diff options
Diffstat (limited to 'jni/feature_stab/db_vlvm/db_utilities_poly.cpp')
| -rw-r--r-- | jni/feature_stab/db_vlvm/db_utilities_poly.cpp | 235 |
1 files changed, 235 insertions, 0 deletions
diff --git a/jni/feature_stab/db_vlvm/db_utilities_poly.cpp b/jni/feature_stab/db_vlvm/db_utilities_poly.cpp new file mode 100644 index 000000000..013ac726e --- /dev/null +++ b/jni/feature_stab/db_vlvm/db_utilities_poly.cpp @@ -0,0 +1,235 @@ +/* + * 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; + } +} |