C++ Technical Report 1

General utilities

Reference wrapper – enables passing references, rather than copies, into algorithms or function objects. The feature was based on Boost.Ref. A wrapper reference is obtained from an instance of the template class reference_wrapper. Wrapper references are similar to normal references (‘&’) of the C++ language. To obtain a wrapper reference from any object the template class ref is used (for a constant reference cref is used).

Wrapper references are useful above all for template functions, when argument deduction would not deduce a reference (e.g. when forwarding arguments):

#include <iostream>
#include <tr1/functional>

void f(int& r) { 
    ++r; 
}

template <class Func, class Arg>
void g(Func f, Arg t) {
    f(t);
}

int main() {
    int i = 0;

    g(f, i); // 'g<void(int& r), int>' is instantiated
    std::cout << i << "\n"; // Output: 0

    g(f, std::tr1::ref(i)); // 'g<void(int& r), std::tr1::reference_wrapper<int>>' is instanced
    std::cout << i << "\n"; // Output: 1
}

Smart pointers – adds several classes that simplify object lifetime management in complex cases. Three main classes are added:

• shared_ptr – a reference-counted smart pointer
• weak_ptr – a variant of shared_ptr that doesn't increase the reference count

The proposal is based on Boost Smart Pointer library.

Function objects

These four modules are added to the <functional> header file:

Polymorphic function wrapper (function) – can store any callable function (function pointers, member function pointers, and function objects) that uses a specified function call signature. The type does not depend on the kind of the callable used. Based on Boost.Function

Function object binders (bind) – can bind any parameters to function objects. Function composition is also allowed. This is a generalized version of the standard std::bind1st and std::bind2nd bind functions. The feature is based on Boost Bind library.

Function return types (result_of) – determines the type of a call expression.

Member functions (mem_fn) – enhancement to the standard std::mem_fun and std::mem_fun_ref. Allows pointers to member functions to be treated as function objects. Based on Boost Mem Fn library.

Metaprogramming and type traits

There is now <type_traits> header file that contains many useful trait meta-templates, such as is_pod, has_virtual_destructor, remove_extent, etc. It facilitates metaprogramming by enabling queries on and transformation between different types. The proposal is based on Boost Type Traits library.

Numerical facilities

Mathematical special functions

Some features of TR1, such as the mathematical special functions and certain C99 additions, are not included in the Visual C++ implementation of TR1. The Mathematical special functions library was not standardized in C++11.

• additions to the <cmath>/<math.h> header files – beta, legendre, etc.

These functions will likely be of principal interest to programmers in the engineering and scientific disciplines.

The following table shows all 23 special functions described in TR1.

Function name	Function prototype	Mathematical expression
Associated Laguerre polynomials	double assoc_laguerre(unsigned int n, unsigned int m, double x);	${\displaystyle {L_{n}}^{m}(x)=(-1)^{m}{\frac {d^{m}}{dx^{m}}}L_{n+m}(x),{\text{ for }}x\geq 0}$
Associated Legendre polynomials	double assoc_legendre(unsigned int l, unsigned int m, double x);	${\displaystyle {P_{l}}^{m}(x)=(1-x^{2})^{m/2}{\frac {d^{m}}{dx^{m}}}P_{l}(x),{\text{ for }}x\geq 0}$
Beta function	double beta(double x, double y);	${\displaystyle \mathrm {B} (x,y)={\frac {\Gamma (x)\Gamma (y)}{\Gamma (x+y)}}}$
Complete elliptic integral of the first kind	double comp_ellint_1(double k);	${\displaystyle K(k)=F\left(k,\textstyle {\frac {\pi }{2}}\right)=\int _{0}^{\frac {\pi }{2}}{\frac {d\theta }{\sqrt {1-k^{2}\sin ^{2}\theta }}}}$
Complete elliptic integral of the second kind	double comp_ellint_2(double k);	${\displaystyle E\left(k,\textstyle {\frac {\pi }{2}}\right)=\int _{0}^{\frac {\pi }{2}}{\sqrt {1-k^{2}\sin ^{2}\theta }}\;d\theta }$
Complete elliptic integral of the third kind	double comp_ellint_3(double k, double nu);	${\displaystyle \Pi \left(\nu ,k,\textstyle {\frac {\pi }{2}}\right)=\int _{0}^{\frac {\pi }{2}}{\frac {d\theta }{(1-\nu \sin ^{2}\theta ){\sqrt {1-k^{2}\sin ^{2}\theta }}}}}$
Confluent hypergeometric functions	double conf_hyperg(double a, double c, double x);	${\displaystyle F(a,c,x)={\frac {\Gamma (c)}{\Gamma (a)}}\sum _{n=0}^{\infty }{\frac {\Gamma (a+n)x^{n}}{\Gamma (c+n)n!}}}$
Regular modified cylindrical Bessel functions	double cyl_bessel_i(double nu, double x);	${\displaystyle I_{\nu }(x)=i^{-\nu }J_{\nu }(ix)=\sum _{k=0}^{\infty }{\frac {(x/2)^{\nu +2k}}{k!\;\Gamma (\nu +k+1)}},{\text{ for }}x\geq 0}$
Cylindrical Bessel functions of the first kind	double cyl_bessel_j(double nu, double x);	${\displaystyle J_{\nu }(x)=\sum _{k=0}^{\infty }{\frac {(-1)^{k}\;(x/2)^{\nu +2k}}{k!\;\Gamma (\nu +k+1)}},{\text{ for }}x\geq 0}$
Irregular modified cylindrical Bessel functions	double cyl_bessel_k(double nu, double x);	${\displaystyle {\begin{aligned}K_{\nu }(x)&=\textstyle {\frac {\pi }{2}}i^{\nu +1}{\big (}J_{\nu }(ix)+iN_{\nu }(ix){\big )}\\&={\begin{cases}\displaystyle {\frac {I_{-\nu }(x)-I_{\nu }(x)}{\sin \nu \pi }},&{\text{for }}x\geq 0{\text{ and }}\nu \notin \mathbb {Z} \\[10pt]\displaystyle {\frac {\pi }{2}}\lim _{\mu \to \nu }{\frac {I_{-\mu }(x)-I_{\mu }(x)}{\sin \mu \pi }},&{\text{for }}x<0{\text{ and }}\nu \in \mathbb {Z} \\\end{cases}}\end{aligned}}}$
Cylindrical Neumann functions Cylindrical Bessel functions of the second kind	double cyl_neumann(double nu, double x);	${\displaystyle N_{\nu }(x)={\begin{cases}\displaystyle {\frac {J_{\nu }(x)\cos \nu \pi -J_{-\nu }(x)}{\sin \nu \pi }},&{\text{for }}x\geq 0{\text{ and }}\nu \notin \mathbb {Z} \\[10pt]\displaystyle \lim _{\mu \to \nu }{\frac {J_{\mu }(x)\cos \mu \pi -J_{-\mu }(x)}{\sin \mu \pi }},&{\text{for }}x<0{\text{ and }}\nu \in \mathbb {Z} \\\end{cases}}}$
Incomplete elliptic integral of the first kind	double ellint_1(double k, double phi);	${\displaystyle F(k,\phi )=\int _{0}^{\phi }{\frac {d\theta }{\sqrt {1-k^{2}\sin ^{2}\theta }}},{\text{ for }}\left|k\right|\leq 1}$
Incomplete elliptic integral of the second kind	double ellint_2(double k, double phi);	${\displaystyle \displaystyle E(k,\phi )=\int _{0}^{\phi }{\sqrt {1-k^{2}\sin ^{2}\theta }}d\theta ,{\text{ for }}\left|k\right|\leq 1}$
Incomplete elliptic integral of the third kind	double ellint_3(double k, double nu, double phi);	${\displaystyle \Pi (k,\nu ,\phi )=\int _{0}^{\phi }{\frac {d\theta }{\left(1-\nu \sin ^{2}\theta \right){\sqrt {1-k^{2}\sin ^{2}\theta }}}},{\text{ for }}\left|k\right|\leq 1}$
Exponential integral	double expint(double x);	${\displaystyle {\mbox{E}}i(x)=-\int _{-x}^{\infty }{\frac {e^{-t}}{t}}\,dt}$
Hermite polynomials	double hermite(unsigned int n, double x);	${\displaystyle H_{n}(x)=(-1)^{n}e^{x^{2}}{\frac {d^{n}}{dx^{n}}}e^{-x^{2}}\,\!}$
Hypergeometric series	double hyperg(double a, double b, double c, double x);	${\displaystyle F(a,b,c,x)={\frac {\Gamma (c)}{\Gamma (a)\Gamma (b)}}\sum _{n=0}^{\infty }{\frac {\Gamma (a+n)\Gamma (b+n)}{\Gamma (c+n)}}{\frac {x^{n}}{n!}}}$
Laguerre polynomials	double laguerre(unsigned int n, double x);	${\displaystyle L_{n}(x)={\frac {e^{x}}{n!}}{\frac {d^{n}}{dx^{n}}}\left(x^{n}e^{-x}\right),{\text{ for }}x\geq 0}$
Legendre polynomials	double legendre(unsigned int l, double x);	${\displaystyle P_{l}(x)={1 \over 2^{l}l!}{d^{l} \over dx^{l}}(x^{2}-1)^{l},{\text{ for }}\left|x\right|\leq 1}$
Riemann zeta function	double riemann_zeta(double x);	${\displaystyle \mathrm {Z} (x)={\begin{cases}\displaystyle \sum _{k=1}^{\infty }k^{-x},&{\text{for }}x>1\\[10pt]\displaystyle 2^{x}\pi ^{x-1}\sin \left({\frac {x\pi }{2}}\right)\Gamma (1-x)\zeta (1-x),&{\text{for }}x<1\\\end{cases}}}$
Spherical Bessel functions of the first kind	double sph_bessel(unsigned int n, double x);	${\displaystyle j_{n}(x)={\sqrt {\frac {\pi }{2x}}}J_{n+1/2}(x),{\text{ for }}x\geq 0}$
Spherical associated Legendre functions	double sph_legendre(unsigned int l, unsigned int m, double theta);	${\displaystyle Y_{l}^{m}(\theta ,0){\text{ where }}Y_{l}^{m}(\theta ,\phi )=(-1)^{m}\left[{\frac {(2l+1)}{4\pi }}{\frac {(l-m)!}{(l+m)!}}\right]^{1 \over 2}P_{l}^{m}(\cos \theta )e^{\mathrm {i} m\phi },{\text{ for }}|m|\leq l}$
Spherical Neumann functions Spherical Bessel functions of the second kind	double sph_neumann(unsigned int n, double x);	${\displaystyle n_{n}(x)=\left({\frac {\pi }{2x}}\right)^{\frac {1}{2}}N_{n+{\frac {1}{2}}}(x),{\text{ for }}x\geq 0}$

Each function has two additional variants. Appending the suffix ‘f’ or ‘l’ to a function name gives a function that operates on float or long double values respectively. For example:

float sph_neumannf(unsigned int n, float x);
long double sph_neumannl(unsigned int n, long double x);

Containers

Regular expressions

• new <regex> header file – regex, regex_match, regex_search, regex_replace, etc.
• based on Boost RegEx library
• pattern matching library

C compatibility

C++ is designed to be compatible with the C programming language, but is not a strict superset of C due to diverging standards. TR1 attempts to reconcile some of these differences through additions to various headers in the C++ library, such as <complex>, <locale>, <cmath>, etc. These changes help to bring C++ more in line with the C99 version of the C standard (not all parts of C99 are included in TR1).

Sources

• ISO/IEC JTC1/SC22/WG21 — Draft Technical Report on C++ Library Extensions (PDF) (Report). 2005-06-24.
• ISO/IEC TR 19768:2007 — Information technology — Programming languages — Technical Report on C++ Library Extensions (Report). Nov 2007.
• Becker, Peter (2006). The C++ Standard Library Extensions: A Tutorial and Reference. Addison-Wesley Professional. ISBN 0-321-41299-0.