VVIObjDetails Namespace Reference

Functions
double	cosint (double x)
	Private version of the cosine and sine integral. More...
template<typename F >
int	dzero (double a, double b, double &x0, double &rv, double eps, int mxf, F func)
	Private version of the exponential integral. More...
double	expint (double x)
	Private version of the sine integral. More...
void	sincosint (double x, double &sint, double &cint)
double	sinint (double x)
	Private version of the cosine integral. More...

Function Documentation

double VVIObjDetails::cosint

(

double

x

)

Private version of the cosine and sine integral.

Definition at line 193 of file VVIObj.cc.

References funct::cos(), alignCSCRings::e, fff_deleter::log, AlCaHLTBitMon_ParallelJobs::p, createTree::pp, lumiQueryAPI::q, funct::sin(), x, and detailsBasic3DVector::y.

                          {
    // 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

template<typename F >

int VVIObjDetails::dzero	(	double	a,
		double	b,
		double &	x0,
		double &	rv,
		double	eps,
		int	mxf,
		F	func
	)

Private version of the exponential integral.

Definition at line 570 of file VVIObj.cc.

References f, python.connectstrParser::f1, python.connectstrParser::f2, python.connectstrParser::f3, benchmark_cfg::fa, benchmark_cfg::fb, alignCSCRings::ff, bookConverter::max, and min().

Referenced by VVIObj::VVIObj().

                                                 {
    /* 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

double VVIObjDetails::expint

(

double

x

)

Private version of the sine integral.

Definition at line 448 of file VVIObj.cc.

References create_public_lumi_plots::exp, fff_deleter::log, p1, p2, p3, p4, q1, q2, findQualityFiles::v, x, and detailsBasic3DVector::y.

Referenced by VVIObj::VVIObj().

                        {
  
  // 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

void VVIObjDetails::sincosint	(	double	x,
		double &	sint,
		double &	cint
	)

Definition at line 345 of file VVIObj.cc.

References funct::cos(), alignCSCRings::e, fff_deleter::log, AlCaHLTBitMon_ParallelJobs::p, createTree::pp, lumiQueryAPI::q, funct::sin(), x, and detailsBasic3DVector::y.

Referenced by VVIObj::VVIObj().

                                                         {
    // 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 VVIObjDetails::sinint

(

double

x

)

Private version of the cosine integral.

Definition at line 271 of file VVIObj.cc.

References funct::cos(), alignCSCRings::e, AlCaHLTBitMon_ParallelJobs::p, createTree::pp, lumiQueryAPI::q, alignCSCRings::s, funct::sin(), x, and detailsBasic3DVector::y.

                          {
    // 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