fastmath Namespace Reference

Functions
std::pair< float, float >	atan2r (float y_, float x_, bool overR=false)
std::pair< double, double >	atan2r (double y_, double x_, bool overR=false)
template<typename T >
std::pair< T, T >	etaphi (T x, T y, T z)
float	invSqrt (float in)
double	invSqrt (double in)

Function Documentation

std::pair<float,float> fastmath::atan2r ( float  y_, float  x_, bool  overR = false  )

inline

Definition at line 40 of file FastMath.h.

References fastmath_details::_2pif, fastmath_details::atanbuf_, cuy::cv, f, flags, i, invSqrt(), mag2(), and x().

Referenced by etaphi().

                                                                           {
    using namespace fastmath_details;
    float mag2 = x_ * x_ + y_ * y_;
    if(!(mag2 > 0))  {  return std::pair<float,float>(0.f,0.f); }   // degenerate case
    
    // float r_ = std::sqrt(mag2);
    float rinv = invSqrt(mag2);
    unsigned int flags = 0;
    float x, y;
    union {
      float f;
      int i;
    } yp;
    yp.f = 32768.f;
    if (y_ < 0 ) { flags |= 4; y_ = -y_; }
    if (x_ < 0 ) { flags |= 2; x_ = -x_; }
    if (y_ > x_) {
      flags |= 1;
      x = rinv * y_; y = rinv * x_; yp.f += y;
    }
    else {
      x = rinv * x_; y = rinv * y_; yp.f += y;
    }
    int ind = (yp.i & 0x01FF) * 2;
    
    float* asbuf = (float*)(atanbuf_ + ind);
    float sv = yp.f - 32768.f;
    float cv = asbuf[0];
    float asv = asbuf[1];
    sv = y * cv - x * sv;    // delta sin value
    // ____ compute arcsin directly
    float asvd = 6.f + sv * sv;   sv *= float(1.0f / 6.0f);
    float th = asv + asvd * sv;
    if (flags & 1) { th = (_2pif / 4.f) - th; }
    if (flags & 2) { th = (_2pif / 2.f) - th; }
    if (flags & 4) { th = -th; }
    return std::pair<float,float>(th,overR ? rinv : rinv*mag2);    
  }

std::pair<double, double> fastmath::atan2r ( double  y_, double  x_, bool  overR = false  )

inline

Definition at line 82 of file FastMath.h.

References fastmath_details::_2pi, cuy::cv, ztail::d, fastmath_details::datanbuf_, flags, i, mag2(), mathSSE::sqrt(), and x().

                                                                                {
    using namespace fastmath_details;
    // assert(ataninited);
    double mag2 = x_ * x_ + y_ * y_;
    if(!(mag2 > 0)) { return std::pair<double, double>(0.,0.); }   // degenerate case
    
    double r_ = std::sqrt(mag2);
    double rinv = 1./r_;
    unsigned int flags = 0;
    double x, y;
    const double _2p43 = 65536.0 * 65536.0 * 2048.0;
    union {
      double d;
      int i[2];
    } yp;

    yp.d = _2p43;
    if (y_ < 0) { flags |= 4; y_ = -y_; }
    if (x_ < 0) { flags |= 2; x_ = -x_; }
    if (y_ > x_) {
      flags |= 1;
      x = rinv * y_; y = rinv * x_; yp.d += y;
    }
    else {
      x = rinv * x_; y = rinv * y_; yp.d += y;
    }

    int ind = (yp.i[0] & 0x03FF) * 2;  // 0 for little indian
    
    double* dasbuf = (double*)(datanbuf_ + ind);
    double sv = yp.d - _2p43; // index fraction
    double cv = dasbuf[0];
    double asv = dasbuf[1];
    sv = y * cv - x * sv;    // delta sin value
    // double sv = y *(cv-x);
    // ____ compute arcsin directly
    double asvd = 6 + sv * sv;   sv *= double(1.0 / 6.0);
    double th = asv + asvd * sv;
    if (flags & 1) { th = (_2pi / 4) - th; }
    if (flags & 2) { th = (_2pi / 2) - th; }
    if (flags & 4) { th = -th; }
    return std::pair<double,double>(th,overR ? rinv : r_);    
  }

template<typename T >

std::pair<T,T> fastmath::etaphi ( T  x, T  y, T  z  )

inline

Definition at line 128 of file FastMath.h.

References atan2r(), create_public_lumi_plots::log, and mathSSE::sqrt().

Referenced by L1TdeGCT::analyze(), L1TDEMON::analyze(), DQMHcalIsoTrackAlCaReco::analyze(), IsoTrig::analyze(), L1TdeGCT::bookHistograms(), L1TDEMON::bookHistograms(), spr::getEtaPhi(), and IPTCorrector::produce().

                                             {
    std::pair<T,T> por = atan2r(y,x, true);
    x = z*por.second;
    return std::pair<float,float>( std::log(x+std::sqrt(x*x+T(1))), por.first);
  }

float fastmath::invSqrt ( float  in )

inline

Definition at line 11 of file FastMath.h.

References dbtoconf::out, and mathSSE::sqrt().

Referenced by atan2r().

                                   {
#ifndef __SSE2__
    return 1.f/std::sqrt(in);
#else
    float out;
    _mm_store_ss( &out, _mm_rsqrt_ss( _mm_load_ss( &in ) ) ); // compiles to movss, rsqrtss, movss
    // return out; // already good enough!
    return out * (1.5f - 0.5f * in * out * out); // One (more?) round of Newton's method
#endif
  }

double fastmath::invSqrt ( double  in )

inline

Definition at line 22 of file FastMath.h.

References mathSSE::sqrt().

                                    {
    return 1./std::sqrt(in);
  }