...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
Many of the special functions included in this library are also a part of the
either the C99
Standard ISO/IEC 9899:1999 or the Technical
Report on C++ Library Extensions. Therefore this library includes a
thin wrapper header boost/math/tr1.hpp
that
provides compatibility with these two standards.
There are various pros and cons to using the library in this way:
Pros:
Cons:
float
,
double
and long
double
.
Note | |
---|---|
The separate libraries are required only if you choose to use boost/math/tr1.hpp rather than some other Boost.Math header, the rest of Boost.Math remains header-only. |
The separate libraries required in order to use tr1.hpp can be compiled using bjam from within the libs/math/build directory, or from the Boost root directory using the usual Boost-wide install procedure. Alternatively the source files are located in libs/math/src and each have the same name as the function they implement. The various libraries are named as follows:
Name |
Type |
Functions |
---|---|---|
boost_math_c99f-<suffix> |
float |
C99 Functions |
boost_math_c99-<suffix> |
double |
C99 Functions |
boost_math_c99l-<suffix> |
long double |
C99 Functions |
boost_math_tr1f-<suffix> |
float |
TR1 Functions |
boost_math_tr1-<suffix> |
double |
TR1 Functions |
boost_math_tr1l-<suffix> |
long double |
TR1 Functions |
Where <suffix>
encodes the compiler and build options
used to build the libraries: for example "libboost_math_tr1-vc80-mt-gd.lib"
would be the statically linked TR1 library to use with Visual C++ 8.0, in multithreading
debug mode, with the DLL VC++ runtime, where as "boost_math_tr1-vc80-mt.lib"
would be import library for the TR1 DLL to be used with Visual C++ 8.0 with
the release multithreaded DLL VC++ runtime. Refer to the getting started guide
for a full
explanation of the <suffix>
meanings.
Note | |
---|---|
Visual C++ users will typically have the correct library variant to link against selected for them by boost/math/tr1.hpp based on your compiler settings. Users will need to define BOOST_MATH_TR1_DYN_LINK when building their code if they want to link against the DLL versions of these libraries rather than the static versions. Users can disable auto-linking by defining BOOST_MATH_TR1_NO_LIB when building: this is typically only used when linking against a customised build of the libraries. |
Note | |
---|---|
Linux and Unix users will generally only have one variant of these libraries installed, and can generally just link against -lboost_math_tr1 etc. |
This library now presents the user with a choice:
Which option you choose depends largely on how you prefer to work and how your system is set up.
For example a casual user who just needs the acosh function, would probably
be better off including <boost/math/special_functions/acosh.hpp>
and using boost::math::acosh(x)
in their code.
However, for large scale software development where compile times are significant,
and where the Boost libraries are already built and installed on the system,
then including <boost/math/tr1.hpp>
and using boost::math::tr1::acosh(x)
will speed up compile times, reduce object files sizes (since there are no
templates being instantiated any more), and also speed up debugging runtimes
- since the externally compiled libraries can be compiler optimised, rather
than built using full settings - the difference in performance between release and debug builds can be as much
as 20 times, so for complex applications this can be a big win.
See also the quick reference guide for these functions.
namespace boost{ namespace math{ namespace tr1{ extern "C"{ typedef unspecified float_t; typedef unspecified double_t; double acosh(double x); float acoshf(float x); long double acoshl(long double x); double asinh(double x); float asinhf(float x); long double asinhl(long double x); double atanh(double x); float atanhf(float x); long double atanhl(long double x); double cbrt(double x); float cbrtf(float x); long double cbrtl(long double x); double copysign(double x, double y); float copysignf(float x, float y); long double copysignl(long double x, long double y); double erf(double x); float erff(float x); long double erfl(long double x); double erfc(double x); float erfcf(float x); long double erfcl(long double x); double expm1(double x); float expm1f(float x); long double expm1l(long double x); double fmax(double x, double y); float fmaxf(float x, float y); long double fmaxl(long double x, long double y); double fmin(double x, double y); float fminf(float x, float y); long double fminl(long double x, long double y); double hypot(double x, double y); float hypotf(float x, float y); long double hypotl(long double x, long double y); double lgamma(double x); float lgammaf(float x); long double lgammal(long double x); long long llround(double x); long long llroundf(float x); long long llroundl(long double x); double log1p(double x); float log1pf(float x); long double log1pl(long double x); long lround(double x); long lroundf(float x); long lroundl(long double x); double nextafter(double x, double y); float nextafterf(float x, float y); long double nextafterl(long double x, long double y); double nexttoward(double x, long double y); float nexttowardf(float x, long double y); long double nexttowardl(long double x, long double y); double round(double x); float roundf(float x); long double roundl(long double x); double tgamma(double x); float tgammaf(float x); long double tgammal(long double x); double trunc(double x); float truncf(float x); long double truncl(long double x); }}}} // namespaces
See also the quick reference guide for these functions.
namespace boost{ namespace math{ namespace tr1{ extern "C"{ // [5.2.1.1] associated Laguerre polynomials: double assoc_laguerre(unsigned n, unsigned m, double x); float assoc_laguerref(unsigned n, unsigned m, float x); long double assoc_laguerrel(unsigned n, unsigned m, long double x); // [5.2.1.2] associated Legendre functions: double assoc_legendre(unsigned l, unsigned m, double x); float assoc_legendref(unsigned l, unsigned m, float x); long double assoc_legendrel(unsigned l, unsigned m, long double x); // [5.2.1.3] beta function: double beta(double x, double y); float betaf(float x, float y); long double betal(long double x, long double y); // [5.2.1.4] (complete) elliptic integral of the first kind: double comp_ellint_1(double k); float comp_ellint_1f(float k); long double comp_ellint_1l(long double k); // [5.2.1.5] (complete) elliptic integral of the second kind: double comp_ellint_2(double k); float comp_ellint_2f(float k); long double comp_ellint_2l(long double k); // [5.2.1.6] (complete) elliptic integral of the third kind: double comp_ellint_3(double k, double nu); float comp_ellint_3f(float k, float nu); long double comp_ellint_3l(long double k, long double nu); // [5.2.1.8] regular modified cylindrical Bessel functions: double cyl_bessel_i(double nu, double x); float cyl_bessel_if(float nu, float x); long double cyl_bessel_il(long double nu, long double x); // [5.2.1.9] cylindrical Bessel functions (of the first kind): double cyl_bessel_j(double nu, double x); float cyl_bessel_jf(float nu, float x); long double cyl_bessel_jl(long double nu, long double x); // [5.2.1.10] irregular modified cylindrical Bessel functions: double cyl_bessel_k(double nu, double x); float cyl_bessel_kf(float nu, float x); long double cyl_bessel_kl(long double nu, long double x); // [5.2.1.11] cylindrical Neumann functions; // cylindrical Bessel functions (of the second kind): double cyl_neumann(double nu, double x); float cyl_neumannf(float nu, float x); long double cyl_neumannl(long double nu, long double x); // [5.2.1.12] (incomplete) elliptic integral of the first kind: double ellint_1(double k, double phi); float ellint_1f(float k, float phi); long double ellint_1l(long double k, long double phi); // [5.2.1.13] (incomplete) elliptic integral of the second kind: double ellint_2(double k, double phi); float ellint_2f(float k, float phi); long double ellint_2l(long double k, long double phi); // [5.2.1.14] (incomplete) elliptic integral of the third kind: double ellint_3(double k, double nu, double phi); float ellint_3f(float k, float nu, float phi); long double ellint_3l(long double k, long double nu, long double phi); // [5.2.1.15] exponential integral: double expint(double x); float expintf(float x); long double expintl(long double x); // [5.2.1.16] Hermite polynomials: double hermite(unsigned n, double x); float hermitef(unsigned n, float x); long double hermitel(unsigned n, long double x); // [5.2.1.18] Laguerre polynomials: double laguerre(unsigned n, double x); float laguerref(unsigned n, float x); long double laguerrel(unsigned n, long double x); // [5.2.1.19] Legendre polynomials: double legendre(unsigned l, double x); float legendref(unsigned l, float x); long double legendrel(unsigned l, long double x); // [5.2.1.20] Riemann zeta function: double riemann_zeta(double); float riemann_zetaf(float); long double riemann_zetal(long double); // [5.2.1.21] spherical Bessel functions (of the first kind): double sph_bessel(unsigned n, double x); float sph_besself(unsigned n, float x); long double sph_bessell(unsigned n, long double x); // [5.2.1.22] spherical associated Legendre functions: double sph_legendre(unsigned l, unsigned m, double theta); float sph_legendref(unsigned l, unsigned m, float theta); long double sph_legendrel(unsigned l, unsigned m, long double theta); // [5.2.1.23] spherical Neumann functions; // spherical Bessel functions (of the second kind): double sph_neumann(unsigned n, double x); float sph_neumannf(unsigned n, float x); long double sph_neumannl(unsigned n, long double x); }}}} // namespaces
In addition sufficient additional overloads of the double
versions of the above functions are provided, so that calling the function
with any mixture of float
, double
, long
double
, or integer
arguments is supported, with the return type determined by the result
type calculation rules.
double exp2(double x); float exp2f(float x); long double exp2l(long double x); double fdim(double x, double y); float fdimf(float x, float y); long double fdiml(long double x, long double y); double fma(double x, double y, double z); float fmaf(float x, float y, float z); long double fmal(long double x, long double y, long double z); int ilogb(double x); int ilogbf(float x); int ilogbl(long double x); long long llrint(double x); long long llrintf(float x); long long llrintl(long double x); double log2(double x); float log2f(float x); long double log2l(long double x); double logb(double x); float logbf(float x); long double logbl(long double x); long lrint(double x); long lrintf(float x); long lrintl(long double x); double nan(const char *str); float nanf(const char *str); long double nanl(const char *str); double nearbyint(double x); float nearbyintf(float x); long double nearbyintl(long double x); double remainder(double x, double y); float remainderf(float x, float y); long double remainderl(long double x, long double y); double remquo(double x, double y, int *pquo); float remquof(float x, float y, int *pquo); long double remquol(long double x, long double y, int *pquo); double rint(double x); float rintf(float x); long double rintl(long double x); double scalbln(double x, long ex); float scalblnf(float x, long ex); long double scalblnl(long double x, long ex); double scalbn(double x, int ex); float scalbnf(float x, int ex); long double scalbnl(long double x, int ex);
// [5.2.1.7] confluent hypergeometric functions: double conf_hyperg(double a, double c, double x); float conf_hypergf(float a, float c, float x); long double conf_hypergl(long double a, long double c, long double x); // [5.2.1.17] hypergeometric functions: double hyperg(double a, double b, double c, double x); float hypergf(float a, float b, float c, float x); long double hypergl(long double a, long double b, long double c, long double x);