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

atan2r() [1/2]

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

inline

Definition at line 38 of file FastMath.h.

References fastmath_details::_2pif, fastmath_details::atanbuf_, cuy::cv, f, HLT_2022v12_cff::flags, dqmMemoryStats::float, mps_fire::i, invSqrt(), mag2(), trklet::rinv(), pfDeepBoostedJetPreprocessParams_cfi::sv, 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);
  }

atan2r() [2/2]

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

inline

Definition at line 98 of file FastMath.h.

References fastmath_details::_2pi, cuy::cv, ztail::d, fastmath_details::datanbuf_, HLT_2022v12_cff::flags, mps_fire::i, mag2(), trklet::rinv(), mathSSE::sqrt(), pfDeepBoostedJetPreprocessParams_cfi::sv, 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_);
  }

etaphi()

template<typename T >

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

inline

Definition at line 162 of file FastMath.h.

References atan2r(), dqm-mbProfile::log, mathSSE::sqrt(), and x.

Referenced by L1TdeGCT::analyze(), L1TDEMON::analyze(), DQMHcalIsoTrackAlCaReco::analyze(), HcalGeomCheck::analyze(), IsoTrig::analyze(), L1TdeGCT::bookHistograms(), L1TDEMON::bookHistograms(), JetHTJetPlusHOFilter::filter(), 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);
  }

invSqrt() [1/2]

float fastmath::invSqrt ( float  in )

inline

Definition at line 11 of file FastMath.h.

References recoMuon::in, MillePedeFileConverter_cfg::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
  }

invSqrt() [2/2]

double fastmath::invSqrt ( double  in )

inline

Definition at line 22 of file FastMath.h.

References recoMuon::in, and mathSSE::sqrt().

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