/* * Copyright (C) 2011 The Android Open Source Project * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ /* $Id: db_utilities_poly.cpp,v 1.2 2010/09/03 12:00:10 bsouthall Exp $ */ #include "db_utilities_poly.h" #include "db_utilities.h" /***************************************************************** * Lean and mean begins here * *****************************************************************/ void db_SolveCubic(double *roots,int *nr_roots,double a,double b,double c,double d) { double bp,bp2,cp,dp,q,r,srq; double r2_min_q3,theta,bp_through3,theta_through3; double cos_theta_through3,sin_theta_through3,min2_cos_theta_plu,min2_cos_theta_min; double si_r_srq,A; /*For nondegenerate cubics with three roots [24 mult 9 add 2sqrt 1acos 1cos=33flops 4func] For nondegenerate cubics with one root [16 mult 6 add 1sqrt 1qbrt=24flops 3func]*/ if(a==0.0) db_SolveQuadratic(roots,nr_roots,b,c,d); else { bp=b/a; bp2=bp*bp; cp=c/a; dp=d/a; q=(bp2-3.0*cp)/9.0; r=(2.0*bp2*bp-9.0*bp*cp+27.0*dp)/54.0; r2_min_q3=r*r-q*q*q; if(r2_min_q3<0.0) { *nr_roots=3; /*q has to be > 0*/ srq=sqrt(q); theta=acos(db_maxd(-1.0,db_mind(1.0,r/(q*srq)))); bp_through3=bp/3.0; theta_through3=theta/3.0; cos_theta_through3=cos(theta_through3); sin_theta_through3=sqrt(db_maxd(0.0,1.0-cos_theta_through3*cos_theta_through3)); /*cos(theta_through3+2*pi/3)=cos_theta_through3*cos(2*pi/3)-sin_theta_through3*sin(2*pi/3) = -0.5*cos_theta_through3-sqrt(3)/2.0*sin_theta_through3 = -0.5*(cos_theta_through3+sqrt(3)*sin_theta_through3)*/ min2_cos_theta_plu=cos_theta_through3+DB_SQRT3*sin_theta_through3; min2_cos_theta_min=cos_theta_through3-DB_SQRT3*sin_theta_through3; roots[0]= -2.0*srq*cos_theta_through3-bp_through3; roots[1]=srq*min2_cos_theta_plu-bp_through3; roots[2]=srq*min2_cos_theta_min-bp_through3; } else if(r2_min_q3>0.0) { *nr_roots=1; A= -db_sign(r)*db_CubRoot(db_absd(r)+sqrt(r2_min_q3)); bp_through3=bp/3.0; if(A!=0.0) roots[0]=A+q/A-bp_through3; else roots[0]= -bp_through3; } else { *nr_roots=2; bp_through3=bp/3.0; /*q has to be >= 0*/ si_r_srq=db_sign(r)*sqrt(q); /*Single root*/ roots[0]= -2.0*si_r_srq-bp_through3; /*Double root*/ roots[1]=si_r_srq-bp_through3; } } } void db_SolveQuartic(double *roots,int *nr_roots,double a,double b,double c,double d,double e) { /*Normalized coefficients*/ double c0,c1,c2,c3; /*Temporary coefficients*/ double c3through2,c3through4,c3c3through4_min_c2,min4_c0; double lz,ms,ns,mn,m,n,lz_through2; /*Cubic polynomial roots, nr of roots and coefficients*/ double c_roots[3]; int nr_c_roots; double k0,k1; /*nr additional roots from second quadratic*/ int addroots; /*For nondegenerate quartics [16mult 11add 2sqrt 1cubic 2quadratic=74flops 8funcs]*/ if(a==0.0) db_SolveCubic(roots,nr_roots,b,c,d,e); else if(e==0.0) { db_SolveCubic(roots,nr_roots,a,b,c,d); roots[*nr_roots]=0.0; *nr_roots+=1; } else { /*Compute normalized coefficients*/ c3=b/a; c2=c/a; c1=d/a; c0=e/a; /*Compute temporary coefficients*/ c3through2=c3/2.0; c3through4=c3/4.0; c3c3through4_min_c2=c3*c3through4-c2; min4_c0= -4.0*c0; /*Compute coefficients of cubic*/ k0=min4_c0*c3c3through4_min_c2-c1*c1; k1=c1*c3+min4_c0; /*k2= -c2*/ /*k3=1.0*/ /*Solve it for roots*/ db_SolveCubic(c_roots,&nr_c_roots,1.0,-c2,k1,k0); if(nr_c_roots>0) { lz=c_roots[0]; lz_through2=lz/2.0; ms=lz+c3c3through4_min_c2; ns=lz_through2*lz_through2-c0; mn=lz*c3through4-c1/2.0; if((ms>=0.0)&&(ns>=0.0)) { m=sqrt(ms); n=sqrt(ns)*db_sign(mn); db_SolveQuadratic(roots,nr_roots, 1.0,c3through2+m,lz_through2+n); db_SolveQuadratic(&roots[*nr_roots],&addroots, 1.0,c3through2-m,lz_through2-n); *nr_roots+=addroots; } else *nr_roots=0; } else *nr_roots=0; } } void db_SolveQuarticForced(double *roots,int *nr_roots,double a,double b,double c,double d,double e) { /*Normalized coefficients*/ double c0,c1,c2,c3; /*Temporary coefficients*/ double c3through2,c3through4,c3c3through4_min_c2,min4_c0; double lz,ms,ns,mn,m,n,lz_through2; /*Cubic polynomial roots, nr of roots and coefficients*/ double c_roots[3]; int nr_c_roots; double k0,k1; /*nr additional roots from second quadratic*/ int addroots; /*For nondegenerate quartics [16mult 11add 2sqrt 1cubic 2quadratic=74flops 8funcs]*/ if(a==0.0) db_SolveCubic(roots,nr_roots,b,c,d,e); else if(e==0.0) { db_SolveCubic(roots,nr_roots,a,b,c,d); roots[*nr_roots]=0.0; *nr_roots+=1; } else { /*Compute normalized coefficients*/ c3=b/a; c2=c/a; c1=d/a; c0=e/a; /*Compute temporary coefficients*/ c3through2=c3/2.0; c3through4=c3/4.0; c3c3through4_min_c2=c3*c3through4-c2; min4_c0= -4.0*c0; /*Compute coefficients of cubic*/ k0=min4_c0*c3c3through4_min_c2-c1*c1; k1=c1*c3+min4_c0; /*k2= -c2*/ /*k3=1.0*/ /*Solve it for roots*/ db_SolveCubic(c_roots,&nr_c_roots,1.0,-c2,k1,k0); if(nr_c_roots>0) { lz=c_roots[0]; lz_through2=lz/2.0; ms=lz+c3c3through4_min_c2; ns=lz_through2*lz_through2-c0; mn=lz*c3through4-c1/2.0; if(ms<0.0) ms=0.0; if(ns<0.0) ns=0.0; m=sqrt(ms); n=sqrt(ns)*db_sign(mn); db_SolveQuadratic(roots,nr_roots, 1.0,c3through2+m,lz_through2+n); db_SolveQuadratic(&roots[*nr_roots],&addroots, 1.0,c3through2-m,lz_through2-n); *nr_roots+=addroots; } else *nr_roots=0; } }