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 71 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<>

constexpr float approx_atan2f_P< 13 >

(

float

x

)

Definition at line 81 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<>

constexpr float approx_atan2f_P< 15 >

(

float

x

)

Definition at line 92 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<>

constexpr float approx_atan2f_P< 3 >

(

float

x

)

Definition at line 42 of file approx_atan2.h.

References 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 48 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<>

constexpr float approx_atan2f_P< 7 >

(

float

x

)

Definition at line 55 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<>

constexpr float approx_atan2f_P< 9 >

(

float

x

)

Definition at line 62 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>

constexpr float approx_atan2i_P

(

float

x

)

template<>

constexpr float approx_atan2i_P< 11 >

(

float

x

)

Definition at line 168 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<>

constexpr float approx_atan2i_P< 13 >

(

float

x

)

Definition at line 176 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<>

constexpr float approx_atan2i_P< 15 >

(

float

x

)

Definition at line 184 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<>

constexpr float approx_atan2i_P< 3 >

(

float

x

)

Definition at line 140 of file approx_atan2.h.

References 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 147 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<>

constexpr float approx_atan2i_P< 7 >

(

float

x

)

Definition at line 154 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<>

constexpr float approx_atan2i_P< 9 >

(

float

x

)

Definition at line 161 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)))));
}

template<int DEGREE>

constexpr float approx_atan2s_P

(

float

x

)

template<>

constexpr float approx_atan2s_P< 3 >

(

float

x

)

Definition at line 220 of file approx_atan2.h.

References validate-o2o-wbm::f, 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 226 of file approx_atan2.h.

References validate-o2o-wbm::f, 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 232 of file approx_atan2.h.

References validate-o2o-wbm::f, 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 238 of file approx_atan2.h.

References validate-o2o-wbm::f, 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 275 of file approx_atan2.h.

References mkfit::LL, 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 270 of file approx_atan2.h.

References mkfit::LL, 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 265 of file approx_atan2.h.

References mkfit::LL, 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 280 of file approx_atan2.h.

References 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 123 of file approx_atan2.h.

References validate-o2o-wbm::f, 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 285 of file approx_atan2.h.

References M_PI, and SiStripPI::max.

Referenced by SiPixelPhase1MonitorRecHitsSoA::analyze(), and gpuPixelDoublets::for().

                                   {
  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 118 of file approx_atan2.h.

References 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 103 of file approx_atan2.h.

References funct::abs(), angle(), 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 209 of file approx_atan2.h.

References 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 192 of file approx_atan2.h.

References funct::abs(), angle(), mkfit::LL, 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 261 of file approx_atan2.h.

References 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 245 of file approx_atan2.h.

References funct::abs(), angle(), 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;
}