RecoLocalTracker/SiPixelRecHits/src/VVIObj.cc - master - githubmirror/cmssw

RecoLocalTracker/SiPixelRecHits/src/VVIObj.cc
773 строки23 KB
Purva Chaudhari
applied suggested code checks
05 июл 2021, 11:40
05 июл 2021, 11:40b8725b5
//
//  VVIObj.cc  Version 2.0
//
//  Port of CERNLIB G116 Functions vviden/vvidis
//
// Created by Morris Swartz on 1/14/2010.
// 2010 __TheJohnsHopkinsUniversity__.
//
// V1.1 - make dzero call both fcns with a switch
// V1.2 - remove inappriate initializers and add methods to return non-zero/normalized region
// V2.0 - restructuring and speed improvements by V. Innocente
//

#ifndef SI_PIXEL_TEMPLATE_STANDALONE
// put CMSSW location of SimpleHelix.h here
#include "RecoLocalTracker/SiPixelRecHits/interface/VVIObj.h"
#else
#include "VVIObj.h"
#endif

#include <cmath>
#include <algorithm>

namespace VVIObjDetails {
  void sincosint(double x, double& sint, double& cint);  //! Private version of the cosine and sine integral
  double cosint(double x);                               //! Private version of the cosine integral
  double sinint(double x);                               //! Private version of the sine integral
  double expint(double x);                               //! Private version of the exponential integral

  template <typename F>
  int dzero(double a, double b, double& x0, double& rv, double eps, int mxf, F func);
}  // namespace VVIObjDetails

// ***************************************************************************************************************************************
//! Constructor
//! Set Vavilov parameters kappa and beta2 and define whether to calculate density fcn or distribution fcn
//! \param kappa - (input) Vavilov kappa parameter [0.01 (Landau-like) < kappa < 10. (Gaussian-like)]
//! \param beta2 - (input) Vavilov beta2 parameter (square of particle speed in v/c units)
//! \param mode  - (input) set to 0 to calculate the density function and to 1 to calculate the distribution function
// ***************************************************************************************************************************************

VVIObj::VVIObj(double kappa, double beta2, int mode) : mode_(mode) {
  const double xp[9] = {9.29, 2.47, .89, .36, .15, .07, .03, .02, 0.0};
  const double xq[7] = {.012, .03, .08, .26, .87, 3.83, 11.0};
  double h_[7];
  double q, u, x, c1, c2, c3, c4, d1, h4, h5, h6, q2, x1, d, ll, ul, xf1, xf2, rv;
  int lp, lq, k, l, n;

  // Make sure that the inputs are reasonable

  if (kappa < 0.01)
    kappa = 0.01;
  if (kappa > 10.)
    kappa = 10.;
  if (beta2 < 0.)
    beta2 = 0.;
  if (beta2 > 1.)
    beta2 = 1.;

  h_[4] = 1. - beta2 * 0.42278433999999998 + 7.6 / kappa;
  h_[5] = beta2;
  h_[6] = 1. - beta2;
  h4 = -7.6 / kappa - (beta2 * .57721566 + 1);
  h5 = log(kappa);
  h6 = 1. / kappa;
  t0_ = (h4 - h_[4] * h5 - (h_[4] + beta2) * (log(h_[4]) + VVIObjDetails::expint(h_[4])) + exp(-h_[4])) / h_[4];

  // Set up limits for the root search

  for (lp = 0; lp < 9; ++lp) {
    if (kappa >= xp[lp])
      break;
  }
  ll = -lp - 1.5;
  for (lq = 0; lq < 7; ++lq) {
    if (kappa <= xq[lq])
      break;
  }
  ul = lq - 6.5;
  auto f2 = [h_](double x) {
    return h_[4] - x + h_[5] * (std::log(std::abs(x)) + VVIObjDetails::expint(x)) - h_[6] * std::exp(-x);
  };
  VVIObjDetails::dzero(ll, ul, u, rv, 1.e-5, 1000, f2);
  q = 1. / u;
  t1_ = h4 * q - h5 - (beta2 * q + 1) * (log((fabs(u))) + VVIObjDetails::expint(u)) + exp(-u) * q;
  t_ = t1_ - t0_;
  omega_ = 6.2831853000000004 / t_;
  h_[0] = kappa * (beta2 * .57721566 + 2.) + 9.9166128600000008;
  if (kappa >= .07) {
    h_[0] += 6.90775527;
  }
  h_[1] = beta2 * kappa;
  h_[2] = h6 * omega_;
  h_[3] = omega_ * 1.5707963250000001;
  auto f1 = [h_](double x) { return h_[0] + h_[1] * std::log(h_[2] * x) - h_[3] * x; };
  VVIObjDetails::dzero(5., 155., x0_, rv, 1.e-5, 1000, f1);
  n = x0_ + 1.;
  d = exp(kappa * (beta2 * (.57721566 - h5) + 1.)) * .31830988654751274;
  a_[n - 1] = 0.;
  if (mode_ == 0) {
    a_[n - 1] = omega_ * .31830988654751274;
  }
  q = -1.;
  q2 = 2.;
  for (k = 1; k < n; ++k) {
    l = n - k;
    x = omega_ * k;
    x1 = h6 * x;
    VVIObjDetails::sincosint(x1, c2, c1);
    c1 = log(x) - c1;
    c3 = sin(x1);
    c4 = cos(x1);
    xf1 = kappa * (beta2 * c1 - c4) - x * c2;
    xf2 = x * c1 + kappa * (c3 + beta2 * c2) + t0_ * x;
    if (mode_ == 0) {
      d1 = q * d * omega_ * exp(xf1);
      a_[l - 1] = d1 * cos(xf2);
      b_[l - 1] = -d1 * sin(xf2);
    } else {
      d1 = q * d * exp(xf1) / k;
      a_[l - 1] = d1 * sin(xf2);
      b_[l - 1] = d1 * cos(xf2);
      a_[n - 1] += q2 * a_[l - 1];
    }
    q = -q;
    q2 = -q2;
  }

}  // VVIObj

// *************************************************************************************************************************************
//! Vavilov function method
//! Returns density fcn (mode=0) or distribution fcn (mode=1)
//! \param x  - (input) Argument of function [typically defined as (Q-mpv)/sigma]
// *************************************************************************************************************************************

double VVIObj::fcn(double x) const {
  // Local variables

  double f, u, y, a0, a1;
  double a2 = 0.;
  double b1, b0, b2, cof;
  int k, n, n1;

  n = x0_;
  if (x < t0_) {
    f = 0.;
  } else if (x <= t1_) {
    y = x - t0_;
    u = omega_ * y - 3.141592653589793;
    cof = cos(u) * 2.;
    a1 = 0.;
    a0 = a_[0];
    n1 = n + 1;
    for (k = 2; k <= n1; ++k) {
      a2 = a1;
      a1 = a0;
      a0 = a_[k - 1] + cof * a1 - a2;
    }
    b1 = 0.;
    b0 = b_[0];
    for (k = 2; k <= n; ++k) {
      b2 = b1;
      b1 = b0;
      b0 = b_[k - 1] + cof * b1 - b2;
    }
    f = (a0 - a2) * .5 + b0 * sin(u);
    if (mode_ != 0) {
      f += y / t_;
    }
  } else {
    f = 0.;
    if (mode_ != 0) {
      f = 1.;
    }
  }
  return f;
}  // fcn

// *************************************************************************************************************************************
//! Vavilov limits method
//! \param xl - (output) Smallest value of the argument for the density and the beginning of the normalized region for the distribution
//! \param xu - (output) Largest value of the argument for the density and the end of the normalized region for the distribution
// *************************************************************************************************************************************

void VVIObj::limits(double& xl, double& xu) const {
  xl = t0_;
  xu = t1_;
  return;
}  // limits

namespace VVIObjDetails {
  double cosint(double x) {
    // Initialized data

    const double zero = 0.;
    const double one = 1.;
    const double two = 2.;
    const double eight = 8.;
    const double ce = .57721566490153;
    const double c__[14] = {1.9405491464836,
                            .9413409132865,
                            -.579845034293,
                            .3091572011159,
                            -.0916101792208,
                            .0164437407515,
                            -.0019713091952,
                            1.692538851e-4,
                            -1.09393296e-5,
                            5.522386e-7,
                            -2.23995e-8,
                            7.465e-10,
                            -2.08e-11,
                            5e-13};
    const double p[23] = {
        .96074783975204, -.0371138962124, .00194143988899, -1.7165988425e-4, 2.112637753e-5, -3.27163257e-6,
        6.0069212e-7,    -1.2586794e-7,   2.932563e-8,     -7.45696e-9,      2.04105e-9,     -5.9502e-10,
        1.8323e-10,      -5.921e-11,      1.997e-11,       -7e-12,           2.54e-12,       -9.5e-13,
        3.7e-13,         -1.4e-13,        6e-14,           -2e-14,           1e-14};
    const double q[20] = {.98604065696238, -.0134717382083, 4.5329284117e-4, -3.067288652e-5, 3.13199198e-6,
                          -4.2110196e-7,   6.907245e-8,     -1.318321e-8,    2.83697e-9,      -6.7329e-10,
                          1.734e-10,       -4.787e-11,      1.403e-11,       -4.33e-12,       1.4e-12,
                          -4.7e-13,        1.7e-13,         -6e-14,          2e-14,           -1e-14};

    // System generated locals
    double d__1;

    // Local variables
    double h__;
    int i__;
    double r__, y, b0, b1, b2, pp, qq, alfa;

    // If x==0, return same

    if (x == zero) {
      return zero;
    }
    if (fabs(x) <= eight) {
      y = x / eight;
      // Computing 2nd power
      d__1 = y;
      h__ = two * (d__1 * d__1) - one;
      alfa = -two * h__;
      b1 = zero;
      b2 = zero;
      for (i__ = 13; i__ >= 0; --i__) {
        b0 = c__[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      b1 = ce + log((fabs(x))) - b0 + h__ * b2;
    } else {
      r__ = one / x;
      y = eight * r__;
      // Computing 2nd power
      d__1 = y;
      h__ = two * (d__1 * d__1) - one;
      alfa = -two * h__;
      b1 = zero;
      b2 = zero;
      for (i__ = 22; i__ >= 0; --i__) {
        b0 = p[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      pp = b0 - h__ * b2;
      b1 = zero;
      b2 = zero;
      for (i__ = 19; i__ >= 0; --i__) {
        b0 = q[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      qq = b0 - h__ * b2;
      b1 = r__ * (qq * sin(x) - r__ * pp * cos(x));
    }
    return b1;
  }  // cosint

  double sinint(double x) {
    // Initialized data

    const double zero = 0.;
    const double one = 1.;
    const double two = 2.;
    const double eight = 8.;
    const double pih = 1.5707963267949;
    const double s[14] = {1.9522209759531,
                          -.6884042321257,
                          .4551855132256,
                          -.1804571236838,
                          .0410422133759,
                          -.0059586169556,
                          6.001427414e-4,
                          -4.44708329e-5,
                          2.5300782e-6,
                          -1.141308e-7,
                          4.1858e-9,
                          -1.273e-10,
                          3.3e-12,
                          -1e-13};
    const double p[23] = {
        .96074783975204, -.0371138962124, .00194143988899, -1.7165988425e-4, 2.112637753e-5, -3.27163257e-6,
        6.0069212e-7,    -1.2586794e-7,   2.932563e-8,     -7.45696e-9,      2.04105e-9,     -5.9502e-10,
        1.8323e-10,      -5.921e-11,      1.997e-11,       -7e-12,           2.54e-12,       -9.5e-13,
        3.7e-13,         -1.4e-13,        6e-14,           -2e-14,           1e-14};
    const double q[20] = {.98604065696238, -.0134717382083, 4.5329284117e-4, -3.067288652e-5, 3.13199198e-6,
                          -4.2110196e-7,   6.907245e-8,     -1.318321e-8,    2.83697e-9,      -6.7329e-10,
                          1.734e-10,       -4.787e-11,      1.403e-11,       -4.33e-12,       1.4e-12,
                          -4.7e-13,        1.7e-13,         -6e-14,          2e-14,           -1e-14};

    // System generated locals
    double d__1;

    // Local variables
    double h__;
    int i__;
    double r__, y, b0, b1, b2, pp, qq, alfa;

    if (fabs(x) <= eight) {
      y = x / eight;
      d__1 = y;
      h__ = two * (d__1 * d__1) - one;
      alfa = -two * h__;
      b1 = zero;
      b2 = zero;
      for (i__ = 13; i__ >= 0; --i__) {
        b0 = s[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      b1 = y * (b0 - b2);
    } else {
      r__ = one / x;
      y = eight * r__;
      d__1 = y;
      h__ = two * (d__1 * d__1) - one;
      alfa = -two * h__;
      b1 = zero;
      b2 = zero;
      for (i__ = 22; i__ >= 0; --i__) {
        b0 = p[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      pp = b0 - h__ * b2;
      b1 = zero;
      b2 = zero;
      for (i__ = 19; i__ >= 0; --i__) {
        b0 = q[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      qq = b0 - h__ * b2;
      d__1 = fabs(pih);
      if (x < 0.)
        d__1 = -d__1;
      b1 = d__1 - r__ * (r__ * pp * sin(x) + qq * cos(x));
    }

    return b1;
  }  // sinint

  void sincosint(double x, double& sint, double& cint) {
    // Initialized data

    const double zero = 0.;
    const double one = 1.;
    const double two = 2.;
    const double eight = 8.;
    const double ce = .57721566490153;
    const double pih = 1.5707963267949;
    const double s__[14] = {1.9522209759531,
                            -.6884042321257,
                            .4551855132256,
                            -.1804571236838,
                            .0410422133759,
                            -.0059586169556,
                            6.001427414e-4,
                            -4.44708329e-5,
                            2.5300782e-6,
                            -1.141308e-7,
                            4.1858e-9,
                            -1.273e-10,
                            3.3e-12,
                            -1e-13};

    const double c__[14] = {1.9405491464836,
                            .9413409132865,
                            -.579845034293,
                            .3091572011159,
                            -.0916101792208,
                            .0164437407515,
                            -.0019713091952,
                            1.692538851e-4,
                            -1.09393296e-5,
                            5.522386e-7,
                            -2.23995e-8,
                            7.465e-10,
                            -2.08e-11,
                            5e-13};

    const double p[23] = {
        .96074783975204, -.0371138962124, .00194143988899, -1.7165988425e-4, 2.112637753e-5, -3.27163257e-6,
        6.0069212e-7,    -1.2586794e-7,   2.932563e-8,     -7.45696e-9,      2.04105e-9,     -5.9502e-10,
        1.8323e-10,      -5.921e-11,      1.997e-11,       -7e-12,           2.54e-12,       -9.5e-13,
        3.7e-13,         -1.4e-13,        6e-14,           -2e-14,           1e-14};
    const double q[20] = {.98604065696238, -.0134717382083, 4.5329284117e-4, -3.067288652e-5, 3.13199198e-6,
                          -4.2110196e-7,   6.907245e-8,     -1.318321e-8,    2.83697e-9,      -6.7329e-10,
                          1.734e-10,       -4.787e-11,      1.403e-11,       -4.33e-12,       1.4e-12,
                          -4.7e-13,        1.7e-13,         -6e-14,          2e-14,           -1e-14};

    // System generated locals
    double d__1;

    // Local variables
    double h__;
    int i__;
    double r__, y, b0, b1, b2, pp, qq, alfa;

    sint = 0;
    cint = 0;

    if (fabs(x) <= eight) {
      y = x / eight;
      // Computing 2nd power
      d__1 = y;
      h__ = two * (d__1 * d__1) - one;
      alfa = -two * h__;

      // cos
      if (x != 0) {
        b1 = zero;
        b2 = zero;
        for (i__ = 13; i__ >= 0; --i__) {
          b0 = c__[i__] - alfa * b1 - b2;
          b2 = b1;
          b1 = b0;
        }
        cint = ce + log((fabs(x))) - b0 + h__ * b2;
      }
      // sin
      b1 = zero;
      b2 = zero;
      for (i__ = 13; i__ >= 0; --i__) {
        b0 = s__[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      sint = y * (b0 - b2);

    } else {
      r__ = one / x;
      y = eight * r__;
      // Computing 2nd power
      d__1 = y;
      h__ = two * (d__1 * d__1) - one;
      alfa = -two * h__;
      b1 = zero;
      b2 = zero;
      for (i__ = 22; i__ >= 0; --i__) {
        b0 = p[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      pp = b0 - h__ * b2;
      b1 = zero;
      b2 = zero;
      for (i__ = 19; i__ >= 0; --i__) {
        b0 = q[i__] - alfa * b1 - b2;
        b2 = b1;
        b1 = b0;
      }
      qq = b0 - h__ * b2;
      // cos
      cint = r__ * (qq * sin(x) - r__ * pp * cos(x));
      // sin
      d__1 = pih;
      if (x < 0.)
        d__1 = -d__1;
      sint = d__1 - r__ * (r__ * pp * sin(x) + qq * cos(x));
    }
  }

  double expint(double x) {
    // Initialized data

    const double zero = 0.;
    const double q2[7] = {
        .10340013040487, 3.319092135933, 20.449478501379, 41.280784189142, 32.426421069514, 10.041164382905, 1.};
    const double p3[6] = {
        -2.3909964453136, -147.98219500504, -254.3763397689, -119.55761038372, -19.630408535939, -.9999999999036};
    const double q3[6] = {177.60070940351, 530.68509610812, 462.23027156148, 156.81843364539, 21.630408494238, 1.};
    const double p4[8] = {-8.6693733995107,
                          -549.14226552109,
                          -4210.0161535707,
                          -249301.39345865,
                          -119623.66934925,
                          -22174462.775885,
                          3892804.213112,
                          -391546073.8091};
    const double q4[8] = {34.171875,
                          -1607.0892658722,
                          35730.029805851,
                          -483547.43616216,
                          4285596.2461175,
                          -24903337.574054,
                          89192576.757561,
                          -165254299.72521};
    const double a1[8] = {-2.1808638152072,
                          -21.901023385488,
                          9.3081638566217,
                          25.076281129356,
                          -33.184253199722,
                          60.121799083008,
                          -43.253113287813,
                          1.0044310922808};
    const double b1[8] = {0.,
                          3.9370770185272,
                          300.89264837292,
                          -6.2504116167188,
                          1003.6743951673,
                          14.325673812194,
                          2736.2411988933,
                          .52746885196291};
    const double a2[8] = {-3.4833465360285,
                          -18.65454548834,
                          -8.2856199414064,
                          -32.34673303054,
                          17.960168876925,
                          1.7565631546961,
                          -1.9502232128966,
                          .99999429607471};
    const double b2[8] = {0.,
                          69.500065588743,
                          57.283719383732,
                          25.777638423844,
                          760.76114800773,
                          28.951672792514,
                          -3.4394226689987,
                          1.0008386740264};
    const double a3[6] = {
        -27.780928934438, -10.10479081576, -9.1483008216736, -5.0223317461851, -3.0000077799358, 1.0000000000704};
    const double one = 1.;
    const double b3[6] = {0., 122.39993926823, 2.7276100778779, -7.1897518395045, -2.9990118065262, 1.999999942826};
    const double two = 2.;
    const double three = 3.;
    const double x0 = .37250741078137;
    const double xl[6] = {-24., -12., -6., 0., 1., 4.};
    const double p1[5] = {4.293125234321, 39.894153870321, 292.52518866921, 425.69682638592, -434.98143832952};
    const double q1[5] = {1., 18.899288395003, 150.95038744251, 568.05252718987, 753.58564359843};
    const double p2[7] = {.43096783946939,
                          6.9052252278444,
                          23.019255939133,
                          24.378408879132,
                          9.0416155694633,
                          .99997957705159,
                          4.656271079751e-7};

    /* Local variables */
    double v, y, ap, bp, aq, dp, bq, dq;

    if (x <= xl[0]) {
      ap = a3[0] - x;
      for (int i__ = 2; i__ <= 5; ++i__) {
        /* L1: */
        ap = a3[i__ - 1] - x + b3[i__ - 1] / ap;
      }
      y = exp(-x) / x * (one - (a3[5] + b3[5] / ap) / x);
    } else if (x <= xl[1]) {
      ap = a2[0] - x;
      for (int i__ = 2; i__ <= 7; ++i__) {
        ap = a2[i__ - 1] - x + b2[i__ - 1] / ap;
      }
      y = exp(-x) / x * (a2[7] + b2[7] / ap);
    } else if (x <= xl[2]) {
      ap = a1[0] - x;
      for (int i__ = 2; i__ <= 7; ++i__) {
        ap = a1[i__ - 1] - x + b1[i__ - 1] / ap;
      }
      y = exp(-x) / x * (a1[7] + b1[7] / ap);
    } else if (x < xl[3]) {
      v = -two * (x / three + one);
      bp = zero;
      dp = p4[0];
      for (int i__ = 2; i__ <= 8; ++i__) {
        ap = bp;
        bp = dp;
        dp = p4[i__ - 1] - ap + v * bp;
      }
      bq = zero;
      dq = q4[0];
      for (int i__ = 2; i__ <= 8; ++i__) {
        aq = bq;
        bq = dq;
        dq = q4[i__ - 1] - aq + v * bq;
      }
      y = -log(-x / x0) + (x + x0) * (dp - ap) / (dq - aq);
    } else if (x == xl[3]) {
      return zero;
    } else if (x < xl[4]) {
      ap = p1[0];
      aq = q1[0];
      for (int i__ = 2; i__ <= 5; ++i__) {
        ap = p1[i__ - 1] + x * ap;
        aq = q1[i__ - 1] + x * aq;
      }
      y = -log(x) + ap / aq;
    } else if (x <= xl[5]) {
      y = one / x;
      ap = p2[0];
      aq = q2[0];
      for (int i__ = 2; i__ <= 7; ++i__) {
        ap = p2[i__ - 1] + y * ap;
        aq = q2[i__ - 1] + y * aq;
      }
      y = exp(-x) * ap / aq;
    } else {
      y = one / x;
      ap = p3[0];
      aq = q3[0];
      for (int i__ = 2; i__ <= 6; ++i__) {
        ap = p3[i__ - 1] + y * ap;
        aq = q3[i__ - 1] + y * aq;
      }
      y = exp(-x) * y * (one + y * ap / aq);
    }
    return y;
  }  // expint

  template <typename F>
  int dzero(double a, double b, double& x0, double& rv, double eps, int mxf, F func) {
    /* System generated locals */
    double d__1, d__2, d__3, d__4;

    // Local variables
    double f1, f2, f3, u1, u2, x1, x2, u3, u4, x3, ca, cb, cc, fa, fb, ee, ff;
    int mc;
    double xa, xb, fx, xx, su4;

    xa = std::min(a, b);
    xb = std::max(a, b);
    fa = func(xa);
    fb = func(xb);
    if (fa * fb > 0.) {
      rv = (xb - xa) * -2;
      x0 = 0.;
      return 1;
    }
    mc = 0;
  L1:
    x0 = (xa + xb) * .5;
    rv = x0 - xa;
    ee = eps * (fabs(x0) + 1);
    if (rv <= ee) {
      rv = ee;
      ff = func(x0);
      return 0;
    }
    f1 = fa;
    x1 = xa;
    f2 = fb;
    x2 = xb;
  L2:
    fx = func(x0);
    ++mc;
    if (mc > mxf) {
      rv = (d__1 = xb - xa, fabs(d__1)) * -.5;
      x0 = 0.;
      return 0;
    }
    if (fx * fa > 0.) {
      xa = x0;
      fa = fx;
    } else {
      xb = x0;
      fb = fx;
    }
  L3:
    u1 = f1 - f2;
    u2 = x1 - x2;
    u3 = f2 - fx;
    u4 = x2 - x0;
    if (u2 == 0. || u4 == 0.) {
      goto L1;
    }
    f3 = fx;
    x3 = x0;
    u1 /= u2;
    u2 = u3 / u4;
    ca = u1 - u2;
    cb = (x1 + x2) * u2 - (x2 + x0) * u1;
    cc = (x1 - x0) * f1 - x1 * (ca * x1 + cb);
    if (ca == 0.) {
      if (cb == 0.) {
        goto L1;
      }
      x0 = -cc / cb;
    } else {
      u3 = cb / (ca * 2);
      u4 = u3 * u3 - cc / ca;
      if (u4 < 0.) {
        goto L1;
      }
      su4 = fabs(u4);
      if (x0 + u3 < 0.f) {
        su4 = -su4;
      }
      x0 = -u3 + su4;
    }
    if (x0 < xa || x0 > xb) {
      goto L1;
    }
    // Computing MIN
    d__3 = (d__1 = x0 - x3, fabs(d__1)), d__4 = (d__2 = x0 - x2, fabs(d__2));
    rv = std::min(d__3, d__4);
    ee = eps * (fabs(x0) + 1);
    if (rv > ee) {
      f1 = f2;
      x1 = x2;
      f2 = f3;
      x2 = x3;
      goto L2;
    }
    fx = func(x0);
    if (fx == 0.) {
      rv = ee;
      ff = func(x0);
      return 0;
    }
    if (fx * fa < 0.) {
      xx = x0 - ee;
      if (xx <= xa) {
        rv = ee;
        ff = func(x0);
        return 0;
      }
      ff = func(xx);
      fb = ff;
      xb = xx;
    } else {
      xx = x0 + ee;
      if (xx >= xb) {
        rv = ee;
        ff = func(x0);
        return 0;
      }
      ff = func(xx);
      fa = ff;
      xa = xx;
    }
    if (fx * ff > 0.) {
      mc += 2;
      if (mc > mxf) {
        rv = (d__1 = xb - xa, fabs(d__1)) * -.5;
        x0 = 0.;
        return 0;
      }
      f1 = f3;
      x1 = x3;
      f2 = fx;
      x2 = x0;
      x0 = xx;
      fx = ff;
      goto L3;
    }
    /* L4: */
    rv = ee;
    ff = func(x0);
    return 0;
  }  // dzero

}  // namespace VVIObjDetails