doom3-bfg/neo/idlib/math/Polynomial.h

770 lines
16 KiB
C++

/*
===========================================================================
Doom 3 BFG Edition GPL Source Code
Copyright (C) 1993-2012 id Software LLC, a ZeniMax Media company.
This file is part of the Doom 3 BFG Edition GPL Source Code ("Doom 3 BFG Edition Source Code").
Doom 3 BFG Edition 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 BFG Edition 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 BFG Edition Source Code. If not, see <http://www.gnu.org/licenses/>.
In addition, the Doom 3 BFG Edition 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 BFG Edition 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.
===========================================================================
*/
#ifndef __MATH_POLYNOMIAL_H__
#define __MATH_POLYNOMIAL_H__
/*
===============================================================================
Polynomial of arbitrary degree with real coefficients.
===============================================================================
*/
class idPolynomial
{
public:
idPolynomial();
explicit idPolynomial( int d );
explicit idPolynomial( float a, float b );
explicit idPolynomial( float a, float b, float c );
explicit idPolynomial( float a, float b, float c, float d );
explicit idPolynomial( float a, float b, float c, float d, float e );
float operator[]( int index ) const;
float& operator[]( int index );
idPolynomial operator-() const;
idPolynomial& operator=( const idPolynomial& p );
idPolynomial operator+( const idPolynomial& p ) const;
idPolynomial operator-( const idPolynomial& p ) const;
idPolynomial operator*( const float s ) const;
idPolynomial operator/( const float s ) const;
idPolynomial& operator+=( const idPolynomial& p );
idPolynomial& operator-=( const idPolynomial& p );
idPolynomial& operator*=( const float s );
idPolynomial& operator/=( const float s );
bool Compare( const idPolynomial& p ) const; // exact compare, no epsilon
bool Compare( const idPolynomial& p, const float epsilon ) const;// compare with epsilon
bool operator==( const idPolynomial& p ) const; // exact compare, no epsilon
bool operator!=( const idPolynomial& p ) const; // exact compare, no epsilon
void Zero();
void Zero( int d );
int GetDimension() const; // get the degree of the polynomial
int GetDegree() const; // get the degree of the polynomial
float GetValue( const float x ) const; // evaluate the polynomial with the given real value
idComplex GetValue( const idComplex& x ) const; // evaluate the polynomial with the given complex value
idPolynomial GetDerivative() const; // get the first derivative of the polynomial
idPolynomial GetAntiDerivative() const; // get the anti derivative of the polynomial
int GetRoots( idComplex* roots ) const; // get all roots
int GetRoots( float* roots ) const; // get the real roots
static int GetRoots1( float a, float b, float* roots );
static int GetRoots2( float a, float b, float c, float* roots );
static int GetRoots3( float a, float b, float c, float d, float* roots );
static int GetRoots4( float a, float b, float c, float d, float e, float* roots );
const float* ToFloatPtr() const;
float* ToFloatPtr();
const char* ToString( int precision = 2 ) const;
static void Test();
private:
int degree;
int allocated;
float* coefficient;
void Resize( int d, bool keep );
int Laguer( const idComplex* coef, const int degree, idComplex& r ) const;
};
ID_INLINE idPolynomial::idPolynomial()
{
degree = -1;
allocated = 0;
coefficient = NULL;
}
ID_INLINE idPolynomial::idPolynomial( int d )
{
degree = -1;
allocated = 0;
coefficient = NULL;
Resize( d, false );
}
ID_INLINE idPolynomial::idPolynomial( float a, float b )
{
degree = -1;
allocated = 0;
coefficient = NULL;
Resize( 1, false );
coefficient[0] = b;
coefficient[1] = a;
}
ID_INLINE idPolynomial::idPolynomial( float a, float b, float c )
{
degree = -1;
allocated = 0;
coefficient = NULL;
Resize( 2, false );
coefficient[0] = c;
coefficient[1] = b;
coefficient[2] = a;
}
ID_INLINE idPolynomial::idPolynomial( float a, float b, float c, float d )
{
degree = -1;
allocated = 0;
coefficient = NULL;
Resize( 3, false );
coefficient[0] = d;
coefficient[1] = c;
coefficient[2] = b;
coefficient[3] = a;
}
ID_INLINE idPolynomial::idPolynomial( float a, float b, float c, float d, float e )
{
degree = -1;
allocated = 0;
coefficient = NULL;
Resize( 4, false );
coefficient[0] = e;
coefficient[1] = d;
coefficient[2] = c;
coefficient[3] = b;
coefficient[4] = a;
}
ID_INLINE float idPolynomial::operator[]( int index ) const
{
assert( index >= 0 && index <= degree );
return coefficient[ index ];
}
ID_INLINE float& idPolynomial::operator[]( int index )
{
assert( index >= 0 && index <= degree );
return coefficient[ index ];
}
ID_INLINE idPolynomial idPolynomial::operator-() const
{
int i;
idPolynomial n;
n = *this;
for( i = 0; i <= degree; i++ )
{
n[i] = -n[i];
}
return n;
}
ID_INLINE idPolynomial& idPolynomial::operator=( const idPolynomial& p )
{
Resize( p.degree, false );
for( int i = 0; i <= degree; i++ )
{
coefficient[i] = p.coefficient[i];
}
return *this;
}
ID_INLINE idPolynomial idPolynomial::operator+( const idPolynomial& p ) const
{
int i;
idPolynomial n;
if( degree > p.degree )
{
n.Resize( degree, false );
for( i = 0; i <= p.degree; i++ )
{
n.coefficient[i] = coefficient[i] + p.coefficient[i];
}
for( ; i <= degree; i++ )
{
n.coefficient[i] = coefficient[i];
}
n.degree = degree;
}
else if( p.degree > degree )
{
n.Resize( p.degree, false );
for( i = 0; i <= degree; i++ )
{
n.coefficient[i] = coefficient[i] + p.coefficient[i];
}
for( ; i <= p.degree; i++ )
{
n.coefficient[i] = p.coefficient[i];
}
n.degree = p.degree;
}
else
{
n.Resize( degree, false );
n.degree = 0;
for( i = 0; i <= degree; i++ )
{
n.coefficient[i] = coefficient[i] + p.coefficient[i];
if( n.coefficient[i] != 0.0f )
{
n.degree = i;
}
}
}
return n;
}
ID_INLINE idPolynomial idPolynomial::operator-( const idPolynomial& p ) const
{
int i;
idPolynomial n;
if( degree > p.degree )
{
n.Resize( degree, false );
for( i = 0; i <= p.degree; i++ )
{
n.coefficient[i] = coefficient[i] - p.coefficient[i];
}
for( ; i <= degree; i++ )
{
n.coefficient[i] = coefficient[i];
}
n.degree = degree;
}
else if( p.degree >= degree )
{
n.Resize( p.degree, false );
for( i = 0; i <= degree; i++ )
{
n.coefficient[i] = coefficient[i] - p.coefficient[i];
}
for( ; i <= p.degree; i++ )
{
n.coefficient[i] = - p.coefficient[i];
}
n.degree = p.degree;
}
else
{
n.Resize( degree, false );
n.degree = 0;
for( i = 0; i <= degree; i++ )
{
n.coefficient[i] = coefficient[i] - p.coefficient[i];
if( n.coefficient[i] != 0.0f )
{
n.degree = i;
}
}
}
return n;
}
ID_INLINE idPolynomial idPolynomial::operator*( const float s ) const
{
idPolynomial n;
if( s == 0.0f )
{
n.degree = 0;
}
else
{
n.Resize( degree, false );
for( int i = 0; i <= degree; i++ )
{
n.coefficient[i] = coefficient[i] * s;
}
}
return n;
}
ID_INLINE idPolynomial idPolynomial::operator/( const float s ) const
{
float invs;
idPolynomial n;
assert( s != 0.0f );
n.Resize( degree, false );
invs = 1.0f / s;
for( int i = 0; i <= degree; i++ )
{
n.coefficient[i] = coefficient[i] * invs;
}
return n;
}
ID_INLINE idPolynomial& idPolynomial::operator+=( const idPolynomial& p )
{
int i;
if( degree > p.degree )
{
for( i = 0; i <= p.degree; i++ )
{
coefficient[i] += p.coefficient[i];
}
}
else if( p.degree > degree )
{
Resize( p.degree, true );
for( i = 0; i <= degree; i++ )
{
coefficient[i] += p.coefficient[i];
}
for( ; i <= p.degree; i++ )
{
coefficient[i] = p.coefficient[i];
}
}
else
{
for( i = 0; i <= degree; i++ )
{
coefficient[i] += p.coefficient[i];
if( coefficient[i] != 0.0f )
{
degree = i;
}
}
}
return *this;
}
ID_INLINE idPolynomial& idPolynomial::operator-=( const idPolynomial& p )
{
int i;
if( degree > p.degree )
{
for( i = 0; i <= p.degree; i++ )
{
coefficient[i] -= p.coefficient[i];
}
}
else if( p.degree > degree )
{
Resize( p.degree, true );
for( i = 0; i <= degree; i++ )
{
coefficient[i] -= p.coefficient[i];
}
for( ; i <= p.degree; i++ )
{
coefficient[i] = - p.coefficient[i];
}
}
else
{
for( i = 0; i <= degree; i++ )
{
coefficient[i] -= p.coefficient[i];
if( coefficient[i] != 0.0f )
{
degree = i;
}
}
}
return *this;
}
ID_INLINE idPolynomial& idPolynomial::operator*=( const float s )
{
if( s == 0.0f )
{
degree = 0;
}
else
{
for( int i = 0; i <= degree; i++ )
{
coefficient[i] *= s;
}
}
return *this;
}
ID_INLINE idPolynomial& idPolynomial::operator/=( const float s )
{
float invs;
assert( s != 0.0f );
invs = 1.0f / s;
for( int i = 0; i <= degree; i++ )
{
coefficient[i] = invs;
}
return *this;;
}
ID_INLINE bool idPolynomial::Compare( const idPolynomial& p ) const
{
if( degree != p.degree )
{
return false;
}
for( int i = 0; i <= degree; i++ )
{
if( coefficient[i] != p.coefficient[i] )
{
return false;
}
}
return true;
}
ID_INLINE bool idPolynomial::Compare( const idPolynomial& p, const float epsilon ) const
{
if( degree != p.degree )
{
return false;
}
for( int i = 0; i <= degree; i++ )
{
if( idMath::Fabs( coefficient[i] - p.coefficient[i] ) > epsilon )
{
return false;
}
}
return true;
}
ID_INLINE bool idPolynomial::operator==( const idPolynomial& p ) const
{
return Compare( p );
}
ID_INLINE bool idPolynomial::operator!=( const idPolynomial& p ) const
{
return !Compare( p );
}
ID_INLINE void idPolynomial::Zero()
{
degree = 0;
}
ID_INLINE void idPolynomial::Zero( int d )
{
Resize( d, false );
for( int i = 0; i <= degree; i++ )
{
coefficient[i] = 0.0f;
}
}
ID_INLINE int idPolynomial::GetDimension() const
{
return degree;
}
ID_INLINE int idPolynomial::GetDegree() const
{
return degree;
}
ID_INLINE float idPolynomial::GetValue( const float x ) const
{
float y, z;
y = coefficient[0];
z = x;
for( int i = 1; i <= degree; i++ )
{
y += coefficient[i] * z;
z *= x;
}
return y;
}
ID_INLINE idComplex idPolynomial::GetValue( const idComplex& x ) const
{
idComplex y, z;
y.Set( coefficient[0], 0.0f );
z = x;
for( int i = 1; i <= degree; i++ )
{
y += coefficient[i] * z;
z *= x;
}
return y;
}
ID_INLINE idPolynomial idPolynomial::GetDerivative() const
{
idPolynomial n;
if( degree == 0 )
{
return n;
}
n.Resize( degree - 1, false );
for( int i = 1; i <= degree; i++ )
{
n.coefficient[i - 1] = i * coefficient[i];
}
return n;
}
ID_INLINE idPolynomial idPolynomial::GetAntiDerivative() const
{
idPolynomial n;
if( degree == 0 )
{
return n;
}
n.Resize( degree + 1, false );
n.coefficient[0] = 0.0f;
for( int i = 0; i <= degree; i++ )
{
n.coefficient[i + 1] = coefficient[i] / ( i + 1 );
}
return n;
}
ID_INLINE int idPolynomial::GetRoots1( float a, float b, float* roots )
{
assert( a != 0.0f );
roots[0] = - b / a;
return 1;
}
ID_INLINE int idPolynomial::GetRoots2( float a, float b, float c, float* roots )
{
float inva, ds;
if( a != 1.0f )
{
assert( a != 0.0f );
inva = 1.0f / a;
c *= inva;
b *= inva;
}
ds = b * b - 4.0f * c;
if( ds < 0.0f )
{
return 0;
}
else if( ds > 0.0f )
{
ds = idMath::Sqrt( ds );
roots[0] = 0.5f * ( -b - ds );
roots[1] = 0.5f * ( -b + ds );
return 2;
}
else
{
roots[0] = 0.5f * -b;
return 1;
}
}
ID_INLINE int idPolynomial::GetRoots3( float a, float b, float c, float d, float* roots )
{
float inva, f, g, halfg, ofs, ds, dist, angle, cs, ss, t;
if( a != 1.0f )
{
assert( a != 0.0f );
inva = 1.0f / a;
d *= inva;
c *= inva;
b *= inva;
}
f = ( 1.0f / 3.0f ) * ( 3.0f * c - b * b );
g = ( 1.0f / 27.0f ) * ( 2.0f * b * b * b - 9.0f * c * b + 27.0f * d );
halfg = 0.5f * g;
ofs = ( 1.0f / 3.0f ) * b;
ds = 0.25f * g * g + ( 1.0f / 27.0f ) * f * f * f;
if( ds < 0.0f )
{
dist = idMath::Sqrt( ( -1.0f / 3.0f ) * f );
angle = ( 1.0f / 3.0f ) * idMath::ATan( idMath::Sqrt( -ds ), -halfg );
cs = idMath::Cos( angle );
ss = idMath::Sin( angle );
roots[0] = 2.0f * dist * cs - ofs;
roots[1] = -dist * ( cs + idMath::SQRT_THREE * ss ) - ofs;
roots[2] = -dist * ( cs - idMath::SQRT_THREE * ss ) - ofs;
return 3;
}
else if( ds > 0.0f )
{
ds = idMath::Sqrt( ds );
t = -halfg + ds;
if( t >= 0.0f )
{
roots[0] = idMath::Pow( t, ( 1.0f / 3.0f ) );
}
else
{
roots[0] = -idMath::Pow( -t, ( 1.0f / 3.0f ) );
}
t = -halfg - ds;
if( t >= 0.0f )
{
roots[0] += idMath::Pow( t, ( 1.0f / 3.0f ) );
}
else
{
roots[0] -= idMath::Pow( -t, ( 1.0f / 3.0f ) );
}
roots[0] -= ofs;
return 1;
}
else
{
if( halfg >= 0.0f )
{
t = -idMath::Pow( halfg, ( 1.0f / 3.0f ) );
}
else
{
t = idMath::Pow( -halfg, ( 1.0f / 3.0f ) );
}
roots[0] = 2.0f * t - ofs;
roots[1] = -t - ofs;
roots[2] = roots[1];
return 3;
}
}
ID_INLINE int idPolynomial::GetRoots4( float a, float b, float c, float d, float e, float* roots )
{
int count;
float inva, y, ds, r, s1, s2, t1, t2, tp, tm;
float roots3[3];
if( a != 1.0f )
{
assert( a != 0.0f );
inva = 1.0f / a;
e *= inva;
d *= inva;
c *= inva;
b *= inva;
}
count = 0;
GetRoots3( 1.0f, -c, b * d - 4.0f * e, -b * b * e + 4.0f * c * e - d * d, roots3 );
y = roots3[0];
ds = 0.25f * b * b - c + y;
if( ds < 0.0f )
{
return 0;
}
else if( ds > 0.0f )
{
r = idMath::Sqrt( ds );
t1 = 0.75f * b * b - r * r - 2.0f * c;
t2 = ( 4.0f * b * c - 8.0f * d - b * b * b ) / ( 4.0f * r );
tp = t1 + t2;
tm = t1 - t2;
if( tp >= 0.0f )
{
s1 = idMath::Sqrt( tp );
roots[count++] = -0.25f * b + 0.5f * ( r + s1 );
roots[count++] = -0.25f * b + 0.5f * ( r - s1 );
}
if( tm >= 0.0f )
{
s2 = idMath::Sqrt( tm );
roots[count++] = -0.25f * b + 0.5f * ( s2 - r );
roots[count++] = -0.25f * b - 0.5f * ( s2 + r );
}
return count;
}
else
{
t2 = y * y - 4.0f * e;
if( t2 >= 0.0f )
{
t2 = 2.0f * idMath::Sqrt( t2 );
t1 = 0.75f * b * b - 2.0f * c;
if( t1 + t2 >= 0.0f )
{
s1 = idMath::Sqrt( t1 + t2 );
roots[count++] = -0.25f * b + 0.5f * s1;
roots[count++] = -0.25f * b - 0.5f * s1;
}
if( t1 - t2 >= 0.0f )
{
s2 = idMath::Sqrt( t1 - t2 );
roots[count++] = -0.25f * b + 0.5f * s2;
roots[count++] = -0.25f * b - 0.5f * s2;
}
}
return count;
}
}
ID_INLINE const float* idPolynomial::ToFloatPtr() const
{
return coefficient;
}
ID_INLINE float* idPolynomial::ToFloatPtr()
{
return coefficient;
}
ID_INLINE void idPolynomial::Resize( int d, bool keep )
{
int alloc = ( d + 1 + 3 ) & ~3;
if( alloc > allocated )
{
float* ptr = ( float* ) Mem_Alloc16( alloc * sizeof( float ), TAG_MATH );
if( coefficient != NULL )
{
if( keep )
{
for( int i = 0; i <= degree; i++ )
{
ptr[i] = coefficient[i];
}
}
Mem_Free16( coefficient );
}
allocated = alloc;
coefficient = ptr;
}
degree = d;
}
#endif /* !__MATH_POLYNOMIAL_H__ */