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/*
* Copyright (c) 2004 MUSIC TECHNOLOGY GROUP (MTG)
* UNIVERSITAT POMPEU FABRA
*
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program 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
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#ifndef __CLAM_MATH__
#define __CLAM_MATH__
#include <cmath>
#include "DataTypes.hxx"
#include "FastRounding.hxx"
//The following constants are defined also in OSDefines but only for windows and using the #define preprocessor
//directive. It is much better to use const float declarations
const float PI_ = 3.1415926535897932384626433832795028841972; /* pi */
const float ONE_OVER_PI = (0.3183098861837906661338147750939f);
const float TWOPI = (6.2831853071795864769252867665590057683943f); /* 2*pi */
const float ONE_OVER_TWOPI = (0.15915494309189535682609381638f);
const float PI_2 = (1.5707963267948966192313216916397514420986f); /* pi/2 */
const float TWO_OVER_PI = (0.636619772367581332267629550188f);
const float LN2 = (0.6931471805599453094172321214581765680755f); /* ln(2) */
const float ONE_OVER_LN2 = (1.44269504088896333066907387547f);
const float LN10 = (2.3025850929940456840179914546843642076011f); /* ln(10) */
const float ONE_OVER_LN10 = (0.43429448190325177635683940025f);
const float LN2_OVER_LN10 = LN2*ONE_OVER_LN10;
const float TIMES20LN2_OVER_LN10 = 20*LN2_OVER_LN10;
const long LONG_OFFSET = 4096L;
const float FLOAT_OFFSET = 4096.0;
const float HUGE_ = 1.0e8;
const float ROOT2 = (1.4142135623730950488016887242096980785697f); /* sqrt(2) */
/** Efficient versions of common functions*/
inline float CLAM_sin(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) sin((double)x);
#else
x *= ONE_OVER_PI;
register float accumulator, xPower, xSquared;
register long evenIntPart = ((long)(0.5f*x + 1024.5) - 1024)<<1;
x -= (float)evenIntPart;
xSquared = x*x;
accumulator = 3.14159265358979f*x;
xPower = xSquared*x;
accumulator += -5.16731953364340f*xPower;
xPower *= xSquared;
accumulator += 2.54620566822659f*xPower;
xPower *= xSquared;
accumulator += -0.586027023087261f*xPower;
xPower *= xSquared;
accumulator += 0.06554823491427f*xPower;
return accumulator;
#endif
}
inline float CLAM_cos(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) cos((double)x);
#else
x *= ONE_OVER_PI;
register float accumulator, xPower, xSquared;
register long evenIntPart = ((long)(0.5f*x + 1024.5f) - 1024)<<1;
x -= (float)evenIntPart;
xSquared = x*x;
accumulator = 1.57079632679490f*x; /* series for sin(PI/2*x) */
xPower = xSquared*x;
accumulator += -0.64596406188166f*xPower;
xPower *= xSquared;
accumulator += 0.07969158490912f*xPower;
xPower *= xSquared;
accumulator += -0.00467687997706f*xPower;
xPower *= xSquared;
accumulator += 0.00015303015470f*xPower;
return 1.0f - 2.0f*accumulator*accumulator; /* cos(w) = 1 - 2*(sin(w/2))^2 */
#endif
}
inline float CLAM_atan(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) atan((double)x);
#else
register float accumulator, xPower, xSquared, offset;
offset = 0.0f;
if (x < -1.0f)
{
offset = -PI_2;
x = -1.0f/x;
}
else if (x > 1.0f)
{
offset = PI_2;
x = -1.0f/x;
}
xSquared = x*x;
accumulator = 1.0f;
xPower = xSquared;
accumulator += 0.33288950512027f*xPower;
xPower *= xSquared;
accumulator += -0.08467922817644f*xPower;
xPower *= xSquared;
accumulator += 0.03252232640125f*xPower;
xPower *= xSquared;
accumulator += -0.00749305860992f*xPower;
return offset + x/accumulator;
#endif
}
inline float CLAM_atan2(float Imag, float Real)
{
#ifndef CLAM_OPTIMIZE
return (float) atan2((double)Imag, (double)Real);
#else
if(Real==0 && Imag==0) return 0.f;
register float accumulator, xPower, xSquared, offset, x;
if (Imag > 0.0f)
{
if (Imag <= -Real)
{
offset = PI_;
x = Imag/Real;
}
else if (Imag > Real)
{
offset = PI_2;
x = -Real/Imag;
}
else
{
offset = 0.0f;
x = Imag/Real;
}
}
else
{
if (Imag >= Real)
{
offset = -PI_;
x = Imag/Real;
}
else if (Imag < -Real)
{
offset = -PI_2;
x = -Real/Imag;
}
else
{
offset = 0.0f;
x = Imag/Real;
}
}
xSquared = x*x;
accumulator = 1.0f;
xPower = xSquared;
accumulator += 0.33288950512027f*xPower;
xPower *= xSquared;
accumulator += -0.08467922817644f*xPower;
xPower *= xSquared;
accumulator += 0.03252232640125f*xPower;
xPower *= xSquared;
accumulator += -0.00749305860992f*xPower;
return offset + x/accumulator;
#endif
}
inline float CLAM_exp2(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) exp(LN2*(double)x);
#else
if (x >= -127.0f)
{
register float accumulator, xPower;
register union {float f; long i;} xBits;
xBits.i = (long)(x + FLOAT_OFFSET) - LONG_OFFSET; /* integer part */
x -= (float)(xBits.i); /* fractional part */
accumulator = 1.0f + 0.69303212081966f*x;
xPower = x*x;
accumulator += 0.24137976293709f*xPower;
xPower *= x;
accumulator += 0.05203236900844f*xPower;
xPower *= x;
accumulator += 0.01355574723481f*xPower;
xBits.i += 127; /* bias integer part */
xBits.i <<= 23; /* move biased int part into exponent bits */
return accumulator * xBits.f;
}
else
{
return 0.0f;
}
#endif
}
inline float CLAM_log2(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) (ONE_OVER_LN2*log((double)x));
#else
if (x > 5.877471754e-39f)
{
register float accumulator, xPower;
register long intPart;
register union {float f; long i;} xBits;
xBits.f = x;
intPart = ((xBits.i)>>23); /* get biased exponent */
intPart -= 127; /* unbias it */
x = (float)(xBits.i & 0x007FFFFF); /* mask off exponent leaving 0x800000*(mantissa - 1) */
x *= 1.192092895507812e-07f; /* divide by 0x800000 */
accumulator = 1.44254494359510f*x;
xPower = x*x;
accumulator += -0.71814525675041f*xPower;
xPower *= x;
accumulator += 0.45754919692582f*xPower;
xPower *= x;
accumulator += -0.27790534462866f*xPower;
xPower *= x;
accumulator += 0.12179791068782f*xPower;
xPower *= x;
accumulator += -0.02584144982967f*xPower;
return accumulator + (float)intPart;
}
else
{
return -HUGE_;
}
#endif
}
inline float CLAM_pow(float x, float y)
{
#ifndef CLAM_OPTIMIZE
return (float) pow((double)x, (double)y);
#else
return CLAM_exp2(y*CLAM_log2(x));
#endif
}
inline float CLAM_sqrt(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) sqrt((double)x);
#else
if (x > 5.877471754e-39f)
{
register float accumulator, xPower;
register long intPart;
register union {float f; long i;} xBits;
xBits.f = x;
intPart = ((xBits.i)>>23); /* get biased exponent */
intPart -= 127; /* unbias it */
x = (float)(xBits.i & 0x007FFFFF); /* mask off exponent leaving 0x800000*(mantissa - 1) */
x *= 1.192092895507812e-07f; /* divide by 0x800000 */
accumulator = 1.0f + 0.49959804148061f*x;
xPower = x*x;
accumulator += -0.12047308243453f*xPower;
xPower *= x;
accumulator += 0.04585425015501f*xPower;
xPower *= x;
accumulator += -0.01076564682800f*xPower;
if (intPart & 0x00000001)
{
accumulator *= ROOT2; /* an odd input exponent means an extra sqrt(2) in the output */
}
xBits.i = intPart >> 1; /* divide exponent by 2, lose LSB */
xBits.i += 127; /* rebias exponent */
xBits.i <<= 23; /* move biased exponent into exponent bits */
return accumulator * xBits.f;
}
else
{
return 0.0f;
}
#endif
}
inline float CLAM_log(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) log((double)x);
#else
return LN2*CLAM_log2(x);
#endif
}
inline float CLAM_log10(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) log10((double)x);
#else
return LN2_OVER_LN10*CLAM_log2(x);
#endif
}
inline float CLAM_20log10(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) 20*log10((double)x);
#else
return TIMES20LN2_OVER_LN10*CLAM_log2(x);
#endif
}
inline float CLAM_exp(register float x)
{
#ifndef CLAM_OPTIMIZE
return (float) exp((double)x);
#else
return CLAM_exp2(ONE_OVER_LN2*x);
#endif
}
#if defined _MSC_VER && _MSC_VER < 1310 // MSVC++ 6
#undef min
#undef max
namespace std
{
template < typename T >
const T& max( const T& a, const T& b) {
return (a>=b)? a : b;
}
template < typename T >
const T& min(const T& a, const T& b) {
return (a<=b)? a : b;
}
} // namespace std
#endif // MSVC++ 6
#if defined _MSC_VER // MSVC++7
namespace std
{
template <typename T>
bool isnan(T data)
{
return _isnan(data) == 1;
}
template <typename T>
bool isinf(T data)
{
return _isnan(data) == 1;
}
}
#endif // MSVC++ 7
#ifndef __USE_ISOC99
#ifndef __APPLE__
inline double round(double _X)
{return (floor(_X+0.5)); }
inline float round(float _X)
{return (floorf(_X+0.5f)); }
#endif // __APPLE__
#endif // __USE_ISOC99
/** Fast "pow" for converting a logarithmic value into linear value ( assumes a log
scale factor of 20 ). Warning, float should be TData but includes should then be changed**/
inline float log2lin( float x )
{
// static double magic = 1.0 / (20.0 * log10(exp(1.0)))=0.1151292546497;
return CLAM_exp( x * 0.1151292546497f );
}
/**
* Returns true if the given (unsigned) integer n is
* a power-of-two.
* Will return true for n = 0 and n = 1.
**/
inline bool isPowerOfTwo( CLAM::TUInt32 n)
{
return (((n - 1) & n) == 0);
}
/**
* Returns the closest power-of-two number greater or equal
* to n for the given (unsigned) integer n.
* Will return 0 when n = 0 and 1 when n = 1.
**/
inline CLAM::TUInt32 nextPowerOfTwo( CLAM::TUInt32 n)
{
--n;
n |= n >> 16;
n |= n >> 8;
n |= n >> 4;
n |= n >> 2;
n |= n >> 1;
++n;
return n;
}
namespace CLAM
{
/*Non member function, returns absolute value of class T*/
template <class T> inline T Abs(T value)
{
return ( value < 0 ) ? -value : value;
}
/* DB */
// Default scaling
#define CLAM_DB_SCALING 20
inline double DB(double linData, int scaling=20)
{
return (scaling*CLAM_log10(linData));
}
inline double Lin(double logData, int scaling=20 )
{
return (CLAM_pow(double(10),(logData/scaling)) );
}
/** Definition of CLAM_min and CLAM_max. Note1: we are not returning a const reference
* because in some specializations this is not possible. Note2: we are not using std::max and
* std::min by default because in Windows these functions are implemented with different names
*/
template<class T> inline
T CLAM_max(const T& x, const T& y)
{return (x < y ? y : x); }
template<class T> inline
T CLAM_min(const T& x, const T& y)
{return (x > y ? y : x); }
}
#endif // CLAM_Math.hxx
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