287 lines
8.3 KiB
C++
287 lines
8.3 KiB
C++
//| Copyright: (C) 2020-2024 Kevin Larke <contact AT larke DOT org>
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//| License: GNU GPL version 3.0 or above. See the accompanying LICENSE file.
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#ifndef cwMath_h
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#define cwMath_h
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namespace cw
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{
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namespace math
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{
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double x80ToDouble( unsigned char s[10] );
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void doubleToX80( double v, unsigned char s[10] );
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bool isPowerOfTwo( unsigned i );
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unsigned nextPowerOfTwo( unsigned i );
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unsigned nearPowerOfTwo( unsigned i );
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bool isOddU( unsigned v );
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bool isEvenU( unsigned v );
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unsigned nextOddU( unsigned v );
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unsigned prevOddU( unsigned v );
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unsigned nextEvenU( unsigned v );
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unsigned prevEvenU( unsigned v );
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/// Increment or decrement 'idx' by 'delta' always wrapping the result into the range
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/// 0 to (maxN-1).
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/// 'idx': initial value
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/// 'delta': incremental amount
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/// 'maxN' - 1 : maximum return value.
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unsigned modIncr(int idx, int delta, int maxN );
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// modified bessel function of first kind, order 0
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// ref: orfandis appendix B io.m
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template< typename T >
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T bessel0( T x )
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{
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T eps = pow(10.0,-9.0);
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T n = 1.0;
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T S = 1.0;
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T D = 1.0;
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while(D > eps*S)
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{
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T t = x /(2.0*n);
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n = n+1;
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D = D * pow(t,2.0);
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S = S + D;
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}
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return S;
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}
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//=================================================================
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// The following elliptic-related function approximations come from
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// Parks & Burrus, Digital Filter Design, Appendix program 9, pp. 317-326
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// which in turn draws directly on other sources
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// Calculate complete elliptic integral (quarter period) K
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// given *complimentary* modulus kc.
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template< typename T >
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T ellipK( T kc )
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{
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T a = 1, b = kc, c = 1, tmp;
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while( c > std::numeric_limits<T>::epsilon )
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{
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c = 0.5*(a-b);
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tmp = 0.5*(a+b);
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b = sqrt(a*b);
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a = tmp;
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}
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return M_PI/(2*a);
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}
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// Calculate elliptic modulus k
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// given ratio of complete elliptic integrals r = K/K'
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// (solves the "degree equation" for fixed N = K*K1'/K'K1)
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template< typename T >
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T ellipDeg( T r )
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{
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T q,a,b,c,d;
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a = b = c = 1;
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d = q = exp(-M_PI*r);
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while( c > std::numeric_limits<T>::epsilon )
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{
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a = a + 2*c*d;
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c = c*d*d;
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b = b + c;
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d = d*q;
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}
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return 4*sqrt(q)*pow(b/a,2);
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}
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// calculate arc elliptic tangent u (elliptic integral of the 1st kind)
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// given argument x = sc(u,k) and *complimentary* modulus kc
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template< typename T >
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T ellipArcSc( T x, T kc )
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{
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T a = 1, b = kc, y = 1/x, tmp;
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unsigned L = 0;
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while( true )
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{
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tmp = a*b;
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a += b;
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b = 2*sqrt(tmp);
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y -= tmp/y;
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if( y == 0 )
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y = sqrt(tmp) * 1E-10;
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if( fabs(a-b)/a < std::numeric_limits<T>::epsilon )
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break;
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L *= 2;
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if( y < 0 )
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L++;
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}
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if( y < 0 )
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L++;
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return (atan(a/y) + M_PI*L)/a;
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}
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// calculate Jacobi elliptic functions sn, cn, and dn
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// given argument u and *complimentary* modulus kc
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template< typename T >
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rc_t ellipJ( T u, T kc, T* sn, T* cn, T* dn )
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{
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assert( sn != NULL || cn != NULL || dn != NULL );
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if( u == 0 )
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{
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if( sn != NULL ) *sn = 0;
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if( cn != NULL ) *cn = 1;
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if( dn != NULL ) *dn = 1;
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return kOkRC;
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}
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int i;
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T a,b,c,d,e,tmp,_sn,_cn,_dn;
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T aa[16], bb[16];
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a = 1;
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b = kc;
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for( i = 0; i < 16; i++ )
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{
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aa[i] = a;
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bb[i] = b;
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tmp = (a+b)/2;
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b = sqrt(a*b);
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a = tmp;
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if( (a-b)/a < std::numeric_limits<T>::epsilon )
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break;
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}
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c = a/tan(u*a);
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d = 1;
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for( ; i >= 0; i-- )
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{
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e = c*c/a;
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c = c*d;
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a = aa[i];
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d = (e + bb[i]) / (e+a);
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}
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_sn = 1/sqrt(1+c*c);
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_cn = _sn*c;
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_dn = d;
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if( sn != NULL ) *sn = _sn;
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if( cn != NULL ) *cn = _cn;
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if( dn != NULL ) *dn = _dn;
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return kOkRC;
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}
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//=================================================================
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// bilinear transform
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// z = (2*sr + s)/(2*sr - s)
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template< typename T >
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rc_t blt( unsigned n, T sr, T* rp, T* ip )
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{
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unsigned i;
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T a = 2*sr,
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tr, ti, td;
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for( i = 0; i < n; i++ )
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{
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tr = rp[i];
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ti = ip[i];
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td = pow(a-tr, 2) + ti*ti;
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rp[i] = (a*a - tr*tr - ti*ti)/td;
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ip[i] = 2*a*ti/td;
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if( tr < -1E15 )
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rp[i] = 0;
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if( fabs(ti) > 1E15 )
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ip[i] = 0;
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}
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return kOkRC;
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}
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//=================================================================
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// Pitch conversion
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unsigned hzToMidi( double hz );
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float midiToHz( unsigned midi );
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//=================================================================
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// Floating point byte swapping
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unsigned ffSwapFloatToUInt( float v );
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float ffSwapUIntToFloat( unsigned v );
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unsigned long long ffSwapDoubleToULLong( double v );
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double ffSwapULLongToDouble( unsigned long long v );
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//=================================================================
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template< typename T >
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T rand_range(T min, T max )
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{
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assert( min <= max );
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T range = max - min;
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return min + std::max(0,std::min(range,(T)range * rand() / RAND_MAX));
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}
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int randInt( int min, int max );
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unsigned randUInt( unsigned min, unsigned max );
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float randFloat( float min, float max );
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double randDouble( double min, double max );
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//=================================================================
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bool isCloseD( double x0, double x1, double eps );
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bool isCloseF( float x0, float x1, double eps );
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bool isCloseI( int x0, int x1, double eps );
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bool isCloseU( unsigned x0, unsigned x1, double eps );
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//=================================================================
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// Run a length 'lfsrN' linear feedback shift register (LFSR) for 'yN' iterations to
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// produce a length 'yN' bit string in yV[yN].
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// 'lfsrN' count of bits in the shift register range: 2<= lfsrN <= 32.
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// 'tapMask' is a bit mask which gives the tap indexes positions for the LFSR.
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// The least significant bit corresponds to the maximum delay tap position.
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// The min tap position is therefore denoted by the tap mask bit location 1 << (lfsrN-1).
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// A minimum of two taps must exist.
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// 'seed' sets the initial delay state.
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// 'yV[yN]' is the the output vector
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// 'yN' is count of elements in yV.
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// The function resturn kOkAtRC on success or kInvalidArgsRCRC if any arguments are invalid.
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// /sa lFSR_Test.
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void lFSR( unsigned lfsrN, unsigned tapMask, unsigned seed, unsigned* yV, unsigned yN );
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// Example and test code for lFSR()
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bool lFSR_Test();
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// Generate a set of 'goldN' Gold codes using the Maximum Length Sequences (MLS) generated
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// by a length 'lfsrN' linear feedback shift register.
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// 'err' is an error object to be set if the the function fails.
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// 'lfsrN' is the length of the Linear Feedback Shift Registers (LFSR) used to generate the MLS.
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// 'poly_coeff0' tap mask for the first LFSR.
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// 'coeff1' tap mask the the second LFSR.
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// 'goldN' is the count of Gold codes to generate.
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// 'yM[mlsN', goldN] is a column major output matrix where each column contains a Gold code.
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// 'mlsN' is the length of the maximum length sequence for each Gold code which can be
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// calculated as mlsN = (1 << a->lfsrN) - 1.
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// Note that values of 'lfsrN' and the 'poly_coeffx' must be carefully selected such that
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// they will produce a MLS. For example to generate a MLS with length 31 set 'lfsrN' to 5 and
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// then select poly_coeff from two different elements of the set {0x12 0x14 0x17 0x1B 0x1D 0x1E}.
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// See http://www.ece.u.edu/~koopman/lfsr/index.html for a complete set of MSL polynomial
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// coefficients for given LFSR lengths.
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// Returns false if insufficient balanced pairs exist.
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bool genGoldCodes( unsigned lfsrN, unsigned poly_coeff0, unsigned poly_coeff1, unsigned goldN, int* yM, unsigned mlsN );
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}
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}
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#endif
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