C++ Technical Report 1

Document that proposed additions to the C++ standard library

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C++ Technical Report 1 (TR1) is the common name for ISO/IEC TR 19768, C++ Library Extensions, which is a document that proposed additions to the C++ standard library for the C++03 language standard. The additions include regular expressions, smart pointers, hash tables, and random number generators. TR1 was not a standard itself, but rather a draft document. However, most of its proposals became part of the later official standard, C++11. Before C++11 was standardized, vendors used this document as a guide to create extensions. The report's goal was "to build more widespread existing practice for an expanded C++ standard library".

The report was first circulated in draft form in 2005 as Draft Technical Report on C++ Library Extensions, then published in 2007 as an ISO/IEC standard as ISO/IEC TR 19768:2007.

Function name	Function prototype	Mathematical expression
Associated Laguerre polynomials	`doubleassoc_laguerre(unsignedintn,unsignedintm,doublex);`	${L_{n}}^{m}(x)=(-1)^{m}{\frac {d^{m}}{dx^{m}}}L_{n+m}(x),{\text{ for }}x\geq 0$ {\displaystyle {L_{n}}^{m}(x)=(-1)^{m}{\frac {d^{m}}{dx^{m}}}L_{n+m}(x),{\text{ for }}x\geq 0}
Associated Legendre polynomials	`doubleassoc_legendre(unsignedintl,unsignedintm,doublex);`	${P_{l}}^{m}(x)=(1-x^{2})^{m/2}{\frac {d^{m}}{dx^{m}}}P_{l}(x),{\text{ for }}x\geq 0$ {\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	`doublebeta(doublex,doubley);`	$\mathrm {B} (x,y)={\frac {\Gamma (x)\Gamma (y)}{\Gamma (x+y)}}$ {\displaystyle \mathrm {B} (x,y)={\frac {\Gamma (x)\Gamma (y)}{\Gamma (x+y)}}}
Complete elliptic integral of the first kind	`doublecomp_ellint_1(doublek);`	$K(k)=F\left(k,\textstyle {\frac {\pi }{2}}\right)=\int _{0}^{\frac {\pi }{2}}{\frac {d\theta }{\sqrt {1-k^{2}\sin ^{2}\theta }}}$ {\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	`doublecomp_ellint_2(doublek);`	$E\left(k,\textstyle {\frac {\pi }{2}}\right)=\int _{0}^{\frac {\pi }{2}}{\sqrt {1-k^{2}\sin ^{2}\theta }}\;d\theta$ {\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	`doublecomp_ellint_3(doublek,doublenu);`	$\Pi \left(\nu ,k,\textstyle {\frac {\pi }{2}}\right)=\int _{0}^{\frac {\pi }{2}}{\frac {d\theta }{(1-\nu \sin ^{2}\theta ){\sqrt {1-k^{2}\sin ^{2}\theta }}}}$ {\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	`doubleconf_hyperg(doublea,doublec,doublex);`	$F(a,c,x)={\frac {\Gamma (c)}{\Gamma (a)}}\sum _{n=0}^{\infty }{\frac {\Gamma (a+n)x^{n}}{\Gamma (c+n)n!}}$ {\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	`doublecyl_bessel_i(doublenu,doublex);`	$I_{\nu }(x)=i^{-\nu }J_{\nu }(ix)=\sum _{k=0}^{\infty }{\frac {(x/2)^{\nu +2k}}{k!\;\Gamma (\nu +k+1)}},{\text{ for }}x\geq 0$ {\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	`doublecyl_bessel_j(doublenu,doublex);`	$J_{\nu }(x)=\sum _{k=0}^{\infty }{\frac {(-1)^{k}\;(x/2)^{\nu +2k}}{k!\;\Gamma (\nu +k+1)}},{\text{ for }}x\geq 0$ {\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	`doublecyl_bessel_k(doublenu,doublex);`	${\begin{aligned}K_{\nu }(x)&=\textstyle {\frac {\pi }{2}}i^{\nu +1}{\big (}J_{\nu }(ix)+iN_{\nu }(ix){\big )}\\&={\begin{cases}\displaystyle {\frac {I_{-\nu }(x)-I_{\nu }(x)}{\sin \nu \pi }},&{\text{for }}x\geq 0{\text{ and }}\nu \notin \mathbb {Z} \\[10pt]\displaystyle {\frac {\pi }{2}}\lim _{\mu \to \nu }{\frac {I_{-\mu }(x)-I_{\mu }(x)}{\sin \mu \pi }},&{\text{for }}x<0{\text{ and }}\nu \in \mathbb {Z} \\\end{cases}}\end{aligned}}$ {\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	`doublecyl_neumann(doublenu,doublex);`	$N_{\nu }(x)={\begin{cases}\displaystyle {\frac {J_{\nu }(x)\cos \nu \pi -J_{-\nu }(x)}{\sin \nu \pi }},&{\text{for }}x\geq 0{\text{ and }}\nu \notin \mathbb {Z} \\[10pt]\displaystyle \lim _{\mu \to \nu }{\frac {J_{\mu }(x)\cos \mu \pi -J_{-\mu }(x)}{\sin \mu \pi }},&{\text{for }}x<0{\text{ and }}\nu \in \mathbb {Z} \\\end{cases}}$ {\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	`doubleellint_1(doublek,doublephi);`	$F(k,\phi )=\int _{0}^{\phi }{\frac {d\theta }{\sqrt {1-k^{2}\sin ^{2}\theta }}},{\text{ for }}\left\|k\right\|\leq 1$ {\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	`doubleellint_2(doublek,doublephi);`	$\displaystyle E(k,\phi )=\int _{0}^{\phi }{\sqrt {1-k^{2}\sin ^{2}\theta }}d\theta ,{\text{ for }}\left\|k\right\|\leq 1$ {\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	`doubleellint_3(doublek,doublenu,doublephi);`	$\Pi (k,\nu ,\phi )=\int _{0}^{\phi }{\frac {d\theta }{\left(1-\nu \sin ^{2}\theta \right){\sqrt {1-k^{2}\sin ^{2}\theta }}}},{\text{ for }}\left\|k\right\|\leq 1$ {\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	`doubleexpint(doublex);`	${\mbox{E}}i(x)=-\int _{-x}^{\infty }{\frac {e^{-t}}{t}},円dt$ {\displaystyle {\mbox{E}}i(x)=-\int _{-x}^{\infty }{\frac {e^{-t}}{t}},円dt}
Hermite polynomials	`doublehermite(unsignedintn,doublex);`	$H_{n}(x)=(-1)^{n}e^{x^{2}}{\frac {d^{n}}{dx^{n}}}e^{-x^{2}},円\!$ {\displaystyle H_{n}(x)=(-1)^{n}e^{x^{2}}{\frac {d^{n}}{dx^{n}}}e^{-x^{2}},円\!}
Hypergeometric series	`doublehyperg(doublea,doubleb,doublec,doublex);`	$F(a,b,c,x)={\frac {\Gamma (c)}{\Gamma (a)\Gamma (b)}}\sum _{n=0}^{\infty }{\frac {\Gamma (a+n)\Gamma (b+n)}{\Gamma (c+n)}}{\frac {x^{n}}{n!}}$ {\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	`doublelaguerre(unsignedintn,doublex);`	$L_{n}(x)={\frac {e^{x}}{n!}}{\frac {d^{n}}{dx^{n}}}\left(x^{n}e^{-x}\right),{\text{ for }}x\geq 0$ {\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	`doublelegendre(unsignedintl,doublex);`	$P_{l}(x)={1 \over 2^{l}l!}{d^{l} \over dx^{l}}(x^{2}-1)^{l},{\text{ for }}\left\|x\right\|\leq 1$ {\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	`doubleriemann_zeta(doublex);`	$\mathrm {Z} (x)={\begin{cases}\displaystyle \sum _{k=1}^{\infty }k^{-x},&{\text{for }}x>1\\[10pt]\displaystyle 2^{x}\pi ^{x-1}\sin \left({\frac {x\pi }{2}}\right)\Gamma (1-x)\zeta (1-x),&{\text{for }}x<1\\\end{cases}}$ {\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	`doublesph_bessel(unsignedintn,doublex);`	$j_{n}(x)={\sqrt {\frac {\pi }{2x}}}J_{n+1/2}(x),{\text{ for }}x\geq 0$ {\displaystyle j_{n}(x)={\sqrt {\frac {\pi }{2x}}}J_{n+1/2}(x),{\text{ for }}x\geq 0}
Spherical associated Legendre functions	`doublesph_legendre(unsignedintl,unsignedintm,doubletheta);`	$Y_{l}^{m}(\theta ,0){\text{ where }}Y_{l}^{m}(\theta ,\phi )=(-1)^{m}\left[{\frac {(2l+1)}{4\pi }}{\frac {(l-m)!}{(l+m)!}}\right]^{1 \over 2}P_{l}^{m}(\cos \theta )e^{\mathrm {i} m\phi },{\text{ for }}\|m\|\leq l$ {\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	`doublesph_neumann(unsignedintn,doublex);`	$n_{n}(x)=\left({\frac {\pi }{2x}}\right)^{\frac {1}{2}}N_{n+{\frac {1}{2}}}(x),{\text{ for }}x\geq 0$ {\displaystyle n_{n}(x)=\left({\frac {\pi }{2x}}\right)^{\frac {1}{2}}N_{n+{\frac {1}{2}}}(x),{\text{ for }}x\geq 0}

Overview

Components

General utilities

Function objects

Metaprogramming and type traits

Numerical facilities

Random number generation

Mathematical special functions

Containers

Tuple types

Fixed size array

Hash tables

Regular expressions

C compatibility

Technical Report 2

See also

References

Sources

External links