mirror of
https://github.com/dhewm/dhewm3.git
synced 2024-11-23 12:53:09 +00:00
242 lines
6.4 KiB
C++
242 lines
6.4 KiB
C++
/*
|
|
===========================================================================
|
|
|
|
Doom 3 GPL Source Code
|
|
Copyright (C) 1999-2011 id Software LLC, a ZeniMax Media company.
|
|
|
|
This file is part of the Doom 3 GPL Source Code (?Doom 3 Source Code?).
|
|
|
|
Doom 3 Source Code is free software: you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation, either version 3 of the License, or
|
|
(at your option) any later version.
|
|
|
|
Doom 3 Source Code is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with Doom 3 Source Code. If not, see <http://www.gnu.org/licenses/>.
|
|
|
|
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.
|
|
|
|
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.
|
|
|
|
===========================================================================
|
|
*/
|
|
|
|
#include "../precompiled.h"
|
|
#pragma hdrstop
|
|
|
|
const float EPSILON = 1e-6f;
|
|
|
|
/*
|
|
=============
|
|
idPolynomial::Laguer
|
|
=============
|
|
*/
|
|
int idPolynomial::Laguer( const idComplex *coef, const int degree, idComplex &x ) const {
|
|
const int MT = 10, MAX_ITERATIONS = MT * 8;
|
|
static const float frac[] = { 0.0f, 0.5f, 0.25f, 0.75f, 0.13f, 0.38f, 0.62f, 0.88f, 1.0f };
|
|
int i, j;
|
|
float abx, abp, abm, err;
|
|
idComplex dx, cx, b, d, f, g, s, gps, gms, g2;
|
|
|
|
for ( i = 1; i <= MAX_ITERATIONS; i++ ) {
|
|
b = coef[degree];
|
|
err = b.Abs();
|
|
d.Zero();
|
|
f.Zero();
|
|
abx = x.Abs();
|
|
for ( j = degree - 1; j >= 0; j-- ) {
|
|
f = x * f + d;
|
|
d = x * d + b;
|
|
b = x * b + coef[j];
|
|
err = b.Abs() + abx * err;
|
|
}
|
|
if ( b.Abs() < err * EPSILON ) {
|
|
return i;
|
|
}
|
|
g = d / b;
|
|
g2 = g * g;
|
|
s = ( ( degree - 1 ) * ( degree * ( g2 - 2.0f * f / b ) - g2 ) ).Sqrt();
|
|
gps = g + s;
|
|
gms = g - s;
|
|
abp = gps.Abs();
|
|
abm = gms.Abs();
|
|
if ( abp < abm ) {
|
|
gps = gms;
|
|
}
|
|
if ( Max( abp, abm ) > 0.0f ) {
|
|
dx = degree / gps;
|
|
} else {
|
|
dx = idMath::Exp( idMath::Log( 1.0f + abx ) ) * idComplex( idMath::Cos( i ), idMath::Sin( i ) );
|
|
}
|
|
cx = x - dx;
|
|
if ( x == cx ) {
|
|
return i;
|
|
}
|
|
if ( i % MT == 0 ) {
|
|
x = cx;
|
|
} else {
|
|
x -= frac[i/MT] * dx;
|
|
}
|
|
}
|
|
return i;
|
|
}
|
|
|
|
/*
|
|
=============
|
|
idPolynomial::GetRoots
|
|
=============
|
|
*/
|
|
int idPolynomial::GetRoots( idComplex *roots ) const {
|
|
int i, j;
|
|
idComplex x, b, c, *coef;
|
|
|
|
coef = (idComplex *) _alloca16( ( degree + 1 ) * sizeof( idComplex ) );
|
|
for ( i = 0; i <= degree; i++ ) {
|
|
coef[i].Set( coefficient[i], 0.0f );
|
|
}
|
|
|
|
for ( i = degree - 1; i >= 0; i-- ) {
|
|
x.Zero();
|
|
Laguer( coef, i + 1, x );
|
|
if ( idMath::Fabs( x.i ) < 2.0f * EPSILON * idMath::Fabs( x.r ) ) {
|
|
x.i = 0.0f;
|
|
}
|
|
roots[i] = x;
|
|
b = coef[i+1];
|
|
for ( j = i; j >= 0; j-- ) {
|
|
c = coef[j];
|
|
coef[j] = b;
|
|
b = x * b + c;
|
|
}
|
|
}
|
|
|
|
for ( i = 0; i <= degree; i++ ) {
|
|
coef[i].Set( coefficient[i], 0.0f );
|
|
}
|
|
for ( i = 0; i < degree; i++ ) {
|
|
Laguer( coef, degree, roots[i] );
|
|
}
|
|
|
|
for ( i = 1; i < degree; i++ ) {
|
|
x = roots[i];
|
|
for ( j = i - 1; j >= 0; j-- ) {
|
|
if ( roots[j].r <= x.r ) {
|
|
break;
|
|
}
|
|
roots[j+1] = roots[j];
|
|
}
|
|
roots[j+1] = x;
|
|
}
|
|
|
|
return degree;
|
|
}
|
|
|
|
/*
|
|
=============
|
|
idPolynomial::GetRoots
|
|
=============
|
|
*/
|
|
int idPolynomial::GetRoots( float *roots ) const {
|
|
int i, num;
|
|
idComplex *complexRoots;
|
|
|
|
switch( degree ) {
|
|
case 0: return 0;
|
|
case 1: return GetRoots1( coefficient[1], coefficient[0], roots );
|
|
case 2: return GetRoots2( coefficient[2], coefficient[1], coefficient[0], roots );
|
|
case 3: return GetRoots3( coefficient[3], coefficient[2], coefficient[1], coefficient[0], roots );
|
|
case 4: return GetRoots4( coefficient[4], coefficient[3], coefficient[2], coefficient[1], coefficient[0], roots );
|
|
}
|
|
|
|
// The Abel-Ruffini theorem states that there is no general solution
|
|
// in radicals to polynomial equations of degree five or higher.
|
|
// A polynomial equation can be solved by radicals if and only if
|
|
// its Galois group is a solvable group.
|
|
|
|
complexRoots = (idComplex *) _alloca16( degree * sizeof( idComplex ) );
|
|
|
|
GetRoots( complexRoots );
|
|
|
|
for ( num = i = 0; i < degree; i++ ) {
|
|
if ( complexRoots[i].i == 0.0f ) {
|
|
roots[i] = complexRoots[i].r;
|
|
num++;
|
|
}
|
|
}
|
|
return num;
|
|
}
|
|
|
|
/*
|
|
=============
|
|
idPolynomial::ToString
|
|
=============
|
|
*/
|
|
const char *idPolynomial::ToString( int precision ) const {
|
|
return idStr::FloatArrayToString( ToFloatPtr(), GetDimension(), precision );
|
|
}
|
|
|
|
/*
|
|
=============
|
|
idPolynomial::Test
|
|
=============
|
|
*/
|
|
void idPolynomial::Test( void ) {
|
|
int i, num;
|
|
float roots[4], value;
|
|
idComplex complexRoots[4], complexValue;
|
|
idPolynomial p;
|
|
|
|
p = idPolynomial( -5.0f, 4.0f );
|
|
num = p.GetRoots( roots );
|
|
for ( i = 0; i < num; i++ ) {
|
|
value = p.GetValue( roots[i] );
|
|
assert( idMath::Fabs( value ) < 1e-4f );
|
|
}
|
|
|
|
p = idPolynomial( -5.0f, 4.0f, 3.0f );
|
|
num = p.GetRoots( roots );
|
|
for ( i = 0; i < num; i++ ) {
|
|
value = p.GetValue( roots[i] );
|
|
assert( idMath::Fabs( value ) < 1e-4f );
|
|
}
|
|
|
|
p = idPolynomial( 1.0f, 4.0f, 3.0f, -2.0f );
|
|
num = p.GetRoots( roots );
|
|
for ( i = 0; i < num; i++ ) {
|
|
value = p.GetValue( roots[i] );
|
|
assert( idMath::Fabs( value ) < 1e-4f );
|
|
}
|
|
|
|
p = idPolynomial( 5.0f, 4.0f, 3.0f, -2.0f );
|
|
num = p.GetRoots( roots );
|
|
for ( i = 0; i < num; i++ ) {
|
|
value = p.GetValue( roots[i] );
|
|
assert( idMath::Fabs( value ) < 1e-4f );
|
|
}
|
|
|
|
p = idPolynomial( -5.0f, 4.0f, 3.0f, 2.0f, 1.0f );
|
|
num = p.GetRoots( roots );
|
|
for ( i = 0; i < num; i++ ) {
|
|
value = p.GetValue( roots[i] );
|
|
assert( idMath::Fabs( value ) < 1e-4f );
|
|
}
|
|
|
|
p = idPolynomial( 1.0f, 4.0f, 3.0f, -2.0f );
|
|
num = p.GetRoots( complexRoots );
|
|
for ( i = 0; i < num; i++ ) {
|
|
complexValue = p.GetValue( complexRoots[i] );
|
|
assert( idMath::Fabs( complexValue.r ) < 1e-4f && idMath::Fabs( complexValue.i ) < 1e-4f );
|
|
}
|
|
|
|
p = idPolynomial( 5.0f, 4.0f, 3.0f, -2.0f );
|
|
num = p.GetRoots( complexRoots );
|
|
for ( i = 0; i < num; i++ ) {
|
|
complexValue = p.GetValue( complexRoots[i] );
|
|
assert( idMath::Fabs( complexValue.r ) < 1e-4f && idMath::Fabs( complexValue.i ) < 1e-4f );
|
|
}
|
|
}
|