approx_atan2.h File Reference

#include <cstdint>
#include <cmath>
#include <limits>
#include <algorithm>

Go to the source code of this file.

Functions
template<int DEGREE>
float	approx_atan2f_P (float x)
template<>
float	approx_atan2f_P< 11 > (float x)
template<>
float	approx_atan2f_P< 13 > (float x)
template<>
float	approx_atan2f_P< 15 > (float x)
template<>
float	approx_atan2f_P< 3 > (float x)
template<>
float	approx_atan2f_P< 5 > (float x)
template<>
float	approx_atan2f_P< 7 > (float x)
template<>
float	approx_atan2f_P< 9 > (float x)
template<int DEGREE>
float	approx_atan2i_P (float x)
template<>
float	approx_atan2i_P< 11 > (float x)
template<>
float	approx_atan2i_P< 13 > (float x)
template<>
float	approx_atan2i_P< 15 > (float x)
template<>
float	approx_atan2i_P< 3 > (float x)
template<>
float	approx_atan2i_P< 5 > (float x)
template<>
float	approx_atan2i_P< 7 > (float x)
template<>
float	approx_atan2i_P< 9 > (float x)
double	int2dphi (int x)
float	int2phi (int x)
int	phi2int (float x)
short	phi2short (float x)
template<int DEGREE>
float	safe_atan2f (float y, float x)
float	short2phi (short x)
template<int DEGREE>
float	unsafe_atan2f (float y, float x)
template<int DEGREE>
float	unsafe_atan2f_impl (float y, float x)
template<int DEGREE>
int	unsafe_atan2i (float y, float x)
template<int DEGREE>
int	unsafe_atan2i_impl (float y, float x)

Function Documentation

template<int DEGREE>

float approx_atan2f_P ( float  x )

inline

template<>

float approx_atan2f_P< 11 > ( float  x )

inline

Definition at line 69 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                      {
  auto z = x*x;
  return x * (float(-0xf.ffe82p-4) + z * (float(0x5.526c8p-4) + z * (float(-0x3.18bea8p-4) + z * (float(0x1.dce3bcp-4) + z * (float(-0xd.7a64ap-8) + z * float(0x3.000eap-8))))));
}

template<>

float approx_atan2f_P< 13 > ( float  x )

inline

Definition at line 75 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                      {
  auto z = x*x;
  return  x * (float(-0xf.fffbep-4) + z * (float(0x5.54adp-4) + z * (float(-0x3.2b4df8p-4) + z * (float(0x2.1df79p-4) + z * (float(-0x1.46081p-4) + z * (float(0x8.99028p-8) + z * float(-0x1.be0bc4p-8))))))) ;
}

template<>

float approx_atan2f_P< 15 > ( float  x )

inline

Definition at line 81 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                      {
  auto z = x*x;
  return x * (float(-0xf.ffff4p-4) + z * (float(0x5.552f9p-4 + z * (float(-0x3.30f728p-4) + z * (float(0x2.39826p-4) + z * (float(-0x1.8a880cp-4) + z * (float(0xe.484d6p-8) + z * (float(-0x5.93d5p-8) + z * float(0x1.0875dcp-8)))))))));
}

template<>

float approx_atan2f_P< 3 > ( float  x )

inline

Definition at line 46 of file approx_atan2.h.

References x.

                                                     {
  return x * (float(-0xf.8eed2p-4) + x*x * float(0x3.1238p-4)) ;
}

template<>

float approx_atan2f_P< 5 > ( float  x )

inline

Definition at line 51 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                     {
  auto z = x*x;
  return  x * (float(-0xf.ecfc8p-4) + z * (float(0x4.9e79dp-4) + z * float(-0x1.44f924p-4) ) );
}

template<>

float approx_atan2f_P< 7 > ( float  x )

inline

Definition at line 57 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                     {
  auto z = x*x;
  return  x * (float(-0xf.fcc7ap-4) + z * (float(0x5.23886p-4) + z * (float(-0x2.571968p-4) + z * float(0x9.fb05p-8) ) ) ) ;
}

template<>

float approx_atan2f_P< 9 > ( float  x )

inline

Definition at line 63 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                     {
  auto z = x*x;
  return x * (float(-0xf.ff73ep-4) + z * (float(0x5.48ee1p-4) + z * (float(-0x2.e1efe8p-4) + z * (float(0x1.5cce54p-4) + z * float(-0x5.56245p-8) ) ) ) ); 
}

template<int DEGREE>

float approx_atan2i_P ( float  x )

inline

template<>

float approx_atan2i_P< 11 > ( float  x )

inline

Definition at line 155 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                      {
 auto z = x*x;
 return   x * (-683549696.f + z * (227369312.f + z * (-132297008.f + z * (79584144.f + z * (-35987016.f + z * 8010488.f)))));
}

template<>

float approx_atan2i_P< 13 > ( float  x )

inline

Definition at line 161 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                      {
 auto z = x*x;
 return  x * (-683562624.f + z * (227746080.f + z * (-135400128.f + z * (90460848.f + z * (-54431464.f + z * (22973256.f + z * (-4657049.f)))))));
}

template<>

float approx_atan2i_P< 15 > ( float  x )

inline

Definition at line 166 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                      {
 auto z = x*x;
 return  x * (-683562624.f + z * (227746080.f + z * (-135400128.f + z * (90460848.f + z * (-54431464.f + z * (22973256.f + z * (-4657049.f)))))));
}

template<>

float approx_atan2i_P< 3 > ( float  x )

inline

Definition at line 131 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                     {
 auto z = x*x;
 return x * (-664694912.f + z * 131209024.f);
}

template<>

float approx_atan2i_P< 5 > ( float  x )

inline

Definition at line 137 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                     {
 auto z = x*x;
 return x * (-680392064.f + z * (197338400.f + z * (-54233256.f)));
}

template<>

float approx_atan2i_P< 7 > ( float  x )

inline

Definition at line 143 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                     {
 auto z = x*x;
 return  x * (-683027840.f + z * (219543904.f + z * (-99981040.f + z * 26649684.f)));
}

template<>

float approx_atan2i_P< 9 > ( float  x )

inline

Definition at line 149 of file approx_atan2.h.

References x, and detailsBasic3DVector::z.

                                                     {
 auto z = x*x;
 return   x * (-683473920.f + z * (225785056.f + z * (-123151184.f + z * (58210592.f + z * (-14249276.f)))));
}

double int2dphi ( int  x )

inline

Definition at line 212 of file approx_atan2.h.

References constexpr, M_PI, and bookConverter::max.

                       {
  constexpr double i2p = M_PI/( (long long)(std::numeric_limits<int>::max())+1LL );
  return x*i2p;
}

float int2phi ( int  x )

inline

Definition at line 206 of file approx_atan2.h.

References constexpr, M_PI, and bookConverter::max.

                     {
  constexpr float i2p = M_PI/( (long long)(std::numeric_limits<int>::max())+1LL );
  return float(x)*i2p;
}

int phi2int ( float  x )

inline

Definition at line 200 of file approx_atan2.h.

References constexpr, M_PI, and bookConverter::max.

                     {
  constexpr float p2i = ( (long long)(std::numeric_limits<int>::max())+1LL )/M_PI;
  return std::round(x*p2i);
}

short phi2short ( float  x )

inline

Definition at line 219 of file approx_atan2.h.

References constexpr, M_PI, and bookConverter::max.

                         {
  constexpr float p2i = ( (int)(std::numeric_limits<short>::max())+1 )/M_PI;
  return std::round(x*p2i);
}

template<int DEGREE>

float safe_atan2f ( float  y, float  x  )

inline

Definition at line 112 of file approx_atan2.h.

References f, x, and detailsBasic3DVector::y.

                                           {
  return unsafe_atan2f_impl<DEGREE>( y, (y==0.f)&(x==0.f) ? 0.2f :  x);
  // return (y==0.f)&(x==0.f) ? 0.f :  unsafe_atan2f_impl<DEGREE>( y, x);

}

float short2phi ( short  x )

inline

Definition at line 225 of file approx_atan2.h.

References constexpr, M_PI, and bookConverter::max.

                         {
  constexpr float i2p = M_PI/( (int)(std::numeric_limits<short>::max())+1 );
  return float(x)*i2p;
}

template<int DEGREE>

float unsafe_atan2f ( float  y, float  x  )

inline

Definition at line 106 of file approx_atan2.h.

References x, and detailsBasic3DVector::y.

                                             {
  return unsafe_atan2f_impl<DEGREE>(y,x);

}

template<int DEGREE>

float unsafe_atan2f_impl ( float  y, float  x  )

inline

Definition at line 88 of file approx_atan2.h.

References funct::abs(), angle(), constexpr, and alignCSCRings::r.

                                                  {

  constexpr float pi4f =  3.1415926535897932384626434/4;
  constexpr float pi34f = 3.1415926535897932384626434*3/4;

  auto r= (std::abs(x) - std::abs(y))/(std::abs(x) + std::abs(y));
  if (x<0) r = -r;

  auto angle = (x>=0) ? pi4f : pi34f;
  angle += approx_atan2f_P<DEGREE>(r);
  

  return ( (y < 0)) ? - angle : angle ;


}

template<int DEGREE>

int unsafe_atan2i ( float  y, float  x  )

inline

Definition at line 194 of file approx_atan2.h.

References x, and detailsBasic3DVector::y.

                                           {
  return unsafe_atan2i_impl<DEGREE>(y,x);

}

template<int DEGREE>

int unsafe_atan2i_impl ( float  y, float  x  )

inline

Definition at line 173 of file approx_atan2.h.

References funct::abs(), angle(), constexpr, bookConverter::max, and alignCSCRings::r.

                                                {


  constexpr long long maxint = (long long)(std::numeric_limits<int>::max())+1LL;
  constexpr int pi4 =  int(maxint/4LL);
  constexpr int pi34 = int(3LL*maxint/4LL);

  auto r= (std::abs(x) - std::abs(y))/(std::abs(x) + std::abs(y));
  if (x<0) r = -r;

  auto angle = (x>=0) ? pi4 : pi34;
  angle += int(approx_atan2i_P<DEGREE>(r));
  // angle += int(std::round(approx_atan2i_P<DEGREE>(r)));


  return (y < 0) ? - angle : angle ;


}