| /* |
| * (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 /test/lib |
| * @modules java.base/jdk.internal.misc |
| * java.management |
| * |
| * @run main/timeout=300 compiler.c2.PolynomialRoot |
| */ |
| |
| package compiler.c2; |
| |
| 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; |
| } |
| 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) |
| { |
| if (System.getProperty("os.arch").equals("x86") || |
| System.getProperty("os.arch").equals("amd64") || |
| System.getProperty("os.arch").equals("x86_64")){ |
| final long t0=System.currentTimeMillis(); |
| final double eps=1e-6; |
| //checkRoots(); |
| final Random r = Utils.getRandomInstance(); |
| printSpecialValues(); |
| |
| final int n_tests=100000; |
| //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 $"); |
| System.out.println("PASSED"); |
| } else { |
| System.out.println("PASS test for non-x86"); |
| } |
| } |
| |
| |
| |
| } |