1 // $Id: RandGaussQ.cc,v 1.6 2010/06/16 17:24:53 garren Exp $
2 // -*- C++ -*-
3 //
4 // -----------------------------------------------------------------------
5 // HEP Random
6 // --- RandGaussQ ---
7 // class implementation file
8 // -----------------------------------------------------------------------
9
10 // =======================================================================
11 // M Fischler - Created 24 Jan 2000
12 // M Fischler - put and get to/from streams 12/13/04
13 // =======================================================================
14
15 #include "CLHEP/Random/defs.h"
16 #include "CLHEP/Random/RandGaussQ.h"
17 #include "CLHEP/Units/PhysicalConstants.h"
18 #include <iostream>
19 #include <cmath> // for std::log()
20
21 namespace CLHEP {
22
name() const23 std::string RandGaussQ::name() const {return "RandGaussQ";}
engine()24 HepRandomEngine & RandGaussQ::engine() {return RandGauss::engine();}
25
~RandGaussQ()26 RandGaussQ::~RandGaussQ() {
27 }
28
operator ()()29 double RandGaussQ::operator()() {
30 return transformQuick(localEngine->flat()) * defaultStdDev + defaultMean;
31 }
32
operator ()(double mean,double stdDev)33 double RandGaussQ::operator()( double mean, double stdDev ) {
34 return transformQuick(localEngine->flat()) * stdDev + mean;
35 }
36
shootArray(const int size,double * vect,double mean,double stdDev)37 void RandGaussQ::shootArray( const int size, double* vect,
38 double mean, double stdDev )
39 {
40 for( double* v = vect; v != vect + size; ++v )
41 *v = shoot(mean,stdDev);
42 }
43
shootArray(HepRandomEngine * anEngine,const int size,double * vect,double mean,double stdDev)44 void RandGaussQ::shootArray( HepRandomEngine* anEngine,
45 const int size, double* vect,
46 double mean, double stdDev )
47 {
48 for( double* v = vect; v != vect + size; ++v )
49 *v = shoot(anEngine,mean,stdDev);
50 }
51
fireArray(const int size,double * vect)52 void RandGaussQ::fireArray( const int size, double* vect)
53 {
54 for( double* v = vect; v != vect + size; ++v )
55 *v = fire( defaultMean, defaultStdDev );
56 }
57
fireArray(const int size,double * vect,double mean,double stdDev)58 void RandGaussQ::fireArray( const int size, double* vect,
59 double mean, double stdDev )
60 {
61 for( double* v = vect; v != vect + size; ++v )
62 *v = fire( mean, stdDev );
63 }
64
65
66 //
67 // Table of errInts, for use with transform(r) and quickTransform(r)
68 //
69
70 // Since all these are this is static to this compilation unit only, the
71 // info is establised a priori and not at each invocation.
72
73 // The main data is of course the gaussQTables table; the rest is all
74 // bookkeeping to know what the tables mean.
75
76 #define Table0size 250
77 #define Table1size 1000
78 #define TableSize (Table0size+Table1size)
79
80 #define Table0step (2.0E-6)
81 #define Table1step (5.0E-4)
82
83 #define Table0scale (1.0/Table1step)
84
85 #define Table0offset 0
86 #define Table1offset (Table0size)
87
88 // Here comes the big (5K bytes) table, kept in a file ---
89
90 static const float gaussTables [TableSize] = {
91 #include "gaussQTables.cdat"
92 };
93
94
transformQuick(double r)95 double RandGaussQ::transformQuick (double r) {
96 double sign = +1.0; // We always compute a negative number of
97 // sigmas. For r > 0 we will multiply by
98 // sign = -1 to return a positive number.
99 if ( r > .5 ) {
100 r = 1-r;
101 sign = -1.0;
102 }
103
104 int index;
105 double dx;
106
107 if ( r >= Table1step ) {
108 index = int((Table1size<<1) * r); // 1 to Table1size
109 if (index == Table1size) return 0.0;
110 dx = (Table1size<<1) * r - index; // fraction of way to next bin
111 index += Table1offset-1;
112 } else if ( r > Table0step ) {
113 double rr = r * Table0scale;
114 index = int(Table0size * rr); // 1 to Table0size
115 dx = Table0size * rr - index; // fraction of way to next bin
116 index += Table0offset-1;
117 } else { // r <= Table0step - not in tables
118 return sign*transformSmall(r);
119 }
120
121 double y0 = gaussTables [index++];
122 double y1 = gaussTables [index];
123
124 return (float) (sign * ( y1 * dx + y0 * (1.0-dx) ));
125
126 } // transformQuick()
127
128
129
transformSmall(double r)130 double RandGaussQ::transformSmall (double r) {
131
132 // Solve for -v in the asymtotic formula
133 //
134 // errInt (-v) = std::exp(-v*v/2) 1 1*3 1*3*5
135 // ------------ * (1 - ---- + ---- - ----- + ... )
136 // v*std::sqrt(2*pi) v**2 v**4 v**6
137
138 // The value of r (=errInt(-v)) supplied is going to less than 2.0E-13,
139 // which is such that v < -7.25. Since the value of r is meaningful only
140 // to an absolute error of 1E-16 (double precision accuracy for a number
141 // which on the high side could be of the form 1-epsilon), computing
142 // v to more than 3-4 digits of accuracy is suspect; however, to ensure
143 // smoothness with the table generator (which uses quite a few terms) we
144 // also use terms up to 1*3*5* ... *13/v**14, and insist on accuracy of
145 // solution at the level of 1.0e-7.
146
147 // This routine is called less than one time in a million firings, so
148 // speed is of no concern. As a matter of technique, we terminate the
149 // iterations in case they would be infinite, but this should not happen.
150
151 double eps = 1.0e-7;
152 double guess = 7.5;
153 double v;
154
155 for ( int i = 1; i < 50; i++ ) {
156 double vn2 = 1.0/(guess*guess);
157 double s1 = -13*11*9*7*5*3 * vn2*vn2*vn2*vn2*vn2*vn2*vn2;
158 s1 += 11*9*7*5*3 * vn2*vn2*vn2*vn2*vn2*vn2;
159 s1 += -9*7*5*3 * vn2*vn2*vn2*vn2*vn2;
160 s1 += 7*5*3 * vn2*vn2*vn2*vn2;
161 s1 += -5*3 * vn2*vn2*vn2;
162 s1 += 3 * vn2*vn2 - vn2 + 1.0;
163 v = std::sqrt ( 2.0 * std::log ( s1 / (r*guess*std::sqrt(CLHEP::twopi)) ) );
164 if ( std::fabs(v-guess) < eps ) break;
165 guess = v;
166 }
167 return -v;
168
169 } // transformSmall()
170
put(std::ostream & os) const171 std::ostream & RandGaussQ::put ( std::ostream & os ) const {
172 int pr=os.precision(20);
173 os << " " << name() << "\n";
174 RandGauss::put(os);
175 os.precision(pr);
176 return os;
177 }
178
get(std::istream & is)179 std::istream & RandGaussQ::get ( std::istream & is ) {
180 std::string inName;
181 is >> inName;
182 if (inName != name()) {
183 is.clear(std::ios::badbit | is.rdstate());
184 std::cerr << "Mismatch when expecting to read state of a "
185 << name() << " distribution\n"
186 << "Name found was " << inName
187 << "\nistream is left in the badbit state\n";
188 return is;
189 }
190 RandGauss::get(is);
191 return is;
192 }
193
194 } // namespace CLHEP
195