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+/*************************************************************************
+ *                                                                       *
+ * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       *
+ * All rights reserved.  Email: russ@q12.org   Web: www.q12.org          *
+ *                                                                       *
+ * This library is free software; you can redistribute it and/or         *
+ * modify it under the terms of EITHER:                                  *
+ *   (1) The GNU Lesser General Public License as published by the Free  *
+ *       Software Foundation; either version 2.1 of the License, or (at  *
+ *       your option) any later version. The text of the GNU Lesser      *
+ *       General Public License is included with this library in the     *
+ *       file LICENSE.TXT.                                               *
+ *   (2) The BSD-style license that is included with this library in     *
+ *       the file LICENSE-BSD.TXT.                                       *
+ *                                                                       *
+ * This library is distributed in the hope that it will be useful,       *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files    *
+ * LICENSE.TXT and LICENSE-BSD.TXT for more details.                     *
+ *                                                                       *
+ *************************************************************************/
+
+#ifndef _ODE_ODEMATH_H_
+#define _ODE_ODEMATH_H_
+
+#include <ode/common.h>
+
+#ifdef __GNUC__
+#define PURE_INLINE extern inline
+#else
+#define PURE_INLINE inline
+#endif
+
+/*
+ * macro to access elements i,j in an NxM matrix A, independent of the
+ * matrix storage convention.
+ */
+#define dACCESS33(A,i,j) ((A)[(i)*4+(j)])
+
+/*
+ * Macro to test for valid floating point values
+ */
+#define dVALIDVEC3(v) (!(dIsNan(v[0]) || dIsNan(v[1]) || dIsNan(v[2])))
+#define dVALIDVEC4(v) (!(dIsNan(v[0]) || dIsNan(v[1]) || dIsNan(v[2]) || dIsNan(v[3])))
+#define dVALIDMAT3(m) (!(dIsNan(m[0]) || dIsNan(m[1]) || dIsNan(m[2]) || dIsNan(m[3]) || dIsNan(m[4]) || dIsNan(m[5]) || dIsNan(m[6]) || dIsNan(m[7]) || dIsNan(m[8]) || dIsNan(m[9]) || dIsNan(m[10]) || dIsNan(m[11])))
+#define dVALIDMAT4(m) (!(dIsNan(m[0]) || dIsNan(m[1]) || dIsNan(m[2]) || dIsNan(m[3]) || dIsNan(m[4]) || dIsNan(m[5]) || dIsNan(m[6]) || dIsNan(m[7]) || dIsNan(m[8]) || dIsNan(m[9]) || dIsNan(m[10]) || dIsNan(m[11]) || dIsNan(m[12]) || dIsNan(m[13]) || dIsNan(m[14]) || dIsNan(m[15]) ))
+
+
+
+/*
+ * General purpose vector operations with other vectors or constants.
+ */
+
+#define dOP(a,op,b,c) \
+    (a)[0] = ((b)[0]) op ((c)[0]); \
+    (a)[1] = ((b)[1]) op ((c)[1]); \
+    (a)[2] = ((b)[2]) op ((c)[2]);
+#define dOPC(a,op,b,c) \
+    (a)[0] = ((b)[0]) op (c); \
+    (a)[1] = ((b)[1]) op (c); \
+    (a)[2] = ((b)[2]) op (c);
+#define dOPE(a,op,b) \
+    (a)[0] op ((b)[0]); \
+    (a)[1] op ((b)[1]); \
+    (a)[2] op ((b)[2]);
+#define dOPEC(a,op,c) \
+    (a)[0] op (c); \
+    (a)[1] op (c); \
+    (a)[2] op (c);
+
+
+/*
+ * Length, and squared length helpers. dLENGTH returns the length of a dVector3.
+ * dLENGTHSQUARED return the squared length of a dVector3.
+ */
+
+#define dLENGTHSQUARED(a) (((a)[0])*((a)[0]) + ((a)[1])*((a)[1]) + ((a)[2])*((a)[2]))
+
+#ifdef __cplusplus
+
+PURE_INLINE dReal dLENGTH (const dReal *a) { return dSqrt(dLENGTHSQUARED(a)); }
+
+#else
+
+#define dLENGTH(a) ( dSqrt( ((a)[0])*((a)[0]) + ((a)[1])*((a)[1]) + ((a)[2])*((a)[2]) ) )
+
+#endif /* __cplusplus */
+
+
+
+
+
+/*
+ * 3-way dot product. dDOTpq means that elements of `a' and `b' are spaced
+ * p and q indexes apart respectively. dDOT() means dDOT11.
+ * in C++ we could use function templates to get all the versions of these
+ * functions - but on some compilers this will result in sub-optimal code.
+ */
+
+#define dDOTpq(a,b,p,q) ((a)[0]*(b)[0] + (a)[p]*(b)[q] + (a)[2*(p)]*(b)[2*(q)])
+
+#ifdef __cplusplus
+
+PURE_INLINE dReal dDOT   (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,1); }
+PURE_INLINE dReal dDOT13 (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,3); }
+PURE_INLINE dReal dDOT31 (const dReal *a, const dReal *b) { return dDOTpq(a,b,3,1); }
+PURE_INLINE dReal dDOT33 (const dReal *a, const dReal *b) { return dDOTpq(a,b,3,3); }
+PURE_INLINE dReal dDOT14 (const dReal *a, const dReal *b) { return dDOTpq(a,b,1,4); }
+PURE_INLINE dReal dDOT41 (const dReal *a, const dReal *b) { return dDOTpq(a,b,4,1); }
+PURE_INLINE dReal dDOT44 (const dReal *a, const dReal *b) { return dDOTpq(a,b,4,4); }
+
+#else
+
+#define dDOT(a,b)   dDOTpq(a,b,1,1)
+#define dDOT13(a,b) dDOTpq(a,b,1,3)
+#define dDOT31(a,b) dDOTpq(a,b,3,1)
+#define dDOT33(a,b) dDOTpq(a,b,3,3)
+#define dDOT14(a,b) dDOTpq(a,b,1,4)
+#define dDOT41(a,b) dDOTpq(a,b,4,1)
+#define dDOT44(a,b) dDOTpq(a,b,4,4)
+
+#endif /* __cplusplus */
+
+
+/*
+ * cross product, set a = b x c. dCROSSpqr means that elements of `a', `b'
+ * and `c' are spaced p, q and r indexes apart respectively.
+ * dCROSS() means dCROSS111. `op' is normally `=', but you can set it to
+ * +=, -= etc to get other effects.
+ */
+
+#define dCROSS(a,op,b,c) \
+do { \
+  (a)[0] op ((b)[1]*(c)[2] - (b)[2]*(c)[1]); \
+  (a)[1] op ((b)[2]*(c)[0] - (b)[0]*(c)[2]); \
+  (a)[2] op ((b)[0]*(c)[1] - (b)[1]*(c)[0]); \
+} while(0)
+#define dCROSSpqr(a,op,b,c,p,q,r) \
+do { \
+  (a)[  0] op ((b)[  q]*(c)[2*r] - (b)[2*q]*(c)[  r]); \
+  (a)[  p] op ((b)[2*q]*(c)[  0] - (b)[  0]*(c)[2*r]); \
+  (a)[2*p] op ((b)[  0]*(c)[  r] - (b)[  q]*(c)[  0]); \
+} while(0)
+#define dCROSS114(a,op,b,c) dCROSSpqr(a,op,b,c,1,1,4)
+#define dCROSS141(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,1)
+#define dCROSS144(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,4)
+#define dCROSS411(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,1)
+#define dCROSS414(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,4)
+#define dCROSS441(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,1)
+#define dCROSS444(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,4)
+
+
+/*
+ * set a 3x3 submatrix of A to a matrix such that submatrix(A)*b = a x b.
+ * A is stored by rows, and has `skip' elements per row. the matrix is
+ * assumed to be already zero, so this does not write zero elements!
+ * if (plus,minus) is (+,-) then a positive version will be written.
+ * if (plus,minus) is (-,+) then a negative version will be written.
+ */
+
+#define dCROSSMAT(A,a,skip,plus,minus) \
+do { \
+  (A)[1] = minus (a)[2]; \
+  (A)[2] = plus (a)[1]; \
+  (A)[(skip)+0] = plus (a)[2]; \
+  (A)[(skip)+2] = minus (a)[0]; \
+  (A)[2*(skip)+0] = minus (a)[1]; \
+  (A)[2*(skip)+1] = plus (a)[0]; \
+} while(0)
+
+
+/*
+ * compute the distance between two 3D-vectors
+ */
+
+#ifdef __cplusplus
+PURE_INLINE dReal dDISTANCE (const dVector3 a, const dVector3 b)
+        { return dSqrt( (a[0]-b[0])*(a[0]-b[0]) + (a[1]-b[1])*(a[1]-b[1]) + (a[2]-b[2])*(a[2]-b[2]) ); }
+#else
+#define dDISTANCE(a,b) \
+        (dSqrt( ((a)[0]-(b)[0])*((a)[0]-(b)[0]) + ((a)[1]-(b)[1])*((a)[1]-(b)[1]) + ((a)[2]-(b)[2])*((a)[2]-(b)[2]) ))
+#endif
+
+
+/*
+ * special case matrix multipication, with operator selection
+ */
+
+#define dMULTIPLYOP0_331(A,op,B,C) \
+do { \
+  (A)[0] op dDOT((B),(C)); \
+  (A)[1] op dDOT((B+4),(C)); \
+  (A)[2] op dDOT((B+8),(C)); \
+} while(0)
+#define dMULTIPLYOP1_331(A,op,B,C) \
+do { \
+  (A)[0] op dDOT41((B),(C)); \
+  (A)[1] op dDOT41((B+1),(C)); \
+  (A)[2] op dDOT41((B+2),(C)); \
+} while(0)
+#define dMULTIPLYOP0_133(A,op,B,C) \
+do { \
+  (A)[0] op dDOT14((B),(C)); \
+  (A)[1] op dDOT14((B),(C+1)); \
+  (A)[2] op dDOT14((B),(C+2)); \
+} while(0)
+#define dMULTIPLYOP0_333(A,op,B,C) \
+do { \
+  (A)[0] op dDOT14((B),(C)); \
+  (A)[1] op dDOT14((B),(C+1)); \
+  (A)[2] op dDOT14((B),(C+2)); \
+  (A)[4] op dDOT14((B+4),(C)); \
+  (A)[5] op dDOT14((B+4),(C+1)); \
+  (A)[6] op dDOT14((B+4),(C+2)); \
+  (A)[8] op dDOT14((B+8),(C)); \
+  (A)[9] op dDOT14((B+8),(C+1)); \
+  (A)[10] op dDOT14((B+8),(C+2)); \
+} while(0)
+#define dMULTIPLYOP1_333(A,op,B,C) \
+do { \
+  (A)[0] op dDOT44((B),(C)); \
+  (A)[1] op dDOT44((B),(C+1)); \
+  (A)[2] op dDOT44((B),(C+2)); \
+  (A)[4] op dDOT44((B+1),(C)); \
+  (A)[5] op dDOT44((B+1),(C+1)); \
+  (A)[6] op dDOT44((B+1),(C+2)); \
+  (A)[8] op dDOT44((B+2),(C)); \
+  (A)[9] op dDOT44((B+2),(C+1)); \
+  (A)[10] op dDOT44((B+2),(C+2)); \
+} while(0)
+#define dMULTIPLYOP2_333(A,op,B,C) \
+do { \
+  (A)[0] op dDOT((B),(C)); \
+  (A)[1] op dDOT((B),(C+4)); \
+  (A)[2] op dDOT((B),(C+8)); \
+  (A)[4] op dDOT((B+4),(C)); \
+  (A)[5] op dDOT((B+4),(C+4)); \
+  (A)[6] op dDOT((B+4),(C+8)); \
+  (A)[8] op dDOT((B+8),(C)); \
+  (A)[9] op dDOT((B+8),(C+4)); \
+  (A)[10] op dDOT((B+8),(C+8)); \
+} while(0)
+
+#ifdef __cplusplus
+
+#define DECL template <class TA, class TB, class TC> PURE_INLINE void
+
+DECL dMULTIPLY0_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_331(A,=,B,C); }
+DECL dMULTIPLY1_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_331(A,=,B,C); }
+DECL dMULTIPLY0_133(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_133(A,=,B,C); }
+DECL dMULTIPLY0_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_333(A,=,B,C); }
+DECL dMULTIPLY1_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_333(A,=,B,C); }
+DECL dMULTIPLY2_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP2_333(A,=,B,C); }
+
+DECL dMULTIPLYADD0_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_331(A,+=,B,C); }
+DECL dMULTIPLYADD1_331(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_331(A,+=,B,C); }
+DECL dMULTIPLYADD0_133(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_133(A,+=,B,C); }
+DECL dMULTIPLYADD0_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP0_333(A,+=,B,C); }
+DECL dMULTIPLYADD1_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP1_333(A,+=,B,C); }
+DECL dMULTIPLYADD2_333(TA *A, const TB *B, const TC *C) { dMULTIPLYOP2_333(A,+=,B,C); }
+
+#undef DECL
+
+#else
+
+#define dMULTIPLY0_331(A,B,C) dMULTIPLYOP0_331(A,=,B,C)
+#define dMULTIPLY1_331(A,B,C) dMULTIPLYOP1_331(A,=,B,C)
+#define dMULTIPLY0_133(A,B,C) dMULTIPLYOP0_133(A,=,B,C)
+#define dMULTIPLY0_333(A,B,C) dMULTIPLYOP0_333(A,=,B,C)
+#define dMULTIPLY1_333(A,B,C) dMULTIPLYOP1_333(A,=,B,C)
+#define dMULTIPLY2_333(A,B,C) dMULTIPLYOP2_333(A,=,B,C)
+
+#define dMULTIPLYADD0_331(A,B,C) dMULTIPLYOP0_331(A,+=,B,C)
+#define dMULTIPLYADD1_331(A,B,C) dMULTIPLYOP1_331(A,+=,B,C)
+#define dMULTIPLYADD0_133(A,B,C) dMULTIPLYOP0_133(A,+=,B,C)
+#define dMULTIPLYADD0_333(A,B,C) dMULTIPLYOP0_333(A,+=,B,C)
+#define dMULTIPLYADD1_333(A,B,C) dMULTIPLYOP1_333(A,+=,B,C)
+#define dMULTIPLYADD2_333(A,B,C) dMULTIPLYOP2_333(A,+=,B,C)
+
+#endif
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/*
+ * normalize 3x1 and 4x1 vectors (i.e. scale them to unit length)
+ */
+ODE_API int  dSafeNormalize3 (dVector3 a);
+ODE_API int  dSafeNormalize4 (dVector4 a);
+
+// For some reason demo_chain1.c does not understand "inline" keyword.
+static __inline void _dNormalize3(dVector3 a)
+{
+        int bNormalizationResult = dSafeNormalize3(a);
+        dIASSERT(bNormalizationResult);
+        dVARIABLEUSED(bNormalizationResult);
+}
+
+static __inline void _dNormalize4(dVector4 a)
+{
+        int bNormalizationResult = dSafeNormalize4(a);
+        dIASSERT(bNormalizationResult);
+        dVARIABLEUSED(bNormalizationResult);
+}
+
+// For DLL export
+ODE_API void dNormalize3 (dVector3 a); // Potentially asserts on zero vec
+ODE_API void dNormalize4 (dVector4 a); // Potentially asserts on zero vec
+
+// For internal use
+#define dNormalize3(a) _dNormalize3(a)
+#define dNormalize4(a) _dNormalize4(a)
+
+/*
+ * given a unit length "normal" vector n, generate vectors p and q vectors
+ * that are an orthonormal basis for the plane space perpendicular to n.
+ * i.e. this makes p,q such that n,p,q are all perpendicular to each other.
+ * q will equal n x p. if n is not unit length then p will be unit length but
+ * q wont be.
+ */
+
+ODE_API void dPlaneSpace (const dVector3 n, dVector3 p, dVector3 q);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif