Merging upstream version 1.46.3.

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 0 insertions, 788 deletions

diff --git a/database/KolmogorovSmirnovDist.c b/database/KolmogorovSmirnovDist.c
deleted file mode 100644
index 1486abc7b..000000000
--- a/database/KolmogorovSmirnovDist.c
+++ /dev/null
@@ -1,788 +0,0 @@
-// SPDX-License-Identifier: GPL-3.0
-
-/********************************************************************
- *
- * File:          KolmogorovSmirnovDist.c
- * Environment:   ISO C99 or ANSI C89
- * Author:        Richard Simard
- * Organization:  DIRO, Université de Montréal
- * Date:          1 February 2012
- * Version        1.1
-
- * Copyright 1 march 2010 by Université de Montréal,
-                             Richard Simard and Pierre L'Ecuyer
- =====================================================================
-
-    This program 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, version 3 of the License.
-
-    This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
-
- =====================================================================*/
-
-#include "KolmogorovSmirnovDist.h"
-#include <math.h>
-#include <stdlib.h>
-
-#define num_Pi     3.14159265358979323846 /* PI */
-#define num_Ln2    0.69314718055994530941 /* log(2) */
-
-/* For x close to 0 or 1, we use the exact formulae of Ruben-Gambino in all
-   cases. For n <= NEXACT, we use exact algorithms: the Durbin matrix and
-   the Pomeranz algorithms. For n > NEXACT, we use asymptotic methods
-   except for x close to 0 where we still use the method of Durbin
-   for n <= NKOLMO. For n > NKOLMO, we use asymptotic methods only and
-   so the precision is less for x close to 0.
-   We could increase the limit NKOLMO to 10^6 to get better precision
-   for x close to 0, but at the price of a slower speed. */
-#define NEXACT 500
-#define NKOLMO 100000
-
-/* The Durbin matrix algorithm for the Kolmogorov-Smirnov distribution */
-static double DurbinMatrix (int n, double d);
-
-
-/*========================================================================*/
-#if 0
-
-/* For ANSI C89 only, not for ISO C99 */
-#define MAXI 50
-#define EPSILON 1.0e-15
-
-double log1p (double x)
-{
-   /* returns a value equivalent to log(1 + x) accurate also for small x. */
-   if (fabs (x) > 0.1) {
-      return log (1.0 + x);
-   } else {
-      double term = x;
-      double sum = x;
-      int s = 2;
-      while ((fabs (term) > EPSILON * fabs (sum)) && (s < MAXI)) {
-         term *= -x;
-         sum += term / s;
-         s++;
-      }
-      return sum;
-   }
-}
-
-#undef MAXI
-#undef EPSILON
-
-#endif
-
-/*========================================================================*/
-#define MFACT 30
-
-/* The natural logarithm of factorial n! for  0 <= n <= MFACT */
-static double LnFactorial[MFACT + 1] = {
-   0.,
-   0.,
-   0.6931471805599453,
-   1.791759469228055,
-   3.178053830347946,
-   4.787491742782046,
-   6.579251212010101,
-   8.525161361065415,
-   10.60460290274525,
-   12.80182748008147,
-   15.10441257307552,
-   17.50230784587389,
-   19.98721449566188,
-   22.55216385312342,
-   25.19122118273868,
-   27.89927138384088,
-   30.67186010608066,
-   33.50507345013688,
-   36.39544520803305,
-   39.33988418719949,
-   42.33561646075348,
-   45.3801388984769,
-   48.47118135183522,
-   51.60667556776437,
-   54.7847293981123,
-   58.00360522298051,
-   61.26170176100199,
-   64.55753862700632,
-   67.88974313718154,
-   71.257038967168,
-   74.65823634883016
-};
-
-/*------------------------------------------------------------------------*/
-
-static double getLogFactorial (int n)
-{
-   /* Returns the natural logarithm of factorial n! */
-   if (n <= MFACT) {
-      return LnFactorial[n];
-
-   } else {
-      double x = (double) (n + 1);
-      double y = 1.0 / (x * x);
-      double z = ((-(5.95238095238E-4 * y) + 7.936500793651E-4) * y -
-         2.7777777777778E-3) * y + 8.3333333333333E-2;
-      z = ((x - 0.5) * log (x) - x) + 9.1893853320467E-1 + z / x;
-      return z;
-   }
-}
-
-/*------------------------------------------------------------------------*/
-
-static double rapfac (int n)
-{
-   /* Computes n! / n^n */
-   int i;
-   double res = 1.0 / n;
-   for (i = 2; i <= n; i++) {
-      res *= (double) i / n;
-   }
-   return res;
-}
-
-
-/*========================================================================*/
-
-static double **CreateMatrixD (int N, int M)
-{
-   int i;
-   double **T2;
-
-   T2 = (double **) malloc (N * sizeof (double *));
-   T2[0] = (double *) malloc ((size_t) N * M * sizeof (double));
-   for (i = 1; i < N; i++)
-      T2[i] = T2[0] + i * M;
-   return T2;
-}
-
-
-static void DeleteMatrixD (double **T)
-{
-   free (T[0]);
-   free (T);
-}
-
-
-/*========================================================================*/
-
-static double KSPlusbarAsymp (int n, double x)
-{
-   /* Compute the probability of the KS+ distribution using an asymptotic
-      formula */
-   double t = (6.0 * n * x + 1);
-   double z = t * t / (18.0 * n);
-   double v = 1.0 - (2.0 * z * z - 4.0 * z - 1.0) / (18.0 * n);
-   if (v <= 0.0)
-      return 0.0;
-   v = v * exp (-z);
-   if (v >= 1.0)
-      return 1.0;
-   return v;
-}
-
-
-/*-------------------------------------------------------------------------*/
-
-static double KSPlusbarUpper (int n, double x)
-{
-   /* Compute the probability of the KS+ distribution in the upper tail using
-      Smirnov's stable formula */
-   const double EPSILON = 1.0E-12;
-   double q;
-   double Sum = 0.0;
-   double term;
-   double t;
-   double LogCom;
-   double LOGJMAX;
-   int j;
-   int jdiv;
-   int jmax = (int) (n * (1.0 - x));
-
-   if (n > 200000)
-      return KSPlusbarAsymp (n, x);
-
-   /* Avoid log(0) for j = jmax and q ~ 1.0 */
-   if ((1.0 - x - (double) jmax / n) <= 0.0)
-      jmax--;
-
-   if (n > 3000)
-      jdiv = 2;
-   else
-      jdiv = 3;
-
-   j = jmax / jdiv + 1;
-   LogCom = getLogFactorial (n) - getLogFactorial (j) -
-            getLogFactorial (n - j);
-   LOGJMAX = LogCom;
-
-   while (j <= jmax) {
-      q = (double) j / n + x;
-      term = LogCom + (j - 1) * log (q) + (n - j) * log1p (-q);
-      t = exp (term);
-      Sum += t;
-      LogCom += log ((double) (n - j) / (j + 1));
-      if (t <= Sum * EPSILON)
-         break;
-      j++;
-   }
-
-   j = jmax / jdiv;
-   LogCom = LOGJMAX + log ((double) (j + 1) / (n - j));
-
-   while (j > 0) {
-      q = (double) j / n + x;
-      term = LogCom + (j - 1) * log (q) + (n - j) * log1p (-q);
-      t = exp (term);
-      Sum += t;
-      LogCom += log ((double) j / (n - j + 1));
-      if (t <= Sum * EPSILON)
-         break;
-      j--;
-   }
-
-   Sum *= x;
-   /* add the term j = 0 */
-   Sum += exp (n * log1p (-x));
-   return Sum;
-}
-
-
-/*========================================================================*/
-
-static double Pelz (int n, double x)
-{
-   /* Approximating the Lower Tail-Areas of the Kolmogorov-Smirnov One-Sample
-      Statistic,
-      Wolfgang Pelz and I. J. Good,
-      Journal of the Royal Statistical Society, Series B.
-      Vol. 38, No. 2 (1976), pp. 152-156
-   */
-
-   const int JMAX = 20;
-   const double EPS = 1.0e-10;
-   const double C = 2.506628274631001;         /* sqrt(2*Pi) */
-   const double C2 = 1.2533141373155001;       /* sqrt(Pi/2) */
-   const double PI2 = num_Pi * num_Pi;
-   const double PI4 = PI2 * PI2;
-   const double RACN = sqrt ((double) n);
-   const double z = RACN * x;
-   const double z2 = z * z;
-   const double z4 = z2 * z2;
-   const double z6 = z4 * z2;
-   const double w = PI2 / (2.0 * z * z);
-   double ti, term, tom;
-   double sum;
-   int j;
-
-   term = 1;
-   j = 0;
-   sum = 0;
-   while (j <= JMAX && term > EPS * sum) {
-      ti = j + 0.5;
-      term = exp (-ti * ti * w);
-      sum += term;
-      j++;
-   }
-   sum *= C / z;
-
-   term = 1;
-   tom = 0;
-   j = 0;
-   while (j <= JMAX && fabs (term) > EPS * fabs (tom)) {
-      ti = j + 0.5;
-      term = (PI2 * ti * ti - z2) * exp (-ti * ti * w);
-      tom += term;
-      j++;
-   }
-   sum += tom * C2 / (RACN * 3.0 * z4);
-
-   term = 1;
-   tom = 0;
-   j = 0;
-   while (j <= JMAX && fabs (term) > EPS * fabs (tom)) {
-      ti = j + 0.5;
-      term = 6 * z6 + 2 * z4 + PI2 * (2 * z4 - 5 * z2) * ti * ti +
-         PI4 * (1 - 2 * z2) * ti * ti * ti * ti;
-      term *= exp (-ti * ti * w);
-      tom += term;
-      j++;
-   }
-   sum += tom * C2 / (n * 36.0 * z * z6);
-
-   term = 1;
-   tom = 0;
-   j = 1;
-   while (j <= JMAX && term > EPS * tom) {
-      ti = j;
-      term = PI2 * ti * ti * exp (-ti * ti * w);
-      tom += term;
-      j++;
-   }
-   sum -= tom * C2 / (n * 18.0 * z * z2);
-
-   term = 1;
-   tom = 0;
-   j = 0;
-   while (j <= JMAX && fabs (term) > EPS * fabs (tom)) {
-      ti = j + 0.5;
-      ti = ti * ti;
-      term = -30 * z6 - 90 * z6 * z2 + PI2 * (135 * z4 - 96 * z6) * ti +
-         PI4 * (212 * z4 - 60 * z2) * ti * ti + PI2 * PI4 * ti * ti * ti * (5 -
-         30 * z2);
-      term *= exp (-ti * w);
-      tom += term;
-      j++;
-   }
-   sum += tom * C2 / (RACN * n * 3240.0 * z4 * z6);
-
-   term = 1;
-   tom = 0;
-   j = 1;
-   while (j <= JMAX && fabs (term) > EPS * fabs (tom)) {
-      ti = j * j;
-      term = (3 * PI2 * ti * z2 - PI4 * ti * ti) * exp (-ti * w);
-      tom += term;
-      j++;
-   }
-   sum += tom * C2 / (RACN * n * 108.0 * z6);
-
-   return sum;
-}
-
-
-/*=========================================================================*/
-
-static void CalcFloorCeil (
-   int n,                         /* sample size */
-   double t,                      /* = nx */
-   double *A,                     /* A_i */
-   double *Atflo,                 /* floor (A_i - t) */
-   double *Atcei                  /* ceiling (A_i + t) */
-   )
-{
-   /* Precompute A_i, floors, and ceilings for limits of sums in the Pomeranz
-      algorithm */
-   int i;
-   int ell = (int) t;             /* floor (t) */
-   double z = t - ell;            /* t - floor (t) */
-   double w = ceil (t) - t;
-
-   if (z > 0.5) {
-      for (i = 2; i <= 2 * n + 2; i += 2)
-         Atflo[i] = i / 2 - 2 - ell;
-      for (i = 1; i <= 2 * n + 2; i += 2)
-         Atflo[i] = i / 2 - 1 - ell;
-
-      for (i = 2; i <= 2 * n + 2; i += 2)
-         Atcei[i] = i / 2 + ell;
-      for (i = 1; i <= 2 * n + 2; i += 2)
-         Atcei[i] = i / 2 + 1 + ell;
-
-   } else if (z > 0.0) {
-      for (i = 1; i <= 2 * n + 2; i++)
-         Atflo[i] = i / 2 - 1 - ell;
-
-      for (i = 2; i <= 2 * n + 2; i++)
-         Atcei[i] = i / 2 + ell;
-      Atcei[1] = 1 + ell;
-
-   } else {                       /* z == 0 */
-      for (i = 2; i <= 2 * n + 2; i += 2)
-         Atflo[i] = i / 2 - 1 - ell;
-      for (i = 1; i <= 2 * n + 2; i += 2)
-         Atflo[i] = i / 2 - ell;
-
-      for (i = 2; i <= 2 * n + 2; i += 2)
-         Atcei[i] = i / 2 - 1 + ell;
-      for (i = 1; i <= 2 * n + 2; i += 2)
-         Atcei[i] = i / 2 + ell;
-   }
-
-   if (w < z)
-      z = w;
-   A[0] = A[1] = 0;
-   A[2] = z;
-   A[3] = 1 - A[2];
-   for (i = 4; i <= 2 * n + 1; i++)
-      A[i] = A[i - 2] + 1;
-   A[2 * n + 2] = n;
-}
-
-
-/*========================================================================*/
-
-static double Pomeranz (int n, double x)
-{
-   /* The Pomeranz algorithm to compute the KS distribution */
-   const double EPS = 1.0e-15;
-   const int ENO = 350;
-   const double RENO = ldexp (1.0, ENO); /* for renormalization of V */
-   int coreno;                    /* counter: how many renormalizations */
-   const double t = n * x;
-   double w, sum, minsum;
-   int i, j, k, s;
-   int r1, r2;                    /* Indices i and i-1 for V[i][] */
-   int jlow, jup, klow, kup, kup0;
-   double *A;
-   double *Atflo;
-   double *Atcei;
-   double **V;
-   double **H;                    /* = pow(w, j) / Factorial(j) */
-
-   A = (double *) calloc ((size_t) (2 * n + 3), sizeof (double));
-   Atflo = (double *) calloc ((size_t) (2 * n + 3), sizeof (double));
-   Atcei = (double *) calloc ((size_t) (2 * n + 3), sizeof (double));
-   V = (double **) CreateMatrixD (2, n + 2);
-   H = (double **) CreateMatrixD (4, n + 2);
-
-   CalcFloorCeil (n, t, A, Atflo, Atcei);
-
-   for (j = 1; j <= n + 1; j++)
-      V[0][j] = 0;
-   for (j = 2; j <= n + 1; j++)
-      V[1][j] = 0;
-   V[1][1] = RENO;
-   coreno = 1;
-
-   /* Precompute H[][] = (A[j] - A[j-1]^k / k! for speed */
-   H[0][0] = 1;
-   w = 2.0 * A[2] / n;
-   for (j = 1; j <= n + 1; j++)
-      H[0][j] = w * H[0][j - 1] / j;
-
-   H[1][0] = 1;
-   w = (1.0 - 2.0 * A[2]) / n;
-   for (j = 1; j <= n + 1; j++)
-      H[1][j] = w * H[1][j - 1] / j;
-
-   H[2][0] = 1;
-   w = A[2] / n;
-   for (j = 1; j <= n + 1; j++)
-      H[2][j] = w * H[2][j - 1] / j;
-
-   H[3][0] = 1;
-   for (j = 1; j <= n + 1; j++)
-      H[3][j] = 0;
-
-   r1 = 0;
-   r2 = 1;
-   for (i = 2; i <= 2 * n + 2; i++) {
-      jlow = 2 + (int) Atflo[i];
-      if (jlow < 1)
-         jlow = 1;
-      jup = (int) Atcei[i];
-      if (jup > n + 1)
-         jup = n + 1;
-
-      klow = 2 + (int) Atflo[i - 1];
-      if (klow < 1)
-         klow = 1;
-      kup0 = (int) Atcei[i - 1];
-
-      /* Find to which case it corresponds */
-      w = (A[i] - A[i - 1]) / n;
-      s = -1;
-      for (j = 0; j < 4; j++) {
-         if (fabs (w - H[j][1]) <= EPS) {
-            s = j;
-            break;
-         }
-      }
-      /* assert (s >= 0, "Pomeranz: s < 0"); */
-
-      minsum = RENO;
-      r1 = (r1 + 1) & 1;          /* i - 1 */
-      r2 = (r2 + 1) & 1;          /* i */
-
-      for (j = jlow; j <= jup; j++) {
-         kup = kup0;
-         if (kup > j)
-            kup = j;
-         sum = 0;
-         for (k = kup; k >= klow; k--)
-            sum += V[r1][k] * H[s][j - k];
-         V[r2][j] = sum;
-         if (sum < minsum)
-            minsum = sum;
-      }
-
-      if (minsum < 1.0e-280) {
-         /* V is too small: renormalize to avoid underflow of probabilities */
-         for (j = jlow; j <= jup; j++)
-            V[r2][j] *= RENO;
-         coreno++;                /* keep track of log of RENO */
-      }
-   }
-
-   sum = V[r2][n + 1];
-   free (A);
-   free (Atflo);
-   free (Atcei);
-   DeleteMatrixD (H);
-   DeleteMatrixD (V);
-   w = getLogFactorial (n) - coreno * ENO * num_Ln2 + log (sum);
-   if (w >= 0.)
-      return 1.;
-   return exp (w);
-}
-
-
-/*========================================================================*/
-
-static double cdfSpecial (int n, double x)
-{
-   /* The KS distribution is known exactly for these cases */
-
-   /* For nx^2 > 18, KSfbar(n, x) is smaller than 5e-16 */
-   if ((n * x * x >= 18.0) || (x >= 1.0))
-      return 1.0;
-
-   if (x <= 0.5 / n)
-      return 0.0;
-
-   if (n == 1)
-      return 2.0 * x - 1.0;
-
-   if (x <= 1.0 / n) {
-      double t = 2.0 * x * n - 1.0;
-      double w;
-      if (n <= NEXACT) {
-         w = rapfac (n);
-         return w * pow (t, (double) n);
-      }
-      w = getLogFactorial (n) + n * log (t / n);
-      return exp (w);
-   }
-
-   if (x >= 1.0 - 1.0 / n) {
-      return 1.0 - 2.0 * pow (1.0 - x, (double) n);
-   }
-
-   return -1.0;
-}
-
-
-/*========================================================================*/
-
-double KScdf (int n, double x)
-{
-   const double w = n * x * x;
-   double u = cdfSpecial (n, x);
-   if (u >= 0.0)
-      return u;
-
-   if (n <= NEXACT) {
-      if (w < 0.754693)
-         return DurbinMatrix (n, x);
-      if (w < 4.0)
-         return Pomeranz (n, x);
-      return 1.0 - KSfbar (n, x);
-   }
-
-   if ((w * x * n <= 7.0) && (n <= NKOLMO))
-      return DurbinMatrix (n, x);
-
-   return Pelz (n, x);
-}
-
-
-/*=========================================================================*/
-
-static double fbarSpecial (int n, double x)
-{
-   const double w = n * x * x;
-
-   if ((w >= 370.0) || (x >= 1.0))
-      return 0.0;
-   if ((w <= 0.0274) || (x <= 0.5 / n))
-      return 1.0;
-   if (n == 1)
-      return 2.0 - 2.0 * x;
-
-   if (x <= 1.0 / n) {
-      double z;
-      double t = 2.0 * x * n - 1.0;
-      if (n <= NEXACT) {
-         z = rapfac (n);
-         return 1.0 - z * pow (t, (double) n);
-      }
-      z = getLogFactorial (n) + n * log (t / n);
-      return 1.0 - exp (z);
-   }
-
-   if (x >= 1.0 - 1.0 / n) {
-      return 2.0 * pow (1.0 - x, (double) n);
-   }
-   return -1.0;
-}
-
-
-/*========================================================================*/
-
-double KSfbar (int n, double x)
-{
-   const double w = n * x * x;
-   double v = fbarSpecial (n, x);
-   if (v >= 0.0)
-      return v;
-
-   if (n <= NEXACT) {
-      if (w < 4.0)
-         return 1.0 - KScdf (n, x);
-      else
-         return 2.0 * KSPlusbarUpper (n, x);
-   }
-
-   if (w >= 2.65)
-      return 2.0 * KSPlusbarUpper (n, x);
-
-   return 1.0 - KScdf (n, x);
-}
-
-
-/*=========================================================================
-
-The following implements the Durbin matrix algorithm and was programmed by
-G. Marsaglia, Wai Wan Tsang and Jingbo Wong.
-
-I have made small modifications in their program. (Richard Simard)
-
-
-
-=========================================================================*/
-
-/*
- The C program to compute Kolmogorov's distribution
-
-             K(n,d) = Prob(D_n < d),         where
-
-      D_n = max(x_1-0/n,x_2-1/n...,x_n-(n-1)/n,1/n-x_1,2/n-x_2,...,n/n-x_n)
-
-    with  x_1<x_2,...<x_n  a purported set of n independent uniform [0,1)
-    random variables sorted into increasing order.
-    See G. Marsaglia, Wai Wan Tsang and Jingbo Wong,
-       J.Stat.Software, 8, 18, pp 1--4, (2003).
-*/
-
-#define NORM 1.0e140
-#define INORM 1.0e-140
-#define LOGNORM 140
-
-
-/* Matrix product */
-static void mMultiply (double *A, double *B, double *C, int m);
-
-/* Matrix power */
-static void mPower (double *A, int eA, double *V, int *eV, int m, int n);
-
-
-static double DurbinMatrix (int n, double d)
-{
-   int k, m, i, j, g, eH, eQ;
-   double h, s, *H, *Q;
-   /* OMIT NEXT TWO LINES IF YOU REQUIRE >7 DIGIT ACCURACY IN THE RIGHT TAIL */
-#if 0
-   s = d * d * n;
-   if (s > 7.24 || (s > 3.76 && n > 99))
-      return 1 - 2 * exp (-(2.000071 + .331 / sqrt (n) + 1.409 / n) * s);
-#endif
-   k = (int) (n * d) + 1;
-   m = 2 * k - 1;
-   h = k - n * d;
-   H = (double *) malloc ((m * m) * sizeof (double));
-   Q = (double *) malloc ((m * m) * sizeof (double));
-   for (i = 0; i < m; i++)
-      for (j = 0; j < m; j++)
-         if (i - j + 1 < 0)
-            H[i * m + j] = 0;
-         else
-            H[i * m + j] = 1;
-   for (i = 0; i < m; i++) {
-      H[i * m] -= pow (h, (double) (i + 1));
-      H[(m - 1) * m + i] -= pow (h, (double) (m - i));
-   }
-   H[(m - 1) * m] += (2 * h - 1 > 0 ? pow (2 * h - 1, (double) m) : 0);
-   for (i = 0; i < m; i++)
-      for (j = 0; j < m; j++)
-         if (i - j + 1 > 0)
-            for (g = 1; g <= i - j + 1; g++)
-               H[i * m + j] /= g;
-   eH = 0;
-   mPower (H, eH, Q, &eQ, m, n);
-   s = Q[(k - 1) * m + k - 1];
-
-   for (i = 1; i <= n; i++) {
-      s = s * (double) i / n;
-      if (s < INORM) {
-         s *= NORM;
-         eQ -= LOGNORM;
-      }
-   }
-   s *= pow (10., (double) eQ);
-   free (H);
-   free (Q);
-   return s;
-}
-
-
-static void mMultiply (double *A, double *B, double *C, int m)
-{
-   int i, j, k;
-   double s;
-   for (i = 0; i < m; i++)
-      for (j = 0; j < m; j++) {
-         s = 0.;
-         for (k = 0; k < m; k++)
-            s += A[i * m + k] * B[k * m + j];
-         C[i * m + j] = s;
-      }
-}
-
-
-static void renormalize (double *V, int m, int *p)
-{
-   int i;
-   for (i = 0; i < m * m; i++)
-      V[i] *= INORM;
-   *p += LOGNORM;
-}
-
-
-static void mPower (double *A, int eA, double *V, int *eV, int m, int n)
-{
-   double *B;
-   int eB, i;
-   if (n == 1) {
-      for (i = 0; i < m * m; i++)
-         V[i] = A[i];
-      *eV = eA;
-      return;
-   }
-   mPower (A, eA, V, eV, m, n / 2);
-   B = (double *) malloc ((m * m) * sizeof (double));
-   mMultiply (V, V, B, m);
-   eB = 2 * (*eV);
-   if (B[(m / 2) * m + (m / 2)] > NORM)
-      renormalize (B, m, &eB);
-
-   if (n % 2 == 0) {
-      for (i = 0; i < m * m; i++)
-         V[i] = B[i];
-      *eV = eB;
-   } else {
-      mMultiply (A, B, V, m);
-      *eV = eA + eB;
-   }
-
-   if (V[(m / 2) * m + (m / 2)] > NORM)
-      renormalize (V, m, eV);
-   free (B);
-}