libcm/cmMath.h

#ifndef cmMath_h
#define cmMath_h

#ifdef __cplusplus
extern "C" {
#endif

  //( { file_desc:"Math utility functions" kw:[math] }
  
  double   cmX80ToDouble( unsigned char s[10] );
  void     cmDoubleToX80( double v, unsigned char s[10] );

  bool     cmIsPowerOfTwo(   unsigned i );
  unsigned cmNextPowerOfTwo( unsigned i );
  unsigned cmNearPowerOfTwo( unsigned i );

  bool     cmIsOddU(    unsigned v );
  bool     cmIsEvenU(   unsigned v );
  unsigned cmNextOddU(  unsigned v );
  unsigned cmPrevOddU(  unsigned v );
  unsigned cmNextEvenU( unsigned v );
  unsigned cmPrevEvenU( unsigned v );

  /// Increment or decrement 'idx' by 'delta' always wrapping the result into the range
  /// 0 to (maxN-1).
  /// 'idx': initial value 
  /// 'delta':  incremental amount
  /// 'maxN' - 1 : maximum return value.
  unsigned cmModIncr(int idx, int delta, int maxN );

  // modified bessel function of first kind, order 0
  // ref: orfandis appendix B io.m
  double   cmBessel0( double x );


  //=================================================================
  // The following elliptic-related function approximations come from
  // Parks & Burrus, Digital Filter Design, Appendix program 9, pp. 317-326
  // which in turn draws directly on other sources

  // calculate complete elliptic integral (quarter period) K
  // given *complimentary* modulus kc
  cmReal_t cmEllipK( cmReal_t kc );

  // calculate elliptic modulus k
  // given ratio of complete elliptic integrals r = K/K'
  // (solves the "degree equation" for fixed N = K*K1'/K'K1)
  cmReal_t cmEllipDeg( cmReal_t r );

  // calculate arc elliptic tangent u (elliptic integral of the 1st kind)
  // given argument x = sc(u,k) and *complimentary* modulus kc
  cmReal_t cmEllipArcSc( cmReal_t x, cmReal_t kc );

  // calculate Jacobi elliptic functions sn, cn, and dn
  // given argument u and *complimentary* modulus kc
  cmRC_t   cmEllipJ( cmReal_t u, cmReal_t kc, cmReal_t* sn, cmReal_t* cn, cmReal_t* dn );


  //=================================================================
  // bilinear transform
  // z = (2*sr + s)/(2*sr - s)
  cmRC_t cmBlt( unsigned n, cmReal_t sr, cmReal_t* rp, cmReal_t* ip );


  //=================================================================
  // Pitch conversion
  unsigned cmHzToMidi( double hz );
  float    cmMidiToHz( unsigned midi );

  //=================================================================
  // Floating point byte swapping
  unsigned           cmFfSwapFloatToUInt( float v );
  float              cmFfSwapUIntToFloat( unsigned v );
  unsigned long long cmFfSwapDoubleToULLong( double v );
  double             cmFfSwapULLongToDouble( unsigned long long v );

  //=================================================================
  int      cmRandInt( int min, int max );
  unsigned cmRandUInt( unsigned min, unsigned max );
  float    cmRandFloat( float min, float max );
  double   cmRandDouble( double min, double max );

  //=================================================================
  bool cmIsCloseD( double   x0, double   x1, double eps );
  bool cmIsCloseF( float    x0, float    x1, double eps );
  bool cmIsCloseI( int      x0, int      x1, double eps );
  bool cmIsCloseU( unsigned x0, unsigned x1, double eps );

  //=================================================================
  // Run a length 'lfsrN' linear feedback shift register (LFSR) for 'yN' iterations to
  // produce a length 'yN' bit string in yV[yN].
  // 'lfsrN' count of bits in the shift register range: 2<= lfsrN <= 32.
  // 'tapMask' is a bit mask which gives the tap indexes positions for the LFSR. 
  // The least significant bit corresponds to the maximum delay tap position.  
  // The min tap position is therefore denoted by the tap mask bit location 1 << (lfsrN-1).
  // A minimum of two taps must exist.
  // 'seed' sets the initial delay state.
  // 'yV[yN]' is the the output vector
  // 'yN' is count of elements in yV.
  // The function resturn kOkAtRC on success or kInvalidArgsRCRC if any arguments are invalid.
  // /sa cmLFSR_Test.
  void   cmLFSR( unsigned lfsrN, unsigned tapMask, unsigned seed, unsigned* yV, unsigned yN );

  // Example and test code for cmLFSR() 
  bool cmLFSR_Test();


  // Generate a set of 'goldN' Gold codes using the Maximum Length Sequences (MLS) generated
  // by a length 'lfsrN' linear feedback shift register.
  // 'err' is an error object to be set if the the function fails.
  // 'lfsrN' is the length of the Linear Feedback Shift Registers (LFSR) used to generate the MLS.
  // 'poly_coeff0' tap mask for the first LFSR.
  // 'coeff1' tap mask the the second LFSR.
  // 'goldN' is the count of Gold codes to generate. 
  // 'yM[mlsN', goldN] is a column major output matrix where each column contains a Gold code.
  // 'mlsN' is the length of the maximum length sequence for each Gold code which can be
  // calculated as mlsN = (1 << a->lfsrN) - 1.
  // Note that values of 'lfsrN' and the 'poly_coeffx' must be carefully selected such that
  // they will produce a MLS.  For example to generate a MLS with length 31 set 'lfsrN' to 5 and
  // then select poly_coeff from two different elements of the set {0x12 0x14 0x17 0x1B 0x1D 0x1E}.
  // See http://www.ece.cmu.edu/~koopman/lfsr/index.html for a complete set of MSL polynomial
  // coefficients for given LFSR lengths.
  // Returns false if insufficient balanced pairs exist.
  bool   cmGenGoldCodes( unsigned lfsrN, unsigned poly_coeff0, unsigned poly_coeff1, unsigned goldN, int* yM, unsigned mlsN  );

  //)
  
#ifdef __cplusplus
}
#endif

#endif