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mathlib_base.cpp
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4303 lines (3603 loc) · 111 KB
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//========= 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 )