source-engine/mathlib/mathlib_base.cpp

//========= Copyright Valve Corporation, All rights reserved. ============//
//
// Purpose: Math primitives.
//
//===========================================================================//

/// FIXME: As soon as all references to mathlib.c are gone, include it in here

#include <math.h>
#include <float.h>	// Needed for FLT_EPSILON

#include "tier0/basetypes.h"
#include <memory.h>
#include "tier0/dbg.h"

#include "tier0/vprof.h"
//#define _VPROF_MATHLIB

#pragma warning(disable:4244)   // "conversion from 'const int' to 'float', possible loss of data"
#pragma warning(disable:4730)	// "mixing _m64 and floating point expressions may result in incorrect code"

#include "mathlib/mathlib.h"
#include "mathlib/vector.h"
#if !defined( _X360 )
#include "mathlib/amd3dx.h"
#ifndef OSX
#include "3dnow.h"
#endif
#include "sse.h"
#endif

#include "mathlib/ssemath.h"
#include "mathlib/ssequaternion.h"

// memdbgon must be the last include file in a .cpp file!!!
#include "tier0/memdbgon.h"

bool s_bMathlibInitialized = false;

#ifdef PARANOID
// User must provide an implementation of Sys_Error()
void Sys_Error (char *error, ...);
#endif

const Vector vec3_origin(0,0,0);
const QAngle vec3_angle(0,0,0);
const Vector vec3_invalid( FLT_MAX, FLT_MAX, FLT_MAX );
const int nanmask = 255<<23;

//-----------------------------------------------------------------------------
// Standard C implementations of optimized routines:
//-----------------------------------------------------------------------------
float _sqrtf(float _X)
{
	Assert( s_bMathlibInitialized );
	return sqrtf(_X); 
}

float _rsqrtf(float x)
{
	Assert( s_bMathlibInitialized );

	return 1.f / _sqrtf( x );
}

float FASTCALL _VectorNormalize (Vector& vec)
{
#ifdef _VPROF_MATHLIB
	VPROF_BUDGET( "_VectorNormalize", "Mathlib" );
#endif
	Assert( s_bMathlibInitialized );
	float radius = sqrtf(vec.x*vec.x + vec.y*vec.y + vec.z*vec.z);

	// FLT_EPSILON is added to the radius to eliminate the possibility of divide by zero.
	float iradius = 1.f / ( radius + FLT_EPSILON );
	
	vec.x *= iradius;
	vec.y *= iradius;
	vec.z *= iradius;
	
	return radius;
}

// TODO: Add fast C VectorNormalizeFast.
// Perhaps use approximate rsqrt trick, if the accuracy isn't too bad.
void FASTCALL _VectorNormalizeFast (Vector& vec)
{
	Assert( s_bMathlibInitialized );

	// FLT_EPSILON is added to the radius to eliminate the possibility of divide by zero.
	float iradius = 1.f / ( sqrtf(vec.x*vec.x + vec.y*vec.y + vec.z*vec.z) + FLT_EPSILON );
	
	vec.x *= iradius;
	vec.y *= iradius;
	vec.z *= iradius;
	
}

float _InvRSquared(const float* v)
{
	Assert( s_bMathlibInitialized );
	float	r2 = DotProduct(v, v);
	return r2 < 1.f ? 1.f : 1/r2;
}

//-----------------------------------------------------------------------------
// Function pointers selecting the appropriate implementation
//-----------------------------------------------------------------------------
float (*pfSqrt)(float x)  = _sqrtf;
float (*pfRSqrt)(float x) = _rsqrtf;
float (*pfRSqrtFast)(float x) = _rsqrtf;
float (FASTCALL *pfVectorNormalize)(Vector& v) = _VectorNormalize;
void  (FASTCALL *pfVectorNormalizeFast)(Vector& v) = _VectorNormalizeFast;
float (*pfInvRSquared)(const float* v) = _InvRSquared;
void  (*pfFastSinCos)(float x, float* s, float* c) = SinCos;
float (*pfFastCos)(float x) = cosf;

float SinCosTable[SIN_TABLE_SIZE];
void InitSinCosTable()
{
	for( int i = 0; i < SIN_TABLE_SIZE; i++ )
	{
		SinCosTable[i] = sin(i * 2.0 * M_PI / SIN_TABLE_SIZE);
	}
}

qboolean VectorsEqual( const float *v1, const float *v2 )
{
	Assert( s_bMathlibInitialized );
	return ( ( v1[0] == v2[0] ) &&
		     ( v1[1] == v2[1] ) &&
			 ( v1[2] == v2[2] ) );
}


//-----------------------------------------------------------------------------
// Purpose: Generates Euler angles given a left-handed orientation matrix. The
//			columns of the matrix contain the forward, left, and up vectors.
// Input  : matrix - Left-handed orientation matrix.
//			angles[PITCH, YAW, ROLL]. Receives right-handed counterclockwise
//				rotations in degrees around Y, Z, and X respectively.
//-----------------------------------------------------------------------------

void MatrixAngles( const matrix3x4_t& matrix, RadianEuler &angles, Vector &position )
{
	MatrixGetColumn( matrix, 3, position );
	MatrixAngles( matrix, angles );
}

void MatrixAngles( const matrix3x4_t &matrix, Quaternion &q, Vector &pos )
{
#ifdef _VPROF_MATHLIB
	VPROF_BUDGET( "MatrixQuaternion", "Mathlib" );
#endif
	float trace;
	trace = matrix[0][0] + matrix[1][1] + matrix[2][2] + 1.0f;
	if( trace > 1.0f + FLT_EPSILON ) 
	{
		// VPROF_INCREMENT_COUNTER("MatrixQuaternion A",1);
		q.x = ( matrix[2][1] - matrix[1][2] );
		q.y = ( matrix[0][2] - matrix[2][0] );
		q.z = ( matrix[1][0] - matrix[0][1] );
		q.w = trace;
	} 
	else if ( matrix[0][0] > matrix[1][1] && matrix[0][0] > matrix[2][2] ) 
	{
		// VPROF_INCREMENT_COUNTER("MatrixQuaternion B",1);
		trace = 1.0f + matrix[0][0] - matrix[1][1] - matrix[2][2];
		q.x = trace;
		q.y = (matrix[1][0] + matrix[0][1] );
		q.z = (matrix[0][2] + matrix[2][0] );
		q.w = (matrix[2][1] - matrix[1][2] );
	} 
	else if (matrix[1][1] > matrix[2][2])
	{
		// VPROF_INCREMENT_COUNTER("MatrixQuaternion C",1);
		trace = 1.0f + matrix[1][1] - matrix[0][0] - matrix[2][2];
		q.x = (matrix[0][1] + matrix[1][0] );
		q.y = trace;
		q.z = (matrix[2][1] + matrix[1][2] );
		q.w = (matrix[0][2] - matrix[2][0] );
	}
	else
	{
		// VPROF_INCREMENT_COUNTER("MatrixQuaternion D",1);
		trace = 1.0f + matrix[2][2] - matrix[0][0] - matrix[1][1];
		q.x = (matrix[0][2] + matrix[2][0] );
		q.y = (matrix[2][1] + matrix[1][2] );
		q.z = trace;
		q.w = (matrix[1][0] - matrix[0][1] );
	}

	QuaternionNormalize( q );

#if 0
	// check against the angle version
	RadianEuler ang;
	MatrixAngles( matrix, ang );
	Quaternion test;
	AngleQuaternion( ang, test );
	float d = QuaternionDotProduct( q, test );
	Assert( fabs(d) > 0.99 && fabs(d) < 1.01 );
#endif

	MatrixGetColumn( matrix, 3, pos );
}

void MatrixAngles( const matrix3x4_t& matrix, float *angles )
{ 
#ifdef _VPROF_MATHLIB
	VPROF_BUDGET( "MatrixAngles", "Mathlib" );
#endif
	Assert( s_bMathlibInitialized );
	float forward[3];
	float left[3];
	float up[3];

	//
	// Extract the basis vectors from the matrix. Since we only need the Z
	// component of the up vector, we don't get X and Y.
	//
	forward[0] = matrix[0][0];
	forward[1] = matrix[1][0];
	forward[2] = matrix[2][0];
	left[0] = matrix[0][1];
	left[1] = matrix[1][1];
	left[2] = matrix[2][1];
	up[2] = matrix[2][2];

	float xyDist = sqrtf( forward[0] * forward[0] + forward[1] * forward[1] );
	
	// enough here to get angles?
	if ( xyDist > 0.001f )
	{
		// (yaw)	y = ATAN( forward.y, forward.x );		-- in our space, forward is the X axis
		angles[1] = RAD2DEG( atan2f( forward[1], forward[0] ) );

		// (pitch)	x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
		angles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );

		// (roll)	z = ATAN( left.z, up.z );
		angles[2] = RAD2DEG( atan2f( left[2], up[2] ) );
	}
	else	// forward is mostly Z, gimbal lock-
	{
		// (yaw)	y = ATAN( -left.x, left.y );			-- forward is mostly z, so use right for yaw
		angles[1] = RAD2DEG( atan2f( -left[0], left[1] ) );

		// (pitch)	x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
		angles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );

		// Assume no roll in this case as one degree of freedom has been lost (i.e. yaw == roll)
		angles[2] = 0;
	}
}


// transform in1 by the matrix in2
void VectorTransform (const float *in1, const matrix3x4_t& in2, float *out)
{
	Assert( s_bMathlibInitialized );
	Assert( in1 != out );
	out[0] = DotProduct(in1, in2[0]) + in2[0][3];
	out[1] = DotProduct(in1, in2[1]) + in2[1][3];
	out[2] = DotProduct(in1, in2[2]) + in2[2][3];
}


// assuming the matrix is orthonormal, transform in1 by the transpose (also the inverse in this case) of in2.
void VectorITransform (const float *in1, const matrix3x4_t& in2, float *out)
{
	Assert( s_bMathlibInitialized );
	float in1t[3];

	in1t[0] = in1[0] - in2[0][3];
	in1t[1] = in1[1] - in2[1][3];
	in1t[2] = in1[2] - in2[2][3];

	out[0] = in1t[0] * in2[0][0] + in1t[1] * in2[1][0] + in1t[2] * in2[2][0];
	out[1] = in1t[0] * in2[0][1] + in1t[1] * in2[1][1] + in1t[2] * in2[2][1];
	out[2] = in1t[0] * in2[0][2] + in1t[1] * in2[1][2] + in1t[2] * in2[2][2];
}


// assume in2 is a rotation and rotate the input vector
void VectorRotate( const float *in1, const matrix3x4_t& in2, float *out )
{
	Assert( s_bMathlibInitialized );
	Assert( in1 != out );
	out[0] = DotProduct( in1, in2[0] );
	out[1] = DotProduct( in1, in2[1] );
	out[2] = DotProduct( in1, in2[2] );
}

// assume in2 is a rotation and rotate the input vector
void VectorRotate( const Vector &in1, const QAngle &in2, Vector &out )
{
	matrix3x4_t matRotate;
	AngleMatrix( in2, matRotate );
	VectorRotate( in1, matRotate, out );
}

// assume in2 is a rotation and rotate the input vector
void VectorRotate( const Vector &in1, const Quaternion &in2, Vector &out )
{
	matrix3x4_t matRotate;
	QuaternionMatrix( in2, matRotate );
	VectorRotate( in1, matRotate, out );
}


// rotate by the inverse of the matrix
void VectorIRotate( const float *in1, const matrix3x4_t& in2, float *out )
{
	Assert( s_bMathlibInitialized );
	Assert( in1 != out );
	out[0] = in1[0]*in2[0][0] + in1[1]*in2[1][0] + in1[2]*in2[2][0];
	out[1] = in1[0]*in2[0][1] + in1[1]*in2[1][1] + in1[2]*in2[2][1];
	out[2] = in1[0]*in2[0][2] + in1[1]*in2[1][2] + in1[2]*in2[2][2];
}

#ifndef VECTOR_NO_SLOW_OPERATIONS
// transform a set of angles in the output space of parentMatrix to the input space
QAngle TransformAnglesToLocalSpace( const QAngle &angles, const matrix3x4_t &parentMatrix )
{
	matrix3x4_t angToWorld, worldToParent, localMatrix;
	MatrixInvert( parentMatrix, worldToParent );
	AngleMatrix( angles, angToWorld );
	ConcatTransforms( worldToParent, angToWorld, localMatrix );
	
	QAngle out;
	MatrixAngles( localMatrix, out );
	return out;
}

// transform a set of angles in the input space of parentMatrix to the output space
QAngle TransformAnglesToWorldSpace( const QAngle &angles, const matrix3x4_t &parentMatrix )
{
	matrix3x4_t angToParent, angToWorld;
	AngleMatrix( angles, angToParent );
	ConcatTransforms( parentMatrix, angToParent, angToWorld );
	QAngle out;
	MatrixAngles( angToWorld, out );
	return out;
}

#endif // VECTOR_NO_SLOW_OPERATIONS

void MatrixInitialize( matrix3x4_t &mat, const Vector &vecOrigin, const Vector &vecXAxis, const Vector &vecYAxis, const Vector &vecZAxis )
{
	MatrixSetColumn( vecXAxis, 0, mat );
	MatrixSetColumn( vecYAxis, 1, mat );
	MatrixSetColumn( vecZAxis, 2, mat );
	MatrixSetColumn( vecOrigin, 3, mat );
}

void MatrixCopy( const matrix3x4_t& in, matrix3x4_t& out )
{
	Assert( s_bMathlibInitialized );
	memcpy( out.Base(), in.Base(), sizeof( float ) * 3 * 4 );
}

//-----------------------------------------------------------------------------
// Matrix equality test
//-----------------------------------------------------------------------------
bool MatricesAreEqual( const matrix3x4_t &src1, const matrix3x4_t &src2, float flTolerance )
{
	for ( int i = 0; i < 3; ++i )
	{
		for ( int j = 0; j < 4; ++j )
		{
			if ( fabs( src1[i][j] - src2[i][j] ) > flTolerance )
				return false;
		}
	}
	return true;
}

// NOTE: This is just the transpose not a general inverse
void MatrixInvert( const matrix3x4_t& in, matrix3x4_t& out )
{
	Assert( s_bMathlibInitialized );
	if ( &in == &out )
	{
		V_swap(out[0][1],out[1][0]);
		V_swap(out[0][2],out[2][0]);
		V_swap(out[1][2],out[2][1]);
	}
	else
	{
		// transpose the matrix
		out[0][0] = in[0][0];
		out[0][1] = in[1][0];
		out[0][2] = in[2][0];

		out[1][0] = in[0][1];
		out[1][1] = in[1][1];
		out[1][2] = in[2][1];

		out[2][0] = in[0][2];
		out[2][1] = in[1][2];
		out[2][2] = in[2][2];
	}

	// now fix up the translation to be in the other space
	float tmp[3];
	tmp[0] = in[0][3];
	tmp[1] = in[1][3];
	tmp[2] = in[2][3];

	out[0][3] = -DotProduct( tmp, out[0] );
	out[1][3] = -DotProduct( tmp, out[1] );
	out[2][3] = -DotProduct( tmp, out[2] );
}

void MatrixGetColumn( const matrix3x4_t& in, int column, Vector &out )
{
	out.x = in[0][column];
	out.y = in[1][column];
	out.z = in[2][column];
}

void MatrixSetColumn( const Vector &in, int column, matrix3x4_t& out )
{
	out[0][column] = in.x;
	out[1][column] = in.y;
	out[2][column] = in.z;
}

void MatrixScaleBy ( const float flScale, matrix3x4_t &out )
{
	out[0][0] *= flScale;
	out[1][0] *= flScale;
	out[2][0] *= flScale;
	out[0][1] *= flScale;
	out[1][1] *= flScale;
	out[2][1] *= flScale;
	out[0][2] *= flScale;
	out[1][2] *= flScale;
	out[2][2] *= flScale;
}

void MatrixScaleByZero ( matrix3x4_t &out )
{
	out[0][0] = 0.0f;
	out[1][0] = 0.0f;
	out[2][0] = 0.0f;
	out[0][1] = 0.0f;
	out[1][1] = 0.0f;
	out[2][1] = 0.0f;
	out[0][2] = 0.0f;
	out[1][2] = 0.0f;
	out[2][2] = 0.0f;
}



int VectorCompare (const float *v1, const float *v2)
{
	Assert( s_bMathlibInitialized );
	int		i;
	
	for (i=0 ; i<3 ; i++)
		if (v1[i] != v2[i])
			return 0;
			
	return 1;
}

void CrossProduct (const float* v1, const float* v2, float* cross)
{
	Assert( s_bMathlibInitialized );
	Assert( v1 != cross );
	Assert( v2 != cross );
	cross[0] = v1[1]*v2[2] - v1[2]*v2[1];
	cross[1] = v1[2]*v2[0] - v1[0]*v2[2];
	cross[2] = v1[0]*v2[1] - v1[1]*v2[0];
}

int Q_log2(int val)
{
	int answer=0;
	while (val>>=1)
		answer++;
	return answer;
}

// Matrix is right-handed x=forward, y=left, z=up.  We a left-handed convention for vectors in the game code (forward, right, up)
void MatrixVectors( const matrix3x4_t &matrix, Vector* pForward, Vector *pRight, Vector *pUp )
{
	MatrixGetColumn( matrix, 0, *pForward );
	MatrixGetColumn( matrix, 1, *pRight );
	MatrixGetColumn( matrix, 2, *pUp );
	*pRight *= -1.0f;
}


void VectorVectors( const Vector &forward, Vector &right, Vector &up )
{
	Assert( s_bMathlibInitialized );
	Vector tmp;

	if (forward[0] == 0 && forward[1] == 0)
	{
		// pitch 90 degrees up/down from identity
		right[0] = 0;	
		right[1] = -1; 
		right[2] = 0;
		up[0] = -forward[2]; 
		up[1] = 0; 
		up[2] = 0;
	}
	else
	{
		tmp[0] = 0; tmp[1] = 0; tmp[2] = 1.0;
		CrossProduct( forward, tmp, right );
		VectorNormalize( right );
		CrossProduct( right, forward, up );
		VectorNormalize( up );
	}
}

void VectorMatrix( const Vector &forward, matrix3x4_t& matrix)
{
	Assert( s_bMathlibInitialized );
	Vector right, up;
	VectorVectors(forward, right, up);

	MatrixSetColumn( forward, 0, matrix );
	MatrixSetColumn( -right, 1, matrix );
	MatrixSetColumn( up, 2, matrix );
}


void VectorAngles( const float *forward, float *angles )
{
	Assert( s_bMathlibInitialized );
	float	tmp, yaw, pitch;
	
	if (forward[1] == 0 && forward[0] == 0)
	{
		yaw = 0;
		if (forward[2] > 0)
			pitch = 270;
		else
			pitch = 90;
	}
	else
	{
		yaw = (atan2(forward[1], forward[0]) * 180 / M_PI);
		if (yaw < 0)
			yaw += 360;

		tmp = sqrt (forward[0]*forward[0] + forward[1]*forward[1]);
		pitch = (atan2(-forward[2], tmp) * 180 / M_PI);
		if (pitch < 0)
			pitch += 360;
	}
	
	angles[0] = pitch;
	angles[1] = yaw;
	angles[2] = 0;
}


/*
================
R_ConcatRotations
================
*/
void ConcatRotations (const float in1[3][3], const float in2[3][3], float out[3][3])
{
	Assert( s_bMathlibInitialized );
	Assert( in1 != out );
	Assert( in2 != out );
	out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
				in1[0][2] * in2[2][0];
	out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
				in1[0][2] * in2[2][1];
	out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
				in1[0][2] * in2[2][2];
	out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
				in1[1][2] * in2[2][0];
	out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
				in1[1][2] * in2[2][1];
	out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
				in1[1][2] * in2[2][2];
	out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
				in1[2][2] * in2[2][0];
	out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
				in1[2][2] * in2[2][1];
	out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
				in1[2][2] * in2[2][2];
}

void ConcatTransforms_Aligned( const matrix3x4_t &m0, const matrix3x4_t &m1, matrix3x4_t &out )
{
	Assert( (((size_t)&m0) % 16) == 0 );
	Assert( (((size_t)&m1) % 16) == 0 );
	Assert( (((size_t)&out) % 16) == 0 );

	fltx4 lastMask = *(fltx4 *)(&g_SIMD_ComponentMask[3]);
	fltx4 rowA0 = LoadAlignedSIMD( m0.m_flMatVal[0] );
	fltx4 rowA1 = LoadAlignedSIMD( m0.m_flMatVal[1] );
	fltx4 rowA2 = LoadAlignedSIMD( m0.m_flMatVal[2] );

	fltx4 rowB0 = LoadAlignedSIMD( m1.m_flMatVal[0] );
	fltx4 rowB1 = LoadAlignedSIMD( m1.m_flMatVal[1] );
	fltx4 rowB2 = LoadAlignedSIMD( m1.m_flMatVal[2] );

	// now we have the rows of m0 and the columns of m1
	// first output row
	fltx4 A0 = SplatXSIMD(rowA0);
	fltx4 A1 = SplatYSIMD(rowA0);
	fltx4 A2 = SplatZSIMD(rowA0);
	fltx4 mul00 = MulSIMD( A0, rowB0 );
	fltx4 mul01 = MulSIMD( A1, rowB1 );
	fltx4 mul02 = MulSIMD( A2, rowB2 );
	fltx4 out0 = AddSIMD( mul00, AddSIMD(mul01,mul02) );

	// second output row
	A0 = SplatXSIMD(rowA1);
	A1 = SplatYSIMD(rowA1);
	A2 = SplatZSIMD(rowA1);
	fltx4 mul10 = MulSIMD( A0, rowB0 );
	fltx4 mul11 = MulSIMD( A1, rowB1 );
	fltx4 mul12 = MulSIMD( A2, rowB2 );
	fltx4 out1 = AddSIMD( mul10, AddSIMD(mul11,mul12) );

	// third output row
	A0 = SplatXSIMD(rowA2);
	A1 = SplatYSIMD(rowA2);
	A2 = SplatZSIMD(rowA2);
	fltx4 mul20 = MulSIMD( A0, rowB0 );
	fltx4 mul21 = MulSIMD( A1, rowB1 );
	fltx4 mul22 = MulSIMD( A2, rowB2 );
	fltx4 out2 = AddSIMD( mul20, AddSIMD(mul21,mul22) );

	// add in translation vector
	A0 = AndSIMD(rowA0,lastMask);
	A1 = AndSIMD(rowA1,lastMask);
	A2 = AndSIMD(rowA2,lastMask);
	out0 = AddSIMD(out0, A0);
	out1 = AddSIMD(out1, A1);
	out2 = AddSIMD(out2, A2);

	StoreAlignedSIMD( out.m_flMatVal[0], out0 );
	StoreAlignedSIMD( out.m_flMatVal[1], out1 );
	StoreAlignedSIMD( out.m_flMatVal[2], out2 );
}

/*
================
R_ConcatTransforms
================
*/

void ConcatTransforms (const matrix3x4_t& in1, const matrix3x4_t& in2, matrix3x4_t& out)
{
#if 0
	// test for ones that'll be 2x faster
	if ( (((size_t)&in1) % 16) == 0 && (((size_t)&in2) % 16) == 0 && (((size_t)&out) % 16) == 0 )
	{
		ConcatTransforms_Aligned( in1, in2, out );
		return;
	}
#endif

	fltx4 lastMask = *(fltx4 *)(&g_SIMD_ComponentMask[3]);
	fltx4 rowA0 = LoadUnalignedSIMD( in1.m_flMatVal[0] );
	fltx4 rowA1 = LoadUnalignedSIMD( in1.m_flMatVal[1] );
	fltx4 rowA2 = LoadUnalignedSIMD( in1.m_flMatVal[2] );

	fltx4 rowB0 = LoadUnalignedSIMD( in2.m_flMatVal[0] );
	fltx4 rowB1 = LoadUnalignedSIMD( in2.m_flMatVal[1] );
	fltx4 rowB2 = LoadUnalignedSIMD( in2.m_flMatVal[2] );

	// now we have the rows of m0 and the columns of m1
	// first output row
	fltx4 A0 = SplatXSIMD(rowA0);
	fltx4 A1 = SplatYSIMD(rowA0);
	fltx4 A2 = SplatZSIMD(rowA0);
	fltx4 mul00 = MulSIMD( A0, rowB0 );
	fltx4 mul01 = MulSIMD( A1, rowB1 );
	fltx4 mul02 = MulSIMD( A2, rowB2 );
	fltx4 out0 = AddSIMD( mul00, AddSIMD(mul01,mul02) );

	// second output row
	A0 = SplatXSIMD(rowA1);
	A1 = SplatYSIMD(rowA1);
	A2 = SplatZSIMD(rowA1);
	fltx4 mul10 = MulSIMD( A0, rowB0 );
	fltx4 mul11 = MulSIMD( A1, rowB1 );
	fltx4 mul12 = MulSIMD( A2, rowB2 );
	fltx4 out1 = AddSIMD( mul10, AddSIMD(mul11,mul12) );

	// third output row
	A0 = SplatXSIMD(rowA2);
	A1 = SplatYSIMD(rowA2);
	A2 = SplatZSIMD(rowA2);
	fltx4 mul20 = MulSIMD( A0, rowB0 );
	fltx4 mul21 = MulSIMD( A1, rowB1 );
	fltx4 mul22 = MulSIMD( A2, rowB2 );
	fltx4 out2 = AddSIMD( mul20, AddSIMD(mul21,mul22) );

	// add in translation vector
	A0 = AndSIMD(rowA0,lastMask);
	A1 = AndSIMD(rowA1,lastMask);
	A2 = AndSIMD(rowA2,lastMask);
	out0 = AddSIMD(out0, A0);
	out1 = AddSIMD(out1, A1);
	out2 = AddSIMD(out2, A2);

	// write to output
	StoreUnalignedSIMD( out.m_flMatVal[0], out0 );
	StoreUnalignedSIMD( out.m_flMatVal[1], out1 );
	StoreUnalignedSIMD( out.m_flMatVal[2], out2 );
}


/*
===================
FloorDivMod

Returns mathematically correct (floor-based) quotient and remainder for
numer and denom, both of which should contain no fractional part. The
quotient must fit in 32 bits.
====================
*/

void FloorDivMod (double numer, double denom, int *quotient,
		int *rem)
{
	Assert( s_bMathlibInitialized );
	int		q, r;
	double	x;

#ifdef PARANOID
	if (denom <= 0.0)
		Sys_Error ("FloorDivMod: bad denominator %d\n", denom);

//	if ((floor(numer) != numer) || (floor(denom) != denom))
//		Sys_Error ("FloorDivMod: non-integer numer or denom %f %f\n",
//				numer, denom);
#endif

	if (numer >= 0.0)
	{

		x = floor(numer / denom);
		q = (int)x;
		r = Floor2Int(numer - (x * denom));
	}
	else
	{
		//
		// perform operations with positive values, and fix mod to make floor-based
		//
		x = floor(-numer / denom);
		q = -(int)x;
		r = Floor2Int(-numer - (x * denom));
		if (r != 0)
		{
			q--;
			r = (int)denom - r;
		}
	}

	*quotient = q;
	*rem = r;
}


/*
===================
GreatestCommonDivisor
====================
*/
int GreatestCommonDivisor (int i1, int i2)
{
	Assert( s_bMathlibInitialized );
	if (i1 > i2)
	{
		if (i2 == 0)
			return (i1);
		return GreatestCommonDivisor (i2, i1 % i2);
	}
	else
	{
		if (i1 == 0)
			return (i2);
		return GreatestCommonDivisor (i1, i2 % i1);
	}
}


bool IsDenormal( const float &val )
{
	const int x = *reinterpret_cast <const int *> (&val); // needs 32-bit int
	const int abs_mantissa = x & 0x007FFFFF;
	const int biased_exponent = x & 0x7F800000;
	
	return  ( biased_exponent == 0 && abs_mantissa != 0 );
}

int SignbitsForPlane (cplane_t *out)
{
	Assert( s_bMathlibInitialized );
	int	bits, j;

	// for fast box on planeside test

	bits = 0;
	for (j=0 ; j<3 ; j++)
	{
		if (out->normal[j] < 0)
			bits |= 1<<j;
	}
	return bits;
}

/*
==================
BoxOnPlaneSide

Returns 1, 2, or 1 + 2
==================
*/
int __cdecl BoxOnPlaneSide (const float *emins, const float *emaxs, const cplane_t *p)
{
	Assert( s_bMathlibInitialized );
	float	dist1, dist2;
	int		sides;

	// fast axial cases
	if (p->type < 3)
	{
		if (p->dist <= emins[p->type])
			return 1;
		if (p->dist >= emaxs[p->type])
			return 2;
		return 3;
	}
	
	// general case
	switch (p->signbits)
	{
	case 0:
		dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
		dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
		break;
	case 1:
		dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
		dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
		break;
	case 2:
		dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
		dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
		break;
	case 3:
		dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
		dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
		break;
	case 4:
		dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
		dist2 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
		break;
	case 5:
		dist1 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emins[2];
		dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emaxs[2];
		break;
	case 6:
		dist1 = p->normal[0]*emaxs[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
		dist2 = p->normal[0]*emins[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
		break;
	case 7:
		dist1 = p->normal[0]*emins[0] + p->normal[1]*emins[1] + p->normal[2]*emins[2];
		dist2 = p->normal[0]*emaxs[0] + p->normal[1]*emaxs[1] + p->normal[2]*emaxs[2];
		break;
	default:
		dist1 = dist2 = 0;		// shut up compiler
		Assert( 0 );
		break;
	}

	sides = 0;
	if (dist1 >= p->dist)
		sides = 1;
	if (dist2 < p->dist)
		sides |= 2;

	Assert( sides != 0 );

	return sides;
}

//-----------------------------------------------------------------------------
// Euler QAngle -> Basis Vectors
//-----------------------------------------------------------------------------

void AngleVectors (const QAngle &angles, Vector *forward)
{
	Assert( s_bMathlibInitialized );
	Assert( forward );
	
	float	sp, sy, cp, cy;
	
	SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
	SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
	
	forward->x = cp*cy;
	forward->y = cp*sy;
	forward->z = -sp;
}

//-----------------------------------------------------------------------------
// Euler QAngle -> Basis Vectors.  Each vector is optional
//-----------------------------------------------------------------------------
void AngleVectors( const QAngle &angles, Vector *forward, Vector *right, Vector *up )
{
	Assert( s_bMathlibInitialized );
	
	float sr, sp, sy, cr, cp, cy;

#ifdef _X360
	fltx4 radians, scale, sine, cosine;
	radians = LoadUnaligned3SIMD( angles.Base() );
	scale = ReplicateX4( M_PI_F / 180.f ); 
	radians = MulSIMD( radians, scale );
	SinCos3SIMD( sine, cosine, radians ); 	
	sp = SubFloat( sine, 0 );	sy = SubFloat( sine, 1 );	sr = SubFloat( sine, 2 );
	cp = SubFloat( cosine, 0 );	cy = SubFloat( cosine, 1 );	cr = SubFloat( cosine, 2 );
#else
	SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
	SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
	SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );
#endif

	if (forward)
	{
		forward->x = cp*cy;
		forward->y = cp*sy;
		forward->z = -sp;
	}

	if (right)
	{
		right->x = (-1*sr*sp*cy+-1*cr*-sy);
		right->y = (-1*sr*sp*sy+-1*cr*cy);
		right->z = -1*sr*cp;
	}

	if (up)
	{
		up->x = (cr*sp*cy+-sr*-sy);
		up->y = (cr*sp*sy+-sr*cy);
		up->z = cr*cp;
	}
}

//-----------------------------------------------------------------------------
// Euler QAngle -> Basis Vectors transposed
//-----------------------------------------------------------------------------

void AngleVectorsTranspose (const QAngle &angles, Vector *forward, Vector *right, Vector *up)
{
	Assert( s_bMathlibInitialized );
	float sr, sp, sy, cr, cp, cy;
	
	SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
	SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
	SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );

	if (forward)
	{
		forward->x	= cp*cy;
		forward->y	= (sr*sp*cy+cr*-sy);
		forward->z	= (cr*sp*cy+-sr*-sy);
	}
	
	if (right)
	{
		right->x	= cp*sy;
		right->y	= (sr*sp*sy+cr*cy);
		right->z	= (cr*sp*sy+-sr*cy);
	}

	if (up)
	{
		up->x		= -sp;
		up->y		= sr*cp;
		up->z		= cr*cp;
	}
}

//-----------------------------------------------------------------------------
// Forward direction vector -> Euler angles
//-----------------------------------------------------------------------------

void VectorAngles( const Vector& forward, QAngle &angles )
{
	Assert( s_bMathlibInitialized );
	float	tmp, yaw, pitch;
	
	if (forward[1] == 0 && forward[0] == 0)
	{
		yaw = 0;
		if (forward[2] > 0)
			pitch = 270;
		else
			pitch = 90;
	}
	else
	{
		yaw = (atan2(forward[1], forward[0]) * 180 / M_PI);
		if (yaw < 0)
			yaw += 360;

		tmp = FastSqrt (forward[0]*forward[0] + forward[1]*forward[1]);
		pitch = (atan2(-forward[2], tmp) * 180 / M_PI);
		if (pitch < 0)
			pitch += 360;
	}
	
	angles[0] = pitch;
	angles[1] = yaw;
	angles[2] = 0;
}

//-----------------------------------------------------------------------------
// Forward direction vector with a reference up vector -> Euler angles
//-----------------------------------------------------------------------------

void VectorAngles( const Vector &forward, const Vector &pseudoup, QAngle &angles )
{
	Assert( s_bMathlibInitialized );

	Vector left;

	CrossProduct( pseudoup, forward, left );
	VectorNormalizeFast( left );		
	
	float xyDist = sqrtf( forward[0] * forward[0] + forward[1] * forward[1] );

	// enough here to get angles?
	if ( xyDist > 0.001f )
	{
		// (yaw)	y = ATAN( forward.y, forward.x );		-- in our space, forward is the X axis
		angles[1] = RAD2DEG( atan2f( forward[1], forward[0] ) );

		// The engine does pitch inverted from this, but we always end up negating it in the DLL
		// UNDONE: Fix the engine to make it consistent
		// (pitch)	x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
		angles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );

		float up_z = (left[1] * forward[0]) - (left[0] * forward[1]);

		// (roll)	z = ATAN( left.z, up.z );
		angles[2] = RAD2DEG( atan2f( left[2], up_z ) );
	}
	else	// forward is mostly Z, gimbal lock-
	{
		// (yaw)	y = ATAN( -left.x, left.y );			-- forward is mostly z, so use right for yaw
		angles[1] = RAD2DEG( atan2f( -left[0], left[1] ) ); //This was originally copied from the "void MatrixAngles( const matrix3x4_t& matrix, float *angles )" code, and it's 180 degrees off, negated the values and it all works now (Dave Kircher)

		// The engine does pitch inverted from this, but we always end up negating it in the DLL
		// UNDONE: Fix the engine to make it consistent
		// (pitch)	x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
		angles[0] = RAD2DEG( atan2f( -forward[2], xyDist ) );

		// Assume no roll in this case as one degree of freedom has been lost (i.e. yaw == roll)
		angles[2] = 0;
	}	
}

void SetIdentityMatrix( matrix3x4_t& matrix )
{
	memset( matrix.Base(), 0, sizeof(float)*3*4 );
	matrix[0][0] = 1.0;
	matrix[1][1] = 1.0;
	matrix[2][2] = 1.0;
}


//-----------------------------------------------------------------------------
// Builds a scale matrix
//-----------------------------------------------------------------------------
void SetScaleMatrix( float x, float y, float z, matrix3x4_t &dst )
{
	dst[0][0] = x;		dst[0][1] = 0.0f;	dst[0][2] = 0.0f;	dst[0][3] = 0.0f;
	dst[1][0] = 0.0f;	dst[1][1] = y;		dst[1][2] = 0.0f;	dst[1][3] = 0.0f;
	dst[2][0] = 0.0f;	dst[2][1] = 0.0f;	dst[2][2] = z;		dst[2][3] = 0.0f;
}


//-----------------------------------------------------------------------------
// Purpose: Builds the matrix for a counterclockwise rotation about an arbitrary axis.
//
//		   | ax2 + (1 - ax2)cosQ		axay(1 - cosQ) - azsinQ		azax(1 - cosQ) + aysinQ |
// Ra(Q) = | axay(1 - cosQ) + azsinQ	ay2 + (1 - ay2)cosQ			ayaz(1 - cosQ) - axsinQ |
//		   | azax(1 - cosQ) - aysinQ	ayaz(1 - cosQ) + axsinQ		az2 + (1 - az2)cosQ     |
//          
// Input  : mat - 
//			vAxisOrRot - 
//			angle - 
//-----------------------------------------------------------------------------
void MatrixBuildRotationAboutAxis( const Vector &vAxisOfRot, float angleDegrees, matrix3x4_t &dst )
{
	float radians;
	float axisXSquared;
	float axisYSquared;
	float axisZSquared;
	float fSin;
	float fCos;

	radians = angleDegrees * ( M_PI / 180.0 );
	fSin = sin( radians );
	fCos = cos( radians );

	axisXSquared = vAxisOfRot[0] * vAxisOfRot[0];
	axisYSquared = vAxisOfRot[1] * vAxisOfRot[1];
	axisZSquared = vAxisOfRot[2] * vAxisOfRot[2];

	// Column 0:
	dst[0][0] = axisXSquared + (1 - axisXSquared) * fCos;
	dst[1][0] = vAxisOfRot[0] * vAxisOfRot[1] * (1 - fCos) + vAxisOfRot[2] * fSin;
	dst[2][0] = vAxisOfRot[2] * vAxisOfRot[0] * (1 - fCos) - vAxisOfRot[1] * fSin;

	// Column 1:
	dst[0][1] = vAxisOfRot[0] * vAxisOfRot[1] * (1 - fCos) - vAxisOfRot[2] * fSin;
	dst[1][1] = axisYSquared + (1 - axisYSquared) * fCos;
	dst[2][1] = vAxisOfRot[1] * vAxisOfRot[2] * (1 - fCos) + vAxisOfRot[0] * fSin;

	// Column 2:
	dst[0][2] = vAxisOfRot[2] * vAxisOfRot[0] * (1 - fCos) + vAxisOfRot[1] * fSin;
	dst[1][2] = vAxisOfRot[1] * vAxisOfRot[2] * (1 - fCos) - vAxisOfRot[0] * fSin;
	dst[2][2] = axisZSquared + (1 - axisZSquared) * fCos;

	// Column 3:
	dst[0][3] = 0;
	dst[1][3] = 0;
	dst[2][3] = 0;
}


//-----------------------------------------------------------------------------
// Computes the transpose
//-----------------------------------------------------------------------------
void MatrixTranspose( matrix3x4_t& mat )
{
	vec_t tmp;
	tmp = mat[0][1]; mat[0][1] = mat[1][0]; mat[1][0] = tmp;
	tmp = mat[0][2]; mat[0][2] = mat[2][0]; mat[2][0] = tmp;
	tmp = mat[1][2]; mat[1][2] = mat[2][1]; mat[2][1] = tmp;
}

void MatrixTranspose( const matrix3x4_t& src, matrix3x4_t& dst )
{
	dst[0][0] = src[0][0]; dst[0][1] = src[1][0]; dst[0][2] = src[2][0]; dst[0][3] = 0.0f;
	dst[1][0] = src[0][1]; dst[1][1] = src[1][1]; dst[1][2] = src[2][1]; dst[1][3] = 0.0f;
	dst[2][0] = src[0][2]; dst[2][1] = src[1][2]; dst[2][2] = src[2][2]; dst[2][3] = 0.0f;
}


//-----------------------------------------------------------------------------
// Purpose: converts engine euler angles into a matrix
// Input  : vec3_t angles - PITCH, YAW, ROLL
// Output : *matrix - left-handed column matrix
//			the basis vectors for the rotations will be in the columns as follows:
//			matrix[][0] is forward
//			matrix[][1] is left
//			matrix[][2] is up
//-----------------------------------------------------------------------------
void AngleMatrix( RadianEuler const &angles, const Vector &position, matrix3x4_t& matrix )
{
	AngleMatrix( angles, matrix );
	MatrixSetColumn( position, 3, matrix );
}

void AngleMatrix( const RadianEuler& angles, matrix3x4_t& matrix )
{
	QAngle quakeEuler( RAD2DEG( angles.y ), RAD2DEG( angles.z ), RAD2DEG( angles.x ) );

	AngleMatrix( quakeEuler, matrix );
}


void AngleMatrix( const QAngle &angles, const Vector &position, matrix3x4_t& matrix )
{
	AngleMatrix( angles, matrix );
	MatrixSetColumn( position, 3, matrix );
}

void AngleMatrix( const QAngle &angles, matrix3x4_t& matrix )
{
#ifdef _VPROF_MATHLIB
	VPROF_BUDGET( "AngleMatrix", "Mathlib" );
#endif
	Assert( s_bMathlibInitialized );

	float sr, sp, sy, cr, cp, cy;

#ifdef _X360
	fltx4 radians, scale, sine, cosine;
	radians = LoadUnaligned3SIMD( angles.Base() );
	scale = ReplicateX4( M_PI_F / 180.f ); 
	radians = MulSIMD( radians, scale );
	SinCos3SIMD( sine, cosine, radians ); 	

	sp = SubFloat( sine, 0 );	sy = SubFloat( sine, 1 );	sr = SubFloat( sine, 2 );
	cp = SubFloat( cosine, 0 );	cy = SubFloat( cosine, 1 );	cr = SubFloat( cosine, 2 );
#else
	SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
	SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
	SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );
#endif

	// matrix = (YAW * PITCH) * ROLL
	matrix[0][0] = cp*cy;
	matrix[1][0] = cp*sy;
	matrix[2][0] = -sp;

	float crcy = cr*cy;
	float crsy = cr*sy;
	float srcy = sr*cy;
	float srsy = sr*sy;
	matrix[0][1] = sp*srcy-crsy;
	matrix[1][1] = sp*srsy+crcy;
	matrix[2][1] = sr*cp;

	matrix[0][2] = (sp*crcy+srsy);
	matrix[1][2] = (sp*crsy-srcy);
	matrix[2][2] = cr*cp;

	matrix[0][3] = 0.0f;
	matrix[1][3] = 0.0f;
	matrix[2][3] = 0.0f;
}

void AngleIMatrix( const RadianEuler& angles, matrix3x4_t& matrix )
{
	QAngle quakeEuler( RAD2DEG( angles.y ), RAD2DEG( angles.z ), RAD2DEG( angles.x ) );

	AngleIMatrix( quakeEuler, matrix );
}

void AngleIMatrix (const QAngle& angles, matrix3x4_t& matrix )
{
	Assert( s_bMathlibInitialized );
	float		sr, sp, sy, cr, cp, cy;
	
	SinCos( DEG2RAD( angles[YAW] ), &sy, &cy );
	SinCos( DEG2RAD( angles[PITCH] ), &sp, &cp );
	SinCos( DEG2RAD( angles[ROLL] ), &sr, &cr );

	// matrix = (YAW * PITCH) * ROLL
	matrix[0][0] = cp*cy;
	matrix[0][1] = cp*sy;
	matrix[0][2] = -sp;
	matrix[1][0] = sr*sp*cy+cr*-sy;
	matrix[1][1] = sr*sp*sy+cr*cy;
	matrix[1][2] = sr*cp;
	matrix[2][0] = (cr*sp*cy+-sr*-sy);
	matrix[2][1] = (cr*sp*sy+-sr*cy);
	matrix[2][2] = cr*cp;
	matrix[0][3] = 0.f;
	matrix[1][3] = 0.f;
	matrix[2][3] = 0.f;
}

void AngleIMatrix (const QAngle &angles, const Vector &position, matrix3x4_t &mat )
{
	AngleIMatrix( angles, mat );

	Vector vecTranslation;
	VectorRotate( position, mat, vecTranslation );
	vecTranslation *= -1.0f;
	MatrixSetColumn( vecTranslation, 3, mat );
}


//-----------------------------------------------------------------------------
// Bounding box construction methods
//-----------------------------------------------------------------------------

void ClearBounds (Vector& mins, Vector& maxs)
{
	Assert( s_bMathlibInitialized );
	mins[0] = mins[1] = mins[2] = 99999;
	maxs[0] = maxs[1] = maxs[2] = -99999;
}

void AddPointToBounds (const Vector& v, Vector& mins, Vector& maxs)
{
	Assert( s_bMathlibInitialized );
	int		i;
	vec_t	val;

	for (i=0 ; i<3 ; i++)
	{
		val = v[i];
		if (val < mins[i])
			mins[i] = val;
		if (val > maxs[i])
			maxs[i] = val;
	}
}

// solve a x^2 + b x + c = 0
bool SolveQuadratic( float a, float b, float c, float &root1, float &root2 )
{
	Assert( s_bMathlibInitialized );
	if (a == 0)
	{
		if (b != 0)
		{
			// no x^2 component, it's a linear system
			root1 = root2 = -c / b;
			return true;
		}
		if (c == 0)
		{
			// all zero's
			root1 = root2 = 0;
			return true;
		}
		return false;
	}

	float tmp = b * b - 4.0f * a * c;

	if (tmp < 0)
	{
		// imaginary number, bah, no solution.
		return false;
	}

	tmp = sqrt( tmp );
	root1 = (-b + tmp) / (2.0f * a);
	root2 = (-b - tmp) / (2.0f * a);
	return true;
}

// solves for "a, b, c" where "a x^2 + b x + c = y", return true if solution exists
bool SolveInverseQuadratic( float x1, float y1, float x2, float y2, float x3, float y3, float &a, float &b, float &c )
{
	float det = (x1 - x2)*(x1 - x3)*(x2 - x3);

	// FIXME: check with some sort of epsilon
	if (det == 0.0)
		return false;

	a = (x3*(-y1 + y2) + x2*(y1 - y3) + x1*(-y2 + y3)) / det;

	b = (x3*x3*(y1 - y2) + x1*x1*(y2 - y3) + x2*x2*(-y1 + y3)) / det;

    c = (x1*x3*(-x1 + x3)*y2 + x2*x2*(x3*y1 - x1*y3) + x2*(-(x3*x3*y1) + x1*x1*y3)) / det;

	return true;
}

bool SolveInverseQuadraticMonotonic( float x1, float y1, float x2, float y2, float x3, float y3, 
									 float &a, float &b, float &c )
{
	// use SolveInverseQuadratic, but if the sigm of the derivative at the start point is the wrong
	// sign, displace the mid point
	
	// first, sort parameters
	if (x1>x2)
	{
		V_swap(x1,x2);
		V_swap(y1,y2);
	}
	if (x2>x3)
	{
		V_swap(x2,x3);
		V_swap(y2,y3);
	}
	if (x1>x2)
	{
		V_swap(x1,x2);
		V_swap(y1,y2);
	}
	// this code is not fast. what it does is when the curve would be non-monotonic, slowly shifts
	// the center point closer to the linear line between the endpoints. Should anyone need htis
	// function to be actually fast, it would be fairly easy to change it to be so.
	for(float blend_to_linear_factor=0.0;blend_to_linear_factor<=1.0;blend_to_linear_factor+=0.05)
	{
		float tempy2=(1-blend_to_linear_factor)*y2+blend_to_linear_factor*FLerp(y1,y3,x1,x3,x2);
		if (!SolveInverseQuadratic(x1,y1,x2,tempy2,x3,y3,a,b,c))
			return false;
		float derivative=2.0*a+b;
		if ( (y1<y2) && (y2<y3))							// monotonically increasing
		{
			if (derivative>=0.0)
				return true;
		}
		else
		{
			if ( (y1>y2) && (y2>y3))							// monotonically decreasing
			{
				if (derivative<=0.0)
					return true;
			}
			else
				return true;
		}
	}
	return true;
}


// solves for "a, b, c" where "1/(a x^2 + b x + c ) = y", return true if solution exists
bool SolveInverseReciprocalQuadratic( float x1, float y1, float x2, float y2, float x3, float y3, float &a, float &b, float &c )
{
	float det = (x1 - x2)*(x1 - x3)*(x2 - x3)*y1*y2*y3;

	// FIXME: check with some sort of epsilon
	if (det == 0.0)
		return false;

	a = (x1*y1*(y2 - y3) + x3*(y1 - y2)*y3 + x2*y2*(-y1 + y3)) / det;

	b = (x2*x2*y2*(y1 - y3) + x3*x3*(-y1 + y2)*y3 + x1*x1*y1*(-y2 + y3)) / det;

	c = (x2*(x2 - x3)*x3*y2*y3 + x1*x1*y1*(x2*y2 - x3*y3) + x1*(-(x2*x2*y1*y2) + x3*x3*y1*y3)) / det;

	return true;
}


// Rotate a vector around the Z axis (YAW)
void VectorYawRotate( const Vector &in, float flYaw, Vector &out)
{
	Assert( s_bMathlibInitialized );
	if (&in == &out )
	{
		Vector tmp;
		tmp = in;
		VectorYawRotate( tmp, flYaw, out );
		return;
	}

	float sy, cy;

	SinCos( DEG2RAD(flYaw), &sy, &cy );

	out.x = in.x * cy - in.y * sy;
	out.y = in.x * sy + in.y * cy;
	out.z = in.z;
}



float Bias( float x, float biasAmt )
{
	// WARNING: not thread safe
	static float lastAmt = -1;
	static float lastExponent = 0;
	if( lastAmt != biasAmt )
	{
		lastExponent = log( biasAmt ) * -1.4427f; // (-1.4427 = 1 / log(0.5))
	}
	float fRet = pow( x, lastExponent );
	Assert ( !IS_NAN( fRet ) );
	return fRet;
}


float Gain( float x, float biasAmt )
{
	// WARNING: not thread safe
	if( x < 0.5 )
		return 0.5f * Bias( 2*x, 1-biasAmt );
	else
		return 1 - 0.5f * Bias( 2 - 2*x, 1-biasAmt );
}


float SmoothCurve( float x )
{
	// Actual smooth curve. Visualization:
	// http://www.wolframalpha.com/input/?i=plot%5B+0.5+*+%281+-+cos%5B2+*+pi+*+x%5D%29+for+x+%3D+%280%2C+1%29+%5D
	return 0.5f * (1 - cos( 2.0f * M_PI * x ) );
}


inline float MovePeak( float x, float flPeakPos )
{
	// Todo: make this higher-order?
	if( x < flPeakPos )
		return x * 0.5f / flPeakPos;
	else
		return 0.5 + 0.5 * (x - flPeakPos) / (1 - flPeakPos);
}


float SmoothCurve_Tweak( float x, float flPeakPos, float flPeakSharpness )
{
	float flMovedPeak = MovePeak( x, flPeakPos );
	float flSharpened = Gain( flMovedPeak, flPeakSharpness );
	return SmoothCurve( flSharpened );
}

//-----------------------------------------------------------------------------
// make sure quaternions are within 180 degrees of one another, if not, reverse q
//-----------------------------------------------------------------------------

void QuaternionAlign( const Quaternion &p, const Quaternion &q, Quaternion &qt )
{
	Assert( s_bMathlibInitialized );

	// FIXME: can this be done with a quat dot product?

	int i;
	// decide if one of the quaternions is backwards
	float a = 0;
	float b = 0;
	for (i = 0; i < 4; i++) 
	{
		a += (p[i]-q[i])*(p[i]-q[i]);
		b += (p[i]+q[i])*(p[i]+q[i]);
	}
	if (a > b) 
	{
		for (i = 0; i < 4; i++) 
		{
			qt[i] = -q[i];
		}
	}
	else if (&qt != &q)
	{
		for (i = 0; i < 4; i++) 
		{
			qt[i] = q[i];
		}
	}
}


//-----------------------------------------------------------------------------
// Do a piecewise addition of the quaternion elements. This actually makes little 
// mathematical sense, but it's a cheap way to simulate a slerp.
//-----------------------------------------------------------------------------
void QuaternionBlend( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt )
{
	Assert( s_bMathlibInitialized );
#if ALLOW_SIMD_QUATERNION_MATH
	fltx4 psimd, qsimd, qtsimd;
	psimd = LoadUnalignedSIMD( p.Base() );
	qsimd = LoadUnalignedSIMD( q.Base() );
	qtsimd = QuaternionBlendSIMD( psimd, qsimd, t );
	StoreUnalignedSIMD( qt.Base(), qtsimd );
#else
	// decide if one of the quaternions is backwards
	Quaternion q2;
	QuaternionAlign( p, q, q2 );
	QuaternionBlendNoAlign( p, q2, t, qt );
#endif
}


void QuaternionBlendNoAlign( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt )
{
	Assert( s_bMathlibInitialized );
	float sclp, sclq;
	int i;

	// 0.0 returns p, 1.0 return q.
	sclp = 1.0f - t;
	sclq = t;
	for (i = 0; i < 4; i++) {
		qt[i] = sclp * p[i] + sclq * q[i];
	}
	QuaternionNormalize( qt );
}



void QuaternionIdentityBlend( const Quaternion &p, float t, Quaternion &qt )
{
	Assert( s_bMathlibInitialized );
	float sclp;

	sclp = 1.0f - t;

	qt.x = p.x * sclp;
	qt.y = p.y * sclp;
	qt.z = p.z * sclp;
	if (qt.w < 0.0)
	{
		qt.w = p.w * sclp - t;
	}
	else
	{
		qt.w = p.w * sclp + t;
	}
	QuaternionNormalize( qt );
}

//-----------------------------------------------------------------------------
// Quaternion sphereical linear interpolation
//-----------------------------------------------------------------------------

void QuaternionSlerp( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt )
{
	Quaternion q2;
	// 0.0 returns p, 1.0 return q.

	// decide if one of the quaternions is backwards
	QuaternionAlign( p, q, q2 );

	QuaternionSlerpNoAlign( p, q2, t, qt );
}


void QuaternionSlerpNoAlign( const Quaternion &p, const Quaternion &q, float t, Quaternion &qt )
{
	Assert( s_bMathlibInitialized );
	float omega, cosom, sinom, sclp, sclq;
	int i;

	// 0.0 returns p, 1.0 return q.

	cosom = p[0]*q[0] + p[1]*q[1] + p[2]*q[2] + p[3]*q[3];

	if ((1.0f + cosom) > 0.000001f) {
		if ((1.0f - cosom) > 0.000001f) {
			omega = acos( cosom );
			sinom = sin( omega );
			sclp = sin( (1.0f - t)*omega) / sinom;
			sclq = sin( t*omega ) / sinom;
		}
		else {
			// TODO: add short circuit for cosom == 1.0f?
			sclp = 1.0f - t;
			sclq = t;
		}
		for (i = 0; i < 4; i++) {
			qt[i] = sclp * p[i] + sclq * q[i];
		}
	}
	else {
		Assert( &qt != &q );

		qt[0] = -q[1];
		qt[1] = q[0];
		qt[2] = -q[3];
		qt[3] = q[2];
		sclp = sin( (1.0f - t) * (0.5f * M_PI));
		sclq = sin( t * (0.5f * M_PI));
		for (i = 0; i < 3; i++) {
			qt[i] = sclp * p[i] + sclq * qt[i];
		}
	}

	Assert( qt.IsValid() );
}


//-----------------------------------------------------------------------------
// Purpose: Returns the angular delta between the two normalized quaternions in degrees.
//-----------------------------------------------------------------------------
float QuaternionAngleDiff( const Quaternion &p, const Quaternion &q )
{
#if 1
	// this code path is here for 2 reasons:
	// 1 - acos maps 1-epsilon to values much larger than epsilon (vs asin, which maps epsilon to itself)
	//     this means that in floats, anything below ~0.05 degrees truncates to 0
	// 2 - normalized quaternions are frequently slightly non-normalized due to float precision issues,
	//     and the epsilon off of normalized can be several percents of a degree
	Quaternion qInv, diff;
	QuaternionConjugate( q, qInv );
	QuaternionMult( p, qInv, diff );

	// Note if the quaternion is slightly non-normalized the square root below may be more than 1,
	// the value is clamped to one otherwise it may result in asin() returning an undefined result.
	float sinang = MIN( 1.0f, sqrt( diff.x * diff.x + diff.y * diff.y + diff.z * diff.z ) );
	float angle = RAD2DEG( 2 * asin( sinang ) );
	return angle;
#else
	Quaternion q2;
	QuaternionAlign( p, q, q2 );

	Assert( s_bMathlibInitialized );
	float cosom = p.x * q2.x + p.y * q2.y + p.z * q2.z + p.w * q2.w;

	if ( cosom > -1.0f )
	{
		if ( cosom < 1.0f )
		{
			float omega = 2 * fabs( acos( cosom ) );
			return RAD2DEG( omega );
		}
		return 0.0f;
	}

	return 180.0f;
#endif
}

void QuaternionConjugate( const Quaternion &p, Quaternion &q )
{
	Assert( s_bMathlibInitialized );
	Assert( q.IsValid() );

	q.x = -p.x;
	q.y = -p.y;
	q.z = -p.z;
	q.w = p.w;
}

void QuaternionInvert( const Quaternion &p, Quaternion &q )
{
	Assert( s_bMathlibInitialized );
	Assert( q.IsValid() );

	QuaternionConjugate( p, q );

	float magnitudeSqr = QuaternionDotProduct( p, p );
	Assert( magnitudeSqr );
	if ( magnitudeSqr )
	{
		float inv = 1.0f / magnitudeSqr;
		q.x *= inv;
		q.y *= inv;
		q.z *= inv;
		q.w *= inv;
	}
}

//-----------------------------------------------------------------------------
// Make sure the quaternion is of unit length
//-----------------------------------------------------------------------------
float QuaternionNormalize( Quaternion &q )
{
	Assert( s_bMathlibInitialized );
	float radius, iradius;

	Assert( q.IsValid() );

	radius = q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];

	if ( radius ) // > FLT_EPSILON && ((radius < 1.0f - 4*FLT_EPSILON) || (radius > 1.0f + 4*FLT_EPSILON))
	{
		radius = sqrt(radius);
		iradius = 1.0f/radius;
		q[3] *= iradius;
		q[2] *= iradius;
		q[1] *= iradius;
		q[0] *= iradius;
	}
	return radius;
}


void QuaternionScale( const Quaternion &p, float t, Quaternion &q )
{
	Assert( s_bMathlibInitialized );

#if 0
	Quaternion p0;
	Quaternion q;
	p0.Init( 0.0, 0.0, 0.0, 1.0 );

	// slerp in "reverse order" so that p doesn't get realigned
	QuaternionSlerp( p, p0, 1.0 - fabs( t ), q );
	if (t < 0.0)
	{
		q.w = -q.w;
	}
#else
	float r;

	// FIXME: nick, this isn't overly sensitive to accuracy, and it may be faster to 
	// use the cos part (w) of the quaternion (sin(omega)*N,cos(omega)) to figure the new scale.
	float sinom = sqrt( DotProduct( &p.x, &p.x ) );
	sinom = min( sinom, 1.f );

	float sinsom = sin( asin( sinom ) * t );

	t = sinsom / (sinom + FLT_EPSILON);
	VectorScale( &p.x, t, &q.x );

	// rescale rotation
	r = 1.0f - sinsom * sinsom;

	// Assert( r >= 0 );
	if (r < 0.0f) 
		r = 0.0f;
	r = sqrt( r );

	// keep sign of rotation
	if (p.w < 0)
		q.w = -r;
	else
		q.w = r;
#endif

	Assert( q.IsValid() );

	return;
}


void QuaternionAdd( const Quaternion &p, const Quaternion &q, Quaternion &qt )
{
	Assert( s_bMathlibInitialized );
	Assert( p.IsValid() );
	Assert( q.IsValid() );

	// decide if one of the quaternions is backwards
	Quaternion q2;
	QuaternionAlign( p, q, q2 );

	// is this right???
	qt[0] = p[0] + q2[0];
	qt[1] = p[1] + q2[1];
	qt[2] = p[2] + q2[2];
	qt[3] = p[3] + q2[3];

	return;
}


float QuaternionDotProduct( const Quaternion &p, const Quaternion &q )
{
	Assert( s_bMathlibInitialized );
	Assert( p.IsValid() );
	Assert( q.IsValid() );

	return p.x * q.x + p.y * q.y + p.z * q.z + p.w * q.w;
}


// qt = p * q
void QuaternionMult( const Quaternion &p, const Quaternion &q, Quaternion &qt )
{
	Assert( s_bMathlibInitialized );
	Assert( p.IsValid() );
	Assert( q.IsValid() );

	if (&p == &qt)
	{
		Quaternion p2 = p;
		QuaternionMult( p2, q, qt );
		return;
	}

	// decide if one of the quaternions is backwards
	Quaternion q2;
	QuaternionAlign( p, q, q2 );

	qt.x =  p.x * q2.w + p.y * q2.z - p.z * q2.y + p.w * q2.x;
	qt.y = -p.x * q2.z + p.y * q2.w + p.z * q2.x + p.w * q2.y;
	qt.z =  p.x * q2.y - p.y * q2.x + p.z * q2.w + p.w * q2.z;
	qt.w = -p.x * q2.x - p.y * q2.y - p.z * q2.z + p.w * q2.w;
}


void QuaternionMatrix( const Quaternion &q, const Vector &pos, matrix3x4_t& matrix )
{
	if ( !HushAsserts() )
	{
		Assert( pos.IsValid() );
	}

	QuaternionMatrix( q, matrix );

	matrix[0][3] = pos.x;
	matrix[1][3] = pos.y;
	matrix[2][3] = pos.z;
}

void QuaternionMatrix( const Quaternion &q, matrix3x4_t& matrix )
{
	Assert( s_bMathlibInitialized );
	if ( !HushAsserts() )
	{
		Assert( q.IsValid() );
	}

#ifdef _VPROF_MATHLIB
	VPROF_BUDGET( "QuaternionMatrix", "Mathlib" );
#endif

// Original code
// This should produce the same code as below with optimization, but looking at the assmebly,
// it doesn't.  There are 7 extra multiplies in the release build of this, go figure.
#if 1
	matrix[0][0] = 1.0 - 2.0 * q.y * q.y - 2.0 * q.z * q.z;
	matrix[1][0] = 2.0 * q.x * q.y + 2.0 * q.w * q.z;
	matrix[2][0] = 2.0 * q.x * q.z - 2.0 * q.w * q.y;

	matrix[0][1] = 2.0f * q.x * q.y - 2.0f * q.w * q.z;
	matrix[1][1] = 1.0f - 2.0f * q.x * q.x - 2.0f * q.z * q.z;
	matrix[2][1] = 2.0f * q.y * q.z + 2.0f * q.w * q.x;

	matrix[0][2] = 2.0f * q.x * q.z + 2.0f * q.w * q.y;
	matrix[1][2] = 2.0f * q.y * q.z - 2.0f * q.w * q.x;
	matrix[2][2] = 1.0f - 2.0f * q.x * q.x - 2.0f * q.y * q.y;

	matrix[0][3] = 0.0f;
	matrix[1][3] = 0.0f;
	matrix[2][3] = 0.0f;
#else
   float wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;

    // precalculate common multiplitcations
    x2 = q.x + q.x; 
	y2 = q.y + q.y; 
    z2 = q.z + q.z;
    xx = q.x * x2;
	xy = q.x * y2;
	xz = q.x * z2;
    yy = q.y * y2;
	yz = q.y * z2;
	zz = q.z * z2;
    wx = q.w * x2;
	wy = q.w * y2;
	wz = q.w * z2;

    matrix[0][0] = 1.0 - (yy + zz);
    matrix[0][1] = xy - wz;
	matrix[0][2] = xz + wy;
    matrix[0][3] = 0.0f;

    matrix[1][0] = xy + wz;
	matrix[1][1] = 1.0 - (xx + zz);
    matrix[1][2] = yz - wx;
	matrix[1][3] = 0.0f;

    matrix[2][0] = xz - wy;
	matrix[2][1] = yz + wx;
    matrix[2][2] = 1.0 - (xx + yy);
	matrix[2][3] = 0.0f;
#endif
}


//-----------------------------------------------------------------------------
// Purpose: Converts a quaternion into engine angles
// Input  : *quaternion - q3 + q0.i + q1.j + q2.k
//			*outAngles - PITCH, YAW, ROLL
//-----------------------------------------------------------------------------
void QuaternionAngles( const Quaternion &q, QAngle &angles )
{
	Assert( s_bMathlibInitialized );
	Assert( q.IsValid() );

#ifdef _VPROF_MATHLIB
	VPROF_BUDGET( "QuaternionAngles", "Mathlib" );
#endif

#if 1
	// FIXME: doing it this way calculates too much data, needs to do an optimized version...
	matrix3x4_t matrix;
	QuaternionMatrix( q, matrix );
	MatrixAngles( matrix, angles );
#else
	float m11, m12, m13, m23, m33;

	m11 = ( 2.0f * q.w * q.w ) + ( 2.0f * q.x * q.x ) - 1.0f;
	m12 = ( 2.0f * q.x * q.y ) + ( 2.0f * q.w * q.z );
	m13 = ( 2.0f * q.x * q.z ) - ( 2.0f * q.w * q.y );
	m23 = ( 2.0f * q.y * q.z ) + ( 2.0f * q.w * q.x );
	m33 = ( 2.0f * q.w * q.w ) + ( 2.0f * q.z * q.z ) - 1.0f;

	// FIXME: this code has a singularity near PITCH +-90
	angles[YAW] = RAD2DEG( atan2(m12, m11) );
	angles[PITCH] = RAD2DEG( asin(-m13) );
	angles[ROLL] = RAD2DEG( atan2(m23, m33) );
#endif

	Assert( angles.IsValid() );
}

//-----------------------------------------------------------------------------
// Purpose: Converts a quaternion to an axis / angle in degrees
//			(exponential map)
//-----------------------------------------------------------------------------
void QuaternionAxisAngle( const Quaternion &q, Vector &axis, float &angle )
{
	angle = RAD2DEG(2 * acos(q.w));
	if ( angle > 180 )
	{
		angle -= 360;
	}
	axis.x = q.x;
	axis.y = q.y;
	axis.z = q.z;
	VectorNormalize( axis );
}

//-----------------------------------------------------------------------------
// Purpose: Converts an exponential map (ang/axis) to a quaternion
//-----------------------------------------------------------------------------
void AxisAngleQuaternion( const Vector &axis, float angle, Quaternion &q )
{
	float sa, ca;
	
	SinCos( DEG2RAD(angle) * 0.5f, &sa, &ca );
	
	q.x = axis.x * sa;
	q.y = axis.y * sa;
	q.z = axis.z * sa;
	q.w = ca;
}


//-----------------------------------------------------------------------------
// Purpose: Converts radian-euler axis aligned angles to a quaternion
// Input  : *pfAngles - Right-handed Euler angles in radians
//			*outQuat - quaternion of form (i,j,k,real)
//-----------------------------------------------------------------------------
void AngleQuaternion( const RadianEuler &angles, Quaternion &outQuat )
{
	Assert( s_bMathlibInitialized );
//	Assert( angles.IsValid() );

#ifdef _VPROF_MATHLIB
	VPROF_BUDGET( "AngleQuaternion", "Mathlib" );
#endif

	float sr, sp, sy, cr, cp, cy;

#ifdef _X360
	fltx4 radians, scale, sine, cosine;
	radians = LoadUnaligned3SIMD( &angles.x );
	scale = ReplicateX4( 0.5f ); 
	radians = MulSIMD( radians, scale );
	SinCos3SIMD( sine, cosine, radians ); 	

	// NOTE: The ordering here is *different* from the AngleQuaternion below
	// because p, y, r are not in the same locations in QAngle + RadianEuler. Yay!
	sr = SubFloat( sine, 0 );	sp = SubFloat( sine, 1 );	sy = SubFloat( sine, 2 );	
	cr = SubFloat( cosine, 0 );	cp = SubFloat( cosine, 1 );	cy = SubFloat( cosine, 2 );	
#else
	SinCos( angles.z * 0.5f, &sy, &cy );
	SinCos( angles.y * 0.5f, &sp, &cp );
	SinCos( angles.x * 0.5f, &sr, &cr );
#endif

	// NJS: for some reason VC6 wasn't recognizing the common subexpressions:
	float srXcp = sr * cp, crXsp = cr * sp;
	outQuat.x = srXcp*cy-crXsp*sy; // X
	outQuat.y = crXsp*cy+srXcp*sy; // Y

	float crXcp = cr * cp, srXsp = sr * sp;
	outQuat.z = crXcp*sy-srXsp*cy; // Z
	outQuat.w = crXcp*cy+srXsp*sy; // W (real component)
}


//-----------------------------------------------------------------------------
// Purpose: Converts engine-format euler angles to a quaternion
// Input  : angles - Right-handed Euler angles in degrees as follows:
//				[0]: PITCH: Clockwise rotation around the Y axis.
//				[1]: YAW:	Counterclockwise rotation around the Z axis.
//				[2]: ROLL:	Counterclockwise rotation around the X axis.
//			*outQuat - quaternion of form (i,j,k,real)
//-----------------------------------------------------------------------------
void AngleQuaternion( const QAngle &angles, Quaternion &outQuat )
{
#ifdef _VPROF_MATHLIB
	VPROF_BUDGET( "AngleQuaternion", "Mathlib" );
#endif

	float sr, sp, sy, cr, cp, cy;

#ifdef _X360
	fltx4 radians, scale, sine, cosine;
	radians = LoadUnaligned3SIMD( angles.Base() );
	scale = ReplicateX4( 0.5f * M_PI_F / 180.f ); 
	radians = MulSIMD( radians, scale );
	SinCos3SIMD( sine, cosine, radians ); 	

	// NOTE: The ordering here is *different* from the AngleQuaternion above
	// because p, y, r are not in the same locations in QAngle + RadianEuler. Yay!
	sp = SubFloat( sine, 0 );	sy = SubFloat( sine, 1 );	sr = SubFloat( sine, 2 );	
	cp = SubFloat( cosine, 0 );	cy = SubFloat( cosine, 1 );	cr = SubFloat( cosine, 2 );	
#else
	SinCos( DEG2RAD( angles.y ) * 0.5f, &sy, &cy );
	SinCos( DEG2RAD( angles.x ) * 0.5f, &sp, &cp );
	SinCos( DEG2RAD( angles.z ) * 0.5f, &sr, &cr );
#endif

	// NJS: for some reason VC6 wasn't recognizing the common subexpressions:
	float srXcp = sr * cp, crXsp = cr * sp;
	outQuat.x = srXcp*cy-crXsp*sy; // X
	outQuat.y = crXsp*cy+srXcp*sy; // Y

	float crXcp = cr * cp, srXsp = sr * sp;
	outQuat.z = crXcp*sy-srXsp*cy; // Z
	outQuat.w = crXcp*cy+srXsp*sy; // W (real component)
}


//-----------------------------------------------------------------------------
// Purpose: Converts a basis to a quaternion
//-----------------------------------------------------------------------------
void BasisToQuaternion( const Vector &vecForward, const Vector &vecRight, const Vector &vecUp, Quaternion &q )
{
	Assert( fabs( vecForward.LengthSqr() - 1.0f ) < 1e-3 );
	Assert( fabs( vecRight.LengthSqr() - 1.0f ) < 1e-3 );
	Assert( fabs( vecUp.LengthSqr() - 1.0f ) < 1e-3 );

	Vector vecLeft;
	VectorMultiply( vecRight, -1.0f, vecLeft );

	// FIXME: Don't know why, but this doesn't match at all with other result
	// so we can't use this super-fast way.
	/*
	// Find the trace of the matrix:
	float flTrace = vecForward.x + vecLeft.y + vecUp.z + 1.0f;
	if ( flTrace > 1e-6 )
	{
		float flSqrtTrace = FastSqrt( flTrace );
		float s = 0.5f / flSqrtTrace;
		q.x = ( vecUp.y - vecLeft.z ) * s;
		q.y = ( vecForward.z - vecUp.x ) * s;
		q.z = ( vecLeft.x - vecForward.y ) * s;
		q.w = 0.5f * flSqrtTrace;
	}
	else
	{
		if (( vecForward.x > vecLeft.y ) && ( vecForward.x > vecUp.z ) )
		{
			float flSqrtTrace = FastSqrt( 1.0f + vecForward.x - vecLeft.y - vecUp.z );
			float s = 0.5f / flSqrtTrace;
			q.x = 0.5f * flSqrtTrace;
			q.y = ( vecForward.y + vecLeft.x ) * s;
			q.z = ( vecUp.x + vecForward.z ) * s;
			q.w = ( vecUp.y - vecLeft.z ) * s;
		}
		else if ( vecLeft.y > vecUp.z )
		{
			float flSqrtTrace = FastSqrt( 1.0f + vecLeft.y - vecForward.x - vecUp.z );
			float s = 0.5f / flSqrtTrace;
			q.x = ( vecForward.y + vecLeft.x ) * s;
			q.y = 0.5f * flSqrtTrace;
			q.z = ( vecUp.y + vecLeft.z ) * s;
			q.w = ( vecForward.z - vecUp.x ) * s;
		}
		else
		{
			float flSqrtTrace = FastSqrt( 1.0 + vecUp.z - vecForward.x - vecLeft.y );
			float s = 0.5f / flSqrtTrace;
			q.x = ( vecUp.x + vecForward.z ) * s;
			q.y = ( vecUp.y + vecLeft.z ) * s;
			q.z = 0.5f * flSqrtTrace;
			q.w = ( vecLeft.x - vecForward.y ) * s;
		}
	}
	QuaternionNormalize( q );
	*/

	// Version 2: Go through angles

	matrix3x4_t mat;
	MatrixSetColumn( vecForward, 0, mat );
	MatrixSetColumn( vecLeft, 1, mat );
	MatrixSetColumn( vecUp, 2, mat );

	QAngle angles;
	MatrixAngles( mat, angles );

//	Quaternion q2;
	AngleQuaternion( angles, q );

//	Assert( fabs(q.x - q2.x) < 1e-3 );
//	Assert( fabs(q.y - q2.y) < 1e-3 );
//	Assert( fabs(q.z - q2.z) < 1e-3 );
//	Assert( fabs(q.w - q2.w) < 1e-3 );
}

// FIXME: Optimize!
void MatrixQuaternion( const matrix3x4_t &mat, Quaternion &q )
{
	QAngle angles;
	MatrixAngles( mat, angles );
	AngleQuaternion( angles, q );
}


//-----------------------------------------------------------------------------
// Purpose: Converts a quaternion into engine angles
// Input  : *quaternion - q3 + q0.i + q1.j + q2.k
//			*outAngles - PITCH, YAW, ROLL
//-----------------------------------------------------------------------------
void QuaternionAngles( const Quaternion &q, RadianEuler &angles )
{
	Assert( s_bMathlibInitialized );
	Assert( q.IsValid() );

	// FIXME: doing it this way calculates too much data, needs to do an optimized version...
	matrix3x4_t matrix;
	QuaternionMatrix( q, matrix );
	MatrixAngles( matrix, angles );

	Assert( angles.IsValid() );
}

//-----------------------------------------------------------------------------
// Purpose: A helper function to normalize p2.x->p1.x and p3.x->p4.x to 
//  be the same length as p2.x->p3.x
// Input  : &p2 - 
//			&p4 - 
//			p4n - 
//-----------------------------------------------------------------------------
void Spline_Normalize( 
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	Vector& p1n,
	Vector& p4n )
{
	float dt = p3.x - p2.x;

	p1n = p1;
	p4n = p4;

	if ( dt != 0.0 )
	{
		if (p1.x != p2.x)
		{
			// Equivalent to p1n = p2 - (p2 - p1) * (dt / (p2.x - p1.x));
			VectorLerp( p2, p1, dt / (p2.x - p1.x), p1n );
		}
		if (p4.x != p3.x)
		{
			// Equivalent to p4n = p3 + (p4 - p3) * (dt / (p4.x - p3.x));
			VectorLerp( p3, p4, dt / (p4.x - p3.x), p4n );
		}
	}
}

//-----------------------------------------------------------------------------
// Purpose: 
// Input  : 
//-----------------------------------------------------------------------------

void Catmull_Rom_Spline(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Assert( s_bMathlibInitialized );
	float tSqr = t*t*0.5f;
	float tSqrSqr = t*tSqr;
	t *= 0.5f;

	Assert( &output != &p1 );
	Assert( &output != &p2 );
	Assert( &output != &p3 );
	Assert( &output != &p4 );

	output.Init();

	Vector a, b, c, d;

	// matrix row 1
	VectorScale( p1, -tSqrSqr, a );		// 0.5 t^3 * [ (-1*p1) + ( 3*p2) + (-3*p3) + p4 ]
	VectorScale( p2, tSqrSqr*3, b );
	VectorScale( p3, tSqrSqr*-3, c );
	VectorScale( p4, tSqrSqr, d );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );
	VectorAdd( d, output, output );

	// matrix row 2
	VectorScale( p1, tSqr*2,  a );		// 0.5 t^2 * [ ( 2*p1) + (-5*p2) + ( 4*p3) - p4 ]
	VectorScale( p2, tSqr*-5, b );
	VectorScale( p3, tSqr*4,  c );
	VectorScale( p4, -tSqr,    d );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );
	VectorAdd( d, output, output );

	// matrix row 3
	VectorScale( p1, -t, a );			// 0.5 t * [ (-1*p1) + p3 ]
	VectorScale( p3, t,  b );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );

	// matrix row 4
	VectorAdd( p2, output, output );	// p2
}

void Catmull_Rom_Spline_Tangent(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Assert( s_bMathlibInitialized );
	float tOne = 3*t*t*0.5f;
	float tTwo = 2*t*0.5f;
	float tThree = 0.5;

	Assert( &output != &p1 );
	Assert( &output != &p2 );
	Assert( &output != &p3 );
	Assert( &output != &p4 );

	output.Init();

	Vector a, b, c, d;

	// matrix row 1
	VectorScale( p1, -tOne, a );		// 0.5 t^3 * [ (-1*p1) + ( 3*p2) + (-3*p3) + p4 ]
	VectorScale( p2, tOne*3, b );
	VectorScale( p3, tOne*-3, c );
	VectorScale( p4, tOne, d );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );
	VectorAdd( d, output, output );

	// matrix row 2
	VectorScale( p1, tTwo*2,  a );		// 0.5 t^2 * [ ( 2*p1) + (-5*p2) + ( 4*p3) - p4 ]
	VectorScale( p2, tTwo*-5, b );
	VectorScale( p3, tTwo*4,  c );
	VectorScale( p4, -tTwo,    d );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );
	VectorAdd( d, output, output );

	// matrix row 3
	VectorScale( p1, -tThree, a );			// 0.5 t * [ (-1*p1) + p3 ]
	VectorScale( p3, tThree,  b );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
}

// area under the curve [0..t]
void Catmull_Rom_Spline_Integral( 
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	output = p2*t
			-0.25f*(p1 - p3)*t*t 
			+ (1.0f/6.0f)*(2.0f*p1 - 5.0f*p2 + 4.0f*p3 - p4)*t*t*t
			- 0.125f*(p1 - 3.0f*p2 + 3.0f*p3 - p4)*t*t*t*t;
}


// area under the curve [0..1]
void Catmull_Rom_Spline_Integral( 
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	Vector& output )
{
	output = (-0.25f * p1 + 3.25f * p2 + 3.25f * p3 - 0.25f * p4) * (1.0f / 6.0f);
}


void Catmull_Rom_Spline_Normalize(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
	float dt = p3.DistTo(p2);

	Vector p1n, p4n;
	VectorSubtract( p1, p2, p1n );
	VectorSubtract( p4, p3, p4n );

	VectorNormalize( p1n );
	VectorNormalize( p4n );

	VectorMA( p2, dt, p1n, p1n );
	VectorMA( p3, dt, p4n, p4n );
	
	Catmull_Rom_Spline( p1n, p2, p3, p4n, t, output );
}


void Catmull_Rom_Spline_Integral_Normalize(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
	float dt = p3.DistTo(p2);

	Vector p1n, p4n;
	VectorSubtract( p1, p2, p1n );
	VectorSubtract( p4, p3, p4n );

	VectorNormalize( p1n );
	VectorNormalize( p4n );

	VectorMA( p2, dt, p1n, p1n );
	VectorMA( p3, dt, p4n, p4n );
	
	Catmull_Rom_Spline_Integral( p1n, p2, p3, p4n, t, output );
}


void Catmull_Rom_Spline_NormalizeX(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Vector p1n, p4n;
	Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
	Catmull_Rom_Spline( p1n, p2, p3, p4n, t, output );
}


//-----------------------------------------------------------------------------
// Purpose: basic hermite spline.  t = 0 returns p1, t = 1 returns p2, 
//			d1 and d2 are used to entry and exit slope of curve
// Input  : 
//-----------------------------------------------------------------------------

void Hermite_Spline(
	const Vector &p1,
	const Vector &p2,
	const Vector &d1,
	const Vector &d2,
	float t, 
	Vector& output )
{
	Assert( s_bMathlibInitialized );
	float tSqr = t*t;
	float tCube = t*tSqr;

	Assert( &output != &p1 );
	Assert( &output != &p2 );
	Assert( &output != &d1 );
	Assert( &output != &d2 );

	float b1 = 2.0f*tCube-3.0f*tSqr+1.0f;
	float b2 = 1.0f - b1; // -2*tCube+3*tSqr;
	float b3 = tCube-2*tSqr+t;
	float b4 = tCube-tSqr;

	VectorScale( p1, b1, output );
	VectorMA( output, b2, p2, output );
	VectorMA( output, b3, d1, output );
	VectorMA( output, b4, d2, output );
}

float Hermite_Spline(
	float p1,
	float p2,
	float d1,
	float d2,
	float t )
{
	Assert( s_bMathlibInitialized );
	float output;
	float tSqr = t*t;
	float tCube = t*tSqr;

	float b1 = 2.0f*tCube-3.0f*tSqr+1.0f;
	float b2 = 1.0f - b1; // -2*tCube+3*tSqr;
	float b3 = tCube-2*tSqr+t;
	float b4 = tCube-tSqr;

	output = p1 * b1;
	output += p2 * b2;
	output += d1 * b3;
	output += d2 * b4;

	return output;
}


void Hermite_SplineBasis( float t, float basis[4] )
{
	float tSqr = t*t;
	float tCube = t*tSqr;

	basis[0] = 2.0f*tCube-3.0f*tSqr+1.0f;
	basis[1] = 1.0f - basis[0]; // -2*tCube+3*tSqr;
	basis[2] = tCube-2*tSqr+t;
	basis[3] = tCube-tSqr;
}

//-----------------------------------------------------------------------------
// Purpose: simple three data point hermite spline.  
//			t = 0 returns p1, t = 1 returns p2, 
//			slopes are generated from the p0->p1 and p1->p2 segments
//			this is reasonable C1 method when there's no "p3" data yet.
// Input  : 
//-----------------------------------------------------------------------------

// BUG: the VectorSubtract()'s calls go away if the global optimizer is enabled
#pragma optimize( "g", off )

void Hermite_Spline( const Vector &p0, const Vector &p1, const Vector &p2, float t, Vector& output )
{
	Vector e10, e21;
	VectorSubtract( p1, p0, e10 );
	VectorSubtract( p2, p1, e21 );
	Hermite_Spline( p1, p2, e10, e21, t, output );
}

#pragma optimize( "", on )

float Hermite_Spline( float p0, float p1, float p2,	float t )
{
	return Hermite_Spline( p1, p2, p1 - p0, p2 - p1, t );
}


void Hermite_Spline( const Quaternion &q0, const Quaternion &q1, const Quaternion &q2, float t, Quaternion &output )
{
	// cheap, hacked version of quaternions
	Quaternion q0a;
	Quaternion q1a;

	QuaternionAlign( q2, q0, q0a );
	QuaternionAlign( q2, q1, q1a );

	output.x = Hermite_Spline( q0a.x, q1a.x, q2.x, t );
	output.y = Hermite_Spline( q0a.y, q1a.y, q2.y, t );
	output.z = Hermite_Spline( q0a.z, q1a.z, q2.z, t );
	output.w = Hermite_Spline( q0a.w, q1a.w, q2.w, t );

	QuaternionNormalize( output );
}

// See http://en.wikipedia.org/wiki/Kochanek-Bartels_curves
// 
// Tension:  -1 = Round -> 1 = Tight
// Bias:     -1 = Pre-shoot (bias left) -> 1 = Post-shoot (bias right)
// Continuity: -1 = Box corners -> 1 = Inverted corners
//
// If T=B=C=0 it's the same matrix as Catmull-Rom.
// If T=1 & B=C=0 it's the same as Cubic.
// If T=B=0 & C=-1 it's just linear interpolation
// 
// See http://news.povray.org/povray.binaries.tutorials/attachment/%3CXns91B880592482seed7@povray.org%3E/Splines.bas.txt
// for example code and descriptions of various spline types...
// 
void Kochanek_Bartels_Spline(
	float tension, 
	float bias, 
	float continuity,
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Assert( s_bMathlibInitialized );

	float ffa, ffb, ffc, ffd;

	ffa = ( 1.0f - tension ) * ( 1.0f + continuity ) * ( 1.0f + bias );
	ffb = ( 1.0f - tension ) * ( 1.0f - continuity ) * ( 1.0f - bias );
	ffc = ( 1.0f - tension ) * ( 1.0f - continuity ) * ( 1.0f + bias );
	ffd = ( 1.0f - tension ) * ( 1.0f + continuity ) * ( 1.0f - bias );

	float tSqr = t*t*0.5f;
	float tSqrSqr = t*tSqr;
	t *= 0.5f;

	Assert( &output != &p1 );
	Assert( &output != &p2 );
	Assert( &output != &p3 );
	Assert( &output != &p4 );

	output.Init();

	Vector a, b, c, d;

	// matrix row 1
	VectorScale( p1, tSqrSqr * -ffa, a );		
	VectorScale( p2, tSqrSqr * ( 4.0f + ffa - ffb - ffc ), b );
	VectorScale( p3, tSqrSqr * ( -4.0f + ffb + ffc - ffd ), c );
	VectorScale( p4, tSqrSqr * ffd, d );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );
	VectorAdd( d, output, output );

	// matrix row 2
	VectorScale( p1, tSqr* 2 * ffa,  a );		
	VectorScale( p2, tSqr * ( -6 - 2 * ffa + 2 * ffb + ffc ), b );
	VectorScale( p3, tSqr * ( 6 - 2 * ffb - ffc + ffd ),  c );
	VectorScale( p4, tSqr * -ffd,    d );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );
	VectorAdd( d, output, output );

	// matrix row 3
	VectorScale( p1, t * -ffa,  a );		
	VectorScale( p2, t * ( ffa - ffb ), b );
	VectorScale( p3, t * ffb,  c );
	// p4 unchanged

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );

	// matrix row 4
	// p1, p3, p4 unchanged
	// p2 is multiplied by 1 and added, so just added it directly

	VectorAdd( p2, output, output );
}

void Kochanek_Bartels_Spline_NormalizeX(
	float tension, 
	float bias, 
	float continuity,
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Vector p1n, p4n;
	Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
	Kochanek_Bartels_Spline( tension, bias, continuity, p1n, p2, p3, p4n, t, output );
}

void Cubic_Spline(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Assert( s_bMathlibInitialized );

	float tSqr = t*t;
	float tSqrSqr = t*tSqr;

	Assert( &output != &p1 );
	Assert( &output != &p2 );
	Assert( &output != &p3 );
	Assert( &output != &p4 );

	output.Init();

	Vector a, b, c, d;

	// matrix row 1
	VectorScale( p2, tSqrSqr * 2, b );
	VectorScale( p3, tSqrSqr * -2, c );

	VectorAdd( b, output, output );
	VectorAdd( c, output, output );

	// matrix row 2
	VectorScale( p2, tSqr * -3, b );
	VectorScale( p3, tSqr * 3,  c );

	VectorAdd( b, output, output );
	VectorAdd( c, output, output );

	// matrix row 3
	// no influence
	// p4 unchanged

	// matrix row 4
	// p1, p3, p4 unchanged
	VectorAdd( p2, output, output );
}

void Cubic_Spline_NormalizeX(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Vector p1n, p4n;
	Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
	Cubic_Spline( p1n, p2, p3, p4n, t, output );
}

void BSpline(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Assert( s_bMathlibInitialized );

	float oneOver6 = 1.0f / 6.0f;

	float tSqr = t * t * oneOver6;
	float tSqrSqr = t*tSqr;
	t *= oneOver6;

	Assert( &output != &p1 );
	Assert( &output != &p2 );
	Assert( &output != &p3 );
	Assert( &output != &p4 );

	output.Init();

	Vector a, b, c, d;

	// matrix row 1
	VectorScale( p1, -tSqrSqr, a );		
	VectorScale( p2, tSqrSqr * 3.0f, b );
	VectorScale( p3, tSqrSqr * -3.0f, c );
	VectorScale( p4, tSqrSqr, d );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );
	VectorAdd( d, output, output );

	// matrix row 2
	VectorScale( p1, tSqr * 3.0f,  a );		
	VectorScale( p2, tSqr * -6.0f, b );
	VectorScale( p3, tSqr * 3.0f,  c );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );

	// matrix row 3
	VectorScale( p1, t * -3.0f,  a );		
	VectorScale( p3, t * 3.0f,  c );
	// p4 unchanged

	VectorAdd( a, output, output );
	VectorAdd( c, output, output );

	// matrix row 4
	// p1 and p3 scaled by 1.0f, so done below
	VectorScale( p1, oneOver6, a );
	VectorScale( p2, 4.0f * oneOver6, b );
	VectorScale( p3, oneOver6, c );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );
}

void BSpline_NormalizeX(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Vector p1n, p4n;
	Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
	BSpline( p1n, p2, p3, p4n, t, output );
}

void Parabolic_Spline(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Assert( s_bMathlibInitialized );

	float tSqr = t*t*0.5f;
	t *= 0.5f;

	Assert( &output != &p1 );
	Assert( &output != &p2 );
	Assert( &output != &p3 );
	Assert( &output != &p4 );

	output.Init();

	Vector a, b, c, d;

	// matrix row 1
	// no influence from t cubed

	// matrix row 2
	VectorScale( p1, tSqr,  a );		
	VectorScale( p2, tSqr * -2.0f, b );
	VectorScale( p3, tSqr,  c );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
	VectorAdd( c, output, output );

	// matrix row 3
	VectorScale( p1, t * -2.0f,  a );		
	VectorScale( p2, t * 2.0f,  b );
	// p4 unchanged

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );

	// matrix row 4
	VectorScale( p1, 0.5f,  a );		
	VectorScale( p2, 0.5f,  b );

	VectorAdd( a, output, output );
	VectorAdd( b, output, output );
}

void Parabolic_Spline_NormalizeX(
	const Vector &p1,
	const Vector &p2,
	const Vector &p3,
	const Vector &p4,
	float t, 
	Vector& output )
{
	Vector p1n, p4n;
	Spline_Normalize( p1, p2, p3, p4, p1n, p4n );
	Parabolic_Spline( p1n, p2, p3, p4n, t, output );
}

//-----------------------------------------------------------------------------
// Purpose: Compress the input values for a ranged result such that from 75% to 200% smoothly of the range maps 
//-----------------------------------------------------------------------------

float RangeCompressor( float flValue, float flMin, float flMax, float flBase )
{
	// clamp base
	if (flBase < flMin)
		flBase = flMin;
	if (flBase > flMax)
		flBase = flMax;

	flValue += flBase;

	// convert to 0 to 1 value
	float flMid = (flValue - flMin) / (flMax - flMin);
	// convert to -1 to 1 value
	float flTarget = flMid * 2 - 1;

	if (fabs(flTarget) > 0.75)
	{
		float t = (fabs(flTarget) - 0.75) / (1.25);
		if (t < 1.0)
		{
			if (flTarget > 0)
			{
				flTarget = Hermite_Spline( 0.75, 1, 0.75, 0, t );
			}
			else
			{
				flTarget = -Hermite_Spline( 0.75, 1, 0.75, 0, t );
			}
		}
		else
		{
			flTarget = (flTarget > 0) ? 1.0f : -1.0f;
		}
	}

	flMid = (flTarget + 1 ) / 2.0;
	flValue = flMin * (1 - flMid) + flMax * flMid;

	flValue -= flBase;

	return flValue;
}


//#pragma optimize( "", on )

//-----------------------------------------------------------------------------
// Transforms a AABB into another space; which will inherently grow the box.
//-----------------------------------------------------------------------------
void TransformAABB( const matrix3x4_t& transform, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut )
{
	Vector localCenter;
	VectorAdd( vecMinsIn, vecMaxsIn, localCenter );
	localCenter *= 0.5f;

	Vector localExtents;
	VectorSubtract( vecMaxsIn, localCenter, localExtents );

	Vector worldCenter;
	VectorTransform( localCenter, transform, worldCenter );

	Vector worldExtents;
	worldExtents.x = DotProductAbs( localExtents, transform[0] );
	worldExtents.y = DotProductAbs( localExtents, transform[1] );
	worldExtents.z = DotProductAbs( localExtents, transform[2] );

	VectorSubtract( worldCenter, worldExtents, vecMinsOut );
	VectorAdd( worldCenter, worldExtents, vecMaxsOut );
}


//-----------------------------------------------------------------------------
// Uses the inverse transform of in1
//-----------------------------------------------------------------------------
void ITransformAABB( const matrix3x4_t& transform, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut )
{
	Vector worldCenter;
	VectorAdd( vecMinsIn, vecMaxsIn, worldCenter );
	worldCenter *= 0.5f;

	Vector worldExtents;
	VectorSubtract( vecMaxsIn, worldCenter, worldExtents );

	Vector localCenter;
	VectorITransform( worldCenter, transform, localCenter );

	Vector localExtents;
	localExtents.x =	FloatMakePositive( worldExtents.x * transform[0][0] ) + 
						FloatMakePositive( worldExtents.y * transform[1][0] ) + 
						FloatMakePositive( worldExtents.z * transform[2][0] );
	localExtents.y =	FloatMakePositive( worldExtents.x * transform[0][1] ) + 
						FloatMakePositive( worldExtents.y * transform[1][1] ) + 
						FloatMakePositive( worldExtents.z * transform[2][1] );
	localExtents.z =	FloatMakePositive( worldExtents.x * transform[0][2] ) + 
						FloatMakePositive( worldExtents.y * transform[1][2] ) + 
						FloatMakePositive( worldExtents.z * transform[2][2] );

	VectorSubtract( localCenter, localExtents, vecMinsOut );
	VectorAdd( localCenter, localExtents, vecMaxsOut );
}


//-----------------------------------------------------------------------------
// Rotates a AABB into another space; which will inherently grow the box. 
// (same as TransformAABB, but doesn't take the translation into account)
//-----------------------------------------------------------------------------
void RotateAABB( const matrix3x4_t &transform, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut )
{
	Vector localCenter;
	VectorAdd( vecMinsIn, vecMaxsIn, localCenter );
	localCenter *= 0.5f;

	Vector localExtents;
	VectorSubtract( vecMaxsIn, localCenter, localExtents );

	Vector newCenter;
	VectorRotate( localCenter, transform, newCenter );

	Vector newExtents;
	newExtents.x = DotProductAbs( localExtents, transform[0] );
	newExtents.y = DotProductAbs( localExtents, transform[1] );
	newExtents.z = DotProductAbs( localExtents, transform[2] );

	VectorSubtract( newCenter, newExtents, vecMinsOut );
	VectorAdd( newCenter, newExtents, vecMaxsOut );
}


//-----------------------------------------------------------------------------
// Uses the inverse transform of in1
//-----------------------------------------------------------------------------
void IRotateAABB( const matrix3x4_t &transform, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut )
{
	Vector oldCenter;
	VectorAdd( vecMinsIn, vecMaxsIn, oldCenter );
	oldCenter *= 0.5f;

	Vector oldExtents;
	VectorSubtract( vecMaxsIn, oldCenter, oldExtents );

	Vector newCenter;
	VectorIRotate( oldCenter, transform, newCenter );

	Vector newExtents;
	newExtents.x =	FloatMakePositive( oldExtents.x * transform[0][0] ) + 
					FloatMakePositive( oldExtents.y * transform[1][0] ) + 
					FloatMakePositive( oldExtents.z * transform[2][0] );
	newExtents.y =	FloatMakePositive( oldExtents.x * transform[0][1] ) + 
					FloatMakePositive( oldExtents.y * transform[1][1] ) + 
					FloatMakePositive( oldExtents.z * transform[2][1] );
	newExtents.z =	FloatMakePositive( oldExtents.x * transform[0][2] ) + 
					FloatMakePositive( oldExtents.y * transform[1][2] ) + 
					FloatMakePositive( oldExtents.z * transform[2][2] );

	VectorSubtract( newCenter, newExtents, vecMinsOut );
	VectorAdd( newCenter, newExtents, vecMaxsOut );
}


float CalcSqrDistanceToAABB( const Vector &mins, const Vector &maxs, const Vector &point )
{
	float flDelta;
	float flDistSqr = 0.0f;

	if ( point.x < mins.x )
	{
		flDelta = (mins.x - point.x);
		flDistSqr += flDelta * flDelta;
	}
	else if ( point.x > maxs.x )
	{
		flDelta = (point.x - maxs.x);
		flDistSqr += flDelta * flDelta;
	}

	if ( point.y < mins.y )
	{
		flDelta = (mins.y - point.y);
		flDistSqr += flDelta * flDelta;
	}
	else if ( point.y > maxs.y )
	{
		flDelta = (point.y - maxs.y);
		flDistSqr += flDelta * flDelta;
	}

	if ( point.z < mins.z )
	{
		flDelta = (mins.z - point.z);
		flDistSqr += flDelta * flDelta;
	}
	else if ( point.z > maxs.z )
	{
		flDelta = (point.z - maxs.z);
		flDistSqr += flDelta * flDelta;
	}

	return flDistSqr;
}


void CalcClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut )
{
	closestOut.x = clamp( point.x, mins.x, maxs.x );
	closestOut.y = clamp( point.y, mins.y, maxs.y );
	closestOut.z = clamp( point.z, mins.z, maxs.z );
}

void CalcSqrDistAndClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut, float &distSqrOut )
{
	distSqrOut = 0.0f;
	for ( int i = 0; i < 3; i++ )
	{
		if ( point[i] < mins[i] )
		{
			closestOut[i] = mins[i];
			float flDelta = closestOut[i] - mins[i];
			distSqrOut += flDelta * flDelta;
		}
		else if ( point[i] > maxs[i] )
		{
			closestOut[i] = maxs[i];
			float flDelta = closestOut[i] - maxs[i];
			distSqrOut += flDelta * flDelta;
		}
		else
		{
			closestOut[i] = point[i];
		}
	}

}

float CalcClosestPointToLineT( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vDir )
{
	Assert( s_bMathlibInitialized );
	VectorSubtract( vLineB, vLineA, vDir );

	// D dot [P - (A + D*t)] = 0
	// t = ( DP - DA) / DD
	float div = vDir.Dot( vDir );
	if( div < 0.00001f )
	{
		return 0;
	}
	else
	{
		return (vDir.Dot( P ) - vDir.Dot( vLineA )) / div;
	}
}

void CalcClosestPointOnLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector vDir;
	float t = CalcClosestPointToLineT( P, vLineA, vLineB, vDir );
	if ( outT ) *outT = t;
	vClosest.MulAdd( vLineA, vDir, t );
}


float CalcDistanceToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector vClosest;
	CalcClosestPointOnLine( P, vLineA, vLineB, vClosest, outT );
	return P.DistTo(vClosest);
}

float CalcDistanceSqrToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector vClosest;
	CalcClosestPointOnLine( P, vLineA, vLineB, vClosest, outT );
	return P.DistToSqr(vClosest);
}

void CalcClosestPointOnLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *outT )
{
	Vector vDir;
	float t = CalcClosestPointToLineT( P, vLineA, vLineB, vDir );
	t = clamp( t, 0.f, 1.f );
	if ( outT ) 
	{
		*outT = t;
	}
	vClosest.MulAdd( vLineA, vDir, t );
}


float CalcDistanceToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector vClosest;
	CalcClosestPointOnLineSegment( P, vLineA, vLineB, vClosest, outT );
	return P.DistTo( vClosest );
}

float CalcDistanceSqrToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector vClosest;
	CalcClosestPointOnLineSegment( P, vLineA, vLineB, vClosest, outT );
	return P.DistToSqr(vClosest);
}

float CalcClosestPointToLineT2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, Vector2D &vDir )
{
	Assert( s_bMathlibInitialized );
	Vector2DSubtract( vLineB, vLineA, vDir );

	// D dot [P - (A + D*t)] = 0
	// t = (DP - DA) / DD
	float div = vDir.Dot( vDir );
	if( div < 0.00001f )
	{
		return 0;
	}
	else
	{
		return (vDir.Dot( P ) - vDir.Dot( vLineA )) / div;
	}
}

void CalcClosestPointOnLine2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, Vector2D &vClosest, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector2D vDir;
	float t = CalcClosestPointToLineT2D( P, vLineA, vLineB, vDir );
	if ( outT ) *outT = t;
	vClosest.MulAdd( vLineA, vDir, t );
}

float CalcDistanceToLine2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector2D vClosest;
	CalcClosestPointOnLine2D( P, vLineA, vLineB, vClosest, outT );
	return P.DistTo( vClosest );
}

float CalcDistanceSqrToLine2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector2D vClosest;
	CalcClosestPointOnLine2D( P, vLineA, vLineB, vClosest, outT );
	return P.DistToSqr(vClosest);
}

void CalcClosestPointOnLineSegment2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, Vector2D &vClosest, float *outT )
{
	Vector2D vDir;
	float t = CalcClosestPointToLineT2D( P, vLineA, vLineB, vDir );
	t = clamp( t, 0.f, 1.f );
	if ( outT )
	{
		*outT = t;
	}
	vClosest.MulAdd( vLineA, vDir, t );
}

float CalcDistanceToLineSegment2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector2D vClosest;
	CalcClosestPointOnLineSegment2D( P, vLineA, vLineB, vClosest, outT );
	return P.DistTo( vClosest );
}

float CalcDistanceSqrToLineSegment2D( const Vector2D &P, const Vector2D &vLineA, const Vector2D &vLineB, float *outT )
{
	Assert( s_bMathlibInitialized );
	Vector2D vClosest;
	CalcClosestPointOnLineSegment2D( P, vLineA, vLineB, vClosest, outT );
	return P.DistToSqr( vClosest );
}

// Do we have another epsilon we could use
#define LINE_EPS ( 0.000001f )

//-----------------------------------------------------------------------------
// Purpose: Given lines p1->p2 and p3->p4, computes a line segment (pa->pb) and returns the parameters 0->1 multipliers
//  along each segment for the returned points
// Input  : p1 - 
//			p2 - 
//			p3 - 
//			p4 - 
//			*s1 - 
//			*s2 - 
// Output : Returns true on success, false on failure.
//-----------------------------------------------------------------------------
bool CalcLineToLineIntersectionSegment(
   const Vector& p1,const Vector& p2,const Vector& p3,const Vector& p4,Vector *s1,Vector *s2,
   float *t1, float *t2)
{
   Vector p13,p43,p21;
   float d1343,d4321,d1321,d4343,d2121;
   float numer,denom;

   p13.x = p1.x - p3.x;
   p13.y = p1.y - p3.y;
   p13.z = p1.z - p3.z;
   p43.x = p4.x - p3.x;
   p43.y = p4.y - p3.y;
   p43.z = p4.z - p3.z;

   if (fabs(p43.x)  < LINE_EPS && fabs(p43.y)  < LINE_EPS && fabs(p43.z)  < LINE_EPS)
      return false;
   p21.x = p2.x - p1.x;
   p21.y = p2.y - p1.y;
   p21.z = p2.z - p1.z;
   if (fabs(p21.x)  < LINE_EPS && fabs(p21.y)  < LINE_EPS && fabs(p21.z)  < LINE_EPS)
      return false;

   d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z;
   d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z;
   d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z;
   d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z;
   d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z;

   denom = d2121 * d4343 - d4321 * d4321;
   if (fabs(denom) < LINE_EPS)
      return false;
   numer = d1343 * d4321 - d1321 * d4343;

   *t1 = numer / denom;
   *t2 = (d1343 + d4321 * (*t1)) / d4343;

   s1->x = p1.x + *t1 * p21.x;
   s1->y = p1.y + *t1 * p21.y;
   s1->z = p1.z + *t1 * p21.z;
   s2->x = p3.x + *t2 * p43.x;
   s2->y = p3.y + *t2 * p43.y;
   s2->z = p3.z + *t2 * p43.z;

   return true;
}

#pragma optimize( "", off )

#ifndef EXCEPTION_EXECUTE_HANDLER
#define EXCEPTION_EXECUTE_HANDLER       1
#endif

#pragma optimize( "", on )

static bool s_b3DNowEnabled = false;
static bool s_bMMXEnabled = false;
static bool s_bSSEEnabled = false;
static bool s_bSSE2Enabled = false;

void MathLib_Init( float gamma, float texGamma, float brightness, int overbright, bool bAllow3DNow, bool bAllowSSE, bool bAllowSSE2, bool bAllowMMX )
{
	if ( s_bMathlibInitialized )
		return;

	// FIXME: Hook SSE into VectorAligned + Vector4DAligned

#if !defined( _X360 )
	// Grab the processor information:
	const CPUInformation& pi = *GetCPUInformation();

	// Select the default generic routines.
	pfSqrt = _sqrtf;
	pfRSqrt = _rsqrtf;
	pfRSqrtFast = _rsqrtf;
	pfVectorNormalize = _VectorNormalize;
	pfVectorNormalizeFast = _VectorNormalizeFast;
	pfInvRSquared = _InvRSquared;
	pfFastSinCos = SinCos;
	pfFastCos = cosf;

	if ( bAllowMMX && pi.m_bMMX )
	{
		// Select the MMX specific routines if available
		// (MMX routines were used by SW span fillers - not currently used for HW)
		s_bMMXEnabled = true;
	}
	else
	{
		s_bMMXEnabled = false;
	}

	// SSE Generally performs better than 3DNow when present, so this is placed 
	// first to allow SSE to override these settings.
#if !defined( OSX ) && !defined( PLATFORM_WINDOWS_PC64 ) && !defined(LINUX) && !defined(PLATFORM_BSD)
	if ( bAllow3DNow && pi.m_b3DNow )
	{
		s_b3DNowEnabled = true;

		// Select the 3DNow specific routines if available;
		pfVectorNormalize = _3DNow_VectorNormalize;
		pfVectorNormalizeFast = _3DNow_VectorNormalizeFast;
		pfInvRSquared = _3DNow_InvRSquared;
		pfSqrt = _3DNow_Sqrt;
		pfRSqrt = _3DNow_RSqrt;
		pfRSqrtFast = _3DNow_RSqrt;
	}
	else
#endif
	{
		s_b3DNowEnabled = false;
	}

	if ( bAllowSSE && pi.m_bSSE )
	{
		s_bSSEEnabled = true;

#ifndef PLATFORM_WINDOWS_PC64
		// These are not yet available.
		// Select the SSE specific routines if available
		pfVectorNormalize = _VectorNormalize;
		pfVectorNormalizeFast = _SSE_VectorNormalizeFast;
		pfInvRSquared = _SSE_InvRSquared;
		pfSqrt = _SSE_Sqrt;
		pfRSqrt = _SSE_RSqrtAccurate;
		pfRSqrtFast = _SSE_RSqrtFast;
#endif
#ifdef PLATFORM_WINDOWS_PC32
		pfFastSinCos = _SSE_SinCos;
		pfFastCos = _SSE_cos;
#endif
	}
	else
	{
		s_bSSEEnabled = false;
	}

	if ( bAllowSSE2 && pi.m_bSSE2 )
	{
		s_bSSE2Enabled = true;
#ifdef PLATFORM_WINDOWS_PC32
		pfFastSinCos = _SSE2_SinCos;
		pfFastCos = _SSE2_cos;
#endif
	} 
	else
	{
		s_bSSE2Enabled = false;
	}
#endif // !_X360

	s_bMathlibInitialized = true;

	InitSinCosTable();
	BuildGammaTable( gamma, texGamma, brightness, overbright );
}

bool MathLib_3DNowEnabled( void )
{
	Assert( s_bMathlibInitialized );
	return s_b3DNowEnabled;
}

bool MathLib_MMXEnabled( void )
{
	Assert( s_bMathlibInitialized );
	return s_bMMXEnabled;
}

bool MathLib_SSEEnabled( void )
{
	Assert( s_bMathlibInitialized );
	return s_bSSEEnabled;
}

bool MathLib_SSE2Enabled( void )
{
	Assert( s_bMathlibInitialized );
	return s_bSSE2Enabled;
}

float Approach( float target, float value, float speed )
{
	float delta = target - value;

	if ( delta > speed )
		value += speed;
	else if ( delta < -speed )
		value -= speed;
	else 
		value = target;

	return value;
}

// BUGBUG: Why doesn't this call angle diff?!?!?
float ApproachAngle( float target, float value, float speed )
{
	target = anglemod( target );
	value = anglemod( value );
	
	float delta = target - value;

	// Speed is assumed to be positive
	if ( speed < 0 )
		speed = -speed;

	if ( delta < -180 )
		delta += 360;
	else if ( delta > 180 )
		delta -= 360;

	if ( delta > speed )
		value += speed;
	else if ( delta < -speed )
		value -= speed;
	else 
		value = target;

	return value;
}


// BUGBUG: Why do we need both of these?
float AngleDiff( float destAngle, float srcAngle )
{
	float delta;

	delta = fmodf(destAngle - srcAngle, 360.0f);
	if ( destAngle > srcAngle )
	{
		if ( delta >= 180 )
			delta -= 360;
	}
	else
	{
		if ( delta <= -180 )
			delta += 360;
	}
	return delta;
}


float AngleDistance( float next, float cur )
{
	float delta = next - cur;

	if ( delta < -180 )
		delta += 360;
	else if ( delta > 180 )
		delta -= 360;

	return delta;
}


float AngleNormalize( float angle )
{
	angle = fmodf(angle, 360.0f);
	if (angle > 180) 
	{
		angle -= 360;
	}
	if (angle < -180)
	{
		angle += 360;
	}
	return angle;
}

//--------------------------------------------------------------------------------------------------------------
// ensure that 0 <= angle <= 360
float AngleNormalizePositive( float angle )
{
	angle = fmodf( angle, 360.0f );

	if (angle < 0.0f)
	{
		angle += 360.0f;
	}

	return angle;
}

//--------------------------------------------------------------------------------------------------------------
bool AnglesAreEqual( float a, float b, float tolerance )
{
	return (fabs( AngleDiff( a, b ) ) < tolerance);
}

void RotationDeltaAxisAngle( const QAngle &srcAngles, const QAngle &destAngles, Vector &deltaAxis, float &deltaAngle )
{
	Quaternion srcQuat, destQuat, srcQuatInv, out;
	AngleQuaternion( srcAngles, srcQuat );
	AngleQuaternion( destAngles, destQuat );
	QuaternionScale( srcQuat, -1, srcQuatInv );
	QuaternionMult( destQuat, srcQuatInv, out );

	QuaternionNormalize( out );
	QuaternionAxisAngle( out, deltaAxis, deltaAngle );
}

void RotationDelta( const QAngle &srcAngles, const QAngle &destAngles, QAngle *out )
{
	matrix3x4_t src, srcInv;
	matrix3x4_t dest;
	AngleMatrix( srcAngles, src );
	AngleMatrix( destAngles, dest );
	// xform = src(-1) * dest
	MatrixInvert( src, srcInv );
	matrix3x4_t xform;
	ConcatTransforms( dest, srcInv, xform );
	QAngle xformAngles;
	MatrixAngles( xform, xformAngles );
	if ( out )
	{
		*out = xformAngles;
	}
}

//-----------------------------------------------------------------------------
// Purpose: Computes a triangle normal
//-----------------------------------------------------------------------------
void ComputeTrianglePlane( const Vector& v1, const Vector& v2, const Vector& v3, Vector& normal, float& intercept )
{
	Vector e1, e2;
	VectorSubtract( v2, v1, e1 );
	VectorSubtract( v3, v1, e2 );
	CrossProduct( e1, e2, normal );
	VectorNormalize( normal );
	intercept = DotProduct( normal, v1 ); 
}

//-----------------------------------------------------------------------------
// Purpose: This is a clone of BaseWindingForPlane()
// Input  : *outVerts - an array of preallocated verts to build the polygon in
//			normal - the plane normal
//			dist - the plane constant
// Output : int - vert count (always 4)
//-----------------------------------------------------------------------------
int PolyFromPlane( Vector *outVerts, const Vector& normal, float dist, float fHalfScale )
{
	int		i, x;
	vec_t	max, v;
	Vector	org, vright, vup;

	// find the major axis

	max = -16384; //MAX_COORD_INTEGER
	x = -1;
	for (i=0 ; i<3; i++)
	{
		v = fabs(normal[i]);
		if (v > max)
		{
			x = i;
			max = v;
		}
	}

	if (x==-1)
		return 0;

	// Build a unit vector along something other than the major axis
	VectorCopy (vec3_origin, vup);	
	switch (x)
	{
	case 0:
	case 1:
		vup[2] = 1;
		break;		
	case 2:
		vup[0] = 1;
		break;		
	}

	// Remove the component of this vector along the normal
	v = DotProduct (vup, normal);
	VectorMA (vup, -v, normal, vup);
	// Make it a unit (perpendicular)
	VectorNormalize (vup);

	// Center of the poly is at normal * dist
	VectorScale (normal, dist, org);
	// Calculate the third orthonormal basis vector for our plane space (this one and vup are in the plane)
	CrossProduct (vup, normal, vright);

	// Make the plane's basis vectors big (these are the half-sides of the polygon we're making)
	VectorScale (vup, fHalfScale, vup);
	VectorScale (vright, fHalfScale, vright);

	// Move diagonally away from org to create the corner verts
	VectorSubtract (org, vright, outVerts[0]);	// left
	VectorAdd (outVerts[0], vup, outVerts[0]);	// up

	VectorAdd (org, vright, outVerts[1]);		// right
	VectorAdd (outVerts[1], vup, outVerts[1]);	// up

	VectorAdd (org, vright, outVerts[2]);		// right
	VectorSubtract (outVerts[2], vup, outVerts[2]);	// down

	VectorSubtract (org, vright, outVerts[3]);		// left
	VectorSubtract (outVerts[3], vup, outVerts[3]);	// down

	// The four corners form a planar quadrilateral normal to "normal"
	return 4;
}

//-----------------------------------------------------------------------------
// Purpose: clip a poly to the plane and return the poly on the front side of the plane
// Input  : *inVerts - input polygon
//			vertCount - # verts in input poly
//			*outVerts - destination poly
//			normal - plane normal
//			dist - plane constant
// Output : int - # verts in output poly
//-----------------------------------------------------------------------------

int ClipPolyToPlane( Vector *inVerts, int vertCount, Vector *outVerts, const Vector& normal, float dist, float fOnPlaneEpsilon )
{
	vec_t	*dists = (vec_t *)stackalloc( sizeof(vec_t) * vertCount * 4 ); //4x vertcount should cover all cases
	int		*sides = (int *)stackalloc( sizeof(vec_t) * vertCount * 4 );
	int		counts[3];
	vec_t	dot;
	int		i, j;
	Vector	mid = vec3_origin;
	int		outCount;

	counts[0] = counts[1] = counts[2] = 0;

	// determine sides for each point
	for ( i = 0; i < vertCount; i++ )
	{
		dot = DotProduct( inVerts[i], normal) - dist;
		dists[i] = dot;
		if ( dot > fOnPlaneEpsilon )
		{
			sides[i] = SIDE_FRONT;
		}
		else if ( dot < -fOnPlaneEpsilon )
		{
			sides[i] = SIDE_BACK;
		}
		else
		{
			sides[i] = SIDE_ON;
		}
		counts[sides[i]]++;
	}
	sides[i] = sides[0];
	dists[i] = dists[0];

	if (!counts[0])
		return 0;

	if (!counts[1])
	{
		// Copy to output verts
		for ( i = 0; i < vertCount; i++ )
		{
			VectorCopy( inVerts[i], outVerts[i] );
		}
		return vertCount;
	}

	outCount = 0;
	for ( i = 0; i < vertCount; i++ )
	{
		Vector& p1 = inVerts[i];

		if (sides[i] == SIDE_ON)
		{
			VectorCopy( p1, outVerts[outCount]);
			outCount++;
			continue;
		}

		if (sides[i] == SIDE_FRONT)
		{
			VectorCopy( p1, outVerts[outCount]);
			outCount++;
		}

		if (sides[i+1] == SIDE_ON || sides[i+1] == sides[i])
			continue;

		// generate a split point
		Vector& p2 = inVerts[(i+1)%vertCount];

		dot = dists[i] / (dists[i]-dists[i+1]);
		for (j=0 ; j<3 ; j++)
		{	// avoid round off error when possible
			if (normal[j] == 1)
				mid[j] = dist;
			else if (normal[j] == -1)
				mid[j] = -dist;
			else
				mid[j] = p1[j] + dot*(p2[j]-p1[j]);
		}

		VectorCopy (mid, outVerts[outCount]);
		outCount++;
	}

	return outCount;
}


int ClipPolyToPlane_Precise( double *inVerts, int vertCount, double *outVerts, const double *normal, double dist, double fOnPlaneEpsilon )
{
	double	*dists = (double *)stackalloc( sizeof(double) * vertCount * 4 ); //4x vertcount should cover all cases
	int		*sides = (int *)stackalloc( sizeof(double) * vertCount * 4 );
	int		counts[3];
	double	dot;
	int		i, j;
	//Vector	mid = vec3_origin;
	double mid[3];
	mid[0] = 0.0;
	mid[1] = 0.0;
	mid[2] = 0.0;
	int		outCount;

	counts[0] = counts[1] = counts[2] = 0;

	// determine sides for each point
	for ( i = 0; i < vertCount; i++ )
	{
		//dot = DotProduct( inVerts[i], normal) - dist;
		dot = ((inVerts[i*3 + 0] * normal[0]) + (inVerts[i*3 + 1] * normal[1]) + (inVerts[i*3 + 2] * normal[2])) - dist;
		dists[i] = dot;
		if ( dot > fOnPlaneEpsilon )
		{
			sides[i] = SIDE_FRONT;
		}
		else if ( dot < -fOnPlaneEpsilon )
		{
			sides[i] = SIDE_BACK;
		}
		else
		{
			sides[i] = SIDE_ON;
		}
		counts[sides[i]]++;
	}
	sides[i] = sides[0];
	dists[i] = dists[0];

	if (!counts[0])
		return 0;

	if (!counts[1])
	{
		// Copy to output verts
		//for ( i = 0; i < vertCount; i++ )
		for ( i = 0; i < vertCount * 3; i++ )
		{
			//VectorCopy( inVerts[i], outVerts[i] );
			outVerts[i] = inVerts[i];
		}
		return vertCount;
	}

	outCount = 0;
	for ( i = 0; i < vertCount; i++ )
	{
		//Vector& p1 = inVerts[i];
		double *p1 = &inVerts[i*3];
		//p1[0] = inVerts[i*3 + 0];
		//p1[1] = inVerts[i*3 + 1];
		//p1[2] = inVerts[i*3 + 2];

		if (sides[i] == SIDE_ON)
		{
			//VectorCopy( p1, outVerts[outCount]);
			outVerts[outCount*3 + 0] = p1[0];
			outVerts[outCount*3 + 1] = p1[1];
			outVerts[outCount*3 + 2] = p1[2];
			outCount++;
			continue;
		}

		if (sides[i] == SIDE_FRONT)
		{
			//VectorCopy( p1, outVerts[outCount]);
			outVerts[outCount*3 + 0] = p1[0];
			outVerts[outCount*3 + 1] = p1[1];
			outVerts[outCount*3 + 2] = p1[2];
			outCount++;
		}

		if (sides[i+1] == SIDE_ON || sides[i+1] == sides[i])
			continue;

		// generate a split point
		//Vector& p2 = inVerts[(i+1)%vertCount];
		int wrappedindex = (i+1)%vertCount;
		double *p2 = &inVerts[wrappedindex*3];
		//p2[0] = inVerts[wrappedindex*3 + 0];
		//p2[1] = inVerts[wrappedindex*3 + 1];
		//p2[2] = inVerts[wrappedindex*3 + 2];

		dot = dists[i] / (dists[i]-dists[i+1]);
		for (j=0 ; j<3 ; j++)
		{
			mid[j] = (double)p1[j] + dot*((double)p2[j]-(double)p1[j]);
		}

		//VectorCopy (mid, outVerts[outCount]);
		outVerts[outCount*3 + 0] = mid[0];
		outVerts[outCount*3 + 1] = mid[1];
		outVerts[outCount*3 + 2] = mid[2];
		outCount++;
	}

	return outCount;
}

int CeilPow2( int in )
{
	int retval;
	
	retval = 1;
	while( retval < in )
		retval <<= 1;
	return retval;
}

int FloorPow2( int in )
{
	int retval;
	
	retval = 1;
	while( retval < in )
		retval <<= 1;
	return retval >> 1;
}


//-----------------------------------------------------------------------------
// Computes Y fov from an X fov and a screen aspect ratio
//-----------------------------------------------------------------------------
float CalcFovY( float flFovX, float flAspect )
{
	if ( flFovX < 1 || flFovX > 179)
	{
		flFovX = 90;	// error, set to 90
	}

	// The long, but illustrative version (more closely matches CShaderAPIDX8::PerspectiveX, which
	// is what it's based on).
	//
	//float width = 2 * zNear * tan( DEG2RAD( fov_x / 2.0 ) );
	//float height = width / screenaspect;
	//float yRadians = atan( (height/2.0) / zNear );
	//return RAD2DEG( yRadians ) * 2;

	// The short and sweet version.
	float val = atan( tan( DEG2RAD( flFovX ) * 0.5f ) / flAspect );
	val = RAD2DEG( val ) * 2.0f;
	return val;
}

float CalcFovX( float flFovY, float flAspect )
{
	return RAD2DEG( atan( tan( DEG2RAD( flFovY ) * 0.5f ) * flAspect ) ) * 2.0f;
}


//-----------------------------------------------------------------------------
// Generate a frustum based on perspective view parameters
//-----------------------------------------------------------------------------
void GeneratePerspectiveFrustum( const Vector& origin, const Vector &forward, 
	const Vector &right, const Vector &up, float flZNear, float flZFar, 
	float flFovX, float flFovY, Frustum_t &frustum )
{
	float flIntercept = DotProduct( origin, forward );

	// Setup the near and far planes.
	frustum.SetPlane( FRUSTUM_FARZ, PLANE_ANYZ, -forward, -flZFar - flIntercept );
	frustum.SetPlane( FRUSTUM_NEARZ, PLANE_ANYZ, forward, flZNear + flIntercept );

	flFovX *= 0.5f;
	flFovY *= 0.5f;

	float flTanX = tan( DEG2RAD( flFovX ) );
	float flTanY = tan( DEG2RAD( flFovY ) );

	// OPTIMIZE: Normalizing these planes is not necessary for culling
	Vector normalPos, normalNeg;

	VectorMA( right, flTanX, forward, normalPos );
	VectorMA( normalPos, -2.0f, right, normalNeg );

	VectorNormalize( normalPos );
	VectorNormalize( normalNeg );

	frustum.SetPlane( FRUSTUM_LEFT, PLANE_ANYZ, normalPos, normalPos.Dot( origin ) );
	frustum.SetPlane( FRUSTUM_RIGHT, PLANE_ANYZ, normalNeg, normalNeg.Dot( origin ) );

	VectorMA( up, flTanY, forward, normalPos );
	VectorMA( normalPos, -2.0f, up, normalNeg );

	VectorNormalize( normalPos );
	VectorNormalize( normalNeg );

	frustum.SetPlane( FRUSTUM_BOTTOM, PLANE_ANYZ, normalPos, normalPos.Dot( origin ) );
	frustum.SetPlane( FRUSTUM_TOP, PLANE_ANYZ, normalNeg, normalNeg.Dot( origin ) );
}


//-----------------------------------------------------------------------------
// Version that accepts angles instead of vectors
//-----------------------------------------------------------------------------
void GeneratePerspectiveFrustum( const Vector& origin, const QAngle &angles, float flZNear, float flZFar, float flFovX, float flAspectRatio, Frustum_t &frustum )
{
	Vector vecForward, vecRight, vecUp;
	AngleVectors( angles, &vecForward, &vecRight, &vecUp );
	float flFovY = CalcFovY( flFovX, flAspectRatio );
	GeneratePerspectiveFrustum( origin, vecForward, vecRight, vecUp, flZNear, flZFar, flFovX, flFovY, frustum );
}

bool R_CullBox( const Vector& mins, const Vector& maxs, const Frustum_t &frustum )
{
	return (( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_RIGHT) ) == 2 ) || 
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_LEFT) ) == 2 ) ||
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_TOP) ) == 2 ) ||
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_BOTTOM) ) == 2 ) ||
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_NEARZ) ) == 2 ) ||
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_FARZ) ) == 2 ) );
}

bool R_CullBoxSkipNear( const Vector& mins, const Vector& maxs, const Frustum_t &frustum )
{
	return (( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_RIGHT) ) == 2 ) || 
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_LEFT) ) == 2 ) ||
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_TOP) ) == 2 ) ||
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_BOTTOM) ) == 2 ) ||
			( BoxOnPlaneSide( mins, maxs, frustum.GetPlane(FRUSTUM_FARZ) ) == 2 ) );
}


// NOTE: This routine was taken (and modified) from NVidia's BlinnReflection demo
// Creates basis vectors, based on a vertex and index list.
// See the NVidia white paper 'GDC2K PerPixel Lighting' for a description
// of how this computation works
#define SMALL_FLOAT 1e-12

void CalcTriangleTangentSpace( const Vector &p0, const Vector &p1, const Vector &p2,
							   const Vector2D &t0, const Vector2D &t1, const Vector2D& t2,
							   Vector &sVect, Vector &tVect )
{
	/* Compute the partial derivatives of X, Y, and Z with respect to S and T. */
	sVect.Init( 0.0f, 0.0f, 0.0f );
	tVect.Init( 0.0f, 0.0f, 0.0f );

	// x, s, t
	Vector edge01( p1.x - p0.x, t1.x - t0.x, t1.y - t0.y );
	Vector edge02( p2.x - p0.x, t2.x - t0.x, t2.y - t0.y );

	Vector cross;
	CrossProduct( edge01, edge02, cross );
	if ( fabs( cross.x ) > SMALL_FLOAT )
	{
		sVect.x += -cross.y / cross.x;
		tVect.x += -cross.z / cross.x;
	}

	// y, s, t
	edge01.Init( p1.y - p0.y, t1.x - t0.x, t1.y - t0.y );
	edge02.Init( p2.y - p0.y, t2.x - t0.x, t2.y - t0.y );

	CrossProduct( edge01, edge02, cross );
	if ( fabs( cross.x ) > SMALL_FLOAT )
	{
		sVect.y += -cross.y / cross.x;
		tVect.y += -cross.z / cross.x;
	}

	// z, s, t
	edge01.Init( p1.z - p0.z, t1.x - t0.x, t1.y - t0.y );
	edge02.Init( p2.z - p0.z, t2.x - t0.x, t2.y - t0.y );

	CrossProduct( edge01, edge02, cross );
	if( fabs( cross.x ) > SMALL_FLOAT )
	{
		sVect.z += -cross.y / cross.x;
		tVect.z += -cross.z / cross.x;
	}

	// Normalize sVect and tVect
	VectorNormalize( sVect );
	VectorNormalize( tVect );
}


//-----------------------------------------------------------------------------
// Convert RGB to HSV
//-----------------------------------------------------------------------------
void RGBtoHSV( const Vector &rgb, Vector &hsv )
{
	float flMax = max( rgb.x, rgb.y );
	flMax = max( flMax, rgb.z );
	float flMin = min( rgb.x, rgb.y );
	flMin = min( flMin, rgb.z );

	// hsv.z is the value
	hsv.z = flMax;

	// hsv.y is the saturation
	if (flMax != 0.0F)
	{
		hsv.y = (flMax - flMin) / flMax;
	}
	else
	{
		hsv.y = 0.0F;
	}

	// hsv.x is the hue
	if (hsv.y == 0.0F)
	{
		hsv.x = -1.0f;
	}
	else
	{
		float32 d = flMax - flMin;
		if (rgb.x == flMax)		
		{
			hsv.x = (rgb.y - rgb.z) / d;
		}
		else if (rgb.y == flMax)	
		{
			hsv.x = 2.0F + (rgb.z - rgb.x) / d;
		}
		else				
		{
			hsv.x = 4.0F + (rgb.x - rgb.y) / d;
		}
		hsv.x *= 60.0F;
		if ( hsv.x < 0.0F ) 
		{
			hsv.x += 360.0F;
		}
	}
}


//-----------------------------------------------------------------------------
// Convert HSV to RGB
//-----------------------------------------------------------------------------
void HSVtoRGB( const Vector &hsv, Vector &rgb )
{         
	if ( hsv.y == 0.0F )
	{
		rgb.Init( hsv.z, hsv.z, hsv.z );
		return;
	}

	float32 hue = hsv.x;
	if (hue == 360.0F) 
	{	
		hue = 0.0F;
	}
	hue /= 60.0F;
	int     i = hue;        // integer part
	float32 f = hue - i;    // fractional part
	float32 p = hsv.z * (1.0F - hsv.y);
	float32 q = hsv.z * (1.0F - hsv.y * f);
	float32 t = hsv.z * (1.0F - hsv.y * (1.0F - f));
	switch(i)
	{
	case 0: rgb.Init( hsv.z, t, p ); break;
	case 1: rgb.Init( q, hsv.z, p ); break;
	case 2: rgb.Init( p, hsv.z, t ); break;
	case 3: rgb.Init( p, q, hsv.z ); break;
	case 4: rgb.Init( t, p, hsv.z ); break;
	case 5: rgb.Init( hsv.z, p, q ); break;
	}
}


void GetInterpolationData( float const *pKnotPositions, 
						   float const *pKnotValues,
						   int nNumValuesinList,
						   int nInterpolationRange,
						   float flPositionToInterpolateAt,
						   bool bWrap,
						   float *pValueA, 
						   float *pValueB,
						   float *pInterpolationValue)
{
	// first, find the bracketting knots by looking for the first knot >= our index
	
	int idx;
	for(idx = 0; idx < nNumValuesinList; idx++ )
	{
		if ( pKnotPositions[idx] >= flPositionToInterpolateAt )
			break;
	}
	int nKnot1, nKnot2;
	float flOffsetFromStartOfGap, flSizeOfGap;
	if ( idx == 0)
	{
		if ( bWrap )
		{
			nKnot1 = nNumValuesinList-1;
			nKnot2 = 0;
			flSizeOfGap =
				( pKnotPositions[nKnot2] + ( nInterpolationRange-pKnotPositions[nKnot1] ) );
			flOffsetFromStartOfGap = 
				flPositionToInterpolateAt + ( nInterpolationRange-pKnotPositions[nKnot1] );
		}
		else
		{
			*pValueA = *pValueB = pKnotValues[0];
			*pInterpolationValue = 1.0;
			return;
		}
	}
	else if ( idx == nNumValuesinList )						// ran out of values
	{
		if ( bWrap )
		{
			nKnot1 = nNumValuesinList -1;
			nKnot2 = 0;
			flSizeOfGap = ( pKnotPositions[nKnot2] + 
						 ( nInterpolationRange-pKnotPositions[nKnot1] ) );
			flOffsetFromStartOfGap = flPositionToInterpolateAt - pKnotPositions[nKnot1];
		}
		else
		{
			*pValueA = *pValueB = pKnotValues[nNumValuesinList-1];
			*pInterpolationValue = 1.0;
			return;
		}

	}
	else
	{
		nKnot1 = idx-1;
		nKnot2 = idx;
		flSizeOfGap = pKnotPositions[nKnot2]-pKnotPositions[nKnot1];
		flOffsetFromStartOfGap = flPositionToInterpolateAt-pKnotPositions[nKnot1];
	}

	*pValueA = pKnotValues[nKnot1];
	*pValueB = pKnotValues[nKnot2];
	*pInterpolationValue = FLerp( 0, 1, 0, flSizeOfGap, flOffsetFromStartOfGap );
	return;
}

float RandomVectorInUnitSphere( Vector *pVector )
{
	// Guarantee uniform random distribution within a sphere
	// Graphics gems III contains this algorithm ("Nonuniform random point sets via warping")
	float u = ((float)rand() / VALVE_RAND_MAX);
	float v = ((float)rand() / VALVE_RAND_MAX);
	float w = ((float)rand() / VALVE_RAND_MAX);

	float flPhi = acos( 1 - 2 * u );
	float flTheta = 2 * M_PI * v;
	float flRadius = powf( w, 1.0f / 3.0f );

	float flSinPhi, flCosPhi;
	float flSinTheta, flCosTheta;
	SinCos( flPhi, &flSinPhi, &flCosPhi );
	SinCos( flTheta, &flSinTheta, &flCosTheta );

	pVector->x = flRadius * flSinPhi * flCosTheta;
	pVector->y = flRadius * flSinPhi * flSinTheta;
	pVector->z = flRadius * flCosPhi;
	return flRadius;
}

float RandomVectorInUnitCircle( Vector2D *pVector )
{
	// Guarantee uniform random distribution within a sphere
	// Graphics gems III contains this algorithm ("Nonuniform random point sets via warping")
	float u = ((float)rand() / VALVE_RAND_MAX);
	float v = ((float)rand() / VALVE_RAND_MAX);

	float flTheta = 2 * M_PI * v;
	float flRadius = powf( u, 1.0f / 2.0f );

	float flSinTheta, flCosTheta;
	SinCos( flTheta, &flSinTheta, &flCosTheta );

	pVector->x = flRadius * flCosTheta;
	pVector->y = flRadius * flSinTheta;
	return flRadius;
}
#ifdef FP_EXCEPTIONS_ENABLED
#include <float.h> // For _clearfp and _controlfp_s
#endif

// FPExceptionDisable and FPExceptionEnabler taken from my blog post
// at http://www.altdevblogaday.com/2012/04/20/exceptional-floating-point/

#ifdef FP_EXCEPTIONS_ENABLED
// These functions are all inlined NOPs if FP_EXCEPTIONS_ENABLED is not defined.
FPExceptionDisabler::FPExceptionDisabler()
{
	// Retrieve the current state of the exception flags. This
	// must be done before changing them. _MCW_EM is a bit
	// mask representing all available exception masks.
	_controlfp_s(&mOldValues, 0, 0);
	// Set all of the exception flags, which suppresses FP
	// exceptions on the x87 and SSE units.
	_controlfp_s(0, _MCW_EM, _MCW_EM);
}

FPExceptionDisabler::~FPExceptionDisabler()
{
	// Clear any pending FP exceptions. This must be done
	// prior to enabling FP exceptions since otherwise there
	// may be a 'deferred crash' as soon the exceptions are
	// enabled.
	_clearfp();

	// Reset (possibly enabling) the exception status.
	_controlfp_s(0, mOldValues, _MCW_EM);
}

// Overflow, divide-by-zero, and invalid-operation are the FP
// exceptions most frequently associated with bugs.
FPExceptionEnabler::FPExceptionEnabler(unsigned int enableBits /*= _EM_OVERFLOW | _EM_ZERODIVIDE | _EM_INVALID*/)
{
	// Retrieve the current state of the exception flags. This
	// must be done before changing them. _MCW_EM is a bit
	// mask representing all available exception masks.
	_controlfp_s(&mOldValues, 0, 0);

	// Make sure no non-exception flags have been specified,
	// to avoid accidental changing of rounding modes, etc.
	enableBits &= _MCW_EM;

	// Clear any pending FP exceptions. This must be done
	// prior to enabling FP exceptions since otherwise there
	// may be a 'deferred crash' as soon the exceptions are
	// enabled.
	_clearfp();

	// Zero out the specified bits, leaving other bits alone.
	_controlfp_s(0, ~enableBits, enableBits);
}

FPExceptionEnabler::~FPExceptionEnabler()
{
	// Reset the exception state.
	_controlfp_s(0, mOldValues, _MCW_EM);
}
#endif