trigonometric.h

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// Copyright 2019-2020 CERN and copyright holders of ALICE O2.
// See https://alice-o2.web.cern.ch/copyright for details of the copyright holders.
// All rights not expressly granted are reserved.
//
// This software is distributed under the terms of the GNU General Public
// License v3 (GPL Version 3), copied verbatim in the file "COPYING".
//
// In applying this license CERN does not waive the privileges and immunities
// granted to it by virtue of its status as an Intergovernmental Organization
// or submit itself to any jurisdiction.
 
 
#ifndef MATHUTILS_INCLUDE_MATHUTILS_DETAIL_TRIGONOMETRIC_H_
#define MATHUTILS_INCLUDE_MATHUTILS_DETAIL_TRIGONOMETRIC_H_
 
#include "GPUCommonDef.h"
#include "GPUCommonMath.h"
#include "CommonConstants/MathConstants.h"
#include "MathUtils/detail/basicMath.h"
 
#ifndef GPUCA_GPUCODE_DEVICE
#include <cmath>
#include <tuple>
#include <array>
#endif
 
namespace o2
{
namespace math_utils
{
namespace detail
{
 
template <typename T>
GPUhdi() T to02Pi(T phi)
{
  T res = phi;
  // ensure angle in [0:2pi] for the input in [-pi:pi] or [0:pi]
  if (res < 0.f) {
    res += o2::constants::math::TwoPI;
  }
  return res;
}
 
template <typename T>
GPUhdi() void bringTo02Pi(T& phi)
{
  phi = to02Pi<T>(phi);
}
 
template <typename T>
inline T to02PiGen(T phi)
{
  T res = phi;
  // ensure angle in [0:2pi] for the any input angle
  while (res < 0.f) {
    res += o2::constants::math::TwoPI;
  }
  while (res > o2::constants::math::TwoPI) {
    res -= o2::constants::math::TwoPI;
  }
  return res;
}
 
template <typename T>
inline void bringTo02PiGen(T& phi)
{
  phi = to02PiGen<T>(phi);
}
 
template <typename T>
GPUhdi() T toPMPi(T phi)
{
  T res = phi;
  // ensure angle in [-pi:pi] for the input in [-pi:pi] or [0:pi]
  if (res > o2::constants::math::PI) {
    res -= o2::constants::math::TwoPI;
  } else if (res < -o2::constants::math::PI) {
    res += o2::constants::math::TwoPI;
  }
  return res;
}
 
template <typename T>
GPUhdi() void bringToPMPi(T& phi)
{
  phi = toPMPi<T>(phi);
}
 
template <typename T>
inline T toPMPiGen(T phi)
{
  // ensure angle in [-pi:pi] for any input angle
  T res = phi;
  while (res < -o2::constants::math::PI) {
    res += o2::constants::math::TwoPI;
  }
  while (res > o2::constants::math::PI) {
    res -= o2::constants::math::TwoPI;
  }
  return res;
}
 
template <typename T>
inline void bringToPMPiGen(T& phi)
{
  phi = toPMPiGen<T>(phi);
}
 
#ifdef __OPENCL__ // TODO: get rid of that stupid workaround for OpenCL template address spaces
template <typename T, typename S, typename U>
GPUhdi() void sincos(T ang, S& s, U& c)
{
  return o2::gpu::GPUCommonMath::SinCos(ang, s, c);
}
#else
template <typename T>
GPUhdi() void sincos(T ang, T& s, T& c)
{
  return o2::gpu::GPUCommonMath::SinCos(ang, s, c);
}
template <>
GPUhdi() void sincos(double ang, double& s, double& c)
{
  return o2::gpu::GPUCommonMath::SinCosd(ang, s, c);
}
#endif
 
#ifndef GPUCA_GPUCODE_DEVICE
 
template <typename T>
GPUhdi() std::tuple<T, T> sincos(T ang)
{
  T sin = 0;
  T cos = 0;
  sincos<T>(ang, sin, cos);
  return std::make_tuple(sin, cos);
}
 
template <typename T>
inline std::tuple<T, T> rotateZ(T xL, T yL, T snAlp, T csAlp)
{
  // 2D rotation of the point by angle alpha (local to global)
  return std::make_tuple(xL * csAlp - yL * snAlp, xL * snAlp + yL * csAlp);
}
 
template <typename T>
GPUhdi() std::tuple<T, T> rotateZInv(T xG, T yG, T snAlp, T csAlp)
{
  // inverse 2D rotation of the point by angle alpha (global to local)
  return rotateZ<T>(xG, yG, -snAlp, csAlp);
}
 
#endif
 
template <typename T>
GPUhdi() void rotateZ(std::array<T, 3>& xy, T alpha)
{
  // transforms vector in tracking frame alpha to global frame
  T sin, cos;
  sincos<T>(alpha, sin, cos);
  const T x = xy[0];
  xy[0] = x * cos - xy[1] * sin;
  xy[1] = x * sin + xy[1] * cos;
}
 
template <typename T>
GPUhdi() void rotateZ(T xL, T yL, T& xG, T& yG, T snAlp, T csAlp)
{
  xG = xL * csAlp - yL * snAlp;
  yG = xL * snAlp + yL * csAlp;
  ;
  // std::tie(xG, yG) = rotateZ<T>(xL, yL, snAlp, csAlp); // must not use std:: - versions on GPU
}
 
template <typename T>
GPUhdi() void rotateZInv(T xG, T yG, T& xL, T& yL, T snAlp, T csAlp)
{
  // inverse 2D rotation of the point by angle alpha (global to local)
  rotateZ<T>(xG, yG, xL, yL, -snAlp, csAlp);
}
 
template <typename T = float>
GPUhdi() constexpr T sectorDAlpha()
{
  return o2::constants::math::SectorSpanRad * 0.5;
}
 
template <typename T>
GPUhdi() int angle2Sector(T phi)
{
  // convert angle to sector ID, phi can be either in 0:2pi or -pi:pi convention
  int sect = phi * o2::constants::math::Rad2Deg / o2::constants::math::SectorSpanDeg;
  if (phi < 0.f) {
    sect += o2::constants::math::NSectors - 1;
  }
  return sect % o2::constants::math::NSectors;
}
 
template <typename T>
GPUhdi() T sector2Angle(int sect)
{
  // convert sector to its angle center, in -pi:pi convention
  T ang = o2::constants::math::SectorSpanRad * (0.5f + sect);
  bringToPMPi<T>(ang);
  return ang;
}
 
template <typename T>
GPUhdi() T angle2Alpha(T phi)
{
  // convert angle to its sector alpha
  return sector2Angle<T>(angle2Sector<T>(phi));
}
 
template <typename T>
GPUhdi() constexpr bool okForPhiMin(T phiMin, T phi)
{
  // check if phi is above the phiMin, phi's must be in 0-2pi range
  const T dphi = phi - phiMin;
  return ((dphi > 0 && dphi < constants::math::PI) || dphi < -constants::math::PI) ? true : false;
}
 
template <typename T>
GPUhdi() constexpr bool okForPhiMax(T phiMax, T phi)
{
  // check if phi is below the phiMax, phi's must be in 0-2pi range
  const T dphi = phi - phiMax;
  return ((dphi < 0 && dphi > -constants::math::PI) || dphi > constants::math::PI) ? true : false;
}
 
template <typename T>
GPUhdi() constexpr T meanPhiSmall(T phi0, T phi1)
{
  // return mean phi, assume phis in 0:2pi
  T phi;
  if (!okForPhiMin(phi0, phi1)) {
    phi = phi0;
    phi0 = phi1;
    phi1 = phi;
  }
  if (phi0 > phi1) {
    phi = 0.5 * (phi1 - (constants::math::TwoPI - phi0)); // wrap
  } else {
    phi = 0.5 * (phi0 + phi1);
  }
  bringTo02Pi(phi);
  return phi;
}
 
template <typename T>
GPUhdi() constexpr T deltaPhiSmall(T phi0, T phi1)
{
  // return delta phi, assume phi is in 0:2pi
  T del;
  if (!okForPhiMin(phi0, phi1)) {
    del = phi0;
    phi0 = phi1;
    phi1 = del;
  }
  del = phi1 - phi0;
  if (del < 0) {
    del += constants::math::TwoPI;
  }
  return del;
}
 
template <typename T>
GPUhdi() T fastATan2(T y, T x)
{
  // Fast atan2(y,x) for any angle [-Pi,Pi]
  // Average inaccuracy: 0.00048
  // Max inaccuracy: 0.00084
  // Speed: 6.2 times faster than atan2f()
  constexpr T Pi = 3.1415926535897932384626433832795;
 
  auto atan = [](T a) -> T {
    // returns the arctan for the angular range [-Pi/4, Pi/4]
    // the polynomial coefficients are taken from:
    // https://stackoverflow.com/questions/42537957/fast-accurate-atan-arctan-approximation-algorithm
    constexpr T A = 0.0776509570923569;
    constexpr T B = -0.287434475393028;
    constexpr T C = (Pi / 4 - A - B);
    const T a2 = a * a;
    return ((A * a2 + B) * a2 + C) * a;
  };
 
  auto atan2P = [atan](T yy, T xx) -> T {
    // fast atan2(yy,xx) for the angular range [0,+Pi]
    constexpr T Pi025 = 1 * Pi / 4;
    constexpr T Pi075 = 3 * Pi / 4;
    const T x1 = xx + yy; //  point p1 (x1,y1) = (xx,yy) - Pi/4
    const T y1 = yy - xx;
    T phi0 = 0;
    T tan = 0;
    if (xx < 0) { // p1 is in the range [Pi/4, 3*Pi/4]
      phi0 = Pi075;
      tan = -x1 / y1;
    } else { // p1 is in the range [-Pi/4, Pi/4]
      phi0 = Pi025;
      tan = y1 / x1;
    }
    return phi0 + atan(tan);
  };
 
  // fast atan2(y,x) for any angle [-Pi,Pi]
  return copysign<T>(atan2P(o2::gpu::GPUCommonMath::Abs(y), x), y);
}
 
template <class T>
GPUdi() T asin(T x)
{
  return o2::gpu::GPUCommonMath::ASin(x);
};
 
template <class T>
GPUdi() T acos(T x)
{
  return o2::gpu::GPUCommonMath::ACos(x);
};
 
template <class T>
GPUdi() T atan(T x)
{
  return o2::gpu::GPUCommonMath::ATan(x);
};
 
template <class T>
GPUdi() T atan2(T y, T x)
{
  return o2::gpu::GPUCommonMath::ATan2(y, x);
};
 
template <class T>
GPUdi() T sin(T x)
{
  return o2::gpu::GPUCommonMath::Sin(x);
};
 
template <class T>
GPUdi() T cos(T x)
{
  return o2::gpu::GPUCommonMath::Cos(x);
};
 
template <class T>
GPUdi() T tan(T x)
{
  return o2::gpu::GPUCommonMath::Tan(x);
};
 
template <class T>
GPUdi() T twoPi()
{
  return o2::gpu::GPUCommonMath::TwoPi();
};
 
template <>
GPUdi() double twoPi()
{
  return o2::constants::math::TwoPI;
};
 
template <class T>
GPUdi() T pi()
{
  return o2::gpu::GPUCommonMath::Pi();
}
 
template <>
GPUdi() double pi()
{
  return o2::constants::math::PI;
}
 
#ifndef GPUCA_GPUCODE_DEVICE
template <>
GPUdi() double tan(double x)
{
  return std::tan(x);
};
template <>
GPUdi() double sin(double x)
{
  return std::sin(x);
};
template <>
GPUdi() double atan2(double y, double x)
{
  return std::atan2(y, x);
};
template <>
GPUdi() double atan(double x)
{
  return std::atan(x);
};
template <>
GPUdi() double asin(double x)
{
  return std::asin(x);
};
template <>
GPUdi() double acos(double x)
{
  return std::acos(x);
};
template <>
GPUdi() double cos(double x)
{
  return std::cos(x);
};
#endif
 
} // namespace detail
} // namespace math_utils
} // namespace o2
 
#endif /* MATHUTILS_INCLUDE_MATHUTILS_DETAIL_TRIGONOMETRIC_H_ */