#ifndef cwMath_h #define cwMath_h namespace cw { namespace math { double x80ToDouble( unsigned char s[10] ); void doubleToX80( double v, unsigned char s[10] ); bool isPowerOfTwo( unsigned i ); unsigned nextPowerOfTwo( unsigned i ); unsigned nearPowerOfTwo( unsigned i ); bool isOddU( unsigned v ); bool isEvenU( unsigned v ); unsigned nextOddU( unsigned v ); unsigned prevOddU( unsigned v ); unsigned nextEvenU( unsigned v ); unsigned prevEvenU( 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 modIncr(int idx, int delta, int maxN ); // modified bessel function of first kind, order 0 // ref: orfandis appendix B io.m template< typename T > T bessel0( T x ) { T eps = pow(10.0,-9.0); T n = 1.0; T S = 1.0; T D = 1.0; while(D > eps*S) { T t = x /(2.0*n); n = n+1; D = D * pow(t,2.0); S = S + D; } return S; } //================================================================= // 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. template< typename T > T ellipK( T kc ) { T a = 1, b = kc, c = 1, tmp; while( c > std::numeric_limits::epsilon ) { c = 0.5*(a-b); tmp = 0.5*(a+b); b = sqrt(a*b); a = tmp; } return M_PI/(2*a); } // Calculate elliptic modulus k // given ratio of complete elliptic integrals r = K/K' // (solves the "degree equation" for fixed N = K*K1'/K'K1) template< typename T > T ellipDeg( T r ) { T q,a,b,c,d; a = b = c = 1; d = q = exp(-M_PI*r); while( c > std::numeric_limits::epsilon ) { a = a + 2*c*d; c = c*d*d; b = b + c; d = d*q; } return 4*sqrt(q)*pow(b/a,2); } // calculate arc elliptic tangent u (elliptic integral of the 1st kind) // given argument x = sc(u,k) and *complimentary* modulus kc template< typename T > T ellipArcSc( T x, T kc ) { T a = 1, b = kc, y = 1/x, tmp; unsigned L = 0; while( true ) { tmp = a*b; a += b; b = 2*sqrt(tmp); y -= tmp/y; if( y == 0 ) y = sqrt(tmp) * 1E-10; if( fabs(a-b)/a < std::numeric_limits::epsilon ) break; L *= 2; if( y < 0 ) L++; } if( y < 0 ) L++; return (atan(a/y) + M_PI*L)/a; } // calculate Jacobi elliptic functions sn, cn, and dn // given argument u and *complimentary* modulus kc template< typename T > rc_t ellipJ( T u, T kc, T* sn, T* cn, T* dn ) { assert( sn != NULL || cn != NULL || dn != NULL ); if( u == 0 ) { if( sn != NULL ) *sn = 0; if( cn != NULL ) *cn = 1; if( dn != NULL ) *dn = 1; return kOkRC; } int i; T a,b,c,d,e,tmp,_sn,_cn,_dn; T aa[16], bb[16]; a = 1; b = kc; for( i = 0; i < 16; i++ ) { aa[i] = a; bb[i] = b; tmp = (a+b)/2; b = sqrt(a*b); a = tmp; if( (a-b)/a < std::numeric_limits::epsilon ) break; } c = a/tan(u*a); d = 1; for( ; i >= 0; i-- ) { e = c*c/a; c = c*d; a = aa[i]; d = (e + bb[i]) / (e+a); } _sn = 1/sqrt(1+c*c); _cn = _sn*c; _dn = d; if( sn != NULL ) *sn = _sn; if( cn != NULL ) *cn = _cn; if( dn != NULL ) *dn = _dn; return kOkRC; } //================================================================= // bilinear transform // z = (2*sr + s)/(2*sr - s) template< typename T > rc_t blt( unsigned n, T sr, T* rp, T* ip ) { unsigned i; T a = 2*sr, tr, ti, td; for( i = 0; i < n; i++ ) { tr = rp[i]; ti = ip[i]; td = pow(a-tr, 2) + ti*ti; rp[i] = (a*a - tr*tr - ti*ti)/td; ip[i] = 2*a*ti/td; if( tr < -1E15 ) rp[i] = 0; if( fabs(ti) > 1E15 ) ip[i] = 0; } return kOkRC; } //================================================================= // Pitch conversion unsigned hzToMidi( double hz ); float midiToHz( unsigned midi ); //================================================================= // Floating point byte swapping unsigned ffSwapFloatToUInt( float v ); float ffSwapUIntToFloat( unsigned v ); unsigned long long ffSwapDoubleToULLong( double v ); double ffSwapULLongToDouble( unsigned long long v ); //================================================================= template< typename T > T rand_range(T min, T max ) { assert( min <= max ); T range = max - min; return min + std::max(0,std::min(range,(T)range * rand() / RAND_MAX)); } int randInt( int min, int max ); unsigned randUInt( unsigned min, unsigned max ); float randFloat( float min, float max ); double randDouble( double min, double max ); //================================================================= bool isCloseD( double x0, double x1, double eps ); bool isCloseF( float x0, float x1, double eps ); bool isCloseI( int x0, int x1, double eps ); bool isCloseU( 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 lFSR_Test. void lFSR( unsigned lfsrN, unsigned tapMask, unsigned seed, unsigned* yV, unsigned yN ); // Example and test code for lFSR() bool lFSR_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.u.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 genGoldCodes( unsigned lfsrN, unsigned poly_coeff0, unsigned poly_coeff1, unsigned goldN, int* yM, unsigned mlsN ); } } #endif