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Boost-Commit : |
Subject: [Boost-commit] svn:boost r76336 - sandbox/math_constants/boost/math/constants
From: pbristow_at_[hidden]
Date: 2012-01-07 07:02:02
Author: pbristow
Date: 2012-01-07 07:02:01 EST (Sat, 07 Jan 2012)
New Revision: 76336
URL: http://svn.boost.org/trac/boost/changeset/76336
Log:
Removed TODO comments, regenerated, and retested constants.hpp
Text files modified:
sandbox/math_constants/boost/math/constants/calculate_constants.hpp | 102 +++++++++++++++++++--------------------
sandbox/math_constants/boost/math/constants/constants.hpp | 2
2 files changed, 51 insertions(+), 53 deletions(-)
Modified: sandbox/math_constants/boost/math/constants/calculate_constants.hpp
==============================================================================
--- sandbox/math_constants/boost/math/constants/calculate_constants.hpp (original)
+++ sandbox/math_constants/boost/math/constants/calculate_constants.hpp 2012-01-07 07:02:01 EST (Sat, 07 Jan 2012)
@@ -1,5 +1,5 @@
-// Copyright John Maddock 2010.
-// Copyright Paul A. Bristow 2011.
+// Copyright John Maddock 2010, 2012.
+// Copyright Paul A. Bristow 2011, 2012.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
@@ -22,7 +22,7 @@
/*
// Although this code works well, it's usually more accurate to just call acos
- // and access the numner types own representation of PI which is usually calculated
+ // and access the number types own representation of PI which is usually calculated
// at slightly higher precision...
T result;
@@ -180,7 +180,7 @@
inline T constant_one_div_euler<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
- return static_cast<T>(1)
+ return static_cast<T>(1)
/ euler<T, policies::policy<policies::digits2<N> > >();
}
@@ -377,7 +377,7 @@
inline T constant_pi_pow_e<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
- return pow(pi<T, policies::policy<policies::digits2<N> > >(), e<T, policies::policy<policies::digits2<N> > >()); //
+ return pow(pi<T, policies::policy<policies::digits2<N> > >(), e<T, policies::policy<policies::digits2<N> > >()); //
}
template <class T>
@@ -386,7 +386,7 @@
{
BOOST_MATH_STD_USING
return pi<T, policies::policy<policies::digits2<N> > >()
- * pi<T, policies::policy<policies::digits2<N> > >() ; //
+ * pi<T, policies::policy<policies::digits2<N> > >() ; //
}
template <class T>
@@ -396,7 +396,7 @@
BOOST_MATH_STD_USING
return pi<T, policies::policy<policies::digits2<N> > >()
* pi<T, policies::policy<policies::digits2<N> > >()
- / static_cast<T>(6); //
+ / static_cast<T>(6); //
}
@@ -408,7 +408,7 @@
return pi<T, policies::policy<policies::digits2<N> > >()
* pi<T, policies::policy<policies::digits2<N> > >()
* pi<T, policies::policy<policies::digits2<N> > >()
- ; //
+ ; //
}
template <class T>
@@ -435,7 +435,7 @@
inline T constant_e_pow_pi<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
- return pow(e<T, policies::policy<policies::digits2<N> > >(), pi<T, policies::policy<policies::digits2<N> > >()); //
+ return pow(e<T, policies::policy<policies::digits2<N> > >(), pi<T, policies::policy<policies::digits2<N> > >()); //
}
template <class T>
@@ -471,8 +471,8 @@
{
BOOST_MATH_STD_USING
return pi<T, policies::policy<policies::digits2<N> > >()
- / static_cast<T>(180)
- ; //
+ / static_cast<T>(180)
+ ; //
}
template <class T>
@@ -482,7 +482,7 @@
BOOST_MATH_STD_USING
return static_cast<T>(180)
/ pi<T, policies::policy<policies::digits2<N> > >()
- ; //
+ ; //
}
template <class T>
@@ -490,7 +490,7 @@
inline T constant_sin_one<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
- return sin(static_cast<T>(1)) ; //
+ return sin(static_cast<T>(1)) ; //
}
template <class T>
@@ -498,7 +498,7 @@
inline T constant_cos_one<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
- return cos(static_cast<T>(1)) ; //
+ return cos(static_cast<T>(1)) ; //
}
template <class T>
@@ -506,7 +506,7 @@
inline T constant_sinh_one<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
- return sinh(static_cast<T>(1)) ; //
+ return sinh(static_cast<T>(1)) ; //
}
template <class T>
@@ -514,7 +514,7 @@
inline T constant_cosh_one<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
- return cosh(static_cast<T>(1)) ; //
+ return cosh(static_cast<T>(1)) ; //
}
template <class T>
@@ -522,7 +522,7 @@
inline T constant_phi<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
- return (static_cast<T>(1) + sqrt(static_cast<T>(5)) )/static_cast<T>(2) ; //
+ return (static_cast<T>(1) + sqrt(static_cast<T>(5)) )/static_cast<T>(2) ; //
}
template <class T>
@@ -574,7 +574,6 @@
);
// T gamma("0.57721566490153286060651209008240243104215933593992");
return gamma;
- // TODO calculate this - JM has code.
}
@@ -584,7 +583,7 @@
{
BOOST_MATH_STD_USING
- return static_cast<T>(1)
+ return static_cast<T>(1)
/ gamma<T, policies::policy<policies::digits2<N> > >();
}
@@ -607,7 +606,7 @@
inline T constant_zeta_two<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
{
BOOST_MATH_STD_USING
-
+
return pi<T, policies::policy<policies::digits2<N> > >()
* pi<T, policies::policy<policies::digits2<N> > >()
/static_cast<T>(6);
@@ -630,9 +629,9 @@
//"1.2020569031595942 double
// http://www.spaennare.se/SSPROG/ssnum.pdf // section 11, Algorithmfor Apery’s constant zeta(3).
// Programs to Calculate some Mathematical Constants to Large Precision, Document Version 1.50
-
+
// by Stefan Spannare September 19, 2007
- // zeta(3) = 1/64 * sum
+ // zeta(3) = 1/64 * sum
T n_fact=static_cast<T>(1); // build n! for n = 0.
T sum = static_cast<double>(77); // Start with n = 0 case.
// for n = 0, (77/1) /64 = 1.203125
@@ -715,9 +714,9 @@
BOOST_MATH_STD_USING
//
// This is algorithm 3 from:
- //
- // "An Efficient Algorithm for the Riemann Zeta Function", P. Borwein,
- // Canadian Mathematical Society, Conference Proceedings.
+ //
+ // "An Efficient Algorithm for the Riemann Zeta Function", P. Borwein,
+ // Canadian Mathematical Society, Conference Proceedings, 2000.
// See: http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
//
BOOST_MATH_STD_USING
@@ -728,7 +727,7 @@
for(int j = 0; j < n; ++j)
{
sum += ej_sign * -two_n / pow(T(j + 1), s);
- ej_sign = -ej_sign;
+ ej_sign = -ej_sign;
}
T ej_sum = 1;
T ej_term = 1;
@@ -774,7 +773,7 @@
template <class T>
template<int N>
inline T constant_khinchin<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
-{
+{
return khinchin_detail::khinchin<T>();
}
@@ -812,10 +811,10 @@
//
// The derivative of the zeta function is computed by direct differentiation
// of the relation:
-// (1-2^(1-s))zeta(s) = SUM(n=0, INF){ (-n)^n / (n+1)^s }
+// (1-2^(1-s))zeta(s) = SUM(n=0, INF){ (-n)^n / (n+1)^s }
// Which gives us 2 slowly converging but alternating sums to compute,
// for this we use Algorithm 1 from "Convergent Acceleration of Alternating Series",
-// Henri Cohen, Fernando Rodriguez Villegas and Don Zagier, Experimental Mathematics 9:1.
+// Henri Cohen, Fernando Rodriguez Villegas and Don Zagier, Experimental Mathematics 9:1 (1999).
// See http://www.math.utexas.edu/users/villegas/publications/conv-accel.pdf
//
template <class T>
@@ -882,17 +881,12 @@
+ zeta_series_derivative_lead_2<T>() * zeta_series_2<T>();
}
-} // detail
+} // namespace detail
template <class T>
template<int N>
inline T constant_glaisher<T>::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>))
-{ // from http://mpmath.googlecode.com/svn/data/glaisher.txt
- // 20,000 digits of the Glaisher-Kinkelin constant A = exp(1/2 - zeta'(-1))
- // Computed using A = exp((6 (-zeta'(2))/pi^2 + log 2 pi + gamma)/12)
- // with Euler-Maclaurin summation for zeta'(2).
- // No good references/algorithms for this found yet.
- // TODO calculate this?
+{
BOOST_MATH_STD_USING
typedef policies::policy<policies::digits2<N> > forwarding_policy;
@@ -904,21 +898,25 @@
v /= -12;
return exp(v);
- /*
+ /*
+ // from http://mpmath.googlecode.com/svn/data/glaisher.txt
+ // 20,000 digits of the Glaisher-Kinkelin constant A = exp(1/2 - zeta'(-1))
+ // Computed using A = exp((6 (-zeta'(2))/pi^2 + log 2 pi + gamma)/12)
+ // with Euler-Maclaurin summation for zeta'(2).
T g(
-"1.282427129100622636875342568869791727767688927325001192063740021740406308858826"
-"46112973649195820237439420646120399000748933157791362775280404159072573861727522"
-"14334327143439787335067915257366856907876561146686449997784962754518174312394652"
-"76128213808180219264516851546143919901083573730703504903888123418813674978133050"
-"93770833682222494115874837348064399978830070125567001286994157705432053927585405"
-"81731588155481762970384743250467775147374600031616023046613296342991558095879293"
-"36343887288701988953460725233184702489001091776941712153569193674967261270398013"
-"52652668868978218897401729375840750167472114895288815996668743164513890306962645"
-"59870469543740253099606800842447417554061490189444139386196089129682173528798629"
-"88434220366989900606980888785849587494085307347117090132667567503310523405221054"
-"14176776156308191919997185237047761312315374135304725819814797451761027540834943"
-"14384965234139453373065832325673954957601692256427736926358821692159870775858274"
-"69575162841550648585890834128227556209547002918593263079373376942077522290940187");
+ "1.282427129100622636875342568869791727767688927325001192063740021740406308858826"
+ "46112973649195820237439420646120399000748933157791362775280404159072573861727522"
+ "14334327143439787335067915257366856907876561146686449997784962754518174312394652"
+ "76128213808180219264516851546143919901083573730703504903888123418813674978133050"
+ "93770833682222494115874837348064399978830070125567001286994157705432053927585405"
+ "81731588155481762970384743250467775147374600031616023046613296342991558095879293"
+ "36343887288701988953460725233184702489001091776941712153569193674967261270398013"
+ "52652668868978218897401729375840750167472114895288815996668743164513890306962645"
+ "59870469543740253099606800842447417554061490189444139386196089129682173528798629"
+ "88434220366989900606980888785849587494085307347117090132667567503310523405221054"
+ "14176776156308191919997185237047761312315374135304725819814797451761027540834943"
+ "14384965234139453373065832325673954957601692256427736926358821692159870775858274"
+ "69575162841550648585890834128227556209547002918593263079373376942077522290940187");
return g;
*/
@@ -931,11 +929,11 @@
// 1100 digits of the Rayleigh distribution skewness
// Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
-T rs(2 * root_pi<T, policies::policy<policies::digits2<N> > >()
+T rs(2 * root_pi<T, policies::policy<policies::digits2<N> > >()
* pi_minus_three<T, policies::policy<policies::digits2<N> > >()
/ pow(four_minus_pi<T, policies::policy<policies::digits2<N> > >(), static_cast<T>(3./2))
);
- // 6.31110657818937138191899351544227779844042203134719497658094585692926819617473725459905027032537306794400047264,
+ // 6.31110657818937138191899351544227779844042203134719497658094585692926819617473725459905027032537306794400047264,
//"0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067"
//"9440004726436754739597525250317640394102954301685809920213808351450851396781817932734836994829371322"
Modified: sandbox/math_constants/boost/math/constants/constants.hpp
==============================================================================
--- sandbox/math_constants/boost/math/constants/constants.hpp (original)
+++ sandbox/math_constants/boost/math/constants/constants.hpp 2012-01-07 07:02:01 EST (Sat, 07 Jan 2012)
@@ -265,8 +265,8 @@
BOOST_DEFINE_MATH_CONSTANT(zeta_two, 1.644934066848226436472415166646025189e+00, "1.64493406684822643647241516664602518921894990120679843773555822937000747040320087383362890061975870530400431896e+00");
BOOST_DEFINE_MATH_CONSTANT(zeta_three, 1.202056903159594285399738161511449990e+00, "1.20205690315959428539973816151144999076498629234049888179227155534183820578631309018645587360933525814619915780e+00");
BOOST_DEFINE_MATH_CONSTANT(catalan, 9.159655941772190150546035149323841107e-01, "9.15965594177219015054603514932384110774149374281672134266498119621763019776254769479356512926115106248574422619e-01");
- BOOST_DEFINE_MATH_CONSTANT(khinchin, 2.685452001065306445309714835481795693e+00, "2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515346591e+00");
BOOST_DEFINE_MATH_CONSTANT(glaisher, 1.282427129100622636875342568869791727e+00, "1.28242712910062263687534256886979172776768892732500119206374002174040630885882646112973649195820237439420646120e+00");
+ BOOST_DEFINE_MATH_CONSTANT(khinchin, 2.685452001065306445309714835481795693e+00, "2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515346591e+00");
BOOST_DEFINE_MATH_CONSTANT(extreme_value_skewness, 1.139547099404648657492793019389846112e+00, "1.13954709940464865749279301938984611208759979583655182472165571008524800770607068570718754688693851501894272049e+00");
BOOST_DEFINE_MATH_CONSTANT(rayleigh_skewness, 6.311106578189371381918993515442277798e-01, "6.31110657818937138191899351544227779844042203134719497658094585692926819617473725459905027032537306794400047264e-01");
BOOST_DEFINE_MATH_CONSTANT(rayleigh_kurtosis, 3.245089300687638062848660410619754415e+00, "3.24508930068763806284866041061975441541706673178920936177133764493367904540874159051490619368679348977426462633e+00");
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