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library test suite.
+
+The GNU MP Library test suite is free software; you can redistribute it
+and/or modify it under the terms of the GNU 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 MP Library test suite 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 General
+Public License for more details.
+
+You should have received a copy of the GNU General Public License along with
+the GNU MP Library test suite.  If not, see https://www.gnu.org/licenses/.  */
+
+/* The theories for these functions are taken from D. Knuth's "The Art
+of Computer Programming: Volume 2, Seminumerical Algorithms", Third
+Edition, Addison Wesley, 1998. */
+
+/* Implementation notes.
+
+The Kolmogorov-Smirnov test.
+
+Eq. (13) in Knuth, p. 50, says that if X1, X2, ..., Xn are independent
+observations arranged into ascending order
+
+	Kp = sqr(n) * max(j/n - F(Xj))		for all 1<=j<=n
+	Km = sqr(n) * max(F(Xj) - (j-1)/n))	for all 1<=j<=n
+
+where F(x) = Pr(X <= x) = probability that (X <= x), which for a
+uniformly distributed random real number between zero and one is
+exactly the number itself (x).
+
+
+The answer to exercise 23 gives the following implementation, which
+doesn't need the observations to be sorted in ascending order:
+
+for (k = 0; k < m; k++)
+	a[k] = 1.0
+	b[k] = 0.0
+	c[k] = 0
+
+for (each observation Xj)
+	Y = F(Xj)
+	k = floor (m * Y)
+	a[k] = min (a[k], Y)
+	b[k] = max (b[k], Y)
+	c[k] += 1
+
+	j = 0
+	rp = rm = 0
+	for (k = 0; k < m; k++)
+		if (c[k] > 0)
+			rm = max (rm, a[k] - j/n)
+			j += c[k]
+			rp = max (rp, j/n - b[k])
+
+Kp = sqr (n) * rp
+Km = sqr (n) * rm
+
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include "gmpstat.h"
+
+/* ks (Kp, Km, X, P, n) -- Perform a Kolmogorov-Smirnov test on the N
+   real numbers between zero and one in vector X.  P is the
+   distribution function, called for each entry in X, which should
+   calculate the probability of X being greater than or equal to any
+   number in the sequence.  (For a uniformly distributed sequence of
+   real numbers between zero and one, this is simply equal to X.)  The
+   result is put in Kp and Km.  */
+
+void
+ks (mpf_t Kp,
+    mpf_t Km,
+    mpf_t X[],
+    void (P) (mpf_t, mpf_t),
+    unsigned long int n)
+{
+  mpf_t Kt;			/* temp */
+  mpf_t f_x;
+  mpf_t f_j;			/* j */
+  mpf_t f_jnq;			/* j/n or (j-1)/n */
+  unsigned long int j;
+
+  /* Sort the vector in ascending order. */
+  qsort (X, n, sizeof (__mpf_struct), mpf_cmp);
+
+  /* K-S test. */
+  /*	Kp = sqr(n) * max(j/n - F(Xj))		for all 1<=j<=n
+	Km = sqr(n) * max(F(Xj) - (j-1)/n))	for all 1<=j<=n
+  */
+
+  mpf_init (Kt); mpf_init (f_x); mpf_init (f_j); mpf_init (f_jnq);
+  mpf_set_ui (Kp, 0);  mpf_set_ui (Km, 0);
+  for (j = 1; j <= n; j++)
+    {
+      P (f_x, X[j-1]);
+      mpf_set_ui (f_j, j);
+
+      mpf_div_ui (f_jnq, f_j, n);
+      mpf_sub (Kt, f_jnq, f_x);
+      if (mpf_cmp (Kt, Kp) > 0)
+	mpf_set (Kp, Kt);
+      if (g_debug > DEBUG_2)
+	{
+	  printf ("j=%lu ", j);
+	  printf ("P()="); mpf_out_str (stdout, 10, 2, f_x); printf ("\t");
+
+	  printf ("jnq="); mpf_out_str (stdout, 10, 2, f_jnq); printf (" ");
+	  printf ("diff="); mpf_out_str (stdout, 10, 2, Kt); printf (" ");
+	  printf ("Kp="); mpf_out_str (stdout, 10, 2, Kp); printf ("\t");
+	}
+      mpf_sub_ui (f_j, f_j, 1);
+      mpf_div_ui (f_jnq, f_j, n);
+      mpf_sub (Kt, f_x, f_jnq);
+      if (mpf_cmp (Kt, Km) > 0)
+	mpf_set (Km, Kt);
+
+      if (g_debug > DEBUG_2)
+	{
+	  printf ("jnq="); mpf_out_str (stdout, 10, 2, f_jnq); printf (" ");
+	  printf ("diff="); mpf_out_str (stdout, 10, 2, Kt); printf (" ");
+	  printf ("Km="); mpf_out_str (stdout, 10, 2, Km); printf (" ");
+	  printf ("\n");
+	}
+    }
+  mpf_sqrt_ui (Kt, n);
+  mpf_mul (Kp, Kp, Kt);
+  mpf_mul (Km, Km, Kt);
+
+  mpf_clear (Kt); mpf_clear (f_x); mpf_clear (f_j); mpf_clear (f_jnq);
+}
+
+/* ks_table(val, n) -- calculate probability for Kp/Km less than or
+   equal to VAL with N observations.  See [Knuth section 3.3.1] */
+
+void
+ks_table (mpf_t p, mpf_t val, const unsigned int n)
+{
+  /* We use Eq. (27), Knuth p.58, skipping O(1/n) for simplicity.
+     This shortcut will result in too high probabilities, especially
+     when n is small.
+
+     Pr(Kp(n) <= s) = 1 - pow(e, -2*s^2) * (1 - 2/3*s/sqrt(n) + O(1/n)) */
+
+  /* We have 's' in variable VAL and store the result in P. */
+
+  mpf_t t1, t2;
+
+  mpf_init (t1); mpf_init (t2);
+
+  /* t1 = 1 - 2/3 * s/sqrt(n) */
+  mpf_sqrt_ui (t1, n);
+  mpf_div (t1, val, t1);
+  mpf_mul_ui (t1, t1, 2);
+  mpf_div_ui (t1, t1, 3);
+  mpf_ui_sub (t1, 1, t1);
+
+  /* t2 = pow(e, -2*s^2) */
+#ifndef OLDGMP
+  mpf_pow_ui (t2, val, 2);	/* t2 = s^2 */
+  mpf_set_d (t2, exp (-(2.0 * mpf_get_d (t2))));
+#else
+  /* hmmm, gmp doesn't have pow() for floats.  use doubles. */
+  mpf_set_d (t2, pow (M_E, -(2 * pow (mpf_get_d (val), 2))));
+#endif
+
+  /* p = 1 - t1 * t2 */
+  mpf_mul (t1, t1, t2);
+  mpf_ui_sub (p, 1, t1);
+
+  mpf_clear (t1); mpf_clear (t2);
+}
+
+static double x2_table_X[][7] = {
+  { -2.33, -1.64, -.674, 0.0, 0.674, 1.64, 2.33 }, /* x */
+  { 5.4289, 2.6896, .454276, 0.0, .454276, 2.6896, 5.4289} /* x^2 */
+};
+
+#define _2D3 ((double) .6666666666)
+
+/* x2_table (t, v, n) -- return chi-square table row for V in T[]. */
+void
+x2_table (double t[],
+	  unsigned int v)
+{
+  int f;
+
+
+  /* FIXME: Do a table lookup for v <= 30 since the following formula
+     [Knuth, vol 2, 3.3.1] is only good for v > 30. */
+
+  /* value = v + sqrt(2*v) * X[p] + (2/3) * X[p]^2 - 2/3 + O(1/sqrt(t) */
+  /* NOTE: The O() term is ignored for simplicity. */
+
+  for (f = 0; f < 7; f++)
+      t[f] =
+	v +
+	sqrt (2 * v) * x2_table_X[0][f] +
+	_2D3 * x2_table_X[1][f] - _2D3;
+}
+
+
+/* P(p, x) -- Distribution function.  Calculate the probability of X
+being greater than or equal to any number in the sequence.  For a
+random real number between zero and one given by a uniformly
+distributed random number generator, this is simply equal to X. */
+
+static void
+P (mpf_t p, mpf_t x)
+{
+  mpf_set (p, x);
+}
+
+/* mpf_freqt() -- Frequency test using KS on N real numbers between zero
+   and one.  See [Knuth vol 2, p.61]. */
+void
+mpf_freqt (mpf_t Kp,
+	   mpf_t Km,
+	   mpf_t X[],
+	   const unsigned long int n)
+{
+  ks (Kp, Km, X, P, n);
+}
+
+
+/* The Chi-square test.  Eq. (8) in Knuth vol. 2 says that if Y[]
+   holds the observations and p[] is the probability for.. (to be
+   continued!)
+
+   V = 1/n * sum((s=1 to k) Y[s]^2 / p[s]) - n */
+
+void
+x2 (mpf_t V,			/* result */
+    unsigned long int X[],	/* data */
+    unsigned int k,		/* #of categories */
+    void (P) (mpf_t, unsigned long int, void *), /* probability func */
+    void *x,			/* extra user data passed to P() */
+    unsigned long int n)	/* #of samples */
+{
+  unsigned int f;
+  mpf_t f_t, f_t2;		/* temp floats */
+
+  mpf_init (f_t); mpf_init (f_t2);
+
+
+  mpf_set_ui (V, 0);
+  for (f = 0; f < k; f++)
+    {
+      if (g_debug > DEBUG_2)
+	fprintf (stderr, "%u: P()=", f);
+      mpf_set_ui (f_t, X[f]);
+      mpf_mul (f_t, f_t, f_t);	/* f_t = X[f]^2 */
+      P (f_t2, f, x);		/* f_t2 = Pr(f) */
+      if (g_debug > DEBUG_2)
+	mpf_out_str (stderr, 10, 2, f_t2);
+      mpf_div (f_t, f_t, f_t2);
+      mpf_add (V, V, f_t);
+      if (g_debug > DEBUG_2)
+	{
+	  fprintf (stderr, "\tV=");
+	  mpf_out_str (stderr, 10, 2, V);
+	  fprintf (stderr, "\t");
+	}
+    }
+  if (g_debug > DEBUG_2)
+    fprintf (stderr, "\n");
+  mpf_div_ui (V, V, n);
+  mpf_sub_ui (V, V, n);
+
+  mpf_clear (f_t); mpf_clear (f_t2);
+}
+
+/* Pzf(p, s, x) -- Probability for category S in mpz_freqt().  It's
+   1/d for all S.  X is a pointer to an unsigned int holding 'd'. */
+static void
+Pzf (mpf_t p, unsigned long int s, void *x)
+{
+  mpf_set_ui (p, 1);
+  mpf_div_ui (p, p, *((unsigned int *) x));
+}
+
+/* mpz_freqt(V, X, imax, n) -- Frequency test on integers.  [Knuth,
+   vol 2, 3.3.2].  Keep IMAX low on this one, since we loop from 0 to
+   IMAX.  128 or 256 could be nice.
+
+   X[] must not contain numbers outside the range 0 <= X <= IMAX.
+
+   Return value is number of observations actually used, after
+   discarding entries out of range.
+
+   Since X[] contains integers between zero and IMAX, inclusive, we
+   have IMAX+1 categories.
+
+   Note that N should be at least 5*IMAX.  Result is put in V and can
+   be compared to output from x2_table (v=IMAX). */
+
+unsigned long int
+mpz_freqt (mpf_t V,
+	   mpz_t X[],
+	   unsigned int imax,
+	   const unsigned long int n)
+{
+  unsigned long int *v;		/* result */
+  unsigned int f;
+  unsigned int d;		/* number of categories = imax+1 */
+  unsigned int uitemp;
+  unsigned long int usedn;
+
+
+  d = imax + 1;
+
+  v = (unsigned long int *) calloc (imax + 1, sizeof (unsigned long int));
+  if (NULL == v)
+    {
+      fprintf (stderr, "mpz_freqt(): out of memory\n");
+      exit (1);
+    }
+
+  /* count */
+  usedn = n;			/* actual number of observations */
+  for (f = 0; f < n; f++)
+    {
+      uitemp = mpz_get_ui(X[f]);
+      if (uitemp > imax)	/* sanity check */
+	{
+	  if (g_debug)
+	    fprintf (stderr, "mpz_freqt(): warning: input insanity: %u, "\
+		     "ignored.\n", uitemp);
+	  usedn--;
+	  continue;
+	}
+      v[uitemp]++;
+    }
+
+  if (g_debug > DEBUG_2)
+    {
+      fprintf (stderr, "counts:\n");
+      for (f = 0; f <= imax; f++)
+	fprintf (stderr, "%u:\t%lu\n", f, v[f]);
+    }
+
+  /* chi-square with k=imax+1 and P(x)=1/(imax+1) for all x.*/
+  x2 (V, v, d, Pzf, (void *) &d, usedn);
+
+  free (v);
+  return (usedn);
+}
+
+/* debug dummy to drag in dump funcs */
+void
+foo_debug ()
+{
+  if (0)
+    {
+      mpf_dump (0);
+#ifndef OLDGMP
+      mpz_dump (0);
+#endif
+    }
+}
+
+/* merit (rop, t, v, m) -- calculate merit for spectral test result in
+   dimension T, see Knuth p. 105.  BUGS: Only valid for 2 <= T <=
+   6. */
+void
+merit (mpf_t rop, unsigned int t, mpf_t v, mpz_t m)
+{
+  int f;
+  mpf_t f_m, f_const, f_pi;
+
+  mpf_init (f_m);
+  mpf_set_z (f_m, m);
+  mpf_init_set_d (f_const, M_PI);
+  mpf_init_set_d (f_pi, M_PI);
+
+  switch (t)
+    {
+    case 2:			/* PI */
+      break;
+    case 3:			/* PI * 4/3 */
+      mpf_mul_ui (f_const, f_const, 4);
+      mpf_div_ui (f_const, f_const, 3);
+      break;
+    case 4:			/* PI^2 * 1/2 */
+      mpf_mul (f_const, f_const, f_pi);
+      mpf_div_ui (f_const, f_const, 2);
+      break;
+    case 5:			/* PI^2 * 8/15 */
+      mpf_mul (f_const, f_const, f_pi);
+      mpf_mul_ui (f_const, f_const, 8);
+      mpf_div_ui (f_const, f_const, 15);
+      break;
+    case 6:			/* PI^3 * 1/6 */
+      mpf_mul (f_const, f_const, f_pi);
+      mpf_mul (f_const, f_const, f_pi);
+      mpf_div_ui (f_const, f_const, 6);
+      break;
+    default:
+      fprintf (stderr,
+	       "spect (merit): can't calculate merit for dimensions > 6\n");
+      mpf_set_ui (f_const, 0);
+      break;
+    }
+
+  /* rop = v^t */
+  mpf_set (rop, v);
+  for (f = 1; f < t; f++)
+    mpf_mul (rop, rop, v);
+  mpf_mul (rop, rop, f_const);
+  mpf_div (rop, rop, f_m);
+
+  mpf_clear (f_m);
+  mpf_clear (f_const);
+  mpf_clear (f_pi);
+}
+
+double
+merit_u (unsigned int t, mpf_t v, mpz_t m)
+{
+  mpf_t rop;
+  double res;
+
+  mpf_init (rop);
+  merit (rop, t, v, m);
+  res = mpf_get_d (rop);
+  mpf_clear (rop);
+  return res;
+}
+
+/* f_floor (rop, op) -- Set rop = floor (op). */
+void
+f_floor (mpf_t rop, mpf_t op)
+{
+  mpz_t z;
+
+  mpz_init (z);
+
+  /* No mpf_floor().  Convert to mpz and back. */
+  mpz_set_f (z, op);
+  mpf_set_z (rop, z);
+
+  mpz_clear (z);
+}
+
+
+/* vz_dot (rop, v1, v2, nelem) -- compute dot product of z-vectors V1,
+   V2.  N is number of elements in vectors V1 and V2. */
+
+void
+vz_dot (mpz_t rop, mpz_t V1[], mpz_t V2[], unsigned int n)
+{
+  mpz_t t;
+
+  mpz_init (t);
+  mpz_set_ui (rop, 0);
+  while (n--)
+    {
+      mpz_mul (t, V1[n], V2[n]);
+      mpz_add (rop, rop, t);
+    }
+
+  mpz_clear (t);
+}
+
+void
+spectral_test (mpf_t rop[], unsigned int T, mpz_t a, mpz_t m)
+{
+  /* Knuth "Seminumerical Algorithms, Third Edition", section 3.3.4
+     (pp. 101-103). */
+
+  /* v[t] = min { sqrt (x[1]^2 + ... + x[t]^2) |
+     x[1] + a*x[2] + ... + pow (a, t-1) * x[t] is congruent to 0 (mod m) } */
+
+
+  /* Variables. */
+  unsigned int ui_t;
+  unsigned int ui_i, ui_j, ui_k, ui_l;
+  mpf_t f_tmp1, f_tmp2;
+  mpz_t tmp1, tmp2, tmp3;
+  mpz_t U[GMP_SPECT_MAXT][GMP_SPECT_MAXT],
+    V[GMP_SPECT_MAXT][GMP_SPECT_MAXT],
+    X[GMP_SPECT_MAXT],
+    Y[GMP_SPECT_MAXT],
+    Z[GMP_SPECT_MAXT];
+  mpz_t h, hp, r, s, p, pp, q, u, v;
+
+  /* GMP inits. */
+  mpf_init (f_tmp1);
+  mpf_init (f_tmp2);
+  for (ui_i = 0; ui_i < GMP_SPECT_MAXT; ui_i++)
+    {
+      for (ui_j = 0; ui_j < GMP_SPECT_MAXT; ui_j++)
+	{
+	  mpz_init_set_ui (U[ui_i][ui_j], 0);
+	  mpz_init_set_ui (V[ui_i][ui_j], 0);
+	}
+      mpz_init_set_ui (X[ui_i], 0);
+      mpz_init_set_ui (Y[ui_i], 0);
+      mpz_init (Z[ui_i]);
+    }
+  mpz_init (tmp1);
+  mpz_init (tmp2);
+  mpz_init (tmp3);
+  mpz_init (h);
+  mpz_init (hp);
+  mpz_init (r);
+  mpz_init (s);
+  mpz_init (p);
+  mpz_init (pp);
+  mpz_init (q);
+  mpz_init (u);
+  mpz_init (v);
+
+  /* Implementation inits. */
+  if (T > GMP_SPECT_MAXT)
+    T = GMP_SPECT_MAXT;			/* FIXME: Lazy. */
+
+  /* S1 [Initialize.] */
+  ui_t = 2 - 1;			/* NOTE: `t' in description == ui_t + 1
+				   for easy indexing */
+  mpz_set (h, a);
+  mpz_set (hp, m);
+  mpz_set_ui (p, 1);
+  mpz_set_ui (pp, 0);
+  mpz_set (r, a);
+  mpz_pow_ui (s, a, 2);
+  mpz_add_ui (s, s, 1);		/* s = 1 + a^2 */
+
+  /* S2 [Euclidean step.] */
+  while (1)
+    {
+      if (g_debug > DEBUG_1)
+	{
+	  mpz_mul (tmp1, h, pp);
+	  mpz_mul (tmp2, hp, p);
+	  mpz_sub (tmp1, tmp1, tmp2);
+	  if (mpz_cmpabs (m, tmp1))
+	    {
+	      printf ("***BUG***: h*pp - hp*p = ");
+	      mpz_out_str (stdout, 10, tmp1);
+	      printf ("\n");
+	    }
+	}
+      if (g_debug > DEBUG_2)
+	{
+	  printf ("hp = ");
+	  mpz_out_str (stdout, 10, hp);
+	  printf ("\nh = ");
+	  mpz_out_str (stdout, 10, h);
+	  printf ("\n");
+	  fflush (stdout);
+	}
+
+      if (mpz_sgn (h))
+	mpz_tdiv_q (q, hp, h);	/* q = floor(hp/h) */
+      else
+	mpz_set_ui (q, 1);
+
+      if (g_debug > DEBUG_2)
+	{
+	  printf ("q = ");
+	  mpz_out_str (stdout, 10, q);
+	  printf ("\n");
+	  fflush (stdout);
+	}
+
+      mpz_mul (tmp1, q, h);
+      mpz_sub (u, hp, tmp1);	/* u = hp - q*h */
+
+      mpz_mul (tmp1, q, p);
+      mpz_sub (v, pp, tmp1);	/* v = pp - q*p */
+
+      mpz_pow_ui (tmp1, u, 2);
+      mpz_pow_ui (tmp2, v, 2);
+      mpz_add (tmp1, tmp1, tmp2);
+      if (mpz_cmp (tmp1, s) < 0)
+	{
+	  mpz_set (s, tmp1);	/* s = u^2 + v^2 */
+	  mpz_set (hp, h);	/* hp = h */
+	  mpz_set (h, u);	/* h = u */
+	  mpz_set (pp, p);	/* pp = p */
+	  mpz_set (p, v);	/* p = v */
+	}
+      else
+	break;
+    }
+
+  /* S3 [Compute v2.] */
+  mpz_sub (u, u, h);
+  mpz_sub (v, v, p);
+
+  mpz_pow_ui (tmp1, u, 2);
+  mpz_pow_ui (tmp2, v, 2);
+  mpz_add (tmp1, tmp1, tmp2);
+  if (mpz_cmp (tmp1, s) < 0)
+    {
+      mpz_set (s, tmp1);	/* s = u^2 + v^2 */
+      mpz_set (hp, u);
+      mpz_set (pp, v);
+    }
+  mpf_set_z (f_tmp1, s);
+  mpf_sqrt (rop[ui_t - 1], f_tmp1);
+
+  /* S4 [Advance t.] */
+  mpz_neg (U[0][0], h);
+  mpz_set (U[0][1], p);
+  mpz_neg (U[1][0], hp);
+  mpz_set (U[1][1], pp);
+
+  mpz_set (V[0][0], pp);
+  mpz_set (V[0][1], hp);
+  mpz_neg (V[1][0], p);
+  mpz_neg (V[1][1], h);
+  if (mpz_cmp_ui (pp, 0) > 0)
+    {
+      mpz_neg (V[0][0], V[0][0]);
+      mpz_neg (V[0][1], V[0][1]);
+      mpz_neg (V[1][0], V[1][0]);
+      mpz_neg (V[1][1], V[1][1]);
+    }
+
+  while (ui_t + 1 != T)		/* S4 loop */
+    {
+      ui_t++;
+      mpz_mul (r, a, r);
+      mpz_mod (r, r, m);
+
+      /* Add new row and column to U and V.  They are initialized with
+	 all elements set to zero, so clearing is not necessary. */
+
+      mpz_neg (U[ui_t][0], r); /* U: First col in new row. */
+      mpz_set_ui (U[ui_t][ui_t], 1); /* U: Last col in new row. */
+
+      mpz_set (V[ui_t][ui_t], m); /* V: Last col in new row. */
+
+      /* "Finally, for 1 <= i < t,
+	   set q = round (vi1 * r / m),
+	   vit = vi1*r - q*m,
+	   and Ut=Ut+q*Ui */
+
+      for (ui_i = 0; ui_i < ui_t; ui_i++)
+	{
+	  mpz_mul (tmp1, V[ui_i][0], r); /* tmp1=vi1*r */
+	  zdiv_round (q, tmp1, m); /* q=round(vi1*r/m) */
+	  mpz_mul (tmp2, q, m);	/* tmp2=q*m */
+	  mpz_sub (V[ui_i][ui_t], tmp1, tmp2);
+
+	  for (ui_j = 0; ui_j <= ui_t; ui_j++) /* U[t] = U[t] + q*U[i] */
+	    {
+	      mpz_mul (tmp1, q, U[ui_i][ui_j]);	/* tmp=q*uij */
+	      mpz_add (U[ui_t][ui_j], U[ui_t][ui_j], tmp1); /* utj = utj + q*uij */
+	    }
+	}
+
+      /* s = min (s, zdot (U[t], U[t]) */
+      vz_dot (tmp1, U[ui_t], U[ui_t], ui_t + 1);
+      if (mpz_cmp (tmp1, s) < 0)
+	mpz_set (s, tmp1);
+
+      ui_k = ui_t;
+      ui_j = 0;			/* WARNING: ui_j no longer a temp. */
+
+      /* S5 [Transform.] */
+      if (g_debug > DEBUG_2)
+	printf ("(t, k, j, q1, q2, ...)\n");
+      do
+	{
+	  if (g_debug > DEBUG_2)
+	    printf ("(%u, %u, %u", ui_t + 1, ui_k + 1, ui_j + 1);
+
+	  for (ui_i = 0; ui_i <= ui_t; ui_i++)
+	    {
+	      if (ui_i != ui_j)
+		{
+		  vz_dot (tmp1, V[ui_i], V[ui_j], ui_t + 1); /* tmp1=dot(Vi,Vj). */
+		  mpz_abs (tmp2, tmp1);
+		  mpz_mul_ui (tmp2, tmp2, 2); /* tmp2 = 2*abs(dot(Vi,Vj) */
+		  vz_dot (tmp3, V[ui_j], V[ui_j], ui_t + 1); /* tmp3=dot(Vj,Vj). */
+
+		  if (mpz_cmp (tmp2, tmp3) > 0)
+		    {
+		      zdiv_round (q, tmp1, tmp3); /* q=round(Vi.Vj/Vj.Vj) */
+		      if (g_debug > DEBUG_2)
+			{
+			  printf (", ");
+			  mpz_out_str (stdout, 10, q);
+			}
+
+		      for (ui_l = 0; ui_l <= ui_t; ui_l++)
+			{
+			  mpz_mul (tmp1, q, V[ui_j][ui_l]);
+			  mpz_sub (V[ui_i][ui_l], V[ui_i][ui_l], tmp1); /* Vi=Vi-q*Vj */
+			  mpz_mul (tmp1, q, U[ui_i][ui_l]);
+			  mpz_add (U[ui_j][ui_l], U[ui_j][ui_l], tmp1); /* Uj=Uj+q*Ui */
+			}
+
+		      vz_dot (tmp1, U[ui_j], U[ui_j], ui_t + 1); /* tmp1=dot(Uj,Uj) */
+		      if (mpz_cmp (tmp1, s) < 0) /* s = min(s,dot(Uj,Uj)) */
+			mpz_set (s, tmp1);
+		      ui_k = ui_j;
+		    }
+		  else if (g_debug > DEBUG_2)
+		    printf (", #"); /* 2|Vi.Vj| <= Vj.Vj */
+		}
+	      else if (g_debug > DEBUG_2)
+		printf (", *");	/* i == j */
+	    }
+
+	  if (g_debug > DEBUG_2)
+	    printf (")\n");
+
+	  /* S6 [Advance j.] */
+	  if (ui_j == ui_t)
+	    ui_j = 0;
+	  else
+	    ui_j++;
+	}
+      while (ui_j != ui_k);	/* S5 */
+
+      /* From Knuth p. 104: "The exhaustive search in steps S8-S10
+	 reduces the value of s only rarely." */
+#ifdef DO_SEARCH
+      /* S7 [Prepare for search.] */
+      /* Find minimum in (x[1], ..., x[t]) satisfying condition
+	 x[k]^2 <= f(y[1], ...,y[t]) * dot(V[k],V[k]) */
+
+      ui_k = ui_t;
+      if (g_debug > DEBUG_2)
+	{
+	  printf ("searching...");
+	  /*for (f = 0; f < ui_t*/
+	  fflush (stdout);
+	}
+
+      /* Z[i] = floor (sqrt (floor (dot(V[i],V[i]) * s / m^2))); */
+      mpz_pow_ui (tmp1, m, 2);
+      mpf_set_z (f_tmp1, tmp1);
+      mpf_set_z (f_tmp2, s);
+      mpf_div (f_tmp1, f_tmp2, f_tmp1);	/* f_tmp1 = s/m^2 */
+      for (ui_i = 0; ui_i <= ui_t; ui_i++)
+	{
+	  vz_dot (tmp1, V[ui_i], V[ui_i], ui_t + 1);
+	  mpf_set_z (f_tmp2, tmp1);
+	  mpf_mul (f_tmp2, f_tmp2, f_tmp1);
+	  f_floor (f_tmp2, f_tmp2);
+	  mpf_sqrt (f_tmp2, f_tmp2);
+	  mpz_set_f (Z[ui_i], f_tmp2);
+	}
+
+      /* S8 [Advance X[k].] */
+      do
+	{
+	  if (g_debug > DEBUG_2)
+	    {
+	      printf ("X[%u] = ", ui_k);
+	      mpz_out_str (stdout, 10, X[ui_k]);
+	      printf ("\tZ[%u] = ", ui_k);
+	      mpz_out_str (stdout, 10, Z[ui_k]);
+	      printf ("\n");
+	      fflush (stdout);
+	    }
+
+	  if (mpz_cmp (X[ui_k], Z[ui_k]))
+	    {
+	      mpz_add_ui (X[ui_k], X[ui_k], 1);
+	      for (ui_i = 0; ui_i <= ui_t; ui_i++)
+		mpz_add (Y[ui_i], Y[ui_i], U[ui_k][ui_i]);
+
+	      /* S9 [Advance k.] */
+	      while (++ui_k <= ui_t)
+		{
+		  mpz_neg (X[ui_k], Z[ui_k]);
+		  mpz_mul_ui (tmp1, Z[ui_k], 2);
+		  for (ui_i = 0; ui_i <= ui_t; ui_i++)
+		    {
+		      mpz_mul (tmp2, tmp1, U[ui_k][ui_i]);
+		      mpz_sub (Y[ui_i], Y[ui_i], tmp2);
+		    }
+		}
+	      vz_dot (tmp1, Y, Y, ui_t + 1);
+	      if (mpz_cmp (tmp1, s) < 0)
+		mpz_set (s, tmp1);
+	    }
+	}
+      while (--ui_k);
+#endif /* DO_SEARCH */
+      mpf_set_z (f_tmp1, s);
+      mpf_sqrt (rop[ui_t - 1], f_tmp1);
+#ifdef DO_SEARCH
+      if (g_debug > DEBUG_2)
+	printf ("done.\n");
+#endif /* DO_SEARCH */
+    } /* S4 loop */
+
+  /* Clear GMP variables. */
+
+  mpf_clear (f_tmp1);
+  mpf_clear (f_tmp2);
+  for (ui_i = 0; ui_i < GMP_SPECT_MAXT; ui_i++)
+    {
+      for (ui_j = 0; ui_j < GMP_SPECT_MAXT; ui_j++)
+	{
+	  mpz_clear (U[ui_i][ui_j]);
+	  mpz_clear (V[ui_i][ui_j]);
+	}
+      mpz_clear (X[ui_i]);
+      mpz_clear (Y[ui_i]);
+      mpz_clear (Z[ui_i]);
+    }
+  mpz_clear (tmp1);
+  mpz_clear (tmp2);
+  mpz_clear (tmp3);
+  mpz_clear (h);
+  mpz_clear (hp);
+  mpz_clear (r);
+  mpz_clear (s);
+  mpz_clear (p);
+  mpz_clear (pp);
+  mpz_clear (q);
+  mpz_clear (u);
+  mpz_clear (v);
+
+  return;
+}