GlobalCoordsObtainer.cc

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#include "L1Trigger/DTTriggerPhase2/interface/GlobalCoordsObtainer.h"

using namespace edm;
using namespace cmsdt;

// ============================================================================
// Constructors and destructor
// ============================================================================
GlobalCoordsObtainer::GlobalCoordsObtainer(const ParameterSet& pset) {
  global_coords_filename_ = pset.getParameter<edm::FileInPath>("global_coords_filename");
  std::ifstream ifin3(global_coords_filename_.fullPath());

  if (ifin3.fail()) {
    throw cms::Exception("Missing Input File")
        << "GlobalCoordsObtainer::GlobalCoordsObtainer() -  Cannot find " << global_coords_filename_.fullPath();
  }

  int wh, st, se, sl;
  double perp, x_phi0;
  std::string line;

  global_constant_per_sl sl1_constants;
  global_constant_per_sl sl3_constants;

  while (ifin3.good()) {
    ifin3 >> wh >> st >> se >> sl >> perp >> x_phi0;

    if (sl == 1) {
      sl1_constants.perp = perp;
      sl1_constants.x_phi0 = x_phi0;
    } else {
      sl3_constants.perp = perp;
      sl3_constants.x_phi0 = x_phi0;

      DTChamberId ChId(wh, st, se);
      global_constants.push_back({ChId.rawId(), sl1_constants, sl3_constants});
    }
  }
}

GlobalCoordsObtainer::~GlobalCoordsObtainer() {}

void GlobalCoordsObtainer::generate_luts() {
  for (auto& global_constant : global_constants) {
    int sgn = 1;
    DTChamberId ChId(global_constant.chid);
    // typical hasPosRF function
    if (ChId.wheel() > 0 || (ChId.wheel() == 0 && ChId.sector() % 4 > 1)) {
      sgn = -1;
    }

    auto phi1 = calc_atan_lut(12,
                              6,
                              (1. / 16) / (global_constant.sl1.perp * 10),
                              global_constant.sl1.x_phi0 / global_constant.sl1.perp,
                              1. / std::pow(2, 17),
                              10,
                              3,
                              12,
                              20,
                              sgn);

    auto phi3 = calc_atan_lut(12,
                              6,
                              (1. / 16) / (global_constant.sl3.perp * 10),
                              global_constant.sl3.x_phi0 / global_constant.sl3.perp,
                              1. / std::pow(2, 17),
                              10,
                              3,
                              12,
                              20,
                              sgn);

    double max_x_phi0 = global_constant.sl1.x_phi0;
    if (global_constant.sl3.x_phi0 > max_x_phi0) {
      max_x_phi0 = global_constant.sl3.x_phi0;
    }

    auto phic = calc_atan_lut(12,
                              6,
                              (1. / 16) / ((global_constant.sl1.perp + global_constant.sl3.perp) / .2),
                              max_x_phi0 / ((global_constant.sl1.perp + global_constant.sl3.perp) / 2),
                              1. / std::pow(2, 17),
                              10,
                              3,
                              12,
                              20,
                              sgn);

    auto phib = calc_atan_lut(9, 6, 1. / 4096, 0., 4. / std::pow(2, 13), 10, 3, 10, 16, sgn);

    luts[global_constant.chid] = {phic, phi1, phi3, phib};
  }
}

std::map<int, lut_value> GlobalCoordsObtainer::calc_atan_lut(int msb_num,
                                                             int lsb_num,
                                                             double in_res,
                                                             double abscissa_0,
                                                             double out_res,
                                                             int a_extra_bits,
                                                             int b_extra_bits,
                                                             int a_size,
                                                             int b_size,
                                                             int sgn) {
  // Calculates the coefficients needed to calculate the arc-tan function in fw
  // by doing a piece-wise linear approximation.
  // In fw, input (x) and output (y) are integers, these conversions are needed
  //   t = x*in_res - abscissa_0
  //   phi = arctan(t)
  //   y = phi/out_res
  //   => y = arctan(x*in_res - abcissa_0)/out_res
  // The linear function is approximated as
  //   y = a*x_lsb + b
  // Where a, b = func(x_msb) are the coefficients stored in the lut

  // a is stored as unsigned, b as signed, with their respective sizes a_size, b_size,
  // previously shifted left by a_extra_bits and b_extra_bits, respectively

  long int a_min = -std::pow(2, (a_size - 1));
  long int a_max = std::pow(2, (a_size - 1)) - 1;
  long int b_min = -std::pow(2, (b_size - 1));
  long int b_max = std::pow(2, (b_size - 1)) - 1;

  std::map<int, lut_value> lut;

  for (long int x_msb = -(long int)std::pow(2, msb_num - 1); x_msb < (long int)std::pow(2, msb_num - 1); x_msb++) {
    int x1 = ((x_msb) << lsb_num);
    int x2 = ((x_msb + 1) << lsb_num) - 1;

    double t1 = x1 * in_res - abscissa_0;
    double t2 = x2 * in_res - abscissa_0;

    double phi1 = sgn * atan(t1);
    double phi2 = sgn * atan(t2);

    double y1 = phi1 / out_res;
    double y2 = phi2 / out_res;

    // we want to find a, b so that the error in the extremes is the same as the error in the center
    // so the error in the extremes will be the same, so the "a" is determined by those points
    double a = (y2 - y1) / (x2 - x1);

    // by derivating the error function and equaling to 0, you get this is the point
    // towards the interval center with the highest error
    // err_f = y - (a*x+b) = sgn*arctan(x*in_res - abcissa_0)/out_res - (a*x+b)
    // d(err_f)/dx = sgn*(1/(1+(x*in_res - abcissa_0)^2))*in_res/out_res - a
    // d(err_f)/dx = 0 => x_max_err = (sqrt(in_res/out_res/a-1) + abscissa_0)/in_res
    // There is sign ambiguity in the sqrt operation. The sqrt has units of t (adimensional).
    // It is resolved by setting the sqrt to have the same sign as (t1+t2)/2

    double t_max_err = sqrt(sgn * in_res / out_res / a - 1);
    if ((t1 + t2) < 0) {
      t_max_err *= -1;
    }

    double x_max_err = (t_max_err + abscissa_0) / in_res;
    double phi_max_err = sgn * atan(t_max_err);
    double y_max_err = phi_max_err / out_res;

    // once you have the point of max error, the "b" parameter is chosen as the average between
    // those two numbers, which makes the error at the center be equal in absolute value
    // to the error in the extremes
    // units: rad

    double b = (y1 + y_max_err - a * (x_max_err - x1)) / 2;

    // increase b in 1/2 of y_lsb, so that fw truncate operation on the of the result
    // is equivalent to a round function instead of a floor function
    b += 0.5;

    // shift left and round
    long int a_int = (long int)(round(a * (pow(2, a_extra_bits))));
    long int b_int = (long int)(round(b * (pow(2, b_extra_bits))));

    // tuck a, b constants into the bit size of the output (un)signed integer
    std::vector<long int> as = {a_min, a_int, a_max};
    std::vector<long int> bs = {b_min, b_int, b_max};

    std::sort(as.begin(), as.end());
    std::sort(bs.begin(), bs.end());

    a_int = as.at(1);
    b_int = bs.at(1);

    // // convert a, b to two's complement
    // auto a_signed = a_int % (long int) (pow(2, a_size));
    // auto b_signed = b_int % (long int) (pow(2, b_size));

    // convert x_msb to two's complement signed
    int index = to_two_comp(x_msb, msb_num);
    lut[index] = {a_int, b_int};
  }
  return lut;
}

std::vector<double> GlobalCoordsObtainer::get_global_coordinates(uint32_t chid, int sl, int x, int tanpsi) {
  // Depending on the type of primitive (SL1, SL3 or correlated), choose the
  // appropriate input data (x, tanpsi) from the input primitive data structure
  // and the corresponding phi-lut from the 3 available options
  auto phi_lut = &luts[chid].phic;
  if (sl == 1) {
    phi_lut = &luts[chid].phi1;
  } else if (sl == 3) {
    phi_lut = &luts[chid].phi3;
  }

  auto phib_lut = &luts[chid].phib;

  // x and slope are given in two's complement in fw
  x = to_two_comp(x, X_SIZE);
  tanpsi = to_two_comp(tanpsi, TANPSI_SIZE);

  // Slice x and tanpsi
  // Both x and tanpsi are represented in vhdl as signed, this means their values
  // are stored as two's complement.

  // The MSB part is going to be used to index the luts and obtain a and b parameters
  // Converting the upper part of the signed to an integer (with sign).

  int x_msb = x >> (X_SIZE - PHI_LUT_ADDR_WIDTH);
  x_msb = from_two_comp(x_msb, PHI_LUT_ADDR_WIDTH);

  int tanpsi_msb = tanpsi >> (TANPSI_SIZE - PHIB_LUT_ADDR_WIDTH);
  tanpsi_msb = from_two_comp(tanpsi_msb, PHIB_LUT_ADDR_WIDTH);

  // The LSB part can be sliced right away because it must yield a positive integer
  int x_lsb = x & (int)(std::pow(2, (X_SIZE - PHI_LUT_ADDR_WIDTH)) - 1);
  int tanpsi_lsb = tanpsi & (int)(std::pow(2, (TANPSI_SIZE - PHIB_LUT_ADDR_WIDTH)) - 1);

  // Index the luts wiht the MSB parts already calculated
  auto phi_lut_q = phi_lut->at(to_two_comp(x_msb, PHI_LUT_ADDR_WIDTH));
  auto phib_lut_q = phib_lut->at(to_two_comp(tanpsi_msb, PHIB_LUT_ADDR_WIDTH));

  // Separate this data into the coefficients a and b
  auto phi_lut_a = phi_lut_q.a;
  auto phi_lut_b = phi_lut_q.b;
  auto phib_lut_a = phib_lut_q.a;
  auto phib_lut_b = phib_lut_q.b;

  // Do the linear piece-wise operations
  // At this point all variables that can be negative have already been converted
  // so will yield negative values when necessary
  int phi_uncut = (phi_lut_b << PHI_B_SHL_BITS) + x_lsb * phi_lut_a;
  int psi_uncut = (phib_lut_b << PHIB_B_SHL_BITS) + tanpsi_lsb * phib_lut_a;

  // Trim phi to its final size
  int phi = (phi_uncut >> PHI_MULT_SHR_BITS);

  // Calculate phi_bending from the uncut version of phi and psi, and the trim it to size
  int phib_uncut = psi_uncut - (phi_uncut >> (PHI_PHIB_RES_DIFF_BITS + PHI_MULT_SHR_BITS - PHIB_MULT_SHR_BITS));
  int phib = (phib_uncut >> PHIB_MULT_SHR_BITS);

  double phi_f = (double)phi / pow(2, PHI_SIZE);
  double phib_f = (double)phib / pow(2, PHIB_SIZE);

  return std::vector({phi_f, phib_f});
}