1097 lines
35 KiB
C++
1097 lines
35 KiB
C++
//===== Copyright © 1996-2005, Valve Corporation, All rights reserved. ======//
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//
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// Purpose: - defines SIMD "structure of arrays" classes and functions.
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//
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//===========================================================================//
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#ifndef SSEQUATMATH_H
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#define SSEQUATMATH_H
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#ifdef _WIN32
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#pragma once
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#endif
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#include "mathlib/ssemath.h"
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// Use this #define to allow SSE versions of Quaternion math
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// to exist on PC.
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// On PC, certain horizontal vector operations are not supported.
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// This causes the SSE implementation of quaternion math to mix the
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// vector and scalar floating point units, which is extremely
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// performance negative if you don't compile to native SSE2 (which
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// we don't as of Sept 1, 2007). So, it's best not to allow these
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// functions to exist at all. It's not good enough to simply replace
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// the contents of the functions with scalar math, because each call
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// to LoadAligned and StoreAligned will result in an unnecssary copy
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// of the quaternion, and several moves to and from the XMM registers.
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//
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// Basically, the problem you run into is that for efficient SIMD code,
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// you need to load the quaternions and vectors into SIMD registers and
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// keep them there as long as possible while doing only SIMD math,
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// whereas for efficient scalar code, each time you copy onto or ever
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// use a fltx4, it hoses your pipeline. So the difference has to be
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// in the management of temporary variables in the calling function,
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// not inside the math functions.
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//
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// If you compile assuming the presence of SSE2, the MSVC will abandon
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// the traditional x87 FPU operations altogether and make everything use
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// the SSE2 registers, which lessens this problem a little.
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// permitted only on 360, as we've done careful tuning on its Altivec math.
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// FourQuaternions, however, are always allowed, because vertical ops are
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// fine on SSE.
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#ifdef _X360
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#define ALLOW_SIMD_QUATERNION_MATH 1 // not on PC!
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#endif
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//---------------------------------------------------------------------
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// Load/store quaternions
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//---------------------------------------------------------------------
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#ifndef _X360
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// Using STDC or SSE
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FORCEINLINE fltx4 LoadAlignedSIMD( const QuaternionAligned & pSIMD )
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{
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fltx4 retval = LoadAlignedSIMD( pSIMD.Base() );
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return retval;
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}
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FORCEINLINE fltx4 LoadAlignedSIMD( const QuaternionAligned * RESTRICT pSIMD )
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{
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fltx4 retval = LoadAlignedSIMD( pSIMD->Base() );
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return retval;
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}
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FORCEINLINE void StoreAlignedSIMD( QuaternionAligned * RESTRICT pSIMD, const fltx4 & a )
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{
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StoreAlignedSIMD( pSIMD->Base(), a );
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}
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#else
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// for the transitional class -- load a QuaternionAligned
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FORCEINLINE fltx4 LoadAlignedSIMD( const QuaternionAligned & pSIMD )
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{
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fltx4 retval = XMLoadVector4A( pSIMD.Base() );
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return retval;
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}
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FORCEINLINE fltx4 LoadAlignedSIMD( const QuaternionAligned * RESTRICT pSIMD )
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{
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fltx4 retval = XMLoadVector4A( pSIMD );
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return retval;
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}
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FORCEINLINE void StoreAlignedSIMD( QuaternionAligned * RESTRICT pSIMD, const fltx4 & a )
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{
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XMStoreVector4A( pSIMD->Base(), a );
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}
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// From a RadianEuler packed onto a fltx4, to a quaternion
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fltx4 AngleQuaternionSIMD( FLTX4 vAngles );
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#endif
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#if ALLOW_SIMD_QUATERNION_MATH
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//---------------------------------------------------------------------
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// Make sure quaternions are within 180 degrees of one another, if not, reverse q
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//---------------------------------------------------------------------
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FORCEINLINE fltx4 QuaternionAlignSIMD( const fltx4 &p, const fltx4 &q )
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{
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// decide if one of the quaternions is backwards
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fltx4 a = SubSIMD( p, q );
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fltx4 b = AddSIMD( p, q );
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a = Dot4SIMD( a, a );
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b = Dot4SIMD( b, b );
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fltx4 cmp = CmpGtSIMD( a, b );
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fltx4 result = MaskedAssign( cmp, NegSIMD(q), q );
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return result;
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}
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//---------------------------------------------------------------------
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// Normalize Quaternion
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//---------------------------------------------------------------------
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#if USE_STDC_FOR_SIMD
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FORCEINLINE fltx4 QuaternionNormalizeSIMD( const fltx4 &q )
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{
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fltx4 radius, result;
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radius = Dot4SIMD( q, q );
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if ( SubFloat( radius, 0 ) ) // > FLT_EPSILON && ((radius < 1.0f - 4*FLT_EPSILON) || (radius > 1.0f + 4*FLT_EPSILON))
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{
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float iradius = 1.0f / sqrt( SubFloat( radius, 0 ) );
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result = ReplicateX4( iradius );
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result = MulSIMD( result, q );
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return result;
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}
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return q;
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}
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#else
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// SSE + X360 implementation
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FORCEINLINE fltx4 QuaternionNormalizeSIMD( const fltx4 &q )
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{
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fltx4 radius, result, mask;
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radius = Dot4SIMD( q, q );
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mask = CmpEqSIMD( radius, Four_Zeros ); // all ones iff radius = 0
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result = ReciprocalSqrtSIMD( radius );
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result = MulSIMD( result, q );
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return MaskedAssign( mask, q, result ); // if radius was 0, just return q
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}
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#endif
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//---------------------------------------------------------------------
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// 0.0 returns p, 1.0 return q.
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//---------------------------------------------------------------------
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FORCEINLINE fltx4 QuaternionBlendNoAlignSIMD( const fltx4 &p, const fltx4 &q, float t )
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{
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fltx4 sclp, sclq, result;
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sclq = ReplicateX4( t );
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sclp = SubSIMD( Four_Ones, sclq );
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result = MulSIMD( sclp, p );
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result = MaddSIMD( sclq, q, result );
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return QuaternionNormalizeSIMD( result );
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}
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//---------------------------------------------------------------------
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// Blend Quaternions
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//---------------------------------------------------------------------
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FORCEINLINE fltx4 QuaternionBlendSIMD( const fltx4 &p, const fltx4 &q, float t )
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{
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// decide if one of the quaternions is backwards
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fltx4 q2, result;
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q2 = QuaternionAlignSIMD( p, q );
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result = QuaternionBlendNoAlignSIMD( p, q2, t );
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return result;
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}
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//---------------------------------------------------------------------
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// Multiply Quaternions
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//---------------------------------------------------------------------
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#ifndef _X360
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// SSE and STDC
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FORCEINLINE fltx4 QuaternionMultSIMD( const fltx4 &p, const fltx4 &q )
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{
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// decide if one of the quaternions is backwards
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fltx4 q2, result;
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q2 = QuaternionAlignSIMD( p, q );
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SubFloat( result, 0 ) = SubFloat( p, 0 ) * SubFloat( q2, 3 ) + SubFloat( p, 1 ) * SubFloat( q2, 2 ) - SubFloat( p, 2 ) * SubFloat( q2, 1 ) + SubFloat( p, 3 ) * SubFloat( q2, 0 );
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SubFloat( result, 1 ) = -SubFloat( p, 0 ) * SubFloat( q2, 2 ) + SubFloat( p, 1 ) * SubFloat( q2, 3 ) + SubFloat( p, 2 ) * SubFloat( q2, 0 ) + SubFloat( p, 3 ) * SubFloat( q2, 1 );
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SubFloat( result, 2 ) = SubFloat( p, 0 ) * SubFloat( q2, 1 ) - SubFloat( p, 1 ) * SubFloat( q2, 0 ) + SubFloat( p, 2 ) * SubFloat( q2, 3 ) + SubFloat( p, 3 ) * SubFloat( q2, 2 );
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SubFloat( result, 3 ) = -SubFloat( p, 0 ) * SubFloat( q2, 0 ) - SubFloat( p, 1 ) * SubFloat( q2, 1 ) - SubFloat( p, 2 ) * SubFloat( q2, 2 ) + SubFloat( p, 3 ) * SubFloat( q2, 3 );
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return result;
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}
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#else
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// X360
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extern const fltx4 g_QuatMultRowSign[4];
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FORCEINLINE fltx4 QuaternionMultSIMD( const fltx4 &p, const fltx4 &q )
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{
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fltx4 q2, row, result;
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q2 = QuaternionAlignSIMD( p, q );
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row = XMVectorSwizzle( q2, 3, 2, 1, 0 );
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row = MulSIMD( row, g_QuatMultRowSign[0] );
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result = Dot4SIMD( row, p );
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row = XMVectorSwizzle( q2, 2, 3, 0, 1 );
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row = MulSIMD( row, g_QuatMultRowSign[1] );
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row = Dot4SIMD( row, p );
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result = __vrlimi( result, row, 4, 0 );
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row = XMVectorSwizzle( q2, 1, 0, 3, 2 );
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row = MulSIMD( row, g_QuatMultRowSign[2] );
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row = Dot4SIMD( row, p );
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result = __vrlimi( result, row, 2, 0 );
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row = MulSIMD( q2, g_QuatMultRowSign[3] );
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row = Dot4SIMD( row, p );
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result = __vrlimi( result, row, 1, 0 );
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return result;
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}
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#endif
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//---------------------------------------------------------------------
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// Quaternion scale
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//---------------------------------------------------------------------
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#ifndef _X360
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// SSE and STDC
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FORCEINLINE fltx4 QuaternionScaleSIMD( const fltx4 &p, float t )
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{
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float r;
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fltx4 q;
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// FIXME: nick, this isn't overly sensitive to accuracy, and it may be faster to
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// use the cos part (w) of the quaternion (sin(omega)*N,cos(omega)) to figure the new scale.
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float sinom = sqrt( SubFloat( p, 0 ) * SubFloat( p, 0 ) + SubFloat( p, 1 ) * SubFloat( p, 1 ) + SubFloat( p, 2 ) * SubFloat( p, 2 ) );
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sinom = min( sinom, 1.f );
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float sinsom = sin( asin( sinom ) * t );
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t = sinsom / (sinom + FLT_EPSILON);
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SubFloat( q, 0 ) = t * SubFloat( p, 0 );
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SubFloat( q, 1 ) = t * SubFloat( p, 1 );
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SubFloat( q, 2 ) = t * SubFloat( p, 2 );
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// rescale rotation
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r = 1.0f - sinsom * sinsom;
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// Assert( r >= 0 );
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if (r < 0.0f)
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r = 0.0f;
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r = sqrt( r );
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// keep sign of rotation
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SubFloat( q, 3 ) = fsel( SubFloat( p, 3 ), r, -r );
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return q;
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}
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#else
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// X360
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FORCEINLINE fltx4 QuaternionScaleSIMD( const fltx4 &p, float t )
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{
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fltx4 sinom = Dot3SIMD( p, p );
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sinom = SqrtSIMD( sinom );
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sinom = MinSIMD( sinom, Four_Ones );
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fltx4 sinsom = ArcSinSIMD( sinom );
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fltx4 t4 = ReplicateX4( t );
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sinsom = MulSIMD( sinsom, t4 );
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sinsom = SinSIMD( sinsom );
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sinom = AddSIMD( sinom, Four_Epsilons );
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sinom = ReciprocalSIMD( sinom );
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t4 = MulSIMD( sinsom, sinom );
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fltx4 result = MulSIMD( p, t4 );
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// rescale rotation
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sinsom = MulSIMD( sinsom, sinsom );
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fltx4 r = SubSIMD( Four_Ones, sinsom );
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r = MaxSIMD( r, Four_Zeros );
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r = SqrtSIMD( r );
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// keep sign of rotation
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fltx4 cmp = CmpGeSIMD( p, Four_Zeros );
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r = MaskedAssign( cmp, r, NegSIMD( r ) );
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result = __vrlimi(result, r, 1, 0);
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return result;
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}
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// X360
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// assumes t4 contains a float replicated to each slot
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FORCEINLINE fltx4 QuaternionScaleSIMD( const fltx4 &p, const fltx4 &t4 )
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{
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fltx4 sinom = Dot3SIMD( p, p );
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sinom = SqrtSIMD( sinom );
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sinom = MinSIMD( sinom, Four_Ones );
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fltx4 sinsom = ArcSinSIMD( sinom );
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sinsom = MulSIMD( sinsom, t4 );
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sinsom = SinSIMD( sinsom );
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sinom = AddSIMD( sinom, Four_Epsilons );
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sinom = ReciprocalSIMD( sinom );
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fltx4 result = MulSIMD( p, MulSIMD( sinsom, sinom ) );
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// rescale rotation
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sinsom = MulSIMD( sinsom, sinsom );
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fltx4 r = SubSIMD( Four_Ones, sinsom );
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r = MaxSIMD( r, Four_Zeros );
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r = SqrtSIMD( r );
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// keep sign of rotation
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fltx4 cmp = CmpGeSIMD( p, Four_Zeros );
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r = MaskedAssign( cmp, r, NegSIMD( r ) );
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result = __vrlimi(result, r, 1, 0);
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return result;
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}
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#endif
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//-----------------------------------------------------------------------------
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// Quaternion sphereical linear interpolation
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//-----------------------------------------------------------------------------
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#ifndef _X360
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// SSE and STDC
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FORCEINLINE fltx4 QuaternionSlerpNoAlignSIMD( const fltx4 &p, const fltx4 &q, float t )
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{
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float omega, cosom, sinom, sclp, sclq;
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fltx4 result;
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// 0.0 returns p, 1.0 return q.
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cosom = SubFloat( p, 0 ) * SubFloat( q, 0 ) + SubFloat( p, 1 ) * SubFloat( q, 1 ) +
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SubFloat( p, 2 ) * SubFloat( q, 2 ) + SubFloat( p, 3 ) * SubFloat( q, 3 );
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if ( (1.0f + cosom ) > 0.000001f )
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{
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if ( (1.0f - cosom ) > 0.000001f )
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{
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omega = acos( cosom );
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sinom = sin( omega );
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sclp = sin( (1.0f - t)*omega) / sinom;
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sclq = sin( t*omega ) / sinom;
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}
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else
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{
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// TODO: add short circuit for cosom == 1.0f?
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sclp = 1.0f - t;
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sclq = t;
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}
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SubFloat( result, 0 ) = sclp * SubFloat( p, 0 ) + sclq * SubFloat( q, 0 );
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SubFloat( result, 1 ) = sclp * SubFloat( p, 1 ) + sclq * SubFloat( q, 1 );
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SubFloat( result, 2 ) = sclp * SubFloat( p, 2 ) + sclq * SubFloat( q, 2 );
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SubFloat( result, 3 ) = sclp * SubFloat( p, 3 ) + sclq * SubFloat( q, 3 );
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}
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else
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{
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SubFloat( result, 0 ) = -SubFloat( q, 1 );
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SubFloat( result, 1 ) = SubFloat( q, 0 );
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SubFloat( result, 2 ) = -SubFloat( q, 3 );
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SubFloat( result, 3 ) = SubFloat( q, 2 );
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sclp = sin( (1.0f - t) * (0.5f * M_PI));
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sclq = sin( t * (0.5f * M_PI));
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SubFloat( result, 0 ) = sclp * SubFloat( p, 0 ) + sclq * SubFloat( result, 0 );
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SubFloat( result, 1 ) = sclp * SubFloat( p, 1 ) + sclq * SubFloat( result, 1 );
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SubFloat( result, 2 ) = sclp * SubFloat( p, 2 ) + sclq * SubFloat( result, 2 );
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}
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return result;
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}
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#else
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// X360
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FORCEINLINE fltx4 QuaternionSlerpNoAlignSIMD( const fltx4 &p, const fltx4 &q, float t )
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{
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return XMQuaternionSlerp( p, q, t );
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}
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#endif
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FORCEINLINE fltx4 QuaternionSlerpSIMD( const fltx4 &p, const fltx4 &q, float t )
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{
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fltx4 q2, result;
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q2 = QuaternionAlignSIMD( p, q );
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result = QuaternionSlerpNoAlignSIMD( p, q2, t );
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return result;
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}
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#endif // ALLOW_SIMD_QUATERNION_MATH
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/// class FourVectors stores 4 independent vectors for use in SIMD processing. These vectors are
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/// stored in the format x x x x y y y y z z z z so that they can be efficiently SIMD-accelerated.
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class ALIGN16 FourQuaternions
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{
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public:
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fltx4 x,y,z,w;
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FourQuaternions(void)
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{
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}
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FourQuaternions( const fltx4 &_x,
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const fltx4 &_y,
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const fltx4 &_z,
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const fltx4 &_w )
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: x(_x), y(_y), z(_z), w(_w)
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{}
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FourQuaternions( FourQuaternions const &src )
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{
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x=src.x;
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y=src.y;
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z=src.z;
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w=src.w;
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}
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FORCEINLINE void operator=( FourQuaternions const &src )
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{
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x=src.x;
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y=src.y;
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z=src.z;
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w=src.w;
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}
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/// this = this * q;
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FORCEINLINE FourQuaternions Mul( FourQuaternions const &q ) const;
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/// negate the vector part
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FORCEINLINE FourQuaternions Conjugate() const;
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/// for a quaternion representing a rotation of angle theta, return
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/// one of angle s*theta
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/// scale is four floats -- one for each quat
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FORCEINLINE FourQuaternions ScaleAngle( const fltx4 &scale ) const;
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/// ret = this * ( s * q )
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/// In other words, for a quaternion representing a rotation of angle theta, return
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/// one of angle s*theta
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/// s is four floats in a fltx4 -- one for each quaternion
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FORCEINLINE FourQuaternions MulAc( const fltx4 &s, const FourQuaternions &q ) const;
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/// ret = ( s * this ) * q
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FORCEINLINE FourQuaternions ScaleMul( const fltx4 &s, const FourQuaternions &q ) const;
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/// Slerp four quaternions at once, FROM me TO the specified out.
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FORCEINLINE FourQuaternions Slerp( const FourQuaternions &to, const fltx4 &t );
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FORCEINLINE FourQuaternions SlerpNoAlign( const FourQuaternions &originalto, const fltx4 &t );
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/// LoadAndSwizzleAligned - load 4 QuaternionAligneds into a FourQuaternions, performing transpose op.
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/// all 4 vectors must be 128 bit boundary
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FORCEINLINE void LoadAndSwizzleAligned(const float *RESTRICT a, const float *RESTRICT b, const float *RESTRICT c, const float *RESTRICT d)
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{
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#if _X360
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fltx4 tx = LoadAlignedSIMD(a);
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fltx4 ty = LoadAlignedSIMD(b);
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fltx4 tz = LoadAlignedSIMD(c);
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fltx4 tw = LoadAlignedSIMD(d);
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fltx4 r0 = __vmrghw(tx, tz);
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fltx4 r1 = __vmrghw(ty, tw);
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fltx4 r2 = __vmrglw(tx, tz);
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fltx4 r3 = __vmrglw(ty, tw);
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x = __vmrghw(r0, r1);
|
|
y = __vmrglw(r0, r1);
|
|
z = __vmrghw(r2, r3);
|
|
w = __vmrglw(r2, r3);
|
|
#else
|
|
x = LoadAlignedSIMD(a);
|
|
y = LoadAlignedSIMD(b);
|
|
z = LoadAlignedSIMD(c);
|
|
w = LoadAlignedSIMD(d);
|
|
// now, matrix is:
|
|
// x y z w
|
|
// x y z w
|
|
// x y z w
|
|
// x y z w
|
|
TransposeSIMD(x, y, z, w);
|
|
#endif
|
|
}
|
|
|
|
FORCEINLINE void LoadAndSwizzleAligned(const QuaternionAligned * RESTRICT a,
|
|
const QuaternionAligned * RESTRICT b,
|
|
const QuaternionAligned * RESTRICT c,
|
|
const QuaternionAligned * RESTRICT d)
|
|
{
|
|
LoadAndSwizzleAligned(a->Base(), b->Base(), c->Base(), d->Base() );
|
|
}
|
|
|
|
|
|
/// LoadAndSwizzleAligned - load 4 consecutive QuaternionAligneds into a FourQuaternions,
|
|
/// performing transpose op.
|
|
/// all 4 vectors must be 128 bit boundary
|
|
FORCEINLINE void LoadAndSwizzleAligned(const QuaternionAligned *qs)
|
|
{
|
|
#if _X360
|
|
fltx4 tx = LoadAlignedSIMD(qs++);
|
|
fltx4 ty = LoadAlignedSIMD(qs++);
|
|
fltx4 tz = LoadAlignedSIMD(qs++);
|
|
fltx4 tw = LoadAlignedSIMD(qs);
|
|
fltx4 r0 = __vmrghw(tx, tz);
|
|
fltx4 r1 = __vmrghw(ty, tw);
|
|
fltx4 r2 = __vmrglw(tx, tz);
|
|
fltx4 r3 = __vmrglw(ty, tw);
|
|
|
|
x = __vmrghw(r0, r1);
|
|
y = __vmrglw(r0, r1);
|
|
z = __vmrghw(r2, r3);
|
|
w = __vmrglw(r2, r3);
|
|
#else
|
|
x = LoadAlignedSIMD(qs++);
|
|
y = LoadAlignedSIMD(qs++);
|
|
z = LoadAlignedSIMD(qs++);
|
|
w = LoadAlignedSIMD(qs++);
|
|
// now, matrix is:
|
|
// x y z w
|
|
// x y z w
|
|
// x y z w
|
|
// x y z w
|
|
TransposeSIMD(x, y, z, w);
|
|
#endif
|
|
}
|
|
|
|
// Store the FourQuaternions out to four nonconsecutive ordinary quaternions in memory.
|
|
FORCEINLINE void SwizzleAndStoreAligned(QuaternionAligned *a, QuaternionAligned *b, QuaternionAligned *c, QuaternionAligned *d)
|
|
{
|
|
#if _X360
|
|
fltx4 r0 = __vmrghw(x, z);
|
|
fltx4 r1 = __vmrghw(y, w);
|
|
fltx4 r2 = __vmrglw(x, z);
|
|
fltx4 r3 = __vmrglw(y, w);
|
|
|
|
fltx4 rx = __vmrghw(r0, r1);
|
|
fltx4 ry = __vmrglw(r0, r1);
|
|
fltx4 rz = __vmrghw(r2, r3);
|
|
fltx4 rw = __vmrglw(r2, r3);
|
|
|
|
StoreAlignedSIMD(a, rx);
|
|
StoreAlignedSIMD(b, ry);
|
|
StoreAlignedSIMD(c, rz);
|
|
StoreAlignedSIMD(d, rw);
|
|
#else
|
|
fltx4 dupes[4] = { x, y, z, w };
|
|
TransposeSIMD(dupes[0], dupes[1], dupes[2], dupes[3]);
|
|
StoreAlignedSIMD(a, dupes[0]);
|
|
StoreAlignedSIMD(b, dupes[1]);
|
|
StoreAlignedSIMD(c, dupes[2]);
|
|
StoreAlignedSIMD(d, dupes[3]);
|
|
#endif
|
|
}
|
|
|
|
// Store the FourQuaternions out to four consecutive ordinary quaternions in memory.
|
|
FORCEINLINE void SwizzleAndStoreAligned(QuaternionAligned *qs)
|
|
{
|
|
#if _X360
|
|
fltx4 r0 = __vmrghw(x, z);
|
|
fltx4 r1 = __vmrghw(y, w);
|
|
fltx4 r2 = __vmrglw(x, z);
|
|
fltx4 r3 = __vmrglw(y, w);
|
|
|
|
fltx4 rx = __vmrghw(r0, r1);
|
|
fltx4 ry = __vmrglw(r0, r1);
|
|
fltx4 rz = __vmrghw(r2, r3);
|
|
fltx4 rw = __vmrglw(r2, r3);
|
|
|
|
StoreAlignedSIMD(qs, rx);
|
|
StoreAlignedSIMD(++qs, ry);
|
|
StoreAlignedSIMD(++qs, rz);
|
|
StoreAlignedSIMD(++qs, rw);
|
|
#else
|
|
SwizzleAndStoreAligned(qs, qs+1, qs+2, qs+3);
|
|
#endif
|
|
}
|
|
|
|
// Store the FourQuaternions out to four consecutive ordinary quaternions in memory.
|
|
// The mask specifies which of the quaternions are actually written out -- each
|
|
// word in the fltx4 should be all binary ones or zeros. Ones means the corresponding
|
|
// quat will be written.
|
|
FORCEINLINE void SwizzleAndStoreAlignedMasked(QuaternionAligned * RESTRICT qs, const fltx4 &controlMask)
|
|
{
|
|
fltx4 originals[4];
|
|
originals[0] = LoadAlignedSIMD(qs);
|
|
originals[1] = LoadAlignedSIMD(qs+1);
|
|
originals[2] = LoadAlignedSIMD(qs+2);
|
|
originals[3] = LoadAlignedSIMD(qs+3);
|
|
|
|
fltx4 masks[4] = { SplatXSIMD(controlMask),
|
|
SplatYSIMD(controlMask),
|
|
SplatZSIMD(controlMask),
|
|
SplatWSIMD(controlMask) };
|
|
|
|
#if _X360
|
|
fltx4 r0 = __vmrghw(x, z);
|
|
fltx4 r1 = __vmrghw(y, w);
|
|
fltx4 r2 = __vmrglw(x, z);
|
|
fltx4 r3 = __vmrglw(y, w);
|
|
|
|
fltx4 rx = __vmrghw(r0, r1);
|
|
fltx4 ry = __vmrglw(r0, r1);
|
|
fltx4 rz = __vmrghw(r2, r3);
|
|
fltx4 rw = __vmrglw(r2, r3);
|
|
#else
|
|
fltx4 rx = x;
|
|
fltx4 ry = y;
|
|
fltx4 rz = z;
|
|
fltx4 rw = w;
|
|
TransposeSIMD( rx, ry, rz, rw );
|
|
#endif
|
|
|
|
StoreAlignedSIMD( qs+0, MaskedAssign(masks[0], rx, originals[0]));
|
|
StoreAlignedSIMD( qs+1, MaskedAssign(masks[1], ry, originals[1]));
|
|
StoreAlignedSIMD( qs+2, MaskedAssign(masks[2], rz, originals[2]));
|
|
StoreAlignedSIMD( qs+3, MaskedAssign(masks[3], rw, originals[3]));
|
|
}
|
|
};
|
|
|
|
FORCEINLINE FourQuaternions FourQuaternions::Conjugate( ) const
|
|
{
|
|
return FourQuaternions( NegSIMD(x), NegSIMD(y), NegSIMD(z), w );
|
|
}
|
|
|
|
|
|
|
|
|
|
FORCEINLINE const fltx4 Dot(const FourQuaternions &a, const FourQuaternions &b)
|
|
{
|
|
return
|
|
MaddSIMD(a.x, b.x,
|
|
MaddSIMD(a.y, b.y,
|
|
MaddSIMD(a.z,b.z, MulSIMD(a.w,b.w))
|
|
)
|
|
);
|
|
}
|
|
|
|
|
|
FORCEINLINE const FourQuaternions Madd(const FourQuaternions &a, const fltx4 &scale, const FourQuaternions &c)
|
|
{
|
|
FourQuaternions ret;
|
|
ret.x = MaddSIMD(a.x,scale,c.x);
|
|
ret.y = MaddSIMD(a.y,scale,c.y);
|
|
ret.z = MaddSIMD(a.z,scale,c.z);
|
|
ret.w = MaddSIMD(a.w,scale,c.w);
|
|
return ret;
|
|
}
|
|
|
|
FORCEINLINE const FourQuaternions Mul(const FourQuaternions &a, const fltx4 &scale)
|
|
{
|
|
FourQuaternions ret;
|
|
ret.x = MulSIMD(a.x,scale);
|
|
ret.y = MulSIMD(a.y,scale);
|
|
ret.z = MulSIMD(a.z,scale);
|
|
ret.w = MulSIMD(a.w,scale);
|
|
return ret;
|
|
}
|
|
|
|
FORCEINLINE const FourQuaternions Add(const FourQuaternions &a,const FourQuaternions &b)
|
|
{
|
|
FourQuaternions ret;
|
|
ret.x = AddSIMD(a.x,b.x);
|
|
ret.y = AddSIMD(a.y,b.y);
|
|
ret.z = AddSIMD(a.z,b.z);
|
|
ret.w = AddSIMD(a.w,b.w);
|
|
return ret;
|
|
}
|
|
|
|
FORCEINLINE const FourQuaternions Sub(const FourQuaternions &a,const FourQuaternions &b)
|
|
{
|
|
FourQuaternions ret;
|
|
ret.x = SubSIMD(a.x,b.x);
|
|
ret.y = SubSIMD(a.y,b.y);
|
|
ret.z = SubSIMD(a.z,b.z);
|
|
ret.w = SubSIMD(a.w,b.w);
|
|
return ret;
|
|
}
|
|
|
|
FORCEINLINE const FourQuaternions Neg(const FourQuaternions &q)
|
|
{
|
|
FourQuaternions ret;
|
|
ret.x = NegSIMD(q.x);
|
|
ret.y = NegSIMD(q.y);
|
|
ret.z = NegSIMD(q.z);
|
|
ret.w = NegSIMD(q.w);
|
|
return ret;
|
|
}
|
|
|
|
FORCEINLINE const FourQuaternions MaskedAssign(const fltx4 &mask, const FourQuaternions &a, const FourQuaternions &b)
|
|
{
|
|
FourQuaternions ret;
|
|
ret.x = MaskedAssign(mask,a.x,b.x);
|
|
ret.y = MaskedAssign(mask,a.y,b.y);
|
|
ret.z = MaskedAssign(mask,a.z,b.z);
|
|
ret.w = MaskedAssign(mask,a.w,b.w);
|
|
return ret;
|
|
}
|
|
|
|
|
|
FORCEINLINE FourQuaternions QuaternionAlign( const FourQuaternions &p, const FourQuaternions &q )
|
|
{
|
|
// decide if one of the quaternions is backwards
|
|
fltx4 cmp = CmpLtSIMD( Dot(p,q), Four_Zeros );
|
|
return MaskedAssign( cmp, Neg(q), q );
|
|
}
|
|
|
|
|
|
FORCEINLINE const FourQuaternions QuaternionNormalize( const FourQuaternions &q )
|
|
{
|
|
fltx4 radius = Dot( q, q );
|
|
fltx4 mask = CmpEqSIMD( radius, Four_Zeros ); // all ones iff radius = 0
|
|
fltx4 invRadius = ReciprocalSqrtSIMD( radius );
|
|
|
|
FourQuaternions ret = MaskedAssign(mask, q, Mul(q, invRadius));
|
|
return ret;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/// this = this * q;
|
|
FORCEINLINE FourQuaternions FourQuaternions::Mul( FourQuaternions const &q ) const
|
|
{
|
|
// W = w1w2 - x1x2 - y1y2 - z1z2
|
|
FourQuaternions ret;
|
|
fltx4 signMask = LoadAlignedSIMD( (float *) g_SIMD_signmask );
|
|
// as we do the multiplication, also do a dot product, so we know whether
|
|
// one of the quats is backwards and if we therefore have to negate at the end
|
|
fltx4 dotProduct = MulSIMD( w, q.w );
|
|
|
|
ret.w = MulSIMD( w, q.w ); // W = w1w2
|
|
ret.x = MulSIMD( w, q.x ); // X = w1x2
|
|
ret.y = MulSIMD( w, q.y ); // Y = w1y2
|
|
ret.z = MulSIMD( w, q.z ); // Z = w1z2
|
|
|
|
dotProduct = MaddSIMD( x, q.x, dotProduct );
|
|
ret.w = MsubSIMD( x, q.x, ret.w ); // W = w1w2 - x1x2
|
|
ret.x = MaddSIMD( x, q.w, ret.x ); // X = w1x2 + x1w2
|
|
ret.y = MsubSIMD( x, q.z, ret.y ); // Y = w1y2 - x1z2
|
|
ret.z = MaddSIMD( x, q.y, ret.z ); // Z = w1z2 + x1y2
|
|
|
|
dotProduct = MaddSIMD( y, q.y, dotProduct );
|
|
ret.w = MsubSIMD( y, q.y, ret.w ); // W = w1w2 - x1x2 - y1y2
|
|
ret.x = MaddSIMD( y, q.z, ret.x ); // X = w1x2 + x1w2 + y1z2
|
|
ret.y = MaddSIMD( y, q.w, ret.y ); // Y = w1y2 - x1z2 + y1w2
|
|
ret.z = MsubSIMD( y, q.x, ret.z ); // Z = w1z2 + x1y2 - y1x2
|
|
|
|
dotProduct = MaddSIMD( z, q.z, dotProduct );
|
|
ret.w = MsubSIMD( z, q.z, ret.w ); // W = w1w2 - x1x2 - y1y2 - z1z2
|
|
ret.x = MsubSIMD( z, q.y, ret.x ); // X = w1x2 + x1w2 + y1z2 - z1y2
|
|
ret.y = MaddSIMD( z, q.x, ret.y ); // Y = w1y2 - x1z2 + y1w2 + z1x2
|
|
ret.z = MaddSIMD( z, q.w, ret.z ); // Z = w1z2 + x1y2 - y1x2 + z1w2
|
|
|
|
fltx4 Zero = Four_Zeros;
|
|
fltx4 control = CmpLtSIMD( dotProduct, Four_Zeros );
|
|
signMask = MaskedAssign(control, signMask, Zero); // negate quats where q1.q2 < 0
|
|
ret.w = XorSIMD( signMask, ret.w );
|
|
ret.x = XorSIMD( signMask, ret.x );
|
|
ret.y = XorSIMD( signMask, ret.y );
|
|
ret.z = XorSIMD( signMask, ret.z );
|
|
|
|
return ret;
|
|
}
|
|
|
|
/*
|
|
|
|
void QuaternionScale( const Quaternion &p, float t, Quaternion &q )
|
|
{
|
|
Assert( s_bMathlibInitialized );
|
|
|
|
|
|
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;
|
|
|
|
Assert( q.IsValid() );
|
|
|
|
return;
|
|
}
|
|
|
|
*/
|
|
|
|
FORCEINLINE FourQuaternions FourQuaternions::ScaleAngle( const fltx4 &scale ) const
|
|
{
|
|
FourQuaternions ret;
|
|
static const fltx4 OneMinusEpsilon = {1.0f - 0.000001f, 1.0f - 0.000001f, 1.0f - 0.000001f, 1.0f - 0.000001f };
|
|
static const fltx4 tiny = { 0.00001f, 0.00001f, 0.00001f, 0.00001f };
|
|
const fltx4 Zero = Four_Zeros;
|
|
fltx4 signMask = LoadAlignedSIMD( (float *) g_SIMD_signmask );
|
|
// work out if there are any tiny scales or angles, which are unstable
|
|
fltx4 tinyAngles = CmpGtSIMD(w,OneMinusEpsilon);
|
|
fltx4 negativeRotations = CmpLtSIMD(w, Zero); // if any w's are <0, we will need to negate later down
|
|
|
|
// figure out the theta
|
|
fltx4 angles = ArcCosSIMD(w);
|
|
|
|
// test also if w > -1
|
|
fltx4 negativeWs = XorSIMD(signMask, w);
|
|
tinyAngles = OrSIMD( CmpGtSIMD(negativeWs, OneMinusEpsilon ), tinyAngles );
|
|
|
|
// meanwhile start working on computing the dot product of the
|
|
// vector component, and trust in the scheduler to interleave them
|
|
fltx4 vLenSq = MulSIMD( x, x );
|
|
vLenSq = MaddSIMD( y, y, vLenSq );
|
|
vLenSq = MaddSIMD( z, z, vLenSq );
|
|
|
|
// scale the angles
|
|
angles = MulSIMD( angles, scale );
|
|
|
|
// clear out the sign mask where w>=0
|
|
signMask = MaskedAssign( negativeRotations, signMask, Zero);
|
|
|
|
// work out the new w component and vector length
|
|
fltx4 vLenRecip = ReciprocalSqrtSIMD(vLenSq); // interleave with Cos to hide latencies
|
|
fltx4 sine;
|
|
SinCosSIMD( sine, ret.w, angles );
|
|
ret.x = MulSIMD( x, vLenRecip ); // renormalize so the vector length + w = 1
|
|
ret.y = MulSIMD( y, vLenRecip ); // renormalize so the vector length + w = 1
|
|
ret.z = MulSIMD( z, vLenRecip ); // renormalize so the vector length + w = 1
|
|
ret.x = MulSIMD( ret.x, sine );
|
|
ret.y = MulSIMD( ret.y, sine );
|
|
ret.z = MulSIMD( ret.z, sine );
|
|
|
|
// negate where necessary
|
|
ret.x = XorSIMD(ret.x, signMask);
|
|
ret.y = XorSIMD(ret.y, signMask);
|
|
ret.z = XorSIMD(ret.z, signMask);
|
|
ret.w = XorSIMD(ret.w, signMask);
|
|
|
|
// finally, toss results from where cos(theta) is close to 1 -- these are non rotations.
|
|
ret.x = MaskedAssign(tinyAngles, x, ret.x);
|
|
ret.y = MaskedAssign(tinyAngles, y, ret.y);
|
|
ret.z = MaskedAssign(tinyAngles, z, ret.z);
|
|
ret.w = MaskedAssign(tinyAngles, w, ret.w);
|
|
|
|
return ret;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: return = this * ( s * q )
|
|
// In other words, for a quaternion representing a rotation of angle theta, return
|
|
// one of angle s*theta
|
|
// s is four floats in a fltx4 -- one for each quaternion
|
|
//-----------------------------------------------------------------------------
|
|
|
|
FORCEINLINE FourQuaternions FourQuaternions::MulAc( const fltx4 &s, const FourQuaternions &q ) const
|
|
{
|
|
/*
|
|
void QuaternionMA( const Quaternion &p, float s, const Quaternion &q, Quaternion &qt )
|
|
{
|
|
Quaternion p1, q1;
|
|
|
|
QuaternionScale( q, s, q1 );
|
|
QuaternionMult( p, q1, p1 );
|
|
QuaternionNormalize( p1 );
|
|
qt[0] = p1[0];
|
|
qt[1] = p1[1];
|
|
qt[2] = p1[2];
|
|
qt[3] = p1[3];
|
|
}
|
|
*/
|
|
|
|
return Mul(q.ScaleAngle(s));
|
|
}
|
|
|
|
|
|
FORCEINLINE FourQuaternions FourQuaternions::ScaleMul( const fltx4 &s, const FourQuaternions &q ) const
|
|
{
|
|
return ScaleAngle(s).Mul(q);
|
|
}
|
|
|
|
|
|
FORCEINLINE FourQuaternions FourQuaternions::Slerp( const FourQuaternions &originalto, const fltx4 &t )
|
|
{
|
|
FourQuaternions ret;
|
|
static const fltx4 OneMinusEpsilon = {1.0f - 0.000001f, 1.0f - 0.000001f, 1.0f - 0.000001f, 1.0f - 0.000001f };
|
|
|
|
// align if necessary.
|
|
|
|
// actually, before we even do that, start by computing the dot product of
|
|
// the quaternions. it has lots of dependent ops and we can sneak it into
|
|
// the pipeline bubbles as we figure out alignment. Of course we don't know
|
|
// yet if we need to realign, so compute them both -- there's plenty of
|
|
// space in the bubbles. They're roomy, those bubbles.
|
|
fltx4 cosineOmega;
|
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#if 0 // Maybe I don't need to do alignment seperately, using the xb360 technique...
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FourQuaternions to;
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{
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fltx4 diffs[4], sums[4], originalToNeg[4];
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fltx4 dotIfAligned, dotIfNotAligned;
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// compute negations of the TO quaternion.
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originalToNeg[0] = NegSIMD(originalto.x);
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originalToNeg[1] = NegSIMD(originalto.y);
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originalToNeg[2] = NegSIMD(originalto.z);
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originalToNeg[3] = NegSIMD(originalto.w);
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dotIfAligned = MulSIMD(x, originalto.x);
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dotIfNotAligned = MulSIMD(x, originalToNeg[0]);
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diffs[0] = SubSIMD(x, originalto.x);
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diffs[1] = SubSIMD(y, originalto.y);
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diffs[2] = SubSIMD(z, originalto.z);
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diffs[3] = SubSIMD(w, originalto.w);
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sums[0] = AddSIMD(x, originalto.x);
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sums[1] = AddSIMD(y, originalto.y);
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sums[2] = AddSIMD(z, originalto.z);
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sums[3] = AddSIMD(w, originalto.w);
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dotIfAligned = MaddSIMD(y, originalto.y, dotIfAligned);
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dotIfNotAligned = MaddSIMD(y, originalToNeg[1], dotIfNotAligned);
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fltx4 diffsDot, sumsDot;
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diffsDot = MulSIMD(diffs[0], diffs[0]); // x^2
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sumsDot = MulSIMD(sums[0], sums[0] ); // x^2
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// do some work on the dot products while letting the multiplies cook
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dotIfAligned = MaddSIMD(z, originalto.z, dotIfAligned);
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dotIfNotAligned = MaddSIMD(z, originalToNeg[2], dotIfNotAligned);
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diffsDot = MaddSIMD(diffs[1], diffs[1], diffsDot); // x^2 + y^2
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sumsDot = MaddSIMD(sums[1], sums[1], sumsDot );
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diffsDot = MaddSIMD(diffs[2], diffs[2], diffsDot); // x^2 + y^2 + z^2
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sumsDot = MaddSIMD(sums[2], sums[2], sumsDot );
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diffsDot = MaddSIMD(diffs[3], diffs[3], diffsDot); // x^2 + y^2 + z^2 + w^2
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sumsDot = MaddSIMD(sums[3], sums[3], sumsDot );
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// do some work on the dot products while letting the multiplies cook
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dotIfAligned = MaddSIMD(w, originalto.w, dotIfAligned);
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dotIfNotAligned = MaddSIMD(w, originalToNeg[3], dotIfNotAligned);
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// are the differences greater than the sums?
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// if so, we need to negate that quaternion
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fltx4 mask = CmpGtSIMD(diffsDot, sumsDot); // 1 for diffs>0 and 0 elsewhere
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to.x = MaskedAssign(mask, originalToNeg[0], originalto.x);
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to.y = MaskedAssign(mask, originalToNeg[1], originalto.y);
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to.z = MaskedAssign(mask, originalToNeg[2], originalto.z);
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to.w = MaskedAssign(mask, originalToNeg[3], originalto.w);
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cosineOmega = MaskedAssign(mask, dotIfNotAligned, dotIfAligned);
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}
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// right, now to is aligned to be the short way round, and we computed
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// the dot product while we were figuring all that out.
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#else
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const FourQuaternions &to = originalto;
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cosineOmega = MulSIMD(x, to.x);
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cosineOmega = MaddSIMD(y, to.y, cosineOmega);
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cosineOmega = MaddSIMD(z, to.z, cosineOmega);
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cosineOmega = MaddSIMD(w, to.w, cosineOmega);
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#endif
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fltx4 Zero = Four_Zeros;
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fltx4 cosOmegaLessThanZero = CmpLtSIMD(cosineOmega, Zero);
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// fltx4 shouldNegate = MaskedAssign(cosOmegaLessThanZero, Four_NegativeOnes , Four_Ones );
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fltx4 signMask = LoadAlignedSIMD( (float *) g_SIMD_signmask ); // contains a one in the sign bit -- xor against a number to negate it
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fltx4 sinOmega = Four_Ones;
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// negate cosineOmega where necessary
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cosineOmega = MaskedAssign( cosOmegaLessThanZero, XorSIMD(cosineOmega, signMask), cosineOmega );
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fltx4 oneMinusT = SubSIMD(Four_Ones,t);
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fltx4 bCosOmegaLessThanOne = CmpLtSIMD(cosineOmega, OneMinusEpsilon); // we'll use this to mask out null slerps
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// figure out the sin component of the diff quaternion.
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// since sin^2(t) + cos^2(t) = 1...
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sinOmega = MsubSIMD( cosineOmega, cosineOmega, sinOmega ); // = 1 - cos^2(t) = sin^2(t)
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fltx4 invSinOmega = ReciprocalSqrtSIMD( sinOmega ); // 1/sin(t)
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sinOmega = MulSIMD( sinOmega, invSinOmega ); // = sin^2(t) / sin(t) = sin(t)
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// use the arctangent technique to work out omega from tan^-1(sin/cos)
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fltx4 omega = ArcTan2SIMD(sinOmega, cosineOmega);
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// alpha = sin(omega * (1-T))/sin(omega)
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// beta = sin(omega * T)/sin(omega)
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fltx4 alpha = MulSIMD(omega, oneMinusT); // w(1-T)
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fltx4 beta = MulSIMD(omega, t); // w(T)
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signMask = MaskedAssign(cosOmegaLessThanZero, signMask, Zero);
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alpha = SinSIMD(alpha); // sin(w(1-T))
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beta = SinSIMD(beta); // sin(wT)
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alpha = MulSIMD(alpha, invSinOmega);
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beta = MulSIMD(beta, invSinOmega);
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// depending on whether the dot product was less than zero, negate beta, or not
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beta = XorSIMD(beta, signMask);
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// mask out singularities (where omega = 1)
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alpha = MaskedAssign( bCosOmegaLessThanOne, alpha, oneMinusT );
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beta = MaskedAssign( bCosOmegaLessThanOne, beta , t );
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ret.x = MulSIMD(x, alpha);
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ret.y = MulSIMD(y, alpha);
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ret.z = MulSIMD(z, alpha);
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ret.w = MulSIMD(w, alpha);
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ret.x = MaddSIMD(to.x, beta, ret.x);
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ret.y = MaddSIMD(to.y, beta, ret.y);
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ret.z = MaddSIMD(to.z, beta, ret.z);
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ret.w = MaddSIMD(to.w, beta, ret.w);
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return ret;
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|
}
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|
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|
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|
FORCEINLINE FourQuaternions FourQuaternions::SlerpNoAlign( const FourQuaternions &originalto, const fltx4 &t )
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|
{
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|
FourQuaternions ret;
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|
static const fltx4 OneMinusEpsilon = {1.0f - 0.000001f, 1.0f - 0.000001f, 1.0f - 0.000001f, 1.0f - 0.000001f };
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// align if necessary.
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|
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|
// actually, before we even do that, start by computing the dot product of
|
|
// the quaternions. it has lots of dependent ops and we can sneak it into
|
|
// the pipeline bubbles as we figure out alignment. Of course we don't know
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|
// yet if we need to realign, so compute them both -- there's plenty of
|
|
// space in the bubbles. They're roomy, those bubbles.
|
|
fltx4 cosineOmega;
|
|
|
|
const FourQuaternions &to = originalto;
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|
cosineOmega = MulSIMD(x, to.x);
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|
cosineOmega = MaddSIMD(y, to.y, cosineOmega);
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|
cosineOmega = MaddSIMD(z, to.z, cosineOmega);
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|
cosineOmega = MaddSIMD(w, to.w, cosineOmega);
|
|
|
|
fltx4 sinOmega = Four_Ones;
|
|
|
|
fltx4 oneMinusT = SubSIMD(Four_Ones,t);
|
|
fltx4 bCosOmegaLessThanOne = CmpLtSIMD(cosineOmega, OneMinusEpsilon); // we'll use this to mask out null slerps
|
|
|
|
// figure out the sin component of the diff quaternion.
|
|
// since sin^2(t) + cos^2(t) = 1...
|
|
sinOmega = MsubSIMD( cosineOmega, cosineOmega, sinOmega ); // = 1 - cos^2(t) = sin^2(t)
|
|
fltx4 invSinOmega = ReciprocalSqrtSIMD( sinOmega ); // 1/sin(t)
|
|
sinOmega = MulSIMD( sinOmega, invSinOmega ); // = sin^2(t) / sin(t) = sin(t)
|
|
|
|
// use the arctangent technique to work out omega from tan^-1(sin/cos)
|
|
fltx4 omega = ArcTan2SIMD(sinOmega, cosineOmega);
|
|
|
|
// alpha = sin(omega * (1-T))/sin(omega)
|
|
// beta = sin(omega * T)/sin(omega)
|
|
fltx4 alpha = MulSIMD(omega, oneMinusT); // w(1-T)
|
|
fltx4 beta = MulSIMD(omega, t); // w(T)
|
|
alpha = SinSIMD(alpha); // sin(w(1-T))
|
|
beta = SinSIMD(beta); // sin(wT)
|
|
alpha = MulSIMD(alpha, invSinOmega);
|
|
beta = MulSIMD(beta, invSinOmega);
|
|
|
|
// mask out singularities (where omega = 1)
|
|
alpha = MaskedAssign( bCosOmegaLessThanOne, alpha, oneMinusT );
|
|
beta = MaskedAssign( bCosOmegaLessThanOne, beta , t );
|
|
|
|
ret.x = MulSIMD(x, alpha);
|
|
ret.y = MulSIMD(y, alpha);
|
|
ret.z = MulSIMD(z, alpha);
|
|
ret.w = MulSIMD(w, alpha);
|
|
|
|
ret.x = MaddSIMD(to.x, beta, ret.x);
|
|
ret.y = MaddSIMD(to.y, beta, ret.y);
|
|
ret.z = MaddSIMD(to.z, beta, ret.z);
|
|
ret.w = MaddSIMD(to.w, beta, ret.w);
|
|
|
|
return ret;
|
|
}
|
|
|
|
|
|
#endif // SSEQUATMATH_H
|
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|