gt:   final double a=p[2]/vs,b=p[1]/vs,c=p[0]/vs;
context: /*
   * (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
  * @library /testlibrary
  * @modules java.base/sun.misc
  *          java.management
  * @run main/timeout=300 PolynomialRoot
  */
  
  import jdk.test.lib.Utils;
  import java.util.Arrays;
  import java.util.Random;
  
  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=" + 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, 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 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;
    }
  