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/*
* 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;
}
}
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