1 /*
2 Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans  http://continuousphysics.com/Bullet/
3 
4 This software is provided 'as-is', without any express or implied warranty.
5 In no event will the authors be held liable for any damages arising from the use of this software.
6 Permission is granted to anyone to use this software for any purpose,
7 including commercial applications, and to alter it and redistribute it freely,
8 subject to the following restrictions:
9 
10 1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
11 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
12 3. This notice may not be removed or altered from any source distribution.
13 */
14 
15 
16 #ifndef	BT_MATRIX3x3_H
17 #define BT_MATRIX3x3_H
18 
19 #include "btVector3.h"
20 #include "btQuaternion.h"
21 #include <stdio.h>
22 
23 #ifdef BT_USE_SSE
24 //const __m128 ATTRIBUTE_ALIGNED16(v2220) = {2.0f, 2.0f, 2.0f, 0.0f};
25 //const __m128 ATTRIBUTE_ALIGNED16(vMPPP) = {-0.0f, +0.0f, +0.0f, +0.0f};
26 #define vMPPP (_mm_set_ps (+0.0f, +0.0f, +0.0f, -0.0f))
27 #endif
28 
29 #if defined(BT_USE_SSE)
30 #define v1000 (_mm_set_ps(0.0f,0.0f,0.0f,1.0f))
31 #define v0100 (_mm_set_ps(0.0f,0.0f,1.0f,0.0f))
32 #define v0010 (_mm_set_ps(0.0f,1.0f,0.0f,0.0f))
33 #elif defined(BT_USE_NEON)
34 const btSimdFloat4 ATTRIBUTE_ALIGNED16(v1000) = {1.0f, 0.0f, 0.0f, 0.0f};
35 const btSimdFloat4 ATTRIBUTE_ALIGNED16(v0100) = {0.0f, 1.0f, 0.0f, 0.0f};
36 const btSimdFloat4 ATTRIBUTE_ALIGNED16(v0010) = {0.0f, 0.0f, 1.0f, 0.0f};
37 #endif
38 
39 #ifdef BT_USE_DOUBLE_PRECISION
40 #define btMatrix3x3Data	btMatrix3x3DoubleData
41 #else
42 #define btMatrix3x3Data	btMatrix3x3FloatData
43 #endif //BT_USE_DOUBLE_PRECISION
44 
45 
46 /**@brief The btMatrix3x3 class implements a 3x3 rotation matrix, to perform linear algebra in combination with btQuaternion, btTransform and btVector3.
47 * Make sure to only include a pure orthogonal matrix without scaling. */
ATTRIBUTE_ALIGNED16(class)48 ATTRIBUTE_ALIGNED16(class) btMatrix3x3 {
49 
50 	///Data storage for the matrix, each vector is a row of the matrix
51 	btVector3 m_el[3];
52 
53 public:
54 	/** @brief No initializaion constructor */
55 	btMatrix3x3 () {}
56 
57 	//		explicit btMatrix3x3(const btScalar *m) { setFromOpenGLSubMatrix(m); }
58 
59 	/**@brief Constructor from Quaternion */
60 	explicit btMatrix3x3(const btQuaternion& q) { setRotation(q); }
61 	/*
62 	template <typename btScalar>
63 	Matrix3x3(const btScalar& yaw, const btScalar& pitch, const btScalar& roll)
64 	{
65 	setEulerYPR(yaw, pitch, roll);
66 	}
67 	*/
68 	/** @brief Constructor with row major formatting */
69 	btMatrix3x3(const btScalar& xx, const btScalar& xy, const btScalar& xz,
70 		const btScalar& yx, const btScalar& yy, const btScalar& yz,
71 		const btScalar& zx, const btScalar& zy, const btScalar& zz)
72 	{
73 		setValue(xx, xy, xz,
74 			yx, yy, yz,
75 			zx, zy, zz);
76 	}
77 
78 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
79 	SIMD_FORCE_INLINE btMatrix3x3 (const btSimdFloat4 v0, const btSimdFloat4 v1, const btSimdFloat4 v2 )
80 	{
81         m_el[0].mVec128 = v0;
82         m_el[1].mVec128 = v1;
83         m_el[2].mVec128 = v2;
84 	}
85 
86 	SIMD_FORCE_INLINE btMatrix3x3 (const btVector3& v0, const btVector3& v1, const btVector3& v2 )
87 	{
88         m_el[0] = v0;
89         m_el[1] = v1;
90         m_el[2] = v2;
91 	}
92 
93 	// Copy constructor
94 	SIMD_FORCE_INLINE btMatrix3x3(const btMatrix3x3& rhs)
95 	{
96 		m_el[0].mVec128 = rhs.m_el[0].mVec128;
97 		m_el[1].mVec128 = rhs.m_el[1].mVec128;
98 		m_el[2].mVec128 = rhs.m_el[2].mVec128;
99 	}
100 
101 	// Assignment Operator
102 	SIMD_FORCE_INLINE btMatrix3x3& operator=(const btMatrix3x3& m)
103 	{
104 		m_el[0].mVec128 = m.m_el[0].mVec128;
105 		m_el[1].mVec128 = m.m_el[1].mVec128;
106 		m_el[2].mVec128 = m.m_el[2].mVec128;
107 
108 		return *this;
109 	}
110 
111 #else
112 
113 	/** @brief Copy constructor */
114 	SIMD_FORCE_INLINE btMatrix3x3 (const btMatrix3x3& other)
115 	{
116 		m_el[0] = other.m_el[0];
117 		m_el[1] = other.m_el[1];
118 		m_el[2] = other.m_el[2];
119 	}
120 
121 	/** @brief Assignment Operator */
122 	SIMD_FORCE_INLINE btMatrix3x3& operator=(const btMatrix3x3& other)
123 	{
124 		m_el[0] = other.m_el[0];
125 		m_el[1] = other.m_el[1];
126 		m_el[2] = other.m_el[2];
127 		return *this;
128 	}
129 
130 #endif
131 
132 	/** @brief Get a column of the matrix as a vector
133 	*  @param i Column number 0 indexed */
134 	SIMD_FORCE_INLINE btVector3 getColumn(int i) const
135 	{
136 		return btVector3(m_el[0][i],m_el[1][i],m_el[2][i]);
137 	}
138 
139 
140 	/** @brief Get a row of the matrix as a vector
141 	*  @param i Row number 0 indexed */
142 	SIMD_FORCE_INLINE const btVector3& getRow(int i) const
143 	{
144 		btFullAssert(0 <= i && i < 3);
145 		return m_el[i];
146 	}
147 
148 	/** @brief Get a mutable reference to a row of the matrix as a vector
149 	*  @param i Row number 0 indexed */
150 	SIMD_FORCE_INLINE btVector3&  operator[](int i)
151 	{
152 		btFullAssert(0 <= i && i < 3);
153 		return m_el[i];
154 	}
155 
156 	/** @brief Get a const reference to a row of the matrix as a vector
157 	*  @param i Row number 0 indexed */
158 	SIMD_FORCE_INLINE const btVector3& operator[](int i) const
159 	{
160 		btFullAssert(0 <= i && i < 3);
161 		return m_el[i];
162 	}
163 
164 	/** @brief Multiply by the target matrix on the right
165 	*  @param m Rotation matrix to be applied
166 	* Equivilant to this = this * m */
167 	btMatrix3x3& operator*=(const btMatrix3x3& m);
168 
169 	/** @brief Adds by the target matrix on the right
170 	*  @param m matrix to be applied
171 	* Equivilant to this = this + m */
172 	btMatrix3x3& operator+=(const btMatrix3x3& m);
173 
174 	/** @brief Substractss by the target matrix on the right
175 	*  @param m matrix to be applied
176 	* Equivilant to this = this - m */
177 	btMatrix3x3& operator-=(const btMatrix3x3& m);
178 
179 	/** @brief Set from the rotational part of a 4x4 OpenGL matrix
180 	*  @param m A pointer to the beginning of the array of scalars*/
181 	void setFromOpenGLSubMatrix(const btScalar *m)
182 	{
183 		m_el[0].setValue(m[0],m[4],m[8]);
184 		m_el[1].setValue(m[1],m[5],m[9]);
185 		m_el[2].setValue(m[2],m[6],m[10]);
186 
187 	}
188 	/** @brief Set the values of the matrix explicitly (row major)
189 	*  @param xx Top left
190 	*  @param xy Top Middle
191 	*  @param xz Top Right
192 	*  @param yx Middle Left
193 	*  @param yy Middle Middle
194 	*  @param yz Middle Right
195 	*  @param zx Bottom Left
196 	*  @param zy Bottom Middle
197 	*  @param zz Bottom Right*/
198 	void setValue(const btScalar& xx, const btScalar& xy, const btScalar& xz,
199 		const btScalar& yx, const btScalar& yy, const btScalar& yz,
200 		const btScalar& zx, const btScalar& zy, const btScalar& zz)
201 	{
202 		m_el[0].setValue(xx,xy,xz);
203 		m_el[1].setValue(yx,yy,yz);
204 		m_el[2].setValue(zx,zy,zz);
205 	}
206 
207 	/** @brief Set the matrix from a quaternion
208 	*  @param q The Quaternion to match */
209 	void setRotation(const btQuaternion& q)
210 	{
211 		btScalar d = q.length2();
212 		btFullAssert(d != btScalar(0.0));
213 		btScalar s = btScalar(2.0) / d;
214 
215     #if defined BT_USE_SIMD_VECTOR3 && defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE)
216         __m128	vs, Q = q.get128();
217 		__m128i Qi = btCastfTo128i(Q);
218         __m128	Y, Z;
219         __m128	V1, V2, V3;
220         __m128	V11, V21, V31;
221         __m128	NQ = _mm_xor_ps(Q, btvMzeroMask);
222 		__m128i NQi = btCastfTo128i(NQ);
223 
224         V1 = btCastiTo128f(_mm_shuffle_epi32 (Qi, BT_SHUFFLE(1,0,2,3)));	// Y X Z W
225 		V2 = _mm_shuffle_ps(NQ, Q, BT_SHUFFLE(0,0,1,3));     // -X -X  Y  W
226         V3 = btCastiTo128f(_mm_shuffle_epi32 (Qi, BT_SHUFFLE(2,1,0,3)));	// Z Y X W
227         V1 = _mm_xor_ps(V1, vMPPP);	//	change the sign of the first element
228 
229         V11	= btCastiTo128f(_mm_shuffle_epi32 (Qi, BT_SHUFFLE(1,1,0,3)));	// Y Y X W
230 		V21 = _mm_unpackhi_ps(Q, Q);                    //  Z  Z  W  W
231 		V31 = _mm_shuffle_ps(Q, NQ, BT_SHUFFLE(0,2,0,3));	//  X  Z -X -W
232 
233 		V2 = V2 * V1;	//
234 		V1 = V1 * V11;	//
235 		V3 = V3 * V31;	//
236 
237         V11 = _mm_shuffle_ps(NQ, Q, BT_SHUFFLE(2,3,1,3));	//	-Z -W  Y  W
238 		V11 = V11 * V21;	//
239         V21 = _mm_xor_ps(V21, vMPPP);	//	change the sign of the first element
240 		V31 = _mm_shuffle_ps(Q, NQ, BT_SHUFFLE(3,3,1,3));	//	 W  W -Y -W
241         V31 = _mm_xor_ps(V31, vMPPP);	//	change the sign of the first element
242 		Y = btCastiTo128f(_mm_shuffle_epi32 (NQi, BT_SHUFFLE(3,2,0,3)));	// -W -Z -X -W
243 		Z = btCastiTo128f(_mm_shuffle_epi32 (Qi, BT_SHUFFLE(1,0,1,3)));	//  Y  X  Y  W
244 
245 		vs = _mm_load_ss(&s);
246 		V21 = V21 * Y;
247 		V31 = V31 * Z;
248 
249 		V1 = V1 + V11;
250         V2 = V2 + V21;
251         V3 = V3 + V31;
252 
253         vs = bt_splat3_ps(vs, 0);
254             //	s ready
255         V1 = V1 * vs;
256         V2 = V2 * vs;
257         V3 = V3 * vs;
258 
259         V1 = V1 + v1000;
260         V2 = V2 + v0100;
261         V3 = V3 + v0010;
262 
263         m_el[0] = V1;
264         m_el[1] = V2;
265         m_el[2] = V3;
266     #else
267 		btScalar xs = q.x() * s,   ys = q.y() * s,   zs = q.z() * s;
268 		btScalar wx = q.w() * xs,  wy = q.w() * ys,  wz = q.w() * zs;
269 		btScalar xx = q.x() * xs,  xy = q.x() * ys,  xz = q.x() * zs;
270 		btScalar yy = q.y() * ys,  yz = q.y() * zs,  zz = q.z() * zs;
271 		setValue(
272             btScalar(1.0) - (yy + zz), xy - wz, xz + wy,
273 			xy + wz, btScalar(1.0) - (xx + zz), yz - wx,
274 			xz - wy, yz + wx, btScalar(1.0) - (xx + yy));
275 	#endif
276     }
277 
278 
279 	/** @brief Set the matrix from euler angles using YPR around YXZ respectively
280 	*  @param yaw Yaw about Y axis
281 	*  @param pitch Pitch about X axis
282 	*  @param roll Roll about Z axis
283 	*/
284 	void setEulerYPR(const btScalar& yaw, const btScalar& pitch, const btScalar& roll)
285 	{
286 		setEulerZYX(roll, pitch, yaw);
287 	}
288 
289 	/** @brief Set the matrix from euler angles YPR around ZYX axes
290 	* @param eulerX Roll about X axis
291 	* @param eulerY Pitch around Y axis
292 	* @param eulerZ Yaw aboud Z axis
293 	*
294 	* These angles are used to produce a rotation matrix. The euler
295 	* angles are applied in ZYX order. I.e a vector is first rotated
296 	* about X then Y and then Z
297 	**/
298 	void setEulerZYX(btScalar eulerX,btScalar eulerY,btScalar eulerZ) {
299 		///@todo proposed to reverse this since it's labeled zyx but takes arguments xyz and it will match all other parts of the code
300 		btScalar ci ( btCos(eulerX));
301 		btScalar cj ( btCos(eulerY));
302 		btScalar ch ( btCos(eulerZ));
303 		btScalar si ( btSin(eulerX));
304 		btScalar sj ( btSin(eulerY));
305 		btScalar sh ( btSin(eulerZ));
306 		btScalar cc = ci * ch;
307 		btScalar cs = ci * sh;
308 		btScalar sc = si * ch;
309 		btScalar ss = si * sh;
310 
311 		setValue(cj * ch, sj * sc - cs, sj * cc + ss,
312 			cj * sh, sj * ss + cc, sj * cs - sc,
313 			-sj,      cj * si,      cj * ci);
314 	}
315 
316 	/**@brief Set the matrix to the identity */
317 	void setIdentity()
318 	{
319 #if (defined(BT_USE_SSE_IN_API)&& defined (BT_USE_SSE)) || defined(BT_USE_NEON)
320 			m_el[0] = v1000;
321 			m_el[1] = v0100;
322 			m_el[2] = v0010;
323 #else
324 		setValue(btScalar(1.0), btScalar(0.0), btScalar(0.0),
325 			btScalar(0.0), btScalar(1.0), btScalar(0.0),
326 			btScalar(0.0), btScalar(0.0), btScalar(1.0));
327 #endif
328 	}
329 
330 	static const btMatrix3x3&	getIdentity()
331 	{
332 #if (defined(BT_USE_SSE_IN_API)&& defined (BT_USE_SSE)) || defined(BT_USE_NEON)
333         static const btMatrix3x3
334         identityMatrix(v1000, v0100, v0010);
335 #else
336 		static const btMatrix3x3
337         identityMatrix(
338             btScalar(1.0), btScalar(0.0), btScalar(0.0),
339 			btScalar(0.0), btScalar(1.0), btScalar(0.0),
340 			btScalar(0.0), btScalar(0.0), btScalar(1.0));
341 #endif
342 		return identityMatrix;
343 	}
344 
345 	/**@brief Fill the rotational part of an OpenGL matrix and clear the shear/perspective
346 	* @param m The array to be filled */
347 	void getOpenGLSubMatrix(btScalar *m) const
348 	{
349 #if defined BT_USE_SIMD_VECTOR3 && defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE)
350         __m128 v0 = m_el[0].mVec128;
351         __m128 v1 = m_el[1].mVec128;
352         __m128 v2 = m_el[2].mVec128;    //  x2 y2 z2 w2
353         __m128 *vm = (__m128 *)m;
354         __m128 vT;
355 
356         v2 = _mm_and_ps(v2, btvFFF0fMask);  //  x2 y2 z2 0
357 
358         vT = _mm_unpackhi_ps(v0, v1);	//	z0 z1 * *
359         v0 = _mm_unpacklo_ps(v0, v1);	//	x0 x1 y0 y1
360 
361         v1 = _mm_shuffle_ps(v0, v2, BT_SHUFFLE(2, 3, 1, 3) );	// y0 y1 y2 0
362         v0 = _mm_shuffle_ps(v0, v2, BT_SHUFFLE(0, 1, 0, 3) );	// x0 x1 x2 0
363         v2 = btCastdTo128f(_mm_move_sd(btCastfTo128d(v2), btCastfTo128d(vT)));	// z0 z1 z2 0
364 
365         vm[0] = v0;
366         vm[1] = v1;
367         vm[2] = v2;
368 #elif defined(BT_USE_NEON)
369         // note: zeros the w channel. We can preserve it at the cost of two more vtrn instructions.
370         static const uint32x2_t zMask = (const uint32x2_t) {static_cast<uint32_t>(-1), 0 };
371         float32x4_t *vm = (float32x4_t *)m;
372         float32x4x2_t top = vtrnq_f32( m_el[0].mVec128, m_el[1].mVec128 );  // {x0 x1 z0 z1}, {y0 y1 w0 w1}
373         float32x2x2_t bl = vtrn_f32( vget_low_f32(m_el[2].mVec128), vdup_n_f32(0.0f) );       // {x2  0 }, {y2 0}
374         float32x4_t v0 = vcombine_f32( vget_low_f32(top.val[0]), bl.val[0] );
375         float32x4_t v1 = vcombine_f32( vget_low_f32(top.val[1]), bl.val[1] );
376         float32x2_t q = (float32x2_t) vand_u32( (uint32x2_t) vget_high_f32( m_el[2].mVec128), zMask );
377         float32x4_t v2 = vcombine_f32( vget_high_f32(top.val[0]), q );       // z0 z1 z2  0
378 
379         vm[0] = v0;
380         vm[1] = v1;
381         vm[2] = v2;
382 #else
383 		m[0]  = btScalar(m_el[0].x());
384 		m[1]  = btScalar(m_el[1].x());
385 		m[2]  = btScalar(m_el[2].x());
386 		m[3]  = btScalar(0.0);
387 		m[4]  = btScalar(m_el[0].y());
388 		m[5]  = btScalar(m_el[1].y());
389 		m[6]  = btScalar(m_el[2].y());
390 		m[7]  = btScalar(0.0);
391 		m[8]  = btScalar(m_el[0].z());
392 		m[9]  = btScalar(m_el[1].z());
393 		m[10] = btScalar(m_el[2].z());
394 		m[11] = btScalar(0.0);
395 #endif
396 	}
397 
398 	/**@brief Get the matrix represented as a quaternion
399 	* @param q The quaternion which will be set */
400 	void getRotation(btQuaternion& q) const
401 	{
402 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
403         btScalar trace = m_el[0].x() + m_el[1].y() + m_el[2].z();
404         btScalar s, x;
405 
406         union {
407             btSimdFloat4 vec;
408             btScalar f[4];
409         } temp;
410 
411         if (trace > btScalar(0.0))
412         {
413             x = trace + btScalar(1.0);
414 
415             temp.f[0]=m_el[2].y() - m_el[1].z();
416             temp.f[1]=m_el[0].z() - m_el[2].x();
417             temp.f[2]=m_el[1].x() - m_el[0].y();
418             temp.f[3]=x;
419             //temp.f[3]= s * btScalar(0.5);
420         }
421         else
422         {
423             int i, j, k;
424             if(m_el[0].x() < m_el[1].y())
425             {
426                 if( m_el[1].y() < m_el[2].z() )
427                     { i = 2; j = 0; k = 1; }
428                 else
429                     { i = 1; j = 2; k = 0; }
430             }
431             else
432             {
433                 if( m_el[0].x() < m_el[2].z())
434                     { i = 2; j = 0; k = 1; }
435                 else
436                     { i = 0; j = 1; k = 2; }
437             }
438 
439             x = m_el[i][i] - m_el[j][j] - m_el[k][k] + btScalar(1.0);
440 
441             temp.f[3] = (m_el[k][j] - m_el[j][k]);
442             temp.f[j] = (m_el[j][i] + m_el[i][j]);
443             temp.f[k] = (m_el[k][i] + m_el[i][k]);
444             temp.f[i] = x;
445             //temp.f[i] = s * btScalar(0.5);
446         }
447 
448         s = btSqrt(x);
449         q.set128(temp.vec);
450         s = btScalar(0.5) / s;
451 
452         q *= s;
453 #else
454 		btScalar trace = m_el[0].x() + m_el[1].y() + m_el[2].z();
455 
456 		btScalar temp[4];
457 
458 		if (trace > btScalar(0.0))
459 		{
460 			btScalar s = btSqrt(trace + btScalar(1.0));
461 			temp[3]=(s * btScalar(0.5));
462 			s = btScalar(0.5) / s;
463 
464 			temp[0]=((m_el[2].y() - m_el[1].z()) * s);
465 			temp[1]=((m_el[0].z() - m_el[2].x()) * s);
466 			temp[2]=((m_el[1].x() - m_el[0].y()) * s);
467 		}
468 		else
469 		{
470 			int i = m_el[0].x() < m_el[1].y() ?
471 				(m_el[1].y() < m_el[2].z() ? 2 : 1) :
472 				(m_el[0].x() < m_el[2].z() ? 2 : 0);
473 			int j = (i + 1) % 3;
474 			int k = (i + 2) % 3;
475 
476 			btScalar s = btSqrt(m_el[i][i] - m_el[j][j] - m_el[k][k] + btScalar(1.0));
477 			temp[i] = s * btScalar(0.5);
478 			s = btScalar(0.5) / s;
479 
480 			temp[3] = (m_el[k][j] - m_el[j][k]) * s;
481 			temp[j] = (m_el[j][i] + m_el[i][j]) * s;
482 			temp[k] = (m_el[k][i] + m_el[i][k]) * s;
483 		}
484 		q.setValue(temp[0],temp[1],temp[2],temp[3]);
485 #endif
486 	}
487 
488 	/**@brief Get the matrix represented as euler angles around YXZ, roundtrip with setEulerYPR
489 	* @param yaw Yaw around Y axis
490 	* @param pitch Pitch around X axis
491 	* @param roll around Z axis */
492 	void getEulerYPR(btScalar& yaw, btScalar& pitch, btScalar& roll) const
493 	{
494 
495 		// first use the normal calculus
496 		yaw = btScalar(btAtan2(m_el[1].x(), m_el[0].x()));
497 		pitch = btScalar(btAsin(-m_el[2].x()));
498 		roll = btScalar(btAtan2(m_el[2].y(), m_el[2].z()));
499 
500 		// on pitch = +/-HalfPI
501 		if (btFabs(pitch)==SIMD_HALF_PI)
502 		{
503 			if (yaw>0)
504 				yaw-=SIMD_PI;
505 			else
506 				yaw+=SIMD_PI;
507 
508 			if (roll>0)
509 				roll-=SIMD_PI;
510 			else
511 				roll+=SIMD_PI;
512 		}
513 	};
514 
515 
516 	/**@brief Get the matrix represented as euler angles around ZYX
517 	* @param yaw Yaw around X axis
518 	* @param pitch Pitch around Y axis
519 	* @param roll around X axis
520 	* @param solution_number Which solution of two possible solutions ( 1 or 2) are possible values*/
521 	void getEulerZYX(btScalar& yaw, btScalar& pitch, btScalar& roll, unsigned int solution_number = 1) const
522 	{
523 		struct Euler
524 		{
525 			btScalar yaw;
526 			btScalar pitch;
527 			btScalar roll;
528 		};
529 
530 		Euler euler_out;
531 		Euler euler_out2; //second solution
532 		//get the pointer to the raw data
533 
534 		// Check that pitch is not at a singularity
535 		if (btFabs(m_el[2].x()) >= 1)
536 		{
537 			euler_out.yaw = 0;
538 			euler_out2.yaw = 0;
539 
540 			// From difference of angles formula
541 			btScalar delta = btAtan2(m_el[0].x(),m_el[0].z());
542 			if (m_el[2].x() > 0)  //gimbal locked up
543 			{
544 				euler_out.pitch = SIMD_PI / btScalar(2.0);
545 				euler_out2.pitch = SIMD_PI / btScalar(2.0);
546 				euler_out.roll = euler_out.pitch + delta;
547 				euler_out2.roll = euler_out.pitch + delta;
548 			}
549 			else // gimbal locked down
550 			{
551 				euler_out.pitch = -SIMD_PI / btScalar(2.0);
552 				euler_out2.pitch = -SIMD_PI / btScalar(2.0);
553 				euler_out.roll = -euler_out.pitch + delta;
554 				euler_out2.roll = -euler_out.pitch + delta;
555 			}
556 		}
557 		else
558 		{
559 			euler_out.pitch = - btAsin(m_el[2].x());
560 			euler_out2.pitch = SIMD_PI - euler_out.pitch;
561 
562 			euler_out.roll = btAtan2(m_el[2].y()/btCos(euler_out.pitch),
563 				m_el[2].z()/btCos(euler_out.pitch));
564 			euler_out2.roll = btAtan2(m_el[2].y()/btCos(euler_out2.pitch),
565 				m_el[2].z()/btCos(euler_out2.pitch));
566 
567 			euler_out.yaw = btAtan2(m_el[1].x()/btCos(euler_out.pitch),
568 				m_el[0].x()/btCos(euler_out.pitch));
569 			euler_out2.yaw = btAtan2(m_el[1].x()/btCos(euler_out2.pitch),
570 				m_el[0].x()/btCos(euler_out2.pitch));
571 		}
572 
573 		if (solution_number == 1)
574 		{
575 			yaw = euler_out.yaw;
576 			pitch = euler_out.pitch;
577 			roll = euler_out.roll;
578 		}
579 		else
580 		{
581 			yaw = euler_out2.yaw;
582 			pitch = euler_out2.pitch;
583 			roll = euler_out2.roll;
584 		}
585 	}
586 
587 	/**@brief Create a scaled copy of the matrix
588 	* @param s Scaling vector The elements of the vector will scale each column */
589 
590 	btMatrix3x3 scaled(const btVector3& s) const
591 	{
592 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
593 		return btMatrix3x3(m_el[0] * s, m_el[1] * s, m_el[2] * s);
594 #else
595 		return btMatrix3x3(
596             m_el[0].x() * s.x(), m_el[0].y() * s.y(), m_el[0].z() * s.z(),
597 			m_el[1].x() * s.x(), m_el[1].y() * s.y(), m_el[1].z() * s.z(),
598 			m_el[2].x() * s.x(), m_el[2].y() * s.y(), m_el[2].z() * s.z());
599 #endif
600 	}
601 
602 	/**@brief Return the determinant of the matrix */
603 	btScalar            determinant() const;
604 	/**@brief Return the adjoint of the matrix */
605 	btMatrix3x3 adjoint() const;
606 	/**@brief Return the matrix with all values non negative */
607 	btMatrix3x3 absolute() const;
608 	/**@brief Return the transpose of the matrix */
609 	btMatrix3x3 transpose() const;
610 	/**@brief Return the inverse of the matrix */
611 	btMatrix3x3 inverse() const;
612 
613 	/// Solve A * x = b, where b is a column vector. This is more efficient
614 	/// than computing the inverse in one-shot cases.
615 	///Solve33 is from Box2d, thanks to Erin Catto,
616 	btVector3 solve33(const btVector3& b) const
617 	{
618 		btVector3 col1 = getColumn(0);
619 		btVector3 col2 = getColumn(1);
620 		btVector3 col3 = getColumn(2);
621 
622 		btScalar det = btDot(col1, btCross(col2, col3));
623 		if (btFabs(det)>SIMD_EPSILON)
624 		{
625 			det = 1.0f / det;
626 		}
627 		btVector3 x;
628 		x[0] = det * btDot(b, btCross(col2, col3));
629 		x[1] = det * btDot(col1, btCross(b, col3));
630 		x[2] = det * btDot(col1, btCross(col2, b));
631 		return x;
632 	}
633 
634 	btMatrix3x3 transposeTimes(const btMatrix3x3& m) const;
635 	btMatrix3x3 timesTranspose(const btMatrix3x3& m) const;
636 
637 	SIMD_FORCE_INLINE btScalar tdotx(const btVector3& v) const
638 	{
639 		return m_el[0].x() * v.x() + m_el[1].x() * v.y() + m_el[2].x() * v.z();
640 	}
641 	SIMD_FORCE_INLINE btScalar tdoty(const btVector3& v) const
642 	{
643 		return m_el[0].y() * v.x() + m_el[1].y() * v.y() + m_el[2].y() * v.z();
644 	}
645 	SIMD_FORCE_INLINE btScalar tdotz(const btVector3& v) const
646 	{
647 		return m_el[0].z() * v.x() + m_el[1].z() * v.y() + m_el[2].z() * v.z();
648 	}
649 
650 
651 	/**@brief diagonalizes this matrix by the Jacobi method.
652 	* @param rot stores the rotation from the coordinate system in which the matrix is diagonal to the original
653 	* coordinate system, i.e., old_this = rot * new_this * rot^T.
654 	* @param threshold See iteration
655 	* @param iteration The iteration stops when all off-diagonal elements are less than the threshold multiplied
656 	* by the sum of the absolute values of the diagonal, or when maxSteps have been executed.
657 	*
658 	* Note that this matrix is assumed to be symmetric.
659 	*/
660 	void diagonalize(btMatrix3x3& rot, btScalar threshold, int maxSteps)
661 	{
662 		rot.setIdentity();
663 		for (int step = maxSteps; step > 0; step--)
664 		{
665 			// find off-diagonal element [p][q] with largest magnitude
666 			int p = 0;
667 			int q = 1;
668 			int r = 2;
669 			btScalar max = btFabs(m_el[0][1]);
670 			btScalar v = btFabs(m_el[0][2]);
671 			if (v > max)
672 			{
673 				q = 2;
674 				r = 1;
675 				max = v;
676 			}
677 			v = btFabs(m_el[1][2]);
678 			if (v > max)
679 			{
680 				p = 1;
681 				q = 2;
682 				r = 0;
683 				max = v;
684 			}
685 
686 			btScalar t = threshold * (btFabs(m_el[0][0]) + btFabs(m_el[1][1]) + btFabs(m_el[2][2]));
687 			if (max <= t)
688 			{
689 				if (max <= SIMD_EPSILON * t)
690 				{
691 					return;
692 				}
693 				step = 1;
694 			}
695 
696 			// compute Jacobi rotation J which leads to a zero for element [p][q]
697 			btScalar mpq = m_el[p][q];
698 			btScalar theta = (m_el[q][q] - m_el[p][p]) / (2 * mpq);
699 			btScalar theta2 = theta * theta;
700 			btScalar cos;
701 			btScalar sin;
702 			if (theta2 * theta2 < btScalar(10 / SIMD_EPSILON))
703 			{
704 				t = (theta >= 0) ? 1 / (theta + btSqrt(1 + theta2))
705 					: 1 / (theta - btSqrt(1 + theta2));
706 				cos = 1 / btSqrt(1 + t * t);
707 				sin = cos * t;
708 			}
709 			else
710 			{
711 				// approximation for large theta-value, i.e., a nearly diagonal matrix
712 				t = 1 / (theta * (2 + btScalar(0.5) / theta2));
713 				cos = 1 - btScalar(0.5) * t * t;
714 				sin = cos * t;
715 			}
716 
717 			// apply rotation to matrix (this = J^T * this * J)
718 			m_el[p][q] = m_el[q][p] = 0;
719 			m_el[p][p] -= t * mpq;
720 			m_el[q][q] += t * mpq;
721 			btScalar mrp = m_el[r][p];
722 			btScalar mrq = m_el[r][q];
723 			m_el[r][p] = m_el[p][r] = cos * mrp - sin * mrq;
724 			m_el[r][q] = m_el[q][r] = cos * mrq + sin * mrp;
725 
726 			// apply rotation to rot (rot = rot * J)
727 			for (int i = 0; i < 3; i++)
728 			{
729 				btVector3& row = rot[i];
730 				mrp = row[p];
731 				mrq = row[q];
732 				row[p] = cos * mrp - sin * mrq;
733 				row[q] = cos * mrq + sin * mrp;
734 			}
735 		}
736 	}
737 
738 
739 
740 
741 	/**@brief Calculate the matrix cofactor
742 	* @param r1 The first row to use for calculating the cofactor
743 	* @param c1 The first column to use for calculating the cofactor
744 	* @param r1 The second row to use for calculating the cofactor
745 	* @param c1 The second column to use for calculating the cofactor
746 	* See http://en.wikipedia.org/wiki/Cofactor_(linear_algebra) for more details
747 	*/
748 	btScalar cofac(int r1, int c1, int r2, int c2) const
749 	{
750 		return m_el[r1][c1] * m_el[r2][c2] - m_el[r1][c2] * m_el[r2][c1];
751 	}
752 
753 	void	serialize(struct	btMatrix3x3Data& dataOut) const;
754 
755 	void	serializeFloat(struct	btMatrix3x3FloatData& dataOut) const;
756 
757 	void	deSerialize(const struct	btMatrix3x3Data& dataIn);
758 
759 	void	deSerializeFloat(const struct	btMatrix3x3FloatData& dataIn);
760 
761 	void	deSerializeDouble(const struct	btMatrix3x3DoubleData& dataIn);
762 
763 };
764 
765 
766 SIMD_FORCE_INLINE btMatrix3x3&
767 btMatrix3x3::operator*=(const btMatrix3x3& m)
768 {
769 #if defined BT_USE_SIMD_VECTOR3 && defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE)
770     __m128 rv00, rv01, rv02;
771     __m128 rv10, rv11, rv12;
772     __m128 rv20, rv21, rv22;
773     __m128 mv0, mv1, mv2;
774 
775     rv02 = m_el[0].mVec128;
776     rv12 = m_el[1].mVec128;
777     rv22 = m_el[2].mVec128;
778 
779     mv0 = _mm_and_ps(m[0].mVec128, btvFFF0fMask);
780     mv1 = _mm_and_ps(m[1].mVec128, btvFFF0fMask);
781     mv2 = _mm_and_ps(m[2].mVec128, btvFFF0fMask);
782 
783     // rv0
784     rv00 = bt_splat_ps(rv02, 0);
785     rv01 = bt_splat_ps(rv02, 1);
786     rv02 = bt_splat_ps(rv02, 2);
787 
788     rv00 = _mm_mul_ps(rv00, mv0);
789     rv01 = _mm_mul_ps(rv01, mv1);
790     rv02 = _mm_mul_ps(rv02, mv2);
791 
792     // rv1
793     rv10 = bt_splat_ps(rv12, 0);
794     rv11 = bt_splat_ps(rv12, 1);
795     rv12 = bt_splat_ps(rv12, 2);
796 
797     rv10 = _mm_mul_ps(rv10, mv0);
798     rv11 = _mm_mul_ps(rv11, mv1);
799     rv12 = _mm_mul_ps(rv12, mv2);
800 
801     // rv2
802     rv20 = bt_splat_ps(rv22, 0);
803     rv21 = bt_splat_ps(rv22, 1);
804     rv22 = bt_splat_ps(rv22, 2);
805 
806     rv20 = _mm_mul_ps(rv20, mv0);
807     rv21 = _mm_mul_ps(rv21, mv1);
808     rv22 = _mm_mul_ps(rv22, mv2);
809 
810     rv00 = _mm_add_ps(rv00, rv01);
811     rv10 = _mm_add_ps(rv10, rv11);
812     rv20 = _mm_add_ps(rv20, rv21);
813 
814     m_el[0].mVec128 = _mm_add_ps(rv00, rv02);
815     m_el[1].mVec128 = _mm_add_ps(rv10, rv12);
816     m_el[2].mVec128 = _mm_add_ps(rv20, rv22);
817 
818 #elif defined(BT_USE_NEON)
819 
820     float32x4_t rv0, rv1, rv2;
821     float32x4_t v0, v1, v2;
822     float32x4_t mv0, mv1, mv2;
823 
824     v0 = m_el[0].mVec128;
825     v1 = m_el[1].mVec128;
826     v2 = m_el[2].mVec128;
827 
828     mv0 = (float32x4_t) vandq_s32((int32x4_t)m[0].mVec128, btvFFF0Mask);
829     mv1 = (float32x4_t) vandq_s32((int32x4_t)m[1].mVec128, btvFFF0Mask);
830     mv2 = (float32x4_t) vandq_s32((int32x4_t)m[2].mVec128, btvFFF0Mask);
831 
832     rv0 = vmulq_lane_f32(mv0, vget_low_f32(v0), 0);
833     rv1 = vmulq_lane_f32(mv0, vget_low_f32(v1), 0);
834     rv2 = vmulq_lane_f32(mv0, vget_low_f32(v2), 0);
835 
836     rv0 = vmlaq_lane_f32(rv0, mv1, vget_low_f32(v0), 1);
837     rv1 = vmlaq_lane_f32(rv1, mv1, vget_low_f32(v1), 1);
838     rv2 = vmlaq_lane_f32(rv2, mv1, vget_low_f32(v2), 1);
839 
840     rv0 = vmlaq_lane_f32(rv0, mv2, vget_high_f32(v0), 0);
841     rv1 = vmlaq_lane_f32(rv1, mv2, vget_high_f32(v1), 0);
842     rv2 = vmlaq_lane_f32(rv2, mv2, vget_high_f32(v2), 0);
843 
844     m_el[0].mVec128 = rv0;
845     m_el[1].mVec128 = rv1;
846     m_el[2].mVec128 = rv2;
847 #else
848 	setValue(
849         m.tdotx(m_el[0]), m.tdoty(m_el[0]), m.tdotz(m_el[0]),
850 		m.tdotx(m_el[1]), m.tdoty(m_el[1]), m.tdotz(m_el[1]),
851 		m.tdotx(m_el[2]), m.tdoty(m_el[2]), m.tdotz(m_el[2]));
852 #endif
853 	return *this;
854 }
855 
856 SIMD_FORCE_INLINE btMatrix3x3&
857 btMatrix3x3::operator+=(const btMatrix3x3& m)
858 {
859 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
860     m_el[0].mVec128 = m_el[0].mVec128 + m.m_el[0].mVec128;
861     m_el[1].mVec128 = m_el[1].mVec128 + m.m_el[1].mVec128;
862     m_el[2].mVec128 = m_el[2].mVec128 + m.m_el[2].mVec128;
863 #else
864 	setValue(
865 		m_el[0][0]+m.m_el[0][0],
866 		m_el[0][1]+m.m_el[0][1],
867 		m_el[0][2]+m.m_el[0][2],
868 		m_el[1][0]+m.m_el[1][0],
869 		m_el[1][1]+m.m_el[1][1],
870 		m_el[1][2]+m.m_el[1][2],
871 		m_el[2][0]+m.m_el[2][0],
872 		m_el[2][1]+m.m_el[2][1],
873 		m_el[2][2]+m.m_el[2][2]);
874 #endif
875 	return *this;
876 }
877 
878 SIMD_FORCE_INLINE btMatrix3x3
879 operator*(const btMatrix3x3& m, const btScalar & k)
880 {
881 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
882     __m128 vk = bt_splat_ps(_mm_load_ss((float *)&k), 0x80);
883     return btMatrix3x3(
884                 _mm_mul_ps(m[0].mVec128, vk),
885                 _mm_mul_ps(m[1].mVec128, vk),
886                 _mm_mul_ps(m[2].mVec128, vk));
887 #elif defined(BT_USE_NEON)
888     return btMatrix3x3(
889                 vmulq_n_f32(m[0].mVec128, k),
890                 vmulq_n_f32(m[1].mVec128, k),
891                 vmulq_n_f32(m[2].mVec128, k));
892 #else
893 	return btMatrix3x3(
894 		m[0].x()*k,m[0].y()*k,m[0].z()*k,
895 		m[1].x()*k,m[1].y()*k,m[1].z()*k,
896 		m[2].x()*k,m[2].y()*k,m[2].z()*k);
897 #endif
898 }
899 
900 SIMD_FORCE_INLINE btMatrix3x3
901 operator+(const btMatrix3x3& m1, const btMatrix3x3& m2)
902 {
903 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
904 	return btMatrix3x3(
905         m1[0].mVec128 + m2[0].mVec128,
906         m1[1].mVec128 + m2[1].mVec128,
907         m1[2].mVec128 + m2[2].mVec128);
908 #else
909 	return btMatrix3x3(
910         m1[0][0]+m2[0][0],
911         m1[0][1]+m2[0][1],
912         m1[0][2]+m2[0][2],
913 
914         m1[1][0]+m2[1][0],
915         m1[1][1]+m2[1][1],
916         m1[1][2]+m2[1][2],
917 
918         m1[2][0]+m2[2][0],
919         m1[2][1]+m2[2][1],
920         m1[2][2]+m2[2][2]);
921 #endif
922 }
923 
924 SIMD_FORCE_INLINE btMatrix3x3
925 operator-(const btMatrix3x3& m1, const btMatrix3x3& m2)
926 {
927 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
928 	return btMatrix3x3(
929         m1[0].mVec128 - m2[0].mVec128,
930         m1[1].mVec128 - m2[1].mVec128,
931         m1[2].mVec128 - m2[2].mVec128);
932 #else
933 	return btMatrix3x3(
934         m1[0][0]-m2[0][0],
935         m1[0][1]-m2[0][1],
936         m1[0][2]-m2[0][2],
937 
938         m1[1][0]-m2[1][0],
939         m1[1][1]-m2[1][1],
940         m1[1][2]-m2[1][2],
941 
942         m1[2][0]-m2[2][0],
943         m1[2][1]-m2[2][1],
944         m1[2][2]-m2[2][2]);
945 #endif
946 }
947 
948 
949 SIMD_FORCE_INLINE btMatrix3x3&
950 btMatrix3x3::operator-=(const btMatrix3x3& m)
951 {
952 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
953     m_el[0].mVec128 = m_el[0].mVec128 - m.m_el[0].mVec128;
954     m_el[1].mVec128 = m_el[1].mVec128 - m.m_el[1].mVec128;
955     m_el[2].mVec128 = m_el[2].mVec128 - m.m_el[2].mVec128;
956 #else
957 	setValue(
958 	m_el[0][0]-m.m_el[0][0],
959 	m_el[0][1]-m.m_el[0][1],
960 	m_el[0][2]-m.m_el[0][2],
961 	m_el[1][0]-m.m_el[1][0],
962 	m_el[1][1]-m.m_el[1][1],
963 	m_el[1][2]-m.m_el[1][2],
964 	m_el[2][0]-m.m_el[2][0],
965 	m_el[2][1]-m.m_el[2][1],
966 	m_el[2][2]-m.m_el[2][2]);
967 #endif
968 	return *this;
969 }
970 
971 
972 SIMD_FORCE_INLINE btScalar
determinant()973 btMatrix3x3::determinant() const
974 {
975 	return btTriple((*this)[0], (*this)[1], (*this)[2]);
976 }
977 
978 
979 SIMD_FORCE_INLINE btMatrix3x3
absolute()980 btMatrix3x3::absolute() const
981 {
982 #if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
983     return btMatrix3x3(
984             _mm_and_ps(m_el[0].mVec128, btvAbsfMask),
985             _mm_and_ps(m_el[1].mVec128, btvAbsfMask),
986             _mm_and_ps(m_el[2].mVec128, btvAbsfMask));
987 #elif defined(BT_USE_NEON)
988     return btMatrix3x3(
989             (float32x4_t)vandq_s32((int32x4_t)m_el[0].mVec128, btv3AbsMask),
990             (float32x4_t)vandq_s32((int32x4_t)m_el[1].mVec128, btv3AbsMask),
991             (float32x4_t)vandq_s32((int32x4_t)m_el[2].mVec128, btv3AbsMask));
992 #else
993 	return btMatrix3x3(
994             btFabs(m_el[0].x()), btFabs(m_el[0].y()), btFabs(m_el[0].z()),
995             btFabs(m_el[1].x()), btFabs(m_el[1].y()), btFabs(m_el[1].z()),
996             btFabs(m_el[2].x()), btFabs(m_el[2].y()), btFabs(m_el[2].z()));
997 #endif
998 }
999 
1000 SIMD_FORCE_INLINE btMatrix3x3
transpose()1001 btMatrix3x3::transpose() const
1002 {
1003 #if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
1004     __m128 v0 = m_el[0].mVec128;
1005     __m128 v1 = m_el[1].mVec128;
1006     __m128 v2 = m_el[2].mVec128;    //  x2 y2 z2 w2
1007     __m128 vT;
1008 
1009     v2 = _mm_and_ps(v2, btvFFF0fMask);  //  x2 y2 z2 0
1010 
1011     vT = _mm_unpackhi_ps(v0, v1);	//	z0 z1 * *
1012     v0 = _mm_unpacklo_ps(v0, v1);	//	x0 x1 y0 y1
1013 
1014     v1 = _mm_shuffle_ps(v0, v2, BT_SHUFFLE(2, 3, 1, 3) );	// y0 y1 y2 0
1015     v0 = _mm_shuffle_ps(v0, v2, BT_SHUFFLE(0, 1, 0, 3) );	// x0 x1 x2 0
1016     v2 = btCastdTo128f(_mm_move_sd(btCastfTo128d(v2), btCastfTo128d(vT)));	// z0 z1 z2 0
1017 
1018 
1019     return btMatrix3x3( v0, v1, v2 );
1020 #elif defined(BT_USE_NEON)
1021     // note: zeros the w channel. We can preserve it at the cost of two more vtrn instructions.
1022     static const uint32x2_t zMask = (const uint32x2_t) {static_cast<uint32_t>(-1), 0 };
1023     float32x4x2_t top = vtrnq_f32( m_el[0].mVec128, m_el[1].mVec128 );  // {x0 x1 z0 z1}, {y0 y1 w0 w1}
1024     float32x2x2_t bl = vtrn_f32( vget_low_f32(m_el[2].mVec128), vdup_n_f32(0.0f) );       // {x2  0 }, {y2 0}
1025     float32x4_t v0 = vcombine_f32( vget_low_f32(top.val[0]), bl.val[0] );
1026     float32x4_t v1 = vcombine_f32( vget_low_f32(top.val[1]), bl.val[1] );
1027     float32x2_t q = (float32x2_t) vand_u32( (uint32x2_t) vget_high_f32( m_el[2].mVec128), zMask );
1028     float32x4_t v2 = vcombine_f32( vget_high_f32(top.val[0]), q );       // z0 z1 z2  0
1029     return btMatrix3x3( v0, v1, v2 );
1030 #else
1031 	return btMatrix3x3( m_el[0].x(), m_el[1].x(), m_el[2].x(),
1032                         m_el[0].y(), m_el[1].y(), m_el[2].y(),
1033                         m_el[0].z(), m_el[1].z(), m_el[2].z());
1034 #endif
1035 }
1036 
1037 SIMD_FORCE_INLINE btMatrix3x3
adjoint()1038 btMatrix3x3::adjoint() const
1039 {
1040 	return btMatrix3x3(cofac(1, 1, 2, 2), cofac(0, 2, 2, 1), cofac(0, 1, 1, 2),
1041 		cofac(1, 2, 2, 0), cofac(0, 0, 2, 2), cofac(0, 2, 1, 0),
1042 		cofac(1, 0, 2, 1), cofac(0, 1, 2, 0), cofac(0, 0, 1, 1));
1043 }
1044 
1045 SIMD_FORCE_INLINE btMatrix3x3
inverse()1046 btMatrix3x3::inverse() const
1047 {
1048 	btVector3 co(cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1));
1049 	btScalar det = (*this)[0].dot(co);
1050 	//btFullAssert(det != btScalar(0.0));
1051 	btAssert(det != btScalar(0.0));
1052 	btScalar s = btScalar(1.0) / det;
1053 	return btMatrix3x3(co.x() * s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
1054 		co.y() * s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s,
1055 		co.z() * s, cofac(0, 1, 2, 0) * s, cofac(0, 0, 1, 1) * s);
1056 }
1057 
1058 SIMD_FORCE_INLINE btMatrix3x3
transposeTimes(const btMatrix3x3 & m)1059 btMatrix3x3::transposeTimes(const btMatrix3x3& m) const
1060 {
1061 #if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
1062     // zeros w
1063 //    static const __m128i xyzMask = (const __m128i){ -1ULL, 0xffffffffULL };
1064     __m128 row = m_el[0].mVec128;
1065     __m128 m0 = _mm_and_ps( m.getRow(0).mVec128, btvFFF0fMask );
1066     __m128 m1 = _mm_and_ps( m.getRow(1).mVec128, btvFFF0fMask);
1067     __m128 m2 = _mm_and_ps( m.getRow(2).mVec128, btvFFF0fMask );
1068     __m128 r0 = _mm_mul_ps(m0, _mm_shuffle_ps(row, row, 0));
1069     __m128 r1 = _mm_mul_ps(m0, _mm_shuffle_ps(row, row, 0x55));
1070     __m128 r2 = _mm_mul_ps(m0, _mm_shuffle_ps(row, row, 0xaa));
1071     row = m_el[1].mVec128;
1072     r0 = _mm_add_ps( r0, _mm_mul_ps(m1, _mm_shuffle_ps(row, row, 0)));
1073     r1 = _mm_add_ps( r1, _mm_mul_ps(m1, _mm_shuffle_ps(row, row, 0x55)));
1074     r2 = _mm_add_ps( r2, _mm_mul_ps(m1, _mm_shuffle_ps(row, row, 0xaa)));
1075     row = m_el[2].mVec128;
1076     r0 = _mm_add_ps( r0, _mm_mul_ps(m2, _mm_shuffle_ps(row, row, 0)));
1077     r1 = _mm_add_ps( r1, _mm_mul_ps(m2, _mm_shuffle_ps(row, row, 0x55)));
1078     r2 = _mm_add_ps( r2, _mm_mul_ps(m2, _mm_shuffle_ps(row, row, 0xaa)));
1079     return btMatrix3x3( r0, r1, r2 );
1080 
1081 #elif defined BT_USE_NEON
1082     // zeros w
1083     static const uint32x4_t xyzMask = (const uint32x4_t){ static_cast<uint32_t>(-1), static_cast<uint32_t>(-1), static_cast<uint32_t>(-1), 0 };
1084     float32x4_t m0 = (float32x4_t) vandq_u32( (uint32x4_t) m.getRow(0).mVec128, xyzMask );
1085     float32x4_t m1 = (float32x4_t) vandq_u32( (uint32x4_t) m.getRow(1).mVec128, xyzMask );
1086     float32x4_t m2 = (float32x4_t) vandq_u32( (uint32x4_t) m.getRow(2).mVec128, xyzMask );
1087     float32x4_t row = m_el[0].mVec128;
1088     float32x4_t r0 = vmulq_lane_f32( m0, vget_low_f32(row), 0);
1089     float32x4_t r1 = vmulq_lane_f32( m0, vget_low_f32(row), 1);
1090     float32x4_t r2 = vmulq_lane_f32( m0, vget_high_f32(row), 0);
1091     row = m_el[1].mVec128;
1092     r0 = vmlaq_lane_f32( r0, m1, vget_low_f32(row), 0);
1093     r1 = vmlaq_lane_f32( r1, m1, vget_low_f32(row), 1);
1094     r2 = vmlaq_lane_f32( r2, m1, vget_high_f32(row), 0);
1095     row = m_el[2].mVec128;
1096     r0 = vmlaq_lane_f32( r0, m2, vget_low_f32(row), 0);
1097     r1 = vmlaq_lane_f32( r1, m2, vget_low_f32(row), 1);
1098     r2 = vmlaq_lane_f32( r2, m2, vget_high_f32(row), 0);
1099     return btMatrix3x3( r0, r1, r2 );
1100 #else
1101     return btMatrix3x3(
1102 		m_el[0].x() * m[0].x() + m_el[1].x() * m[1].x() + m_el[2].x() * m[2].x(),
1103 		m_el[0].x() * m[0].y() + m_el[1].x() * m[1].y() + m_el[2].x() * m[2].y(),
1104 		m_el[0].x() * m[0].z() + m_el[1].x() * m[1].z() + m_el[2].x() * m[2].z(),
1105 		m_el[0].y() * m[0].x() + m_el[1].y() * m[1].x() + m_el[2].y() * m[2].x(),
1106 		m_el[0].y() * m[0].y() + m_el[1].y() * m[1].y() + m_el[2].y() * m[2].y(),
1107 		m_el[0].y() * m[0].z() + m_el[1].y() * m[1].z() + m_el[2].y() * m[2].z(),
1108 		m_el[0].z() * m[0].x() + m_el[1].z() * m[1].x() + m_el[2].z() * m[2].x(),
1109 		m_el[0].z() * m[0].y() + m_el[1].z() * m[1].y() + m_el[2].z() * m[2].y(),
1110 		m_el[0].z() * m[0].z() + m_el[1].z() * m[1].z() + m_el[2].z() * m[2].z());
1111 #endif
1112 }
1113 
1114 SIMD_FORCE_INLINE btMatrix3x3
timesTranspose(const btMatrix3x3 & m)1115 btMatrix3x3::timesTranspose(const btMatrix3x3& m) const
1116 {
1117 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
1118     __m128 a0 = m_el[0].mVec128;
1119     __m128 a1 = m_el[1].mVec128;
1120     __m128 a2 = m_el[2].mVec128;
1121 
1122     btMatrix3x3 mT = m.transpose(); // we rely on transpose() zeroing w channel so that we don't have to do it here
1123     __m128 mx = mT[0].mVec128;
1124     __m128 my = mT[1].mVec128;
1125     __m128 mz = mT[2].mVec128;
1126 
1127     __m128 r0 = _mm_mul_ps(mx, _mm_shuffle_ps(a0, a0, 0x00));
1128     __m128 r1 = _mm_mul_ps(mx, _mm_shuffle_ps(a1, a1, 0x00));
1129     __m128 r2 = _mm_mul_ps(mx, _mm_shuffle_ps(a2, a2, 0x00));
1130     r0 = _mm_add_ps(r0, _mm_mul_ps(my, _mm_shuffle_ps(a0, a0, 0x55)));
1131     r1 = _mm_add_ps(r1, _mm_mul_ps(my, _mm_shuffle_ps(a1, a1, 0x55)));
1132     r2 = _mm_add_ps(r2, _mm_mul_ps(my, _mm_shuffle_ps(a2, a2, 0x55)));
1133     r0 = _mm_add_ps(r0, _mm_mul_ps(mz, _mm_shuffle_ps(a0, a0, 0xaa)));
1134     r1 = _mm_add_ps(r1, _mm_mul_ps(mz, _mm_shuffle_ps(a1, a1, 0xaa)));
1135     r2 = _mm_add_ps(r2, _mm_mul_ps(mz, _mm_shuffle_ps(a2, a2, 0xaa)));
1136     return btMatrix3x3( r0, r1, r2);
1137 
1138 #elif defined BT_USE_NEON
1139     float32x4_t a0 = m_el[0].mVec128;
1140     float32x4_t a1 = m_el[1].mVec128;
1141     float32x4_t a2 = m_el[2].mVec128;
1142 
1143     btMatrix3x3 mT = m.transpose(); // we rely on transpose() zeroing w channel so that we don't have to do it here
1144     float32x4_t mx = mT[0].mVec128;
1145     float32x4_t my = mT[1].mVec128;
1146     float32x4_t mz = mT[2].mVec128;
1147 
1148     float32x4_t r0 = vmulq_lane_f32( mx, vget_low_f32(a0), 0);
1149     float32x4_t r1 = vmulq_lane_f32( mx, vget_low_f32(a1), 0);
1150     float32x4_t r2 = vmulq_lane_f32( mx, vget_low_f32(a2), 0);
1151     r0 = vmlaq_lane_f32( r0, my, vget_low_f32(a0), 1);
1152     r1 = vmlaq_lane_f32( r1, my, vget_low_f32(a1), 1);
1153     r2 = vmlaq_lane_f32( r2, my, vget_low_f32(a2), 1);
1154     r0 = vmlaq_lane_f32( r0, mz, vget_high_f32(a0), 0);
1155     r1 = vmlaq_lane_f32( r1, mz, vget_high_f32(a1), 0);
1156     r2 = vmlaq_lane_f32( r2, mz, vget_high_f32(a2), 0);
1157     return btMatrix3x3( r0, r1, r2 );
1158 
1159 #else
1160 	return btMatrix3x3(
1161 		m_el[0].dot(m[0]), m_el[0].dot(m[1]), m_el[0].dot(m[2]),
1162 		m_el[1].dot(m[0]), m_el[1].dot(m[1]), m_el[1].dot(m[2]),
1163 		m_el[2].dot(m[0]), m_el[2].dot(m[1]), m_el[2].dot(m[2]));
1164 #endif
1165 }
1166 
1167 SIMD_FORCE_INLINE btVector3
1168 operator*(const btMatrix3x3& m, const btVector3& v)
1169 {
1170 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
1171     return v.dot3(m[0], m[1], m[2]);
1172 #else
1173 	return btVector3(m[0].dot(v), m[1].dot(v), m[2].dot(v));
1174 #endif
1175 }
1176 
1177 
1178 SIMD_FORCE_INLINE btVector3
1179 operator*(const btVector3& v, const btMatrix3x3& m)
1180 {
1181 #if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
1182 
1183     const __m128 vv = v.mVec128;
1184 
1185     __m128 c0 = bt_splat_ps( vv, 0);
1186     __m128 c1 = bt_splat_ps( vv, 1);
1187     __m128 c2 = bt_splat_ps( vv, 2);
1188 
1189     c0 = _mm_mul_ps(c0, _mm_and_ps(m[0].mVec128, btvFFF0fMask) );
1190     c1 = _mm_mul_ps(c1, _mm_and_ps(m[1].mVec128, btvFFF0fMask) );
1191     c0 = _mm_add_ps(c0, c1);
1192     c2 = _mm_mul_ps(c2, _mm_and_ps(m[2].mVec128, btvFFF0fMask) );
1193 
1194     return btVector3(_mm_add_ps(c0, c2));
1195 #elif defined(BT_USE_NEON)
1196     const float32x4_t vv = v.mVec128;
1197     const float32x2_t vlo = vget_low_f32(vv);
1198     const float32x2_t vhi = vget_high_f32(vv);
1199 
1200     float32x4_t c0, c1, c2;
1201 
1202     c0 = (float32x4_t) vandq_s32((int32x4_t)m[0].mVec128, btvFFF0Mask);
1203     c1 = (float32x4_t) vandq_s32((int32x4_t)m[1].mVec128, btvFFF0Mask);
1204     c2 = (float32x4_t) vandq_s32((int32x4_t)m[2].mVec128, btvFFF0Mask);
1205 
1206     c0 = vmulq_lane_f32(c0, vlo, 0);
1207     c1 = vmulq_lane_f32(c1, vlo, 1);
1208     c2 = vmulq_lane_f32(c2, vhi, 0);
1209     c0 = vaddq_f32(c0, c1);
1210     c0 = vaddq_f32(c0, c2);
1211 
1212     return btVector3(c0);
1213 #else
1214 	return btVector3(m.tdotx(v), m.tdoty(v), m.tdotz(v));
1215 #endif
1216 }
1217 
1218 SIMD_FORCE_INLINE btMatrix3x3
1219 operator*(const btMatrix3x3& m1, const btMatrix3x3& m2)
1220 {
1221 #if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
1222 
1223     __m128 m10 = m1[0].mVec128;
1224     __m128 m11 = m1[1].mVec128;
1225     __m128 m12 = m1[2].mVec128;
1226 
1227     __m128 m2v = _mm_and_ps(m2[0].mVec128, btvFFF0fMask);
1228 
1229     __m128 c0 = bt_splat_ps( m10, 0);
1230     __m128 c1 = bt_splat_ps( m11, 0);
1231     __m128 c2 = bt_splat_ps( m12, 0);
1232 
1233     c0 = _mm_mul_ps(c0, m2v);
1234     c1 = _mm_mul_ps(c1, m2v);
1235     c2 = _mm_mul_ps(c2, m2v);
1236 
1237     m2v = _mm_and_ps(m2[1].mVec128, btvFFF0fMask);
1238 
1239     __m128 c0_1 = bt_splat_ps( m10, 1);
1240     __m128 c1_1 = bt_splat_ps( m11, 1);
1241     __m128 c2_1 = bt_splat_ps( m12, 1);
1242 
1243     c0_1 = _mm_mul_ps(c0_1, m2v);
1244     c1_1 = _mm_mul_ps(c1_1, m2v);
1245     c2_1 = _mm_mul_ps(c2_1, m2v);
1246 
1247     m2v = _mm_and_ps(m2[2].mVec128, btvFFF0fMask);
1248 
1249     c0 = _mm_add_ps(c0, c0_1);
1250     c1 = _mm_add_ps(c1, c1_1);
1251     c2 = _mm_add_ps(c2, c2_1);
1252 
1253     m10 = bt_splat_ps( m10, 2);
1254     m11 = bt_splat_ps( m11, 2);
1255     m12 = bt_splat_ps( m12, 2);
1256 
1257     m10 = _mm_mul_ps(m10, m2v);
1258     m11 = _mm_mul_ps(m11, m2v);
1259     m12 = _mm_mul_ps(m12, m2v);
1260 
1261     c0 = _mm_add_ps(c0, m10);
1262     c1 = _mm_add_ps(c1, m11);
1263     c2 = _mm_add_ps(c2, m12);
1264 
1265     return btMatrix3x3(c0, c1, c2);
1266 
1267 #elif defined(BT_USE_NEON)
1268 
1269     float32x4_t rv0, rv1, rv2;
1270     float32x4_t v0, v1, v2;
1271     float32x4_t mv0, mv1, mv2;
1272 
1273     v0 = m1[0].mVec128;
1274     v1 = m1[1].mVec128;
1275     v2 = m1[2].mVec128;
1276 
1277     mv0 = (float32x4_t) vandq_s32((int32x4_t)m2[0].mVec128, btvFFF0Mask);
1278     mv1 = (float32x4_t) vandq_s32((int32x4_t)m2[1].mVec128, btvFFF0Mask);
1279     mv2 = (float32x4_t) vandq_s32((int32x4_t)m2[2].mVec128, btvFFF0Mask);
1280 
1281     rv0 = vmulq_lane_f32(mv0, vget_low_f32(v0), 0);
1282     rv1 = vmulq_lane_f32(mv0, vget_low_f32(v1), 0);
1283     rv2 = vmulq_lane_f32(mv0, vget_low_f32(v2), 0);
1284 
1285     rv0 = vmlaq_lane_f32(rv0, mv1, vget_low_f32(v0), 1);
1286     rv1 = vmlaq_lane_f32(rv1, mv1, vget_low_f32(v1), 1);
1287     rv2 = vmlaq_lane_f32(rv2, mv1, vget_low_f32(v2), 1);
1288 
1289     rv0 = vmlaq_lane_f32(rv0, mv2, vget_high_f32(v0), 0);
1290     rv1 = vmlaq_lane_f32(rv1, mv2, vget_high_f32(v1), 0);
1291     rv2 = vmlaq_lane_f32(rv2, mv2, vget_high_f32(v2), 0);
1292 
1293 	return btMatrix3x3(rv0, rv1, rv2);
1294 
1295 #else
1296 	return btMatrix3x3(
1297 		m2.tdotx( m1[0]), m2.tdoty( m1[0]), m2.tdotz( m1[0]),
1298 		m2.tdotx( m1[1]), m2.tdoty( m1[1]), m2.tdotz( m1[1]),
1299 		m2.tdotx( m1[2]), m2.tdoty( m1[2]), m2.tdotz( m1[2]));
1300 #endif
1301 }
1302 
1303 /*
1304 SIMD_FORCE_INLINE btMatrix3x3 btMultTransposeLeft(const btMatrix3x3& m1, const btMatrix3x3& m2) {
1305 return btMatrix3x3(
1306 m1[0][0] * m2[0][0] + m1[1][0] * m2[1][0] + m1[2][0] * m2[2][0],
1307 m1[0][0] * m2[0][1] + m1[1][0] * m2[1][1] + m1[2][0] * m2[2][1],
1308 m1[0][0] * m2[0][2] + m1[1][0] * m2[1][2] + m1[2][0] * m2[2][2],
1309 m1[0][1] * m2[0][0] + m1[1][1] * m2[1][0] + m1[2][1] * m2[2][0],
1310 m1[0][1] * m2[0][1] + m1[1][1] * m2[1][1] + m1[2][1] * m2[2][1],
1311 m1[0][1] * m2[0][2] + m1[1][1] * m2[1][2] + m1[2][1] * m2[2][2],
1312 m1[0][2] * m2[0][0] + m1[1][2] * m2[1][0] + m1[2][2] * m2[2][0],
1313 m1[0][2] * m2[0][1] + m1[1][2] * m2[1][1] + m1[2][2] * m2[2][1],
1314 m1[0][2] * m2[0][2] + m1[1][2] * m2[1][2] + m1[2][2] * m2[2][2]);
1315 }
1316 */
1317 
1318 /**@brief Equality operator between two matrices
1319 * It will test all elements are equal.  */
1320 SIMD_FORCE_INLINE bool operator==(const btMatrix3x3& m1, const btMatrix3x3& m2)
1321 {
1322 #if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
1323 
1324     __m128 c0, c1, c2;
1325 
1326     c0 = _mm_cmpeq_ps(m1[0].mVec128, m2[0].mVec128);
1327     c1 = _mm_cmpeq_ps(m1[1].mVec128, m2[1].mVec128);
1328     c2 = _mm_cmpeq_ps(m1[2].mVec128, m2[2].mVec128);
1329 
1330     c0 = _mm_and_ps(c0, c1);
1331     c0 = _mm_and_ps(c0, c2);
1332 
1333 	int m = _mm_movemask_ps((__m128)c0);
1334 	return (0x7 == (m & 0x7));
1335 
1336 #else
1337 	return
1338     (   m1[0][0] == m2[0][0] && m1[1][0] == m2[1][0] && m1[2][0] == m2[2][0] &&
1339 		m1[0][1] == m2[0][1] && m1[1][1] == m2[1][1] && m1[2][1] == m2[2][1] &&
1340 		m1[0][2] == m2[0][2] && m1[1][2] == m2[1][2] && m1[2][2] == m2[2][2] );
1341 #endif
1342 }
1343 
1344 ///for serialization
1345 struct	btMatrix3x3FloatData
1346 {
1347 	btVector3FloatData m_el[3];
1348 };
1349 
1350 ///for serialization
1351 struct	btMatrix3x3DoubleData
1352 {
1353 	btVector3DoubleData m_el[3];
1354 };
1355 
1356 
1357 
1358 
serialize(struct btMatrix3x3Data & dataOut)1359 SIMD_FORCE_INLINE	void	btMatrix3x3::serialize(struct	btMatrix3x3Data& dataOut) const
1360 {
1361 	for (int i=0;i<3;i++)
1362 		m_el[i].serialize(dataOut.m_el[i]);
1363 }
1364 
serializeFloat(struct btMatrix3x3FloatData & dataOut)1365 SIMD_FORCE_INLINE	void	btMatrix3x3::serializeFloat(struct	btMatrix3x3FloatData& dataOut) const
1366 {
1367 	for (int i=0;i<3;i++)
1368 		m_el[i].serializeFloat(dataOut.m_el[i]);
1369 }
1370 
1371 
deSerialize(const struct btMatrix3x3Data & dataIn)1372 SIMD_FORCE_INLINE	void	btMatrix3x3::deSerialize(const struct	btMatrix3x3Data& dataIn)
1373 {
1374 	for (int i=0;i<3;i++)
1375 		m_el[i].deSerialize(dataIn.m_el[i]);
1376 }
1377 
deSerializeFloat(const struct btMatrix3x3FloatData & dataIn)1378 SIMD_FORCE_INLINE	void	btMatrix3x3::deSerializeFloat(const struct	btMatrix3x3FloatData& dataIn)
1379 {
1380 	for (int i=0;i<3;i++)
1381 		m_el[i].deSerializeFloat(dataIn.m_el[i]);
1382 }
1383 
deSerializeDouble(const struct btMatrix3x3DoubleData & dataIn)1384 SIMD_FORCE_INLINE	void	btMatrix3x3::deSerializeDouble(const struct	btMatrix3x3DoubleData& dataIn)
1385 {
1386 	for (int i=0;i<3;i++)
1387 		m_el[i].deSerializeDouble(dataIn.m_el[i]);
1388 }
1389 
1390 #endif //BT_MATRIX3x3_H
1391 
1392