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Math.h
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1// @(#)root/mathcore:$Id$
2// Author: L. Moneta Tue Nov 14 15:44:38 2006
3
4/**********************************************************************
5 * *
6 * Copyright (c) 2006 LCG ROOT Math Team, CERN/PH-SFT *
7 * *
8 * *
9 **********************************************************************/
10
11// mathematical constants like Pi
12
13#ifndef ROOT_Math_Math
14#define ROOT_Math_Math
15
16#ifdef _MSC_VER
17#define _USE_MATH_DEFINES
18#endif
19
20#include <cmath>
21
22#if defined(__sun) || defined(_MSC_VER)
23//Microsoft and solaris definition of cmath does not include math.h which has the definitions of numerical constants
24#include <math.h>
25#endif
26
27
28#ifdef HAVE_NO_EXPM1
29// needed to implement expm1
30#include <limits>
31#endif
32
33
34#ifndef M_PI
35
36#define M_PI 3.14159265358979323846264338328 // Pi
37#endif
38
39#ifndef M_PI_2
40#define M_PI_2 1.57079632679489661923132169164 // Pi/2
41#endif
42
43#ifndef M_PI_4
44#define M_PI_4 0.78539816339744830961566084582 // Pi/4
45#endif
46
47/**
48 \namespace ROOT
49 Namespace for new ROOT classes and functions
50 */
51
52namespace ROOT {
53
54/**
55\namespace Math
56Namespace for new Math classes and functions.
57See the \ref Math "Math Libraries" page for a detailed description.
58*/
59
60namespace Math {
61// Enable Vc/VecCore template instantiations to replace std math functions.
62//
63// Vc declares `std::sqrt(Vc-type)`. To use this for Vc-`SCALAR`s, the call
64// to `sqrt()` must only be resolved at the template instantiation time, when
65// the Vc headers are guaranteed to be included, and thus its `sqrt()`
66// overloads have been declared.
67// The trick is to keep sqrt() dependent (on its argument type) by making it
68// an unqualified name. The `std::` of `std::sqrt()` makes it a qualified
69// name, so the code here has to use `sqrt()`, not `std::sqrt()`. To still
70// find `std::sqrt()` we pull `std::sqrt()` into the surrounding namespace.
71//
72// We don't want to use 'using namespace std' because it would polute the including headers.
73using std::atan2;
74using std::cos;
75using std::cosh;
76using std::exp;
77using std::floor;
78using std::log;
79using std::pow;
80using std::sin;
81using std::sinh;
82using std::sqrt;
83using std::tan;
84
85/**
86 Mathematical constants
87*/
88inline double Pi()
89{
90 return M_PI;
91 }
92
93 /**
94 declarations for functions which are not implemented by some compilers
95 */
96
97 /// log(1+x) with error cancelatio when x is small
98 inline double log1p(double x)
99 {
100#ifndef HAVE_NO_LOG1P
102#else
103 // if log1p is not in c math library
104 volatile double y;
105 y = 1 + x;
106 return std::log(y) - ((y-1)-x)/y ; /* cancels errors with IEEE arithmetic */
107#endif
108}
109/// exp(x) -1 with error cancellation when x is small
110inline double expm1( double x) {
111#ifndef HAVE_NO_EXPM1
113#else
114 // compute using taylor expansion until difference is less than epsilon
115 // use for values smaller than 0.5 (for larger (exp(x)-1 is fine
116 if (std::abs(x) < 0.5)
117 {
118 // taylor series S = x + (1/2!) x^2 + (1/3!) x^3 + ...
119
120 double i = 1.0;
121 double sum = x;
122 double term = x / 1.0;
123 do {
124 i++ ;
125 term *= x/i;
126 sum += term;
127 }
128 while (std::abs(term) > std::abs(sum) * std::numeric_limits<double>::epsilon() ) ;
129
130 return sum ;
131 }
132 else
133 {
134 return std::exp(x) - 1;
135 }
136#endif
137}
138
139 } // end namespace Math
140
141} // end namespace ROOT
142
143
144
145
146
147#endif /* ROOT_Math_Math */
#define M_PI
Definition: Math.h:36
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
Namespace for new Math classes and functions.
double log1p(double x)
declarations for functions which are not implemented by some compilers
Definition: Math.h:98
double Pi()
Mathematical constants.
Definition: Math.h:88
double expm1(double x)
exp(x) -1 with error cancellation when x is small
Definition: Math.h:110
VecExpr< UnaryOp< Sqrt< T >, VecExpr< A, T, D >, T >, T, D > sqrt(const VecExpr< A, T, D > &rhs)
tbb::task_arena is an alias of tbb::interface7::task_arena, which doesn't allow to forward declare tb...
REAL epsilon
Definition: triangle.c:618