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https://github.com/dhewm/dhewm3.git
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736ec20d4d
Don't include the lazy precompiled.h everywhere, only what's required for the compilation unit. platform.h needs to be included instead to provide all essential defines and types. All includes use the relative path to the neo or the game specific root. Move all idlib related includes from idlib/Lib.h to precompiled.h. precompiled.h still exists for the MFC stuff in tools/. Add some missing header guards.
244 lines
6.5 KiB
C++
244 lines
6.5 KiB
C++
/*
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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 "sys/platform.h"
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#include "idlib/Str.h"
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#include "idlib/math/Polynomial.h"
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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 id_attribute((unused));
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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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