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moMath.h
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1 /*******************************************************************************
2 
3  moMath.h
4 
5  ****************************************************************************
6  * *
7  * This source is free software; you can redistribute it and/or modify *
8  * it under the terms of the GNU General Public License as published by *
9  * the Free Software Foundation; either version 2 of the License, or *
10  * (at your option) any later version. *
11  * *
12  * This code is distributed in the hope that it will be useful, but *
13  * WITHOUT ANY WARRANTY; without even the implied warranty of *
14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
15  * General Public License for more details. *
16  * *
17  * A copy of the GNU General Public License is available on the World *
18  * Wide Web at <http://www.gnu.org/copyleft/gpl.html>. You can also *
19  * obtain it by writing to the Free Software Foundation, *
20  * Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. *
21  * *
22  ****************************************************************************
23 
24  Copyright(C) 2006 Fabricio Costa
25 
26  Authors:
27  Fabricio Costa
28  Andrés Colubri
29 
30  Portions taken from
31  Wild Magic Source Code
32  David Eberly
33  http://www.geometrictools.com
34  Copyright (c) 1998-2007
35 
36 *******************************************************************************/
37 
38 #ifndef __MO_MATH_H__
39 #define __MO_MATH_H__
40 
41 #include "moTypes.h"
42 #include "moAbstract.h"
43 
44 #ifndef NOMINMAX
45 #ifndef momax
46 #define momax(a,b) ((a)>(b)?(a):(b))
47 #endif
48 #ifndef momin
49 #define momin(a,b) ((a)<(b)?(a):(b))
50 #endif
51 #endif
52 
63  template <class Real>
64 class LIBMOLDEO_API moMath
65 {
66 public:
70  moMath() {}
74  ~moMath() {}
75 
81  inline static Real ACos (Real fValue)
82  {
83  if (-(Real)1.0 < fValue)
84  {
85  if (fValue < (Real)1.0)
86  {
87  return (Real)acos((double)fValue);
88  }
89  else
90  {
91  return (Real)0.0;
92  }
93  }
94  else
95  {
96  return moMath::PI;
97  }
98  }
99 
105  inline static Real ASin (Real fValue)
106  {
107  if (-(Real)1.0 < fValue)
108  {
109  if (fValue < (Real)1.0)
110  {
111  return (Real)asin((double)fValue);
112  }
113  else
114  {
115  return HALF_PI;
116  }
117  }
118  else
119  {
120  return -HALF_PI;
121  }
122  }
123 
129  inline static Real ATan (Real fValue)
130  {
131  return (Real)atan((double)fValue);
132  }
133 
140  inline static Real ATan2 (Real fY, Real fX)
141  {
142  return (Real)atan2((double)fY,(double)fX);
143  }
144 
150  inline static Real Ceil (Real fValue)
151  {
152  return (Real)ceil((double)fValue);
153  }
154 
160  inline static Real Cos (Real fValue)
161  {
162  return (Real)cos((double)fValue);
163  }
164 
170  inline static Real Exp (Real fValue)
171  {
172  return (Real)exp((double)fValue);
173  }
174 
180  inline static Real FAbs (Real fValue)
181  {
182  return (Real)fabs((double)fValue);
183  }
184 
190  inline static Real Floor (Real fValue)
191  {
192  return (Real)floor((double)fValue);
193  }
194 
200  inline static Real FMod (Real fX, Real fY)
201  {
202  return (Real)fmod((double)fX,(double)fY);
203  }
204 
210  inline static Real InvSqrt (Real fValue)
211  {
212  return (Real)(1.0/sqrt((double)fValue));
213  }
214 
220  inline static Real Log (Real fValue)
221  {
222  return (Real)log((double)fValue);
223  }
224 
230  inline static Real Log2 (Real fValue)
231  {
232  return moMath<Real>::INV_LN_2 * (Real)log((double)fValue);
233  }
234 
240  inline static Real Log10 (Real fValue)
241  {
242  return moMath<Real>::INV_LN_10 * (Real)log((double)fValue);
243  }
244 
250  inline static Real Pow (Real fBase, Real fExponent)
251  {
252  return (Real)pow((double)fBase,(double)fExponent);
253  }
254 
260  inline static Real Sin (Real fValue)
261  {
262  return (Real)sin((double)fValue);
263  }
264 
270  inline static Real Sqr (Real fValue) {
271  return fValue*fValue;
272  }
273 
279  inline static Real Sqrt (Real fValue) {
280  return (Real)sqrt((double)fValue);
281  }
282 
288  inline static Real Tan (Real fValue) {
289  return (Real)tan((double)fValue);
290  }
291 
297  inline bool IsPowerOfTwo (int iValue) {
298  return (iValue > 0) && ((iValue & (iValue - 1)) == 0);
299  }
300 
306  inline unsigned int Log2OfPowerOfTwo (unsigned int uiPowerOfTwo) {
307  unsigned int uiLog2 = (uiPowerOfTwo & 0xAAAAAAAA) != 0;
308  uiLog2 |= ((uiPowerOfTwo & 0xFFFF0000) != 0) << 4;
309  uiLog2 |= ((uiPowerOfTwo & 0xFF00FF00) != 0) << 3;
310  uiLog2 |= ((uiPowerOfTwo & 0xF0F0F0F0) != 0) << 2;
311  uiLog2 |= ((uiPowerOfTwo & 0xCCCCCCCC) != 0) << 1;
312  return uiLog2;
313  }
314 
322  inline static int ScaledFloatToInt(float fFloat, int iLog)
323  {
324  int iInt;
325  int iShift;
326  iShift = 150 - iLog - ((*(int*)(&fFloat) >> 23) & 0xFF);
327  if ( iShift < 24 )
328  {
329  iInt = ((*(int*)(&fFloat) & 0x007FFFFF) | 0x00800000) >> iShift;
330  if ( iInt == (1 << iLog) ) iInt--;
331  }
332  else iInt = 0;
333  return iInt;
334  }
335 
341  inline static char Sign (int iValue) {
342  if (iValue > 0)
343  {
344  return 1;
345  }
346 
347  if (iValue < 0)
348  {
349  return -1;
350  }
351 
352  return 0;
353  }
354 
360  inline static Real Sign (Real fValue) {
361  if (fValue > (Real)0.0)
362  {
363  return (Real)1.0;
364  }
365 
366  if (fValue < (Real)0.0)
367  {
368  return -(Real)1.0;
369  }
370 
371  return (Real)0.0;
372  }
373 
380  inline static Real UnitRandom (unsigned int uiSeed = 0) {
381  if (uiSeed > 0)
382  {
383  srand(uiSeed);
384  }
385 
386  double dRatio = ((double)rand())/((double)(RAND_MAX));
387  return (Real)dRatio;
388  }
389 
396  inline static Real SymmetricRandom (unsigned int uiSeed = 0) {
397  if (uiSeed > 0.0)
398  {
399  srand(uiSeed);
400  }
401 
402  double dRatio = ((double)rand())/((double)(RAND_MAX));
403  return (Real)(2.0*dRatio - 1.0);
404  }
405 
414  inline static Real IntervalRandom (Real fMin, Real fMax,
415  unsigned int uiSeed = 0) {
416  if (uiSeed > 0)
417  {
418  srand(uiSeed);
419  }
420 
421  double dRatio = ((double)rand())/((double)(RAND_MAX));
422  return fMin+(fMax-fMin)*((Real)dRatio);
423  }
424 
431  inline static Real UnitRandom (Real rSeed) {
432  return UnitRandom ((unsigned int)rSeed);
433  }
440  inline static Real SymmetricRandom (Real rSeed) {
441  return SymmetricRandom ((unsigned int)rSeed);
442  }
451  inline static Real IntervalRandom (Real fMin, Real fMax, Real rSeed) {
452  return IntervalRandom (fMin, fMax, (unsigned int)rSeed);
453  }
454 
460  inline static Real FastSin0 (Real fAngle) {
461  Real fASqr = fAngle*fAngle;
462  Real fResult = (Real)7.61e-03;
463  fResult *= fASqr;
464  fResult -= (Real)1.6605e-01;
465  fResult *= fASqr;
466  fResult += (Real)1.0;
467  fResult *= fAngle;
468  return fResult;
469  }
470 
476  inline static Real FastSin1 (Real fAngle) {
477  Real fASqr = fAngle*fAngle;
478  Real fResult = -(Real)2.39e-08;
479  fResult *= fASqr;
480  fResult += (Real)2.7526e-06;
481  fResult *= fASqr;
482  fResult -= (Real)1.98409e-04;
483  fResult *= fASqr;
484  fResult += (Real)8.3333315e-03;
485  fResult *= fASqr;
486  fResult -= (Real)1.666666664e-01;
487  fResult *= fASqr;
488  fResult += (Real)1.0;
489  fResult *= fAngle;
490  return fResult;
491  }
492 
498  inline static Real FastCos0 (Real fAngle) {
499  Real fASqr = fAngle*fAngle;
500  Real fResult = (Real)3.705e-02;
501  fResult *= fASqr;
502  fResult -= (Real)4.967e-01;
503  fResult *= fASqr;
504  fResult += (Real)1.0;
505  return fResult;
506  }
507 
513  inline static Real FastCos1 (Real fAngle) {
514  Real fASqr = fAngle*fAngle;
515  Real fResult = -(Real)2.605e-07;
516  fResult *= fASqr;
517  fResult += (Real)2.47609e-05;
518  fResult *= fASqr;
519  fResult -= (Real)1.3888397e-03;
520  fResult *= fASqr;
521  fResult += (Real)4.16666418e-02;
522  fResult *= fASqr;
523  fResult -= (Real)4.999999963e-01;
524  fResult *= fASqr;
525  fResult += (Real)1.0;
526  return fResult;
527  }
528 
534  inline static Real FastTan0 (Real fAngle) {
535  Real fASqr = fAngle*fAngle;
536  Real fResult = (Real)2.033e-01;
537  fResult *= fASqr;
538  fResult += (Real)3.1755e-01;
539  fResult *= fASqr;
540  fResult += (Real)1.0;
541  fResult *= fAngle;
542  return fResult;
543  }
544 
550  inline static Real FastTan1 (Real fAngle) {
551  Real fASqr = fAngle*fAngle;
552  Real fResult = (Real)9.5168091e-03;
553  fResult *= fASqr;
554  fResult += (Real)2.900525e-03;
555  fResult *= fASqr;
556  fResult += (Real)2.45650893e-02;
557  fResult *= fASqr;
558  fResult += (Real)5.33740603e-02;
559  fResult *= fASqr;
560  fResult += (Real)1.333923995e-01;
561  fResult *= fASqr;
562  fResult += (Real)3.333314036e-01;
563  fResult *= fASqr;
564  fResult += (Real)1.0;
565  fResult *= fAngle;
566  return fResult;
567  }
568 
574  inline static Real FastInvSin0 (Real fValue) {
575  Real fRoot = moMath<Real>::Sqrt(((Real)1.0)-fValue);
576  Real fResult = -(Real)0.0187293;
577  fResult *= fValue;
578  fResult += (Real)0.0742610;
579  fResult *= fValue;
580  fResult -= (Real)0.2121144;
581  fResult *= fValue;
582  fResult += (Real)1.5707288;
583  fResult = HALF_PI - fRoot*fResult;
584  return fResult;
585  }
586 
592  inline static Real FastInvSin1 (Real fValue) {
593  Real fRoot = moMath<Real>::Sqrt(FAbs(((Real)1.0)-fValue));
594  Real fResult = -(Real)0.0012624911;
595  fResult *= fValue;
596  fResult += (Real)0.0066700901;
597  fResult *= fValue;
598  fResult -= (Real)0.0170881256;
599  fResult *= fValue;
600  fResult += (Real)0.0308918810;
601  fResult *= fValue;
602  fResult -= (Real)0.0501743046;
603  fResult *= fValue;
604  fResult += (Real)0.0889789874;
605  fResult *= fValue;
606  fResult -= (Real)0.2145988016;
607  fResult *= fValue;
608  fResult += (Real)1.5707963050;
609  fResult = HALF_PI - fRoot*fResult;
610  return fResult;
611  }
612 
618  inline static Real FastInvCos0 (Real fValue) {
619  Real fRoot = moMath<Real>::Sqrt(((Real)1.0)-fValue);
620  Real fResult = -(Real)0.0187293;
621  fResult *= fValue;
622  fResult += (Real)0.0742610;
623  fResult *= fValue;
624  fResult -= (Real)0.2121144;
625  fResult *= fValue;
626  fResult += (Real)1.5707288;
627  fResult *= fRoot;
628  return fResult;
629  }
630 
636  inline static Real FastInvCos1 (Real fValue) {
637  Real fRoot = moMath<Real>::Sqrt(FAbs(((Real)1.0)-fValue));
638  Real fResult = -(Real)0.0012624911;
639  fResult *= fValue;
640  fResult += (Real)0.0066700901;
641  fResult *= fValue;
642  fResult -= (Real)0.0170881256;
643  fResult *= fValue;
644  fResult += (Real)0.0308918810;
645  fResult *= fValue;
646  fResult -= (Real)0.0501743046;
647  fResult *= fValue;
648  fResult += (Real)0.0889789874;
649  fResult *= fValue;
650  fResult -= (Real)0.2145988016;
651  fResult *= fValue;
652  fResult += (Real)1.5707963050;
653  fResult *= fRoot;
654  return fResult;
655  }
656 
662  inline static Real FastInvTan0 (Real fValue) {
663  Real fVSqr = fValue*fValue;
664  Real fResult = (Real)0.0208351;
665  fResult *= fVSqr;
666  fResult -= (Real)0.085133;
667  fResult *= fVSqr;
668  fResult += (Real)0.180141;
669  fResult *= fVSqr;
670  fResult -= (Real)0.3302995;
671  fResult *= fVSqr;
672  fResult += (Real)0.999866;
673  fResult *= fValue;
674  return fResult;
675  }
676 
682  inline static Real FastInvTan1 (Real fValue) {
683  Real fVSqr = fValue*fValue;
684  Real fResult = (Real)0.0028662257;
685  fResult *= fVSqr;
686  fResult -= (Real)0.0161657367;
687  fResult *= fVSqr;
688  fResult += (Real)0.0429096138;
689  fResult *= fVSqr;
690  fResult -= (Real)0.0752896400;
691  fResult *= fVSqr;
692  fResult += (Real)0.1065626393;
693  fResult *= fVSqr;
694  fResult -= (Real)0.1420889944;
695  fResult *= fVSqr;
696  fResult += (Real)0.1999355085;
697  fResult *= fVSqr;
698  fResult -= (Real)0.3333314528;
699  fResult *= fVSqr;
700  fResult += (Real)1.0;
701  fResult *= fValue;
702  return fResult;
703  }
704 
710  static Real FastInvSqrt (Real fValue);
711 
717  inline static Real FastNegExp0 (Real fValue) {
718  Real fResult = (Real)0.0038278;
719  fResult *= fValue;
720  fResult += (Real)0.0292732;
721  fResult *= fValue;
722  fResult += (Real)0.2507213;
723  fResult *= fValue;
724  fResult += (Real)1.0;
725  fResult *= fResult;
726  fResult *= fResult;
727  fResult = ((Real)1.0)/fResult;
728  return fResult;
729  }
730 
736  inline static Real FastNegExp1 (Real fValue) {
737  Real fResult = (Real)0.00026695;
738  fResult *= fValue;
739  fResult += (Real)0.00227723;
740  fResult *= fValue;
741  fResult += (Real)0.03158565;
742  fResult *= fValue;
743  fResult += (Real)0.24991035;
744  fResult *= fValue;
745  fResult += (Real)1.0;
746  fResult *= fResult;
747  fResult *= fResult;
748  fResult = ((Real)1.0)/fResult;
749  return fResult;
750  }
751 
757  inline static Real FastNegExp2 (Real fValue) {
758  Real fResult = (Real)0.000014876;
759  fResult *= fValue;
760  fResult += (Real)0.000127992;
761  fResult *= fValue;
762  fResult += (Real)0.002673255;
763  fResult *= fValue;
764  fResult += (Real)0.031198056;
765  fResult *= fValue;
766  fResult += (Real)0.250010936;
767  fResult *= fValue;
768  fResult += (Real)1.0;
769  fResult *= fResult;
770  fResult *= fResult;
771  fResult = ((Real)1.0)/fResult;
772  return fResult;
773  }
774 
780  inline static Real FastNegExp3 (Real fValue) {
781  Real fResult = (Real)0.0000006906;
782  fResult *= fValue;
783  fResult += (Real)0.0000054302;
784  fResult *= fValue;
785  fResult += (Real)0.0001715620;
786  fResult *= fValue;
787  fResult += (Real)0.0025913712;
788  fResult *= fValue;
789  fResult += (Real)0.0312575832;
790  fResult *= fValue;
791  fResult += (Real)0.2499986842;
792  fResult *= fValue;
793  fResult += (Real)1.0;
794  fResult *= fResult;
795  fResult *= fResult;
796  fResult = ((Real)1.0)/fResult;
797  return fResult;
798  }
799 
805  inline static Real DegToRad(Real iDeg)
806  {
807  return DEG_TO_RAD * iDeg;
808  }
809 
815  inline static Real RadToDeg(Real iRad)
816  {
817  return RAD_TO_DEG * iRad;
818  }
819 
823  static const Real EPSILON;
824  static const Real ZERO_TOLERANCE;
825  static const Real MAX_REAL;
826  static const Real PI;
827  static const Real TWO_PI;
828  static const Real HALF_PI;
829  static const Real INV_PI;
830  static const Real INV_TWO_PI;
831  static const Real DEG_TO_RAD;
832  static const Real RAD_TO_DEG;
833  static const Real LN_2;
834  static const Real LN_10;
835  static const Real INV_LN_2;
836  static const Real INV_LN_10;
837 };
838 
839 #ifndef MO_MACOSX
840 #ifndef MO_RASPBIAN
841 #ifndef MO_WIN32
842 template class LIBMOLDEO_API moMath<long>;
843 template class LIBMOLDEO_API moMath<double>;
844 template class LIBMOLDEO_API moMath<float>;
845 #endif
846 #endif
847 #endif
848 
849 typedef moMath<long> moMathi;
850 typedef moMath<double> moMathd;
851 typedef moMath<float> moMathf;
852 
853 #ifdef MO_USING_VCXX
854  template<> const MOlong moMath<MOlong>::EPSILON = FLT_EPSILON;
855  template<> const MOlong moMath<MOlong>::ZERO_TOLERANCE = 1e-06f;
856  template<> const MOlong moMath<MOlong>::MAX_REAL = FLT_MAX;
857  template<> const MOlong moMath<MOlong>::PI = (MOlong)(4.0*atan(1.0));
858  template<> const MOlong moMath<MOlong>::TWO_PI = 2.0f*moMath<MOlong>::PI;
859  template<> const MOlong moMath<MOlong>::HALF_PI = 0.5f*moMath<MOlong>::PI;
860  template<> const MOlong moMath<MOlong>::INV_PI = 1.0f/moMath<MOlong>::PI;
861  template<> const MOlong moMath<MOlong>::INV_TWO_PI = 1.0f/moMath<MOlong>::TWO_PI;
862  template<> const MOlong moMath<MOlong>::DEG_TO_RAD = moMath<MOlong>::PI/180.0f;
863  template<> const MOlong moMath<MOlong>::RAD_TO_DEG = 180.0f/moMath<MOlong>::PI;
864  template<> const MOlong moMath<MOlong>::LN_2 = moMath<MOlong>::Log(2.0f);
865  template<> const MOlong moMath<MOlong>::LN_10 = moMath<MOlong>::Log(10.0f);
866  template<> const MOlong moMath<MOlong>::INV_LN_2 = 1.0f/moMath<MOlong>::LN_2;
867  template<> const MOlong moMath<MOlong>::INV_LN_10 = 1.0f/moMath<MOlong>::LN_10;
868 
869  template<> const MOfloat moMath<MOfloat>::EPSILON = FLT_EPSILON;
870  template<> const MOfloat moMath<MOfloat>::ZERO_TOLERANCE = 1e-06f;
871  template<> const MOfloat moMath<MOfloat>::MAX_REAL = FLT_MAX;
872  template<> const MOfloat moMath<MOfloat>::PI = (MOfloat)(4.0*atan(1.0));
873  template<> const MOfloat moMath<MOfloat>::TWO_PI = 2.0f*moMath<MOfloat>::PI;
874  template<> const MOfloat moMath<MOfloat>::HALF_PI = 0.5f*moMath<MOfloat>::PI;
875  template<> const MOfloat moMath<MOfloat>::INV_PI = 1.0f/moMath<MOfloat>::PI;
876  template<> const MOfloat moMath<MOfloat>::INV_TWO_PI = 1.0f/moMath<MOfloat>::TWO_PI;
877  template<> const MOfloat moMath<MOfloat>::DEG_TO_RAD = moMath<MOfloat>::PI/180.0f;
878  template<> const MOfloat moMath<MOfloat>::RAD_TO_DEG = 180.0f/moMath<MOfloat>::PI;
879  template<> const MOfloat moMath<MOfloat>::LN_2 = moMath<MOfloat>::Log(2.0f);
880  template<> const MOfloat moMath<MOfloat>::LN_10 = moMath<MOfloat>::Log(10.0f);
881  template<> const MOfloat moMath<MOfloat>::INV_LN_2 = 1.0f/moMath<MOfloat>::LN_2;
882  template<> const MOfloat moMath<MOfloat>::INV_LN_10 = 1.0f/moMath<MOfloat>::LN_10;
883 
884  template<> const MOdouble moMath<MOdouble>::EPSILON = DBL_EPSILON;
885  template<> const MOdouble moMath<MOdouble>::ZERO_TOLERANCE = 1e-08;
886  template<> const MOdouble moMath<MOdouble>::MAX_REAL = DBL_MAX;
887  template<> const MOdouble moMath<MOdouble>::PI = 4.0*atan(1.0);
888  template<> const MOdouble moMath<MOdouble>::TWO_PI = 2.0*moMath<MOdouble>::PI;
889  template<> const MOdouble moMath<MOdouble>::HALF_PI = 0.5*moMath<MOdouble>::PI;
890  template<> const MOdouble moMath<MOdouble>::INV_PI = 1.0/moMath<MOdouble>::PI;
891  template<> const MOdouble moMath<MOdouble>::INV_TWO_PI = 1.0/moMath<MOdouble>::TWO_PI;
892  template<> const MOdouble moMath<MOdouble>::DEG_TO_RAD = moMath<MOdouble>::PI/180.0;
893  template<> const MOdouble moMath<MOdouble>::RAD_TO_DEG = 180.0/moMath<MOdouble>::PI;
894  template<> const MOdouble moMath<MOdouble>::LN_2 = moMath<MOdouble>::Log(2.0);
895  template<> const MOdouble moMath<MOdouble>::LN_10 = moMath<MOdouble>::Log(10.0);
896  template<> const MOdouble moMath<MOdouble>::INV_LN_2 = 1.0/moMath<MOdouble>::LN_2;
897  template<> const MOdouble moMath<MOdouble>::INV_LN_10 = 1.0/moMath<MOdouble>::LN_10;
898 
899  template <>
900  long moMath<MOlong>::FastInvSqrt (MOlong fValue)
901  {
902 
903  return fValue;
904  }
905 
906  template <>
907  float moMath<MOfloat>::FastInvSqrt (MOfloat fValue)
908  {
909  MOfloat fHalf = 0.5f*fValue;
910  int i = *(int*)&fValue;
911  i = 0x5f3759df - (i >> 1);
912  fValue = *(MOfloat*)&i;
913  fValue = fValue*(1.5f - fHalf*fValue*fValue);
914  return fValue;
915  }
916 
917  template <>
918  MOdouble moMath<MOdouble>::FastInvSqrt (MOdouble dValue)
919  {
920  MOdouble dHalf = 0.5*dValue;
921  MOlonglong i = *(MOlonglong*)&dValue;
922  #if defined(WM4_USING_VC70) || defined(WM4_USING_VC6)
923  i = 0x5fe6ec85e7de30da - (i >> 1);
924  #else
925  i = 0x5fe6ec85e7de30daLL - (i >> 1);
926  #endif
927  dValue = *(MOdouble*)&i;
928  dValue = dValue*(1.5 - dHalf*dValue*dValue);
929  return dValue;
930  }
931 #endif
932 
933 #endif /*__MO_MATH_H__*/
934 
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