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00001 //
00002 //  VVIObjF.cc  Version 2.0 
00003 //
00004 //  Port of CERNLIB G116 Functions vviden/vvidis
00005 //
00006 // Created by Morris Swartz on 1/14/2010.
00007 // Copyright 2010 __TheJohnsHopkinsUniversity__. All rights reserved.
00008 //
00009 // V1.1 - make dzero call both fcns with a switch
00010 // V1.2 - remove inappriate initializers and add methods to return non-zero/normalized region
00011 // V2.0 - restructuring and speed improvements by V. Innocente
00012 //
00013 
00014 #ifndef SI_PIXEL_TEMPLATE_STANDALONE
00015 // put CMSSW location of SimpleHelix.h here
00016 #include "RecoLocalTracker/SiPixelRecHits/interface/VVIObjF.h"
00017 #else
00018 #include "VVIObjF.h"
00019 #endif
00020 
00021 
00022 #include <cmath>
00023 #include <algorithm>
00024 #include "vdt/vdtMath.h"
00025 
00026 namespace VVIObjFDetails {
00027   void sincosint(float x, float & sint, float & cint);  
00028   float expint(float x);    
00029   
00030   template<typename F>
00031   int dzero(float a, float b, float& x0, 
00032             float& rv, float eps, int mxf, F func);
00033 }
00034 
00035 
00036 
00037 // ***************************************************************************************************************************************
00043 // *************************************************************************************************************************************** 
00044 
00045 VVIObjF::VVIObjF(float kappa, float beta2, int mode) : mode_(mode) {
00046   
00047   const float xp[9] = { 9.29,2.47,.89,.36,.15,.07,.03,.02,0.0 };
00048   const float xq[7] = { .012,.03,.08,.26,.87,3.83,11.0 };
00049   float h_[7];
00050   float  q, u, x, c1, c2, c3, c4, d1, h4, h5, h6, q2, x1, d, ll, ul, xf1, xf2, rv;
00051   int lp, lq, k, l, n;
00052   
00053   // Make sure that the inputs are reasonable
00054   
00055   if(kappa < 0.01f) kappa = 0.01f;
00056   if(kappa > 10.f) kappa = 10.f;
00057   if(beta2 < 0.f) beta2 = 0.f;
00058   if(beta2 > 1.f) beta2 = 1.f;
00059   
00060   float invKappa = 1.f/kappa;
00061   h_[4] = 1.f - beta2*0.42278433999999998f + (7.6f*invKappa);
00062   h_[5] = beta2;
00063   h_[6] = 1.f - beta2;
00064   h4 = - (7.6f*invKappa) - (beta2 * .57721566f + 1.f);
00065   h5 = vdt::fast_logf(kappa);
00066   h6 = invKappa;
00067   t0_ = (h4 - h_[4]*h5 - (h_[4] + beta2)*(vdt::fast_logf(h_[4]) + VVIObjFDetails::expint(h_[4])) + vdt::fast_expf(-h_[4]))/h_[4];
00068   
00069   // Set up limits for the root search
00070   
00071   for (lp = 0; lp < 9; ++lp) {
00072     if (kappa >= xp[lp]) break;
00073   }
00074   ll = -float(lp) - 1.5f;
00075   for (lq = 0; lq < 7; ++lq) {
00076     if (kappa <= xq[lq]) break;
00077   }
00078   ul = lq - 6.5f;
00079   auto f2 = [h_](float x) { return h_[4]-x+h_[5]*(vdt::fast_logf(std::abs(x))+VVIObjFDetails::expint(x))-h_[6]*vdt::fast_expf(-x);};
00080   VVIObjFDetails::dzero(ll, ul, u, rv, 1.e-3f, 100, f2);
00081   q = 1./u;
00082   t1_ = h4 * q - h5 - (beta2 * q + 1.f) * (vdt::fast_logf((fabs(u))) + VVIObjFDetails::expint(u)) + vdt::fast_expf(-u) * q;
00083   t_ = t1_ - t0_;
00084   omega_ = 6.2831853000000004f/t_;
00085   h_[0] = kappa * (beta2 * .57721566f + 2.f) + 9.9166128600000008f;
00086   if (kappa >= .07) {h_[0] += 6.90775527f;}
00087   h_[1] = beta2 * kappa;
00088   h_[2] = h6 * omega_;
00089   h_[3] = omega_ * 1.5707963250000001f;
00090   auto f1 = [h_](float x){ return h_[0]+h_[1]*vdt::fast_logf(h_[2]*x)-h_[3]*x;};
00091   VVIObjFDetails::dzero(5.f, 155.f, x0_, rv, 1.e-3f, 100, f1);
00092   n = x0_ + 1.;
00093   d = vdt::fast_expf(kappa * (beta2 * (.57721566f - h5) + 1.f)) * .31830988654751274f;
00094   a_[n - 1] = 0.f;
00095   if (mode_ == 0) {
00096     a_[n - 1] = omega_ * .31830988654751274f;
00097   }
00098   q = -1.;
00099   q2 = 2.;
00100   for (k = 1; k < n; ++k) {
00101     l = n - k;
00102     x = omega_ * k;
00103     x1 = h6 * x;
00104     VVIObjFDetails::sincosint(x1,c2,c1);
00105     c1 = vdt::fast_logf(x) - c1;
00106     vdt::fast_sincosf(x1,c3,c4);
00107     xf1 = kappa * (beta2 * c1 - c4) - x * c2;
00108     xf2 = x * c1 + kappa * (c3 + beta2 * c2) + t0_ * x;
00109     float s,c; vdt::fast_sincosf(xf2,s,c);
00110     if (mode_ == 0) {
00111       d1 = q * d * omega_ * vdt::fast_expf(xf1);
00112       a_[l - 1] = d1 * c;
00113       b_[l - 1] = -d1 * s;
00114     } else {
00115       d1 = q * d * vdt::fast_expf(xf1)/k;
00116       a_[l - 1] = d1 * s;
00117       b_[l - 1] = d1 * c;
00118       a_[n - 1] += q2 * a_[l - 1];
00119     }
00120     q = -q;
00121     q2 = -q2;
00122   }
00123   
00124 } // VVIObjF
00125 
00126 // *************************************************************************************************************************************
00130 // ************************************************************************************************************************************* 
00131 
00132 
00133 float VVIObjF::fcn(float x) const {
00134         
00135         // Local variables
00136         
00137         float f, u, y, a0, a1;
00138         float a2 = 0.;
00139         float b1, b0, b2, cof;
00140         int k, n, n1;
00141         
00142         n = x0_;
00143         if (x < t0_) {
00144                 f = 0.f;
00145         } else if (x <= t1_) {
00146           y = x - t0_;
00147           u = omega_ * y - 3.141592653589793f;
00148           float su,cu; vdt::fast_sincosf(u,su,cu);
00149           cof = cu * 2.f;
00150           a1 = 0.;
00151           a0 = a_[0];
00152           n1=n+1;
00153           for (k = 2; k <= n1; ++k) {
00154             a2 = a1;
00155             a1 = a0;
00156             a0 = a_[k - 1] + cof * a1 - a2;
00157           }
00158           b1 = 0.;
00159           b0 = b_[0];
00160           for (k = 2; k <= n; ++k) {
00161             b2 = b1;
00162             b1 = b0;
00163             b0 = b_[k - 1] + cof * b1 - b2;
00164           }
00165           f = (a0 - a2) * .5f + b0 * su;
00166           if (mode_ != 0) {f += y / t_;}
00167         } else {
00168           f = 0.f;
00169           if (mode_ != 0) {f = 1.f;}
00170         }
00171         return f;
00172 } // fcn
00173 
00174 
00175 
00176 // *************************************************************************************************************************************
00180 // ************************************************************************************************************************************* 
00181 
00182 
00183 void VVIObjF::limits(float& xl, float& xu) const {
00184         
00185    xl = t0_;
00186    xu = t1_;
00187         return;
00188 } // limits
00189 
00190 
00191 #include "sicif.h"
00192 namespace VVIObjFDetails {
00193   void sincosint(float x, float & sint, float & cint) {
00194     sicif(x,sint,cint);
00195   }
00196 
00197 
00198 float expint(float x) {
00199   
00200   // Initialized data
00201   
00202   const float zero = 0.;
00203   const float q2[7] = { .10340013040487,3.319092135933,
00204                          20.449478501379,41.280784189142,32.426421069514,10.041164382905,
00205                          1. };
00206   const float p3[6] = { -2.3909964453136,-147.98219500504,
00207                          -254.3763397689,-119.55761038372,-19.630408535939,-.9999999999036 
00208   };
00209   const float q3[6] = { 177.60070940351,530.68509610812,
00210                          462.23027156148,156.81843364539,21.630408494238,1. };
00211   const float p4[8] = { -8.6693733995107,-549.14226552109,
00212                          -4210.0161535707,-249301.39345865,-119623.66934925,
00213                          -22174462.775885,3892804.213112,-391546073.8091 };
00214   const float q4[8] = { 34.171875,-1607.0892658722,35730.029805851,
00215                          -483547.43616216,4285596.2461175,-24903337.574054,89192576.757561,
00216                          -165254299.72521 };
00217   const float a1[8] = { -2.1808638152072,-21.901023385488,
00218                          9.3081638566217,25.076281129356,-33.184253199722,60.121799083008,
00219                          -43.253113287813,1.0044310922808 };
00220   const float b1[8] = { 0.,3.9370770185272,300.89264837292,
00221                          -6.2504116167188,1003.6743951673,14.325673812194,2736.2411988933,
00222                          .52746885196291 };
00223   const float a2[8] = { -3.4833465360285,-18.65454548834,
00224                          -8.2856199414064,-32.34673303054,17.960168876925,1.7565631546961,
00225                          -1.9502232128966,.99999429607471 };
00226   const float b2[8] = { 0.,69.500065588743,57.283719383732,
00227                          25.777638423844,760.76114800773,28.951672792514,-3.4394226689987,
00228                          1.0008386740264 };
00229   const float a3[6] = { -27.780928934438,-10.10479081576,
00230                          -9.1483008216736,-5.0223317461851,-3.0000077799358,
00231                          1.0000000000704 };
00232   const float one = 1.;
00233   const float b3[6] = { 0.,122.39993926823,2.7276100778779,
00234                          -7.1897518395045,-2.9990118065262,1.999999942826 };
00235   const float two = 2.;
00236   const float three = 3.;
00237   const float x0 = .37250741078137;
00238   const float xl[6] = { -24.,-12.,-6.,0.,1.,4. };
00239   const float p1[5] = { 4.293125234321,39.894153870321,
00240                          292.52518866921,425.69682638592,-434.98143832952 };
00241   const float q1[5] = { 1.,18.899288395003,150.95038744251,
00242                          568.05252718987,753.58564359843 };
00243   const float p2[7] = { .43096783946939,6.9052252278444,
00244                          23.019255939133,24.378408879132,9.0416155694633,.99997957705159,
00245                          4.656271079751e-7 };
00246   
00247   // Local variables 
00248    float v, y, ap, bp, aq, dp, bq, dq;
00249   
00250   if (x <= xl[0]) {
00251     ap = a3[0] - x;
00252     for ( int i__ = 2; i__ <= 5; ++i__) {
00253       ap = a3[i__ - 1] - x + b3[i__ - 1] / ap;
00254     }
00255     y = vdt::fast_expf(-x) / x * (one - (a3[5] + b3[5] / ap) / x);
00256   } else if (x <= xl[1]) {
00257     ap = a2[0] - x;
00258     for ( int i__ = 2; i__ <= 7; ++i__) {
00259       ap = a2[i__ - 1] - x + b2[i__ - 1] / ap;
00260     }
00261     y = vdt::fast_expf(-x) / x * (a2[7] + b2[7] / ap);
00262   } else if (x <= xl[2]) {
00263     ap = a1[0] - x;
00264     for ( int i__ = 2; i__ <= 7; ++i__) {
00265       ap = a1[i__ - 1] - x + b1[i__ - 1] / ap;
00266     }
00267     y = vdt::fast_expf(-x) / x * (a1[7] + b1[7] / ap);
00268   } else if (x < xl[3]) {
00269     v = -two * (x / three + one);
00270     bp = zero;
00271     dp = p4[0];
00272     for ( int i__ = 2; i__ <= 8; ++i__) {
00273       ap = bp;
00274       bp = dp;
00275       dp = p4[i__ - 1] - ap + v * bp;
00276     }
00277     bq = zero;
00278     dq = q4[0];
00279     for ( int i__ = 2; i__ <= 8; ++i__) {
00280       aq = bq;
00281       bq = dq;
00282       dq = q4[i__ - 1] - aq + v * bq;
00283     }
00284     y = -vdt::fast_logf(-x / x0) + (x + x0) * (dp - ap) / (dq - aq);
00285   } else if (x == xl[3]) {
00286     return zero;
00287   } else if (x < xl[4]) {
00288     ap = p1[0];
00289     aq = q1[0];
00290     for ( int i__ = 2; i__ <= 5; ++i__) {
00291       ap = p1[i__ - 1] + x * ap;
00292       aq = q1[i__ - 1] + x * aq;
00293     }
00294     y = -vdt::fast_logf(x) + ap / aq;
00295   } else if (x <= xl[5]) {
00296     y = one / x;
00297     ap = p2[0];
00298     aq = q2[0];
00299     for ( int i__ = 2; i__ <= 7; ++i__) {
00300       ap = p2[i__ - 1] + y * ap;
00301       aq = q2[i__ - 1] + y * aq;
00302     }
00303     y = vdt::fast_expf(-x) * ap / aq;
00304   } else {
00305     y = one / x;
00306     ap = p3[0];
00307     aq = q3[0];
00308     for ( int i__ = 2; i__ <= 6; ++i__) {
00309       ap = p3[i__ - 1] + y * ap;
00310       aq = q3[i__ - 1] + y * aq;
00311     }
00312     y = vdt::fast_expf(-x) * y * (one + y * ap / aq);
00313   }
00314   return y;
00315 } // expint
00316   
00317 
00318 
00319 
00320   template<typename F>
00321   int dzero(float a, float b, float& x0, 
00322             float& rv, float eps, int mxf, F func) {
00323     /* System generated locals */
00324     float d__1, d__2, d__3, d__4;
00325     
00326     // Local variables
00327     float f1, f2, f3, u1, u2, x1, x2, u3, u4, x3, ca, cb, cc, fa, fb, ee, ff;
00328     int mc;
00329     float xa, xb, fx, xx, su4;
00330     
00331     xa = std::min(a,b);
00332     xb = std::max(a,b);
00333     fa = func(xa);
00334     fb = func(xb);
00335     if (fa * fb > 0.f) {
00336       rv = (xb - xa) * -2.f;
00337       x0 = 0.f;
00338       return 1;
00339     }
00340     mc = 0;
00341   L1:
00342     x0 = (xa + xb) * 0.5f;
00343     rv = x0 - xa;
00344     ee = eps * (std::abs(x0) + 1.f);
00345     if (rv <= ee) {
00346       rv = ee;
00347       ff = func(x0);
00348       return 0;
00349     }
00350     f1 = fa;
00351     x1 = xa;
00352     f2 = fb;
00353     x2 = xb;
00354   L2:
00355     fx = func(x0);
00356     ++mc;
00357     if (mc > mxf) {
00358       rv = (d__1 = xb - xa, fabs(d__1)) * -0.5f;
00359       x0 = 0.;
00360       return 0;
00361     }
00362     if (fx * fa > 0.f) {
00363       xa = x0;
00364       fa = fx;
00365     } else {
00366       xb = x0;
00367       fb = fx;
00368     }
00369   L3:
00370     u1 = f1 - f2;
00371     u2 = x1 - x2;
00372     u3 = f2 - fx;
00373     u4 = x2 - x0;
00374     if (u2 == 0.f || u4 == 0.f) {goto L1;}
00375     f3 = fx;
00376     x3 = x0;
00377     u1 /= u2;
00378     u2 = u3 / u4;
00379     ca = u1 - u2;
00380     cb = (x1 + x2) * u2 - (x2 + x0) * u1;
00381     cc = (x1 - x0) * f1 - x1 * (ca * x1 + cb);
00382     if (ca == 0.f) {
00383       if (cb == 0.f) {goto L1;}
00384       x0 = -cc / cb;
00385     } else {
00386       u3 = cb / (ca * 2.f);
00387       u4 = u3 * u3 - cc / ca;
00388       if (u4 < 0.f) {goto L1;}
00389       su4 = std::abs(u4);
00390       if (x0 + u3 < 0.f) {su4 = -su4;}
00391       x0 = -u3 + su4;
00392     }
00393     if (x0 < xa || x0 > xb) {goto L1;}
00394     // Computing MIN
00395     d__3 = (d__1 = x0 - x3, std::abs(d__1));
00396     d__4 = (d__2 = x0 - x2, std::abs(d__2));
00397     rv = std::min(d__3,d__4);
00398     ee = eps * (std::abs(x0) + 1);
00399     if (rv > ee) {
00400       f1 = f2;
00401       x1 = x2;
00402       f2 = f3;
00403       x2 = x3;
00404       goto L2;
00405     }
00406     fx = func(x0);
00407     if (fx == 0.f) {
00408       rv = ee;
00409       ff = func(x0);
00410       return 0;
00411     }
00412     if (fx * fa < 0.f) {
00413       xx = x0 - ee;
00414       if (xx <= xa) {
00415         rv = ee;
00416         ff = func(x0);
00417         return 0;
00418       }
00419       ff = func(xx);
00420       fb = ff;
00421       xb = xx;
00422     } else {
00423       xx = x0 + ee;
00424       if (xx >= xb) {
00425         rv = ee;
00426         ff = func(x0);
00427         return 0;
00428       }
00429       ff = func(xx);
00430       fa = ff;
00431       xa = xx;
00432     }
00433     if (fx * ff > 0.f) {
00434       mc += 2;
00435       if (mc > mxf) {
00436         rv = (d__1 = xb - xa, std::abs(d__1)) * -0.5f;
00437         x0 = 0.f;
00438         return 0;
00439       }
00440       f1 = f3;
00441       x1 = x3;
00442       f2 = fx;
00443       x2 = x0;
00444       x0 = xx;
00445       fx = ff;
00446       goto L3;
00447     }
00448     /* L4: */
00449     rv = ee;
00450     ff = func(x0);
00451     return 0;
00452   } // dzero
00453   
00454 }
/data/refman/pasoursint/CMSSW_6_1_2_SLHC4_patch1/src/RecoLocalTracker/SiPixelRecHits/src/VVIObjF.cc
