Mercurial > hg > graal-compiler
view test/compiler/8005956/PolynomialRoot.java @ 21777:76c162c69c2f
Drop stamp information of OSR proxies in graph builder.
author | Roland Schatz <roland.schatz@oracle.com> |
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date | Mon, 08 Jun 2015 12:09:37 +0200 |
parents | e554162ab094 |
children |
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//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/timeout=300 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) { 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 java.util.Random r=new java.util.Random(-1381923); 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"); } } }