# HG changeset patch
# User adlertz
# Date 1372200013 -7200
# Node ID 9347cae673f0c82a1fcb6e4b8373d34ca7d2ca7c
# Parent  3aa636f2a7435040dcb740e69f66c2c28021499e
8017510: Add a regression test for 8005956
Summary: Regression test for 8005956
Reviewed-by: kvn, twisti

diff -r 3aa636f2a743 -r 9347cae673f0 test/compiler/8005956/PolynomialRoot.java
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/compiler/8005956/PolynomialRoot.java	Wed Jun 26 00:40:13 2013 +0200
@@ -0,0 +1,776 @@
+//package com.polytechnik.utils;
+/*
+ * (C) Vladislav Malyshkin 2010
+ * This file is under GPL version 3.
+ *
+ */
+
+/** Polynomial root.
+ *  @version $Id: PolynomialRoot.java,v 1.105 2012/08/18 00:00:05 mal Exp $
+ *  @author Vladislav Malyshkin mal@gromco.com
+ */
+
+/**
+* @test
+* @bug 8005956
+* @summary C2: assert(!def_outside->member(r)) failed: Use of external LRG overlaps the same LRG defined in this block
+*
+* @run main PolynomialRoot
+*/
+
+public class PolynomialRoot  {
+
+
+public static int findPolynomialRoots(final int n,
+              final double [] p,
+              final double [] re_root,
+              final double [] im_root)
+{
+    if(n==4)
+    {
+  return root4(p,re_root,im_root);
+    }
+    else if(n==3)
+    {
+  return root3(p,re_root,im_root);
+    }
+    else if(n==2)
+    {
+  return root2(p,re_root,im_root);
+    }
+    else if(n==1)
+    {
+  return root1(p,re_root,im_root);
+    }
+    else
+    {
+  throw new RuntimeException("n="+n+" is not supported yet");
+    }
+}
+
+
+
+static final double SQRT3=Math.sqrt(3.0),SQRT2=Math.sqrt(2.0);
+
+
+private static final boolean PRINT_DEBUG=false;
+
+public static int root4(final double [] p,final double [] re_root,final double [] im_root)
+{
+  if(PRINT_DEBUG) System.err.println("=====================root4:p="+java.util.Arrays.toString(p));
+  final double vs=p[4];
+  if(PRINT_DEBUG) System.err.println("p[4]="+p[4]);
+  if(!(Math.abs(vs)>EPS))
+  {
+      re_root[0]=re_root[1]=re_root[2]=re_root[3]=
+    im_root[0]=im_root[1]=im_root[2]=im_root[3]=Double.NaN;
+      return -1;
+  }
+
+/* zsolve_quartic.c - finds the complex roots of
+ *  x^4 + a x^3 + b x^2 + c x + d = 0
+ */
+  final double a=p[3]/vs,b=p[2]/vs,c=p[1]/vs,d=p[0]/vs;
+  if(PRINT_DEBUG) System.err.println("input a="+a+" b="+b+" c="+c+" d="+d);
+
+
+  final double r4 = 1.0 / 4.0;
+  final double q2 = 1.0 / 2.0, q4 = 1.0 / 4.0, q8 = 1.0 / 8.0;
+  final double q1 = 3.0 / 8.0, q3 = 3.0 / 16.0;
+  final int mt;
+
+  /* Deal easily with the cases where the quartic is degenerate. The
+   * ordering of solutions is done explicitly. */
+  if (0 == b && 0 == c)
+  {
+      if (0 == d)
+      {
+    re_root[0]=-a;
+    im_root[0]=im_root[1]=im_root[2]=im_root[3]=0;
+    re_root[1]=re_root[2]=re_root[3]=0;
+    return 4;
+      }
+      else if (0 == a)
+      {
+    if (d > 0)
+    {
+        final double sq4 = Math.sqrt(Math.sqrt(d));
+        re_root[0]=sq4*SQRT2/2;
+        im_root[0]=re_root[0];
+        re_root[1]=-re_root[0];
+        im_root[1]=re_root[0];
+        re_root[2]=-re_root[0];
+        im_root[2]=-re_root[0];
+        re_root[3]=re_root[0];
+        im_root[3]=-re_root[0];
+        if(PRINT_DEBUG) System.err.println("Path a=0 d>0");
+    }
+    else
+    {
+        final double sq4 = Math.sqrt(Math.sqrt(-d));
+        re_root[0]=sq4;
+        im_root[0]=0;
+        re_root[1]=0;
+        im_root[1]=sq4;
+        re_root[2]=0;
+        im_root[2]=-sq4;
+        re_root[3]=-sq4;
+        im_root[3]=0;
+        if(PRINT_DEBUG) System.err.println("Path a=0 d<0");
+    }
+    return 4;
+      }
+  }
+
+  if (0.0 == c && 0.0 == d)
+  {
+      root2(new double []{p[2],p[3],p[4]},re_root,im_root);
+      re_root[2]=im_root[2]=re_root[3]=im_root[3]=0;
+      return 4;
+  }
+
+  if(PRINT_DEBUG) System.err.println("G Path c="+c+" d="+d);
+  final double [] u=new double[3];
+
+  if(PRINT_DEBUG) System.err.println("Generic Path");
+  /* For non-degenerate solutions, proceed by constructing and
+   * solving the resolvent cubic */
+  final double aa = a * a;
+  final double pp = b - q1 * aa;
+  final double qq = c - q2 * a * (b - q4 * aa);
+  final double rr = d - q4 * a * (c - q4 * a * (b - q3 * aa));
+  final double rc = q2 * pp , rc3 = rc / 3;
+  final double sc = q4 * (q4 * pp * pp - rr);
+  final double tc = -(q8 * qq * q8 * qq);
+  if(PRINT_DEBUG) System.err.println("aa="+aa+" pp="+pp+" qq="+qq+" rr="+rr+" rc="+rc+" sc="+sc+" tc="+tc);
+  final boolean flag_realroots;
+
+  /* This code solves the resolvent cubic in a convenient fashion
+   * for this implementation of the quartic. If there are three real
+   * roots, then they are placed directly into u[].  If two are
+   * complex, then the real root is put into u[0] and the real
+   * and imaginary part of the complex roots are placed into
+   * u[1] and u[2], respectively. */
+  {
+      final double qcub = (rc * rc - 3 * sc);
+      final double rcub = (rc*(2 * rc * rc - 9 * sc) + 27 * tc);
+
+      final double Q = qcub / 9;
+      final double R = rcub / 54;
+
+      final double Q3 = Q * Q * Q;
+      final double R2 = R * R;
+
+      final double CR2 = 729 * rcub * rcub;
+      final double CQ3 = 2916 * qcub * qcub * qcub;
+
+      if(PRINT_DEBUG) System.err.println("CR2="+CR2+" CQ3="+CQ3+" R="+R+" Q="+Q);
+
+      if (0 == R && 0 == Q)
+      {
+    flag_realroots=true;
+    u[0] = -rc3;
+    u[1] = -rc3;
+    u[2] = -rc3;
+      }
+      else if (CR2 == CQ3)
+      {
+    flag_realroots=true;
+    final double sqrtQ = Math.sqrt (Q);
+    if (R > 0)
+    {
+        u[0] = -2 * sqrtQ - rc3;
+        u[1] = sqrtQ - rc3;
+        u[2] = sqrtQ - rc3;
+    }
+    else
+    {
+        u[0] = -sqrtQ - rc3;
+        u[1] = -sqrtQ - rc3;
+        u[2] = 2 * sqrtQ - rc3;
+    }
+      }
+      else if (R2 < Q3)
+      {
+    flag_realroots=true;
+    final double ratio = (R >= 0?1:-1) * Math.sqrt (R2 / Q3);
+    final double theta = Math.acos (ratio);
+    final double norm = -2 * Math.sqrt (Q);
+
+    u[0] = norm * Math.cos (theta / 3) - rc3;
+    u[1] = norm * Math.cos ((theta + 2.0 * Math.PI) / 3) - rc3;
+    u[2] = norm * Math.cos ((theta - 2.0 * Math.PI) / 3) - rc3;
+      }
+      else
+      {
+    flag_realroots=false;
+    final double A = -(R >= 0?1:-1)*Math.pow(Math.abs(R)+Math.sqrt(R2-Q3),1.0/3.0);
+    final double B = Q / A;
+
+    u[0] = A + B - rc3;
+    u[1] = -0.5 * (A + B) - rc3;
+    u[2] = -(SQRT3*0.5) * Math.abs (A - B);
+      }
+      if(PRINT_DEBUG) System.err.println("u[0]="+u[0]+" u[1]="+u[1]+" u[2]="+u[2]+" qq="+qq+" disc="+((CR2 - CQ3) / 2125764.0));
+  }
+  /* End of solution to resolvent cubic */
+
+  /* Combine the square roots of the roots of the cubic
+   * resolvent appropriately. Also, calculate 'mt' which
+   * designates the nature of the roots:
+   * mt=1 : 4 real roots
+   * mt=2 : 0 real roots
+   * mt=3 : 2 real roots
+   */
+
+
+  final double w1_re,w1_im,w2_re,w2_im,w3_re,w3_im,mod_w1w2,mod_w1w2_squared;
+  if (flag_realroots)
+  {
+      mod_w1w2=-1;
+      mt = 2;
+      int jmin=0;
+      double vmin=Math.abs(u[jmin]);
+      for(int j=1;j<3;j++)
+      {
+    final double vx=Math.abs(u[j]);
+    if(vx<vmin)
+    {
+        vmin=vx;
+        jmin=j;
+    }
+      }
+      final double u1=u[(jmin+1)%3],u2=u[(jmin+2)%3];
+      mod_w1w2_squared=Math.abs(u1*u2);
+      if(u1>=0)
+      {
+    w1_re=Math.sqrt(u1);
+    w1_im=0;
+      }
+      else
+      {
+    w1_re=0;
+    w1_im=Math.sqrt(-u1);
+      }
+      if(u2>=0)
+      {
+    w2_re=Math.sqrt(u2);
+    w2_im=0;
+      }
+      else
+      {
+    w2_re=0;
+    w2_im=Math.sqrt(-u2);
+      }
+      if(PRINT_DEBUG) System.err.println("u1="+u1+" u2="+u2+" jmin="+jmin);
+  }
+  else
+  {
+      mt = 3;
+      final double w_mod2_sq=u[1]*u[1]+u[2]*u[2],w_mod2=Math.sqrt(w_mod2_sq),w_mod=Math.sqrt(w_mod2);
+      if(w_mod2_sq<=0)
+      {
+    w1_re=w1_im=0;
+      }
+      else
+      {
+    // calculate square root of a complex number (u[1],u[2])
+    // the result is in the (w1_re,w1_im)
+    final double absu1=Math.abs(u[1]),absu2=Math.abs(u[2]),w;
+    if(absu1>=absu2)
+    {
+        final double t=absu2/absu1;
+        w=Math.sqrt(absu1*0.5 * (1.0 + Math.sqrt(1.0 + t * t)));
+        if(PRINT_DEBUG) System.err.println(" Path1 ");
+    }
+    else
+    {
+        final double t=absu1/absu2;
+        w=Math.sqrt(absu2*0.5 * (t + Math.sqrt(1.0 + t * t)));
+        if(PRINT_DEBUG) System.err.println(" Path1a ");
+    }
+    if(u[1]>=0)
+    {
+        w1_re=w;
+        w1_im=u[2]/(2*w);
+        if(PRINT_DEBUG) System.err.println(" Path2 ");
+    }
+    else
+    {
+        final double vi = (u[2] >= 0) ? w : -w;
+        w1_re=u[2]/(2*vi);
+        w1_im=vi;
+        if(PRINT_DEBUG) System.err.println(" Path2a ");
+    }
+      }
+      final double absu0=Math.abs(u[0]);
+      if(w_mod2>=absu0)
+      {
+    mod_w1w2=w_mod2;
+    mod_w1w2_squared=w_mod2_sq;
+    w2_re=w1_re;
+    w2_im=-w1_im;
+      }
+      else
+      {
+    mod_w1w2=-1;
+    mod_w1w2_squared=w_mod2*absu0;
+    if(u[0]>=0)
+    {
+        w2_re=Math.sqrt(absu0);
+        w2_im=0;
+    }
+    else
+    {
+        w2_re=0;
+        w2_im=Math.sqrt(absu0);
+    }
+      }
+      if(PRINT_DEBUG) System.err.println("u[0]="+u[0]+"u[1]="+u[1]+" u[2]="+u[2]+" absu0="+absu0+" w_mod="+w_mod+" w_mod2="+w_mod2);
+  }
+
+  /* Solve the quadratic in order to obtain the roots
+   * to the quartic */
+  if(mod_w1w2>0)
+  {
+      // a shorcut to reduce rounding error
+      w3_re=qq/(-8)/mod_w1w2;
+      w3_im=0;
+  }
+  else if(mod_w1w2_squared>0)
+  {
+      // regular path
+      final double mqq8n=qq/(-8)/mod_w1w2_squared;
+      w3_re=mqq8n*(w1_re*w2_re-w1_im*w2_im);
+      w3_im=-mqq8n*(w1_re*w2_im+w2_re*w1_im);
+  }
+  else
+  {
+      // typically occur when qq==0
+      w3_re=w3_im=0;
+  }
+
+  final double h = r4 * a;
+  if(PRINT_DEBUG) System.err.println("w1_re="+w1_re+" w1_im="+w1_im+" w2_re="+w2_re+" w2_im="+w2_im+" w3_re="+w3_re+" w3_im="+w3_im+" h="+h);
+
+  re_root[0]=w1_re+w2_re+w3_re-h;
+  im_root[0]=w1_im+w2_im+w3_im;
+  re_root[1]=-(w1_re+w2_re)+w3_re-h;
+  im_root[1]=-(w1_im+w2_im)+w3_im;
+  re_root[2]=w2_re-w1_re-w3_re-h;
+  im_root[2]=w2_im-w1_im-w3_im;
+  re_root[3]=w1_re-w2_re-w3_re-h;
+  im_root[3]=w1_im-w2_im-w3_im;
+
+  return 4;
+}
+
+
+
+    static void setRandomP(final double [] p,final int n,java.util.Random r)
+    {
+  if(r.nextDouble()<0.1)
+  {
+      // integer coefficiens
+      for(int j=0;j<p.length;j++)
+      {
+    if(j<=n)
+    {
+        p[j]=(r.nextInt(2)<=0?-1:1)*r.nextInt(10);
+    }
+    else
+    {
+        p[j]=0;
+    }
+      }
+  }
+  else
+  {
+      // real coefficiens
+      for(int j=0;j<p.length;j++)
+      {
+    if(j<=n)
+    {
+        p[j]=-1+2*r.nextDouble();
+    }
+    else
+    {
+        p[j]=0;
+    }
+      }
+  }
+  if(Math.abs(p[n])<1e-2)
+  {
+      p[n]=(r.nextInt(2)<=0?-1:1)*(0.1+r.nextDouble());
+  }
+    }
+
+
+    static void checkValues(final double [] p,
+          final int n,
+          final double rex,
+          final double imx,
+          final double eps,
+          final String txt)
+    {
+  double res=0,ims=0,sabs=0;
+  final double xabs=Math.abs(rex)+Math.abs(imx);
+  for(int k=n;k>=0;k--)
+  {
+      final double res1=(res*rex-ims*imx)+p[k];
+      final double ims1=(ims*rex+res*imx);
+      res=res1;
+      ims=ims1;
+      sabs+=xabs*sabs+p[k];
+  }
+  sabs=Math.abs(sabs);
+  if(false && sabs>1/eps?
+     (!(Math.abs(res/sabs)<=eps)||!(Math.abs(ims/sabs)<=eps))
+     :
+     (!(Math.abs(res)<=eps)||!(Math.abs(ims)<=eps)))
+  {
+      throw new RuntimeException(
+    getPolinomTXT(p)+"\n"+
+    "\t x.r="+rex+" x.i="+imx+"\n"+
+    "res/sabs="+(res/sabs)+" ims/sabs="+(ims/sabs)+
+    " sabs="+sabs+
+    "\nres="+res+" ims="+ims+" n="+n+" eps="+eps+" "+
+    " sabs>1/eps="+(sabs>1/eps)+
+    " f1="+(!(Math.abs(res/sabs)<=eps)||!(Math.abs(ims/sabs)<=eps))+
+    " f2="+(!(Math.abs(res)<=eps)||!(Math.abs(ims)<=eps))+
+    " "+txt);
+  }
+    }
+
+    static String getPolinomTXT(final double [] p)
+    {
+  final StringBuilder buf=new StringBuilder();
+  buf.append("order="+(p.length-1)+"\t");
+  for(int k=0;k<p.length;k++)
+  {
+      buf.append("p["+k+"]="+p[k]+";");
+  }
+  return buf.toString();
+    }
+
+    static String getRootsTXT(int nr,final double [] re,final double [] im)
+    {
+  final StringBuilder buf=new StringBuilder();
+  for(int k=0;k<nr;k++)
+  {
+      buf.append("x."+k+"("+re[k]+","+im[k]+")\n");
+  }
+  return buf.toString();
+    }
+
+    static void testRoots(final int n,
+        final int n_tests,
+        final java.util.Random rn,
+        final double eps)
+    {
+  final double [] p=new double [n+1];
+  final double [] rex=new double [n],imx=new double [n];
+  for(int i=0;i<n_tests;i++)
+  {
+    for(int dg=n;dg-->-1;)
+    {
+      for(int dr=3;dr-->0;)
+      {
+        setRandomP(p,n,rn);
+        for(int j=0;j<=dg;j++)
+        {
+      p[j]=0;
+        }
+        if(dr==0)
+        {
+      p[0]=-1+2.0*rn.nextDouble();
+        }
+        else if(dr==1)
+        {
+      p[0]=p[1]=0;
+        }
+
+        findPolynomialRoots(n,p,rex,imx);
+
+        for(int j=0;j<n;j++)
+        {
+      //System.err.println("j="+j);
+      checkValues(p,n,rex[j],imx[j],eps," t="+i);
+        }
+      }
+    }
+  }
+  System.err.println("testRoots(): n_tests="+n_tests+" OK, dim="+n);
+    }
+
+
+
+
+    static final double EPS=0;
+
+    public static int root1(final double [] p,final double [] re_root,final double [] im_root)
+    {
+  if(!(Math.abs(p[1])>EPS))
+  {
+      re_root[0]=im_root[0]=Double.NaN;
+      return -1;
+  }
+  re_root[0]=-p[0]/p[1];
+  im_root[0]=0;
+  return 1;
+    }
+
+    public static int root2(final double [] p,final double [] re_root,final double [] im_root)
+    {
+  if(!(Math.abs(p[2])>EPS))
+  {
+      re_root[0]=re_root[1]=im_root[0]=im_root[1]=Double.NaN;
+      return -1;
+  }
+  final double b2=0.5*(p[1]/p[2]),c=p[0]/p[2],d=b2*b2-c;
+  if(d>=0)
+  {
+      final double sq=Math.sqrt(d);
+      if(b2<0)
+      {
+    re_root[1]=-b2+sq;
+    re_root[0]=c/re_root[1];
+      }
+      else if(b2>0)
+      {
+    re_root[0]=-b2-sq;
+    re_root[1]=c/re_root[0];
+      }
+      else
+      {
+    re_root[0]=-b2-sq;
+    re_root[1]=-b2+sq;
+      }
+      im_root[0]=im_root[1]=0;
+  }
+  else
+  {
+      final double sq=Math.sqrt(-d);
+      re_root[0]=re_root[1]=-b2;
+      im_root[0]=sq;
+      im_root[1]=-sq;
+  }
+  return 2;
+    }
+
+    public static int root3(final double [] p,final double [] re_root,final double [] im_root)
+    {
+  final double vs=p[3];
+  if(!(Math.abs(vs)>EPS))
+  {
+      re_root[0]=re_root[1]=re_root[2]=
+    im_root[0]=im_root[1]=im_root[2]=Double.NaN;
+      return -1;
+  }
+  final double a=p[2]/vs,b=p[1]/vs,c=p[0]/vs;
+  /* zsolve_cubic.c - finds the complex roots of x^3 + a x^2 + b x + c = 0
+   */
+  final double q = (a * a - 3 * b);
+  final double r = (a*(2 * a * a - 9 * b) + 27 * c);
+
+  final double Q = q / 9;
+  final double R = r / 54;
+
+  final double Q3 = Q * Q * Q;
+  final double R2 = R * R;
+
+  final double CR2 = 729 * r * r;
+  final double CQ3 = 2916 * q * q * q;
+  final double a3=a/3;
+
+  if (R == 0 && Q == 0)
+  {
+      re_root[0]=re_root[1]=re_root[2]=-a3;
+      im_root[0]=im_root[1]=im_root[2]=0;
+      return 3;
+  }
+  else if (CR2 == CQ3)
+  {
+      /* this test is actually R2 == Q3, written in a form suitable
+         for exact computation with integers */
+
+      /* Due to finite precision some double roots may be missed, and
+         will be considered to be a pair of complex roots z = x +/-
+         epsilon i close to the real axis. */
+
+      final double sqrtQ = Math.sqrt (Q);
+
+      if (R > 0)
+      {
+    re_root[0] = -2 * sqrtQ - a3;
+    re_root[1]=re_root[2]=sqrtQ - a3;
+    im_root[0]=im_root[1]=im_root[2]=0;
+      }
+      else
+      {
+    re_root[0]=re_root[1] = -sqrtQ - a3;
+    re_root[2]=2 * sqrtQ - a3;
+    im_root[0]=im_root[1]=im_root[2]=0;
+      }
+      return 3;
+  }
+  else if (R2 < Q3)
+  {
+      final double sgnR = (R >= 0 ? 1 : -1);
+      final double ratio = sgnR * Math.sqrt (R2 / Q3);
+      final double theta = Math.acos (ratio);
+      final double norm = -2 * Math.sqrt (Q);
+      final double r0 = norm * Math.cos (theta/3) - a3;
+      final double r1 = norm * Math.cos ((theta + 2.0 * Math.PI) / 3) - a3;
+      final double r2 = norm * Math.cos ((theta - 2.0 * Math.PI) / 3) - a3;
+
+      re_root[0]=r0;
+      re_root[1]=r1;
+      re_root[2]=r2;
+      im_root[0]=im_root[1]=im_root[2]=0;
+      return 3;
+  }
+  else
+  {
+      final double sgnR = (R >= 0 ? 1 : -1);
+      final double A = -sgnR * Math.pow (Math.abs (R) + Math.sqrt (R2 - Q3), 1.0 / 3.0);
+      final double B = Q / A;
+
+      re_root[0]=A + B - a3;
+      im_root[0]=0;
+      re_root[1]=-0.5 * (A + B) - a3;
+      im_root[1]=-(SQRT3*0.5) * Math.abs(A - B);
+      re_root[2]=re_root[1];
+      im_root[2]=-im_root[1];
+      return 3;
+  }
+
+    }
+
+
+    static void root3a(final double [] p,final double [] re_root,final double [] im_root)
+    {
+  if(Math.abs(p[3])>EPS)
+  {
+      final double v=p[3],
+    a=p[2]/v,b=p[1]/v,c=p[0]/v,
+    a3=a/3,a3a=a3*a,
+    pd3=(b-a3a)/3,
+    qd2=a3*(a3a/3-0.5*b)+0.5*c,
+    Q=pd3*pd3*pd3+qd2*qd2;
+      if(Q<0)
+      {
+    // three real roots
+    final double SQ=Math.sqrt(-Q);
+    final double th=Math.atan2(SQ,-qd2);
+    im_root[0]=im_root[1]=im_root[2]=0;
+    final double f=2*Math.sqrt(-pd3);
+    re_root[0]=f*Math.cos(th/3)-a3;
+    re_root[1]=f*Math.cos((th+2*Math.PI)/3)-a3;
+    re_root[2]=f*Math.cos((th+4*Math.PI)/3)-a3;
+    //System.err.println("3r");
+      }
+      else
+      {
+    // one real & two complex roots
+    final double SQ=Math.sqrt(Q);
+    final double r1=-qd2+SQ,r2=-qd2-SQ;
+    final double v1=Math.signum(r1)*Math.pow(Math.abs(r1),1.0/3),
+        v2=Math.signum(r2)*Math.pow(Math.abs(r2),1.0/3),
+        sv=v1+v2;
+    // real root
+    re_root[0]=sv-a3;
+    im_root[0]=0;
+    // complex roots
+    re_root[1]=re_root[2]=-0.5*sv-a3;
+    im_root[1]=(v1-v2)*(SQRT3*0.5);
+    im_root[2]=-im_root[1];
+    //System.err.println("1r2c");
+      }
+  }
+  else
+  {
+      re_root[0]=re_root[1]=re_root[2]=im_root[0]=im_root[1]=im_root[2]=Double.NaN;
+  }
+    }
+
+
+    static void printSpecialValues()
+    {
+  for(int st=0;st<6;st++)
+  {
+      //final double [] p=new double []{8,1,3,3.6,1};
+      final double [] re_root=new double [4],im_root=new double [4];
+      final double [] p;
+      final int n;
+      if(st<=3)
+      {
+    if(st<=0)
+    {
+        p=new double []{2,-4,6,-4,1};
+        //p=new double []{-6,6,-6,8,-2};
+    }
+    else if(st==1)
+    {
+        p=new double []{0,-4,8,3,-9};
+    }
+    else if(st==2)
+    {
+        p=new double []{-1,0,2,0,-1};
+    }
+    else
+    {
+        p=new double []{-5,2,8,-2,-3};
+    }
+    root4(p,re_root,im_root);
+    n=4;
+      }
+      else
+      {
+    p=new double []{0,2,0,1};
+    if(st==4)
+    {
+        p[1]=-p[1];
+    }
+    root3(p,re_root,im_root);
+    n=3;
+      }
+      System.err.println("======== n="+n);
+      for(int i=0;i<=n;i++)
+      {
+    if(i<n)
+    {
+        System.err.println(String.valueOf(i)+"\t"+
+               p[i]+"\t"+
+               re_root[i]+"\t"+
+               im_root[i]);
+    }
+    else
+    {
+        System.err.println(String.valueOf(i)+"\t"+p[i]+"\t");
+    }
+      }
+  }
+    }
+
+
+
+    public static void main(final String [] args)
+    {
+  final long t0=System.currentTimeMillis();
+  final double eps=1e-6;
+  //checkRoots();
+  final java.util.Random r=new java.util.Random(-1381923);
+  printSpecialValues();
+
+  final int n_tests=10000000;
+  //testRoots(2,n_tests,r,eps);
+  //testRoots(3,n_tests,r,eps);
+  testRoots(4,n_tests,r,eps);
+  final long t1=System.currentTimeMillis();
+  System.err.println("PolynomialRoot.main: "+n_tests+" tests OK done in "+(t1-t0)+" milliseconds. ver=$Id: PolynomialRoot.java,v 1.105 2012/08/18 00:00:05 mal Exp $");
+    }
+
+
+
+}