math.qbk

Boost provides free peer-reviewed portable C++ source libraries. We emphasize libraries that work

[article Math Toolkit
    [quickbook 1.4]
    [copyright 2006, 2007, 2008 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang and Bruno Lalande]
    [purpose ISBN 0-9504833-2-X  978-0-9504833-2-0, Classification 519.2-dc22]
    [license
        Distributed under the Boost Software License, Version 1.0.
        (See accompanying file LICENSE_1_0.txt or copy at
        [@http://www.boost.org/LICENSE_1_0.txt])
    ]
    [authors [Maddock, John], [Bristow, Paul A.], [Holin, Hubert], [Zhang, Xiaogang], [Lalande, Bruno]]
    [category math]
    [purpose mathematics]
    [/last-revision $Date: 2008-07-18 11:43:55 -0400 (Fri, 18 Jul 2008) $]
]

[template equation[name]  '''<inlinemediaobject>
<imageobject role="html">
<imagedata fileref="../equations/'''[name]'''.png"></imagedata>
</imageobject>
<imageobject role="print">
<imagedata fileref="../equations/'''[name]'''.svg"></imagedata>
</imageobject>
</inlinemediaobject>''']

[template graph[name]  '''<inlinemediaobject>
<imageobject role="html">
<imagedata align="center" fileref="../graphs/'''[name]'''.png"></imagedata>
</imageobject>
<imageobject role="print">
<imagedata align="center" fileref="../graphs/'''[name]'''.svg"></imagedata>
</imageobject>
</inlinemediaobject>''']

[include html4_symbols.qbk] [/ just for testing]
[/include latin1_symbols.qbk] [/ just for testing]
[include common_overviews.qbk] [/ overviews that appear in more than one place!]
[include tr1.qbk] [/tr1 docs also appear in more than one place!]
[include roadmap.qbk] [/ for history]

[def __effects [*Effects: ]]
[def __formula [*Formula: ]]
[def __exm1 '''<code>e<superscript>x</superscript> - 1</code>''']
[def __ex '''<code>e<superscript>x</superscript></code>''']
[def __te '''2&#x025B;''']  [/small Latin letter open e]

[def __ceilR '''&#x2309;''']
[def __ceilL '''&#2308;''']
[def __floorR '''&#x230B;''']
[def __floorL '''&#x230A;''']
[def __infin '''&#8734;''']
[def __integral '''&#8747;''']
[def __aacute '''&#225;''']
[def __eacute '''&#233;''']
[def __quarter '''&#x00BC;''']
[def __nearequal '''&#x224A;''']
[def __quarter '''&#x00BC;''']
[def __space '''&#8203;''']

[def __NTL_RR [@http://shoup.net/ntl/doc/RR.txt NTL::RR]]
[def __NTL_quad_float [@http://shoup.net/ntl/doc/quad_float.txt NTL::quad_float]]

[def __godfrey [link godfrey Godfrey]]
[def __pugh [link pugh Pugh]]

[def __caution This is now an official Boost library, but remains a library under 
               construction, the code is fully functional and robust, but 
               interfaces, library structure, and function and distribution names
               may still be changed without notice.]
               
[template tr1[] [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf Technical Report on C++ Library Extensions]]
[template jm_rationals[] [link math_toolkit.backgrounders.implementation.rational_approximations_used devised by JM]]
[def __domain_error [link domain_error domain_error]]
[def __pole_error [link pole_error pole_error]]
[def __overflow_error [link overflow_error overflow_error]]
[def __underflow_error [link underflow_error underflow_error]]
[def __denorm_error [link denorm_error denorm_error]]
[def __evaluation_error [link evaluation_error evaluation_error]]
[def __rounding_error [link rounding_error rounding_error]]
[def __indeterminate_result_error [link indeterminate_result_error indeterminate_result_error]]
[def __checked_narrowing_cast [link checked_narrowing_cast checked_narrowing_cast]]

[def __arg_pomotion_rules [link math_toolkit.main_overview.result_type ['result type calculation rules]]]
[def __sf_result [link math_toolkit.main_overview.result_type ['calculated-result-type]]]

[/ The following macros expand to links to the various special functions
and use the function's name as the link text]

[/Misc]
[def __lanczos [link math_toolkit.backgrounders.lanczos Lanczos approximation]]
[def __zero_error [link zero_error effectively zero error]]
[def __relative_error [link math_toolkit.backgrounders.relative_error relative zero error]]

[/gammas]
[def __lgamma [link math_toolkit.special.sf_gamma.lgamma lgamma]]
[def __digamma [link math_toolkit.special.sf_gamma.digamma digamma]]
[def __tgamma_ratio [link math_toolkit.special.sf_gamma.gamma_ratios tgamma_ratio]]
[def __tgamma_delta_ratio [link math_toolkit.special.sf_gamma.gamma_ratios tgamma_delta_ratio]]
[def __tgamma [link math_toolkit.special.sf_gamma.tgamma tgamma]]
[def __tgamma1pm1 [link math_toolkit.special.sf_gamma.tgamma tgamma1pm1]]
[def __tgamma_lower [link math_toolkit.special.sf_gamma.igamma tgamma_lower]]
[def __gamma_p [link math_toolkit.special.sf_gamma.igamma gamma_p]]
[def __gamma_q [link math_toolkit.special.sf_gamma.igamma gamma_q]]
[def __gamma_q_inv [link math_toolkit.special.sf_gamma.igamma_inv gamma_q_inv]]
[def __gamma_p_inv [link math_toolkit.special.sf_gamma.igamma_inv gamma_p_inv]]
[def __gamma_q_inva [link math_toolkit.special.sf_gamma.igamma_inv gamma_q_inva]]
[def __gamma_p_inva [link math_toolkit.special.sf_gamma.igamma_inv gamma_p_inva]]
[def __gamma_p_derivative [link math_toolkit.special.sf_gamma.gamma_derivatives gamma_p_derivative]]

[/factorials]
[def __factorial [link math_toolkit.special.factorials.sf_factorial factorial]]
[def __unchecked_factorial [link math_toolkit.special.factorials.sf_factorial unchecked_factorial]]
[def __max_factorial [link math_toolkit.special.factorials.sf_factorial max_factorial]]
[def __double_factorial [link math_toolkit.special.factorials.sf_double_factorial double_factorial]]
[def __rising_factorial [link math_toolkit.special.factorials.sf_rising_factorial rising_factorial]]
[def __falling_factorial [link math_toolkit.special.factorials.sf_falling_factorial falling_factorial]]

[/error functions]
[def __erf [link math_toolkit.special.sf_erf.error_function erf]]
[def __erfc [link math_toolkit.special.sf_erf.error_function erfc]]
[def __erf_inv [link math_toolkit.special.sf_erf.error_inv erf_inv]]
[def __erfc_inv [link math_toolkit.special.sf_erf.error_inv erfc_inv]]

[/beta functions]
[def __beta  [link math_toolkit.special.sf_beta.beta_function beta]]
[def __beta3 [link math_toolkit.special.sf_beta.ibeta_function beta]]
[def __betac [link math_toolkit.special.sf_beta.ibeta_function betac]]
[def __ibeta [link math_toolkit.special.sf_beta.ibeta_function ibeta]]
[def __ibetac [link math_toolkit.special.sf_beta.ibeta_function ibetac]]
[def __ibeta_inv [link math_toolkit.special.sf_beta.ibeta_inv_function ibeta_inv]]
[def __ibetac_inv [link math_toolkit.special.sf_beta.ibeta_inv_function ibetac_inv]]
[def __ibeta_inva [link math_toolkit.special.sf_beta.ibeta_inv_function ibeta_inva]]
[def __ibetac_inva [link math_toolkit.special.sf_beta.ibeta_inv_function ibetac_inva]]
[def __ibeta_invb [link math_toolkit.special.sf_beta.ibeta_inv_function ibeta_invb]]
[def __ibetac_invb [link math_toolkit.special.sf_beta.ibeta_inv_function ibetac_invb]]
[def __ibeta_derivative [link math_toolkit.special.sf_beta.beta_derivative ibeta_derivative]]

[/elliptic integrals]
[def __ellint_rj  [link math_toolkit.special.ellint.ellint_carlson ellint_rj]]
[def __ellint_rf  [link math_toolkit.special.ellint.ellint_carlson ellint_rf]]
[def __ellint_rc  [link math_toolkit.special.ellint.ellint_carlson ellint_rc]]
[def __ellint_rd  [link math_toolkit.special.ellint.ellint_carlson ellint_rd]]
[def __ellint_1  [link math_toolkit.special.ellint.ellint_1 ellint_1]]
[def __ellint_2  [link math_toolkit.special.ellint.ellint_2 ellint_2]]
[def __ellint_3  [link math_toolkit.special.ellint.ellint_3 ellint_3]]

[/Bessel functions]
[def __cyl_bessel_j  [link math_toolkit.special.bessel.bessel cyl_bessel_j]]
[def __cyl_neumann  [link math_toolkit.special.bessel.bessel cyl_neumann]]
[def __cyl_bessel_i  [link math_toolkit.special.bessel.mbessel cyl_bessel_i]]
[def __cyl_bessel_k  [link math_toolkit.special.bessel.mbessel cyl_bessel_k]]
[def __sph_bessel  [link math_toolkit.special.bessel.sph_bessel sph_bessel]]
[def __sph_neumann  [link math_toolkit.special.bessel.sph_bessel sph_neumann]]

[/sinus cardinals]
[def __sinc_pi  [link math_toolkit.special.sinc.sinc_pi sinc_pi]]
[def __sinhc_pi  [link math_toolkit.special.sinc.sinhc_pi sinhc_pi]]

[/Inverse hyperbolics]
[def __acosh  [link math_toolkit.special.inv_hyper.acosh acosh]]
[def __asinh  [link math_toolkit.special.inv_hyper.asinh asinh]]
[def __atanh  [link math_toolkit.special.inv_hyper.atanh atanh]]

[/classify]
[def __fpclassify [link math_toolkit.special.fpclass fpclassify]]
[def __isfinite [link math_toolkit.special.fpclass isfinite]]
[def __isnan [link math_toolkit.special.fpclass isnan]]
[def __isinf [link math_toolkit.special.fpclass isinf]]
[def __isnormal [link math_toolkit.special.fpclass isnormal]]

[/powers etc]
[def __expm1 [link math_toolkit.special.powers.expm1 expm1]]
[def __log1p [link math_toolkit.special.powers.log1p log1p]]
[def __cbrt [link math_toolkit.special.powers.cbrt cbrt]]
[def __sqrt1pm1 [link math_toolkit.special.powers.sqrt1pm1 sqrt1pm1]]
[def __powm1 [link math_toolkit.special.powers.powm1 powm1]]
[def __hypot [link math_toolkit.special.powers.hypot hypot]]
[def __pow [link math_toolkit.special.powers.ct_pow pow]]

[/zeta]
[def __zeta [link math_toolkit.special.zetas.zeta zeta]]

[/expint]
[def __expint_i [link math_toolkit.special.expint.expint_i zeta]]
[def __expint_n [link math_toolkit.special.expint.expint_n zeta]]

[/rounding]
[def __round [link math_toolkit.special.rounding.round round]]
[def __lround [link math_toolkit.special.rounding.round round]]
[def __llround [link math_toolkit.special.rounding.round round]]
[def __trunc [link math_toolkit.special.rounding.trunc trunc]]
[def __modf [link math_toolkit.special.rounding.modf modf]]

[/polynomials]
[def __laguerre [link math_toolkit.special.sf_poly.laguerre laguerre]]
[def __legendre [link math_toolkit.special.sf_poly.legendre legendre_p]]
[def __hermite [link math_toolkit.special.sf_poly.hermite hermite]]

[/Misc]
[def __expint [link math_toolkit.special.expint.expint_i expint]]
[def __spherical_harmonic [link math_toolkit.special.sf_poly.sph_harm spherical_harmonic]]



[/ distribution non-members]
[def __cdf [link math.dist.cdf Cumulative Distribution Function]]
[def __pdf [link math.dist.pdf Probability Density Function]]
[def __ccdf [link math.dist.ccdf Complement of the Cumulative Distribution Function]]
[def __quantile [link math.dist.quantile Quantile]]
[def __quantile_c [link math.dist.quantile_c Quantile from the complement of the probability]]
[def __mean [link math.dist.mean mean]]
[def __median [link math.dist.median median]]
[def __mode [link math.dist.mode mode]]
[def __skewness [link math.dist.skewness skewness]]
[def __kurtosis [link math.dist.kurtosis kurtosis]]
[def __kurtosis_excess [link math.dist.kurtosis_excess kurtosis_excess]]
[def __variance [link math.dist.variance variance]]
[def __sd [link math.dist.sd standard deviation]]
[def __hazard [link math.dist.hazard Hazard Function]]
[def __chf [link math.dist.chf Cumulative Hazard Function]]
[def __range [link math.dist.range range]]
[def __support [link math.dist.support support]]

[/ distribution def names end in distrib to avoid clashes]
[def __beta_distrib [link math_toolkit.dist.dist_ref.dists.beta_dist Beta Distribution]]
[def __binomial_distrib [link math_toolkit.dist.dist_ref.dists.binomial_dist Binomial Distribution]]
[def __cauchy_distrib [link math_toolkit.dist.dist_ref.dists.cauchy_dist Cauchy Distribution]]
[def __chi_squared_distrib [link math_toolkit.dist.dist_ref.dists.chi_squared_dist Chi Squared Distribution]]
[def __extreme_distrib [link math_toolkit.dist.dist_ref.dists.extreme_dist Extreme Distributions]]
[def __exp_distrib [link math_toolkit.dist.dist_ref.dists.exp_dist Exponential Distribution]]
[def __F_distrib [link math_toolkit.dist.dist_ref.dists.f_dist Fisher F Distribution]]
[def __gamma_distrib [link math_toolkit.dist.dist_ref.dists.gamma_dist Gamma Distribution]]
[def __lognormal_distrib [link math_toolkit.dist.dist_ref.dists.lognormal_dist Log-normal Distribution]]
[def __negative_binomial_distrib [link math_toolkit.dist.dist_ref.dists.negative_binomial_dist Negative Binomial Distribution]]
[def __non_central_chi_squared_distrib [link math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist Noncentral Chi Squared Distribution]]
[def __non_central_beta_distrib [link math_toolkit.dist.dist_ref.dists.nc_beta_dist Noncentral Beta Distribution]]
[def __non_central_F_distrib [link math_toolkit.dist.dist_ref.dists.nc_f_dist Noncentral F Distribution]]
[def __non_central_T_distrib [link math_toolkit.dist.dist_ref.dists.nc_t_dist Noncentral T Distribution]]
[def __normal_distrib [link math_toolkit.dist.dist_ref.dists.normal_dist Normal Distribution]]
[def __poisson_distrib [link math_toolkit.dist.dist_ref.dists.poisson_dist Poisson Distribution]]