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hello world
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Timothee 'TTimo' Besset
242
neo/idlib/math/Polynomial.cpp
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242
neo/idlib/math/Polynomial.cpp
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/*
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===========================================================================
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Doom 3 GPL Source Code
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Copyright (C) 1999-2011 id Software LLC, a ZeniMax Media company.
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This file is part of the Doom 3 GPL Source Code (?Doom 3 Source Code?).
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Doom 3 Source Code is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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Doom 3 Source Code is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with Doom 3 Source Code. If not, see <http://www.gnu.org/licenses/>.
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In addition, the Doom 3 Source Code is also subject to certain additional terms. You should have received a copy of these additional terms immediately following the terms and conditions of the GNU General Public License which accompanied the Doom 3 Source Code. If not, please request a copy in writing from id Software at the address below.
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If you have questions concerning this license or the applicable additional terms, you may contact in writing id Software LLC, c/o ZeniMax Media Inc., Suite 120, Rockville, Maryland 20850 USA.
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===========================================================================
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*/
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#include "../precompiled.h"
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#pragma hdrstop
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const float EPSILON = 1e-6f;
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/*
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=============
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idPolynomial::Laguer
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=============
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*/
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int idPolynomial::Laguer( const idComplex *coef, const int degree, idComplex &x ) const {
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const int MT = 10, MAX_ITERATIONS = MT * 8;
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static const float frac[] = { 0.0f, 0.5f, 0.25f, 0.75f, 0.13f, 0.38f, 0.62f, 0.88f, 1.0f };
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int i, j;
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float abx, abp, abm, err;
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idComplex dx, cx, b, d, f, g, s, gps, gms, g2;
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for ( i = 1; i <= MAX_ITERATIONS; i++ ) {
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b = coef[degree];
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err = b.Abs();
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d.Zero();
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f.Zero();
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abx = x.Abs();
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for ( j = degree - 1; j >= 0; j-- ) {
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f = x * f + d;
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d = x * d + b;
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b = x * b + coef[j];
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err = b.Abs() + abx * err;
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}
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if ( b.Abs() < err * EPSILON ) {
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return i;
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}
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g = d / b;
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g2 = g * g;
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s = ( ( degree - 1 ) * ( degree * ( g2 - 2.0f * f / b ) - g2 ) ).Sqrt();
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gps = g + s;
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gms = g - s;
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abp = gps.Abs();
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abm = gms.Abs();
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if ( abp < abm ) {
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gps = gms;
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}
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if ( Max( abp, abm ) > 0.0f ) {
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dx = degree / gps;
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} else {
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dx = idMath::Exp( idMath::Log( 1.0f + abx ) ) * idComplex( idMath::Cos( i ), idMath::Sin( i ) );
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}
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cx = x - dx;
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if ( x == cx ) {
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return i;
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}
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if ( i % MT == 0 ) {
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x = cx;
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} else {
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x -= frac[i/MT] * dx;
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}
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}
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return i;
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}
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/*
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=============
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idPolynomial::GetRoots
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=============
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*/
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int idPolynomial::GetRoots( idComplex *roots ) const {
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int i, j;
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idComplex x, b, c, *coef;
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coef = (idComplex *) _alloca16( ( degree + 1 ) * sizeof( idComplex ) );
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for ( i = 0; i <= degree; i++ ) {
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coef[i].Set( coefficient[i], 0.0f );
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}
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for ( i = degree - 1; i >= 0; i-- ) {
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x.Zero();
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Laguer( coef, i + 1, x );
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if ( idMath::Fabs( x.i ) < 2.0f * EPSILON * idMath::Fabs( x.r ) ) {
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x.i = 0.0f;
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}
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roots[i] = x;
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b = coef[i+1];
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for ( j = i; j >= 0; j-- ) {
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c = coef[j];
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coef[j] = b;
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b = x * b + c;
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}
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}
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for ( i = 0; i <= degree; i++ ) {
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coef[i].Set( coefficient[i], 0.0f );
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}
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for ( i = 0; i < degree; i++ ) {
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Laguer( coef, degree, roots[i] );
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}
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for ( i = 1; i < degree; i++ ) {
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x = roots[i];
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for ( j = i - 1; j >= 0; j-- ) {
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if ( roots[j].r <= x.r ) {
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break;
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}
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roots[j+1] = roots[j];
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}
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roots[j+1] = x;
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}
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return degree;
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}
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/*
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=============
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idPolynomial::GetRoots
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=============
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*/
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int idPolynomial::GetRoots( float *roots ) const {
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int i, num;
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idComplex *complexRoots;
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switch( degree ) {
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case 0: return 0;
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case 1: return GetRoots1( coefficient[1], coefficient[0], roots );
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case 2: return GetRoots2( coefficient[2], coefficient[1], coefficient[0], roots );
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case 3: return GetRoots3( coefficient[3], coefficient[2], coefficient[1], coefficient[0], roots );
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case 4: return GetRoots4( coefficient[4], coefficient[3], coefficient[2], coefficient[1], coefficient[0], roots );
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}
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// The Abel-Ruffini theorem states that there is no general solution
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// in radicals to polynomial equations of degree five or higher.
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// A polynomial equation can be solved by radicals if and only if
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// its Galois group is a solvable group.
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complexRoots = (idComplex *) _alloca16( degree * sizeof( idComplex ) );
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GetRoots( complexRoots );
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for ( num = i = 0; i < degree; i++ ) {
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if ( complexRoots[i].i == 0.0f ) {
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roots[i] = complexRoots[i].r;
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num++;
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}
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}
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return num;
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}
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/*
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=============
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idPolynomial::ToString
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=============
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*/
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const char *idPolynomial::ToString( int precision ) const {
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return idStr::FloatArrayToString( ToFloatPtr(), GetDimension(), precision );
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}
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/*
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=============
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idPolynomial::Test
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=============
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*/
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void idPolynomial::Test( void ) {
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int i, num;
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float roots[4], value;
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idComplex complexRoots[4], complexValue;
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idPolynomial p;
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p = idPolynomial( -5.0f, 4.0f );
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num = p.GetRoots( roots );
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for ( i = 0; i < num; i++ ) {
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value = p.GetValue( roots[i] );
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assert( idMath::Fabs( value ) < 1e-4f );
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}
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p = idPolynomial( -5.0f, 4.0f, 3.0f );
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num = p.GetRoots( roots );
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for ( i = 0; i < num; i++ ) {
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value = p.GetValue( roots[i] );
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assert( idMath::Fabs( value ) < 1e-4f );
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}
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p = idPolynomial( 1.0f, 4.0f, 3.0f, -2.0f );
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num = p.GetRoots( roots );
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for ( i = 0; i < num; i++ ) {
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value = p.GetValue( roots[i] );
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assert( idMath::Fabs( value ) < 1e-4f );
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}
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p = idPolynomial( 5.0f, 4.0f, 3.0f, -2.0f );
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num = p.GetRoots( roots );
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for ( i = 0; i < num; i++ ) {
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value = p.GetValue( roots[i] );
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assert( idMath::Fabs( value ) < 1e-4f );
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}
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p = idPolynomial( -5.0f, 4.0f, 3.0f, 2.0f, 1.0f );
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num = p.GetRoots( roots );
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for ( i = 0; i < num; i++ ) {
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value = p.GetValue( roots[i] );
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assert( idMath::Fabs( value ) < 1e-4f );
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}
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p = idPolynomial( 1.0f, 4.0f, 3.0f, -2.0f );
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num = p.GetRoots( complexRoots );
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for ( i = 0; i < num; i++ ) {
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complexValue = p.GetValue( complexRoots[i] );
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assert( idMath::Fabs( complexValue.r ) < 1e-4f && idMath::Fabs( complexValue.i ) < 1e-4f );
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}
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p = idPolynomial( 5.0f, 4.0f, 3.0f, -2.0f );
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num = p.GetRoots( complexRoots );
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for ( i = 0; i < num; i++ ) {
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complexValue = p.GetValue( complexRoots[i] );
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assert( idMath::Fabs( complexValue.r ) < 1e-4f && idMath::Fabs( complexValue.i ) < 1e-4f );
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}
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}
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