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>
constexpr float	approx_atan2f_P (float x)
template<>
constexpr float	approx_atan2f_P< 11 > (float x)
template<>
constexpr float	approx_atan2f_P< 13 > (float x)
template<>
constexpr float	approx_atan2f_P< 15 > (float x)
template<>
constexpr float	approx_atan2f_P< 3 > (float x)
template<>
constexpr float	approx_atan2f_P< 5 > (float x)
template<>
constexpr float	approx_atan2f_P< 7 > (float x)
template<>
constexpr float	approx_atan2f_P< 9 > (float x)
template<int DEGREE>
constexpr float	approx_atan2i_P (float x)
template<>
constexpr float	approx_atan2i_P< 11 > (float x)
template<>
constexpr float	approx_atan2i_P< 13 > (float x)
template<>
constexpr float	approx_atan2i_P< 15 > (float x)
template<>
constexpr float	approx_atan2i_P< 3 > (float x)
template<>
constexpr float	approx_atan2i_P< 5 > (float x)
template<>
constexpr float	approx_atan2i_P< 7 > (float x)
template<>
constexpr float	approx_atan2i_P< 9 > (float x)
template<int DEGREE>
constexpr float	approx_atan2s_P (float x)
template<>
constexpr float	approx_atan2s_P< 3 > (float x)
template<>
constexpr float	approx_atan2s_P< 5 > (float x)
template<>
constexpr float	approx_atan2s_P< 7 > (float x)
template<>
constexpr float	approx_atan2s_P< 9 > (float x)
constexpr double	int2dphi (int x)
constexpr float	int2phi (int x)
constexpr int	phi2int (float x)
constexpr short	phi2short (float x)
template<int DEGREE>
constexpr float	safe_atan2f (float y, float x)
constexpr float	short2phi (short x)
template<int DEGREE>
constexpr float	unsafe_atan2f (float y, float x)
template<int DEGREE>
constexpr float	unsafe_atan2f_impl (float y, float x)
template<int DEGREE>
constexpr int	unsafe_atan2i (float y, float x)
template<int DEGREE>
constexpr int	unsafe_atan2i_impl (float y, float x)
template<int DEGREE>
constexpr short	unsafe_atan2s (float y, float x)
template<int DEGREE>
constexpr short	unsafe_atan2s_impl (float y, float x)

Function Documentation

template<int DEGREE>

constexpr float approx_atan2f_P

(

float

x

)

template<>

constexpr float approx_atan2f_P< 11 >

(

float

x

)

Definition at line 69 of file approx_atan2.h.

References objects.autophobj::float, vertices_cff::x, globals_cff::x1, 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<>

constexpr float approx_atan2f_P< 13 >

(

float

x

)

Definition at line 75 of file approx_atan2.h.

References objects.autophobj::float, vertices_cff::x, globals_cff::x1, globals_cff::x2, 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<>

constexpr float approx_atan2f_P< 15 >

(

float

x

)

Definition at line 81 of file approx_atan2.h.

References objects.autophobj::float, vertices_cff::x, globals_cff::x1, globals_cff::x2, 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<>

constexpr float approx_atan2f_P< 3 >

(

float

x

)

Definition at line 46 of file approx_atan2.h.

References objects.autophobj::float, and vertices_cff::x.

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

template<>

constexpr float approx_atan2f_P< 5 >

(

float

x

)

Definition at line 51 of file approx_atan2.h.

References objects.autophobj::float, vertices_cff::x, globals_cff::x1, and detailsBasic3DVector::z.

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

template<>

constexpr float approx_atan2f_P< 7 >

(

float

x

)

Definition at line 57 of file approx_atan2.h.

References objects.autophobj::float, vertices_cff::x, globals_cff::x2, 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<>

constexpr float approx_atan2f_P< 9 >

(

float

x

)

Definition at line 63 of file approx_atan2.h.

References objects.autophobj::float, vertices_cff::x, globals_cff::x1, globals_cff::x2, 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>

constexpr float approx_atan2i_P

(

float

x

)

Referenced by safe_atan2f().

template<>

constexpr float approx_atan2i_P< 11 >

(

float

x

)

Definition at line 154 of file approx_atan2.h.

References vertices_cff::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<>

constexpr float approx_atan2i_P< 13 >

(

float

x

)

Definition at line 160 of file approx_atan2.h.

References vertices_cff::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<>

constexpr float approx_atan2i_P< 15 >

(

float

x

)

Definition at line 165 of file approx_atan2.h.

References vertices_cff::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<>

constexpr float approx_atan2i_P< 3 >

(

float

x

)

Definition at line 130 of file approx_atan2.h.

References vertices_cff::x, and detailsBasic3DVector::z.

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

template<>

constexpr float approx_atan2i_P< 5 >

(

float

x

)

Definition at line 136 of file approx_atan2.h.

References vertices_cff::x, and detailsBasic3DVector::z.

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

template<>

constexpr float approx_atan2i_P< 7 >

(

float

x

)

Definition at line 142 of file approx_atan2.h.

References vertices_cff::x, and detailsBasic3DVector::z.

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

template<>

constexpr float approx_atan2i_P< 9 >

(

float

x

)

Definition at line 148 of file approx_atan2.h.

References vertices_cff::x, and detailsBasic3DVector::z.

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

template<int DEGREE>

constexpr float approx_atan2s_P

(

float

x

)

Referenced by unsafe_atan2i().

template<>

constexpr float approx_atan2s_P< 3 >

(

float

x

)

Definition at line 206 of file approx_atan2.h.

References f, vertices_cff::x, and detailsBasic3DVector::z.

                                                        {
  auto z = x*x;
  return  x * ((-10142.439453125f) + z * 2002.0908203125f);
}

template<>

constexpr float approx_atan2s_P< 5 >

(

float

x

)

Definition at line 211 of file approx_atan2.h.

References f, vertices_cff::x, and detailsBasic3DVector::z.

                                                        {
  auto z = x*x;
  return   x * ((-10381.9609375f) + z * ((3011.1513671875f) + z * (-827.538330078125f)));
}

template<>

constexpr float approx_atan2s_P< 7 >

(

float

x

)

Definition at line 216 of file approx_atan2.h.

References f, vertices_cff::x, and detailsBasic3DVector::z.

                                                        {
  auto z = x*x;
  return  x * ((-10422.177734375f) + z * (3349.97412109375f + z * ((-1525.589599609375f) + z * 406.64190673828125f))) ;
}

template<>

constexpr float approx_atan2s_P< 9 >

(

float

x

)

Definition at line 221 of file approx_atan2.h.

References f, vertices_cff::x, and detailsBasic3DVector::z.

                                                        {
  auto z = x*x;
  return x * ((-10428.984375f) + z * (3445.20654296875f + z * ((-1879.137939453125f) + z * (888.22314453125f + z * (-217.42669677734375f)))));
}

constexpr double int2dphi

(

int

x

)

Definition at line 269 of file approx_atan2.h.

References constexpr, M_PI, and SiStripPI::max.

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

constexpr float int2phi

(

int

x

)

Definition at line 263 of file approx_atan2.h.

References constexpr, objects.autophobj::float, M_PI, and SiStripPI::max.

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

constexpr int phi2int

(

float

x

)

Definition at line 257 of file approx_atan2.h.

References constexpr, M_PI, and SiStripPI::max.

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

constexpr short phi2short

(

float

x

)

Definition at line 276 of file approx_atan2.h.

References constexpr, createfilelist::int, M_PI, and SiStripPI::max.

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

template<int DEGREE>

constexpr float safe_atan2f	(	float	y,
		float	x
	)

Definition at line 112 of file approx_atan2.h.

References approx_atan2i_P(), constexpr, f, vertices_cff::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);
}

constexpr float short2phi

(

short

x

)

Definition at line 282 of file approx_atan2.h.

References constexpr, objects.autophobj::float, createfilelist::int, M_PI, and SiStripPI::max.

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

template<int DEGREE>

constexpr float unsafe_atan2f	(	float	y,
		float	x
	)

Definition at line 105 of file approx_atan2.h.

References vertices_cff::x, and detailsBasic3DVector::y.

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

}

template<int DEGREE>

constexpr float unsafe_atan2f_impl	(	float	y,
		float	x
	)

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>

constexpr int unsafe_atan2i	(	float	y,
		float	x
	)

Definition at line 193 of file approx_atan2.h.

References approx_atan2s_P(), constexpr, vertices_cff::x, and detailsBasic3DVector::y.

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

}

template<int DEGREE>

constexpr int unsafe_atan2i_impl	(	float	y,
		float	x
	)

Definition at line 172 of file approx_atan2.h.

References funct::abs(), angle(), constexpr, createfilelist::int, SiStripPI::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 ;


}

template<int DEGREE>

constexpr short unsafe_atan2s	(	float	y,
		float	x
	)

Definition at line 247 of file approx_atan2.h.

References constexpr, vertices_cff::x, and detailsBasic3DVector::y.

                                                {
  return unsafe_atan2s_impl<DEGREE>(y,x);
}

template<int DEGREE>

constexpr short unsafe_atan2s_impl	(	float	y,
		float	x
	)

Definition at line 228 of file approx_atan2.h.

References funct::abs(), angle(), constexpr, createfilelist::int, SiStripPI::max, and alignCSCRings::r.

                                                     {


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

  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 += short(approx_atan2s_P<DEGREE>(r));


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

}